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Full text of "Climatic cycles and tree-growth"

i 



CLIMATIC CYCLES 
AND TREE GROWTH 



VOLUME III 



A STUDY OF CYCLES 



BY 

A. E. DOUGLASS 

Research Associate, Carnegie Institution of Washington 
Director, Steward Observatory, University of Arizona 







' 






3$ 



Published by Carnegie Institution of Washington 
Washington, 1936 






CARNEGIE INSTITUTION OF WASHINGTON 
Publication No. 289, Vol. Ill 



WAVERLY PRESS, INC. 
BALTIMORE, MD. 

STANDARD ENGRAVING CO. 
WASHINGTON, D. C. 



CONTENTS 



PAGE 

I. Introduction 1 

The region, climate and 

trees 2 

Need and function of cycles . 4 

Period and cycle 6 

Acknowledgments 6 

Nature of tree-ring data 7 

Trees 7 

Ring records 7 

Dissected trees 7 

Types of ring records 8 

Cross-identity 9 

Ring types and topography 11 

Effect of local topography. . 12 
Significance of cross-iden- 
tity and cycles in tree- 
ring records. . . . ; 13 

Rainfall correlations in North- 
ern Arizona 14 

II. Ctclogkam analysis 17 

Graphic expression of data 17 

Definitions 17 

Original data 17 

Smoothed curves 18 

Mass diagrams and residual 

mass diagrams 19 

Logarithmic plots 21 

Skeleton plot 22 

Standardized curves 25 

Merging 27 

Technique of long records. . 27 

Compressed curves 28 

Curve character figure: 

mean sensitivity 28 

Correlation coefficient 29 

Periodogram 30 

Graphic expression of cycles.. . . 30 
Cycle integration or sum- 
mation 30 

Successive integration 32 

Chrono-integration 34 

Plotting unstable and mixed 

periods 35 

Cyclogram principle 35 

Cyclograph 40 

Development of cyclograph 41 

Cycleplots 44 

Moving rack 46 

Operation and checking . ^ 47 

Accuracy and limitations. . . 47 
General cyclogram interpreta- 
tion 48 

Limits of range 48 

Resolving power 49 

Lag analysis 50 

Cyclogram reading 50 

III. The discontinuous period in 

CYCLOGRAM ANALYSIS 51 

The climatic dilemma 51 

Probabilities and cycles 51 



PAGE 
III. The DISCONTINUOUS PERIOD in 
cyclogram analysis — con- 
tinued 

Bartels' dials 53 

Quasi-persistence in the 

summation dial 56 

Quasi-persistence in the 

cyclogram 56 

Evaluation of quasi-per- 
sistence 58 

The conservation factor .... 58 
Bartels' multiple plot of the 
magnetic character figure 

C 60 

Significance of conservation 61 

Stumpff's periodograph 61 

Applications of the discontinu- 
ous period 63 

IV. Analysis of solar records 65 

Analysis of sunspot numbers .... 67 
Analysis of smoothed an- 
nual sunspot numbers. ... 67 
Analysis of annual numbers 

since 1610 68 

Other cycles in the annual 

numbers 69 

Centers of mass of maxima . . 70 
Possible half -sunspot cycle. 70 
Analysis of monthly sunspot 

numbers 71 

Abbot's radiation measures ..... 72 
Pettit's ultra-violet radiation 

curves ; 75 

International magnetic charac- 
ter figure C . . 76 

Solar rotations in magnetic 

data 77 

Sources of the 6-months 

period 78 

Other periods 79 

Naked-eye sunspot records 80 

Records of Northern Lights .... 80 
V. Analysis of terrestrial 

RECORDS 82 

Characters of cycles in ring 

records ^ 82 

Discontinuous periods 82 

Conservation 82 

Triangle tests 83 

Similarities over areas 85 

Recurrence of cycles in past 

time 85 

Periodogram resemblance to 

solar cycles 85 

Problems 85 

Representation of cycles ... 85 
Individual vs. group in cycle 

analysis 87 

The two-year "scatter" 

cycle 87 



IV 



CONTENTS 



PAGE 

V. Analysis of terrestrial 
records — continued 
Cycles in 42 western groups .... 93 
Evaluation of cycles in the 

42 groups 97 

Records of past climates 98 

Sequoia chronology and cycle 

recurrence 99 

Sequoia chronology cycles. . 104 

Central Pueblo chronology 105 

Central Pueblo chronology 

cycles 106 

Geological material for cycle 

analysis 108 

Its character 108 

Buried trees, cycles 109 

Buried trees 110 

Yellowstone fossil trees 110 

Yellowstone fossil trees, 

cycles Ill 

Analyses of other geological 

material 115 

VI. Relation between terres- 
trial and solar records. 116 

Early results 116 

Evidence of solar relation in 11- 
year cycle 122 

General resemblance in 

cycle types 122 

Evidence by cyclograms. . . . 122 
. The 11-year cycle and its 
half value, the Hellmann 

cycle 123 

Dearth cycles 125 

Summary 126 

Longer cycles 126 

Frequency periodograms and 
the cycle complex 128 



PAGE 

VI. Relation between terres- 
trial AND SOLAR RECORDS — 
continued 
Complex from geological 

material 130 

Physical cause of climatic cycles. 131 
VII. The cycle problem and long- 
range FORECASTING 133 

The problem 133 

The Arizona results 134 

Mississippi Valley 135 

Coast States 136 

Relation to the sun 137 

Prediction technique 138 

Fundamentals of prediction. 138 
Cycles in the Pueblo area . . 139 
Application to winter rain- 
fall of the Pueblo area 139 

The 23-year cycle 139 

The 19-20-year cycle 140 

The 14-year cycle 140 

The 11^-year cycle 140 

Appendix 142 

Studies of the cyclograph — E. 

Schulman 143 

Introduction 143 

Description of the instrument. . . 143 

Operation 145 

Cyclogram formulae 146 

Construction of frequency period- 

ogram 147 

Errors of the instrument 148 

Errors in cyclogram analysis .... 150 

Probability tests 153 

Presentation of cycle data 154 

Cycle summation curves 155 

An automatic optical periodo- 

graph — A. E. Douglass 164 

Variable Star tests 164 

Bibliography 166 



ILLUSTRATIONS 



PLATES 



FACING 
PAGE 

1. Cross-identification of MLK-179 
and MLK-127. (See Plate 8) . . . . 1 

2. Pine forest, Northern Arizona: 
Near San Francisco Peaks, Flag- 
staff (1904) 2 

3. Pine (Ponderosa) forest, Northern 
Arizona — Courtesy of U. S. Forest 
Service 3 

4. Douglas fir site, Mesa Verde 4 

5. Giant sequoia: "Lady Alice" in 
Balch's Park (1925) 5 

6. Complacent and sensitive se- 
quences of rings: 

A. Complacent ring record, BE- 

133, pine 

B. Sensitive ring record, MV-23 

Douglas fir 8 

7. Cross-dating at 125 miles, JPB-17, 
pine, and BK-2, Douglas fir 9 

8. Enlargements of specimens shown 
in frontispiece 

A. MLK-179 

B. MLK-127 

C. Center of MLK-179 10 

9. JCD Signature in F-3992, Flag- 
staff (charcoal) 11 

10. A. Forest interior ring type — 

Pine, FL-131, 3 miles north of 
Flagstaff 
B. Forest border ring type, PR-62. 
Lower forest border, sensitive 
rings : south-east of Prescott ... 12 

11. Tree roots and bed rock; Defiance 

Plateau 13 

12. A. Periodogram (1913) of sunspot 

numbers since 1760 
B. Periodogram (1918) of variable 
star, R Arietis, showing period 
of 187 days (see appendix) 40 

13. A. Cyclogram by spectrometer 

process (1914) 



FACING 
PAGE 

B. "Sweep" or cylindrical pat- 
tern; the original plot, in- 
verted, shows below the sweep . 4 1 

14. A. The cyclograph 44 

B. Analyzing parts of the cyclo- 
graph . . 45 

15. A. Analyzing plate and mounting 
B. Cyclograms of sunspot num- 
bers, using centers of mass 48 

16. A. Multiple standard with discon- 

tinuous periods 

B. Arizona ring record, FAM, 1700 
to 1920 at 21.0 years 

C. Analysis of Flagstaff tree ring 
records (see chapter II, Cyclo- 
gram Reading) 49 

17. Illustration of sunspot cycle by 
changes in calcium flocculi — after 
Adams and Nicholson 66 

18. Cyclograms of monthly sunspot 
numbers, 1750 to 1931 67 

19. A. Cyclograms of Abbot's radia- 

tion curve, December 1918— 
July 1930 

B. Cyclograms of magnetic char- 
acter figure C. 1923-1933 

C. Cycle relief map of the mag- 
netic character figure C, Jan- 
uary 1932 to March 1935 78 

20. Cyclogram test to distinguish be- 
tween natural and random se- 
quences 79 

21. A. Eberswalde, Germany, ring 

sequence, G-6 
B. Eberswalde specimen, G-2. . . . 122 

22. Cyclogram showing Hellmann 
cycles between 1850 and 1900 in 
Europe and North America 123 

23. Enlargement of cyclogram Plate 
22 g, showing Hellmann cycle in 
sequoias 124 

24. Cyclogram analysis of SS Cygni 
(1918). Data cover 1896 to 1917... 125 



TEXT-FIGURES 



PAGE 

1. Circuit uniformity in a prehistoric 
Douglas fir, MLK-127, from north- 
eastern Arizona 8 

2. Cross-identity (similarity of 
growth in each year) in Prescott 
trees 11 

3. a. Cross-identity at 70 miles, Fort 

Defiance and Black Mesa 
groups 
b. Winter rainfall with 2i yr. lag 
in smoothed values, and tree 
growth 15 



PAGE 

4. Tree growth and river run -off 15 

5. Lynch's rainfall indices 1770 to 
1930 (LRI) compared to Bear 
Valley pine record (BV) and Grant 
Park sequoia record (SVI) with a 
pine (RB-7) showing good sequoia 
record supplying data for the 
period 1900-1934 16 

6. Point and column plots of same 
data 18 

7. Smoothing methods compared 19 



VI 



ILLUSTRATIONS 



PAGE 

8. Mass diagram and residual mass 
diagram 20 

9. Logarithmic plot compared with 
non-logarithmic plot 21 

10. a. "Normal" distribution of data 

about mean 
b, c. Frequency distributions 
compared : 

standardized ring widths in 
complacent and sensitive rec- 
ords, 1750-1920. ... . # 22 

d. Frequency distribution : stand- 
ardized ring widths in sensitive 
records, Central Pueblo area. 
Mean group curve (73 trees) 

e, f. Frequency distribution: ring 
widths in datable though not 
sensitive tree records 23 

11. Skeleton count and skeleton plot. . 24 

12. Standardizing 25 

13. Merging diagram 27 

14. a. Summation (integration) curve 

of sunspot numbers at 10.0 
years 

b. Graphic representation of inte- 
gration table 

c. Summation curve at 11.5 years. 31 

15. Plot of sunspot data to show 
changing place of 11.4-year 
maxima in successive 11-year 
intervals 33 

16. Successive integration of FAM 
(Flagstaff area mean curve), 1700- 
1920 34 

17. Two methods of plotting cycles. . 36 

18. Cyclogram demonstration, first 
part 37 

19. Cyclogram demonstration, second 
part 38 

20. Cyclogram plot of sunspot num- 
bers, 1750-1930 39 

21. Schuster's periodogram of sun- 
spot numbers 42 

22. Important parts of the cyclograph 

a. Schematic elevation 

b. Analyzing plate 44 

23. Cycleplot, to show cutting line. 
Standardized tree growth, G-5, 
Eberswalde, Germany 45 

24. The analyzing plate changes 
longitudinal displacement in posi- 
tion of maxima to transverse 45 

25. Bartels' Harmonic Dial of inter- 
national magnetic character figure 
C (from Terrestrial Magnetism, 
March 1935, by permission) 54 

26. Bartels' Summation Dial (from 
Terrestrial Magnetism, March 
1935, by permission) 55 

27. Comparisons between Bartels' 
dials and cyclogram anslysis 57 

28. Plan of Stumpff's periodograph 
(after Stumpff , slightly modified). 62 

29. Butterfly diagram (after Maun- 
der) 66 



PAGE 

30. Monthly sunspot curve to show 
reduced amplitude at minimum 
(after Wolfer) 70 

31. a. Chrono-periodogram of Ab- 
bot's radiation curves analyzed 
cyclogram methods 

b. Abbot's cycles in same 

c. Frequency periodogram 
monthly sunspot numbers, 
1750-1934 73 

d. Chrono-periodogram of same . . 74 

32. Ultra-violet radiation compared 
to monthly sunspot numbers and 
the solar constant 76 

33. International magnetic character 
figure C as related to opposite 
longitudes on sun during a 27-day 
period 79 

34. Effect of smoothing on natural 
sequences and random sequences. 
Flagstaff area — 20-year running 
means 84 

35. Frequency periodograms by three 
processes applied to the same data 
(central Pueblo area; 15 groups — 

73 trees) 87 

36. Two-year reversal test, to show 
similarity in Arizona area in short 
cycles 88 

37. "Reversal" tests for short cycles 

a. Lesser maxima in two-year 
reversal test; showing agree- 
ment between groups in Ari- 
zona area 

b. Two-year test; lesser maxima 
summarized for three western 
zones 90 

38. Two-year reversal tests on random 
data 91 

39. Conservation in successive years 
in Fort Defiance group, shown by 
scatter diagram using departures 
from a mean 92 

40. Successive year conservation in 
departures from a smoothed curve, 
Fort Defiance group 

(a) in natural data; (b) in random 
data 93 

41. Frequency periodograms of 42 
groups : 

(a) obtained by two independent 
observers 

(b) weak and strong cycles com- 
pared (as recorded by Schul- 
man) 97 

42. Hellmann cycle in sequoias, A.D. 
155 to 245, using "triple lag" 
method 100 

43. Scrambled sequoia values tested 

by "triple lag" method 101 

44. Hellmann cycle in recent sequoia 
records. Running means of three 
successive cycles of 23 years 
("triple lag" method, incomplete 
after 1891) 102 



ILLUSTRATIONS 



Vll 



PAGE 

45. Average cycle recurrence in Grant 
Park sequoias in 2100 years 103 

46. Frequency periodograms of Cen- 
tral Pueblo Chronology (CPC) 
and Sequoia Chronology (SVI). . . . 108 

47. Arizona tree growth and Cali- 
fornia rainfall; curves of 1909 116 

48. First western correlations, 1909. . . 117 

49. Western correlations, 1914 (pub- 
lished in "The Climatic Factor"— 

E. Huntington) 118 

50. Correlations, 1919 119 

51. Integrations on 11.4 years of data 
mostly between 1850 and 1900; 
arranged according to prominence 
of second maximum of Hellmann 
cycle 120 



PAGE 

52. Hellman cycle in Flagstaff pines, 
FLC-FLU, since 1420 121 

53. Correlation periodograms (Alter) 
for 

(a) Arizona trees, 1700-1920 

(b) California and Oregon trees, 
1700-1920 127 

54. 57-year cycle in Arizona trees, 
A.D. 1168 to 1503 128 

55. A group of periodograms to show 
resemblance of terrestrial to solar 
cycles 129 

56. Western cycles compared to simple 
fractions of 34 years 130 

57. Construction of a frequency per- 
odogram from ten groups in the 
Central Pueblo area 148 

58. Summation curves 156-163 



I 



FOREWORD 

The study of cycles, like playing with empirical relations between 
numbers, may well have intrigued men from very early times. How 
else should we have been led in Asia and in America to our calendars? 
In celestial mechanics the cycles are exceedingly regular, but there are 
phenomena whether celestial, terrestrial or human in which it is obvious 
that there are oscillations, but in which it is also obvious that the oscilla- 
tions are not regular. Such phenomena raise serious questions for the 
mathematician; it isn't even known whether Schuster's periodogram 
analysis, which is the method most perfected mathematically, is really 
suitable for exploring the series of oscillations. The phenomena also 
offer perplexing challenges to the scientist: Are they, like Brownian 
movements, to be regarded as fortuitous? Is there a relation between 
them and other cyclic phenomena which will permit us to describe, at 
least in part, the ones in terms of the others? And if this be true, what 
is the real explanation of the correlations which have been discovered? 
Finally, is there any possibility of prediction or of control of one phe- 
nomenon by observation or by manipulation of another? 

Professor Douglass has for long been a worker in the field of cycle 
analysis. More than fifteen years ago he described an optical instru- 
ment and method for performing with considerable precision and with 
extreme rapidity a type of cycle analysis. His method seems to have 
been used little, if at all, by other workers. This neglect of a new tool 
for analysis is regrettable. Science advances by its techniques as well 
as by its findings of fact or its formulations of theory. Moreover, sci- 
ence is not a collection of personal opinion or of individual performance, 
it is a collaboration toward a consensus; until others have found out how 
the cyclograph performs for them we have not the basis for a consensus 
as to its merits — we have merely our faith in Douglass, and however 
much he may appreciate this, he would appreciate yet more a demon- 
stration of the justification for that faith. 

The collection of an enormous amount of material on tree-rings, the 
development of methods of cross-dating and the establishment thereby 
of a system of chronology represent a continued effort toward a knowl- 
edge of our past. The correlations of tree-rings with solar and terrestrial 
data and the intercorrelations of these not only illuminate the past, they 
offer hope of some future and greater success in forecasting phenomena of 
scientific importance and, perchance, of immediate significance to man. 

So much of the work on cycles which has been done in the past and 
published with high hope has been found wanting by subsequent in- 

ix 



X FOREWORD 

vestigators, that the scientific world has today a somewhat justifiable 
scepticism of the validity of similar new work. The author and the 
Carnegie Institution offer this data and these findings to the critical 
examination of others to ascertain in how far they may become estab- 
lished in that general consensus which is science and afford a basis for 
further advances into the mathematical difficulties of cycle analysis, into 
the perplexing problems of scientific induction therefrom and into those 
fields of science in which the realization of our present hopes seems 
bound up with a fuller comprehension and utilization of these methods. 

E. B. Wilson 



\ 



Carnegie Inst. Washington Pub. 289. Vol. Ill — Douglass 







CLIMATIC CYCLES AND TREE GROWTH 

A STUDY OF CYCLES 

I. INTRODUCTION 

While seeking information regarding climatic influence on tree-ring growth, 
we have developed an improved method of studying and expressing certain 
climatic changes that have been disappointing to students of cycles. The 
chief purposes of the present writing are to describe and discuss this method 
of cycle analysis, to place on record the results obtained on ring growth in 
favorable regions, to outline the similarities over certain geographical areas, 
to present the resemblance of climatic cycles to certain solar cycles, and to 
begin the study of their use in long-range weather prediction. 

The present work is based on a view sustained by recent advance, namely, 
that having developed an appropriate method, we should specialize upon those 
climatic changes which seem to occur in non-permanent but still obviously 
cyclic form. It is hoped that this treatment will receive consideration in 
connection with problems of reclamation and hydraulic engineering as well as 
in climatology. Although this volume is the third 1 in a series begun in 1919, 
a large mass of basic material still remains unpublished. It is hoped that it 
will be made available in the near future. 

Since presentation of the material involves the facts obtained in the 
measurement of rings of trees, especially the western yellow pine and Douglas 
fir of Arizona, certain formal tests upon our ring records, such as the uni- 
formity of ring records within a tree, the uniformity over local areas, and the 
like will be referred to. In other respects, without undue repetition, we 
desire to bring the basic material up to date. We believe that this should be 
investigated in the district and upon the trees with which we have worked, 
thus avoiding misleading results that have been found in distant localities and 
other environments and different biological material. 

In presenting a new description of the analytical method used now for a 
score of years, we shall endeavor to make clear to those familiar with harmonic 
analysis that the new method is simply a way of finding and expressing the 
facts of climatic change in a more detailed and useful form. The use of the 
word "accidental" will be avoided as far as possible in regard to climatic 
changes because that word begs the question by implying uselessness to human 
welfare. We believe that some of the results will prove useful. From the 
viewpoint of climatology, our investigation is a study of the geographical ex- 
tension of certain climatic similarities, because in this type of expression 
(the cyclogram method) similarities not hitherto observed can be recognized. 

1 References in this book to the preceding volumes are sometimes indicated by I 
and II. 



Z CLIMATIC CYCLES AND TREE GROWTH 

The Region, Climate, and Trees — Tree-ring data may extend in two ways : 
Geographically about the earth, and chronologically in past time. In the 
studies contained in this book a limited geographical area is used, commonly 
known as the Pueblo area. It consists largely of the Colorado Plateau in 
northern Arizona, northern New Mexico, and adjacent parts of Colorado and 
Utah, an extensive area where climatic variations are essentially similar. 
The Colorado Plateau is not flat like a table but is composed of wide-spread 
minor variations culminating at the west in the San Francisco Peaks near 
Flagstaff; thence toward the east it slopes down to the Little Colorado River 
bottom; rises again to the Chuska and Lukachukai Mountains between 
Arizona and New Mexico; descends thence to irregular lands extending across 
the Chaco areas, and rises to Mount Taylor and the Jemez Mountains at the 
west wall of the Rio Grande Valley in New Mexico. This area described has 
become especially adapted to our purpose, because in altitude it extends a 
thousand feet or more above and a thousand feet below the forest-border 
level. Rainfall is locally dependent upon altitude, and hence at the higher 
points forests thrive, while at the lower points the desert prevails. We thus 
have the forest borders and forest areas scattered through the region under 
consideration and we can find similar border conditions 400 miles apart 
without important differences in climate. 

The area above described as a climatic unit has two well-defined rainy 
seasons per year, one in winter and one in summer. The winter rainy season 
has the characteristics of the temperate zone in type and movements of 
storms; clouds cover large areas hundreds of miles in extent and precipitation 
changes from year to year are much alike over a large extent of country. 
Rainfall is, of course, influenced by altitude and by north and south mountain 
ranges. The winter storms come from the west and the precipitation is 
greater on westerly slopes than on easterly. The spring season is exceedingly 
dry and rain in May and June indicates an exceptional year. The autumn is 
also marked by diminished rain, but is not so dry as the spring. The summer 
rains are tropical in their nature and come in July and August, sometimes 
extending into September. They are largely localized thunderstorms which 
are very impressive to the beholder and sometimes dangerous in the swollen 
washes that follow a downpour. However, their contribution to the water 
supply in reservoirs is small in comparison with that of winter rains. 1 They 
do, of course, aid the crops and the feed for cattle on the ranges. Summer 
rains come on southerly winds and are stirred into thunderstorm activity by 
the interference of mountains and by local convection. In the summer rainy 
season the mornings are usually clear and subject to enormous evaporation 
from irrigated or moistened areas. 

In this area the western yellow pine {Pinus ponderosa — now called ponder- 
osa pine by foresters) follows a contour zone cutting across mountains and 
table lands between approximate altitudes of 5000 and 8500 feet where it is 

1 Glenton Sykes, Range Studies for Southwestern Range and Forest Experiment 
Station, Tucson, Arizona. 



Carnegie Inst. Washington Pub. 289, Vol. Ill Douglass 



PLATE 2 




Carnegie Inst. Washington Pub. 289. Vol. Ill— Douglass 




Pine (Ponderosa) forest, Northern Arizona. Courtesy, U. S. Forest Servk 



INTRODUCTION 6 

governed by the moisture supply. Its altitude is generally lower on the 
western sides of the mountains which receive the heavier rainfall and higher 
on the dry eastern sides. The difference is a thousand feet in some cases. 

A zone of Douglas fir (Pseudotsuga taxifolia) lies above the pine zone. The 
usefulness of the Douglas fir ring record equals that of the pine, especially 
in trees that grow in the transitional area along its lower edge where it mingles 
with the pine. Firs extend downward in favorable canyons and shady slopes 
almost as far as the yellow pine, and their ring records are superb in such 
places. Mingling with the yellow pine at the lower edges of its zone is a 
hard pine, the pinyon (Pinus edulis), a tree adapted to a water supply less 
than that required by the yellow pine. 

Below the pine and pinyon on the mountain slopes there stand the juni- 
pers, the last outposts of the forests. They can survive on the scanty water 
supply and so cover large areas at 4000 to 5000 feet. There are several 
species, Juniperus Utahensea, J. monosperma, J. pachyphlcea, and J. scopul- 
orum, not very different in their several ring types and each rarely giving a 
specimen whose rings are readable enough for dating purposes. 

West of the Arizona forested areas there lies the valley of the Big 
Colorado, a large, exceedingly dry area which might be called the climatic 
shadow of the higher mountain ranges of southern California whose westerly 
faces get a substantial rainfall. These ranges are the southern extension of 
the Sierra Nevadas that extend along the east side of California. Near 
the ocean there is a low coast range and between the coast range and the 
Sierra Nevadas there is the large, dry, interior San Joaquin Valley. The 
Sierra Nevadas form a high rampart effectually intercepting the rain-bear- 
ing winds that come in from the Pacific. In a number of favorable spots 
upon these mountains there are found the giant sequoias (Sequoia gigantea) 
at elevations of 5000 to 7000 feet. These magnificent trees have a remark- 
able capacity of withstanding the attacks of pests and fire and by strongly 
tapering shape maintain with extraordinary strength isolated positions on 
fairly exposed ridges. They gather together in large numbers in the inter- 
vening basins which are quite commonly swampy. In this environment they 
show more resemblance to the coast redwoods at far lower levels. In 1924 
it was ascertained that the giant sequoias in the various groves from 
Springville on the south to Calaveras on the north have strong cross-dating char- 
acters. It was found that practically any ring sequence of a few hundred years 
may be dated in terms of the standard sequences developed in the King's 
River region. However, this cross-dating between trees is far more striking 
in the southerly groves, King's River area, Sequoia National Park, and Spring- 
ville. The identification of the date of a ring is easily done in trees grow- 
ing on the uplands and midlands, but becomes difficult in the basins where 
a continuous water supply permits the trees to have an increased rate of 
growth and great regularity from year to year. 

While it is true that our chief studies have been done in the Colorado 
Plateau area, the enormous age of the big sequoias and their cross-dating 



4 CLIMATIC CYCLES AND TREE GROWTH 

qualities make them of the highest value. The exact dating of the rings of 
these giants was obtained by 1919. It is only recently that immensely long 
chronological sequences have been developed in the Colorado Plateau area, 
reaching back to A.D. 11. Although the early 80 years of this latter chronol- 
ogy come from a single tree, it is a Douglas fir and its record may be ac- 
cepted as valuable, subject to future correction should other tree records be 
found. 

The value of these two ancient coincident records covering 1900 years, at 
a distance apart of some 600 miles, becomes very great when we find that in 
cycle analysis they have a distinct resemblance. Meteorological records go 
back commonly less than a century and reach the hundred-year mark in only 
a few accidental spots, but in these trees we find ring records accurately dated 
reaching back to the beginning of our era, in two well-separated localities of 
which one maintains its sequence full 1300 years farther into antiquity. 

Need and Function of Cycles — It is well recognized that development of 
long-range forecasting is highly desirable. This is true in any part of the 
country, but it is especially true in marginal lands that are subject to strong 
climatic variations from year to year — variations whose violence and time 
of coming are of the highest importance, because man's very existence in 
such places depends upon his power of adaptation to such changes. Changes 
of this sort become very graphic in the area under consideration. For ex- 
ample, Mormon Lake, the largest in Arizona, four by six miles in extent, was 
totally dry in 1901 when crossed by the writer. Now its shores have been a 
summer resort since 1909 and the lake is advertised for its fishing. What 
made it go dry, and how can we determine when it will go dry again? In 
the spring of 1935 the desert was covered with wildflowers, while in 1934 it 
was not. That is due to great difference in winter precipitation in the two 
years. What made that difference? 

The problem of drought is more directly human than that. Hundreds 
of homesteads have been taken up in the semi-arid parts of the Southwest. 
The owners put in wells by which to pump water from a supposedly inexhaust- 
ible source below. But that source is not inexhaustible, since it comes from 
the rains which have fallen on a relatively small area. Too great enlarge- 
ment of irrigated districts will make demands upon the water resources far 
beyond their replenishment. It becomes of vital importance, then, to know 
when the replenishment will take place. 

Everyone who has lived long in this country has seen years of drouth and 
cattle lying dead beside dried-up water holes. People of early days learned 
how dangerous it was to travel long distances with horses without full knowl- 
edge of the technique of obtaining water. 1 They recognized that some years 
were far more severe than others in respect to drought ; with no knowledge of 
what would come to pass, they must be prepared for the worst. Obviously 
our duty is to develop all possible methods of foretelling the future. Increase 

1 In 1896 a young cowboy from Beaver Creek, Arizona, could not believe me when 
I told him that in New England we did not carry canteens wherever we went. 



Carnegie Inst. Washington Pub. 289. Vol. Ill — Douglass 



PLATE 4 




Douglas fir site, Mesa Verde: the tall trees (in center) showing in the sunlight are 
Douglas fir in typical site near their lower, dry, margin; view from Cliff Palace, Mesa 
Verde; the trees on the mesa top are mostly juniper. 



Carnegie Inst. Washinston Pub. 289. Vol. Ill — Douglass 



PLATE 5 




Giant sequoia: "Lady Alice" in Balch's Park (1925). 



INTRODUCTION 

of populated areas will make these problems more and more urgent as time 
goes on. 

In a general way there are two approaches to long-range forecasting. One 
might be called the map method and the other the cycle method. The map 
method applies to short-range weather forecasting and delineates the position 
of storm areas, of polar fronts, and of air masses with definite characteristics. 
The average motion of these masses is well known and each day upon receipt 
of reports it is safe to make a short prediction by means of a series of maps 
indicating the temporary position and condition of the several factors. As 
these conditions become expressed for larger and larger geographical areas, 
the predictions can extend (less precisely) farther into the future. A mete- 
orologist who understands the known factors and the mechanics of the motion 
of air masses can sometimes make predictions of value up to some months in 
advance. 

Belonging to the same class, and yet depending on factors whose relation- 
ships are less well known, there is a form of prediction depending upon ocean 
temperatures. This basis of prediction is under special study at the Scripps 
Institution of Oceanography on the coast of southern California. 

Long-range forecasting by a cycle method is highly desirable on many 
grounds. In the first place, the use of the forms of analysis described in this 
paper establishes the fact that an important proportion of climatic changes 
may be expressed in terms of well-defined periods 1 that have four to twenty- 
five or more repetitions. It is here believed that it is a mistake to neglect 
the examination of climatic changes because they do not seem permanent 
and exactly timed and are not molded in an artificial form like a sine curve. 
It is believed that many earlier investigators have committed an error be- 
cause they disregarded variations that could not be expressed in terms of 
harmonic analysis. Observed variations have often been called accidental 
with the implication that they were worthless for investigation. Such an 
implication might be justified by the results of harmonic analysis, but should 
be reconsidered in view of the methods here used. 

In the second place long-range forecasting by the cycle method is urged 
because in cyclogram expression there are evidences of relationship between 
climatic changes and solar variations. In the third place we naturally think 
of atmospheric phenomena on the earth as full of random changes, but these 
changes are found to agree over large areas of country and we conclude that 
we are encountering something general and highly important. Similarities 
over extensive geographical regions are among the important facts to be 
considered in this book (Chapter V). 

But there is still another reason for investigating climatic cycles. We 
have developed accurately dated chronologies 1900 and 3200 years long which 
possess in some cases high climatic value. In these we are finding recurrent 
phenomena or repetition according to some plan. This new investigation we 

1 The word "period" is used with a little stronger sense of precision and stability 
than cycle. 



6 CLIMATIC CYCLES AND TREE GROWTH 

have reason to hope will compensate in substantial measure for the tempor- 
ary character assigned to climatic cycles, and will contribute to the final 
climatic theory that opens the way to scientific long-range prediction. 

Period and Cycle — Some remarks should be given on the use of the words 
period and cycle. In general, the word period is extensively used in astron- 
omy and refers to a repetition that comes at fairly exact intervals or whose 
variations from exactness are due to fully assignable causes. The best 
examples of periods are found in the motions of the planets. To cycle stu- 
dents the word has commonly meant continuous and unending operation at 
closely equal intervals. In these pages the terms discontinuous, or frag- 
mentary or temporary are introduced before period to indicate fairly exact 
repetitions that seem to have a beginning or an end. The word cycle seems 
to us a more general term with fewer requirements as to duration and to the 
stability of its length, phase and amplitude. Thus we refer to the sunspot 
cycle as a series of discontinuous periods in order to describe the fact that it 
remains steadily at one period length through a number of repetitions and 
then changes slightly to some other value, to which it clings for a time. The 
sun's persistence in maintaining a slightly irregular fluctuation in the number 
of spots through the centuries is to some students a most suggestive connota- 
tion in the word cycle. The application of the methods described in this book 
gives the best apparent chance of demonstrating the existence of this char- 
acter in climatic cycles. 

Acknowledgments — Acknowledgment is made of the generous assistance 
given by the Carnegie Institution of Washington for our climatic studies 
since 1918. Aid from that source has been augmented in recent years, and 
at the present time a special grant is making possible our statement of results. 
This grant becomes effective by cooperative arrangement with the University 
of Arizona. The latter has given its assistance for many years in the way 
of laboratory rooms, and for a time, while extensions of the Arizona ring 
chronology were pending, made it possible for the writer to work without 
being subject to class schedules. Great obligation is due the National 
Geographic Society for its financial aid and moral support during several 
years when the Arizona chronology was being extended. To the Society, 
that extension brought about the successful determination of the age of the 
splendid ruin called Pueblo Bonito and other ruins of the Southwest; to us, 
it was, in addition, the extension of a climatic history into far past times in a 
favorable region. The publication of my report of the dating work is now 
made, and I appreciate particularly the gracious willingness of Dr. Grosvenor 
that the important collections made for that purpose may be freely used in 
climatic and other scientific studies. 

Acknowledgments are also most cordially made to Dr. H. S. Colton and 
his colleagues of the Museum of Northern Arizona; to the American Museum 
of Natural History and other institutions through Dr. Clark Wissler and 
Mr. Earl H. Morris; to the Research Corporation of New York; and to many 
others, among whom the students of "tree-ring interpretation" should be 



INTRODUCTION 7 

specially mentioned. In connection with this volume, my special thanks are 
due to Dr. W. S. Glock who made a careful review of the text, to Mr. Edmund 
Schulman who worked with the author on all cycle problems and whose tests 
of the analyzing instrument form the major part of the appendix, to Mr. 
Gordon C. Baldwin, Mr. A. N. Cowperthwait, Mrs. G. Dewey, Mrs. M. B. 
Koenig, Mrs. E. N. Strickler, and others whose valuable help has made it 
possible. The photographs of rings in this volume were made in our labora- 
tories by members of the staff and especially by Mr. H. F. Davis. Land- 
scapes were mostly taken by members of the staff. The drawings are largely 
due to Mr. A. J. Krutmeyer and Mr. Davis; cyclograms and special plates 
were made by Mr. Davis. I am very grateful to Dr. E. B. Wilson, Dr. John 
A. Fleming, Dr. C. G. Abbot, Mr. H. H. Clayton, Dr. S. B. Nicholson, Dr. 
D. Alter, Dr. E. F. Carpenter and others for their careful revision of 
portions of the text. 

NATURE OF TREE-RING DATA 

Trees — Our results have come chiefly from the cone-bearing trees of the 
Colorado Plateau, the ponderosa or western yellow pine, the Douglas fir, 
pinyon and juniper, already mentioned on a preceding page. 

Ring Records — Trees are selected from areas in which obvious conserva- 
tion of water, in brooks or swamps, does not occur; pests and fire effects are 
avoided. A line is marked from the center to the outside of a cross-section 
after the radius most free from defects and irregularities has been found; 
trees with obvious irregularities are not used. Measurements are made of 
the thickness of the ring, taken in the radial direction. 

Measurements are made to 0.01 mm.; practically all measurements used 
in this book are considered good to about 0.03 mm., for the rings themselves 
vary slightly at different points. A few thousand made before 1914 had an 
average error of 0.06 mm. The series of rings, considered as to thickness, 
taken in any one radial or part of a radial from the interior out toward the 
bark is called the ring record of the tree. Obviously, the first fundamental 
fact deals with the uniformity of record in different parts of the tree. In 
taking borings in living trees, or in making V-cuts across the ends of logs, or in 
testing any part of prehistoric logs, or studying fragments of charcoal whose 
position in the tree is unknown, the value of such measurements clearly 
depends upon this uniformity throughout the tree. 

Uniformity of record in pines and Douglas firs of the Pueblo area has 
been found to be fully satisfactory throughout my experience. I have 
searched thousands of times in the last twenty-five years upon full sections of 
northern Arizona trees of these species for identity of rings about the circuit, 
and never, except in the case of obvious injury, have seen any reason what- 
ever to question a very satisfactory circuit uniformity in the pine and fir that 
we are using, nor, in fact, in the pinyon, although that is less universal. 

Dissected Trees — In order to make direct tests of uniformity within the 
trees which we are using for chronological purposes, Dr. Glock and the writer 



s 



CLIMATIC CYCLES AND TREE GROWTH 



selected pines in typical areas near Flagstaff, Arizona. Ring measures were 
made upon several radials about the circuit of the trees and at different 
heights; branches and roots were included; doubling and failure of ring forma- 
tion were noted; the tip growth of the central axis of the tree was observed 
for the various years of the tree's life. The identification of the year of this 
tip growth is easy to anyone able to identify the adjacent rings. Detailed 
reports of this investigation will be given elsewhere ] x it is enough to say here 
that the results exceed our expectation in every respect. The uniformity in 



Radius 



Base 



line 





/^^^\r^^r 



TAD520 30 40 50 60 70 80 90 600 10 20 

Fig. 1 — Circuit uniformity in a prehistoric Douglas fir MLK-127 from 

Northeastern Arizona. See frontispiece and figure 11. 



the trees tested is beyond question. A single illustration of this sort of test 
is given in figure 1, which shows measures in six different radials distributed 
about the circuit of a Douglas fir, MLK-127, whose ring sequence is shown 
in the frontispiece. 

Types of Ring Records. — While such uniformity within a tree is funda- 
mental, we encounter certain differences in type of record in different trees of 
a forest. Some records have the rings all essentially of the same size, or 
presenting slow changes from one size to another depending upon the age 



1 These reports are now in preparation by Dr. Glock, to appear as a separate paper. 



Carneoie Inst. Washington Pub. 289, Vol. Ill— Douglass 

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Carnegie Inst. Washington Pub. 289. Vol. Ill— Douglass 




INTRODUCTION 9 

of the tree, as we estimate them one after the other from center to outside 
of the tree. This kind of series is called "complacent." Other ring records 
contain strong increments from year to year, such as evident in the curves 
shown in figure 1. These are called "sensitive" records. Examples of these 
two types are given in Plate 6 which shows a very complacent ring series in 
BE 133 and a sensitive series in MV 23. Apparent correlation could be very 
high between complacent records and yet such records usually contain no 
identification characters and often are valueless. Hence, another character 
is needed; this has been expressed in previous years as "mean sensitivity." 
Mean sensitivity is the average percentage increment from year to year 
without regard to sign. A tree of high sensitivity is more datable and more 
likely to make a contribution to our studies than a tree with a complacent 
series of rings. This sensitivity, of course, is only determined where there is 
no perceptible injury. 

Cross-Identity — Cross-identity which is established by a process called 
"cross-dating or cross-identification," depends on the sensitive type of ring 
sequence. It is the foundation stone on which long ring records have been 
based. In modern trees it involves the determination of the exact year in 
which each ring grew. 1 There are three practical steps in this process. First, 
one counts in from the bark of trees whose outermost ring has an obvious 
date — for example, the outermost ring in a tree just cut down — and thus 
finds the exact dates for various thin or otherwise well-characterized rings. 
Second, a careful note is made of the time spacing of the specialized rings, 
which may now be regarded as a recognizable group, and search is made for 
an identical group in another tree of unknown cutting date ; when found the 
group rings in the latter tree become known as to exact date. Third, in the 
second tree, a count is now made either to the outside to find when it was cut, 
or toward the center to ascertain the exact dates of earlier groups of specialized 
rings. All this is easily practised in a logging camp where many stumps are 
available. On such stumps near Flagstaff anyone can always count from 
the outside to some distinctly small ring or group of rings and find exactly 
the same count from tree to tree except in the rare cases where some severe 
drouth year has occurred that caused the failure of ring formation in a few 
trees. The identification may then be carried to stumps cut years previous 
to the dating and the date of their cutting ascertained for checking against 
forest records. In this way confidence in the method is easily acquired by 

1 The word correlation has been suggested in place of the words here used, identifica- 
tion and dating. Such a change would abandon the most important fundamental of 
tree-ring work, which is the establishment of identity of the growth-date of the indi- 
vidual ring. It is not resemblance or relation or correlation in date that we endeavor to 
fix, but the actual identity of date, and all the other points of interest and value flow 
from that. The significance of cross-identification and correlation is clearer in the 
statement that the cross-identification of a ring depends on correlations between ring 
distribution within groups and other characters in two or more different sets of rings. 

A definite ring sequence is usually first proved by showing the common identity in 
date of rings within a number of trees without thought of the actual dates; hence the 
word cross-identity or cross-dating to convey the idea that the identity must be carried 
across from tree to tree (and not taken merely within a tree). If this cross-identity can 
be established, then the student is well on the road to actual dating. 



10 CLIMATIC CYCLES AND TREE GROWTH 

anyone who will take the trouble to test it in a favorable locality, such as 
the Flagstaff region. 

Cross-identity was observed in 1904 and recognized as a fundamental part 
of tree-ring work in 1911. From the start it was realized that chronological 
identification can be carried from tree to tree by grouping of the rings them- 
selves as described above. Cross-identification, therefore, depends on a 
succession of specialized rings which, as a group, do not occur in other parts 
of the long chronological ring record. Thin rings are found more useful in 
Arizona in this identification process than wide rings, because ring records 
from different trees show better correlations in thin rings than in wide ones. 

Thus a short series of 10 or 20 rings is not usually datable — that is, it 
can not convincingly establish a cross-identity, but if seemingly recognized 
it may serve as a guide and when these rings are joined with twenty on each 
side also recognized the series of fifty usually becomes datable. Thus, com- 
monly, fifty years is considered desirable for cross-dating. Occasionally 
sequences with some conspicuous grouping of the rings may be considered 
datable if containing twenty or twenty-five years. Often a sequence of a 
hundred can not be dated because it does not contain enough deficient rings 
to render identification possible by comparison with other trees. 

A highly typical case of cross-dating is shown in Plate 7, which represents, 
above, a series of pine rings near the outside of JPB-17 from Pueblo Bonito, 
and, below, a Douglas fir BK-2 from Betatakin, 125 miles away, giving rings 
near the center of the tree. In spite of these differences and the great distance 
apart, the spacing of the deficient rings as indicated is identical in the two 
trees. 

Compact groups of rings which appear almost identical in many different 
trees are sometimes called signatures or fingerprints. Plate 8 gives a series of 
rings showing a compact group from A.D. 611 to 620 which was recognized 
as a specialized group many years before its date was ascertained. It ap- 
peared in M-179, a beautiful Douglas fir specimen collected by Mr. E. H. 
Morris in 1927. Then it was recognized in 1931 as a part of the JCD (John- 
son Canyon Dating) series from the upper La Plata River near Mesa Verde 
National Park, and it has come to be called the JCD signature. It was 
recognized in 1932 in very beautiful form by Dr. Glock in the MLK series 
from Broken Flute Cave west of Shiprock. In the latter part of 1934 it 
was found in a charcoal section, FR-20, collected at Allantown, Arizona, by 
Mr. C. F. Miller under the direction of Dr. F. H. H. Roberts Jr., for the 
Smithsonian Institution. In early 1935 it was found on a charcoal piece, 
F-3992 (Plate 9), from the Baker Ranch Ruin north of the San Francisco 
Peaks, Flagstaff, collected under the direction of Dr. H. S. Colton for the 
Museum of Northern Arizona and handed to me by Mr. J. C. McGregor, 
who does the tree-ring work for that Museum. These locations form a tri- 
angle whose three sides are approximately 95 miles, 150 miles, and 160 miles. 
Plate 8c shows the center of MLK-179, whose central microscopic ring grew 
in the year A.D. 536 and corresponds to the 15th ring from the center of 
MLK-127, shown in the frontispiece. 



Carnegie Inst. Washington Pub. 289, Vol. Ill— Douglass 

A.D. 611 615 



620 



PLATE 8 

O 




Enlargements of specimens shown in frontispiece. 

A. MLK-179, showing JCD signature, A.D. 611 to 620. 

B. MLK-127, showing same. 

C. Center of MLK-179: the microscopic ring at center is A.D. 536; it is the small ring, 
fifteenth ring from the center, in MLK-127. 



Carnegie Inst. Washington Pub. 289. Vol. Ill — Douglass 



PLATE 9 




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INTRODUCTION 



11 



In connection with cross-dating, figure 2 has been arranged to show simi- 
larity in measured values over a small area by comparing the growth records 
of five pine trees collected within an acre near Prescott, Arizona, in 1911. 
The mean mutual correlation coefficient of each to the other four is 0.85 ± 
0.02. Better agreement is noticed in the rings of deficient years than in the 
wider rings. Figure 3a shows the agreement between curves obtained from 
two groups 70 miles apart; one consists of seven pine trees near Fort Defiance 
(LCFD) ; the other has three Douglas firs (group name PNN) from a location 
called Pinyon in the south central part of Black Mesa. 



;ott 




90 1800 10 20 30 40 1850 60 70 80 90 1900 10 

Fig. 2 — Cross-identity (similarity of growth in each year) in Prescott trees. 



The examples of cross-dating over this area are so tremendously numerous 
and the similarities so striking that these ring resemblances over the Pueblo 
Area assume the proportions of a phenomenon which has been overlooked 
because of the stronger human interest in the dating of prehistoric ruins that 
became possible through its agency. Up to the present time only a few 
miscellaneous examples of cross-identification have been published out of 
many thousands. It is hoped that a large display of it will be made in a forth- 
coming volume. 

RING TYPES AND TOPOGRAPHY 

The importance of cross-identification described above was first thoroughly 
realized in 1911 after comparing ring records in trees near Prescott, Arizona. 
An excellent group from near town, whose location I visited at the time, gave 



12 CLIMATIC CYCLES AND TREE GROWTH 

a highly sensitive sequence of rings with immense and sudden changes from 
one ring to the next. (See Plate 10B.) A certain questionable ring in these 
trees — namely, 1904 — was settled by cross-identification with Flagstaff 70 
miles away. The twenty-five Flagstaff tree sections used at that time gave 
less pronounced correlations among themselves, for their ring records were 
relatively complacent. This was later recognized as a different ring type, 
namely, the "forest interior" type showing rings of low sensitivity, though 
not really complacent; the thin rings used for identification were there, but 
were not often highly conspicuous because of their smallness. In 1919 a col- 
lection was made at Aztec, New Mexico. In 1922 a large collection of ancient 
specimens was begun from the Indian country located on the Colorado Plateau 
between Flagstaff and the Rio Grande Valley. It is very obvious to one who 
knows this region that the Indians selected residence locations at the lower 
forest border and from there on down into the desert and cut their building 
timbers from the trees of the neighboring forest edge. Many of their ruined 
villages, now miles from the forest, contain thousands of pine logs. Many 
ring specimens have been secured from these logs, and in 1927 serious work on 
them began. By 1929, with the aid of field trips financed by the National 
Geographic Society, dated sequences were carried back to A.D. 700. 

The character of the prehistoric ring sequences used in constructing this 
early chronology was at once noted as different from the general character 
previously observed at Flagstaff in modern tree growth (Plate 10 A). There 
were sudden and pronounced differences in ring thickness from year to year. 
This made cross-dating almost infallible if conducted with care in the selection 
of uninjured and sensitive specimens. It was at first thought that this 
difference was a climatic change during the centuries. But that idea was 
quickly destroyed by finding highly sensitive modern trees in the Pueblo area 
and complacent records from ancient trees near Flagstaff. 

In connection with the early attempts to date this prehistoric material, 
this difference in ring type was investigated more carefully. Between 1922 
and 1927 many individual collections were made around the Pueblo area for 
the purpose of establishing in modern trees the existence or non-existence of 
cross-dating over that area. Obviously it would be of little use to spend large 
sums of money in excavating prehistoric ruins only to find that the process 
failed and left us without results for the money expended. We were able to 
see as a result of these collections that such dating was highly reliable between 
Flagstaff, the Hopi Villages, Black Mesa, Kayenta, Mesa Verde, Chaco 
Canyon, Chin Lee, Fort Defiance, and the "Rim" eighty miles south of 
Flagstaff. Ease of its application was found to increase as one left the forest 
center and worked nearer the desert. At the very desert edge the trees may 
become difficult from absence of rings. This area outlined forms a rough 
circle about the Chuska-Lukachukai mountain range, and has therefore come 
to be called the "Central Pueblo Area." 

Effect of Local Topography — There still remained characters in the ring 
sequences found that were not explained thus simply by geographical location 



Carnegie Inst. Washington Pub. 289. Vol. Ill— Douglass 




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Carnegie Inst. Washington Pub. 289. Vol. Ill— Douglass 







Tree roots and bed rock, Defiance Plateau. These trees give good climatic records. 



INTRODUCTION 13 

with reference to the forest border. It had been quickly recognized in the 
big sequoias between 1915 and 1918 that there was a great difference in mean 
ring thickness and in sensitivity of ring series, depending on the location of 
the individual trees with reference to character of water supply. High sensi- 
tivity was found in trees growing on the steep slopes of the uplands. Large 
rings, low sensitivity and complacent sequences were found in the swampy 
basins. The mean growth in the basins sometimes was four times as great 
as that on the uplands and ridges. So relation to water supply was studied 
in the pines about Flagstaff and it was realized that trees near a constant 
water source had larger rings and less sensitive sequences than those growing 
where there was little or no chance for accumulation and conservation of 
water. A special search for particularly favorable locations in the Arizona 
regions was made by Dr. Glock and the writer in 1934, with the result of find- 
ing sites where the sensitivity was so high as to introduce many difficulties 
from absent rings. Interesting series of this sort were obtained from Defi- 
ance Plateau between St. Michaels and Ganado at elevations near the lower 
forest border. The soil is exceedingly thin and here and there sandstone 
shows above the ground. Plate 11 shows the stump of a tree that had been 
blown down at this site, whose roots penetrate the cracks between large 
blocks of sandstone. In these trees the sensitivity of the record was ex- 
ceedingly high. 

One other term in the environment of Arizona trees was observed at a 
sufficiently early date to appear in Volume I of Climatic Cycles and Tree 
Growth (page 22), namely, the nature of the soil; and our present knowledge 
is only the beginning of a complex subject. Near Flagstaff there are roughly 
two chief soil types: one has formed on limestone with a varying admixture 
of sandstone products, and the other rests on volcanic rock. The former 
rocks decompose into a porous soil from which moisture readily escapes and 
the rocks themselves possess deep cracks, as may be seen in many places 
about Flagstaff. The volcanic rock decomposes into a clay soil which holds 
water very tightly but usually in small quantity. When the two soils are 
adjacent and somewhat similar in contours as at points near Fort Tuthill, 
five miles south of Flagstaff, the ring records on the lava soils are relatively 
complacent. In the deeper soils and higher precipitation of the forest interior 
the growth seems larger but still complacent. In locations where the soil is 
topped by a granular mulch that aids conservation, the growth in dry years 
may remain small while that in wet years may increase greatly. This results 
in a sensitive record, as in OL-12, the dissected tree referred to above, which 
grew in the "cinder" area northeast of Flagstaff. (Measures of ring growth 
in this area made at the Museum of Northern Arizona by Mr. John C. 
McGregor show large growth.) Thick rings in wet years occur also in the 
granitic areas near Prescott, Arizona, as shown in specimen PR-62 in Plate 
10B. 

Significance of Cross-Identity and Cycles in Tree-Ring Records — It is evident 
at once that cross-identity depends on similarity in the records of different 



14 CLIMATIC CYCLES AND TREE GROWTH 

trees; it may extend over considerable areas; it is obviously not accidental, 
but comes from climatic factors in the environment common to the trees of 
the area. The study of cycles given below seeks to extend this investigation 
of similarities in the environment by picking out the slower and more pro- 
longed reactions in tree growth to climate by the aid of a new method of 
analysis. At the same time, the expression of ring records and other forms of 
long records in terms of cycles puts their details in a form more compact and 
more readily available for human use. 

RAINFALL CORRELATIONS IN NORTHERN ARIZONA 

The powerful cross-identity over the plateau area of northern Arizona and 
northwestern New Mexico has raised the question : What are the climatic or 
other elements that make it possible? 1 Extended discussion of that im- 
portant problem will be reserved for a future volume. It is proposed here 
to give only a very few of the facts. Before 1919 it was found that in the 
time from 1867 to 1910 rainfall and ring growth at Prescott, Arizona, had a 
correlation coefficient of about 0.52 ± 0.05. This rose to well over 70 per 
cent when a conservation correction was introduced. Rainfall and tree 
growth near Flagstaff gave an unsatisfactory correlation which was somewhat 
improved by using winter rainfall only. The trees used in this comparison 
were from the forest interior and so were less sensitive than those used in the 
Prescott tests. 2 

In 1933 Dr. Glock and I attacked the problem of ring growth and rainfall 
once more, using a number of our most important growth curves representing 
some sixty trees from various parts of the area centering on the Chuska 
Mountains. Rainfall curves were constructed from the longer records at 
Flagstaff, Prescott, and Natural Bridge. It was found that the direct correla- 
tion was again between 50 and 55 per cent. The introduction of a conserva- 
tion factor based on a lag in smoothed curves observed by Dr. Glock, raised 
the correlation coefficient to between 70 and 75 per cent. When, however, 
the rainfall curve with conservation and tree-growth curves were smoothed in 
the fashion used for many years in cycle analysis (using a running mean of 
three with double weight at center), the mean correlation coefficient between 
rainfall and tree growth rose to 80 per cent. In figure 3b, the curves showing 
this relationship are reproduced. Figure 4 extends the comparisons by giv- 
ing the runoff of the Rio Grande and the Colorado River near the northern 
boundaries of New Mexico and Arizona, and corresponding curves of ring 
growth. Figure 5 shows similar relation, less close, between southern Cali- 
fornia rainfall and tree growth in the San Bernardino Mountains and in the 
giant sequoias. 

1 Carnegie Inst. Wash. Year Book No. 32, 1932-33, p. 209. 

* Mr. W. E. Davis, at Berkeley, made in 1933 a series of measures upon increment 
cores secured by Mr. Pearson at the Fort Valley Forest Experiment Station, Flagstaff. 
His results were not at all promising for a relation between ring growth and winter pre- 
cipitation. On examining the specimens used by him, I found them all giving com- 
placent records, and that the better ring records had been discarded on the ground that 
the ring identity was uncertain. 



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1900 1910 1920 

Fig. 4 — Tree growth and river run-off. 



1930 



16 



CLIMATIC CYCLES AND TREE GROWTH 




m 



> 



> 



II. CYCLOGRAM ANALYSIS 

GRAPHIC EXPRESSION OF DATA 

Definitions — During this study of cycles and the development of a new 
method of their determination, the meaning of certain special words has 
suffered some modification. So in the somewhat unfamiliar paths of cycle 
study, it is well to clear the way by a brief review of several semi-standardized 
expressions for use in subsequent description, and not as an exhaustive study 
of technical words. 

An "extended" curve is one that represents an unbroken series of data 
through a succession of equal intervals of time. Such curves may take the 
following forms: 

A. Unmodified or Primary Curves 

1. "Original" data, unmodified by special treatment. 

a. Columnar plot. 

b. Point plot. 

B. Modified or Secondary Curves 

2. "Smoothed" curves. 

a. Running means. 

b. Hanned curve, or weighted running mean, sometimes called 

second or fourth intermediates. 

3. Mass diagrams and residual mass diagrams. 

4. Logarithmic plots. 

5. Skeleton and increment plots (simplified curves). 

6. Standardized and equalized curves. 

7. Merged curves. 

8. Compressed curves (a technique for handling long series of data). 

9. Curve character figure; mean sensitivity. 

10. Curve comparisons; correlation coefficient. 

11. Curve summaries; the periodogram. 

Original Data — Original or primary data are data that are unaltered; 
these words distinguish them from integrated or summated data (see below) 
or mass or smoothed or otherwise secondary expressions of data. The original 
plot, which gives a series of values at definite time intervals, may be columnar 
or point, illustrated in figure 6. The latter is the common form but neither 
is perfect. The columnar plot emphasizes only one value during the time 
interval between plotted points. This interval is one year in most of our 
curves. In tree-growth plots, this is accurate, for only one value is com- 
monly measured for the year. But in rainfall it is less satisfactory as the 
known monthly variations are lost sight of. The common plot with lines 
drawn from point to point clips off the corners of the columns and suggests 

17 



18 



CLIMATIC CYCLES AND TREE GROWTH 



an even change from the center of one year to the center of the next. This 
has been regarded by the writer as a form of smoothing. It is the beginning 
of that general process, the grouping of details together in order to bring out 
the larger characters. 

Smoothed Curves — There are two methods of smoothing in current use, 
the unweighted and the weighted running mean. An unweighted or com- 
mon running mean of three is an average of each three successive terms placed 
as a substitute for the middle term. The common weighted running mean 
used for many years gives double weight to the central term. The formula 
for it is: 

y' _ Y n _i -f- 2Y n 4- Y n+ i 



.1810 .1820 ,1830 .1840 .1850 .I860 .1870 

4, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i i I 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L 



1.0 




COLUMNAR PLOT 



■P 



TTTV 
' I ' 



1810 
i ii ill n 



1820 
1 1 1 1 1 1 



1830 
I III Mil 



1840 

ii i iliin 



1850 

i ii i In ii 



I860 

HI I ll 1 1 1 



1870 
llllLl 



LLQ 



Fig. 6 — Point and column plots of same data. 



In our usage this method is adopted to the complete exclusion of simple 
running means because the latter in case of rapid alternations may bring a 
maximum where a minimum should be and vice versa (fig. 7. See also fig. 30). 

This weighted running mean has long been called the "Hann" (the word 
has also been used as a verb) because applied extensively by Julius Hann. 
It is conveniently worked by actual figures as a "second intermediate." In 
this process the average of each two successive values is placed between them, 
but in a separate column, and then the process is repeated for the new column 
thus formed. The quantities thus obtained give the exact values of this 
weighted running mean and are often called Hanned values or second inter- 



CYCLOGRAM ANALYSIS 



19 



mediates. In rare cases two more intermediates have been taken ; the formula 
then becomes 

Y // _ Y n - 2 + 4Y n -i + 6Y n + 4Y n+ i + Y D+2 
n ~ 16 

The Hann is especially useful in a very rapid graphic application, giving 
a result very close to the exact numerical value. Any difficult case may be 
solved quickly by slight additional care. If in an ordinary plot each three 
points in succession be taken as a triangle, and the distance from the middle 
of the base (connecting terms 1 and 3) to the central term be considered, 
then the point § from base to the central term is the running mean of 3 and 
the point \ from base to the central term is the Hanned value or second 
intermediate, giving double weight to the middle term. After trifling prac- 
tise, this is quickly done by hand on a plot and any doubtful case may very 
easily be measured. Figure 7 shows the original data (solid line) and the 



1820 



1825 



1830 



1835 



184-0 



: 






: 


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: 


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^ Running mean o 


Fthnee 


= 




in 


termediate y 




: 


• 






; 



1.50 
1.25 
1.00 
0.75 
0.50 
0.25 



Fig. 7 — Smoothing methods compared. 

same smoothed by second intermediates (broken line) which is practically the 
same as the "graphic Hann," and also smoothed by a running mean of three 
(dotted line). The figure shows that the weighted mean introduces less 
distortion into the original data. Very long running means have been 
abandoned in favor of a general treatment of long curves that will be described 
below. 

Mass diagrams and residual mass diagrams are secondary curves much 
used by hydraulic engineers because they show totals and trends (fig. 8). 
A mass diagram sums up in a single ordinate the totals contained in the pre- 
ceding data. For example, it may be the continued sum of the intake of a 
reservoir and shows easily the total amount entering since any given date. 
The curve inclines rapidly upward. For water use it is convenient, but for 
climatic studies in which causes are sought, it is not well adapted, since the 
latter requires the knowledge of the ratio of any one year to any other year 
and that is not easily obtained from a mass diagram. The residual mass 
diagram is the same thing as the mass diagram, except that departures from 
the mean are used each year in place of the full values. The curve therefore 



20 



CLIMATIC CYCLES AND TREE GROWTH 



assumes an average horizontal direction and is the continued algebraic sum 
of departures from the mean. This same thing has been called "accumulated 
moisture" by the meteorologists. A defect in this sort of curve is that it 
has a quite arbitrary point of beginning that modifies subsequent values. 
Since it adds together successive departures in the same direction, it sums up 
favorable or unfavorable conditions into extreme departures that greatly 
exaggerate the trends; hence small variations in the original data tend to 
disappear. 




-SCO <-> 



30 40 50 60 70 80 90 I900\/ 10 

Fig. 8 — Mass diagram and residual mass diagram. 



When applied to a cycle, it makes the maxima and minima far more 
conspicuous and moves each forward a distance which for the sine curve is 
one-quarter of the cycle length. In that capacity it was used in 1919 to 
express a conservation effect in the relation of rainfall at Prescott, Arizona, 
to the ring growth of trees nearby. In all usage of these mass diagrams for 
cycle purposes it should be remembered that these are modified expressions 
of the original data and hence what they show is more complex than the 
original data, and special care is needed to see that something fictitious is not 
introduced. I have personally hesitated to use them because they are not 
a primary expression of data, but it is not easy to say why cycles derived 
from this sort of curve are not to be given careful consideration. 



CYCLOGRAM ANALYSIS 



21 



Logarithmic plots (fig. 9) have been little used in our studies so far as the 
original data are concerned. In logarithmic curves, the logarithm of each 
term is substituted for the term itself or the data are plotted on paper whose 
ordinates are divided into logarithmic spacing. The general effect is to les- 
sen the relative importance of high values and increase that of low values. 

Although not found convenient for use up to the present time, the log- 
arithmic proposal introduces a general problem whose solution is not herein 
forthcoming. In expressing the thickness of rings, an absent ring receives 
the value 0, but such a value in a curve is by ratio indefinitely farther away 
from the mean (considered as unity) than, for example, 2.00 is, but as drawn 
in the common curve of rain or tree growth it is an equal distance. Are 
data such as annual values of rainfall and tree growth best handled in terms 



mm 

2.0 



i.o 



10.5 



10.0 



9.5 



9.0 



8.5 



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1820 30 



90 



1900 



10 



20 



40 50 60 70 80 

Logarithms of same +10. 
Fig. 9 — Logarithmic plot (below) compared with non-logarithmic plot (above). 



30 



of addition and subtraction or by ratios? Should they be regarded as quanti- 
ties above a base or departures from a mean? When correlation coefficients 
are taken, the data are merely regarded as departures from a mean and the 
position of a real basic zero line need not be known. But rainfall and tree- 
ring values do not cling around a mean in any such manner as micrometer 
measures of a planet's diameter, for example. 

It is to judge this latter type of observation that normal distribution and 
probable error were invented. We can evaluate some curves by determining 
the "distribution" of their values; that is, the frequency of occurrence of 
each separate value whether considered as a departure from the mean or as 
an amount above a base. In normal distribution (see fig. 10a) there are 
many values close to the mean. This is the case in measuring a definite 
quantity like a planet's diameter. Rainfall data usually give a "skew" 



22 



CLIMATIC CYCLES AND TREE GROWTH 



distribution, non-symmetrical on the + and — sides (above and below the 
mean). Complacent ring records show a symmetrical distribution with far 
too many values near the mean (see fig. 10b) ; sensitive records show a skew 
distribution with increased numbers away from the mean (see fig. 10c). 




Fig. 10 — a. "Normal" distribution of data about mean. 



PPT( Pikes Peak timber line) 
.Complacent (b) 




PP B ( Pikes Peak Basin) 
Sensitive (c) 



> -_ 



1.8 



2.0 



Fig. 10 — b, c. Frequency distributions compared : standardized rings widths 
in complacent and sensitive records, 1750-1920. 



At various times attempts have been made to plot curves in different ways 
referred to above to see if any advantage became obvious. But none ap- 
peared and it has always been felt that the simplest possible presentation of 
the data was the most advisable. 

The skeleton plot (fig. 11) was used as early as 1921, but came into extensive 
use in 1927 for the cross-dating of rings. It simply represents in proper time 
order the notably undersized rings in any series. In Arizona similarities 



CYCLOGRAM ANALYSIS 



23 



carry over from one tree, to another better in such rings than in the thick ones. 
Wet years probably lead to more conservation of water and food than dry 
years. This aids the tree, but the amount of aid is greatly influenced by 
topography about the tree, and so trees show some differences in growth. 



30 



25 



20 



««- 



10 



■2 5 
0) 

or 



f • f 

# / 1 

_______ J- I ■ .J 

/ • \ 

d / \ 

— — — — / ^» m — 

• >% ^ ^ 

f 1 I J I I I I I I 



0.5 



1.0 



1.5 



2.0 



Fig. 10 — d. Frequency distribution: standardized ring widths in sensitive 
records, Central Pueblo area. Mean group curve (73 trees). 



30 



25 



20 

>> 

o 

c 

0) 

3 15 

Cr 

<u 

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10 



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01 
























































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1 



0.2 



0.4 



0.6 



0.8 



.0 1.2 1.4 1.6 1.8 2.0 

Fig. 10 — Frequency distribution: ring widths in datable though 
not sensitive tree records. 

e. Susanville, Calif., 1813-1931 (coll. by E. Antevs). 

f. Central Washington, 1813-1931 (coll. by I. Bowman). 



2.2 



Dry years, however, reduce this source of differences between the trees and in 
Arizona become excellent points of agreement. 

So the deficient rings from different trees may readily be compared in the 
field by this plot that skeletonizes the facts about a sequence. This plot 
merely requires a count outward from the central part and a note of the 



24 



CLIMATIC CYCLES AND TREE GROWTH 






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T 



CYCLOGRAM ANALYSIS 



25 



small and microscopic rings. Extra large rings and frost or other injury- 
effects are noted also; they sometimes help. A standard time scale is pre- 
pared along a horizontal axis, and the deficient rings are marked in their 
proper relative places, with solid ordinates made longer and longer as the 
rings are found more and more minute or absent. It is usually very easy 
by comparing two such plots to test cross-identity in two trees and show 
whether they were living trees at the same time. Of course, one of two plots 
compared may represent a well-established chronology with its dates all 
known, and the other may be from a log picked up in an ancient ruin. 

Mr. H. S. Gladwin, Director of the Gila Pueblo at Globe, Arizona, felt 
that too many rings were omitted in this form of plot and has proposed an 
increment plot that promises to be of important use. The increment from 
each ring to the next is measured and inserted on the usual time scale in two 




60 



70 



80 



90 



1900 



10 



-J^^ 




Original measures 



Standardizing line 



2.0 



1.0 















1 








. A 










k 


A 






k>\ 


aaA 


A 


\JV 


V K 


K 


f \th 


W 


J 




VW 


w 


VJ V 


V 


j 


\r 


r 


'—tSS. 

Cent 


;ri 3rin 


4» 










V 





Standardized measures 
G5 Eberswalde, Germany, group 
Fig. 12 — Standardizing. 



colors; pluses are one color and minuses are another, and such colored lines 
are proportional in length to the increments. Thus nearly every ring is 
represented. Averages may be taken and variable rings sometimes have 
two colors on them. Cross-dating by this method becomes very strong. Its 
successful application is even more dramatic to the student than the ordinary 
skeleton plot, but its field use is curtailed by the need of measurement. 

Standardized curves are curves equalized or brought to a uniform mean 
value so that one tree record with large average growth shall not dominate 
other records of small mean growth. If, for example, we have ring records 
that differ greatly in mean ring size and if we plot the record of each tree 
separately and analyze it for cycles, we shall find the cycles existing both in 
the small-growth records and those in the large-growth records as well. 
But if we average the curves together and analyze the mean, we get the cycles 
in the large-growth records and lose some or most of those in the small-growth 



26 CLIMATIC CYCLES AND TREE GROWTH 

records, because in fact, so far as cycles are concerned, the various curves 
have entered the average with weights proportional to their mean sizes. 
Hence in practise, to combine curves for cycle analyses we must bring them 
to the same mean value, which for convenience is unity. (These curves, it 
will be remembered, represent departures from a zero line and not from a 
mean.) This process is easily done by reducing each curve to percentage 
departures from its own mean ; that is, each separate value is divided by the 
mean of the curve. This brings the new mean of each curve to unity, and 
variations expressed in percentage give an illuminating view of what is hap- 
pening in the curve. The average of the equalized curves gives equal im- 
portance to the variations of each curve and is in proper form for analysis. 

There are further points for consideration in this usage. When a tree 
ring is absent and its measure goes to zero, that value tells something impor- 
tant, but whatever it tells is greatly exaggerated. Again, when we examine 
the shorter cycles going on near a minimum of a long cycle, such as short 
cycles in monthly sunspot numbers at minimum of the 11-year sunspot cycle, 
variations from a mean fail to tell the story. Thus we reach the need for 
local equalizing within a curve, which is a more difficult task but absolutely 
necessary if we are to get the cyclical facts. In the case of trees, we are try- 
ing to find the variations common to many trees in identical dates over a 
large area. Obvious idiosyncrasies in individual trees must be removed if 
each tree is to contribute its best to the common result. The western yellow 
pine is an isolated tree and its early rings are very thick to build a framework 
and give it strength. The change in mean ring thickness with age is called 
the age curve. Douglas fir and pinyon usually begin under protection of 
other trees, and their early rings are small and grow larger before beginning 
to diminish regularly with age. These different age curves are easily removed 
by plotting each tree record and drawing the apparent mean age curve as 
nearly straight as possible through it. This mean line or age curve is called 
the standardizing line and at each abscissa is divided into the corresponding 
measured ordinate to produce the standardized value. 

The standardizing line is drawn only by someone of much experience. 
It is made straight or with an irreducible minimum of curving or bending so 
as to avoid inserting or taking out any cycles. A curve with such line is 
shown in figure 12 together with the effect of standardizing. The process of 
standardizing has received specially careful application in connection with 
very long curves in order to disclose long cycles if present. The methods 
developed will be described below under compressed curves. 

The big sequoias are in rare cases subject to "gross" rings or a limited 
succession of rings of greatly exaggerated thickness. They are best examined 
on top of a stump and may be due to a strain or fire injury and a vigorous 
effort of the tree toward recovery. The growth curve of a sequoia becomes 
far more normal when such gross rings are greatly diminished by moving the 
standardizing line upward. Complete removal, however, is never practised. 



CYCLOGRAM ANALYSIS 



27 



These gross rings are very rare in a measured sequence because they are easily 
seen on the stump and the radial cut from the stump is selected to avoid 
erratic growth. Obvious fire or pest injuries or intervals where the rings could 
not be correctly identified are excluded from the record. 

Merging occurs in parts of almost every group average. The several 
trees whose growth curves are to be combined usually end at the same time, 
perhaps in the very same year, but the beginnings extend over a long interval. 
One or two curves may begin a hundred years before the others. The 
shorter curves must be entered without producing fictitious maxima or 
minima. The common method of treatment is to make a plot of all the 
individuals on a large scale for several years before and after the merging 




A.D 350 



360 
Fig. 13 — Merging diagram. 



point. Such a plot is shown in figure 13. An incoming or an outgoing 
curve then easily shows whether its terminal values are in accord with the 
other tree records. If only one or two terms are discordant they may be 
omitted. If ten or fifteen terms are involved, the curve considered has its 
final 9 values (beginning or end, as the case may be) weighted in a diminishing 
scale from 0.9 to 0.1 ending at the final term with the weight of 0.1. Then 
an average by weight merges the new curve into the group without any jar. 
In rare cases a series of 20 has been used for merging. 

Technique of Long Records — The writer has been fortunate in developing 
two accurately dated long ring records having climatic significance, one of 
3200 years in the big sequoias of California, and the other of 1900 years in 
the pines and firs of the Colorado Plateau, chiefly in Arizona and New Mex- 



28 CLIMATIC CYCLES AND TKEE GROWTH 

ico. Consideration of the best form for the expression of such data will 
appear in a later chapter. Some features of that consideration are very- 
general and may be stated here. 

The sequoia curves are continuous records. Weak and defective records 
had to be eliminated and occasionally some merging had to be done. But 
the plateau pines of Arizona and New Mexico have relatively short records. 
They show maximum length of a little over 500 years and a common length 
of less than 200. Hence typical records that were exceptionally long became 
very valuable and much dependence has been placed on them. In spite of 
these the number of mergings is large in the Arizona records. This is not 
all a loss; each "joint" has had years of careful consideration; that means 
in many cases a holding back of the results for years until the evidence was 
convincing. Such care was considered worthwhile with the plateau data 
because they approximate rainfall records so closely. 

Compressed Curves — Long records give a unique opportunity of comparing 
cycle data from two separate geographical locations; they permit the study 
of short cycles back in antiquity, but more especially they give us a chance 
at cycles a century and more long. Adaptation had to be made of these very 
long curves to the capacity of our analyzing instrument which can handle 
400 or 500 terms at a maximum. Again 30 to 40 years has been the maximum 
cycle length adequately analyzed in curves plotted on normal scale of 2 mm. 
to the year. Hence the long curves have been "compressed" into shorter 
lengths; that is, the time scale has been reduced so that longer cycles would 
come within the capacity of the instrument. Different tests have been 
made for effecting this compression, such as smoothing, taking means of 10, 
means of 5, overlapping means of 5. Since our minimum cycle seen on the 
instrument is 5.0 units, simple means of five years, not overlapping, have 
come to be our usage. 

This should not be done on standardized values because of the danger 
that standardizing, although not affecting short cycles, could more easily 
influence long cycles; it must be done on the original measures of each indi- 
vidual tree. Five-year sums so made are plotted and standardized anew for 
each individual tree and averaged together in a new group table. These 
new curves then either for individuals or for the group offer a cycle range of 
25 to 150 years or more. To get yet longer cycles, we again go back to the 
original measures and gather the 5-year means into new groups of 5, standard- 
ize them individually, merge and average them to get cycles between 125 and 
750 years or more. That is perhaps all we are justified in trying to get from 
our long curves. 

Curve Character Figure: Mean Sensitivity — Mean sensitivity is the mean 
percentage change from each measured yearly ring value to the next. It 
uses the reading from a base and can not be obtained merely from a series 
of departures from a mean. It is an important character in cross-dating and 
therefore has a climatic significance, telling us essentially which curves are 
presenting climatic data in the simpler terms. Low sensitivity occurs in the 



CYCLOGRAM ANALYSIS 29 

presence of abundant and lasting water supply; high sensitivity results from 
its scarcity. It is evident that we have here a character figure for tree-growth 
curves containing important information regarding environment. 

Correlation Coefficient — The popular method of expressing relationship 
between two curves is the correlation coefficient. This is in essence the 
ratio between the algebraic sum of the products of corresponding residuals 
(departures from a mean) and the square root of the product of the sum of 
their respective squares. It may be written: 

r = Sxy 



\/2x 2 -y 2 

Thus it may be stated as the average product of residuals divided by the 
square root of the product of their average squares. 

In the correlation coefficient the values are taken as departures from a 
mean or as "residuals." It makes no difference where the zero point is; for 
instance, one set of residuals may average three times as large as the other. 
One set of increments from each term to the next may be three times as 
large as the other, and no change is produced in the coefficient. In tree- 
ring work, this overlooks important features, for cross-identification depends 
on large increments as compared to ring size and fails with small increments. 

The similarity between two trees curves then is only partly expressed by 
a correlation coefficient. The reliability of a bit of cross-identification may 
be estimated at over 90 per cent when the correlation coefficient is below 50 
per cent. Complacent curves may show high correlation coefficient with 
doubtful cross-identity. In general, however, they are not far apart. 

We have made various attempts to hit upon an index of similarity that 
is more satisfactory than the correlation coefficient. Dr. Glock has used a 
"trend coefficient" reached by dividing the sum of the positive products of 
corresponding increments from two curves by the sum total of positive and 
negative products disregarding signs. This is easier to compute than the 
correlation coefficient, but here again one set of increments could be increased 
or diminished in a definite ratio without affecting the result. 

A simple trend comparison, occasionally made use of by ourselves and 
others, is the percentage of cases of agreement in rising or falling value of the 
increment. It gives a fair idea of similarity. 

One of the best devices is the scatter diagram using original values from 
zero and arranging the vertical and horizontal scales so that the mean values 
of each curve come near the center of the diagram and the zeros come at the 
lower left corner. This arrangement appears automatically if each curve 
has been standardized; in fact the comparison is usually made between 
standardized curves. Departures from a mean may be used with equalized 
average residuals. 

The diagram resulting from such plotting of standardized curves gives a 
ready and vivid picture of the points of similarity between two curves by 
the shape of the cloud of dots, especially its departure from the circular form 



30 CLIMATIC CYCLES AND TREE GROWTH 

along the diagonals. Three factors are really needed to give the result: 
the ellipticity of the dotted area, the semimajor axis, and the direction of 
the major axis. (See page 91 for discussion of an example.) 

Periodogram — The periodogram is a summary of cycles found in a series 
of data: the cycle lengths are commonly expressed along the axis of x between 
limits that are evident. The ordinates decide the type of periodogram. In 
Schuster's original form they were derived from amplitudes of the sine curves 
involved in the analysis. Dr. Alter has used the name correlation periodo- 
gram as applied to the curve of correlation coefficient values obtained by 
comparing a curve with itself at lags of 1 year (or unit), 2 years, and so forth, 
up to about half of the total number of terms. 1 With the large number of 
cycles obtained in many curves of considerable length, we find it very con- 
venient to use a diagram showing the number of occurrences of the various 
cycle lengths: this is called a frequency periodogram. When this frequency 
is determined separately for successive intervals of time as for successive 
centuries, we are calling it a "progressive" or chrono-periodogram. (See 
figs. 21 and 55.) 

GRAPHIC EXPRESSION OF CYCLES 

Cycle Integration or Summation — This has been the fundamental method 
of testing for cycles in any succession of data. It consists in placing suc- 
cessive blocks or sets of data one under the other, each just containing the 
cycle length. To illustrate — suppose we have a series of values of sunspot 
data (smoothed annual mean numbers, neglecting the fractions) as follows: 

We can test for a 10-year cycle by adding and averaging the columns as 
they stand, and as a result we find no cycle of any consequence (see fig. 14a). 
But we see in table 1 that the data have a somewhat suggestive distribution 
with the larger numbers moving to the right in each successive set, and to 
see it better we plot figure 14b in a crude quantitative distribution and pass 
an estimated line through the maxima. If the best solution were 11 years, 
the line of maxima would slant to the right 1 year for each decade. It does 
more than that, for it changes to the right about 3 years for each 2 decades. 
That gives us a double value in 23 years, or 11.5 years as a rough solution. 

Now if we wish to integrate these data on an 11.5-year period, we do it 
by the following approximation, which is accurate enough for our purpose, 
namely, to plot a fairly good average of the sun-spot cycle from 1833 to 
1924. 

With this table before us we realize how much extra trouble it is to re- 
arrange our numbers for testing each proposed cycle and especially to test a 
fractional cycle, or one that does not consist of an even number of units. 
This fractional test is especially irksome because the values really should be 
interpolated. We could do all this very easily if we could make the additions 
at any desired diagonal direction, including those giving fractional periods, 

1 Dr. Alter is now using a simpler coefficient in forming a periodogram, see Bibli- 
ography, 1933 (3). 



CYCLOGRAM ANALYSIS 



31 




;i90o 



N.Syears 

(a) Curve, 10 year test 
(CJ Curve, il.Syeantest 








1 


2 


3 


4 


5 


6 


7 


8 


9 


I83C 








o 


O 





000 

0000c 

000 




OOOOO 

888 


888 
000 


82° 
000 
000 


1840 
1850 s 


ooo 
ooo 


ogo 




o 


o 





000 




000 
000 


000 
000 

°8° 


000 


000 

8§8 


s$k 


ooo 
ooo 




ooo 




ooo 




s 








S 



000 




000 
88 


I860 


ooo> 
ooo 

°8° 


o o 

ooo 

00 \ 


ooo 
ooo 


000 

o 



ogo 


000 









ogo 


8 8 g 


1870 


ooo 


ooo 

OOOOo 
OOO 


ooo 

o§8. 


ooo 
ooo 



000 
















a 


1880 


ooo 


o 
ooo 




%h 


8*1* 


» 000 




000 




s 





e 


e ' 


1890 


• 


ogo 




ooo 
ooo 


80S 

OOO 


8^ 
000 

000 


000 
000 


000 













1900 


e 










000 




000 
000 


000. 
0' 


000 

woo 


8°8 


ogo 


1910 


o 
e 













ogo 


000 

OOO 


OOO, 

000 
ogo 


1?l 


000 
000 


1920 


ooo 

e 


ooo 


o 
















% 


\. 



(b) 

Fig. 14 — a. Summation (integration) curve of sunspot numbers at 10.0 years. 

b. Graphic representation of integration table. 

c. Summation curve at 11.5 years. 



Table 1 








1 


2 


3 


4 


5 


6 


7 


8 


9 


1830 








8 


13 


57 


122 


138 


103 


86 


1840 


63 


37 


24 


11 


15 


40 


62 


98 


124 


96 


1850 


66 


64 


54 


39 


21 


7 


4 


23 


55 


94 


1860 


96 


77 


59 


44 


47 


30 


16 


7 


37 


74 


1870 


139 


111 


102 


66 


45 


17 


11 


12 


3 


6 


1880 


32 


54 


60 


64 


64 


52 


25 


13 


7 


6 


1890 


7 


36 


73 


85 


78 


64 


42 


26 


27 


12 


1900 


10 


3 


5 


24 


42 


64 


54 


62 


48 


44 


1910 


18 


6 


4 


1 


10 


47 


57 


104 


81 


64 


1920 


38 


26 


14 
















Sums 


469 


414 


395 


342 


335 


378 


393 


483 


485 


482 


Aver- 


52 


45 


44 


38 


37 


42 


44 


54 


54 


54 


ages 














Mean 


46.4 







32 



CLIMATIC CYCLES AND TKEE GROWTH 



without having to rearrange or interpolate the numbers. This very need 
caused in 1913 the construction and use of the cyclograph to be described 
shortly. 

Integration has its dangers and may be deceptive. Just as above in averag- 
ing curves together into a group, the curves must be equalized or standardized 
or one may dominate to the exclusion of the others, so here we are in fact 
averaging curves together into a group, and a strong configuration in one 
block of data may produce a cycle that exists nowhere but in that one block. 

Since this type of integration is the basis of all mathematical forms of 
cycle analysis, its dangers have been well seen and various protections have 
been devised; for example, a common safeguard is to separate the data into 
two halves and see if the cycle comes out equally well in each half. 1 Such 
a process applied by Schuster in 1906, in his classical work on the sunspot 

Table 2 





l 


2 


3 


4 


5 


6 


7 


8 


9 


10 


ll 


1/2 


1830 
1853 
1876 
1899 
1922 


37 
39 
47 
11 
13 
12 
18 
14 


24 

21 

30 

12 

7 

10 

6 

6 


ii 

7 
16 
3 
6 
3 
4 
17 


8 
15 
4 
7 
6 
7 
5 
1 


13 
40 
23 
37 
32 
36 
24 
10 


57 
62 
55 
74 
54 
73 
42 
47 


122 
98 
94 

139 
60 
85 
64 
57 


138 

124 
96 

111 
64 
78 
54 

104 


103 
96 
77 

102 
64 
64 
62 
81 


86 
66 
59 
66 
52 
42 
48 
64 


63 
64 
44 
45 
25 
26 
44 
38 


54 
17 
27 
26 


Sum 
Average 


191 
24 


116 
14 


67 

8 


53 

7 


215 
27 


464 

58 


719 
90 


769 
96 


649 
81 


483 
60 


473 
12 
39 1 





1 If the extra half-year is placed at some other point in the cycle, the result is practi- 
cally the same. 



numbers, made him see at once that there are other periods in those numbers 
than the well-known one near 11 years. 

Thus integrations of selected values fall far short of giving satisfactory- 
cycle analysis. Not only should each proposed period be tried separately in 
all parts of the data, but all nearby period values should each be tried through- 
out the data. We believe that our method described below is the only safe 
one yet suggested that fills these exacting requirements. 

Successive Integration — In harmonic analysis a definite interval of time, 
usually the full length of the data, is taken as a fundamental, and integral 
parts of this, |, f, J, etc., perhaps to 30 different fractions, are taken as suc- 
cessive periods on which the data are summated, and the qualities of the 
resulting means ascertained. This is multiple integration applied in an effort 
to reach all possible periods that may exist in the data. But while this proc- 
ess covers many possibilities in short period lengths, it leaves large gaps in 

1 For a cycle that is permanent, this test is very helpful, but for discontinuous 
periods it is obviously of little value. 



CYCLOGRAM ANALYSIS 



33 



the longer period lengths. Suspected long periods are often sought by in- 
tegrating several successive values from decidedly less to decidedly more 
than the suspected length and observing whether the cycle amplitude in the 



1833 



1844 



1855 



1866 



1877 



1888 



1899 



1910 



192 



844 



855 



866 




877 



1888 



899 



1910 



100 



932 



Sunspot Nos. 

J_ 




Scale 



Fig. 15 — Plot of sunspot data to show changing place of 11.4-year 
maxima in successive 11-year intervals. 



plotted means increases to a maximum and then falls away, as in figure 16. 
This is called successive integration and can be made very effective over short 
ranges. 



34 



CLIMATIC CYCLES AND TREE GROWTH 



Chrono-Integration— The successive integration above described deals 
with successively increasing cycle values as tested in the same data. Chrono- 

18 YEAR PERIOD 

|«— iSyears— »| 




5years 



)*— I8years— *\ 
19 YEAR PERIOD 

I9years- 




|«- 20 years —J 



21 YEAR PERIOD 

k~ 21 years 




iniU- 

Syears \*—2Zyears 
Fig. 16 — Successive integration of FAM (Flagstaff area mean curve), 1700-1920. 

integration means a series of tests of the same cycle lengths applied in definite 
successive intervals of time. This process was used in connection with the 
first attempts at cycle analysis of our long chronologies (Chapter VI, page 121), 



CYCLOGRAM ANALYSIS 35 

to verify or deny certain changes in an 11-year cycle observed in a cyclogram. 
In carrying out this integration, the 500-year curve was divided into blocks 
of 57 or 68 years (or 69 years) and these intervals integrated at 11.4 years. 
(The results are shown in figure 33 of Volume I, page 103. See also Scientific 
Monthly, December 1933, page 491, fig. 12 and our fig. 52.) In this 
manner certain resemblances between climatic cycles in tree-ring growth 
and solar changes were first observed. 

This chrono-integration method of studying cycle history was then applied 
to the long records of the giant sequoias in similar blocks of 57 or 68 years, 
but no especial result was forthcoming. Integrations at 23 years, however, 
brought results that seemed to show frequent division of 23 years into a small 
number of integral parts. This in turn led to "overlapping integration" at 
23 years, which has seemed the most successful method yet tried. In effect, 
this process consists in taking running means of three 23-year intervals. 

The defect hitherto existing in this overlapping integration is that only 
one cycle length is tested in a very long series of integrations and other cycle 
lengths go untested. The difficulties of testing all cycle lengths as in common 
cycle analysis have been overcome in a process called "lag" analysis (see 
page 50). 

PLOTTING UNSTABLE AND MIXED CYCLES 

We shall find in a few pages that our analyzing instrument called the cy- 
clograph (whose automatic pattern is the cyclogram), in its common visual 
operation combines successive integration (by the moving mirror) with 
chrono-integration (by retaining a time element in the pattern). This is 
accomplished by an "optical correlation" (as named by Dr. Alter) combined 
with a certain method of plotting unstable and mixed cycles. In showing a 
procession of discontinuous or short-lived periods on common rectangular 
coordinates, we have a time scale horizontal as usual and upon this we may 
plot cycle lengths as ordinates, as in figure 17a. But this fails to show a 
continuity that is characteristic of cycle sequences. If, however, we abandon 
the ordinary use of an ordinate scale for cycle lengths and combine a polar 
scale for cycle lengths with a horizontal time scale, we can show continuity 
with instability and even the presence of additional fragmentary periods. 
In this plot directions vary with cycle length as shown in figure 17b which 
obviously presents an 11-year cycle from 1500 to 1650, a 10-year cycle thence 
for a hundred years, and again an 11.4-year cycle from 1750 to 1900. There 
is also expressed the presence of an 8^-year cycle in the early part of the 400 
years and a 14-year cycle in the last hundred years. Thus we can see clearly 
that a combination of polar and rectangular coordinates gives a facility in 
expressing unstable and mixed cycles, of which we will make further use. 

CYCLOGRAM PRINCIPLE 

We find it more advantageous to make use of a method of plotting cycles 
that does not involve two different systems of coordinates but which brings 
the same effect in the plot. It can be developed easily by a series of very 



36 



CLIMATIC CYCLES AND TREE GROWTH 



simple graphic transformations. Figure 18a gives an approximate sunspot 
curve on a horizontal time scale. The first transformation consists in split- 
ting up this curve into 10-year blocks and placing one under the other, as 
in figure 18b, at definite and equal vertical intervals. Each block is ex- 
tended beyond the ten years to 20 years or more. The dotted line A-B-C 
represents the same instant of time in three different blocks. The second 
transformation consists in swinging this line A-B-C so that it becomes hori- 
zontal, as in figure 18c, without changing the horizontal scale of figure 18b; 
that is, each plotted point in the diagram moves downward vertically and 





1 

1500 






1 
1600 






1 

1700 






1 
1800 






1 

1900 






















































































Cycle 
length. i9. 








































vears 






































* 




























































































































































































a 






\ 
































4 






— Nl A 

/\l3 


\ 


8.5 
* 






























A 

'14. 






\ 
\ 
\ 




II 
\ 
























/ 
/ 

/ 






\\-/ 10 






\ 
\ 












10 








11.4 




/ 














\ 
\ 

\ 














/ 






































/ 


,' 











Fig. 17 — a, b. Two methods of plotting cycles. Above, rectangular plot; 
below, combination of rectangular and polar plots. 



not on an arc. By this transition we secure a correct vertical time scale on 
rectangular coordinates. For convenience in use, this diagram as a whole is 
now rotated 90° to bring the main time scale horizontal, as in figure lSd. 1 
This produces a complete time progression from left to right on rectangular 
coordinates. The vertical scale, which was the horizontal scale in b, ex- 
presses residuals from 1840, 1850 which are multiples of 10. It could be 
shown by trial that the exact multiple of any other convenient number could 
equally well be used. 

1 This change in representing cyclograms is apparent in the different position they 
hold in Climatic Cycles and Tree Growth, vol. I, Plate 12 (1919), and vol. II, Plate 9 
(1928). 



CYCLOGRAM ANALYSIS 



37 



In the diagram 18d we have reached the plot we have been seeking, but 
the original ordinates of figure 18a, consisting of sunspot numbers, become 
meaningless in the new position and are therefore swung up into a vertical 
position perpendicular to the page, as in figure 19a, and must be expressed as 
a third dimension, which is easily done by representing light intensities by 



40 
I 



^nTlTnw ^rTTTT>v^/fnTrK ^fmrrh^fmTT^ ^TTTTrv^<lTTrT>>^^Tl 



18.50 



60 



70 

i 



80 
L_ 



90 



1900 



10 
i 



20 
i 



30 
I 



CL Common plot of sunspot numbers 

io 2oYears 

1840 



34 >w^fni TTTT>> 



1850 



TTT^^TTrh-^ 



I860 



TTTN^TTTTn^ 



1870 



Tn^Trt^prrffTT^ 



I88Q ^TTTm>> .^ffnTTTr ^. 



', 890 ^rTTTTr>^iTn"TT>^ 



19 10 ^ -^<nTT>^^r<nTTi 



900 ^fTrTTrr> — ^mTTT^ 



i 920 |v> ^TTfJTTh 

o 10 20 

Years 

The same divided into 
lOyear blocks 



</> Years 




C Last figure changed to 
rectangular coordinates 




<f)±L 
*E 



1850 60 70 80 90 1900 10 20 30 

Time scale 
ci Last figure rotated to bring chief 
time scale horizontal 

Fig. 18 — a, b, c, d. Cyclogram demonstration. 



local enlargement or by some half-tone process as in common photographs. 
Thus all maxima in the original data are retained in the plot. 

This is crudely represented in figure 19a. Here, as stated above, we 
have the main time scale horizontal and a vertical time scale consisting of 
residuals from 10-year multiples. We note here that if we take some date 



38 



CLIMATIC CYCLES AND TREE GROWTH 



such as 1845 and in its proper place on the horizontal axis give it an ordinate 
of 5 years from 1840, we also plot it at 15 years as a residual from 1830 and 



30 



20 



10 



•b 10 

2 



20 



i 1 1 1 1 1 1 1 1 1 

W///// 



I I I L 



X_J I L 



1850 



1900 




Fig. 19 — a, b. Cyclogram demonstration, second part. 

at — 5 years as a residual from 1850, and so on for a number of repetitions in 
a vertical line. Thus we build a pattern that repeats itself. This gives a 
chance to see other cycles beside the one being plotted. 



CYCLOGRAM ANALYSIS 



39 



In this diagram the alignment of the maxima along the direction A-B 
becomes very prominent, much more definite than it showed in previous 
figure 14. We can investigate the meaning of the directional character of 
that line by figure 19b. This diagram, as is evident, is prepared on the co- 
ordinate system of 19a. Starting at any point, for example at A in 19b, 
we lay off the maxima of a 10-year cycle. We find that they produce a 
straight horizontal line as indicated. Now we lay off an 11-year cycle. 



1750 1800 1850 1900 
i i i i i I i i i i i i i i i I i i — I 



B 
C 



'.\\ - I 



r 



in 



m 

L 

s 

•> 

0. 



10- 

o- 

10- 
20- 



*\ 



201 $ rtftb+l/i(fflUr 



c 

B 



l — i — i — r— i — I — i — i — i — ' — i — i — r 
1750 1800 1850 



1900 



1 — i — I 



•20 



-10 


3 






0_ 


m 
c. 


-o 




ro 
0) 




71 


> 


-10 


c 





u 20 



Fig. 20 — Cyclogram plot of sunspot numbers, 1750-1930. 

Note: if the analyzing lines A-B are made to slope the other way, the interference 
sequence CDEFG is inverted. 



This will be built up of 11-year intervals measured to the right on the main 
time scale and 1-year residuals set off upward on the vertical scale. Wher- 
ever we lay off an 11-year interval it will take a slant parallel to this slope 
as plotted up to the right. If we lay off a cycle of that length the maxima 
will form a straight line at that slant. A 12-year cycle produces maxima in 
a straight line at a still steeper inclination wherever it occurs in the data. 
Once started it becomes very easy to lay off a full set of directional values 



40 CLIMATIC CYCLES AND TREE GROWTH 

expressing cycle length between 6 and 13 years. We may now interpolate 
the particular slant shown by the sunspot maxima in figure 19a. By com- 
paring it with our set of position angles just developed, we obtain an approxi- 
mate solution of 11.4 years for the mean cycle length exhibited by the maxima 
since 1833. 

Now on the same coordinate paper let us extend the plot of sunspot 
numbers back to the maximum at about 1749 and see what is indicated by 
the same method of solution. The plot is shown in figure 20 and we see that 
the various maxima instead of being scattered at random do form a broken 
line or a sequence of fragmentary straight lines. Since each straight line is 
a temporary period, we can, I think, consider the maxima sufficiently in 
straight lines to call this diagram a sequence of short-lived or discontinuous 
periods. 

In our polar diagram of figure 19b made in the same coordinates, we have 
an easy solution for the approximate cycle lengths shown by these lines. If 
the polar plot is on transparent paper it is only necessary to superimpose it 
and we find as follows : 

Cycle length from plot : Cycle length from time interval : 

1750-1790 9.7 years between 5 maxima 39/4 or 9.8 years 

1790-1830 14 between 4 maxima 42/3 or 14.0 

1830-1837 7 between 2 maxima 7 

1837-1930 11.5 between 9 maxima 91/8 or 11.4 

It will be noticed that by means of the half-tones, all the original data 
may be represented in figure 19a and, if other cycles are present and suffi- 
ciently conspicuous, they will constitute alignments in other directions as 
indicated in 19b. It is evident that a given alignment does not necessarily 
continue through the whole pattern. If, for example, a cycle did not exist 
before some definite date but did exist after that date, we would find an align- 
ment beginning at that time. (See Plate 16.) Thus we can study cycles or 
periods equally well, whether permanent or fragmentary, provided there are 
a sufficient number of repetitions. Thus the detection of the presence of a 
cycle is necessarily obtained in its full and extended form and not from inte- 
grations and the cycle must become evident in competition with a considerable 
range of values on either side which, if there, show at the same time. So a 
proper and careful selection of value can be made and the analysis is not in 
any sense a special test for a single value. 

CYCLOGRAPH 

Cyclogram analysis can be performed by anyone who has the patience 
to understand it. It has introduced new methods and results in cycle study, 
for fragmentary and interrupted periods can be measured as well as permanent 
ones. This gives a new and more efficient approach to climatic and sunspot 
cycles. The automatic character of this analysis has made it extraordinarily 
rapid. Thus five minutes at the cyclograph has often been enough to 



Carnegie Inst. Washington Pub. 289. Vol. Ill — Douglass 

Years 
-8 



PLATE 12 



84 



11.3 




16.9 



9.8 




A B 

Periodograms 

A. Periodogram (1913) of sunspot numbers since 1760. 

B. Periodogram (1918) of variable star, R Arietis, showing period of 187 days (see 
Appendix). 



Carnegie Inst. Washinoton Pub. 289. Vol. Ill — Douglass 




A. Cyclogram by spectrometer process (1914). 




B. "Sweep" or cylindrical pattern; the original plot, inverted, shows below the sweep. 



CYCLOGRAM ANALYSIS 41 

measure and check all cycles within a length range of 5 to 40 terms in a curve 
showing 175 terms. 

The efficiency of this form of analysis has resulted largely from the 
automatic production of the pattern called the cyclogram. The cyclogram 
may be described as an adjustable 3-dimensional plot 1 containing — 

1. A general horizontal time scale. 

2. An enlarged vertical time scale giving residuals from some convenient 
exact period such as 10 years. This procedure separates different periods 
into different straight lines pointing in different directions. In the mechani- 
cal plotting of the cyclogram this "convenient exact period" may be made to 
take successively changing values over a long range. 

3. The original ordinates are changed into a third dimension and repre- 
sented in half-tones by light intensities. 

DEVELOPMENT OF CYCLOGRAPH 

It was Schuster's work on the periodogram (fig. 21, page 42) that started 
our cyclogram type of analysis. The first step was a question: How can 
we perform quantitative integration in any desired direction other than the 
vertical? and the answer came at once, "By light intensities." So the 
"multiple plot" was tried in 1913 (see vol. I, Climatic Cycles and Tree Growth, 
Carnegie Inst. Wash. Pub. No. 289, 1919, Plate 9b) and its integration at 
continuously changing angle (in A of the same plate) by a cylindrical lens 
and a photographic plate moving across a slit. 

The multiple plot was simply a pictorial reproduction of the integration 
table given a few pages back. The series of data was plotted many times in 
solid white on a black background. These plots were mounted one below 
the other at equal vertical intervals and between each repetition there was 
a constant horizontal off-set amounting to a convenient average cycle length, 
just as in the table. An integration of the light values in the vertical by a 
positive cylindrical lens with vertical axis summated any cycle that existed 
in vertical direction across the multiple plot. The integration was recorded 
on a photographic plate and measured for quantity of light. The whole 
multiple plot was rotated into a different angle and a new integration made 
in the vertical and another period tested. The movements of plot and plate 
were made continuous by clockwork. 

A periodogram was thus produced (see Plate 12A), which indicates the 
presence of a period by breaking up into corrugations, since it is merely the 
merging of periodic maxima in the multiple plot. Volume I, referred to 
above, gives several periodograms in Plate 11. They are very crude but are 
part of the history. Except for these photographs and some tests on vari- 
able stars (in 1918; see appendix) the use of the periodogram was dropped 
after about 1916. 

1 It may also be described as an optical, photometric mechanical plot produced 
automatically in a complete form from a prepared curve of data; in it the time displace- 
ment of any maximum from its periodic position is plotted at its observed time. 



42 



CLIMATIC CYCLES AND TREE GROWTH 



The multiple plot from which the periodogram was made was itself 
laborious to make, and a year's thought was put on the problem of producing 
it automatically (1913-14). Such diagram must consist of duplicate solid 
plots of the data, placed one below the other at equal distances and with 
equal horizontal off-sets from each to the next. A solid plot illuminated 
(later called cycleplot) may be seen in Plate 14, general view of the 
cy olograph. The first bit of progress was obtained by putting on an 
opaque background a transparent solid plot inclined at 45° slant in a window 
of a well-darkened room. Then a camera was mounted on a spectrometer 
plate and rotated a small angle each time between exposures. This gave a 
fixed multiple plot as reproduced in Plate 13A, and incidentally showed a 
20-plus year cycle in Arizona trees. It was recognized at once that this 

















































3000 
























0) 

"a 

3 
























a. 
£ 
< 


- 




J 


1 


1 














1000 






r 





















y* 


-£ 


i 


n 


i — 




i 


i 


i 


i 


i 



8 



10 



22 



24 



12 14 16 18 20 

Years 

Fig. 21 — Schuster's periodogram of sunspot numbers. Note: See also Stumpff's 
periodogram computed by Schuster's method, reproduced in figure 55. 

told a story that could not be found in the periodogram, for it gave not only 

periods but their changes as time passed, -f-, and for a time it was called the 

dt 

"differential pattern." 1 This was still not a satisfactory solution and the 
transparent plot was the only part that survived to become an essential part 
of the final instrument. 

The cyclogram is a chrono-periodogram or a periodogram differentiated 
with respect to time. The cyclogram was produced mechanically in Decem- 
ber 1914 as follows. If a transparent plot is photographed with a camera 
having a positive cylindrical lens with its axis perpendicular to the direction 
of the plot, the resulting image consists of a bank of parallel vertical bands, 
each band receiving its light from a corresponding maximum in the curve 

1 See Astroph. Jour., April 1915, p. 173. 



CYCLOGRAM ANALYSIS 43 

and therefore its light intensity is proportional to the height of that maxi- 
mum. This pattern was first called a "sweep" (Plate 13B, like the effect of 
a broom on a sanded surface) and later it was called the cylindrical pattern. 
If we cut across this cylindrical pattern in any direction with a straight line 
— for example, with a narrow transparent line cut in opaque paper — we find 
coming through this line a complete set of data, taking light intensities for 
ordinates. If now we take a large number of such transparent lines parallel 
to each other and equidistant, we shall find a perfect multiple plot coming 
through. Each separate line contains the full set of data, as far as its length 
permits, is parallel to its neighbors and presents equal offsets each to the 
next, throughout the whole pattern. 

So the basic parts of the cyclograph were established as a cylindrical lens 
in a camera and an analyzing plate made of equally spaced transparent lines 
placed just in front of the photographic plate. In order to read the cycles 
from a pattern so produced, it was necessary to measure the time scale of 
the image and the effective spacing of the analyzing lines and the actual 
angle between lines and bands. This was done by extra lenses and a small 
filar position micrometer. It was a real task to get the cycle length. 

The trouble with any given cyclogram such as those produced in this 
way is that only a small range of cycle lengths could be found in it and there- 
fore many other photographs had to be made. The range can be increased 
in several ways. Two of them have been tried and discarded; namely, rotat- 
ing the analyzing plate and changing the spacing between its lines. The 
former added very little range and made the computation of cycle length a 
more difficult matter. We have called the latter a variable grating cyclo- 
graph. It falls far short of the method finally adopted in flexibility and pro- 
duces confusion between fundamentals and harmonics. 

The simple method finally adopted has all points in its favor. It pro- 
duces results by changing the effective distance from the camera to the plot 
that is being analyzed, thus altering the scale of the image that passes through 
the analyzing plate. The change in scale becomes in effect a change in the 
cycle from which residuals are automatically plotted as described above in 
connection with the cyclogram plot. This change of scale is now done (since 
1920) by altering the distance of a secondary mirror (see fig. 22) interposed 
between the transparent curve and the camera lens. Motion of this mirror 
by diminishing or increasing its distance from the camera changes in inverse 
proportion the size of the cylindrical pattern that falls upon the lines of the 
analyzing plate. The position of the mirror that by trial brings each definite 
cycle length into horizontal position (compared to a stationary thread in 
the field of view) is marked on its track and the instrument becomes in all 
respects a direct reading cycloscope capable of instant adaptation over a 
very large range. 

The general arrangement of the cyclograph is shown in figure 22. The 
light from the illuminated curve, or cycleplot, is reflected in a movable mirror ; 
it then returns to the camera which has in effect a positive cylindrical lens 



44 



CLIMATIC CYCLES AND TREE GROWTH 



with vertical axis. The lens focuses the cylindrical pattern on an analyzing 
plate illustrated at 22b (and Plate 15A) whose transparent lines are inclined 
about 17° to the vertical. The geometrical relation of the parallel lines 
on the analyzing plate and the cylindrical pattern falling upon them are 
shown in figure 24, page 45. As the mirror moves, the size of the cylindrical 
pattern changes and rows of maxima coming through the analyzing plate 
look as if they were rotating about an axis. This is merely the change (al- 



Scale 



\ ft 



U Cycleplot 




Analyzing _ 
plate ^j 



^"Cylindrical lens 



Movable 
mirrors 



CL 




Fig. 22 — Important parts of the cyclograph. 

a. Schematic elevation. 

b. Analyzing plate. 



most instantaneous) from one "basic" cycle length to another (see Plate 15B; 
see also Appendix. 

Cycleplots — Many improvements have taken place in the plots prepared 
for analysis. The original multiple plot was cut out of white paper and 
mounted on a black background. The first cyclograms in 1914 were made 
from a plot cut through black paper; tissue paper was placed over the open- 
ings and lights mounted at the back. A small photographic negative or 
positive of this was tried and found unworkable. The plot was then cut 



+ 



w\ 



Carnegie Inst. Washington Pub. 289, Vol. 1 1 I—Douglass 



PLATE 14A 




jj.g 



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- 5d.S 

- N 

03 j>i 

■s* 

03 +» 

I a 

o." 

JS to 



Sou 
■a 

03 jS 

> O 

s m 

H 



J5 

Oh 

=3 



Carnegie Inst. Washington Pub. 289. Vol. Ill— Douglass 



PLATE 14B 




CYCLOGRAM ANALYSIS 



45 



through coordinate paper whose back was painted with opaque material. 
This was used in front of a long ground-glass behind which lights were placed. 
The present process of making a cycleplot ready for analysis has the origi- 
nal data plotted on a standard scale coordinate paper whose smaller division, 
2 mm., commonly represents one year. This plot is Hanned graphically and 
then the Hanned line is traced over carbon paper upon a strip of heavy brown 
paper 4 inches wide and some 48 inches long. A "cutting" line is marked in 



mm. 



2.0 



i.o 



1820 



30 



4-0 



1850 



60 



70 



80 



90 



1900 



10 









































vbS&zbz 






(£u^^4jXb2 





























Fig. 23— Cycleplot, to show cutting line. Standardized tree growth, 
G 5, Eberswalde, Germany. 




' Images of 

** original 

maxima 



— lOyear cycle 



2 Wj /* 

I2year cycle 



Fig. 24 — The analyzing plate changes longitudinal displacement 
in position of maxima, to transverse. 



a nearly straight line along the minima and the maxima cut out above this 
line with a razor blade. In this way the maxima are sufficiently isolated so 
that they can easily be distinguished. If the original base at zero is used, 
too much light floods the pattern and the maxima are not distinguishable by 
the eye, as was the trouble with the patterns shown in Volume I (Climatic 
Cycles and Tree Growth), Plate 12. 



46 CLIMATIC CYCLES AND TREE GROWTH 

A cutting line should be made as nearly straight as possible or it may con- 
fuse the analysis. This requirement was learned by experience. Certain 
analyses made before 1919 showed the Hellmann cycle, a two-crested 11-year 
cycle, very plainly (vol. I, Plate 12f). Analyses made early in 1932 failed 
to show it. A test on the early cycleplot revealed that a 19-year and even 
a 14-year cycle had been partly removed by a curved cutting line. To 
verify this fact the cutting line was transferred to a cycleplot, analyzed, and 
these two cycles were found in it. So, to extend the test, 19- and 14-year 
cycles were subtracted mathematically from the Flagstaff data and the Hell- 
mann cycle was once more revealed. It is legitimate to remove cycles in 
the cutting line, provided the cutting line is itself analyzed to see what has 
been removed. In general analysis such usage is not advised, but in special 
cases this seems an advantageous way of removing interfering cycles. 

A straight cutting line aids the evaluation of longer cycles by leaving 
them unaltered. The question of the cutting line then becomes a part of 
a larger practical policy dealing with the range of the instrument as to cycle 
length. The range extends from 5.0 years at the minimum to 30 or 40 years 
at the maximum. Beyond 40 years we replot at a compressed horizontal 
scale. At 30 years the visible cyclogram produced in the analyzing instru- 
ment is reduced in length to f of its size at 5 years. Details are lost and the 
larger cycles become visible. Therefore we must make a cycleplot that is 
usable at each of these extremes. The nearly straight cutting line gives us 
the long cycles; then not to lose the short cycles, obvious minima not deep 
enough to reach down to the cutting line are joined to it by narrow "tongues" 
of opaque paper that are visible at short range but disappear at long range. 
One has only to try this to see that it does not distort the result. A cutting 
line with these details is shown in figure 23. 

On the possibility that the cutting line had jeopardized correct analysis, 
many important curves were plotted again upside down and a new cutting 
line put in, encroaching this time a little on the maxima, and the minima 
were cut out and tested. This was not found to change the results and the 
cutting line procedure is considered satisfactory. It is evident that in this 
analytical process the centers of mass of the maxima become the important 
points of the plot whose periodic character is tested. In some cases the curve 
has been modified into a series of centers of mass and the resulting cyclogram 
becomes very brilliant and easy to read. In such cases, of course, caution is 
needed and results obtained in this way are taken as corroborations or sug- 
gestions (see cyclograms in Plate 15B). 

The instrument as it stands covers considerable space; namely 6 or 8 feet 
in width by about 45 feet in length. The mirror is suspended from a track 
attached to the ceiling. The cycle scale is marked on the track after calibra- 
tion by standard curves. Calibration readings are made in connection with 
every analysis. It is difficult to show much of this in any photograph but 
something of it appears in Plate 14 A and B. 

Moving Rack— Many attachments to the cyclograph have been tried, 
including moving picture devices, but the one that has proved its worth is 



CYCLOGRAM ANALYSIS 47 

a large movable rack in which several cycleplots may be placed one above 
the other. By aid of the rack, each plot in turn can be brought directly in 
front of the illuminated ground-glass and analyzed. The plots are arranged 
so that their dates coincide ; hence in a second's time one can change from the 
inspection of one record to that of another. This makes the comparison of 
cycle characters in different records very rapid and accurate. For instance, 
the individual curves of trees in a group can thus be placed one above the 
other and the group cycles derived by the rapid comparison of the different 
records. Comparisons are so quickly made that Mr. Schulman has often 
called the process "simultaneous analysis" because the time interval between 
the views of successive patterns is almost negligible. 1 The rack was first con- 
structed about 1921 in an attempt to carry dating by cycles through Arizona 
trees and into California sequoias. In a considerable number of tests we 
find that results are closely alike, whether by analysis of a group curve or 
the separate analysis of the individuals composing the group. A comparison 
between the results of using these two methods is shown in figure 35. 

OPERATION AND CHECKING 

In performing analyses with the cyclograph, the outward movement of 
the mirror causes rows of maxima to rotate in a clockwise direction. When 
any row reaches a horizontal position indicated by a stationary thread in 
the focal plane the reading is taken (see Plate 15B). It is standard practise 
to note this reading of cycle length while moving the mirror outward and 
to repeat the reading on moving it inward. The different approach some- 
times causes slight change in estimate of the true setting. Record is kept 
of both readings and the mean taken. 

According to the importance of the case, further checking is made. The 
cutting line is put on an inverted curve and cycles are accepted as valid that 
are common to the two tests. It is, of course, most desirable to have someone 
else try the analysis, but for years until very recently that was impossible. 
In 1926 the first wholesale analyses were made of the 42 western groups and 
certain general characters of apparent importance were noted and needed 
checking. Before publication of Volume II, Climatic Cycles and Tree Growth, 
in which the results had been tentatively placed, resort was made to checking 
by replotting at unknown scale and making the analyses myself. This was 
done and results obtained were incorporated as a foot note on page 124. This 
check at unknown scale is given in Reports of Conferences on Cycles, 
Carnegie Institution of Washington, 1929. 

Accuracy and Limitations — During the twenty years of use of the cyclo- 
graph, checking has been done as described, but the need of determining 
fundamental errors, limitations and capacities of the instrument, was fully 
realized. Formal tests along these lines only recently became possible. Mr. 
Edmund Schulman several years ago became skilled in the use of this instru- 

1 We are also using the word "concurrent" but expect to make the word "simulta- 
neous" literally applicable later on. 



48 CLIMATIC CYCLES AND TREE GROWTH 

ment and during 1934 and 1935 was engaged in formal tests of the degree of 
accuracy found in its use. His description of his work is found in the appen- 
dix to which reference is made for details. The enormous amount of analyz- 
ing that has been done upon a thousand or more cycleplots for many different 
purposes offered excellent opportunity for comparisons of results. This 
meant largely the repetition by him of analyses made originally by the writer, 
together with many additional tests to bring out the comparisons. He found 
that we might expect a difference of about one per cent in cycle length as the 
mirror moved out or in. The "unknown scale" test mentioned above 
showed differences in result of 1.9 to 2.5 per cent in cycle length; different 
observers obtained results differing 2.5 to 3.0 per cent. Inversion of curves 
might produce changed reading by 2.0 to 3.0 per cent. Discrepancies in read- 
ings occurred almost altogether in very weak cycles recognized at the time of 
observation as of small weight. Tests were made on synthetic plots prepared 
in a manner totally unknown to the observer. The analyses of these were 
satisfactory. I feel, therefore, that the cycle results obtained with the cyclo- 
graph by Mr. Schulman and myself may be accepted with confidence. 

GENERAL CYCLOGRAM INTERPRETATION 

The cyclogram as previously described is a rectangular plot with a general 
time scale usually placed horizontal and progressing from left to right, and 
a differential time scale in the vertical. The analyzing lines showing in 
the cyclogram are slightly inclined to the vertical, usually about 17°. It is 
better to set them a little out of focus so as not to catch the eye, for a cycle 
is indicated by an alignment of maximal images wholly or partly across the 
cyclogram and not in the direction of the analyzing lines. A horizontal 
thread mounted close to the analyzing plate shows in all cyclograms and 
serves as a reference line for direction of rows of maxima both in calibrating 
the instrument and for getting correct cycle settings. 

Our cyclograms in published prints have nearly always had the analyzing 
lines inclined up to the left. The relation of this to cycle length is easily seen 
by brief study of a cyclogram. A cylindrical pattern of the original data as 
projected upon fixed analyzing lines has a definite and single time interval 
across it from left to right whether taken in a horizontal direction or at any 
inclination. In the horizontal line this time interval is divided by the 
analyzing lines into a definite number of equal parts, equal to the number of 
lines that intersect the pattern along the line of the thread. One can count 
them if desired and divide their number into the time interval and find the 
cycle represented by the horizontal line. This should check with the cycle 
setting of the instrument. If the analyzing lines incline up to the left, then a 
cycle alignment inclining down to the left will take in more of them (than 
when horizontal) and be subdivided into smaller parts, and thus the cycle 
length in this row is less than it would be if horizontal. In the same way, an 
inclination of a cycle row up to the left will cover fewer of the analyzing lines, 
and so an increased cycle length is indicated. 



Carnegie Inst. Washington Pub. 289. Vol. Ill — Douglass 



PLATE 15 




A. Analyzing plate and mounting; the analyzing lines, 50 to the inch and inclined 
some 17 degrees from the vertical, cover the rectangular area in the center. 



Cycle length 
in years 



Cycle length 
in years 



— > 

8-5 








II 4 



10.3 







14.0 




<- 



22. 8 



B. Cyclograms of sunspot numbers, using centers of mass. Notice change of align- 
ment for different cycle lengths. Horizontal alignments at these settings show the basis 
for the periodogram of annual sunspot numbers (figure 55). To see cyclograms best 
hold paper nearly edgewise to the eye so as to look along pattern horizontally. 



Carnegie Inst. Washington Pub 289. Vol. Ill — Douglass 







A B 

A. Multiple standard with discontinuous periods at 7.0 (up to the right in right two-thirds) 
and 9.0 (up to the left in left two-thirds); horizontal direction (thread) set at 8.0. 

B. Arizona ring record, FAM, 1700 to 1920 at 21.0 years: shows 23-year cycle dominating 
early half (L)and 19-year cycle later half (R). Same data treated differently in figure 16, page 34. 



1400 



1900 
I 




W\ 



/ N /; V 






14 



C. Analysis of Flagstaff tree ring records (see Chapter II, Cyclogram Reading). 



CYCLOGRAM ANALYSIS 49 

Limits of Range — The track as first introduced in 1918 carried the analyz- 
ing box toward or away from the cycleplot placed in a window for sky illumi- 
nation. In 1920 the reconstructed instrument had for a time a stationary 
analyzing box and a single movable mirror. This gave a range from 6 out 
to about 25 units. Two more mirrors introduced into the light path extended 
the range to about 35 units. For some years now the range has been extended 
to 42 units by lengthening the track. 

One finds from experience that the mirrors must be very firm and not 
allowed to move in their mountings; the track must be exceedingly straight 
and without irregularities that might change the alignment of the mirrors; 
and that the scale along the track should be tested occasionally to make sure 
that some little vibration has not altered it, or to check for any slight error 
in adjustment of the automatic focusing device. 

Cycle lengths less than the minimum setting of the instrument are rather 
difficult to determine and are best reached by replotting at enlarged hori- 
zontal scale. An attempt was made to use finer analyzing plates with more 
lines to the inch. But that was found to change the scale readings of the 
instrument and the pattern looked unfamiliar; so we resorted to replotting. 
A scale of x4 is used more often than any other. It works well in testing the 
"2-year" cycle (Chapter V). Of course, plots at odd sizes of scale are sent 
to us for analysis and corrections are readily applied to the readings. Tests 
of cycle values at "unknown scale" need only a change of plus or minus 10 
to 50 per cent; a pantograph will do this quickly and accurately. 

Resolving Power — One might class under the resolving power both the 
lower limit of the cycles that can be seen with the instrument and the accuracy 
with which a setting is made on a cycle. The former is a question of range 
but it is not so much a mechanical limitation as a mathematical or statistical 
one. It takes 3 or 4 points in the data to locate a cycle. Our smallest read- 
ing is 5.0, which seems quite safe. But the Hanned curve is used in 90 per 
cent of our work and this process enlarges the independent terms and so 
there are less than 5 in our 5.0 cycle. A running mean of 3 gathers 3 together 
in one point, reducing the number of original data to one-third, and one 
could not rely on settings at 5.0. But the Hann has a statistical "conserva- 
tion" 1 of less than 3; it may be as little as 2, for it does not remove entirely 
the effect of strong individual departures. At any rate, in a Hanned sequence 
we readily see cycles at 4 and even sometimes cycles at 3. This is not by 
direct setting at these figures but by harmonics that are more easily reached. 

The accuracy of making a setting on a row or alignment of maxima de- 
pends on the length of the sequence of maxima, the precision in periodic 
occurrence of the maxima, on the number of repetitions of the cycle and on 
the percentage duration of the maxima in terms of the cycle length. This 
last is usually a quality in the data, but it also depends on the size of the 
opening in the analyzing lines expressed in per cent of the width between 
the centers of the lines. This then becomes in some cases a limiting factor 
in the accuracy of setting. In early forms of the cyclograph this ratio was 

1 See page 58. 



50 CLIMATIC CYCLES AND TREE GROWTH 

0.3; then it was reduced to 0.25, and now for some years it has been close 
to 5 per cent of the constant spacing of the lines. This opening may be said 
to smooth the data by a running mean of its equivalent percentage of the 
cycle length. The smallness of the opening reaches a practical limit when the 
cyclogram becomes too faint to be properly seen or conveniently photographed. 

Lag Analysis — This refers to two prisms so arranged close to the main 
cylindrical lens of the cyclograph that the beam of light from that lens to 
the analyzing plate divides into three parts, two of them making displace- 
ments of the cylindrical pattern on each side of the normal by an amount 
equal to the space between the analyzing lines. In this way analysis is made 
of the data in normal position and with lags of one and two cycle lengths all 
at the same time. This is the equivalent of averaging overlapping cycles, 
which has been found very efficient. 

A small pantograph is being arranged by which to sketch at once any 
pattern on an enlarged scale. A photographic attachment has long been 
used for similar purpose but it is less rapid, though more accurate. A number 
of moving pictures have been taken of the changing cyclogram as the mirror 
moved outward, each one built of about 650 separate exposures. The attach- 
ment for the purpose was built by Dr. V. A. Brown and the pictures were 
taken in 1929 in our laboratory. The pictures show well on the screen but 
improved projection devices and other features are needed to make these 
pictures a practical aid in analysis. 1 

CYCLOGRAM READING 

Attention is called to Plate 16C which gives an analysis of 500 years of 
tree-ring record near Flagstaff. A cyclogram from these data was illustrated 
in Volume I, Plate 12f, and this cyclogram is taken from Volume II, ibid., 
plate 9, figure 7 and figure 19, number 7. Our plate includes the explanatory- 
diagram, showing the cycle lengths indicated in the various alignments. The 
setting is made at cycle length of 14 years. One has a choice here between 
a slightly varying line that passes horizontally through all the data at an 
average value of close to 14 and a straighter line at 14.2, with a 180° phase 
reversal at 1820. There are often some signs of double crests in the 14-year 
cycle and such a phase reversal is not an impossibility. 

From the beginning at about 1400 to about 1635, an 11.3-year cycle (or 
close to that) is evident if one looks at a low angle across this cyclogram. 
During the early part, and even to 1520 or so, this 11.3-year cycle shows two 
crests and thus becomes a Hellmann cycle. The 57-year beats of inter- 
ference between 11 years and 14 years are conspicuous. From 1650 more 
or less to perhaps 1800 one can see the sharply inclined lines of a 10-year 
cycle, or coarser lines slanting the other way that read near a 21-year cycle. 
This cyclogram was made from an early plot that did not carry quite the 
technique used today but it approximated closely enough to give a good 
illustration. (Another cyclogram reading is given on pages 122, 123.) 

1 Construction of a modified form of cyclograph with a much shortened track, is 
now in progress. 



III. DISCONTINUOUS PERIOD IN CYCLOGRAM 

ANALYSIS 

THE CLIMATIC DILEMMA 

Cycles in natural sequences and especially in climate have a very con- 
fusing tendency to stop. Heretofore, if a cycle stopped, its consideration was 
dropped, for on averaging further data its mean amplitude naturally grew 
less and less and became negligible as more and more terms were included. 
This was taken as a sign of its non-importance. 

A few students have examined these cycles that stop ; others say that they 
do not really stop — they merely interfere with one another and appear to 
stop. At this moment, that point does not need to be settled. Many 
interested persons have taken an easy course and become conservative and 
say that probabilities derived from harmonic analysis settle the matter, and 
all these temporary cycles are imaginary. The word imaginary in this case 
is used in its technical sense and amounts merely to a denial of permanent 
reality. This in turn in the minds of many people has led to the thoughtless 
denial of any reality. 

We can understand why the year and the day and other astronomical 
cycles, including a family depending on the moon, must last indefinitely, but 
there are vast numbers of oscillations in nature that do not last: a bell's 
vibration is dampened ; waves on water fade out ; a cyclone movement is short- 
lived, and so is a sunspot. Rotations in fluids may show different rates ; the 
rotation of a tornado varies in velocity and stops eventually. 

These cycles in climate are very real, indeed, while they last, but localities 
differ in their display. Our Atlantic seaboard, for example, seems less affected 
by slow climatic oscillations than Arizona. People living in semi-arid regions 
are more likely to become conscious of them. So it came about that after 
living years in the Southwestern climate the writer felt the intensity of its ebb 
and flow in units longer than the year, and after finding age-long records in 
trees, worked up the cyclogram method of analysis in order to learn something 
about these cycles in trees and climate, that have not been properly examined 
heretofore because they do not last. This has opened a realm of cyclical 
facts in climatic phenomena of which some of the most interesting are simi- 
larities over large terrestrial areas and even between terrestrial changes and 
changes in solar activity. And it is in these cycles that the resemblances 
between sun and earth are found. 

PROBABILITIES AND CYCLES 

Cycle study by harmonic analysis in the last 30 years has provided a suc- 
cessful display of new and long-lasting astronomical periods, chiefly those 

51 



52 CLIMATIC CYCLES AND TREE GROWTH 

depending on the moon's motions. For example, the lunar "tide" in at- 
mospheric pressure 1 and the allied lunar diurnal variations in the terrestrial 
magnetic forces 2 are among the very satisfying results. But in the analysis 
of climatic changes and even in solar variations, harmonic study has produced 
a large number of unconnected facts, each one of which has been regarded with 
distrust because it did not match the astronomic cycles in persistence of 
activity. To these unconnected facts the laws of probability have been 
applied in the hope of getting something tangible, but little or no encourage- 
ment has been found. 

The idea of discontinuous periods, that is, of cycles localized within a 
special part of a time sequence, seems to the writer to open a new field in 
cycle study which has hardly yet received serious consideration. Previous 
to the opening of this new field the discovery and careful study of climatic 
cycles was usually a matter of accident. A common way to search for them 
was to plot a curve of data and test it by eye without mechanical device of 
any sort. Faint permanent periods not evident in that way were appropri- 
ately called "hidden periodicities." If Schuster had merely applied analysis 
to the sunspot record as a whole he would perhaps not have seen any localizing, 
in time, of special cycle lengths. However, he did find some evidence of 
localized cycles by dividing his data from 1750 to 1906 or so into two parts. 
He thus obtained more detailed values which he displayed in the now famous 
periodogram. 

In 1914, H. H. Turner in extending a similar study worked out the "points 
of discontinuity" in the sunspot sequence since 1750. One feels that he was 
rather specially impressed with discontinuity in amplitude as would be nat- 
ural in harmonic analysis. At almost the same time (late 1914) the writer 
obtained his first automatic cyclogram (Ap-J, April 1915, pages 173-4) and 
found the discontinuities in period laid bare for all who understood the cyclo- 
gram method. The multiple plot had in 1913 already shown points of 
discontinuity. 

Clayton encountered a temporary period as long ago as 1884-5 in his 
studies of short cycles in climate (A Lately Discovered Cycle, Amer. Met. 
Jour., vol. I, pp. 130 and 528) . Later he formulated the idea of phase reversal 
and found it frequent in climatic cycles. 3 Arctowski has investigated short 
cycles of 1 to 4 years in weather elements. Alter, recognizing the idea of dis- 
continuity, has made extensive and fine use of subdivisions of his data in order 
to show that each part independently gives the same results. Subdivision 
aids in localizing cycles and yet it can not be carried far because the fragments 
of data become too short. Cyclogram analysis carries subdivision to the 

1 S. Chapman, see Bibliography, 1935. 

2 S. Chapman, see Bibliography, 1925. J. A. Fleming, see Bibliography, 1932. 

3 His continental movements of climatic waves are likely to prove of the first im- 
portance as are his results on terrestrial temperature reactions to changes in solar radi- 
ation. Abbot and Clayton have contributed to similar studies in North America and 
especially the former has supplied the fundamental data on radiation. Arctowski has 
shown the movement of climatic waves. 



DISCONTINUOUS PERIOD IN CYCLOGRAM ANALYSIS 53 

individual maxima but it gives results only when enough of these maxima 
unite into a definite pattern. 

The sunspot cycle was recently described to me as a succession of changes 
in phase. Upon first hearing this, it seemed a complete disagreement with 
our results with cyclogram methods. But on consideration it grew to be a 
good partial statement from the viewpoint of the harmonic approach. Since 
harmonic analysis assumes fixed testing periods, any departure in period 
length comes into view as a change in phase and is so expressed. Hence, it is 
possible that this statement of phase changes in solar data is an attempt to 
express the same thing that I call a sequence of discontinuous periods. The 
critical observational fact in the harmonic method of expressing solar changes 
is whether the phase changes occur just one at a time or shows a succession 
of similar changes. The former is a genuine change in phase; the latter, of 
course, is a genuine change in period, and that, it seems to me, is more closely 
describing what is taking place in the sequence of annual sunspot numbers. 
In the cyclogram this difference is highly prominent. 

The great advantage of harmonic analysis is that its results may be evalu- 
ated by the laws of probability whose principles distinguish between "real" 
and "unreal" results. These adjectives practically refer to permanence; a 
cycle is real that lasts through the data and eventually rises above random 
effects; even a very weak cycle observed in a long series of data may be 
strengthened by repetition and may give an average easily recognized as 
real, while random effects are smoothed out by averaging the repetitions. 

Students of harmonic analysis had long since observed that cycles in 
natural phenomena often exhibit a relation between several successive values, 
statistically called conservation. This has an effect on the cyclical characters 
in the data and affects the reliability of the results. The cause of the con- 
servation is not involved in its purely statistical study. 

BARTELS' DIALS 

Two German students of cycles have approached somewhat nearer to 
the idea of discontinuity, Bartels and Stumpff, the former by development 
of harmonic analysis methods and the latter with theory and a mechanical 
process. 

Bartels' work appears in Random Fluctuations, Persistence and Quasi- 
Persistence in Geophysical and Cosmical Periodicities (Terrestrial Magnetism 
and Atmospheric Electricity, vol. 40, No. 1, pp. 3-60, March 1935), and in 
other papers. In carrying out a skilful study of probabilities as applied to 
periodicities in magnetic phenomena, he has presented mathematical processes 
that take conservation into account and has recognized and named certain 
characters that identify with the phenomena long observed with the cyclo- 
gram. These characters are found in his "harmonic dial" and his "summa- 
tion dial," particularly the latter with its significance and the tests applied to 
it. Thus I hope cyclogram usage and results will become clear to astronomical 
and statistical students. 



54 



CLIMATIC CYCLES AND TREE GROWTH 



He investigates the 27-day period in 28 years of daily records of the inter- 
national magnetic character figure C, which is simply the magnetic disturb- 
ance on the earth estimated by the various observers on a scale of to 2. 
This disturbance is attributed with confidence to a solar origin. The 27- 
day period is an approximate synodic rotation of the sun in the average spot 
latitude that is found to occur in the late parts of the 11-year sunspot cycle. 

The character figures for each 27-day interval are in effect reduced to the 
nearest sine curve of 27-day length, and the amplitude and phase derived. 
In the harmonic dial 1 these amplitudes and phases are expressed on polar 




oec- 



Fig. 25 — Bartels' Harmonic Dial of International Magnetic Character Figure C. 
(From Terrestrial Magnetism and Atmospheric Electricity, March 1935.) 



coordinates, the phase being assigned a certain direction from the pole, and 
the amplitude being represented by the distance from the same. This is 
repeated for the 378 rotations and a cloud of dots obtained, as in figure 25. 
If these dots center on the pole, there is no "real" period. If, however, there 
is a period present, the center of the cloud of dots will be some distance away 
and will show the final total amplitude and phase by its direction and distance 
from the pole. To show reality of a cycle under test, the data are subse- 
quently massed by two's, three's, etc., in larger and larger averages (not 

1 In the nomenclature proposed in a preceding chapter this would be called a sum- 
mation or integration dial as it is without a time scale, and figure 26 would be an ex- 
tended dial. 



DISCONTINUOUS PERIOD IN CYCLOGRAM ANALYSIS 



55 



W5 




N \ \ \ \ 
16 17 /8 /$ 20 
SCALE FOR T/ME OF MAX/ MUM (DAYS) 

ZSf 


/ 

2/ 


/ 
22 

^\ 36 


/ 

23 




/ 
24 


25' 






l^\&k-+ 
















W* 


5 t 


10 *\ 
RADIAL SCALE OF AMPL/ruDES W TERMS OF C 
-4.0 3.0 2D /.O 




45. 








26^ 
27- 









— J3 








128 


117% 

/23 n 


V/3 


/OS 


/-. 


s>* 




240 

\\*? 44 224 

24 ]f\ fzrfiCTf 


/3o\ 
J 92 196 


1 ^ 


iisTf 


12 

60 


f/OS 


2 x 


/» 




^f 230** >« 
^\25S > 


/9o^y 

206 ZX 


184 
ml 


\/34 
k /4S J 


75 




^ioop 
as 


3 
\ 


/» 


\Z60 

tJk 285 - 

/Jes \rf 

L J *280 
270 *&£-+&] 




feh&~* /73 

/*7SS 








4 
\ 






29 ^L^* f?5 




















300*~*\ 




















\30S , 


Jan 


.11, 


1906 














\ 3/ & 31 t 366 

aoy&k* 3 

\320 


-Jan. 4, 


1933 










9 

/ 




3S7 32S *&{ 














5 

X 


36 




I ,-4*344. %330 

7^ 34< *^\^33S 
/l 375 
















373_ 




P a 7 

i36S / 1 








6 
\ 









Fig. 26 — Bartels' Summation Dial. (From Terrestrial Magnetism and 
Atmospheric Electricity, March 1935.) 



56 CLIMATIC CYCLES AND TREE GROWTH 

overlapping), thus reducing the number of dots and bringing them nearer 
their center. If by this means the location of the cloud is found to remain 
distant from the pole, the reality of the period becomes more and more 
evident. 

The summation dial, figure 26, is of special interest to us, for it represents 
the same phases and amplitudes stretched out into a time sequence, though 
an irregular one. It is, therefore, an extended curve, for it gives facts at 
successive equal intervals of time through the full data. Figure 26 doubtless 
was his basis for introducing the middle term in his series of three classes of 
effects: random, quasi-persistent, and persistent. The diagram at first 
glance could be divided into "tangles," or random motions, and "arcs," which 
have a directional effect; in these last the quasi-persistences are more easily 
found. 

Since the harmonic method uses a constant period of 27 days, any actual 
change in it becomes expressed as a change in phase ; and since phase is repre- 
sented as a position angle (direction from pole or a line parallel to such direc- 
tion), a slight semi-persistent departure in period from the assumed value 
is expressed by a series of amplitudes pointing progressively in a changing 
direction; this produces an arc. 

To look at this diagram and think of its possible solar meaning is perhaps 
perfectly natural. As the period here used is the time of rotation of the sun, 
the tangles which occur at sunspot maxima and minima mean that at such 
times magnetic forces are reaching us from widely distributed solar longitudes. 
This is to be expected at maxima. Dr. Bartels has observed its occurrence 
also at the beginning of each new sunspot cycle, which explains its presence 
at minima. The "arcs" indicate a tendency for magnetic forces to emanate 
for considerable intervals from some localized longitudes of the sun. 

Quasi-Persistence in the Summation Dial — The important feature in 
Bartels' summation dial, figure 26, is the representation on an extended time 
scale of certain changes in cyclical character and their evidence of temporary 
stability, if we can so term it, which he calls quasi-persistence and which I 
shall indicate in these paragraphs by the initials QP. Amplitude QP's in the 
summation dial are indicated by the number of equal lengths in succession in 
the short, straight lines, without regard to direction, such as shown in figure 
27a. A quasi-persistence in period is indicated by successive, equal angles 
between these short, straight lines. This develops as a curve and may not 
have any QP in amplitude, as in figure 27b. A complete reversal of phase by 
180° has often been suspected in climatic cycles. Such a change in a summa- 
tion dial would make a pattern somewhat like that in figure 27c. It is pos- 
sible that a change in phase occurs by some other fraction than \. 

Quasi-Persistence in the Cyclogram — The cyclogram is an automatic plot 
in three dimensions capable of instant adjustment over a wide range of cycle 
lengths. In this analysis the portion of the curve below a "cutting line" 
along the lower minima is commonly omitted during analysis, which is analo- 
gous to the usage of harmonic analysis in taking values from a mean and not 



DISCONTINUOUS PERIOD IN CYCLOGRAM ANALYSIS 



57 



from a base. In the cyclogram process we still keep the base available for 
the measurement of real amplitudes by a photometric method. 

A discontinuous period, or QP, is recognized by the maximal images form- 
ing in an obviously straight line, which means constant cycle length. The 
features that attract attention in looking for QP's are : number of repetitions 
of the cycle, straightness of the line of maxima, which is the same as phase 
stability, and strong amplitude due to freedom from interfering maxima. 




A • * 

• * * * m^ • 

• • • • • 

• • • • 

a' 



d 



» n ■ ■ ■ ■ 



A» 


• 


• 


• 


















• 


• 


• 


• L 


H» 


• 


• 


• 


















• 


• 


• 


•F 


(•• 


• 


• 


• 


















• 


• 


• 


•It 


D» 


• 


• 


• 


















• 


• 


• 


•H 



C^o 









• • • 


r • • • • • 

^" • • • • . 

• • • • ■ ■ • 
tr-*- '• • •* 

trr • • • • 
• • • • 



f 



Fig. 27 — Comparisons between Bartels' dials a, b, c and cyclogram analysis d, e, f ; 
a, quasi-persistence in amplitude, b, quasi-persistence in phase, and c, phase reversal; 
d, change of period (same as continued phase change), e, phase reversal, and f, periodic 
phase reversal. In the dial, time progresses along the bent lines; in the cyclogram, it 
moves horizontally left to right. 

The cyclogram is built fundamentally on cycle length and so differentiates 
at once between quasi-persistence in period and in phase. This is illustrated 
in figure 27d, which shows a change in period at A A' by a change in direc- 
tion of the horizontal alignment of dots. A complete 180° reversal in phase 
is shown in figure 27e. The horizontal rows a, b, c, and d are repetitions of 
the same sequence of maxima. A 180° phase reversal puts the new maximal 
lines, e, f, g, and h in the same direction as before but at vertical position 
half-way between the a, b, c, and d lines. 



58 CLIMATIC CYCLES AND TREE GROWTH 

A difficult case, sometimes occurring in natural data, is well brought out by 
this method. When the 180°-phase reversals occur at regular intervals, as in 
figure 27f, the pattern obviously contains an interference between two 
periods, of which one takes the definite direction AB and the other may be 
either CD or EF with "infection," as Bartels has called it, from AB. A 
pattern of this type was encountered in a Southern California rainfall cycle 
near 2 years in length, that could only express itself in winter and thus clings 
a bit to the annual value. In the cyclogram obtained, the interfering cycle 
could be read at once as 1.8 years or 2.2 years and the 1-2-year cycle could be 
stated as a 2-year cycle with regular phase reversals or a 1-year cycle with 
alternating intervals of appearance and suppression. 

Evaluation of Quasi-Persistence — Bartels has done more than recognize 
QP's; he has arranged a criterion 1 which may be applied to express their 
weight. This is derived through a principle of probability. In setting up a 
correct average under normal distribution, the probable error of the average 
is inversely proportional to the square root of the number of terms; the 
standard deviation is the square root of the mean square of the residuals. 
This may be applied to separate random values which are to be averaged into 
a mean but it may be applied equally to separate random sets of values such 
as a cycle length, commonly used in the summation process in deriving the 
form of a cycle that exists in a series of data. A "set" is a row of data cover- 
ing one period of the period length considered. Bartels compares the stand- 
ard deviation of the mean of the sets with a theoretical value derived from the 

average standard deviation of a single set, and uses the —^ relation stated 

vN 

above for estimating the random part of the final values. Thus, if we have 
N random sets of values in which the first set shows a standard deviation of 
mi and the second of m 2 , etc., the average standard deviation m of the sets is 
the square root of the fraction 2m 2 n /N. The mean of the N random sets of 
values theoretically would have an average standard deviation of m/VN. If, 
therefore, we divide the actual standard deviation of the mean by this theoret- 
ical value for random data, we get unity as a ratio in case the data are 
really random values and a sufficiently large number are used; if, however, 
the values are not random but tend to show the same cycle in each set, the 
standard deviation of the mean is larger than this quantity for random values 
and on being divided by it gives a ratio over unity, which for the moment we 
are calling the Bartels A.D. ratio or the A.D. ratio. Such a ratio, therefore, 
becomes a measure of the reality of a cycle when compared with unity on one 
side and with VN on the other. This latter is the maximum value it can 
reach in the case of a cycle with no random values. 

The Conservation Factor 2 — Conservation in natural sequences was recog- 
nized by the writer very early in the study of tree-ring records because it is 

1 C. F. Marvin published in 1921 his "periodocrite" test to which Bartels' criterion 
bears a relation. 

2 In statistical studies conservation refers to correlations between successive values 
without regard to the physical cause. 



DISCONTINUOUS PERIOD IN CYCLOGRAM ANALYSIS 59 

prominent in them. It was not at first called by that name but simply- 
described as a lack of those short cycles which are so characteristic of scram- 
bled or random data. It was used in 1922 and especially in 1932 to dis- 
tinguish between random and natural sequences. It had even started the idea 
of a natural cyclic unit in climatic change which might include several ter- 
restrial units such as the year. Each climatic cycle (even though tempo- 
rary) could possibly be called a natural unit of which several could exist at 
the same time. In 1932 Dr. Alter had applied his lag correlations to certain 
tree-ring data and reported strong conservation of 1 to 3 years. When I 
proposed a natural unit of this sort to Dr. Bartels he referred to his <r, de- 
scribed below, as his idea of a natural unit. 1 This a would become a test of 
the presence of conservation and a measure of its effect on the data. 

From the viewpoint of probabilities (and following Dr. Bartels' discus- 
sion) this conservation is the tying together of several successive values so 
that they are not independent. It affects the reliability of periods suspected 
in the data, which should be evaluated on the basis of the number of inde- 
pendent terms. So we desire to find how many of our original terms must be 
united into one term in order to make the values independent of each other. 

Bartels calls the conservation factor a and describes it (and therefore the 
natural unit) as the equivalent length of the quasi-persistence. The Bartels 
ratio, which we will call B, may be stated thus : 

M _B 



m 



in which M is the standard deviation of the mean; m is the average standard 
deviation of the sets as before; N is the number of sets and B is usually more 
than unity. In random data B is unity. Therefore to make our formula 
produce unity on the right-hand side of the equation — as in random data — 
we must divide each side of the equation by B and we get (placing B under 
the radical) : 

M 



m 



= 1 



• 



N 
B 2 



This B 2 is Bartels' a or the number of sets or unit values, whole or frac- 
tional, that must be grouped together in order to get independent terms, for 
it divides the number of sets N by a quantity over unity and reduces the 
number of independent sets. Of course, we understand that all this becomes 
more strictly true as the number of data or sets increases very greatly. 

For example, in an apparent 11-year cycle in Eberswalde trees (giving a 
correlation coefficient of 0.51 ± 0.07 with the smoothed annual means of 
the sunspot numbers) we find 7 sets with an average standard deviation of 

1 See more recent paper in Bibliography, Bartels, 1935. 2 



60 CLIMATIC CYCLES AND TREE GROWTH 

0.206 per set and a standard deviation of the mean of 0.124. So the Bartels 
ratio for this sequence is 1.6, which places it in the realm of reality; the maxi- 
mum possible value is s/l or 2.65. His a becomes (1.6) 2 or 2.6. 

It has been suggested that we use the fraction of 1.6/2.7 or 0.59 as the 
reliability index. But that seems undesirable because we are only using 
two of the necessary three terms; the unity term has disappeared, and we 
can not let it disappear because it varies with every different number of sets. 
In the present case the unity in the same proportion would be 0.37. We 
might take the logarithms of the three terms; they are 0, 0.20, and 0.43. 
This gives us 0.47 as the index. For the present we should perhaps tell the 
story by saying that in 7 repetitions of the cycle the QP factor is 2.6, which 
is 0.37 of the continuous length 7. 

At this time the subject should not be carried further, but we note that 
if and when the variations that we here class as random become assignable 
terms in other cycles, the variations lose a portion of their random character 
and the QP factor will more nearly reach N, the number of sets used. 1 

This process of Bartels' seems a very promising method of evaluating a 
cycle. In his application of this process to the magnetic character figure C, 
he uses the full series of data in his 378 sets of the cycle length, which implies 
that the QP is not localized at the few places where it has been recognized 
but lasts throughout the data as a general solar character. While we, on 
the other hand, are trying to localize such characters and learn more about 
them, we appreciate the high value of his result as it stands; it is analogous 
to a first statement of mean annual rainfall of a new locality as compared to 
the more detailed monthly values to come later. 

Bartels 1 Multiple Plot of the Magnetic Character Figure C — The writer 
feels that Dr. Bartels had previously reached important results in a graphic 
analysis of discontinuous periods in the magnetic character figure C contained 
in his paper of 1932, Terrestrial-Magnetic Activity and its Relation to Solar 
Phenomena (Terrestrial Magnetism and Atmospheric Electricity, vol. 37, 
No. 1, pp. 1-52, March 1932). To use a term already employed by us, 
his long chart of symbols showing the daily values is a multiple plot. 2 Like 
our figure 14b, page 31, it corresponds in function to a summation table and 
represents quantities by symbols that catch the eye. It thus has the quali- 
ties of the plot mentioned and by the eye alone periods and discontinuities 
may be read off from it as from a cyclogram. Without really naming it as 
a form of analysis, Dr. Bartels has correctly used it as such. He derived 
very important inferences from the diagram. He confirmed the persistence 
in solar longitudes of magnetic source areas which he called M-areas, finding 
them largely independent of sunspot activity. He quotes outstanding exam- 
ples of long 27-day recurrences of disturbed days: 1910-11, 13 rotations; 
1921-22, 14 rotations; 1929-31, 17 rotations. He makes some references to 
activity at opposite longitudes on the sun (as if there were a 13.5-day period) 

1 The co-existence of other cycles may seriously affect the A.D. ratio. 

2 Chree and Stagg used a multiple plot in 1927; see Bibliography. 



DISCONTINUOUS PERIOD IN CYCLOGRAM ANALYSIS 61 

and to indications of longer rotation periods (synodic) than 27 days. These 
features of solar records are examined below by the cyclogram process. 

Significance of Conservation — A better understanding will be reached of 
the analytical work of Bartels and others if we give some attention to the 
physical meaning of conservation in certain solar problems. We can readily 
see that daily values of sunspot data have a large conservation factor both 
statistically and physically; for nearly all spots or groups would be visible 
continuously for 10 or 12 days. Daily results then would amount to a run- 
ning mean of 10 or 12. The monthly number, therefore, is a good figure for 
general use. However, daily observations on spots within definite longitude 
zones some 10° in width would be very desirable in order to secure closer 
correlation in time with magnetic data. This need could be worked out in 
the frequent photographs of the sun taken at many observatories. 

The magnetic character figure is believed to be more nearly related to 
the solar activity near the sun's meridian, and therefore it perhaps involves 
an equivalent running mean of only 1 to 4 days. Hence, in our accompanying 
analyses of this solar record we can use 3-day means and get probably all 
the "resolving power" which the data can yield. 

Bartels' estimates of quasi-persistence in the paper of 1935 were made 
upon a similarity from rotation to rotation of the sun and temporary persist- 
ence of the source areas of magnetic force in solar longitudes. His value of 
v is 3.0 rotations, which means that the quasi-persistent localizing of mag- 
netic source areas averages 3.0 rotations or between 80 and 90 days. 

But it is easy to see that at tinfes such as sunspot maxima we may be 
averaging together outbursts of magnetic activity from many disconnected 
localities in solar longitude, each of which complicates the problem of real 
persistence in longitude. Spot groups, and probably magnetic source areas 
also, cover at maximum a considerable range in solar latitude, and so may 
exhibit a range in rotation periods because of the important fact that different 
solar latitudes have different times of rotation. Hence, we have recourse 
to the cyclogram process which helps to unscramble the various cycles near 
any desired setting of the instrument. On the first attempt, covering data 
near the 1923 sunspot minimum, we found so much more evidence of stability 
in longitude than expected that we seemed to be dealing almost with a new 
group of phenomena. Cyclograms of the magnetic character figure C are 
given herewith in Plate 19B. As the necessary discussion is somewhat ex- 
tended, further description will be found in the next chapter. We find in 
the above discussion an illustration of how a search into the significance of 
statistical conservation led to a better understanding of solar problems. 

STUMPFF'S PERIODOGRAPH 

Dr. Karl Stump ff's researches are presented in Analyse periodischer 
Vorgdnge (Berlin, Gebruder Borntraeger, 1927 ; the method was first described 
in Astronomische Nachrichten, BD. 223, Nr. 12, 1924). In this book there 
will be found theory and description of the periodogram and various mechani- 



62 



CLIMATIC CYCLES AND TREE GROWTH 



cal methods of producing it. His own method interests us not merely be- 
cause it produces an analyzing pattern or periodogram that measures con- 
tinuous periods with precision but also because his "fine structure" displays 
some basic elements of the cyclogram. 

Our automatic cyclogram discussed in the previous chapter is a pattern 
using space distribution of the cycles in a common rectangular plot, derived 
all at once from the extended data; Stumpff arrives at a pattern of somewhat 
similar qualities by a timing device, that is, his pattern is not produced all 
at once but is constructed photographically point by point. Stumpff 's 
inspiration (like the author's) was Schuster's periodogram and a desire to 
produce it automatically. We each developed a pattern of cyclogram type 
and used it in producing the periodogram. The writer began using cyclo- 




Fig. 28— Plan of Stumpff' s periodograph. After Stumpff, slightly modified. 

gram results from the start (1913-14) and essentially abandoned the periodo- 
gram after producing actual photographs in 1918. 

The fundamentals of Stumpff 's apparatus are shown in a slightly modified 
copy of his drawing in figure 28. As I have sketched it here, R is an opening 
through which passes a bundle of parallel rays that are converged on the 
cylindrical lens C by a condensing lens L. K is the curve cut out of opaque 
paper, and G is a grating made up of equidistant openings; each one in width 
is 50 per cent of the constant distance between their centers. W is a cylinder 
with a longitudinal slit ; within the cylinder a drum carrying a photographic 
film slowly rotates. Removing K for the moment and holding G stationary, 
each opening in G will cast an illuminated image upon W, the image being 
elongated perpendicular to the slit. If we should set G in motion in the 
direction of the arrow, these images (for which the name "sweep" was long 
ago suggested) will move to the left along the slit. Now holding G station- 
ary and replacing K and starting the rotation in W, the several openings in 
G will trace longitudinal lines on the rotating film, lines that are perpendicular 



DISCONTINUOUS PERIOD IN CYCLOGRAM ANALYSIS 63 

to the slit ; but these lines will differ one from another in density on account 
of the variations in the curve K that obstruct one or another opening in G. 
Now if we start the curve K in motion, the longitudinal lines on the film W 
will remain straight but will change in density according to the variations in 
the curve K as each part of it passes across each opening in G ; and eventually 
each longitudinal line will make a reproduction of the complete original data 
with ordinates represented by photographic density. The result is a "multi- 
ple plot" with complete reproductions of the data in equidistant parallel 
lines. It is easily seen that if the film W moves very slowly in relation to 
the speed of the curve K, the horizontal offset between these reproductions 
will be very small; but as the film goes faster the horizontal offset between 
the reproductions on the film W will be greater. Thus, the offset in the 
resulting multiple plot depends on the relative rates of motion of K and W. 

In our original attempts at analysis there was no fundamental difference 
between multiple plot and our present cyclogram, merely differences of con- 
venience in production and use. Discontinuous periods were seen in either 
one. There was a little difference in the formula for getting the cycle length. 
The multiple plot could be described as a cyclogram in which the two plot- 
ting axes are not perpendicular to each other. To get them perpendicular 
we choose an axis of x, in time, not perpendicular to the multiple lines of 
the data (the analyzing lines) but perpendicular to the "sweep" lines. It is 
noticeable that in the cyclogram as commonly reproduced the analyzing 
lines slant to right or left of the perpendicular (referring to publications 
subsequent to 1920). Changing the slant from right to left, or the reverse, 
inverts the resulting plot (fig. 20) . The same effects are readily produced in 
Stumpff's apparatus by giving his grating a slow constant motion ; the direc- 
tion of this motion corresponds to the direction of slant of our analyzing 
lines and the rate of motion corresponds to the angular amount of slant. 

An important difference between the two analyzing methods is that 
while each can produce a photograph, ours also gives instantaneous visible 
results and is very readily and rapidly applied to a large range of cycle length. 
If we understand Dr. Stumpff's instrument correctly it is not so well adapted 
as ours to the study of discontinuous periods. 

In describing Dr. Stumpff's instrument in the last few paragraphs, I have 
exemplified the production of a form of multiple plot and a cyclogram by his 
process. Dr. Stumpff's operation of the instrument produces a periodogram. 
This is done by imparting an accelerated motion to the grating G. When 
this motion comes into a definite speed ratio to the motion of different cycle 
maxima in the curve K, a critical resonance point is passed which goes on 
record on the film in the form of a parabola vertex which can be nicely located, 
thus giving data for an accurate determination of the cycle length. 

APPLICATIONS OF THE DISCONTINUOUS PERIOD 

There seem to be several fields in which the discontinuous period should 
find special usefulness. The first is the determination of the terrestrial areas 
(meteorological districts) in which similarity in climatic cycles may be found. 



64 CLIMATIC CYCLES AND TREE GROWTH 

This application of our analytical method makes use of tree-ring and meteoro- 
logical records. The second application will be in examination of the rela- 
tion between climatic or other terrestrial changes and changes in the sun. A 
third, equally important application, is the recurrence of discontinuous 
periods during long time intervals of the earth's history. This makes use of 
very long records in tree rings and varves. 

The fourth and perhaps most general application of the discontinuous 
period is its quantity production from wide but homogeneous sources and its 
grouping into frequency periodograms. Such periodograms can equally 
well be secured from dated or undated material provided the counting is 
accurate and therefore they can bring together evidence from modern trees, 
fossil trees, varves, and other sediments. It offers an exceedingly wide 
opportunity for stating certain general facts about climatic variations. 

The fifth and last application of the discontinuous period in this brief list 
is in climatic prediction problems. Whether climatic cycles are permanent 
or not, whether they come from the sun or not, they become applicable to 
climatic forecasting in their function as natural units of greater length than 
the year. On the basis of the difference between the year and these longer 
natural units we can improve our probabilities of successful prediction and 
lessen our errors without settling beforehand the complete physical source 
of these variations. The fact that now and then one of a group changes or 
even disappears does not overcome the value of using the cycle complex that 
is actually in operation. As we find more and more their physical source 
and the rules of their behavior, the value of prediction will increase toward 
the desired accuracy. If these longer natural units admittedly emanate 
from the sun, then observations of the sun containing valuable advance in- 
formation will become of great importance. 



IV. ANALYSIS OF SOLAR RECORDS 

A vast amount of solar heat passes out from the sun into space and we 
ourselves exist by favor of that minutest fraction caught, in passing, by the 
earth and employed in producing winds and rain and a thousand complex 
processes, including vegetal growth and even human life itself. 

Nothing could be more natural in a discussion of climate and tree-ring 
growth than a study of the variable activity of this great source of terrestrial 
energy. Many of the basic facts about the sun were laid down in past 
centuries; its distance, size, mass, temperature, radiation, and its spots and 
their periodicity and latitude change. Since 1900 the attention of investi- 
gators has gone largely to atomic and spectroscopic studies, the constitution 
of matter, source of the sun's energy, internal motions of sunspots, and com- 
position of different parts of the sun. More closely associated with our pres- 
ent subject are the improved measures upon the rotation of the sun with its 
equatorial acceleration (Adams), the persistence of spots in longitude (Nichol- 
son and others), and, perhaps more fundamental, the magnetic polarity of 
spots and their change at minima, and the polarity of the sun itself (by Hale, 
carried on by Nicholson). 

The sun rotates on its axis in 25 to perhaps 32 days, as seen from the 
stars (siderial rotation), or 27 to 35 days as seen from the earth (synodic 
rotation). The equator takes the faster rate; and high latitudes, north and 
south, the slower. The causes of this "equatorial acceleration" are not yet 
fully understood although this phenomenon has been connected by some with 
the planetesimal hypothesis. In order of time, a cycle of spots, from mini- 
mum to maximum and back, taking about 11 years, begins at 25° north and 
south latitude and works to within about 5° of the equator. Rarely one goes 
beyond the equator. The maximum number of spots occurs at some inter- 
mediate latitude. The best visualizing of that change is obtained from a 
photograph arranged by Dr. W. S. Adams and Dr. S. B. Nicholson of the 
Mount Wilson Solar Observatory of the Carnegie Institution of Washington, 
reproduced here by permission, Plate 17. The spots are relatively inconspicu- 
ous in small scale photographs of the sun and they have substituted photo- 
graphs of the calcium clouds or flocculi that surround the spots and are very 
conspicuous. After allowing for change in slant of the solar equator, one 
can recognize in them the beginning of the spot cycle at high latitudes, the 
increase in numbers at somewhat lower latitudes, then the disappearance on 
close approach to the equator. When this is plotted, it forms what Maunder 
called the "butterfly" diagram, as in figure 29. Dr. George E. Hale at the 
Mount Wilson Observatory in 1908 found magnetic effects in the spots in- 
volving systematic distribution of north and south magnetic poles in pairs 

65 



66 



CLIMATIC CYCLES AND TREE GROWTH 



of spots. This polarity was observed to change from "north" direction to 
"south" direction (or vice versa) at the sunspot minima, 1913, 1923, and 
1933-34, thus raising many complex questions in the problem and locating 
fundamental activity within the body of the sun. Thus we see that in 
studying cycles in the sunspot numbers, the month is the logical time unit, 
since in that time the entire circumference of the sun is reviewed. 

For certain terrestrial effects, however, we need the daily reports. Mag- 
netic storms and the related auroral displays often show direct relation to 
large spots near the center of the solar disk ; the terrestrial effect is observed 



I860 



1990 



,'» " 




—40 



1885 1890 1895 

Max. Min. Max. 

-Butterfly diagram (after Maunder). 



1900 

Min. 






to follow a day or so late. In consequence of this prompt response, the solar 
influence in terrestrial magnetism has long been recognized. It is thought 
to be due to streams of particles coming to the earth at high velocity from 
the solar surface in or near the spot. Physical connection of these magnetic 
effects with meteorological conditions and tree-ring growth has not yet been 
established. It is thought possible that these streams perform some change 
in our upper atmosphere that influences the transmission of heat. 

Meteorological changes depend primarily on the motion of our atmosphere 
which results from heat that comes to us with the velocity of light from the 
sun's surface. Here again there may be effects in our upper atmosphere that 



Carneoie Inst. Washington Pub. 289. Vol. Ill— Douglass 



PLATE 17 




6C 

a 

oS 

JS 
V 



Carnegie Inst. Washington Pub. 289. Vol. Ill— Douglass 



PLATE 18 






a 



Months 
8 






|y :>:;; 













f 





Cyclograms of monthly sunspot numbers, 1750 to 1931: horizontal alignment is at 
10 months: 8, 9, 10, 11 and 12-months directions are indicated in pattern a; time moves 
left to right: first and last dates in the patterns are as follows: 

b. 1750.1-1779.9 e. 1840.3-1884.6 

c. 1770.1-1814.9 /. 1875.4-1915.3 

d. 1805.1-1849.8 g. 1905.1-1931.2 



ANALYSIS OF SOLAR RECORDS 67 

influence admission of heat to the lower atmosphere and the earth's surface, 
but we recognize that the heat radiation from the sun is the obvious factor 
to be studied in connection with rainfall and tree growth. Thanks to Dr. 
Abbot and the Smithsonian Astrophysical Observatory, and others, almost 
daily records of radiation have been obtained since 1918 and we have some 
values going back several years earlier. These, with the results of Dr. 
Pettit and Dr. Nicholson of Mount Wilson Solar Observatory, will be dis- 
cussed later, together with a cyclogram analysis of the international mag- 
netic character figure C. Various long-continued solar records have emerged 
from these investigations and offer a favorable field for cycle analysis by our 
method. 

ANALYSIS OF SUNSPOT NUMBERS 

Very large spots were occasionally seen by the naked eye before the in- 
vention of the telescope in 1610, and after that these solar phenomena were 
observed more or less continuously. After 1750 and especially since 1830, 
they were watched with care. 1 A study of the periodicities in such records 
by aid of cyclogram analysis is a most illuminating example of the method 
and at the same time it is the best introduction to our problems in climatic 
and tree-ring cycles. There are two parts to such analysis: one treats the 
well-known annual values commonly called sunspot numbers, and the other 
handles the monthly values, which are much more irregular. The first 
series gives a persistent cycle averaging something over 11 years since 1750. 
The other gives a flow of several cycles, interlacing, mixed, starting and stop- 
ping, such as we find in climatic and ring records. We find traces of this 
second type of cycle in the first series of common annual sunspot numbers. 
We consider below each of these groups of data in turn and add to them an 
examination of Abbot's and Pettit's radiation measures and the records 
since 1906 of the international magnetic character figure C, followed by a 
review of naked-eye sunspots and northern lights which give traces of solar 
history centuries before the invention of the telescope. 

Analysis of Smoothed Annual Sunspot Numbers — Schwabe in 1843 found 
that the number of spots on the sun had an ebb and flow, in an interval of 
10 or 11 years. They had been well observed since 1750. Starting with that 
date as a maximum, other maxima had fallen approximately at 1761, 1770, 
1778, 1788, 1804, 1816, 1830, and 1837. These intervals are roughly 11, 9, 
8, 10, 16, 12, 14, and 7. Here was a scattering of values that started the 
idea of a cycle as a persistent series of random values that never depart 
very far from a mean. But later this instability of interval quieted down; 
since 1837 the maxima have come steadily on a period averaging 11.4 years, 
1837, 1848, 1860, 1871, 1884, 1895, 1906, 1917, 1928: many of these dates 

1 The reader is referred to any good recent text-book on astronomy for tliscussion 
of modern opinion about sunspots and their cycle. Our sunspot data come from the 
Mitteilungen of Wolf, Wolfer and Brunner. The pre-telescope data come from Fritz 
(Reed's translation in Monthly Weather Review) and Maunder in Splendour of the 
Heavens. 



68 CLIMATIC CYCLES AND TREE GROWTH 

can not be assigned with exactness but they give roughly the intervals 11, 
12, 11, 13, 11, 11, 11, and 11 years. 

In 1906 Schuster performed his celebrated analysis and found several 
different cycles or periods as shown in his periodogram, our figure 21, page 
42. He divided the interval from 1750 to 1906 into two parts and thus se- 
cured an improved idea of the variations in the cycle and the localizing of 
special cycle lengths. Turner in 1913 using similar analysis expressed the 
"discontinuities" in the cycle, as he called them. A discontinuity is an 
interruption or abrupt change in length, phase, or amplitude in any cycle 
sequence. Schuster and Turner, while noticing changes in length, have 
been strongly influenced by the changes in amplitude, and Clayton by changes 
in phase. In a cyclogram, however, the story of change in period is laid out 
clearly for all who can read it. The fundamental form of the cyclogram of 
the sunspot numbers since 1750 is shown in figure 20, page 39, which gives suc- 
cessive cycle values at about 9.5 years, 14 years, 7 years, and 11.4 years in 
length. 1 These changes were evident in the first cyclogram photographed in 
December 1914 (I; Plate 9), and called differential pattern in the Astro- 
physical Journal, April 1915. We can describe the solar changes as a per- 
sistent cycle clinging near a general average of 11.3 years, whose variations 
between 7 and 16 years are not scattered at random but are gathered into 
several short intervals at fairly definite periods. Out of 16 cycle lengths be- 
tween maxima, 9 followed lengths closely similar. In the last hundred years 
the length has been nearly constant. From these facts we have a good prob- 
ability that the next maximum will be separated from the last one by the same 
interval that fell between the last and the one before. This is different from 
random picking of values between 7 and 16 years as implied in some descrip- 
tions of the sunspot variations. Studies have long been in operation to see 
if we can not find what the sunspot cycle was doing in the last thousand years 
or more. 

Analysis of Annual Numbers Since 1610 — Before 1750 the telescopic ob- 
servations of sunspots were far from systematic. After Galileo's first view 
in 1610, many views of them were placed on record but there evidently was 
a great dearth of spots from 1645 to 1715 (Maunder and Spoerer's results). 
A maximum had probably occurred near 1615, very weak; one near 1626, 
stronger, and one near 1639, very weak. The full records during the dearth 
with comments by contemporary observers can be repeated here, after 
Maunder : 

1648-60 often called spot-free. 
1649 exceedingly few spots. 

1660 spots seen April and May. 

1661-70 none seen. 

1671 spots seen August and September. Memorandum: "Now 

20 years since many spots." 

1 The sequence takes a form depending on the slant of the analyzing lines: the 
pattern is inverted but otherwise identical, when the slant is changed from right to left 
or vice versa. Note form also in Plate 15B. 



ANALYSIS OF SOLAR RECORDS 69 

1676 July and August, 3 spots seen. 

1677 April, a group visible. 

1678 2 or 3 spots seen. 
1677-83 almost spotless. 

1680 May, June, and August, spots observed. 

1681 May and June, spots seen. 
1684 Several groups visible. 
1686 2-3 .groups seen. 

1688 several spots seen. 

1689 a few spots seen. 

1695 after "6 years of no spots," in May we find a "great spot; 

only great one in 11 years." 

1700 November, spots seen. 

17041 first occurrences of 2 groups. 

1705/ at once for 60 years. 

1707 2 groups seen twice 

1710 January-October spots visible. 

October 1710 to May 1713, no spots seen. 

1716-21 spot maximum in 1718. 

After this, maxima occurred near 1728, 1739, and 1750. 

These scattered observations have formed the basis of estimates of maxima 
on Newcomb's 11.13-year cycle. It is probably safe to accept estimated 
dates of maxima between 1610 and 1640 and from 1718 on, although they are 
weighted by Maunder about 2 to 5 in comparison with a weight of 10 for 
well-observed maxima. Any assignment of maxima during the dearth 
seems unsafe, since great bursts of spots, even those visible to the naked eye, 
have appeared in all parts of the cycle, though more likely to occur at maxi- 
mum. We are convinced that no minima at all can possibly be assigned 
during that dearth interval, as has been attempted. 

When the actual data are placed in a cyclogram as in Plate 15B, we find 
a good solution for the entire series 1610 to 1930 at 11.2 and another at 11.6 
years, giving us a choice of 28 or 27 cycles in that total interval. Each of 
these solutions appeared in the automatic periodogram of the sunspot num- 
bers made in 1913, Plate 12A. 1 Well-established maxima for the last 
hundred years give a strong value at 11.4; thus it does not decide between 
11.2 and 11.6. If, however, we take the obvious facts of the cyclogram, we 
find for the series between 1615 and 1788 a solution at about 10.2 comparing 
very favorably with 11.2 judging by the decreased average residual obtained 
on applying Maunder's weights to the maxima. These two solutions can 
be applied to those data and it will later appear that during the dearth a 
10-year cycle appears in tree-ring records while the 11-year cycle seems to 
have failed. 

Other Cycles in the Annual Numbers — In the sunspot cyclogram other 
cycles appear prominently as the tests are carried through a range from 5 
to 25 years. After the 10 and 11 year lengths, two others promptly attract 

1 Published in the Astrophysical Journal, October 1914, and in Climatic Cycles and 
Tree Growth, vol. I, 1919, Plate 9A. 



70 



CLIMATIC CYCLES AND TREE GROWTH 



attention, 8.5 and about 14 years. They show well by directions of align- 
ment of increased amplitudes as in Plate 15B. 

Centers of Mass of Maxima — Cyclogram analysis distinctly uses the mass 
of maxima in producing its cycle effects. In the case of well-defined maxi- 
mal masses, as in the sunspot cycle, the use of centers of mass is well indi- 
cated, as in the plate referred to. This use of the centers of mass simplifies 
the general pattern and shows the various lesser cycles, such as 14 years 
and probably 7.0, 8.5, 10, and also suggestions near 17 and 20. The setting 
near 23 in Plate 15B shows a symmetrical arrangement of the maxima and one 
is less conscious of the irregularities in timing near 1800 that looked so large 
in the 11-year setting. The mean departures from a true period after all 
are only two to three years, say 20 to 30 per cent of the cycle length, and on 
a 23-year setting the percentage reduces to 10 or 15. 

Possible Half-Sunspot Cycle — In the analysis of the smoothed annual 
means we do not readily see any half cycle of about 5.7 years, such as found 
in terrestrial phenomena and reported in radiation data (by Abbot). The 
form of the sunspot cycle since 1750 with its bulky maxima and very low 



100 

50 
n 












i 






















h IH 


yl 


rw; 


k 


^ I L 


J\ r 












u< 


tfinA 


f>A 


r^ 


nr 


v^y 


V^" 


J*Y 


V 


^4 


>V-, 


— frn 


■ 


J*d 


flr\ 



1902 1905 1910 1915 

Fig. 30— Monthly sunspot curve to show reduced amplitude at minimum (after 
Wolfer). Note: This gives a striking illustration of a poor smoothing method 



minima gives apparently no indication of a secondary crest in the 11 years. 
One finds it hard to look upon the slight hump that sometimes occurs dur- 
ing decreasing spot activity as any substitute for a secondary maximum 
that would nearly divide the whole cycle length in halves. A secondary 
maximum of activity in the monthly values would be hard to find owing to 
difficulties in evaluating the fluctuations during the long low minima, yet, 
in spite of that, these monthly values seem so far to be the best direct solar 
data in which we have a chance of finding a 5.7-year period, approximating 
the half cycle in length. 

We find, however, in the tree-ring records extensive sequences of a 5.7- 
year recurrence which we have called the Hellmann cycle; we find also 8.5, 
10, 14, 17, 19 or 20, and 23 years, as will appear later. We find also in trees, 
in the last 1000 years, certain cycles close to 12 years in length (see page 107). 
Here is, therefore, the place to ask the question : Can we regard such lengths 
as variants of the well-recognized 11-year cycle? We can not answer yet 
with certainty, but since sunspot numbers had a limited cycle life at 14 
years (1788-1830), we know no reason why 12-year lengths should not occur 
in the sun. 



ANALYSIS OF SOLAR RECORDS 71 

Analysis of Monthly Sunspot Numbers — In our analysis of the monthly 
numbers, 1750 to 1934, instrumental limitations lead us to consider cycles of 
5 months to 30 or 40 in length. The monthly changes are strong and easily 
analyzed within each spot cycle while the spots are relatively numerous, 
but the changes become very weak at the minima. It is difficult to adjust 
the small changing values during minima in order to place them on a level 
with the large changes at maxima on a scale suitable for continued analysis 
over long intervals including both maxima and minima. Nicholson's pro- 
posal is excellent: to study each cycle from minimum to minimum. In 
cyclogram analysis this is done automatically, for the overlapping of two 
sunspot cycles at the minimum is very slight and can easily be marked on 
the plot that is analyzed. 

For purposes of longer analysis, the changes at minima have to be "stand- 
ardized." Other students of cycle analysis will recognize this need and the 
dangers of its application. In our rapid cyclogram analysis it has been 
possible to try several processes. In the first attempt, the smoothed annual 
values were subtracted from the monthly values. This was not satisfactory 
because it left the fluctuations near sunspot minima practically invisible. 
In the second attempt the monthly values were divided by the smoothed 
annual means, thus "standardizing" the curve into monthly percentage 
departures from annual smoothed means taken as unity. But this raised 
the changes at minima to enormous size, obviously a serious exaggeration. 
So since we merely wish to make the minimal changes large enough to have 
an importance of their own but not an equality with the changes at maximum, 
we have used a process in between the two described; we have taken the 
monthly values in their original form, added 10 spot number units to each 
one, and then divided by the mean smoothed line, also with 10 units added, 
and have plotted the results. This has been found to keep the minima sub- 
ordinated without concealing their changes. 

The results obtained represent my own analysis made about 1918, further 
examined in 1922 and repeated recently, and Mr. Schulman's independent 
results obtained recently. Plate 18 gives the data in cyclogram form. 
From the analyses we discover several things. Some cycles do pass 
unchanged through the minima but cycles also seem to start and stop with 
a slight preference for maxima and minima. A crude analysis was made of 
the times of starting and stopping (crude because these times are not well 
defined) and many beginnings and endings seemed to occur in a 10-year 
cycle with occasional cutting to five years. Caution is needed in attaching 
significance to this result. 

Cycles found in the monthly sunspot numbers may be condensed into a 
frequency periodogram as in figure 31c, where the various monthly values are 
brought together for comparison with radiation and other changes studied 
below. The following table gives the data regarding them. 



72 



CLIMATIC CYCLES AND TREE GROWTH 



Cycle Length and Duratiyn: Monthly Sunspot Numbers 




Cycle length, mos. 


Underl.J 


Duration 


Cycle length, moa. 


Underl.s 


Duration 








1840-1885 




174° ' 














5.7 


no 


1852.8-75. 








5.7 


no 


1756.5-61. 


6.7 


1 


76. -85. 


6.0 


no 


67.5-80. 


7.9 


1 


40. -45. 


7.6 


1 


70.5-80. 


8.3 


1 


50. -85. 


8.3 


1 


51. -57. 


11.2 


no 


69.5-82. 


10.4 


1 


49.5-53.5 


11.4 


2 


51. -03. 


10.4 


2 


66. -71.5 


13.8 


no 


65. -80. 


10.4 


X 


74. -80. 


14.1 


no 


40. -65. 


11.2 


no 


57. -02. 


14.5 


1 


40. -49.5 


13.0 


X 


69.5-80 


16.7 (oc i) 
17.9 (oc i 


2 


50. -85. 


13.6 


2 


51.8-56. 






13.6 (oc i) 


no 


61. -74.5 


oc i) 


no 


51.5-85. 


17.0 (much i) 


1 


49.5-57.5 


27.0 


X 


40. -85. 


17 


x 


69 -75 








24.5 (oc i) 
27.1 (all *?) 


no 


49.5-80 
49.5-80. 


1875-1915.5 


no 














6 1 


1 


1908. -15.5 








6.7 


1 


1875. -84.5 


1 


770-1815 




7.6 


1 


1903. -08. 








7 8 

g' j and 


1 


1880. -96.5 








5.5 


no 


1793.8-03. 


1 


98. -03.7 


7.6 


1 


70. -81. 


7!9 or 


1 


80. -03. 


8.9 


no 


85. -91. 


8.8 (much X2) 


no 


1909. -15.5 


10.5 


no 


91. -15. 


10.8 


X 


1875. -15.5 


13.6 


1 


95. -15. 


11.9 


1 


89.5-95.5 


17.5 


no 


85. -05.5 


12.3 (much i) 
12.6 (oc i) 


no 


96.5-15.5 


27.0 


1 


70. -15. 


no 


75. -88. 








15.6 (oc i) 


1 


75. -86. 














17.2 


X 


75. -15.5 


1 


505-1850 




17.9 

25.5 (oc \, oc}) 


1 


1907.5-15.5 
1875. -15.5 








no 


6.9 


no 


1805. -25. 


26.7 


X 


75. -15.5 


7.5 


1 


35.5-50. 








8.0 or 


1 


22.5-43. 


1905-1934. 1 




11.0 


2 


24.5-36. 












13.5 


no 


08. -30. 


5.1 




1926. -31.5 


15.0 


1 


36. -50. 


6.1 




05. -14.5 






(phase change 


6.5 


no 


20.5-28.5 






at 1841±) 


7.2 




31. -34.6 


19.2 


X 


05. -25. 


8.2 




05. -11.5 


24.6 


no 


10. -45. 


8.2 




18.5-22.5 


27.7 


no 


05. -50. 


8.2 
9.9 
10.2 (J) 


no 


22.5-31.5 
15. -24.- 
24. -34.6 








14.4 


no 


05. -34.6 








15.7 


1 


05. -31.5 








17.1 


2 


05. -34.6 



1 Table prepared by Mr. Schulman. 

2 See page 146 for meaning of underlines. 

Thus we find consistent cycles as follows: 6.8 months, weak; 8 months, 
very strong; 11± months, strong; 13.5 to 14 months, strong; 16 to 174- 
months, strong; 25 medium 27 months, strong. 

ABBOT'S RADIATION MEASURES 
The heat reaching us from the sun can be measured by the rate at which 
it raises the temperature of water or silver or other substances suitably black- 



ANALYSIS OF SOLAR RECORDS 



73 



ened and presenting a known area to the sun's rays. Built on such a princi- 
ple, the bolometer invented by Langley and improved by Abbot and the 
silver disk pyrheliometer invented by Abbot have enabled us to secure since 
1918, and to some extent before, exceedingly accurate measures of the amount 
of heat coming from the sun to the outside of our atmosphere ; as well as the 
amount absorbed by our atmosphere, in a few favorable locations, and the 
amounts reaching the ground. The intensity at mean solar distance, out- 



Months 



1 1 1 1 1 1 1 1 1 r— t I | 

10 20 30 



1918 



1920 



I r 

o 



1930 






a 



li_i 



j i 



Months 



7 8 



21 



25 



Relative 
frequency 

(weir ' 

400 



300 
200 
100 













































r 


-\ 










\ 










A 


























/ 


\ 








/ 


\ 




I*-- 


\ 






\ 


















j 


— •. 


/ 


/ 






J~ 


v^ 


7 


I 


/ 


' 


V 


% 


1 


\ 


















1 













5 6 7 8 9 10 II \Z 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 

Months 



Fig. 31 — a. Chrono-periodogram of Abbot's radiation curves analyzed by 
cyclogram methods. 

b. Abbot's cycles in same. 

c . Frequency periodogram monthly sunspot numbers, 1750-1934. 



side of our atmosphere, is known as the "solar constant" and its average in 
standard units is usually given as 1.94 calories per square centimeter per 
minute. 



74 



CLIMATIC CYCLES AND TREE GROWTH 



Abbot, who is unquestionably the highest authority on solar radiation, 
has made cycle analysis of his monthly values using an instrument of his 
own invention, the periodometer. This instrument is especially good at 
cycle summation and subtraction. His cycle lengths are first estimated by 
eye from the original curve. 1 By this form of integration he can test esti- 



Weak cycle Good cycle 

Norma I cycle — Very good cycle — 

6 7 8 9 10 II 12 13 14- 15 16 17 18 19 20 21 22 







































1 






1 




1 


| 




1 






























1 


i 




i 
i 
i 






























■ 
j 






; i 












































i 
i 












1 

i 










1 
i 














i 
i 
i 












1 
























i 
i 




1 

J 










1 

1 

j 














1 






















i 














i 












I 
















































1 














i 
i 

i 


















t 

1 












1 






i 






























1 






i 
i 




















1 








i 


1 


1 










1 














• 










' 


i 










j 
























1 


1 
























1 


1 


1 | 


















! 

| 














1 




1 ! 
i 

i 


1 






1 










l 












1 


i 
i 
i 




1 
i 


1 
































1 





































































1750 
1760 
1770 
1780 
1790 
1800 
1810 
1820 
1830 
1840 
1850 
I860 
1870 
1880 
1890 
1900 
1910 
1920 
1930 



5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 

Months 
d 
Fig. 31 — d. Chrono-periodogram of same. 

1 The periodometer has the data set up on a right-hand drum and integrates it by 
a system of fractioned additions {i.e. it finds the sum of each occurrence divided by 
number of occurrences). This produces on left drum a continuous repetition of equal 
integrations. Then the integrated values on left drum are caused to subtract them- 
selves from the originals on the right drum. Smoothing may be performed also. (See 
Bibliography, 1932 3 and 1935.) 



ANALYSIS OF SOLAR RECORDS 75 

mated cycle lengths and he happily gets away from insistence on some special 
curve of variation, such as a sine curve. His cycles are assumed to continue 
unbroken through the data but one notes that his "eye" method of finding 
cycles, just referred to, permits recognition of discontinuity in cycles and 
hence aids in the selection of preferred data. By his skilful treatment he has 
brought out the cycles expressed in the accompanying periodogram, figure 
31b. On checking his results we found, as he did, a good cycle at 8.0 months, 
a very strong one at 11.0 months (Schulman put it at 11.2) and possible 
shorter cycles at 2.5 and 5.0 months and 3.4 and 7.0 months. Our method 
did not lead us to give weight to our results in longer cycles. Plate 19B shows 
cyclograms of his original curve (Feb. 1932) at 8 and 11 months. 

Abbot's synthetic curve B (see his paper of February 1932) combining 8, 
11, 25 months and others longer, gives 8 and 11 months apparently not quite 
as strong as in the originals. His residuals, C, have apparently no 11-months 
cycle but still contain traces of 8-months cycle, distorted because the original 
varied in amplitude. We found evidence of a lS^-month cycle and Schul- 
man placed a faint cycle at 12.1 months. While no striking resemblance be- 
tween Abbot's radiation curves and monthly sunspot numbers shows since 
1919, using the data as they are, a resemblance may be seen between his radia- 
tion cycles and the general periodogram of monthly numbers. 

The existence of a terrestrial cycle having the same length as the sunspot 
cycle but showing two maxima, usually unequal, instead of one, has raised 
the question : By what physical means could a single-crested cycle in the sun 
produce a two-crested cycle on the earth? It has been suggested that such 
a result might happen if a force acting from the sun upon the earth produced 
an inverted effect when exceeding some critical value. Along this line Ab- 
bot, for instance, has found a temporary, strong reduction in solar constant 
in the presence of an extra large spot. Bollinger has worked out a formula 
of relation of radiation to smoothed annual sunspot numbers that could pro- 
duce a "Hellmann" effect or a double-crested resultant curve in radiation to 
a single-crested original sunspot curve. Clements has observed an inversion 
of relation between drouths and sunspot numbers when the latter rose in 
value above 90. Clayton has found reversals of phase in climatic cycles. 

We found above that Abbot's radiation study shows cycles strikingly 
similar to the general periodogram of cycles in monthly sunspot numbers, 
but that during his observations, 1918 to 1931, the agreement is restricted in 
two cycles, 7.9 months, a strong cycle, and 25 months, a weak cycle. Inver- 
sion of reaction is intimated in some of Abbot's diagrams. 

PETTIT'S ULTRA-VIOLET RADIATION CURVES 

Pettit's ultra-violet radiation measures show something quite different 
from Abbot's data. When we speak of heat radiation as measured by Ab- 
bot, we include all wave lengths, knowing that most of the heat energy is in 
the long waves, and that this energy comes rather generally from the sun's 

1 Abbot finds a 13.6 month cycle well marked in weather; see Bibliography, 1935. 
See also his solar radiation analysis therein. See reference to 28-month cycle in I, 106. 



76 



CLIMATIC CYCLES AND TREE GROWTH 



surface. The ultra-violet rays measured by Pettit are short waves and have 
little effect in heating. They are thought to produce changes in ozone and 
ionization of our upper atmosphere and in plant growth, with other ef- 
fects upon climate and plants not yet worked out. The proportionate 
changes from day to day and year to year are far greater in the ultra-violet 
than in the general heat radiation. And the source of the ultra-violet is 
doubtless different. The short series of observed data, 1924 to 1931 or later, 
shows in parts better resemblance between ultra-violet radiation and sunspot 
numbers than is found between total heat radiation and sunspot numbers. 



1 



1924- 



1925 



1926 



1927 



1928 



1929 



1930 



1931 



53 »- 4 



1.2 



JP 

s 



1.0 

100 



50 





A 










1 






/L if 


M 






I 






4? 


V 


\ 




t\ 


\ 






'V 


Vv 


\ 


M 


Vv 






/ 






\ 


!V\j 


V » 


A 


\ 


/ 




I 


Jltra-viol 


st radiat 


ion ( Pett 


it) 







f j 


V\ 


A^\ 


—h 








r 


vv^ 


w 


V 


w 


\ 






r 


V 






V 


S^ 




y"\ 


* 


Monthly 


sunspot r 


lumbers 




\r * 





156 


A 
















134 


/W 


V^ 


r\ 


KV 


sA 




^ 








^V 




\J 


V\T 


y 




ISZ 






Solan c 


Dnstant 


[Abbo^ 


v v/ 







Fig. 32 — Ultra-violet radiation compared to monthly sunspot numbers 
and the solar constant. 

This intimates a substantial difference in source and points more directly to 
the activity in the spots themselves. Pettit has called attention to an interval 
of possibly reversed correlation from the middle of 1928 to early in 1930. 
Pettit's curve and the monthly sunspot numbers are compared in figure 32. 

INTERNATIONAL MAGNETIC CHARACTER FIGURE C 

The International Magnetic Character Figure C, represents the daily 
"agitation" or rapid irregular changes in the intensity of terrestrial magne- 



ANALYSIS OF SOLAR RECORDS 77 

tism. Disturbances are estimated on a scale of to 2 and averages made of 
many stations so that the data may represent widely distributed terrestrial 
conditions. It is accepted that this phenomenon is due to the sun and yet 
the exact machinery by which these effects reach the earth's magnetism is 
not certain. It is probable that streams of charged particles come from the 
sun from active areas near the solar meridian, but it is also thought possible 
that there is an effect from short-wave radiation in the form of ultra-violet 
light. Motion of our upper atmosphere may carry electric charges received 
from the sun or developed from solar radiation in such a manner that magnetic 
fields are produced. There is close connection between terrestrial magnetic 
disturbances and northern lights, earth currents and the so-called magnetic 
storms that affect telegraph lines. 

Magnetic observations extend back to 1906 and in less accurate form to 
1872 and in crude form to 1835, and constitute one of the longest sets of pre- 
cise observations connected with the sun. In some respects, therefore, these 
data rank very high as source material in any study of periodic values in solar 
activity and must be included in our list. At the same time they illustrate 
certain features of cyclogram analysis and open the way to further studies of 
the sun and its phenomena. 

Observers who have made careful studies of periodicities in magnetic 
data, state that the correlation of magnetic disturbances with sunspot 
values seems to be low in short time intervals such as the day and the month, 
but greatly improves as short variations are smoothed out and long intervals 
(for example, the year) are considered. On the other hand, greatly agitated 
days (magnetic storms) sometimes come when a large sunspot or group of 
sunspots is central on the sun. Well-defined periods of about 27 days have 
been found in the magnetic character figure C. Numerous coincidences with 
known rotation values lead scientists to accept these periods as measures of 
solar rotation. There is also in magnetic data a 6-months cycle that can be 
traced back to 1872. A very minute effect has been isolated, depending on 
the lunar day (Chapman: 1918). 

Solar Rotations in Magnetic Data — One of the productive methods hitherto 
employed in analyzing the magnetic data is Dr. Bartels' graphic solution in a 
multiple plot (1932; see Chree and Stagg in Bibliography; for multiple plot 
see Chapter II) giving daily values arranged in rows as if in a summation 
process. In this pattern his eye has caught discontinuous periods as men- 
tioned above under that topic. Thus he has confirmed the semi-permanence 
of the magnetic source areas or M-regions in solar longitudes and at the same 
time has found some evidence of activity in opposite longitudes of the 
sun. His later application of probability principles produced his theory of 
"quasi-persistence." He treats this phenomenon as a general character 
rather than as a phenomenon localized in time, and yet his summation dial 
enables him to date some cyclical changes. 

In 1935, desiring to compare cyclogram analysis with Bartels' summation 
dial of magnetic data in which he investigated "quasi-persistence" (fig. 26) we 



78 CLIMATIC CYCLES AND TREE GROWTH 

secured the records for 1906 to 1934 in daily values. For convenience these 
were compressed into 3-day averages. 1 The data could then be compressed 
again if needed and longer cycles investigated. In the first examination by 
cy olograph several striking effects appeared at once: the intervals between 
magnetic maxima easily show several definite periods between 26 and 32 days ; 
a period close to 27.0 days is much more persistent than any other; this is 
occasionally reduced to 26 days and sometimes is mixed with longer periods of 
about 30 days. One notes that a synodic period of 30 days in solar rota- 
tion occurs near latitude 40° which is at the outer limit of sunspot area. It 
is difficult to explain how streams of charged particles, leaving the sun in 
lines nearly perpendicular to its surface, can reach the earth from that lati- 
tude ; yet one finds possibilities in the curves of coronal streamers often pho- 
tographed during the total solar eclipse. Periods near 27 days are double- 
crested ; that is, a lesser maximum appears to bisect them as would happen 
if two magnetic source areas were at opposite longitudes of the sun. The 
second maximum is often fainter than the other. Near sunspot maximum 
additional periods make the variations more complex. 

The results of cyclogram analysis confirm strongly the persistence or 
localizing of magnetic source areas in solar longitudes. For example, there 
seems to have been very little change in longitude of a 27.0-day maximum 
from the beginning of 1930 to our latest data in the middle of 1935. A 27.0- 
day period is the one commonly shown by sunspots at 5° to 10° from the equa- 
tor. Hence we presume that near sunspot minima the source areas persist- 
ently active in agitating terrestrial magnetism are sometimes localized for 
long intervals at that latitude on opposite longitudes of the sun. 

Sources of the 6-Months Period — Since the 6-months maxima occur in spring 
and autumn, the question has been raised whether they originate in the sun 
or in the earth and the relation of the magnetic maxima to each has been 
studied. For example, the sun's pole is inclined 7° to the ecliptic in such a 
direction that in early March the sun's southern hemisphere is most inclined 
toward us, and in early September, its northern hemisphere. But late March 
and September are the times of the terrestrial equinoxes and the maxima could 
be related to them through the changing of the earth's hemispheres regarding 
exposure to the sun's radiation. An extensive statistical study of the 6- 
months maxima by Bartels (1932) has demonstrated that the earth is one 
source of this variation, that is, the magnetic forces from the sun are suffi- 
ciently terrestrialized to show an earthly character. 

Cyclogram analysis applied in 1935 presented immediately a complex 
feature. In the vicinity of the sunspot minima and especially in the last one, 
1932-1933, the 6-months maxima alternate in opposite longitudes of the sun. 
This is shown in our diagrams, Plate 19B and C and figure 33. The figure 
summates the magnetic effects that come while opposite halves of the sun 
(longitudinally) are presented towards us. If this effect of alternating 

1 The preparation of these curves was done by Mrs. G. Dewey and Mr. Arthur N. 
Cowperthwait. 



Carnegie Inst. Washington Pub. 289, Vol. Ill— Douglass 







Months 
II 



593 v 









tt*» 







B 




A. Cyclograms of Abbott's radiation curve, December 1918-July 1930. 1, Direc- 
tional values at 11 months. 2, Analysis at 11 months. 3, Analysis at 8 months. 

B. Cyclograms of magnetic character figure C, analvzed for 27.0-day period. 
1, Jan. 21, 1923- Jan. 26, 1926; 2, Jan. 26, 1926-Oct. 29, 1928"; 3, Oct. 18, 1928-Dec. 15, 
1931; 4, Dec. 15, 1931-Nov. 9, 1933. 

Five stronger horizontal rows indicate a 27.0-day period; intermediate rows show 
maxima in reversed phase, that is, in opposite longitudes; rows of maxima pointing down 
to the right indicate periods more than 27.0 days; rows pointing up to the right, less than 
27.0 days. 

C. Cycle relief map of the magnetic character figure C January 1932 to March 
1935. It is made of separate cards cut to contours of 3-day means, slightly smoothed; 
each card has 81 days of data progressing upward in the photograph and beginning on 
each card 27.0 days later than the card to its left. Note the conspicuous horizontal 
alignments and the alternating levels of the 6-months maxima. 



Carnegie Inst. Washington Pub. 289. Vol.. 1 1 1 Douglass 



PLATE 20 



V, \\ >v. 



*m 



mm 



i*ffiiS 






'•••■•'Wu'" 






♦ V 






MP 






Cyclogram test to distinguish between natural sequences, right column, and random 
sequences, other 2 columns: natural sequences have fewer short cycles and hence show 
clearer patterns. 



ANALYSIS OF SOLAR RECORDS 



79 



maxima is correct, the sun shares in causing the 6-months maxima. Until 
this effect is confirmed our results should be considered provisional 

Similar caution must also be exercised in drawing conclusions from this 
apparent relation between the sun and the earth's magnetism Its display in 
1932-33 as analyzed in the cycle contours shown in Plate 19C, suggests that 
these chief magnetic source centers are on opposite sides of the equator and 
hence diametrically opposite each other at some latitude less than 10°. 




Fig. 33 — International Magnetic Character Figure C as related to opposite longi- 
tudes on sun during a 27-day period. Note: Means of approximate first halves of suc- 
cessive 27-day periods provide ordinates for one line and means of second halves of same 
provide them for the other line. Ordinates are relative values on a special scale with 
unity approximating 0.13 unit of character figure C per day above an assumed base of 
about 0.5 unit. This shows alternate 6-months maxima as occurring at the time that 
opposite solar longitudes (near the solar equator) are central as seen from the earth. 



Other Periods — In 1931 there was evidence of a 9-day period operating 
coincidently with those of 13.5 and 27 days. Since 1906 it shows durations of 
more than four months in the following years: 1910, 1914, 1916, 1924, and 
1931. Of these, 1914 exhibits the unusual length of 9.9 days, which is one- 
third of a long cycle showing in that year. Maxima, possibly alternating in 
longitude, show at previous sunspot minima, for example, in 1922 and 1923 on 
a period of 27.0 days; in 1912 and 1913 on a period of 27.3 days. The year 
1914 has a period near 29.4 days; 1916-18 give evidence of a possible period 



80 CLIMATIC CYCLES AND TREE GROWTH 

somewhat over 31 days; 1918.4 to 1920.9 show a period close under 30 days; 
1924 and 1925 do the same. In 1926 and 1927 the common 27-day period 
seems to become 26 days ; this lengthens again to 27 days near the beginning 
of 1928. Thence it continues for two years and in November and December 
of 1929 seems to have a phase change of several days, which leads to the begin- 
ning of the stable sequences of 27.0 days in the years 1930-35. Altogether we 
have a very interesting pattern of rotation periods, here stated only in a pre- 
liminary way. 

NAKED-EYE SUNSPOT RECORDS 

Naked-eye sunspots are not infrequent. They may occur at any part of 
the sunspot cycle but are more likely to be seen near the maximum. Per- 
sonal experience placed three conspicuous naked-eye spots, one at a maximum 
(1917), one two years before a maximum (1882), and one two years before a 
minimum (1921). Each was accompanied by northern lights, especially the 
last. 

Historical accounts of naked-eye sunspots have come chiefly from Chinese 
records and are quoted by Fritz in connection with his studies of northern 
lights. His list gives us really only four groups that might supply or suggest 
dates of maxima. Any well-established date of maximum before 1610 has 
an important value. These groups are as follows (with observed cycles) : 

Intervals Cycles 
Years 

1. A.D. 300-375 10.0 no strong location of maximum: 373 

possible. 
370-400 13.8 no strong location of maximum. 

2. 800-880 11.1 maximum possible at 840. 

3. 1078-1206 8.3 no location of sunspot maximum: 

1120 is possible. 

4. 1369-1383 10. ± evident sunspot maximum 1370-72. 

The second is the weakest of the four but gives rather a clear 11+ year 
cycle. 

RECORDS OF NORTHERN LIGHTS 

The other effect of solar activity visible to the unaided eye and forming 
perhaps a guide to sunspot history is the aurora or northern lights. The 
data here analyzed have been gathered together by Professor H. Fritz, Zurich, 
1893, with a translation by W. W. Reed in the Monthly Weather Review, 
October 1928. (See Bibliography.) Early records of this phenomenon are 
necessarily fragmentary. Fritz has taken the descriptions from historical 
references. These data have been transferred to three cycleplots and 
analyzed, as follows: 



ANALYSIS OF SOLAR RECORDS 81 

Cycles in Fritz's Auroral Records 
Maxima of period named 

577 
585 

809, 840 

1096, 1205, 1263, 1349 
1349 

major max. 1561; lesser max. 
1568 (possible Hellmann cycle) 

It will be noticed that we have here abandoned the maxima assigned by 
Fritz in an 11.1 year cycle and endeavored to find maxima that have intrinsic 
evidence of being sunspot maxima. One might possibly accept A.D. 577 on a 
period of 12.4 years but might feel doubtful about 585 on a period of 15.2. 
A.D. 809 and 840 might occur on a 10-year period but they are not convincing at 
all. A.D. 1096, 1205, 1263 and 1349 on an 11.8-year period seem satisfactory, 
but a maximum on a 13.8-year period does not seem satisfactory. The 11.8 
period from 1432 to 1635, with a major maximum in 1561 and a lesser maxi- 
mum in 1568 seems to be giving us real information by suggesting a Hellman 
cycle which agrees with the tree records of northern Arizona and deserves 
full consideration. 



Cycle length in years 


Duration 


(1) 434-677 A.D. 




12.4 


434-610 


15.2 


all 


(2) 727-1014 




10.0 


727-925 


(3) 1085-1403 




11.8 


all 


13.8 


1349-1403 


(4) 1432-1635 




11.8 


all 



V. ANALYSIS OF TERRESTRIAL RECORDS 

Multitudes of attempts have shown that here and there seemingly pur- 
poseless climatic variations gather themselves into orderly form and give 
cycle effects of limited duration. The obstacle which climatologists have 
everywhere encountered is the short length of the meteorological records; 
they are far too short to permit a general study of climatic cycles. This 
difficulty is now being overcome by the use of tree-ring records having a strong 
climatic correlation. We have a pyramid of ring records consisting of hun- 
dreds of trees that cover the last century diminishing to four that cover 3000 
years. For all this material we have a flexible and rapid form of cycle 
analysis. 

In this study of climatic variations we seek answers to many questions: 
What are the cycles that do appear; when do they come; how long do they 
last; are they of small or large amplitude; do they come over large geo- 
graphical areas at the same time or only by the acre, so to speak; have they 
prevailed at other times in the last 1900 years; do they resemble cycles in 
sunspot numbers or other solar phenomena and how can observations of 
the sun contribute to the problem ; can they be used in long-range prediction? 

These questions state the field to which studies in the succeeding pages 
will be devoted. Attention will be given to the relation between solar and 
climatic changes and a final chapter will take up the practical summary of 
this information in an attempt to point out its most important parts contribut- 
ing to long-range prediction. The remainder of this chapter takes up in a 
series of topics the most distinguishing characters and problems in ring growth 
and climatic cycles that have emerged from many considerations of the sub- 
ject and especially from the use of the cyclogram method of analysis, all 
introductory to the lists of cycles found. 

CHARACTERS OF CYCLES IN RING RECORDS 

Discontinuous Periods — Sometimes called broken periods, fragmentary or 
short-lived periods; sometimes called cycles when their variability is referred 
to. The word cycle is used as a more general term. Reference is made to 
their special discussion in Chapter III. 

Conservation — Persistence of similar values in two or more successive years 
resulting in less frequent crossing of the mean in natural sequences than in 
random sequences, is classed statistically as conservation and should be 
examined under that heading. When three general curves of western tree 
growth were examined by Dr. Dinsmore Alter for lag correlation expressed 
in his correlation periodogram, high correlations were found in short lags of 
1, 2, and 3 years. He at once recognized this conservation and asked whether 
I had otherwise noticed it. I had used a form of it in testing relation of 

82 



ANALYSIS OF TERRESTRIAL RECORDS 83 

Prescott ring growth to rainfall and have found it rather general in that 
relation in the Pueblo Area. I answered that it had been noticed and that 
it would probably be found stronger in the maxima of tree growth than in 
the minima. So he segregated the measures of the general Flagstaff area 
mean curve, FAM, 1780 to 1921, one of the curves already tested for correla- 
tion periodogram, into four successive groups extending from the highest 
value to the lowest and obtained the correlation coefficient between successive 
years for each group separately. The coefficients were as follows: 

Mean value r r/<r r 

Highest 25 p. ct 1.30 0.42 3.2 

Second " .89 .23 1.7 

Third " .67 -.09 .66 

Lowest " .40 .10 .71 

In the highest and lowest groups the correlation was carried backwards 
to the preceding value with this result: 

Highest 25 p. ct 1.14 0.41 3.1 

Lowest " .58 -.12 .86 

He concluded that there is a certainly real positive correlation with the 
succeeding value in the highest one-fourth of the data and a quite probable 
correlation in the second highest 25 per cent of the data. The rest show what 
we should expect from accidental values within the chosen sample. 

The reverse problem, that is, the correlation with the preceding value 
shows, as far as carried, the same result as the forward test. Hence he 
regarded this as evidence that an unusually good growth strongly indicates 
a reserve for the following year and also that the preceding year was good. 
In other words a favorable condition this year can not give the best growth 
this year if the tree was weakened last year. 

Triangle Tests — These are tests for the purpose of distinguishing between 
random and natural sequences. Three curves are prepared, one giving the 
original data and the other two showing the same set of values drawn by lot. 
Attempts were made to select the genuine record from the random records 
by some obvious character in it. Some twenty different growth curves 
averaging 150 to 175 terms (yearly values) in length were tried and in every 
case correct selection was made. This success, we recognize, was due to 
conservation in these natural sequences. 

Two basic methods of choice were used: smoothing and periodogram 
methods. In trying to pick out the genuine from two random curves by 
the first of these methods, each sequence is smoothed by longer and longer 
running means ; the one that most reluctantly becomes a straight line is likely 
to be the genuine. In this treatment we observed a significance in another 
character: namely, that natural sequences, the longer they are, show longer 
and longer cycles 1 (fig. 34). 

1 If a number of group curves are tested at the same time, many of the genuine can 
be picked out from the group by similarity of appearance, for they cross-identify and 
the random sequences do not. 



84 



CLIMATIC CYCLES AND TREE GROWTH 



The periodogram test has been tried out more thoroughly than the other. 
The three sequences were made into cycleplots and at four different cycle 
lengths settings were made on each and cyclograms secured and printed on 
plates, three at a time in an order unknown to me. That made 80 sets of 
3 patterns each. The correct choice was made of the genuine in every case 
simply on the basis of relative freedom from short cycles. Three sets (15 
per cent) were difficult, and the choice held somewhat uncertain. The tests 
also show the domination of longer cycle lengths in natural sequences. This 
charaoter may be stated in periodogram terms by saying that the frequency 
periodograms of natural sequence have a level or upward trend, while those 




GC 

FV 
SH 

NE 

FLU 

RL 



Mean 




1800 

Flagstaff trees 



1900 



1800 1900 

Lot drawings of same 

Fig. 34 — Effect of smoothing on natural sequences (left) and random 
sequences (right). Flagstaff area — 20 year running means 



of random sequences have a downward trend. These conditions make it 
rather evident that short random sequences of 50 or 75 terms become very 
difficult to distinguish from real ones; and that was found to be the case. 

These two types of triangle tests are illustrated in figure 34, giving an 
example of smoothing; and Plate 20, showing the cyclogram test. In the 
latter the right column is genuine. 

Clough has referred to a similar character in natural sequences by observ- 
ing that in random sequences the curve crosses the mean line more often 
than in natural sequences. 



ANALYSIS OF TERRESTRIAL RECORDS 85 

Similarities over Areas — In establishing the chronological identity of rings 
in different trees, we are at the same time proving the climatic similarity 
over the terrain involved. Climatic similarities, however, must be supported 
not merely by a corresponding deficient ring here and there but by the aver- 
age degree of resemblance in all rings used. In addition to the closeness of 
resemblance, we are interested in the size of the area over which it exists. 
Such areas of similarity in ring growth constitute meteorological districts. 
Experience has shown that when cross-identity is perfectly evident within a 
group of trees, we can be confident that the correlation coefficients between , 
each one and the others are high. A mutual correlation coefficient of 0.85 ± 
0.02 was found in five Prescott trees having hundred-year records (see fig. 2). 
Climatic similarities have been tested also by similarities in cycles. (See 
Reports of Conferences, 1929.) Similarity in three cyclograms, shown in 
1928 (vol. II, Plate 9: 1, 2, and 3), joins Flagstaff to the areas near Aztec, New 
Mexico, 225 miles away. The trees of these regions we already knew had 
strong cross-identity. In the Flagstaff area the cycle similarities were suffi- 
ciently pronounced to date correctly unknown fragments, 125 years long, of 
records in local trees, in three cases out of four by cycles only. Such dating 
depended on a well-defined distribution of certain cycles in succession. In 
trying to date unknown fragments, 200 years long from Flagstaff, by com- 
parison with 2000 years of sequoia records, 50 per cent were dated correctly 
by cycles. This 50 per cent is far higher than would be the case in random 
results. It would be conservative to say that the chance of dating in random 
sets would have been not over 5 or 10 per cent. 

Now that we have extended the Arizona ring sequence back to A.D. 11, 
it has become possible to match one locality against another 600 miles away 
through many centuries, and we perceive resemblances which will be described 
below. 

Different sub-groups of the coast redwood have been compared by periodo- 
grams which show evident similarity and a correlation coefficient of 0.56 ± 
0.08; sub-groups of the Central Pueblo Area compared in this way gave a 
correlation coefficient of 0.76 ± 0.05; random data compared in similar man- 
ner show no correlation (0.02 ± 0.12). 

Recurrence of Cycles in Past Time — Fully dated tree-ring records have 
been extended, in California sequoias, 3200 years; and in Colorado Plateau 
pines and firs, 1900 years. These will be discussed later in the chapter. 

Periodogram Resemblance to Solar Cycles — The last item to be listed here 
forms the subject of the following chapter. 

PROBLEMS 

Representation of Cycles — Cyclogram analysis was first used in 1913 by the 
multiple plot and in 1914 and 1915 by cyclograms. Since then its use has 
been continuous. Until 1918 the best method of representing a group of 
cycles was supposed to be the periodogram. In the reconstruction of the 
analyzing instrument in 1918 the automatic periodogram was the goal. 
Photographs which realized that end were made and published in Volume I. 



86 CLIMATIC CYCLES AND TREE GROWTH 

Then the periodogram, after a trial on variable star solutions (Appendix), was 
allowed to lapse. In the next reconstruction of the instrument in 1920 under 
the name of the White Cyclograph, the periodogram part was not included. 

The manner of reporting cycles has progressed, but each stage had fol- 
lowed some time after the changes in the observing process. Until 1912 or 
even later, summated or integrated curves were used. In 1914 the Eber- 
swalde results were given in extended curves with a parallel comparison curve 
of sunspot numbers (Huntington, The Climatic Factor). In 1919 consider- 
able use was made of parallel comparison cycles, which were usually plotted 
in the original diagram by a "templet" made out of cardboard. In 1921 and 
1922 a large piece of analytical work was done on the sequoia records of the 
last 500 years, as a study of the relation of cycles to topography. No way 
was apparent for stating these results in detail, and they never have been 
so reported, although the effect of that investigation appeared in studies of 
environment (vol. II, Chapter VIII, p. 103) in 1928. 

The cyclogram itself as a method of reporting appeared in a single plate 
or two in 1919 (vol. I, Plate 12, called differential pattern) and in 1928 (vol. 
II, Plate 9). It was presented in the hope that some would study it and 
realize its efficiency. 

It is difficult to reproduce by photography the details and precision that 
are apparent in the action of the instrument itself. So in Volume II (1928) 
the very considerable analyses of the 42 western groups were reported in 
descriptive paragraphs that told something of the background of the results, 
such as the location and its topography, the aid obtained in preparing the 
curves, and the cycle lengths and weights observed. The beginnings and 
endings of these discontinuous periods were often observed, but as all the 
analyses were done by the writer, it was impossible to observe and place on 
record such additional detail in any complete form and it was generally 
omitted. 

But in this reluctance to use cyclogram demonstrations, there was prob- 
ably a different factor present in the writer, as well as in others. The fact 
that these cycles are short-lived was seen from the start of cyclogram analysis 
in 1914, but the greatness of the break from the conception of permanent 
cycles, or periods, was not really appreciated until 1932, nor the tight hold 
which the idea of permanence had upon the most enlightened students. 
Hence the present need of more detailed reports of these cycles, including 
especially their time of duration. It is hoped that later reports will contain 
a generous use of cyclograms, but some of the problems of their publication 
are not solved yet. Hence at present this analytical work is reported below 
in a tabular form. 

The analyses here presented were made extensively by Mr. Edmund Schul- 
man and compared minutely with those of the writer as performed at other 
times and for other purposes. Some cyclograms will be given to show how 
that form of presentation can be worked out for more extended use another 
time. 



ANALYSIS OF TERRESTRIAL RECORDS 



87 



The Individual versus the Group in Cycle Analysis — A group of tree records 
represents a geographical locality which may extend from an acre to a square 
mile or more. Whenever averages of such tree records are made, it means 
that the trees in the group cross-identify in the spacing of well-characterized 
rings. Therefore we recognize three methods of reaching a result for the 
group: (1) Analysis of individual records followed by a frequency periodogram 
combining all the results (see fig. 35c); (2) simultaneous (or concurrent) 
analysis of the individuals (described on page 47) and (3) analysis of the mean 
curve of the group (35a). This last was the method used by the writer in pre- 
vious published reports. Methods (2) and (3), simultaneous analysis and 
mean curve analysis, being single analyses result in sharply defined cycle 
lengths as compared to (1), which consists of analyses of many individual 




5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 



Fig. 35 — Frequency periodograms by three processes applied to the 
same data (Central Pueblo Area; 15 groups — 73 trees). 

a. Analysis of one final mean curve. 

b. Simultaneous (concurrent) analysis of 15 curves taken in 2 sets. 

c. Combination of separate analyses of the 15 curves. 



curves and the frequency periodogram combining them. In method (1) 
there are usually scattered individual values intervening between the obvious 
maxima, which have the effect of smoothing the periodogram to some extent. 
We feel that any one of the three methods gives results within the required 
order of accuracy. In the reports below, the mean curve method (3) is taken 
as a standard; that is, it has been applied in every case, but many cases 
have been checked by one or both of the other methods. 

The Two-Year "Scatter" Cycle — In short cycles of the order of two or three 
years in length, we find the maximum difficulty in separating significant from 
non-significant cycles, for in a curve of random data, cycles of two or three 
terms (usually years in our tests) are most frequent, and the frequency dimin- 
ishes as the length increases. Hence we present here some studies of the 
Two- Year "Scatter" Cycle. This cycle has characters that make us feel 



88 



CLIMATIC CYCLES AND TREE GROWTH 



that it is not to be regarded as a random effect whose variations will never 
be explained. The writer made studies of it in 1913, calling it the "2-year 
zigzag." This has been referred to in volume I, page 106, and in Astro- 
physical Journal, vol. XLI, pages 180 to 186. 

This short cycle, or zigzag, is of the highest importance in cross-identifica- 
tion and in mean sensitivity, and it has influenced the development of methods 



1800 I 
2 



20 30 40 1850 60 70 80 90 1900 10 20 30 




Fig. 36 — Two-year reversal test, to show similarity in Arizona area in short cycles. 
FAWR is Pueblo area winter rainfall; LRI (Lynch s Rainfall Indices) applies to south- 
ern California. Note: For example, the general rise toward 1900 and the minor crest 
at that date. 



of analysis because of its great amplitude. Analyses were tried extensively 
upon unsmoothed curves, but resulting cycle lengths came too often in exact 
multiples of one year (the unit used) and this was recognized as an error. 
Resort was made to a form of smoothing which would least distort the general 
march of the data, and that was the Hanned curve, as explained above. 

Next it is recognized that mean sensitivity, or the percentage variation 
from each ring thickness to the next, is very largely a measure of the amount 



ANALYSIS OF TERRESTRIAL RECORDS 89 

of this two-year zigzag. Three degrees of mean sensitivity have been shown 
in previous publications, 11 per cent in complacent sequoias, 35 per cent 
approximately in the sensitive sequoias, and about 65 per cent in the sensitive 
yellow pines of Arizona. It is a matter of investigation to find which of these 
most nearly represents the percentage variation of rainfall from year to 
year and what are the topographic features that bring the best climatic reac- 
tion. Of course, we know that the more sensitive reactions occur near the 
forest border when the trees are growing under the stress of dryness. 

But mean sensitivity is also a measure of cross-identification, and we see 
that the two-year zigzag is strongly responsible for cross-identification and 
all the important resulting operations in climatic history and chronology 
building. Viewed from the opposite direction we see that cross-identifica- 
tion, which we have used widely since 1911, indicates the presence and fair 
uniformity in action of a two-year cycle over a large area. Since the two- 
year zigzag, or scatter cycle, covers considerable areas with uniform results, 
it is not a mere random local effect. 

Our present method of re-observing these facts is the same method used 
in 1913; namely, taking the increments with signs plus or minus, from year 
to year, and reversing alternate signs and making a mass plot of the con- 
tinued algebraic sum of the resulting values. And we discover, as could have 
been expected, that the two-year cycle is very uniform over each of the three 
western zones taken by itself. For instance, figure 36 shows the mass curves 
from several locations in the Arizona zone. Here we get a fairly uniform 
general effect of the rising curve in the last 125 years to a maximum in 1880 
to 1900 and a descent thence to the present time, and a series of minor crests 
in this general curve at average intervals of 5.2 years. The latter are grouped 
for comparison in figure 37. This 5.2 years becomes a beat or interference 
effect between an exact 2.0-year cycle artificially produced by reversing 
alternate signs and a cycle of either 3.23 years or 1.44 years. Hence such 
an interval may be due to a cycle in winter precipitation of either length 
given. 1 

On examining in the same way the Coast Zone and the Rocky Mountain 
Zone we find for each a similar effect. These three results have good agree- 
ment between 1850 and 1900, but before and after that the agreement is 
poorer. This zone summary is shown in figure 37b. Figure 38 shows the 
same process applied to random data. 

One naturally inquires whether this two-year cycle could be due to some 
solar source. The sunspot cycle has been very stable since 1833, and some 
harmonic might produce an effect. Clements has attributed this short cycle 
to short cycles in monthly sunspot numbers. On the other hand, it may be 
terrestrial in origin and result from some oscillation in ocean or atmosphere. 
In any case its explanation is greatly to be desired. 

1 An attempt is being made to locate one or the other of these cycle lengths in 
monthly rainfall values, but the interruptions produced by the short winter rainy season 
necessitate careful compensations which are not yet finished. 



90 



CLIMATIC CYCLES AND TREE GROWTH 



But another situation makes such study imperative — the prediction prob- 
lem. Without a real knowledge of the two-year scatter cycle we can only 
use longer cycles for estimating the future. These are obtained from Hanned 
curves, as explained, from which the two-year cycle has been extracted by 



1810 



1850 60 



a 



I 

I I 



I I 



I I I 



I I 



I 



I 

I 

I 



I 



I ■ 

I 



I I 



I I 

i 

I 
I 

I 
I I 



I I 



I 

I 
I I 



i i.i.l 



DF(Utah) 
GC (Arizona) 
FV( Flagstaff) 

FLU •• 

FL 

LCFD „ 
(Ft. Defiance) 

RL(Rim) 

J (Rim) 

SR 

(Tucson area) 

SC 



Summary 



10 20 30 40 1850 60 70 80 90 1900 10 20 30 



1 1 


1 


1 1 


1 1 


1 


1 1 


1 


• 1 


1 


1 


<*» 


1 


1 


1 ' 


• 1 


1 . 


■ • 


1 . ■ 


ll 


1 


• 


1 1 


1 1 


I 


1 


1 1 


1. 


1 1 


1. 


1 


1 


1 


1 ,1 


.1 


1 


1 


• 1 


1' 


1 . 


1 1 


II 


1. 1 


1 1 


1 , 


1 


1 


1 1 





LRI 



Coast 



Arizona 



Rockies 



Fig. 37 — "Reversal" tests for short cycles. 

a. Lesser maxima in two-year reversal test; showing agreement, 
between groups in Arizona area. 

b. Two-year test; lesser maxima summarized for three western zones. 

smoothing. After such extraction our smoothed curves show very high cor- 
relation, 85 per cent, with similarly smoothed records of winter rainfall. 
Hence prediction by cycles thus obtained can apply only to a similarly 
smoothed curve and without the two-year cycle we can only try to predict 
what amounts to the averages between successive years. Hence the lack of 



ANALYSIS OF TERRESTRIAL RECORDS 



91 



a real two-year cycle analysis is a conspicuous weakness in any prediction 
plan. 

Whether we do or do not identify the exact cycles involved in this two- 
year variation, we must at least examine the probabilities in the case to see 
if we can make use of them in the meantime. We can bring together some 
statistical data on this point through studies of conservation in harmonic 
analysis as in Dr. Alter's correlation periodogram. In working over some 
ring records for me, he found high correlations between each value and the 
next following. At first thought that seems not to agree with the idea of 
the "zigzag" or two-year reversing cycle. So I have made use of scatter 



1810 20 30 40 1850 60 70 80 90 1900 10 20/^ 30 




Random data. LCFD 
Fig. 38 — Two-year reversal tests on random data. 



diagrams to bring out the relationship between each annual value and the 
next following. 

Figure 39 is a scatter diagram to show the relation between successive 
values, whether quantities above a constant base or departures from a con- 
stant mean. Here we have an obvious positive correlation in the evident 
oval of relationship extending up to the right at 45° inclination. If, however, 
we take the departures from a Hanned curve, such as we use in cycle analysis 
— in short, if we take the plus and minus values discarded when we smooth 
the curve for analysis — then we get figure 40a, which has an oval cloud of 
dots whose major axis extends up to the left at 45° or at right angles to the 



92 



CLIMATIC CYCLES AND TREE GROWTH 



former oval and indicates a negative correlation between successive values. 
This changed major axis indicates in the discarded residuals a strong zigzag 
that we need so much for prediction purposes. The axes of the oval have a 
ratio one to the other of 2.3:1.0 and suggest a negative correlation of about 
75 per cent between successive departures from the smoothed curve. 

Information obtained in the last paragraph is important for prediction 
purposes. But in using it we must not forget that random data treated in 
similar manner always give theoretically a ratio over unity. Quoting Dr. 



* 

o 












o 








5 

c 

(0 



P ° 

t >0 

E 
o 

3 

-4-> 

L. 

nj 










^, — 





°^\ 












o 
o 


o 
e 


o 


o y 


\ 

• \ 


o 




/ 
/ 


• 
o 


o 
e 


e 

o ° 

e 

o 


/ o 


o 

1 


' 1 
•1 

/ 




Q 

i 
c 

ID O 


y. 

/ 


/ 


• 


1 

o 

o 


o / « 





oo 

o 


/ . 




-00 

c 
* o 


¥ 

1 

1 • 


e 
e 


e 
o 


1 > 
•/ o 


o 
o 
e 


o o 


V 

/ 






o ~ 
r S 


1 

1 

\ 


o 
o 



o 




o 
o 

o 


o ° 

• 




o 

• 






s 


\ 
\ 


o / 
e / 


3 

e 

o 

i 


o 

o 




/ 










o 


o 


o 












i 


3 C 


3 i 


3 c 
e o 


i 


3 C 
I 


> c 


\ \ 


) a 


I 9 

J 2 



Minus Plus 

The year itself- Departure from mean 

Fig. 39 — Conservation in successive years in Fort Defiance group, 
shown by scatter diagram using departures from a mean 



Bartels, we may have a series of random values, but the differences between 
those values are not entirely random, and if we smooth the data as usually 
done, there is increased chance that successive values will be on opposite 
sides of the smoothed sequence. In a scatter diagram of such random rela- 
tion, the theoretical mean form of the oval should have a ratio of axes of 
1.3:1.0. Therefore, to retain a clearer estimation of the situation we have 
added three curves of the two-year reversal interference test on random 
values in figure 38. They show no relation to each other and thus are very 
different from the action of natural sequences in our western zones. We 



ANALYSIS OF TERRESTRIAL RECORDS 



93 



have also prepared a scatter diagram of relation between successive depar- 
tures from a Hanned mean of random values in figure 40b, which gives a 
circular cloud of dots and therefore is without indication of negative correla- 
tion in successive values. 

The solution of the two-year cycle with its difficulties of distribution 
about the earth has a reasonable chance of being successful; we have now 
an idea of its general action, and by prediction on the basis of short cycles 
and then applying the probable residual derived from the inclined axis of 
figure 40a, we reach the most probable value at this time available. 



40 



!20 



•oo 

•I • 



I c20 
t-'2 



/ 

/ ° 



\> „ 



40 — 

40 



— ^- 



i : 



\ 



\ * 



\ 



^T 



\ 



y .\ 



v 



.«••. 






3^ 



a ft 




20 20 

Minus Plus 

The year itself 
CL 



40 40 20 20 

Minus Plus 

The year itself 
ft 



Fig. 40 — Successive year conservation in departures from a smoothed curve, 
Fort Defiance group (a) in natural data; (b) in random data. Same 
scale as fig. 39. 



CYCLES IN 42 WESTERN GROUPS 

The groups here listed are indicated by the letters used in the former re- 
port, Volume II, Climatic Cycles and Tree Growth, Chapter VII, to which 
reference is made for details of location and collection of specimens and re- 
duction of data. 

The assignment below of exact values in cycle length has seemed advisable 
in order to show the figures on which amplitudes have been computed. Re- 
membering that cycle lengths are subject to errors of 1 to 3 per cent, the 
reader will be able to find identity in many of these that differ less than this 
percentage. The cycle lengths given here are used to form the periodograms, 
figure 41. In these tables the underlines may be taken as nearly equivalent 
to weights. The rows, also sometimes called "sets," are the number of 
repetitions of the cycle length. The second and last columns refer to the 
summation curves in the appendix (see p. 155). Some of the results here 
presented will be slightly modified after subtracting dominating interfering 
cycles. It should be recognized that this is the first attempt to group a large 
number of discontinuous periods together. We expect that more experience 
will show better how to do it. Therefore we must regard this as a series of 



94 



CLIMATIC CYCLES AND TREE GROWTH 



42 Western Groups 1 



Strong Cycles 


Curve 


Number 


Cycle 


Under- 
lines 


Duration 


First 
max. 


Rows 


P. ct. 
Amp. 


A. D. 

ratio 


Vertical 
scale 


BMH 


14 


8.7 


1 


1622-1691 


1628 


8 


15 




0.4 


AE 


6 


7.7 


1 


1740-1916 


1747 


23 


10 




1.0 




16 


9.7 


1 


1723-1916 


1724 


20 


7 


1.02 


1.0 


C 


9 


7.9 


1 


1778-1920 


1779 


18 


9 


1.15 


1.0 




73 


22.3 


1 


1780-1913 


1793 


6 


16 




0.4 


HNT 


56 


18.6 


2 


1828-1920 


1840 


5 


19 


1.50 


0.4 




74 


22.3 


3 


1675-1852 


1680 


8 


23 


1.55 


0.4 




92 


33.3 


1 


1655-1920 


1673 


8 


18 




0.4 


Y 


13 


8.6 


1 


1755-1917 


1758 


19 


4 




1.0 




20 


10.0 


1 


1700-1789 


1709 


9 


7 


1.25 


0.4 




52 


16.9 


2 


1752-1920 


1769 


10 


11 




0.5 




78 


23.6 


1 


1764-1917 


1772 


6i 


11 




0.4 


LNT 


65 


20.2 


1 


1644-1916 


1652 


13* 


9 




0.4 


CC 


19 


9.9 


1 


1742-1840 


1746 


10 


13 


1.57 


0.2 




22 


10.1 


1 


1840-1920 


1847 


7 


9 




0.4 




51 


15.3 


1 


1737-1920 


1746 


12 


13 




0.4 


BES 


35 


12.3 


2 


1775-1909 


1779 


11 


10 


1.38 


1.0 


SF 


21 


10.0 


1 


1824-1913 


1827 


9 


10 


1.41 


0.4 




97 


37.0 


1 


1752-1918 


1755 


4* 


25 




0.2 


BML 


26 


10.5 


1 


1700-1909 


1700 


20 


6 




1.0 




82 or 


24.7 


1 


1716-1875 


1721 


6J 


15 




0.4 




77 or 


23.4 


2 


1700-1910 


1722 


9 


21 


1.45 


0.4 


PPT 


1 


5.8 


1 


1738-1917 


1739 


31 


1 




1.0 




30 


11.6 


1 


1738-1911 


1739 


15 


3 




1.0 




54 


17.4 


1 


1738-1911 


1745 


10 


6 




1.0 




100 


42.0 


1 


1738-1905 


1750 


4 


16 




0.5 


LW 


2 


6.2 


1 


1759-1919 


1760 


26 


4 




0.4 




28 


11.3 


1 


1759-1916 


1768 


14 


10 


0.97 


0.5 




93 or 


33.5 


1 


1758-1924 


1769 


5 


30 




0.5 




96 or 


35.0 


1 


1765-1904 


1768 


4 


34 




0.2 


ST 


17 


9.8 


2 


1754-1920 


1765 


17 


7 




0.5 




64 


19.8 


2 


1743-1920 


1756 


8J 


13 




1.0 


BDF 


10 


7.9 


1 


1782-1915 


1788 


17 


8 


1.42 


1.0 




18 


9.8 


1 


1782-1918 


1787 


14 


7 


0.95 


1.0 




59 


19.0 


1 


1826-1920 


1839 


5 


20 




0.4 


SR 


75 or 


23.0 


2 


1670-1921 


1677 


11 


21 


1.45 


0.4 




72 or 


21.6 


2 


1673-1845 


1681 


8 


27 




0.4 




87 


27.2 


1 


1673-1835 


1676 


6 


21 


1.02 


0.4 


sc 


50 


15.2 


2 


1567-1657 


1571 


6 


20 




0.4 




91 


31.7 


1 


1567-1820 


1575 


8 


20 




0.4 




95 


34.9 


1 


1660-1920 


1670 


7i 


21 




0.4 


PNL 


84 or 


26.7 


1 


1792-1911 


1799 


4* 


37 




0.4 




88 or 


27.2 


1 


1765-1914 


1772 


5* 


31 




0.4 


RH 


24 


10.2 


1 


1860-1920 


1867 


6 


12 




0.5 




46 


14.3 


1 


1760-1916 


1766 


11 


10 


1.49 


0.4 


DF 


61 


19.3 


1 


1760-1913 


1773 


8 


12 


1.67 


0.4 




15 


8.8 


1 


1717-1918 


1722 


23 


2 


0.69 


1.0 


SH 


5 


6.8 


1 


1744-1920 


1750 


26 


4 




0.4 




38 


13.4 


3 


1717-1917 


1718 


15 


22 




0.2 




57 


18.7 


2 


1753-1902 


1756 


8 


32 




0.2 




86 


27.0 


1 


1717-1919 


1718 


7* 


32 




0.1 




98 


37.0 


3 


1717-1920 


1720 


5* 


54 


1.44 


0.1 


RL 


11 


8.0 


1 


1770-1913 


1772 


18 


6 


1.11 


1.0 




60 


19.2 


2 


1770-1903 


1774 


7 


27 


1.53 


0.4 




99 


38.5 


2 


1770-1903 


1791 


3* 


44 




0.2 


FLH 


42 


13.5 


1 


1768-1915 


1771 


11 


8 




0.4 




63 


19.5 


1 


1768-1903 


1772 


7 


12 




0.4 




67 or 


20.4 


1 


1680-1924 


1689 


12 


13 




0.4 



J For column headings see pp. 154-156. 



ANALYSIS OF TERRESTRIAL RECORDS 



95 



4$ Western Groups — Continued 









Strong Cycles — 


Continued 








Curve 


Number 


Cycle 


Under- 
lines 


Duration 


First 
max. 


Rows 


P. ct. 
Amp. 


A. D. 

ratio 


Vertical 
scale 


FLU 


44 


13.6 


2 


1755-1917 


1758 


12 


11 


1.54 


0.5 




68 


20.5 


1 


1755-1917 


1767 


8 


13 




0.4 




89 


27.3 


1 


1700-1917 


1717 


8 


13 




0.4 


J 


80 


24.1 


2 


1760-1916 


1770 


6* 


36 




0.4 




83 or 


24.8 


2 


1655-1902 


1668 


10 


24 




0.4 


NE 


29 


11.5 


1 


1751-1922 


1759 


15 


20 


1.72 


0.4 




45 


13.6 


2 


1755-1917 


1757 


12 


15 


1.10 


0.4 




58 


18.7 


1 


1755-1922 


1759 


9 


26 


1.66 


0.4 


GC 


49 


15.0 


1 


1716-1865 


1717 


10 


24 




0.4 




81 


24.2 


2 


1716-1909 


1720 


8 


27 


1.42 


0.2 


FV 


39 


13.4 


1 


1750-1870 


1759 


9 


16 




0.4 


FL 


40 


13.4 


2 


1764-1910 


1777 


11 


7 


0.80 


1.0 




62 


19.4 


1 


1765-1900 


1672 


7 


12 




0.5 




90 


27.3 


2 


1765-1900 


1776 


5 


12 




1.0 


PV 


47 


14.4 


2 


1755-1826 


1759 


5 


28 


1.44 


0.2 


DL 


4 


6.5 


1 


1765-1920 


1767 


24 


9 




0.4 




37 


12.7 


2 


1765-1916 


1769 


12 


11 




0.5 


CH 


3 


6.4 


2 


1757-1852 


1761 


15 


20 


1.85 


0.5 




55 


18.1 


1 


1723-1921 


1730 


11 


14 




0.4 


CP 


12 


8.1 


1 


1596-1757 


1602 


20 


4 




0.2 


SB 


79 


24.0 


2 


1819-1915 


1826 


4 


28 




0.4 


BO 


36 


12.6 


1 


1711-1924 


1712 


17 


14 




0.4 




70 


21.1 


1 


1660-1891 


1669 


11 


26 




0.2 




101 


42.0 


1 


1660-1911 


1670 


6 


42 


1.45 


0.2 


BI 


23 


10.1 


1 


1657-1797 


1661 


14 


7 




0.5 




32 


11.7 


2 


1776-1915 


1780 


12 


8 


1.27 


1.0 




43 


13.5 


1 


1653-1814 


1657 


12 


10 




0.4 


W 


53 


17.3 


2 


1753-1925 


1768 


10 


10 




0.2 




94 


34.3 


1 


1753-1925 


1770 


5 


20 




0.1 


EP 


7 


7.7 


2 


1827-1918 


1831 


12 


10 




0.5 




31 


11.6 


1 


1785-1912 


1792 


11 


14 


1.50 


0.5 




41 


13.4 


2 


1755-1915 


1762 


12 


14 


1.66 


0.5 




85 


26.8 


1 


1755-1915 


1775 


6 


20 




0.4 


BC 


25 


10.3 


1 


1735-1878 


1738 


14 


5 




0.5 




33 


11.7 


2 


1788-1916 


1790 


11 


9 




0.4 




69 


20.6 


2 


1755-1919 


1769 


8 


10 




0.4 


CVP 


8 


7.7 


2 


1813-1920 


1816 


14 


8 




0.4 




66 


20.3 


1 


1750-1922 


1751 


8* 


12 




0.4 


OC 


27 


10.6 


2 


1717-1886 


1720 


16 


7 




0.4 




34 


11.7 


1 


1732-1907 


1739 


15 


5 




0.4 




48 


14.4 


2 


1768-1911 


1775 


10 


7 




0.4 




71 


21.1 


1 


1710-1910 


1711 


9§ 


7 




0.4 




76 


23.2 


1 


1710-1895 


1716 


8 


8 




0.4 









Weak Cycles 










Curve 


Number 


Cycle 


Duration 


First 
max. 


Rows 


P. ct. 
Amp. 


A. D. 

ratio 


Vertical 
scale 


BMH 


105 


7.6 


1758-1894 


1763 


18 


5 


1.32 


1.0 




107 


10.1 


1638-1859 


1641 


22 


7 


1.22 


1.0 




111 


11.9 


1618-1891 


1628 


23 


3 




1.0 




116 


17.3 


1744-1916 


1747 


10 


14 




0.4 




117 


18.0 


1630-1737 


1635 


6 


16 


1.29 


0.2 




122 


23.9 


1622-1884 


1628 


11 


16 


1.48 


0.4 


AE 


102 


5.9 


1723-1911 


1728 


32 


5 


1.29 


0.5 




118 or 


18.2 


1720-1919 


1726 


11 


12 




0.5 




119 or 


19.5 


1723-1917 


1732 


10 


11 


0.85 


0.4 




121 or 


23.4 


1723-1909 


1723 


8 


30 




0.4 



96 



CLIMATIC CYCLES AND TREE GROWTH 



42 Western Groups — Concluded 



Weak Cycles — Continued 


Curve 


Number 


Cycle 


Duration 


First 
max. 


Rows 


P. ot. 
Amp. 


A. D. 

ratio 


Vertical 
scale 


c 


108 


10.2 


1790-1911 


1796 


12 


7 


1.35 


0.5 




110 


11.2 


1780-1913 


1781 


12 


11 


1.28 


0.4 




115 


15.3 


1780-1917 


1782 


9 


10 


1.35 


0.4 




120 


19.5 


1795-1911 


1796 


6 


17 




0.4 


HNT 


106 


9.3 


1760-1917 


1765 


17 


4 


0.92 


0.5 




109 


11.1 


1760-1914 


1760 


14 


7 


1.01 


1.0 




113 


13.4 


1760-1920 


1761 


12 


4 


0.84 


1.0 




114 


14.7 


1759-1920 


1771 


11 


12 


1.31 


0.5 


Y 


103 


6.2 


1700-1761 


1703 


10 


6 




0.5 




104 


6.5 


1787-1916 


1790 


20 


3 


0.88 


1.0 




112 


12.7 


1700-1915 


1703 


17 


5 


1.15 


1.0 



Preferred Cycles (Supplementary Group) 



Curve 


Number 


Cycle 


Under- 
lines 


Duration 


First 
Max. 


Rows 


P. ct. 
Amp. 


Vertical 
Scale 


LW 


129 


8.2 


2 


1754-1917 


1761 


20 


12 


0.4 


ST 


141 


17.2 




1749-1920 


1757 


10 


07 


0.5 


BDF 


147 


20.4 




1782-1913 


1793 


6J 


19 


0.4 


SR 


139 


14.4 




1749-1921 


1754 


12 


13 


0.5 


SC 


143 


17.4 




1747-1920 


1757 


10 


13 


0.5 


PNL 


128 


7.6 




1760-1919 


1763 


21 


09 


0.5 


RH 


146 


19.9 




1750-1918 


1767 


8* 


13 


0.5 


FLH 


125 


6.9 




1750-1921 


1757 


25 


02 


0.5 




142 


17.3 




1750-1922 


1754 


10 


09 


0.4 


GC 


149 


20.8 




1750-1915 


1765 


8 


27 


0.4 


FV 


148 


20.5 




1750-1913 


1766 


8 


23 


0.4 




161 


35.0 




1746-1920 


1767 


5 


26 


0.2 


FL 


126 


6.9 




1750-1908 


1757 


23 


05 


1.0 


PV 


159 


32.0 




1750-1909 


1761 


5 


27 


0.2 


DL 


127 


7.2 




1765-1922 


1765 


22 


03 


1.0 




138 


14.2 




1765-1920 


1772 


11 


14 


0.4 




140 


16.4 




1765-1920 


1766 


10 


17 


0.5 


KF 


156 


24.2 




1792-1912 


1813 


5 


22 


0.5 




158 


31.2 




1792-1916 


1800 


4 


21 


0.4 


CP 


157 


28.6 




1750-1921 


1755 


6 


16 


0.2 


SB 


154 


23.0 




1819-1910 


1829 


4 


28 


0.4 




133 


9.8 




1819-1921 


1826 


10* 


10 


0.5 


BO 


136 


11.3 




1750-1918 


1757 


15 


03 


0.5 


W 


134 


10.4 




1749-1925 


1749 


17 


04 


0.4 




152 


22.5 




1746-1925 


1748 


8 


12 


0.1 


BC 


151 


21.7 


2 


1746-1919 


1747 


8 


19 


0.2 


CVP 


123 


6.8 




1750-1919 


1751 


25 


04 


1.0 




150 


21.2 




1750-1919 


1751 


8 


13 


0.4 


OC 


153 


22.6 




1750-1907 


1751 


7 


05 


0.4 


BMH 


162 


35.0 




1745-1919 


1767 


5 


23 


0.4 


AE 


155 


24.0 


2 


1750-1917 


1768 


7 


23 


0.4 


C 


132 


9.3 




1778-1916 


1784 


15 


08 


0.5 




145 


18.8 




1778-1918 


1793 


7* 


15 


0.5 


HNT 


124 


6.8 




1750-1919 


1752 


25 


05 


1.0 




130 


8.6 




1749-1920 


1751 


20 


04 


0.5 




160 


34.5 




1749-1920 


1769 


5 


24 


0.4 


LNT 


135 


11.1 




1750-1915 


1760 


15 


06 


1.0 


BES 


131 


8.9 




1775-1916 


1783 


16 


07 


0.5 




137 


14.1 




1775-1915 


1787 


10 


08 


0.5 


SF 


144 


18.4 




1750-1915 


1761 


9 


11 


0.4 



ANALYSIS OF TERRESTRIAL RECORDS 



97 



preliminary results, subject to improvement but certainly showing at this 
time some of the general facts. The summary in a frequency periodogram, 
fig. 55, contains a significant generalization from these data. 

Evaluation of Cycles in the 42 Groups — The preceding lists contain the 
results of analyses by Mr. Schulman of the 42 Western groups with special 
attention given to the dates of beginning and ending of cycles. About 100 
cycles which he had "underlined" form perhaps the basis of the list; under- 
lining means 1 that they showed signs of special strength; approximately 175 
apparently weak cycles in addition to those listed are here omitted. But 
he has included some 40 cycles observed by the writer and reported in Volume 
II (1928, Chapter VII). They have been observed by Mr. Schulman but 
were not underlined. They are, he says, equivalent to a preferred set of 
values without underline. 





Solid line-E.S. 

Dotted line 
A.E.D. 
































- % 
















/, 


,\ 










u' 


\ 










/ 






/ 


-^ 






-- 


," 






ij 


\ 


f s 


X / 






\ 






















;/ 








































; 


Weak cycles 




















































































h- 


Strong cycles 










i 


\ 




































/ 






\ 


f 


k / 












/ 


\ 




s 


/ 


* k 


\ 










r 


A 


/ 


Vx 


J 


\ 


/ 


\J 








/ 


1 vj 


r 








■j 




\ 















































12 13 14 15 

Years 



.16 17 13 19 20 21 22 23 24 25 



Fig. 41 — Frequency periodograms of 42 Groups : 

(a) obtained by two independent observers. 

(b) weak and strong cycles compared (as recorded by Schulman). 



The amplitudes listed were determined by the usual arithmetical summa- 
tion process described in a previous chapter. By actual tests it was found 
that amplitudes are not changed to any appreciable extent in that summation 
by letting some rows run one unit beyond the other rows, as is necessary in 
testing fractional periods (periods that are not integers: See Chapter II). 
After plotting the summated curve, the amplitudes were measured on the 
plots and the value quoted is essentially half the range from the lowest to 
the highest point of the plotted and smoothed curve. The difficulty was 
encountered that the curves were not always of simple and regular type. 
Often there were secondary crests that are non-symmetrical so that the curve 
can not be classed as a multiple. That is quite characteristic of natural 
sequences. 

These summations have formed the basis of a study by Mr. Schulman of 
the meaning of underlines in terms of certain statistical quantities. He finds 

1 See also pages 146 and 147. 



98 



CLIMATIC CYCLES AND TREE GROWTH 



that when the underlining is compared with the amplitude and the A.D. 
ratio, both the percentage amplitude and the A.D. ratio increase with the 
stronger emphasis of each additional underline. In every class, however, 
there is a large amount of scatter about the mean relations between these 
three quantities. The source of the scatter lies in two factors: First, each 
of the four or five underline classes covers a considerable variation in em- 
phasis and hence each estimate of underlines has a personal element. Second, 
many cycles which were quite strong in the cyclogram yield on summation 
small amplitudes and A.D. ratios due to interfering cycles; in other words 
the form of the cycle, the relation of the interfering cycles, and the brevity 
of the data, have not permitted the satisfactory cancellation of the interfer- 
ing effects on which the summation process is based. It is evident that the 
cycle underlining is perhaps fully as important as the percentage amplitude 
or the A.D. ratio. 

There is evident within each emphasis class a systematic decrease in per- 
centage amplitude with increase in the number of rows; this arises partly 
because the number of cycle repetitions is one of the factors considered in 
assigning underlines. 

The preceding discussion is based on the following tables: 



Cycle emphasis class 



2 underlines, ES 
1 underline, ES 
No underlines, ES 

Addit. underl., AED 



Frequency 


Ave. No. 
of Rows 


Mean 
Amp., 
p. ct. 1 


Ave. Dev. 

of Amp., 

p. ct.i 


Mean Amp. 


Ave. Dev. 


36 
66 
19 

41 


9.8 
11.6 
12.6 

11.5 


18.6 
13.9 
10.4 

13.2 


±8.6 
±6.8 
±4.8 

±6.4 


2.16 
2.05 
2.16 

2.06 



Ave. Duration 
Yrs. 



151 
165 

169 (for 195 
cycles) 



Cycle emphasis class 



2 underlines, ES 
1 underline, ES 
No underlines, ES 



Frequency 1 



15 
17 
13 



Ave. A. D. 
ratio 



1.43 
1.30 
1.18 



Stand. Dev. 



±.23 
±.29 
±.20 



A. D. Ratio 



Stand. Dev. 



6.2 
4.5 
5.9 



Mean Amp. 
p. cU 



20.3 

13.2 



Percentage refers to mean ring thickness. 

2 This table includes only cases in which the A. D. ratio had been computed. 



RECORDS OF PAST CLIMATES 

The preceding lists have contained the analyses of many tree-ring records 
that originated in modern times, chiefly since 1750. Those records came 
from thousands of square miles of area and showed similarity in the general 
characters of climatic change for that region. Now we deal with the cog- 
nate idea of extension in time. Appropriate questions at once occur to us: 
If two areas have agreed for the last 150 years, did they agree for the last 
1500 years or more? If the discontinuous periods in climate show resem- 
blance to the sun in the last hundred years while the sunspot cycle was stable, 
did they show resemblance during the preceding hundred years when the 



ANALYSIS OF TERRESTRIAL RECORDS 99 

sunspot cycle was unstable? Can we infer a length of the sunspot cycle and 
dates of maxima or minima from tree records extending back 1900 years in 
Arizona and 3200 years in California, the California records though longer 
having a less well-established relation to rainfall? And, more important 
than the other questions perhaps, can we find evidence of recurrence of the 
same cycle; is there some plan on which it comes back; and can we infer 
any probability of its return at a definite time? Such knowledge would 
compensate for some of the difficulties introduced by the temporary character 
of climatic cycles. What of the cycles in the much more distant past? 
Good tree records are available from tertiary sources, say 50,000,000 years 
ago, perhaps very much more, and sediments carry us to much more distant 
ages. Do we get any hints from these sources regarding the stability or 
instability of our sun? 

We have at this time two types of records of past climates: namely, 
accurately dated records in Arizona and California, abundantly cross- 
identified in great numbers of trees, and, second, undated geological records 
in fossil trees largely without cross-identification, and in sediments with 
cross-identification, in all of which cycles may be studied. 

SEQUOIA CHRONOLOGY AND CYCLE RECURRENCE 

The difficulty with the study of cycles in climate has been the limited 
lifetime or duration of any one cycle. The favorable possibility of finding 
a definite recurrence of cycles has been recognized since 1927, and the great 
sequoias have seemed the most promising location for the search. We have 
in our laboratory 50 radials of these trees, of which about half show 2000 
rings or more, and four extend back 3100 years; one reaches to 1305 B.C. 
They fall into two groups, the Grant Park sequoias and the Springville se- 
quoias, some 40 miles apart. It was discovered about 1921 that the double 
sunspot cycle of 22 or 23 years is more common in these trees than the 11- 
year cycle. The pine tree curve of the Sierra Nevadas resembles the se- 
quoias in giving prominence to a cycle of about 23 years. A correlation 
periodogram of this series of data by Dr. Alter, reproduced in figure 53, 
shows a pronounced crest at about 22^ years and its multiples, thus confirm- 
ing these results. 

In 1927 a study was made of several different sequoia groups in which 
the presence of the solar influence had been suspected. Trials of a 23-year 
cycle give us a series of curves each 23 years long, that are consecutive and 
continuous through nearly 3000 years and each curve is a running or over- 
lapping mean of three successive 23-year intervals. 

A large percentage of these 130 curves show clearly a 23-year cycle or 
some subdivision of it up to five equal parts. The division into 4 parts is 
illustrated in figure 42. Of course, this work is far from finished, but these 
results apparently agree in the two separated sequoia groves. Limited 
checking has also been carried successfully to other sequoia groupings that 
for various reasons have been segregated. As a matter of safety a couple 



100 



CLIMATIC CYCLES AND TREE GROWTH 



of hundred years of sequoia values were "scrambled" and then treated by 
the same integration method, as shown in figure 43. So we learned that the 
manner of smoothing eliminates two-year cycles which in turn leaves three- 
year cycles or eight crests in the curve most numerous (theoretically), seven 



1.00 
0.90 
0.80 





A.D. 132-200 
(155-177) 



A.D. 155-223 
(178-200) 



A.D. 178-246 
(201-223) 




A.D. 201-269 

(224-246) 




A.D. 155-269 



J I L 




Mean curve 



J_l L 



O a 4 6 8 10 12 14 16 18 20 22 23 

Fig. 42 — Hellmann cycle in sequoias, A.D. 155 to 246, using 
"triple lag" method. Note: dotted lines represent the 
original unsmoothed means. 



crests next and so on. One scrambled curve has five crests, and one has 
four, showing that some of the fractionizing in the real curve may be acci- 
dental, especially in isolated cases. In the scrambled curves the same frac- 
tion does not occur twice in succession; but in the natural curves the same 



ANALYSIS OF TERRESTRIAL RECORDS 



101 



occurs three to five or more times in succession and the cycles seem to merge 
as they change and the chances are greatly against accident. As the length 
of the fraction increases, for example, from 4| to 1\ years, accident becomes 
less and less likely. So even three curves in succession showing three sub- 




A.D. 
1213-1327 



2 4 6 8 10 12 14 16 18 20 2223 
Fig. 43 — Scrambled sequoia values tested by "triple lag" method. 



divisions are very probably real. We find, for example, a Hellmann cycle 
lasting from about 1760 to 1910 or so, an interval of 150 years containing 
more than 25 repetitions, as appears in figure 44. It does not disappear 
during the changes in the sunspot cycle near 1800. 



1.00 — 
0.90 — 
0.80 — 



1742 




1903 






1111 



I I I I < I 



2 4 6 8 10 12 14 16 18 20 22 
Years 

Fig. 44 — Hellmann cycle in recent sequoia records. Running means of three 
successive cycles of 23 years ("triple lag" method, incomplete after 1891). 

102 



ANALYSIS OF TERRESTRIAL RECORDS 



103 



In these 130 curves, covering the age of the sequoias, a recurrence cycle 
of about 270 years seems to be a common character, as shown in this prelimi- 
nary study. A cycle about 100 years long is common to them all and some- 
thing near 220 years is seen occasionally. Ordinary cycles of all these values 
are mentioned by Turner. Something near 300 years is discussed by Clough. 
Dr. Alter mentions 250 years for possible recurrence. The double value near 
560 years probably exists in our data, and it is possible that it will prove im- 
portant. In order to visualize the possibilities, a 275-year length is taken 
as a workable solution for the time being. A provisional pattern based on 
this 275-year recurrence is shown in figure 45. This diagram shows the 
sequence of different short cycles in the 275-year pattern derived from 2000 




Fig. 45 — Average cycle recurrence in Grant Park sequoias in 2100 years. 



years of the Grant Park sequoias and is a very promising sign at the present 
time. In it we find that the persistence of the Hellmann cycle since 1750 
agrees with previous recurrences of that cycle. If the various cycles con- 
tinue as they have done, we have some reason to expect that through the 
next 70 years this Hellmann relation should be less conspicuous or absent, 
with a probability of replacement by a 23-year cycle or the same divided 
into five equal parts. 

This pattern therefore encourages us to hope that from the giant sequoias, 
checked by historical material, we shall obtain in some form of cycle sequence 
a real step forward toward a theory of climatic change and long-range pre- 
diction. This is the thought that inspires our attack upon the cycles in 
the long chronologies. 



104 



CLIMATIC CYCLES AND TREE GROWTH 



Sequoia Chronology 1 Cycles 



Cycle, yrs. 


Number 


Underl. 


Duration 


First Max. 


Rows 


P. ct. Amp. 


AD Ratio 


4.9 


163 


2 


1188-1241 


1190 


11 


6 




5.0 


164 


1 


370-499 


370 


26 


3 




5.2 


165 


1 


018-059 


019 


8 


4 




5.2 


166 


no 


782-869 


785 


17 


3 


1.44 


5.2 


167 


no 


1812-1910 


1816 


19 


2 


0.98 


5.6 


168 


no 


215-298 


217 


15 


3 




5.7 


169 


no 


1777-1913 


1781 


24 


4 


1.84 


6.2 


170 


1 


1295-1412 


1300 


19 


4 


2.08 


6.2 


171 


1 


1468-1566 


1471 


16 


5 


2.28 


6.2 


172 


no 


1755-1810 


1755 


9 


8 


2.22 


6.3 


173 


no 


376-501 


376 


20 


2 




6.5 


174 


no 


585-850 


590 


41 


2 


1.08 


6.6 


175 


1 


000-118 


000 


18 


2 




6.6 


176 


2 


226-291 


227 


10 


3 




6.7 


177 


1 


1070-1156 


1076 


13 


5 


1.32 


6.7 


178 


1 


1157-1263 


1160 


16 


3 


1.14 


6.9 


179 


1 


293-368 


296 


11 


6 


1.48 


7.0 


180 


1 


000-146 


003 


21 


2 




7.1 


181 


no 


798-889 


800 


13 


4 




7.3 


182 


no 


1650-1773 


1651 


17 


3 


1.20 


7.5 


183 


1 


450-606 


454 


21 


3 




7.6 


184 


1 


1010-1123 


1011 


15 


4 


1.80 


7.7 


185 


1 


000-114 


004 


15 


4 


1.17 


7.7 


186 


1 


1250-1349 


1252 


13 


4 


1.24 


8.1 


187 


no 


690-762 


693 


9 


7 


1.77 


8.2 


188 


no 


955-1093 


960 


17 


4 


1.04 


8.6 


189 


1 


360-445 


367 


10 


9 


1.63 


8.7 


190 


1 


226-295 


234 


8 


4 




8.9 


191 


X 


1315-1403 


1319 


10 


5 


1.27 


9.2 


192 


1 


033-207 


037 


19 


6 


1.82 


9.2 


193 


no 


630-684 


635 


6 


10 


1.69 


9.7 


194 


no 


877-983 


882 


11 


5 




9.7 


195 


1 


1730-1807 


1732 


8 


8 


1.49 


9.9 


196 


1 


1140-1238 


1141 


10 


6 


1.24 


10.5 


197 


1 


765-1121 


770 


34 


3 




10.5 


198 


1 


1650-1733 


1653 


8 


4 


1.06 


10.5 


199 


1 


1812-1905 


1816 


9 


5 


1.50 


10.7 


200 


no 


800-895 


806 


9 


6 




10.7 


201 


no 


896-1120 


906 


21 


3 




11.2 


202 


1 


677-844 


681 


15 


6 


1.43 


11.2 


203 


no 


350-517 


360 


15 


2 




11.2 


204 


no 


518-674 


526 


14 


5 




11.4 


205 


2 


1777-1913 


1780 


12 


7 


1.60 


11.5 


206 


no 


87-235 


090 


13 


9 




11.8 


207 


2 


1238-1343 


1247 


9 


11 


1.81 


12.1 


208 


1 


1300-1420 


1307 


10 


5 


1.05 


12.1 


209 


2 


1457-1565 


1465 


9 


5 


1.09 


12.1 


210 


2 


1590-1650 


1592 


5 


6 


1.25 


12.6 


211 


1 


360-498 


369 


11 


6 


1.26 


13.1 


212 


1 


000-222 


009 


17 


5 




13.1 


213 


2 


363-768 


365 


31 


5 


1.73 


13.3 


214 


1 


1722-1907 


1733 


14 


7 


1.29 


13.6 


215 


no 


220-355 


233 


10 


6 




14.4 


216 


no 


1650-1750 


1651 


7 


6 


1.34 


14.6 


217 


1 


043-173 


045 


9 


10 


1.25 


15.0 


218 


no 


345-449 


351 


7 


5 




15.1 


219 


no 


1200-1305 


1214 


7 


10 


1.24 


15.2 


220 


no 


000-242 


006 


16 


4 




15.3 


221 


no 


1647-1799 


1648 


10 


6 




15.7 


222 


no 


800-893 


807 


6 


6 




15.9 


223 


no 


1250-1424 


1258 


11 


5 


1.28 



1 For column titles, see p. 154. Percentage amplitude is in terms of mean ring thick- 
ness. Vertical scale is normal for all summation curves, that is, 10 per cent per division. 



ANALYSIS OF TERRESTRIAL RECORDS 



105 



Sequoia Chronology Cycles — Concluded 



Cycle, yrs. 


Number 


Underl. 


Duration 


First Max. 


Rows 


P. ct. Amp. 


AD Ratio 


15.9 


224 


1 


1794-1904 


1799 


7 


8 


1.57 


16.4 


225 


1 


900-1194 


903 


18 


7 


1.51 


17.0 


226 


1 


1500-1907 


1509 


24 


5 


1.11 


18.3 


227 


X 


1300-1738 


1313 


24 


4 




19.2 


228 


no 


000-210 


002 


11 


6 




19.4 


229 


no 


350-853 


363 


26 


3 




20.3 


230 


no 


1400-1906 


1401 


25 


5 




22.1 


231 


no 


800-1296 


814 


22* 


5 




22.3 


232 


no 


1250-1740 


1260 


22 


4 




23.0 


233 


no 


1740-1900 


1745 


7 


10 


1.27 


23.2 


234 


no 


700-977 


710 


12 


5 





The author's analysis of the sequoia chronology was largely done in 1918; this was 
reviewed more recently at various times. Mr. Schulman did this work on these data in 
the last year; the tabular matter here given is based on Mr. Schulman's results, checked 
by the author's. Amplitudes have been worked out under the direction of Dr. W. S. 
Glock, Mr. Edmund Schulman, and Mr. G. C. Baldwin. 

CENTRAL PUEBLO CHRONOLOGY 

The sequoia chronology just described is taken from continuous tree 
records of extraordinary length: four of the trees show more than thirty 
centuries and large numbers reach 2000 years. In sharp contrast, the Arizona 
chronology is built of a large number of overlapping records matched together 
by cross-dating of ring groups. It would perhaps be difficult to find another 
locality where this could be done. It was accomplished by the interest and 
generous aid of the archaeologists. A partial account is given elsewhere. 1 

Besides the National Geographic Society, other institutions and persons 
gave important help: the American Museum of Natural History in New 
York City, the Museum of Northern Arizona, Dr. and Mrs. Colton at Flag- 
staff, the University of Arizona, the Carnegie Institution of Washington and 
many interested students and friends. The archaeological phase started in 
1914 and in 1929 passed a milestone in the closing of a "gap" between dated 
records extending back to or a little before 1300 and a "floating" chronology 
extending back to what later proved to be A.D. 700. This gave to the 
climatologist a bio-climatic record back to that time. The extension back 
to A.D. 11 and the needed strengthening in the early Eighth Century came 
very largely from the splendid collections of Mr. Earl H. Morris between 
1927 and 1933. 2 

Definite work on the portion of this chronology before 700 began in May 
1931 and its accuracy was considered assured by the late summer of 1934. 
Yet certain confirmations in Flagstaff specimens examined in February 1935 

1 Dating Pueblo Bonito and Other Ruins of the Southwest, Technical Monograph 

Eublished by the National Geographic Society; Paper Number 1 in the Pueblo Bonito 
eries. See also the earlier account : The Secret of the Southwest Solved by Talkative Tree 
Rings, Nat. Geog. Mag., Dec. 1929. 

2 The valuable collection work of Mr. Morris was aided by the Carnegie Institution 
of Washington, the American Museum of New York, the University of Colorado, Mr. C. 
L. Bernheimer and others. A specially valuable specimen was collected by Dr. Flor- 
ence M. Hawley while giving field instruction in connection with the Department of 
Archaeology of the University of New Mexico. Other aid is mentioned on pages 6-7. 



106 



CLIMATIC CYCLES AND TREE GROWTH 



Central Pueblo Chronology 



Cycle, 

JT8. 


No. 


Underl. 


Duration 


First 
Max. 


Rows 


P. ct. 
Amp. 


A. D. 
Ratio 


Vertical 

Scale' 


5.2 


235 


2 


1500-1665 


1504 


32 


9 


1.87 




5.7 


236 


no 


1750-1926 


1753 


31 


3 


1.17 




5.9 


237 


no 


088-211 


093 


21 


5 


1.31 




6.1 


238 


no 


1100-1270 


1105 


28 


6 






6.2 


239 


no 


695-768 


697 


12 


13 






6.5 


240 


1 


1500-1746 


1505 


38 


8 






6.7 


241 


1 


60-247 


066 


28 


8 






6.7 


242 


X 


370-503 


375 


20 


4 






6.8 


243 


1 


573-660 


575 


13 


22 






7.0 


244 


no 


1450-1498 


1455 


7 


13 




0.5 


7.0 


245 


1 


200-339 


206 


20 


15 




0.5 


7.0 


246 


no 


340-451 


345 


16 


8 






7.3 


247 


1 


890-977 


891 


12 


9 


1.13 




7.6 


248 


1 


1450-1647 


1453 


26 


11 






8.0 


249 


no 


242-401 


246 


20 


10 






8.1 


250 


1 


1060-1197 


1066 


17 


9 






8.7 


251 


no 


400-616 


408 


25 


11 






9.3 


252 


no 


100-211 


105 


12 


6 


0.97 




9.4 


253 


1 


1194-1259 


1201 


7 


20 


1.68 




9.7 


254 


1 


829-1041 


833 


22 


12 






9.7 


255 


no 


1101-1197 


1107 


10 


10 




0.5 


10.4 


256 


no 


080-204 


083 


12 


7 


1.15 


0.5 


10.4 


257 


1 


1300-1413 


1301 


11 


12 




0.5 


10.4 


258 


no 


1415-1497 


1416 


8 


8 






10.4 


259 


1 


1500-1697 


1505 


19 


11 


1.53 




11.4 


260 


1 


1748-1929 


1749 


16 


11 


1.49 


0.5 


11.5 


261 


1 


1463-1646 


1468 


16 


12 


1.38 




11.8 


262 


no 


060-248 


064 


16 


9 


1.08 




11.9 


263 


no 


270-543 


272 


23 


8 






11.9 


264 


no 


700-901 


708 


17 


10 




0.5 


11.9 


265 


1 


1020-1197 


1029 


15 


14 




0.5 


12.1 


266 


2 


1310-1563 


1320 


21 


14 


1.92 


0.5 


12.3 


267 


1 


170-329 


170 


13 


15 




0.5 


12.8 


268 


1 


950-1205 


950 


20 


12 






13.0 


269 


1 


1500-1772 


1512 


21 


10 


1.47 




13.5 


270 


2 


90-237 


098 


11 


13 


1.41 


0.5 


13.5 


271 


no 


238-194 


250 


19 


10 




0.5 


13.6 


272 


2 


1807-1928 


1812 


9 


13 


1.11 




13.7 


273 


no 


1300-1641 


1305 


25 


10 


1.33 




14.3 


274 


1 


400-685 


408 


20 


12 


1.28 




15.4 


275 


no 


1130-1298 


1133 


11 


13 






15.7 


276 


2 


10-339 


017 


21 


17 


1.93 




15.7 


277 


2 


350-J43 


358 


6 


20 


1.13 




16.5 


278 


2 


150-347 


152 


12 


22 


1.91 


0.5 


16.5 


279 


1 


1691-1822 


1694 


8 


14 






17.0 


280 


X 


700-1192 


703 


29 


3 






17.1 


281 


no 


10-505 


014 


29 


14 (i 
i 


nstead < 
md 16.5) 


}f 15.7 


17.3 


282 


no 


1300-1645 


1305 


20 


7 






17.8 


283 


X 


1500-1766 


1514 


15 


ii 






19.0 


284 


no 


1176-1498 


1185 


17 


8 






19.2 


285 


2 


840-1165 


854 


17 


15 


1.47 




19.5 


286 


no 


1500-1772 


1512 


14 


10 






19.5 


287 


2 


1770-1925 


1772 


8 


17 




0.5 


19.5 


288 


no 


010-496 


027 


25 


8 


0.95 




20.0 


289 


X 


400-649 


402 


12* 


10 




0.5 


22.5 


290 


2 


400-691 


420 


13 


14 






22.5 


291 


no 


1520-1666 


1530 


6* 


15 






23.0 


292 


2 


1734-1929 


1747 


8* 


18 






23.2 


293 


1 


700-989 


712 


12* 


15 


1.25 


0.5 



Vertical scale of summation curves in appendix is 1.0 unless otherwise indicated. 



ANALYSIS OF TERRESTRIAL RECORDS 



107 



Central Pueblo Chronology — Concluded 











Long Cycles 










pp] 


Cycle, 
yrs. 


No. 


Underl. 


Duration 


First 
Max. 


Rows 


P. ct. 
Amp. 


A. D. 
Ratio 


Verticle 
Scale 


7.5 and 


37.0 


294 


2 


1100-1319 


1125 


6 


18 


1.67 




37.5 


295 


1 


1595-1929 


1610 


9 


10 


1.75 




7.5 or 


37.5 


296 


2 


1080-1924 


1085 


22* 


8 


1.98 




10.0 


50.0 


297 


1 


1530-1929 


1560 


8 


11 


1.45 


0.5 


10.5 


52.5 


298 


1 


1250-1534 


1270 


5* 


19 


1.48 


0.5 


11.0 


55.0 


299 


1 


065-669 


110 


11 


10 


1.07 




11.1 


55.5 


300 


2 


640-1139 


675 


9 


16 


1.63 




11.7 


58.5 


301 


1 


705-1929 


725 


21 


9 


1.54 




13.2 


66.0 


302 


1 


125-554 


150 


6* 


14 


1.44 




14.7 


73.5 


303 


1 


555-1914 


585 


18| 


11 


1.45 


0.5 


19.2 


96.0 


304 


2 


010-679 


015 


7 


15 


1.40 




19.6 


98.0 


305 


2 


710-1929 


780 


12* 


13 


1.36 




23.5 


117.5 


306 


2 


700-1929 


730 


10* 


13 






26.0 


130.0 


307 


1 


120-639 


150 


4 


13 







were very gladly recognized. It should perhaps be repeated that the value 
was realized of this continuous ring sequence 1900 years long in a dry region 
where the trees were giving approximate rainfall records. It also seemed to 
the writer that it more than doubled the value of the sequoia chronology 
because it supplied a second sequence for comparison purposes. It also lays 
a foundation for estimates of yearly rainfall values in prehistoric times. 
It should be added that this chronology is not yet in completely final form. 
Improvement is coming through a better understanding of the climatic 
characters in the growth rings. It is not probable that any important 
changes will be required. 

Mr. Schulman is quoted in the following report on cycle comparisons 
between Arizona and California chronologies: 

"Simultaneous analysis of the two long chronologies shows some striking 
points of agreement in the cycle patterns, in spite of the difference of some 
600 miles in the source areas of the respective specimens. At many settings 
the patterns show such fine resemblance in the details as to leave the strong 
impression that the same forces causing fluctuations are operating in both 
regions. However, emphasis on different cycles is visibly different in many 
cases in the two regions, hence there is no perfect correspondence in the con- 
current maxima. Agreement is seen in the entire 1900 years; there is a 
strong suggestion that it is successively better in more recent times. 

"In the settings showing some of the best points of correspondence, given 
below, there is usually not only agreement in the particular cycle setting, but 
also in other cycles evidenced by slant alignments in the cyclogram. The 
following analyses made in five overlapping intervals show cycles common to 
the two chronologies; the cycle lengths listed are of course in years. 
1500 to 1900: 10, 11£ (1750-1900), 13.5 (1750-1900), 17, 19 
1100 to 1600: 10 (1100-1250), 12 (1300-1600), 15 (1100-1300), 19-20, 27 
700 to 1200: 13£ (700-850), 16£ (950-1200), 19, 23 (700-1000) 
450 to 900 : 7, 13 or 14, 27 
10 to 500 : 7, 13 or 14 
"Simultaneous analysis of the compressed curves of the two chronologies 
(5 year means), viewing 1900 years at once, yields even better results. The 
following cycles were found to agree well. 



108 



CLIMATIC CYCLES AND TREE GROWTH 



Years 

37.5 

58 

66 

95-98 

117 



(1000-1914); fainter in sequoias 
very good in both 

(first 1000 years) ; fair but not as important as the others, 
excellent agreement throughout. 

the half-cycle, 57 ± years is frequently seen ; emphasis sometimes 

changes from fundamental to intermediate crests, not always 

similarly in the two regions. 

"In every cycle almost all corresponding maxima may be recognized, 

although there is much variation in maxima strength. There are indications 

of a long cycle of somewhat less than three hundred years which seems to 

form, with the last two above, a controlling group." 



CPC io 
(10-700) 






f\ 










j\ 


r 


w. 


1 


^ 






^\ 






r\ 






..^r- 


f 


\r 


>T 


■m 


/^^\ 


(\ 


r 


^ 


I 




\ 


/ 


/ 




1 




\ 


svi a 

(0-700) , 


















f\ 






































i \ 
























\r, 


/ 


^A 


f* 


*\ 


/ 


'V 


1 \ 


S" 


N 






/ 


K 


\ 








CPC 2° 
(700-1929) 1Q 


















A 














\ 






f 


^ 












t\ 


A 


r 


"V 






/ 


\ 


/ 


\ 


\ 










V 


A. 


h 


\ 


f^ 


m 


1 A 




X 


-S 


/ 


\ 


J 




\ 




J 


\ 


SVI 
(700- 1914) l0 






A. 








V 


A 


s\ 




/ 


V 


A 




t 






'"> 




Vn 




^ 


kj 


A 


i 


1 


A 


. — 


/ 




\ 


■> 


j 


\ 


/ 




\ 


40 

CPC 30 
(10-1929) ^ 

10 






1 
























A 






K 


















\ 














l\ 






P 


V 
















/l 


m r 




h 


[/" 




/ 


\ 








\ 






M 


^v 




K 


n 


/ 




V 




V 


V 


/ 




\ 




1 






V 


j 


N- 


V 


T\ 


l\ 


f 




v 


1 




\ 


J 




\ 


I 






SVI 20 
(0-1914) 1Q 














A 


A/ A 


i 1 


























A 


A 




A 


/ 


/ i 


V 












/ 


\ 


/ 


f "> 


\ 




\a 


1 




v\ 


/ \ 


/ 




Y 1 












r 


\ 


/ 




\ 



5 6 7 8 9 10 II IE 13 14 15 16 17 18 19 20 21 22 23 24 
YEARS 

Fig. 46 — Frequency periodograms of Central Pueblo Chronology (CPC) 
and Sequoia Chronology (SVI). 



GEOLOGICAL MATERIAL FOR CYCLE ANALYSIS 

Its Character — Many collections of fossil wood have been examined but 
nearly always the specimens are massive pieces, and the long, unbroken se- 
quences of rings for which we are searching are quite absent. That is not 
surprising, for the breakage of such wood is not normally radial, as we would 
wish, nor have long sequences been specially sought. In fact the deliberate 
collection of long sequences in the field is very difficult. Unaltered wood 
such as the "buried trees" near Flagstaff or the large logs in the German peat 
beds is far more likely to show desired records. 







Buried Trees 






Cycle, yrs. 


Under!.* 


Duration, yrs. 


Cycle, yrs. 


Underl. 


Duration, yrs. 


Ml: 151 yrs. . 














#9: 80 yrs. 




5.1 


no 


52 








6.0 


no 


151 


7.5 


no 


80 


8.0 


1 


151 


8.5 (oc J) 


no 


80 


9.5 


X 


151 


9.9 


1 


80 


10.1 or 


no 


151 


11.7 


1 


80 


10.9 


X 


151 


14.6 


no 


80 


12.1 (oc J) 


1 


151 


20.8 


no 


80 


13.8 


no 


151 


24. 0± 


no 


80 


16.0 (« 


1 


119 












24. 0± 


no 


151 


#10:93 yrs. 




#2: 141 yrs. 














5.6 (oc |) 


no 


93 








5.1 


X 


141 


7.9 


no 


93 


6.0 


X 


141 


8.4 


no 


93 


8.0 


X 


141 


10.1 


X 


70 


9.5 


1 


141 


11.7 


1 


93 


10.1 


X 


141 


14.0 


2 


93 


10.9 


X 


141 


20.8 


no 


93 


12.1 (oc J) 


no 


141 


24. 0± (oc i) 


no 


93 


13 8 


no 


141 








18> (oc |) 


no 


141 


#11:157 yrs. 




#1 and 2: 153 yrs 


. 












8.9 


X 


157 








5.3 


no 


153 


11.1 


no 


157 


5.9 


no 


30 


12.2 


2 


157 


6.6 


X 


114 


13.9 


X 


157 


8.3 


1 


109 


17.9 


X 


157 


12.2 


1 


153 


22.0 


X 


157 


16 or 


no 


153 








17.2 (oc*) 


1 


153 






24.2 (oc J) 


1 


153 


#13: 181 yrs. 




#3:69 yrs. 




6.9 (oc x2) 


no 


131 






9.3 


1 


141 








6.0 


no 


69 


12.3 


2 


121 


7.4 


no 


69 


14.3 


X 


181 


9.4 


2 


69 


19.2 


1 


181 


12.1 


1 


52 








14! 6 (oc J) 


X 


69 






19.2 (J) 


no 


69 


#14: 174 yrs. 




#7: 181 yrs. 




5.2 


1 


109 






7.1 


X 


174 








5.5 


no 


181 


10.6 (oc i) 


no 


174 


8.3 


X 


181 


11.8 


no 


174 


9.8 


no 


111 


14.5 


2 


174 


11.0 (oc |) 


X 


181 


15.8 


no 


101 


14.0 


2 


181 


17.5 (oc i) 


no 


171 


17 


1 


181 








23! 9 


X 


181 






27.8 (|) 


no 


181 


#15:98 yrs. 




#8:94 yrs. 


5.2 
6.0 


X 


98 

98 








no 


5.2 


no 


94 


7.1 


X 


98 


6.5 


X 


94 


10.2 (oc*) 


1 


98 


8.7 


no 


77 


11.8 


no 


98 


10.4 (oc J) 


1 


94 


14.6 


1 


98 


12.1 


2 


94 


17.5 


1 


98 


17.9 


X 


94 


20.6 (oc i) 


no 


98 



For underlines, etc., see pages 146 and 147. 

109 



110 CLIMATIC CYCLES AND TREE GROWTH 

The varves of De Geer and Antevs provide continuous sequences that 
cover thousands of years. The Permian anhydrites of Udden do the same 
to a less degree. This anhydrite even with errors up to 2 per cent shows 
some 1400 years of practical continuity. The longest continuous sequences 
found by Bradley in the Green River formation of southern Wyoming are 
less than 100 years. I have no doubt that we have barely touched the valu- 
able material along these lines that will eventually be available. 

Since the geological material is without actual dating and is not cross- 
identified, the common way of presenting results from it is in the frequency 
periodogram; that is, a plot of the frequency of occurrence of cycles of dif- 
ferent lengths. Such periodograms may be seen in figure 55, where results 
from widely different sources are compared. 

BURIED TREES 

At Flagstaff, Arizona, in 1904, the writer discovered in an arroyo a tree 
stump in place buried 16 feet deep in the valley fill. In 1919 and for several 
years after, with the aid of Dr. E. S. Miller and Major L. F. Brady, a large 
number of tree sections were secured in the same arroyo from different depths 
between l£ feet and 16 feet. The annual rings in the logs at shallow depth 
were of the sort now growing in the pines thereabouts — dry climate rings. 
The rings at 12 and 16 feet in depth were wet climate rings — large and show- 
ing a slow surge in size characteristic of a relatively continuous water supply. 
This contrast occurring in one locality appeared to indicate a climatic change. 
Ten of these buried trees, chiefly from the upper levels, gave excellent meas- 
ured records aggregating more than 1400 years. 

These records have been analyzed by the writer from time to time, with 
the result of finding cycle lengths at 8.5, 10 or a little less, 11^ with indications 
of a second crest, 14, 17 and 19 years. Mr. Schulman's recent analyses have 
largely duplicated these results but he has gone very much more into detail. 
He places a strong cycle maximum at 12 years. This will appear in his lists 
below and in the frequency periodogram prepared by him and shown in figure 
55. 

Since the curves are not standardized, it was felt that amplitudes obtained 
by the usual methods would not be satisfactory. So a qualitative idea of 
the amplitude is given by the underline number, essentially a weight, in 
column 2. The letter x in that column indicates a weak cycle. One can 
keep in mind that specimens numbered 1, 2, and 3 were from the greatest 
depth, and numbers 11 and 13 were lying near the present flat surface of the 
valley fill. 

YELLOWSTONE FOSSIL TREES 
In 1929 and 1930 collection was made of some 38 Tertiary sequoias 
(Sequoia Langsdorfii) , silicified, from Specimen Ridge in Yellowstone Na- 
tional Park. These fossils were secured by Messrs. Mason and Reade as 
nearly as possible from one single horizon of petrified stumps. Probably 
many of them were living trees at the same time. Like the corresponding 



ANALYSIS OF TERRESTRIAL RECORDS 



111 







Yellowstone Fossil Trees 






Cycles, yrs. 


Underl.* 


Duration, yrs. 


Cycle, yrs. 


Underl. 


Duration, yrs. 


1929 # 1 : 106 yrs. 


#8(2): 118 yrs. 


6.5 ' 

7.5 
10.1 
12.6 
15.1 
23.6 


no 
no 
2 

1 

2 

1 


106 
106 
106 
106 
106 
106 


5.2 
6.4 
7.8 
10.0 
11.0 
12.6 
15.6 


X 

1 

no 
no 
no 

1 

X 


35 
91 
94 

87 
118 
101 
118 


1929 #2: 119 yrs. 


#9: 105 yrs. 


5.1 

5.6 

6.3 

7.8 

9.8 

11.8 

15.3 

24.1 


X 

1 

no 
no 

1 

2 

1 
no 


119 
77 
43 
103 
119 
119 
119 
119 


6.3 
7.7 
9.7 
10.4 
11.3 
12.2 
14.6 
22.3 


no 
1 

no 

X 

1 

no 
1 
1 


105 
73 
105 
105 
105 
81 
105 
105 


1929 #6: 176 yrs. 


#11: 154 yrs. 


6.4 
7.0 
8.6 
12.5 
14.3 
17.0 
19.5 


no 

1 

2 

1 
no 

2 

1 


160 
56 
176 
176 
176 
176 
176 


5.6 
7.0 
8.1 
10.1 
11.4 
13.7 
14.4 
17.4 
20.3 
24.0 


X 

no 
no 

2 

1 

2 
no 

1 

X 

no 


80 
149 

89 
154 

99 
144 
134 
148 
144 
144 


#6(2): 72 yrs. 


6.1 

7.5 

9.9 

11.9 

14.3 

18.8 


no 
no 

1 

no 
no 

1 


72 
72 

72 
72 
72 

72 


#12:91 yrs. 


7.0 
10.3 
11.4 
14.1 
16.9 
21.1 


no 

2 

1 
no 

2 
no 


91 

88 
88 
91 
91 
80 


#6(3): 71 yrs. 


5.9 
7.3 
10.6 
11.7 
14.5 
21.6 


1 
1 
1 
2 
1 

X 


71 
71 
71 
71 
71 
71 


# 13a: 60 yrs. 


5.0 

7.0 

9.8 

11.3 

13.8 


no 

1 
no 

1 

1 


60 
60 
60 
49 
51 


#7(1): 85 yrs. 


8.0 
10.1 
11.8 
14.5 
18.1 
24.1 


1 
no 

2 

no 
no 
no 


85 
85 
85 
85 
85 
85 


#13b: 39 yrs. 


5.2 

7.5 

9.9 

11.7 


no 
no 
1 

X 


39 
34 
39 
39 


#8(1): 184 yrs. 


#14: 361 yrs. 


6.0 
11.4 
12.0 
14.3 
17.5 


1 
no 

1 

no 
no 


74 
184 
184 
184 
184 


5.5 

6.3 

7.5 

11.2 


no 
no 
no 
1 


144 

66 

261 

361 



For underlines, etc., see pages 146 and 147. 





Yellowstone Fossil Trees — Continued 




Cycle, yrs. 


Underl.* 


Duration, yrs. 


Cycle, yrs. 


Underl. 


Duration, yrs. 


# 14: 361 yrs. — Continued 


#19: 79 yrs. 


12.6 
17.0 
18.9 
24.0 


2 
2 

1 

2 


361 
361 
361 
361 


5.6 

7.0 

9.9 

11.3 

14.0 

21.9 


no 
no 

1 
2 

no 
1 


79 
79 
79 
79 
79 
79 


#15a: 512 yrs. 


6.1 

8.7 

14.4 

18.6 


no 
no 

2 

2 


82 
451 
437 
512 


#20a: 136 yrs. 


8.8 
14.4 
17.6 


no 
1 

2 


136 
136 
136 


#15b: 495 yrs. 


13.7 and 
15.3 or 
14.2 
18.7 
21.8 


2 
2 
2 
1 
1 


473 
196 
473 
495 
306 


#20b: 124 yrs. 


9.8 
11.8 
14.4 
18.8 
24.0 


no 

1 

1 

no 
no 


124 
124 
105 
124 
124 


#15c: 511 yrs. 


6.8 

7.5 

9.4 

14.3 

14.1 

18.7 


no 
no 
no 

2 
no 

1 


82 
219 
205 
399 
112 
308 


#21: 99 yrs. 


6.4 

7.9 

11.7 

13.5 

18.8 


no 
no 

1 

1 

1 


99 
63 
99 
99 
99 


#16: 111 yrs. 


6.1 
8.7 
10.3 
11.6 
14.1 
20.7 
23.9 


no 

X 

no 

2 

1 
no 

1 


111 
111 
111 
111 
111 
111 
111 


#21b: 105 yrs. 


7.4 
10.1 
11.4 
14.9 
16.8 
24.2 


1 

1 
no 

1 

1 
no 


105 
100 
83 
105 
105 
105 


#17a: 68 yrs. 


#21c:85yrs. 


6.9 
8.1 
9.5 
11.6 
15.1 
17.0 
19.2 


no 

1 
no 

1 
no 

1 
no 


68 
68 
68 
68 
68 
58 
64 


5.0 
7.2 
10.0 
12.2 
15.1 
18.7 


no 
no 

1 

1 

X 
X 


85 
72 
85 
70 
85 
85 


% 17b: 61 yrs. 


% 22a: 65 yrs. 


7.2 
10.1 
11.3 
14.6 


no 
1 

no 
no 


61 
61 
48 
61 


5.2 

7.0 

10.4 

11.2 

17.8 


no 

X 

1 
no 

X 


65 
65 
65 
60 
65 


#18a: 101 yrs. 


5.8 
7.1 
8.4 
11.6 
14.2 
17.5 
23.9 


1 
1 
1 
1 
2 
2 
1 


101 
101 
61 
101 
101 
101 
101 


% 22b: 54 yrs. 


5.3 

6.6 

7.8 

9.9 

11.4 


no 
1 
1 
1 
1 


40 
54 
54 
54 
54 



112 



ANALYSIS OF TERRESTRIAL RECORDS 



113 



Yellowstone Fossil Trees — Continued 



Cycle, yrs. 


Underl.* 


Duration, yrs. 


Cycle, yrs 


Underl. 


Duration, yrs. 


#24a:602yrs. 


#29b: 200 yrs. 


6.5 
7.4 
10.1 
12.2 
21.5 
24.0 


no 
no 

2 

no 
no 

2 


602 
111 
516 
221 
371 
546 


9.4 
10.1 
12.0 
12.6 
14.2 
15.7 
17.1 
19.0 
23.6 


1 
no 

1 
no 

1 

1 

1 

1 

1 


200 
118 
200 
130 
200 
200 
200 
200 
200 


#24b: 169 yrs. 


6.0 


no 


149 


7.1 


1 


169 








8.7 


no 


169 




« 30: 176 yrs. 




9.8 


no 


169 














12.3 


no 


169 


8.8 


1 


176 


14.3 


2 


169 


10.0 


no 


135 


17.1 


1 


169 


17.1 


no 


176 


20.3 


1 


169 


20.1 
22.1 


1 


176 
176 


#25: 238 yrs. 




5.8 
7.2 
8.9 
11.3 
14.5 
17.7 
22.7 


1 

1 

1 

2 

no 
no 

2 


158 
238 
238 
238 
238 
238 
238 


#31: 167 yrs. 


9.8 
11.4 
12.5 
14.2 
15.7 
22.5 


no 
1 

no 
no 
no 
no 


167 
167 
151 
121 
77 
167 


1 


K26a: 125 yrs. 


















#34: 92 yrs. 




6.4 

. 8.7 




125 
125 






2 


5.3 


no 


92 


10.3 


no 


125 


6.9 


no 


92 


11.9 


no 


125 


8.2 


no 


92 


13.7 


1 


125 


10.1 


no 


85 


16.0 


no 


125 


11.4 


1 


92 


17.3 


no 


125 


13.7 


no 


92 


20.5 


no 


125 


17.0 


X 


80 


23.2 


1 


125 


23.3 


no 


92 


#26b: 94 yrs. 


#35a: 186 yrs. 


6.3 

7.6 

8.5 

9.8 

11.3 

13.5 

20.3 


no 
no 

1 

2 

no 
no 
no 


94 

68 
58 
94 
94 
94 
94 


7.6 
8.4 
10.0 
12.0 
13.2 
14.3 
17.1 
20.1 


2 

1 

1 

1 

no 
no 

1 
no 


71 
141 
186 
186 
181 
186 
186 
186 


#29a: 211 yrs. 


7.0 


no 


173 


f 


if 35b: 106 yrs. 




10.1 
12.5 


1 
1 


141 
207 








9.1 


1 


106 


14.1 


1 


207 


10.1 


no 


106 


17.0 


2 


207 


11.0 


2 


106 


19.4 


no 


211 


14.4 


no 


106 


24.0 


no 


211 


18.7 


1 


106 



114 



CLIMATIC CYCLES AND TREE GROWTH 

Yellowstone Fossil Trees — Concluded 



Cycle, yrs. 


Underl.» 


Duration, yrs. 


Cycle, yrs. 


Underl. 


Duration, yrs. 








#37b: 123 yrs. 






#36: 106 yrs. 














7.0 
9.3 


1 
1 


87 
114 


6.5 


1 


46 


8.2 


1 


87 


11.8 


"no 


123 


9.8 


1 


56 


14.0 


2 


87 


12.2 


1 


81 


14.7 


X 


123 


19.0 


1 


106 


21.1 


no 


123 








23.1 


1 


123 


#37a: 133 yrs. 


#38: 85 yrs. 


5.6 


X 


133 


7.1 


no 


85 


6.6 


no 


133 


9.2 


X 


85 


8.5 


1 


91 


10.2 


2 


70 


12.6 


1 


133 


13.2 


2 


85 


16.9 


X 


133 


16.8 


1 


85 


21.0 


no 


133 


22.0 


no 


76 



species today, the coast redwood, they are cross-dated with difficulty, for 
there are no distinctive drought rings to serve as guides, such as aid so greatly 
in the giant sequoias and the pines of drier regions. The counting therefore 
lacks the precision of cross-dated material, but many duplicate radials were 
counted and measured and it is thought unlikely that important errors have 
entered the results. Over 11,000 rings were measured, plotted, and given pre- 
liminary analysis by Mr. H. F. Davis in 1932. These analyses were checked 
and recently repeated in great detail by Mr. Schulman in order to find various 
statistical characters of the cycles. We all agree on cycle maxima near 
8.5, 10, 11$, 14, 17, and 19 years. Some of the sequences gave groups of 
cycles so closely alike that it may be possible to cross-date by that means. 

It was noted that the frequency periodogram of the Yellowstone fossil 
trees shows great sensitivity; on the whole the cycles in it seem more precise 
and follow more consistently one configuration than do the cycles in either 
the 42 Western Groups, the Arizona and California long chronologies, or 
the California coast redwoods. The newly derived periodogram from the 
fossil trees shows the 10 and the 14-year cycles to be fully as important as 
the 11 ^-year cycle. 

It is highly interesting to make comparisons between frequency periodo- 
grams from the fossil and the coast redwood. A periodogram of cycles in 
the latter trees recomputed in accordance with the present reduction meth- 
ods 1 shows at once a pronounced agreement with the Yellowstone periodo- 
gram. Due to the short average length of curves in the Yellowstone 
group, its periodogram has little weight for cycles longer than about 18 
years. 

The suggestion is strong in the coast redwoods of a liberal sprinkling of 
random effects in the cycle configurations, which have averaged out in the 

1 Using the rings in upper levels of the trees because such rings were found to be 
much less erratic. 



ANALYSIS OF TERRESTRIAL RECORDS 115 

periodogram. In striking contrast, there is a near absence of random effects 
in the Yellowstone analyses. Frequency periodograms are given in figure 55. 

ANALYSES OF OTHER GEOLOGICAL MATERIAL 

The very remarkable records revealed by Professor Gerard DeGeer in 
Sweden and Dr. E. Antevs in North America well deserve careful analysis 
for cycles. Antevs's measurements of the clay layers in the Connecticut 
Valley, left in the retreat of the New England ice sheet, received a brief 
preliminary analysis soon after they were published and a recent, fairly 
complete review. His sequence, examined for cycles, covers about 4000 
years with a break in it. Careful cross-dating has no doubt given the separate 
parts a fine continuity. Cycles between 7 and 8 years in length occur fre- 
quently; at 8.8 and at 10 years there are strong cycles; the 11-year cycle is 
weak or absent; only two good examples of it appear in the 4000 years. 
A cycle shows at 12.5 years, a group at 13 and another at 14.5, some weak 
cycles at 16 and 17, and strong cycles close to 20 years. This result is essen- 
tially repeated in the 736 years of Hudson River varves, recently published 
by Dr. Chester A. Reeds, New York. 

In 1912 a large number of fragments of swamp cypress, Taxodium dis- 
tichum, described to me as Pleistocene, were secured in the peat beds north 
of Dresden, Germany. The total rings measured were 1260 in number, 
distributed in four specimens giving long ring sequences nearly free from 
errors. One 500-year record gave a strong cycle at 10.9 years; another gave 
a good cycle at 10.0 years. Others were not particularly satisfactory, owing 
to the complacency of the growth. These values show resemblance to the 
varve cycles just described. 

Several years ago the late Professor Udden of the University of Texas 
discovered lamination in anhydrite material forming a drill core brought up 
from some 1500 feet in depth in Culbertson County, Texas. He became 
satisfied of the annual character of the layers and with aid of a grant from 
the Carnegie Institution he had them measured. He thought there might 
be an error of the order of 2 per cent in layers lost. The longest good se- 
quence of layers studied has 1443 years. The measures were turned over to 
Dr. E. L. Dodd, whose analyses for cycles showed the presence of cycles of 
10, 11, 19, and 33 years. I was fortunate enough to secure a copy of this 
series of measures and have checked the analysis and confirm Dr. Dodd's 
results within small differences. I find cycles at 7 to 7.5 years, 8.8, a very 
prominent Hellmann cycle at 11.4, a group between 14 and 15 years, a faint 
cycle at 17.5 years, and a little better one at 19 years. I found only a weak 
cycle at 10 years. 



VI. RELATION BETWEEN TERRESTRIAL AND 
SOLAR RECORDS 

EARLY RESULTS 

The first measures of tree rings at Flagstaff in 1904 were made for the 
purpose of finding whether their thicknesses varied from year to year in re- 
lation to the sunspot cycle. Six trees were used whose dating was not free 
from small errors. The measures were smoothed by 9-year running means 
and a comparison with a similar smoothed curve of southern California rain- 
fall showed some resemblance. This was considered encouraging because the 
energy used in carrying moisture from the oceans to these forests comes from 
the sun. In 1906, the ring records of 19 more sections of western yellow pine 
from locations near Flagstaff were compared with rainfall data in long running 
means with similar promising results. These comparisons are shown in 
figure 47. 




i! 

-oO 



1870 1880 1890 1900 

Fig. 47 — Arizona tree growth and California rainfall; curves of 1909. 

Comparisons with rainfall could only reach back to 1898 near Flagstaff, 
1867 near Prescott, and 1851 in southern California, but correlations with 
solar records could extend back to the beginning of the latter in 1610. 
Integrations of sunspot data in a cycle length of 11.4 years were compared 
with similar integrations of tree records (not yet accurately dated), southern 
California rainfall and temperature. This set of curves, prepared in 1908, 
gave the first crude record of the Hellmann cycle in trees, as shown in 
figure 48. In this correlation diagram, two crests appeared in the Arizona 
trees, two crests appeared in southern California rainfall; one crest and a 
possible second are seen in the temperature curve and, of course, only one in 
the sunspot curve. A maximum of tree growth, rainfall, and temperature 
came near the minimum of sunspots. 

116 



RELATION BETWEEN TERRESTRIAL AND SOLAR RECORDS 



117 



In 1911 a full total of about 10,000 ring measures had been made when it was 
proposed to test what seemed a highly improbable relationship; namely, a 
linear positive correlation between ring thickness and annual rainfall. After 

ll'/3 YEAR 
PERIOD 



Rain 
(California) 



in. 
+8.0 

+4.0 

o 

-4.0 
-8.0 

°F. 




Temperature 
(San Diego) ° 



Inverted 
sunspot curve 



1863 






1874 



Tree growth 
(Arizona) 



Fig. 48 — First western correlations, 1909. The horizontal scale gives proportionate 
parts of 11£ years. Rainfall curves are: dotted line — San Francisco; broken line — San 
Diego; full line— their average, approx. 1850-1900. Tree Growth, 1701-1906. 

adjusting the rainfall year to begin near October of the preceding year, com- 
parisons were made upon an accurately dated group just collected and the 
agreement was obvious. In the same year, a group of specimens from Pres- 



118 



CLIMATIC CYCLES AND TREE GROWTH 



cott was used for special comparison with Prescott rainfall since 1867 and 
strong correlation was obtained upon allowing a small conservation. 

But other developments occurred in the next few years. Late in 1912 
an 11-year cycle had been found in German and Swedish trees, figure 51 
(2, 9, 10, 11), similar in form to Hellmann's north German curve of rainfall 
in relation to sunspots. Two of the original sections are shown in Plate 21. 
North German and Swedish trees showed a single crest, paralleling the 
smoothed annual sunspot numbers; other curves showed the beginning of a 
second maximum in growth at sunspot minimum; still others showed this 
second maximum well developed. The crest at sunspot maximum was evi- 



Anzona 

tree growth 

492 years 



California 

coast temp. 

1863-1912 




Calif, coast 
rainfall, 60 yrs. 
1863-1912 



50 Inverted 

sunspot nos. 
, 00 125 years 



1 1. 4 yea ps 



Fig. 49 — Western correlations, 1914 in "The Climatic Factor," by E. Huntington. 

dent through a long period of years (1830 to 1911) and thus gave a high 
correlation with the extended annual sunspot numbers. 

In the spring of 1913 the Flagstaff trees, numbers 7 to 25, still in hand, 
were reviewed and corrected as to yearly identity and a new integration 
made on an 11.4-year cycle, this time with far better success, for the dating 
was correct. The resulting integration diagram is shown in figures 49 
and 50. Hellmann's rainfall curve is included and matches that in California 
rainfall. 1 

1 List of references to extended curves from which the summated curves in figure 51, 
page 120, were made. 

2 (a) Hellmann's curve — Proc. Nat. Acad. Sci., Mar. 1933, vol. 19, p. 354, 

fig. 6. 

3 (j) Flagstaff Hellman— I, p. 102, fig. 32; Proc. Nat. Acad. Sci., vol. 19, 354, 

fig. 8. 

4 (h) Springville Sequoias; not published. 

5 (f) So. Calif, rain— Proc. Nat. Acad. Sci., vol. 19, 354, fig. 7; fig. 5. 

6 (g) Grant Park Seq— II, p. 100, fig. 10; measures— I, 122-3. 

7 (b) 80 Europ. Trees— I, 78, fig. 26. 



RELATION BETWEEN TERRESTRIAL AND SOLAR RECORDS 



119 




o 

3 

cr 

<U 

CO 



o 

c 
•oo 

o 
o> 

c 
H 



0.85 




0.95 
0.9p 

Hellmann 

No German 

rain(50yrs.) 

1851-1900 



/ 



/ ^ x Sequoia (500yrs.) 



J^ 



^ir:._ 



/ \Sequoia(60yrs.y^ \ 

:r^ — \ ^'^ * ^ 




0.9 


/ 


'at 




/ 


r 




/ 






/ 


CL 




/ 




/ 


.n 




-p 


._/ 




o 

c 
■oo 


1.2 




c 


f.o 


/ 
/ 






_y 





1864 E 4 6 8 10 11,4 

Fig. 50— Correlations, 1919. 



8 (i) Bear Valley, San Bernardino Mts., fig. 5. 

9 (c) So. Sweden— I, 75, figs. 22 and 23. 

10 (d) Eberswalde— I, 75, fig. 23. 

11 (e) 57 Europ. trees— I, 77, fig. 25. 

Vermont curve I, 78, fig. 27. 
Oregon curve I, 43, fig. 11. 

The 80 European Trees (7b) include the 57 selected ones (lie) that formed a separate 
group. Curve number 7 is derived from the number of occurrences of maxima in the 
ring thicknesses and not on measures. California rain in curve number 5(f) has the 
same curve in two amplitudes, the larger amplitude showing after subtraction of inter- 
fering cycles. Other extended curves referred to in the text may be found. 



120 



CLIMATIC CYCLES AND TREE GROWTH 



It became very evident that improvement in method of cycle analysis 
was urgently needed. This was accomplished, as related, by the multiple 
plot and the first automatic periodogram. In 1914, the automatic cyclogram 
was made. 




Sunspot cycle showing 
inverted minimum. 
(Dotted line) 



Hellmann's curve, 
No. Germany rain. 

Flagstaff pines 

\ Flagstaff pines. 
(True position) 

Springville sequoias. 



v So.California rain. 
( See note page 178) 

Grant Park sequoias. 

80 European trees, 
Summation showing 
frequency of maximum 
growth. 

Bear Valley (San Bernardino) 
pines. 

So. Sweden pines 
Eberswalde pines 

57 European trees 
Sunspot numbers 



Max. 



Mm. 



Fig. 51 — Integrations on 11.4 years of data mostly between 1850 and 1900; arranged 
according to prominence of second maximum of Hellmann cycle. See footnote pp. 118, 
119. 

Then for several years an obstacle seemed to stand in the way of progress; 
there were too many cycles. The smoothed annual sunspot means had been 
analyzed and, as we know, a clear, well-defined if somewhat variable cycle 
was the most conspicuous character; but not so in climatic and tree-ring 



RELATION BETWEEN TERRESTRIAL AND SOLAR RECORDS 



121 



sequences. Here was a mixture in which, in some places, well-defined cycles 
stood out, including the 11-year length, but there were many others in addi- 
tion and apparently of similar importance. The two-crested 11-year cycle, 
heretofore found by integration, was the gateway into this new forest of al- 
most unknown tree-record cycles. 

One of the first uses of the new analyzing method was an attempt to see 
the cycles in the Flagstaff ring record. A double-crested 11-plus-year cycle 
was evident since about 1400 except for a considerable interval near 1700. 
Mention of this was made in Climatic Cycles and Tree Growth (1919, vol. I, 




1420-1476 



1.0 



1.0 
03 


1477-1533 


1.0 
03 


I534-IG0I 


I.I 
1.0 


1602-1658 


I.I 

1.0 

0.9 


1659-1727 


1728-1784 


0.9 

0.8 


1735-1852 



1853-1909 



2 4- 6 8 10 

Fig. 52 — Hellmann cycle in Flagstaff 
pines, FLC-FLU, since 1420; averages of 
five or six successive 11.4-year intervals. 
Dotted lines show effect of subtracting two 
interfering cycles, 19 and 13.5 years. 

p. 102). The history of the 11-year cycle is shown in figure 33 and in Plate 
12f, of that volume, and in this volume in figure 52; the change and flattening 
of the 11-year cycle between 1660 and 1725 is evident. As Maunder pointed 
out in 1922, this coincides with the great dearth of sunspots described by him 
as extending from 1645 to 1715. In the next few years until 1926, many 
hundreds of cycle plots of tree-growth curves were made and analyzed without 
bringing understanding of why so many cycles existed. In 1925, a collec- 
tion of new ring specimens was made through New Mexico, Colorado, Wyo- 
ming, Idaho, Oregon, Washington, and California. The 42 groups, collected 



122 CLIMATIC CYCLES AND TREE GROWTH 

largely on this trip, using 52,000 measures upon 305 trees, were plotted and 
analyzed in the summer of 1926, and then the next cycle step was made by 
finding what we have called the "cycle complex" or "family" of preferred or 
dominating cycle values. Late in 1926, after prolonged study of these 
analyses, it was recognized that the dominating values in the cycle complex 
matched the various cycle lengths found in the sunspot numbers and usually 
bore a simple ratio to the 11-year cycle. 

Expressions of this same sort of relation have come from Clayton, Abbot, 
C. E. P. Brooks, and others. Clayton in Our Atmosphere and the Sun finds 
certain climatic waves that pass across the country and gets evidence of 
dependence of these on simple ratios of the 11 -year cycle. Abbot has found 
in radiation simple integral parts of 23 years, which is twice the sunspot cycle 
length, and Brooks has expressed the same sort of thing in connection with 
studies of the Nile gauge readings during the last thousand years. 

EVIDENCE OF SOLAR RELATION IN 11-YEAR CYCLE 

General Resemblance in Cycle Types — There is a general resemblance be- 
tween tree growth and solar cycles in their discontinuous or fragmentary 
character. When examined in cyclograms they look alike, save that the 
former are more apt to have several cycles at a time. This may be persist- 
ence of cycles after the cause has changed, possibly a biological character. 
The persistence may occur in the sun in some form less conspicuous than 
the usual smoothed annual sunspot numbers; and a part may be considered 
as related to turbulence in the terrestrial atmosphere. 

Evidence by Cyclograms — Difficulty is anticipated here in communicating 
the evidence we obtain in actual tests with the cyclograph. In spite of 
general unfamiliarity with cyclogram patterns we feel sure that this method 
should be used in the present topic because it is by far the most efficient 
method available. At the start we illustrate the method of reading and inter- 
preting the cyclograms in Plate 22 by reference to an enlargement in Plate 23. 
Here, as in all cyclograms, each dot or spot represents a full crest in the orig- 
inal curve whose analysis produced the cyclogram. The cyclograph is so 
constructed that, when set to analyze at a certain cycle length, any series of 
maxima giving that cycle will take the horizontal position (Plate 23, A-A'). 
To bring out neighboring cycles the primary row of dots is repeated two or 
more times in each pattern (Plate 23, A-A' and A-A'). If a fainter row of 
dots (B-B') appears between the main horizontal rows, it means that two 
crests in the curve rather than one exist in the particular period at which the 
analyzer is set. The entire series of diagrams in Plate 22 was photographed 
with the cyclograph set at 11.4 years. Hence one may readily see not only 
that the 11.4-year cycle is present and dominant but also that in the majority of 
cases it possesses two crests which, by definition, represent the Hellmann cycle. 

If the curve under analysis possesses a period different in length from the 
one at which the instrument was set, its presence will be revealed by an oblique 
or secondary alignment (Plate 23, C-C). The parallel row of dots, D-D', 



Carnegie Inst. Washington Pub. 289, Vol. Ill— Douglass 



I 

PLATE 21 




AD. 1830 



895 1906 




A. Eberswalde, Germany, ring sequence, G-6; sunspot maxima are marked beginning 
with 1830; increased growth is found at or following the maxima. 

B. Eberswalde specimen, G-2; same sunspot maxima are marked. All rings may be 
seen on this specimen, ending in the growth in 1912. The tree was cut in November 1912. 



Carnegie Inst. Washington Pub. 283. Vol. 1 1 1 —Douglass 






CL 



b 



*.* ft 






•TO 










f*vv 



J 









%» 







z 



Cyclograms showing Hellmann cycles between 1850 and 1900 in Europe and North 
America, see text. I shows an artificial Hellmann cycle produced in solar records by 
inverting the sunspot minima. 



RELATION BETWEEN TERRESTRIAL AND SOLAR RECORDS 123 

indicates the double-crested nature of the cycle represented by C-C. In 
fact, the slant downward to the right in patterns g and m as well as in h, i, 
j, k, and 1, is caused by a double-crested 14-year cycle which, it is evident, 
exists both in the tree records and in the sunspot numbers. The last pat- 
tern, 1, is taken directly from the sunspot cycle itself with the minima in- 
verted, which turns it into the Hellmann form. Thus the existence of a 
Hellmann cycle in any pattern may be judged by its similarity to 1. 

The 11 -Year Cycle and Its Half Value, the Hellmann Cycle — These are so 
commonly found merging into each other that they must be considered 
together. The Hellmann cycle was first isolated in Arizona trees in 1908. 
The full 11-year cycle was found in German and Swedish trees in 1912. 
Plate 21 shows German trees (at Eberswalde) whose growth follows the sun- 
spot cycle. Forest men in our country have suggested that these effects 
are due to thinning the forests with characteristic German regularity. On a 
recent visit there, I was assured by the supervisor of the forest in which the 
trees grew, Dr. Wittich, that the forest is thinned every three years or so for 
instruction purposes in the Forest School at Eberswalde. The variations 
therefore are natural. 

Many tree groups show, since 1850, an 11-year cycle with two crests. 
This cycle in actual length varies from 11.2 to 11.8 years, with perhaps the 
commonest value at 11.4, which compares favorably with 11.35 years, the 
average sunspot cycle length since the maximum of 1837. The two crests 
are somewhat unequal in height and in spacing and in stability. In most cases 
one crest comes near sunspot maximum and the other near sunspot minimum. 
The one at maximum seems to be more stable than the one at minimum. 

A cycle that fits this description was found by Hellmann in 1906 in North 
German rainfall; it is shown in figure 51: 2 (a). Though Hellmann had 
little confidence in this relation to the solar cycle, it seems to be sufficiently 
frequent in trees to justify using his name. The existence of this cycle and 
the others mentioned below is based on the cyclogram patterns in Plate 22, 
in which the letters correspond to the letters in figure 51. 

In Plate 22a and figure 51: 2(a), Hellmann's curve of German rainfall is 
extended to 1920 by the Berlin rainfall record. 

In 1912-13 eighty North European trees were sampled. Several hundred 
dates of maximum growth between 1850 and 1907 are collected in figure 
51: 7(b) (and Plate 22b), which give the result of this single qualitative test 
in a symmetrical Hellmann cycle. The only difference from Hellmann's 
curve is in the greater relative height of the crest at maximum. This curve 
has been reproduced in extended form in volume I, Climatic Cycles and Tree 
Growth, page 78. The correlation coefficient between full curve and the 
sunspot numbers is + 0.57 ± 0.07. Extended curves are used here as in 
each case mentioned below. 

Figure 51: 9(c) represents a group of twelve trees from Dalarne, Sweden. 
The mean curve of the twelve, between 1830 and 1907, based on 900 measures, 



124 CLIMATIC CYCLES AND TREE GROWTH 

places the larger maximum directly at the sunspot maximum; the minimum 
crest nearly disappears. The extended curve was reproduced in volume I, 
just mentioned, page 75. Its correlation coefficient with the sunspot numbers 
is + 0.62 ± 0.06. Its cyclogram is shown in Plate 22c. 

In the important group of thirteen trees from Eberswalde, Germany, 1100 
measures, between 1825 and 1907, the crest at minimum has practically gone, 
except in a very few cases, leaving a massive crest at sunspot maximum, as 
is shown in figure 51 : 10(d) and Plate 22d. The extended curve has been re- 
produced in the same volume, page 75. Its correlation coefficient with the 
sunspot numbers is + 0.51 ± 0.07. 

Six groups, 57 trees, of the nine North Europe groups collected in 1912, 
when integrated at 11.4 years, show between 1830 and 1910 practical identity 
with the sunspot cycle similarly integrated, as can be seen in figure 51: 11(e) 
and Plate 22e. This includes about 4500 measures. The minimum crest 
occurs rarely and disappears in the average. The extended curve has been 
reproduced in the same volume, page 77. Its correlation coefficient with the 
sunspot numbers is + 0.56 ±0.05. 

In the United States, a Vermont curve from eleven trees and some 600 
measures, 1852 to 1911, shows a strong 11-year cycle with one crest much 
more prominent than the other, and two or three years phase displacement. 
The total range between maximum and minimum is about 28 per cent of 
the mean value. The correlation coefficient is + 0.53 ± 0.06, after allowing 
for lag of —3 years applied to the solar data. Seventeen Douglas firs on 
the Oregon coast, 900 rings measured, 1854 to 1910, reach a single-crested 
cycle with a range of about 10 per cent. There is also a slight lag. The 
correlation coefficient is -f 0.45 ± 0.07, after allowing for a lag of —2 years 
applied to the solar data. 

The largest American groups come from California and Arizona. These 
are perhaps best introduced by curves of the southern California rainfall, 
using "Lynch's Rainfall Indices," as shown in figure 51: 5(f), extending back 
to 1770, a very important and useful compilation verified by the San Bernar- 
dino Mountain tree record. These indices since 1850, of course, became 
actual rainfall records. Smoothed curves of this rainfall have an obvious 
resemblance to the Hellmann cycle. Cyclogram analysis, 1855-1901, showed 
interference by a double-crested 14-year cycle and a high amplitude short 
variation, apparently a little more or less than two years, which causes an 
apparent scattering of yearly values. Without these the Hellmann cycle 
becomes an excellent cycle with more than 30 per cent range. See Plate 
22f. A study is being made of this two-year cycle. 

Figure 51: 6(g) shows the Hellmann cycle in the sequoias. This comes 
from the tabulated means of eleven trees, about 600 measures, published by 
the Carnegie Institution in 1919. The data originally covering 1810 to 
1914 have been extended to 1930 by collections in the Sequoia National Park. 
The trees are complacent and the range is small; namely, about 8 per cent. 
But the maxima are clean-cut and the crests are very stable as there is little 



Carnegie Inst. Washington Pub. 289. Vol. Ill — Douglass 



c 

D 
A 



A 



B 




B 



A 



B' 



C 
D' 



Enlargement of cyclogram Plate 22 g, showing Hellmann cycle in sequoias. 
AA' and BB' give the Hellmann cycle with its two crests; CC' and DD' show a 14-year 
cycle with two crests. 



Carnegie Inst. Washington Pub. 289, Vol. Ill— Douglass 



PLATE 24 



100 



Days 

117 



no 




20 



130 



WuuMMM* 




•2WW •-' '--VJVWV* 





\20 117 



Cyclogram analysis of SS Cygni (1918) . Data cover 1896 to 1917. Directional values 
given in days, best seen by looking along pattern at low angle. 



RELATION BETWEEN TERRESTRIAL AND SOLAR RECORDS 125 

interference from longer cycles. A cyclogram study of this sequoia record 
extended back to 1804 is shown in Plate 23, which is an enlargement 
of Plate 22 g. 

Figure 51: 4(h), Plate 22 h, show the Hellmann cycle in the southernmost 
sequoia grove, south of Sequoia National Park and near Springville, where 
three 3000-year trees have been found. The curve is made from 500 meas- 
ures covering 1805 to 1890. The topographic conditions are good but not the 
very best obtainable for a climatic record, since the area on which the trees 
grew is rather flat and the ground sometimes very moist. The altitude is 
high enough for large quantities of snow in winter. After removing a 19- 
year cycle by mathematical methods, the Hellmann cycle is evident with a 
range of 15 per cent. 

Figure 51 :8(i) shows the Hellmann cycle in the San Bernardino pines, 
derived from 800 ring values, about 1850 to 1900; Plate 22 i uses the larger 
interval, 1825 to 1925. The trees grew at about 6000 feet elevation in Santa 
Ana Valley, northeast of Redlands. Collection and measurement of this 
group was made with the generous help of Mr. J. J. Prendergast, President 
of Bear Valley Mutual Water Company. After the subtraction of a strong 
14-year cycle the Hellmann cycle shows a range of 16 per cent, and probably 
more. 

The Hellmann curve in the Arizona pines, given in figure 51:3(j), and 
Plate 22 j is derived from 3000 measures in 58 trees, distributed across two 
hundred miles of country, approximately including 1850 to 1905; the cyclo- 
gram, Plate 22 j, uses the interval 1825 to 1920. A 19-year cycle lasting 
since 1800 completely dominates the record. This and a 14-year cycle were 
removed by mathematical methods, whereupon the Hellmann cycle was 
well marked in the curve. It seems to show a lag of two or three years in 
relation to sunspot phase. It should be added that some of the individual 
groups in this large assemblage of trees, such as the one from the Grand 
Canyon, give the Hellmann cycle in prominent form without the interfering 
cycles. 

Plate 22 k shows Grand Canyon tree growth from seven trees, 1825 to 
1920. The effect is here shown of using the center of gravity of the maxima, 
which produces a Hellmann cycle of very good form. There is the same 
probable two or three year lag, as in the general Arizona curve. A lag of 
—3 or —4 years fits many of the curves very well (tree-growth maxima 
preceding sunspot maxima). 

Plate 22 1, as already mentioned, gives a cyclogram of the sunspot numbers 
in which there is an inversion of minimum values for comparison with the 
Hellmann cycles from terrestrial sources. In general we find that the Hell- 
mann cycle is common in trees since 1850 and that the interfering cycles, 
14 and 19 years, are widely distributed. The shorter one is plainly a solar 
cycle, as will appear later, and the longer is probably so. 

Dearth Cycles — The dearth of sunspots is given by Maunder as 1645 to 
1715, during which time spots were very rare; two intervals of ten years and 



126 CLIMATIC CYCLES AND TREE GROWTH 

four or five of five years show no sunspot records at all. (See pages 68 and 
69.) In the 1400's and 1500's, before the dearth, the Hellmann cycle is well 
developed in the Arizona pines and appears weakly in the sequoias. An 
11-year cycle reappeared in good form after 1760. 

During the dearth the Arizona trees show a 10-year cycle; four sequoias, 
which generally show pronounced 11-year cycles, really give a 10-year cycle, 
which according to Schulman is 10.5 years followed by 9.7 years, giving an 
average close to 10. Many sequoias show cycles at 8.5 and about 14 years. 
A long hemlock record in Vermont gives 20 and 28 years with probable half 
values at 10 and 14 (see vol. II, Plate 9). 

Summary — In summarizing the cyclograms of Plate 22, we observe that 
they show the Hellmann cycle by double horizontal rows repeated four or five 
times. The fainter row, which is visible in most of these patterns, means that 
the 11-year cycle is cut into two parts by an additional crest, usually slightly 
non-symmetrical either in spacing or amplitude. The earlier diagrams, 
mostly foreign, show the Hellmann doubling less well developed than the 
American curves, and one remembers that the German trees follow the sunspot 
cycle mostly without the second crest. In the later diagrams the similarity to 
the sunspot cyclogram using inverted minima (1) is very evident. This comes 
not merely in the two lines of crests in 11+ years but also in the secondary 
double-crested cycle at 14 and 7 years. Note especially the agreement of this 
secondary cycle in trees with the well-marked 14-year and 7-year lines in the 
sunspot numbers (with inverted minima) in 1. This shows well in all the 
American trees. Considered historically the dominant cycle, 11 years, 
varies in similar manner in the trees and the sun. The minor cycles, 8£ and 
14 years, are generally present in each. The presence of these cycles in the 
sun is shown independently by cyclogram process and by Schuster's periodo- 
gram, as appears in figure 55. 

LONGER CYCLES 

Early analysis (by inspection) of the Flagstaff 500-year tree records 
(1909) gave a cycle of about 21 years since 1700. This has remained very 
prominent in the last 200 years of Arizona tree growth. In various curves 
of cycle intensity (periodograms) a considerable crest from 19 to 22 has been 
evident. There has always been uncertainty regarding the real length of 
this cycle. A series of integrations at 18, 19, 20, 21, and 22 years, in figure 
16, gives 20 years as a good average value of its length. The best mean values 
from 1700 to 1920 were sent to Dinsmore Alter, who subjected them to 
periodogram analysis in a rapid and skilful mathematical attack. His cor- 
relation periodogram of this sequence is given in figure 53, which shows a 
strong crest at something over 20-years lag, with further conspicuous crests 
of about 40- and 80- and 120-year lags. This indicates a 40-year cycle and 
probably one of 20 years. A cyclogram made of the same data is represented 
in Plate 16B, which shows at once that this 20-year cycle is composite during 
this 220-year interval. Through the first one-third, a cycle of about 23 



RELATION BETWEEN TERRESTRIAL AND SOLAR RECORDS 



127 



years is prominent and in the remainder a strong 19-year cycle appears, each 
of which probably lasts through the entire data. This puzzling but strong 
cycle near 20 years seems to be a composite of two taken in succession. 

A curve of Arizona tree growth plotted at 1/5 horizontal scale for 1200 years 
shows approximately five times the sunspot cycle from A.D. 1168 to 1512. 
(See fig. 54, page 128. Note the 11-year subdivision in the figure.) 

Certain long cycles in terrestrial records could easily result from interfer- 
ence between short solar cycles already mentioned. In the solar records 
we have the Hellmann cycle and also a cycle at 83 years; the interference 
time between these two is 34 years, which gives us the Bruckner cycle, fre- 
quently observed in tree growth. It is mentioned by Dr. Dodd as present in 



+.60 




















































































+.20 




































V, 


















o 








, J 


v v 






/Nj 


r\ 








A 










w 




\k 


A 


\J " 


\ 




/i 


A/ 


\ 


-.20 












\A 


S 




V 


'AA 


,/ 


v v/ 


\ 












V 






V 




*J 




V 


-40 


























V 




La £ in years 



Fig. 53 — Correlation periodograms (Alter) for — 

(a) Arizona trees, 1700-1920; 

(b) California and Oregon trees, 1700-1920. 

Udden's anhydrite measures from Texas. The interference between 14-year 
cycles and 11.4 is about 57 years. The Arizona trees show a strong cycle of 
this length. The interference between the most common values of the 10 and 
11-year cycles (about 10.3 and 11.4) is closely 100 years. This cycle was 
noted by Michelson in his analysis of the sunspot numbers. Many years 
ago it was found by the writer in Huntington's measures of the big sequoias 
as very prominent for nearly 2000 years. Later it has been confirmed, and 
now is being studied, in accurately dated sequoia records. In the 1900-year 
Arizona pine record, a 100-year cycle is very prominent, indeed. All these 
scattering items sustain the idea of a relationship between variations in the 
sun and in tree growth. 



128 



CLIMATIC CYCLES AND TREE GROWTH 



1.50 



1.00 



0.50 



** 


Mea 


n 


^K*' 





































.*.' 




20 30 40 50 56 

Years 

Fig. 54— 57-year cycle in Arizona trees, A.D. 1168 to 1503. 

FREQUENCY PERIODOGRAMS AND THE CYCLE COMPLEX 

In previous pages we have dwelt upon concurrent variations in solar 
and terrestrial data that suggest physical relationship; we now consider 
another sort of evidence in favor of such a relationship. It is the "cycle 
complex" or the group of cycles commonly found both in tree-ring data and 
in the sun. This complex is shown in the form of a frequency periodogram 
which gives the occurrence and weight of various cycle lengths observed. It 
does not require exact amplitudes and epochs and other data discussed in 
Chapter V. Between most of our groups and individuals in the western 
areas, the constants so omitted are in excellent common agreement among 
themselves wherever cross-identification has been done, because cross-identifi- 
cation itself depends on many of the similarities that determine the length 
of cycles. The simplification of data in the frequency periodogram greatly 
enlarges the available material, because we can apply this degree of analysis 
equally to geologic material whose dating and cross-dating are unknown and 
to groups of modern specimens whose dating is uncertain. 



RELATION BETWEEN TERRESTRIAL AND SOLAR RECORDS 



129 



The frequency periodogram is a summary of certain qualities in a group of 
data; hence comparisons between periodograms from two sets of data tell us 
something about the nature of the material in hand. Thus there is no correla- 
tion between the periodograms from two sets of random data but the fre- 
quency periodograms from two different groups of our tree-ring records give 
excellent correlation (see page 153). This shows that definite similarity exists 
over wide areas in those bio-climatic changes that come in time units of five 
years and longer. Five years in this statement is simply a lower limit result- 
ing from the use of an annual unit in tree growth and its adaptation to our 
analyzing instrument. 




Fig. 65 — A group of periodograms to show resemblance of terrestrial to solar cycles. 

Certain cycles in this complex were recognized in terrestrial records years 
ago, such as the 11-year cycle, the Hellmann, a 19 to 21-year cycle, a 35-year 
cycle, and something near 150 years, all noted by 1909. In 1913, cycles at 
8£ years, 14 or so, 22 or 23 were seen. A 100-year cycle came out strongly in 
the sequoias (Huntington's measures, not exactly dated but compensated for 
estimated lost rings) in 1915 (vol. I, p. 109). Something between 250 and 300 
years has been long recognized in Arizona, especially with the development of 
the long Arizona chronology. 

The complex was named in 1926 when the three western zones were com- 
pared in frequency periodograms and their similarity realized. These zones 



130 



CLIMATIC CYCLES AND TREE GROWTH 



were: first, Arizona, including northern Arizona, and New Mexico west of the 
Rio Grande, and the southern parts of Colorado and Utah; second, the Rocky 
Mountain area, Rio Grande, then east to include Pike's Peak and the Rockies 
north to Yellowstone Park; Sante Fe and points near Mesa Verde were in- 
cluded in this easterly group although they actually show substantial cross- 
identity with the Arizona area; third, the Coast Zone, including the mountain 
ranges from points east of San Diego on the south to the Dalles along the 
Columbia River on the north. The Spring Mountains west of Las Vegas, 
Nevada, show excellent relation both to Arizona and California . 

These different zones were found to give much the same cycle lengths 
but with different emphasis in weight or frequencies. It seemed probable 
that the Rockies showed more subdivisions of 34 or 35 years while the Coast 
Zone made more use of 23 years and its subdivisions and simple fractions. 
Arizona partook of each, and so the cycle complex as a whole was plainly 
based on climatic changes over a large and substantial area and not at all on 
one tree or one square mile or one state. It becomes a terrestrial affair and 
seems worth testing in all favorable parts of the earth. It has been found 




Fig. 56 — Western cycles compared to simple fractions of 34 years. 

strongly evident in the coast redwoods though their dating is less secure. 
It shows in Vermont hemlocks and in Douglas firs on the Oregon coast. 

It was then recognized that the cycle lengths appeared to be simple fractions 
of small multiples of about 11.3 years. Thus it was seen that they included 
the secondary or lesser cycles observed in the sunspot numbers. This was the 
result that was checked by the "unknown scale" method (page 47). The 
correspondence between originals and values obtained at unknown scale has 
been shown in "Conferences on Cycles," 1929, and the relation to simple ratios 
of the sunspot cycle appears in figure 56. 

Complex from Geological Material — In the last chapter the various groups 
of geological tree rings or sediments were described and their cycle readings 
discussed. The various analyses of modern and past climates when brought 
together show two chief results of interest to us. First, all these terrestrial 
cycles from geological sources approximate in length the cycles in sunspot 
numbers as well as did those in modern ring records (see fig. 55) ; and second, 
they exhibit the two types of cycle complex or mixture already observed 
historically in the sun and trees; namely, the present common type in which 
an 11.4-year cycle or something near that is conspicuous and the dearth 



RELATION BETWEEN TERRESTRIAL AND SOLAR RECORDS 131 

type practically without an 11-year cycle and with about the same minor 
cycles in each group. Figure 55 brings out the agreement found in modern 
trees in the long chronologies, in buried trees, living perhaps 2000 years ago, 
in Miocene sequoias from Yellowstone Park, with Schuster's periodogram of 
the sunspot numbers — an evident similarity outlining an immense interval 
of time. 

But there is evidence that this cycle complex was not continuous from 
Permian times to the present, for studies of Pleistocene varves and logs of 
swamp cypress, Taxodium distichum, probably of the same age, seem to 
indicate that the Pleistocene cycles resemble the terrestrial and solar cycles 
during the sunspot dearth near A.D. 1700, in the weakness of any 11-year 
cycle. 

It is evident that the cycle complex in rings and in annual sediments offer 
us two or three openings; first, an opportunity of extending to great length 
our information upon certain climatic changes, both about the earth now 
and back into past climates; and second, we can reverse our approach to it, 
as we do in so many lines of knowledge when we have gone far enough to 
make deductions, and find in our cycle complex in past time the probable 
length of the sunspot cycle in geological ages. Thus we can form an opinion 
as to the stability of the sun ; and third, it is even possible that with the long 
chronologies in Arizona and California, covering really a large area, we shall 
be able by proper comparisons to learn something about the actual dates of 
sunspot maxima — if not for every one in the last 1900 years, at least for some 
of them. 

PHYSICAL CAUSE OF CLIMATIC CYCLES 

The correspondences between solar and terrestrial cycles imply a physical 
relationship even though it is not yet traced in details. The direct and evi- 
dent channel of such relation is the heat radiation from the sun that supplies 
the energy which evaporates water and causes the winds to move it over the 
land and produce rain. Ultra-violet and other radiation may play an im- 
portant part in climatic conditions. No one doubts that variations in the 
heat of the sun can cause variations in the rainfall or other climatic elements. 
The difficulties have been quantitative: First, that the sun's variations are 
not great enough; second, that distribution of the effects about the earth 
would be infinitely complex, and such simple expressions of solar changes 
would not be isolated sufficiently to become apparent by our measuring in- 
struments. 

Neither of these difficulties offers any evidence against a relationship be- 
tween climate and sun; they are merely signposts with the word "slow" 
painted on them. And it is well to be cautious, for there are more pitfalls 
in meteorology than in most sciences (see Humphreys's Paradoxes of Meteor- 
ology). 

Imagine an increase of heat from the sun: Water, land, and air grow 
warmer, but the air is set in motion and clouds are formed that permit less 



132 CLIMATIC CYCLES AND TREE GROWTH 

heat to come through than before the increase. What is the balance of effect? 
Again, half of the heat received from the sun falls in equatorial regions be- 
tween 30° north latitude and 30° south. The cloudiness at the poles with 
ice and snow reduces the effective heat at high latitudes. Atmospheric 
circulation is induced with the motive force applied in equatorial regions. 
The earth is rotating and the cold polar areas are small and north temperate 
zones have continents and oceans. All these conditions make the distribu- 
tion of solar energy with movements of air and water a most complex opera- 
tion and many investigators ask why there should be any system anywhere. 

Newcomb, thirty years ago, took averages over the earth as a whole and 
concluded that there was no evidence of connection between meteorological 
changes and the sun ; Bigelow found that solar effects can be positive in some 
regions and negative in others. That statement of Bigelow's opened the 
way for tree-ring studies in Arizona and our effort to find the solar cycle in 
the Arizona trees. 

The disturbing feature in all comparisons between solar and terrestrial 
cycles has been the presence of other cycles on the earth of very different 
lengths and only rarely one of 11 years. The cyclogram method of analysis 
helps to solve this difficulty by the cycle complex and its correspondence 
to actual cycles in the sun. We feel justified in assuming the hypothesis 
that there is a physical relationship between our climatic conditions and 
the sun. 



VII. THE CYCLE PROBLEM AND LONG-RANGE 
FORECASTING 

THE PROBLEM 

In view of the recent great droughts and the need to control erosion and 
generally to conserve natural resources, scientific thought should be directed 
to the very important factor of climatic change and any possibility of fore- 
knowledge or prediction of changes that might affect the value of lands and 
alter economic conditions. 

The problem is this : Can we tell, years in advance, the coming of climatic 
variations that will have an important economic effect? Can we even im- 
prove our present fore-knowledge by ten per cent? The accepted procedure 
today in attempting to arrive at such long-range prediction is merely to 
determine an average climatic line (mean rainfall, for example) and the 
average departure from that mean, and then expect in the future a similar 
mean and similar departures from it, without knowing when the departures 
are likely to occur. The question now is: Can we produce a climatic curve 
of rainfall or temperature or other growing conditions that will reduce the 
errors of the aforesaid expectation by a sensible amount? 

Many attempts to solve this problem have been made without success. 
It is believed that such failures lie in part in three counts. First: Climatic 
cycles have been assumed to be permanent, if existing at all, like the annual 
or monthly cycles that are due to planetary revolutions, whereas, as every 
investigator has found, climatic cycles do not act as if they were permanent 
and should be investigated under this corrected view. 

Second: The usual methods of search for cycles after failing to recognize 
this impermanence except in a very crude way, have without justification 
assumed that the cycles are sine curves, as usually produced by planetary 
movements, whereas we have no evidence that such is the case. 

Third: The mixture of cycles has been too great to be handled by ordinary 
methods of analysis, which do not recognize the discontinuous period. 

The plan proposed below depends on the view that climatic cycles are 
fragmentary or temporary variations and not necessarily of any definite 
contour like a sine curve and that they must be extracted from a complex 
mixture. 

In developing a plan we have three aids. First, a similar type of cycle 
is found in the sunspot numbers and in certain irregular variable stars; sec- 
ond, a different and far more adequate method of analysis has been found in 
the cyclogram process, by which the length, the duration, and, to a great 
extent, the contour or amplitude of the cycle may be read off at a glance; 
and, last, the correctness of a given climatic theory involving cycle solution 

133 



134 CLIMATIC CYCLES AND TREE GROWTH 

can only be checked in an immensely long series of data such as thousands of 
years in which internal evidence can be developed. Because of the discon- 
tinuity of climatic cycles we can not, for example, with 49 years of records, 
tell what the 50th year will be, but with 300 we have a much better chance 
of estimating the 301st and, better still, with 3000 we can judge the 3001st 
much more closely. The absolute need of these long sequences has been met 
to an important extent by the thousands of years of dated tree-ring records 
of tangible, and, in one case at least, of high rainfall value. With these aids 
our procedure is to examine first the results in a region where they are 
best known, and that is in Arizona. 

THE ARIZONA RESULTS 

These tree-ring records show remarkable similarity to each other over 
great areas. This is called cross-identity and is due to meteorological effects. 
The relationship of the ring growth of these trees to winter rainfall is very 
evident over the period of time in which precipitation records are available. 
Because of this development of tree-ring records in northern Arizona and New 
Mexico, the climatic cycles as expressed in rings have been subjected to 
special study. They form a group called the common "cycle complex" be- 
cause in analyzing thousands of tree-ring curves both modern and ancient the 
same cycle lengths are largely found to dominate. These are approximately 
5f , 8-f, 10, 11£, 14, 17, 19 to 20 and 23 years, not all coming at once. We find 
that certain of these prevail over the others in certain areas, perhaps due to a 
selection resulting from degree of water conservation. In Arizona, a 19-20 
year cycle has been very strong; the next is near 14 years. When the great 
Arizona averages, including 50 or 60 trees (Flagstaff Area Mean Curve — 
FAM), have these two cycles subtracted from them, the double-crested 11?- 
year cycle that is called the Hellmann cycle is the chief one left. Some of the 
Arizona groups, such as the Grand Canyon group, show the Hellmann cycle 
without its being necessary to subtract the longer ones mentioned. 

It seems probable that three or four cycles have formed the chief basis 
of Arizona variations in the last 100 years, at least as far as winter rainfall 
is concerned, and their immediate application in prediction might be ad- 
vantageous. There are still three obstacles to the desired fullest solution of 
the problem in Arizona. 

First: These cycles are not permanent and we are not yet certain when 
any one is going to change. That special phase of the problem is called 
cycle sequence or recurrence. 1 There is evidence of a long control cycle of 
about 270 years, in which the shorter cycles tend to recur in orderly sequence. 
It is especially important to note that these cycles in their discontinuity do 
not change all at once but rather one at a time; hence, for short intervals of 
a few years the effect of possible change of one of several becomes actually 

1 See Proceedings National Academy of Sciences, vol. 19, No. 3, 359-360, March 
1933. 



CYCLE PROBLEM AND LONG-RANGE FORECASTING 135 

of less importance than, for example, the two-year cycle mentioned in the 
next paragraph. 

Second: There is a short variation of large amplitude with a length of 
two or three years. This is well known as the most frequent cycle length 
found in purely accidental variations and its harnessing into some system 
must be done with caution. But its consistent dominance in certain form 
over wide areas gives the impression that it is not accident in the common 
meaning of that term and that it can be solved. Pending its solution the 
form for prediction to take, if it is made, will have to be a forecast for the 
mean of each two successive years instead of for individual years. This 
amounts to prediction of a smoothed curve. 

Third: In this Arizona region the winter rains have been found to give 
good correlations with tree growth; what about the summer rains? Summer 
rains have been found to correlate to a degree with tree-ring growth in 
Florida (Lodewick, 1930). A study of summer rains can be made also in 
the Arizona trees, for in the case of "double" rings a definite part of the ring 
is obviously due to summer rains. There is evidence of the dependence of 
summer rains in part on the precipitation of the preceding winter but, in a 
more general way, it is probably related to torrid zone conditions. 

MISSISSIPPI VALLEY 

With regard to great areas like the Mississippi Valley, the problem, it 
seems to the writer, divides itself into two parts, centering respectively about 
winter and summer conditions. The activity of winter storms is probably 
related to the Arizona winter rainfall situation, as both are in the great 
westerly winds, but the Central Valley has its local records modified by latitude 
of the mean storm tracks of each season. In this way great complexity is 
introduced. Any studies that take up, month by month and year by year, 
the relation between the Mississippi Valley with its complex climatic changes 
and Arizona with its long and relatively simple records in trees have now an 
increased importance. Such, for example, are the departure studies now 
carried on by Dr. F. E. Clements. Measures of rings of trees in favorable 
localities should be used if possible to establish any climatic connection be- 
tween these areas in order to use the cycle studies of Arizona for the benefit 
of the Mississippi Valley. 

Summer conditions in the Valley partake of the torrid zone circulation 
in the summer thunder storm, modified here also by the latitudes of the large 
cyclonic storm tracks which still persist but lie farther north than in winter. 

A summer rainfall maximum of thunderstorm type is so characteristic 
of Arizona that these summer rains are sometimes referred to as "Arizona 
rains," but they are more widely distributed than that. They characterize 
the Great Plains lying on the east side of the Rockies. They are quite evi- 
dent as far north as Montana. Toward Texas they increase in intensity, 
taking up more and more of the annual total, thus growing more and more 
like torrid zone rains. In Texas and northern Mexico they even develop a 



136 CLIMATIC CYCLES AND TREE GROWTH 

midsummer minimum that reminds one, and is probably part, of the July 
minimum between spring and autumn maxima of equatorial regions. Thus 
it seems highly probable that Mississippi Valley summer rains will be studied 
in connection with torrid zone conditions and cycles, which may be sub- 
stantially different from those in the temperate zone. 

Thus far we have approached the Mississippi Valley forecasting problem 
by a method of comparison with Arizona conditions; a method that is indis- 
pensable on account of the long records in Arizona. But there is another 
approach to these Valley variations and that is by tree-ring growth in the 
Valley itself. In connection with reclamation and power development in 
certain areas, much-desired climatic work has been carried on by tree-ring 
methods. Many modern and some ancient specimens have been collected, 
measured and plotted and compared with meteorological records. 1 Personal 
examination of specimens has assured me that cross-identification exists to 
some degree in areas tested, although some of its features depart substantially 
from the simpler reactions in our dry areas. Though caution is needed in 
working them out, long sequences of value seem possible of establishment. 
This conforms with results obtained some years ago by Dr. Robbins of the 
University of Missouri. Furthermore a direct correlation between Valley 
tree growth and crops should be sought with care, since its value is more than 
obvious. 

COAST STATES 

Regarding the Atlantic Coast states, the situation is in some respects 
similar to that in the Valley, but complicated by the presence of the Atlantic 
Ocean, so that a slight change in the direction of the wind may have a far 
greater effect than in the Central Valley, both in rainfall and on temperature. 
The latitude of storm tracks is more stable but slow variations in ocean 
temperatures become a factor. Locations close to the coast are likely to be 
the most difficult. It is hard to find cycles in the long rainfall records at 
Boston and New Bedford, Massachusetts, but tree-ring records in 250-year 
old hemlocks in Vermont and rainfall records close by — Hanover, New Hamp- 
shire — give excellent analyses in terms of cycles. 

On the Pacific coast the situation is also complicated by the ocean. 
Precipitation depends extensively on whether storms pass across the Rockies 
at a northerly point or move down the coast. 2 This perhaps is a latitude 
effect and may be part of Kullmer's theory. At any rate, there is in Cali- 
fornia rainfall a short cycle averaging 5f years and giving the effect which 
has been named Hellmann Cycle. It has been sufficiently regular since 
1851 to give great promise of development as a basis of long-range prediction. 
But California rainfall values are strongly subject to the two-year cycle of 
higher amplitude which has a good chance of rendering worthless a predicted 

1 By Dr. Florence M. Hawley and Mr. Roy Lassetter, students of tree-ring work. 

2 Compare Blake, 1935; see Bibliography. 



CYCLE PROBLEM AND LONG-RANGE FORECASTING 137 

annual value. It interferes, however, very little with the prediction of a 
mean value between each two successive years. 

The Pacific Coast states are especially fortunate in having the longest 
known dated tree records whose climatic significance has been demonstrated. 
I refer to the giant sequoias. Sequoias on the high and steep slopes in the 
upper part of the groves give curves that somewhat resemble rainfall in 
central and southern California. The Hellmann cycle shows in the general 
sequoia ring growth curve since 1760. We may look upon California as a 
very favorable point for early prediction tests. 

Of course, these discussions of American climatic cycles are only part of 
a world problem. What is happening in north Europe when certain cycle 
conditions exist in America? What in South America, Africa, and Australia? 
Some day the whole matter will be examined, as it deserves. Inroads into 
the subject have been made here and there by various students — Abbot, 
Alter, Clayton, Arctowski, C. E. P. Brooks, Sir Gilbert Walker, W. J. S. 
Lockyer, C. F. Brooks and others. 

RELATION TO THE SUN 

It has been stated that climatic cycles resemble cycles found in the sun. 
This is based directly on the frequency periodograms illustrated in several 
parts of the last chapter showing that dominating terrestrial cycles have 
lengths coinciding with lengths of cycles in the sun. Practically the same 
group of cycle lengths has been found in fossil trees. Coincidence in time 
of changes in sun and earth has been shown in one case at least (Hellmann 
cycle in Arizona) but this has not been fully tested in other long records. 

The most difficult part of the physical line of cause and effect between 
sun and trees is the distribution about the earth by atmosphere and ocean, 
of the energy received from the sun. Since the earth's energy is derived con- 
tinuously from the sun by some form of radiation, we are justified in holding 
the hypothesis that the sun's part in the drama of climate is more than the 
mere exemplification of certain cycles. The resemblance between their re- 
spective cycles points directly to the sun's radiation as a cause of terrestrial 
changes; and once this is admitted, it brings climatic study into close con- 
tact with astronomy; the study of the sun and its physical characteristics 
and mechanical operations become of great economic importance to the 
human race. 

In view of the facts shown by the periodograms above referred to, and 
from many other reasons for regarding seriously this influence of the sun's 
energy on the earth, we can form a preliminary climatic hypothesis as an 
immediate guide in developing the prediction problem along its most favor- 
able lines. This hypothesis may be expressed in three terms: 

(1) Discontinuous periods in the sunspot cycle and in other solar activi- 
ties produce through radiation climatic cycles on the earth of corresponding 
length. These are disturbed in many places by the complexity of the dis- 
tribution of solar effects about the earth. Conservation and topographic 



138 CLIMATIC CYCLES AND TREE GROWTH 

characters and perhaps other factors cause different localities to emphasize 
different individuals of this cycle complex. 

(2) For any locality the cycles existing in the last 100 to 300 years, or 
more, are found and then each cycle still operating is projected forward to 
construct a curve for a number of years in the future ; these averaged together 
produce a mean which is to be regarded as the expected smoothed value of 
a few succeeding years. 

(3) Less well established but still with some definite foundation in the 
long chronologies there is the recurrence of several well-defined cycles at 
intervals of about 270 years. In this recurrence we believe we are finding 
signs of larger cycles or periods which will aid in removing the uncertainties 
that result from discontinuity in our climatic cycles. 

PREDICTION TECHNIQUE 

We feel that prediction and verification in the popular sense can hardly 
be a reliable guide as to validity of method at the present time. Percentage 
success or failure is very deceptive when watched for a year or two and means 
little in such a complex problem. The problem at this moment is not to 
predict but to lay a basis of knowledge and method out of which conservative 
prediction will develop. It therefore is best at this time to carry through a 
prediction process in a crude preliminary way without any attempt to make 
it exact in the sense of a prediction itself. It merely serves to call our atten- 
tion to various features that require attention. 

Fundamentals of Prediction — The following three classes of prediction are 
based on a consideration of errors or departures of the subsequent facts 
from the predictions: 

(1) Prediction that the mean value will always occur in the future, let the 
departures come as they may. This is the kind we find in climatic maps and 
has its use as important general information. 

(2) Prediction on the average departure from the mean, figuring what 
ought to come if it has not happened recently. This is straight probability 
prediction from the known distribution of the various departures from the 
mean, and the probability of any particular value coming next. It is exten- 
sively used by engineers. 

(3) The third class of prediction is a probability prediction, not from a 
mean straight line, as before, but from a sliding scale, a variable mean, which 
embodies climatic cycles as well determined as possible and, if possible, in- 
cludes a short cycle which we have called the two-year or "scatter" cycle. 

In carrying out our plan of illustrating the prediction process, we en- 
counter at once two parts of the problem that need careful thought. At 
first thought it seems perfectly easy to state the cycles that are operating 
now. Then we realize that several repetitions are needed to cause recogni- 
tion of a cycle. The average number involved in recognition is three or 
four, the average total repetitions before change is eight to twenty. It is 
a quite important matter to consider how soon an incoming cycle can carry 
important weight. Some of the recent ring records in Arizona show a five- 
year cycle operating since 1905. Should we give it full weight? Some cycles 
are not perfectly constant in length or amplitude. Should we give more 



CYCLE PROBLEM AND LONG-RANGE FORECASTING 139 

weight to the last few repetitions than to the preceding many? It is interest- 
ing to note that we have developed a method of trying out questions of this 
type; the results of such studies will be reserved for a future paper. 

The second question naturally is : What is the expectation of continuity 
after a cycle is established as operating at the present time? When is one 
of the cycles likely to stop and when is a new one likely to enter? In the 
case of the sunspot cycle the data show that the intervals between maxima 
more often than not remain within about 10 per cent of the last value. Hence 
one of the most important features in our cycle lists (chapter V) is the 
number of repetitions without material change. That we can be very 
sure of and by simple methods we can increase our knowledge on that point. 

But actual plots (some of them made in 1927) indicate periodic recurrence 
of certain cycles. Here is the line of most promising development of the 
theory of climate, bearing upon the temporary cycles that we encounter. 
That also must be reserved for a future paper. 

Cycles in the Pueblo Area — In picturing the situation for a limited area 
we are taking the only possible course, and no attempt is made to extend 
consideration outside the "Pueblo" area of northern Arizona and New Mexico 
west of the Rio Grande Valley and reaching into the southern parts of Col- 
orado and Utah. Having outlined our area we can consider the cycles found 
there which, together, produce a prediction "mozaic." Considering each 
cycle as a natural unit of some sort, we wish to take the combination of units 
operating now and put each unit or cycle one step or cycle length forward. 
This could be called the "a" stage in the treatment. The "b" stage means 
weighting each cycle by ascertaining its average number of repetitions in 
its previous appearances in the last 2000 years and giving it the proportionate 
part of its average number that remain undone. The "c" stage of treatment 
is an estimate of its tendency to disappear and its probability of return, 
derived from the general study of cycle sequence or recurrence from long 
chronologies. Treatment "d" considers it in relation to cycles of similar or 
related length in solar phenomena. 

It will be appreciated that the above analysis of the prediction problem 
represents the situation at the present moment. As time goes on and larger 
areas of the earth are brought under this kind of study, a much better knowl- 
edge will be reached of the activity of these cycles and the probability of 
their continuance or recurrence. 

Application to Winter Rainfall of the Pueblo Area — Four or five cycles 
stand out as more important in the Pueblo Area; 23 years; 19-20 years, one 
near 14 years, the 1 1 .5-year cycle, and the 2-year cycle. As the unit in tree-ring 
records is the year, we can not cover very satisfactorily lengths under 5.0 
years; certain values between 1\ and Z\ years are derived from the 2-year 
reversal interference test. (See page 89.) Without doubt still longer cycles 
now under investigation are equally important in this problem. 

The 23-Year Cycle — A cycle of this length and of high amplitude was active 
during the 18th century. Since then it seems to have given place to a shorter 
one of 19 or 20 years. 



140 CLIMATIC CYCLES AND TREE GROWTH 

The 19-20-Year Cycle — Several centuries of tree-ring records are necessary 
in order to get a picture of this long cycle and even now it remains uncertain 
whether it is not a mixture rather than one single cycle. A cycle of about this 
length has dominated Arizona ring records since 1800. It shows in recent 
tree growth and in comparative rainfall records, with apparently a lag of some 
two years in the tree records. Its last maximum was near 1928; its total 
range of variation has averaged 35 per cent. In the rainfall records it has 
been about the same. Its number of repetitions has already run very high 
and its expectation is growing less. An examination of long chronologies 
shows that some cycle of this length is very persistent through the centuries 
though its amplitude is far from constant. It would not be surprising if its 
time of diminution were approaching. It does not seem likely to disappear 
altogether. In its solar relation its half value, 10 years, was prominent in the 
sun (and trees) two hundred years ago. The 10-year cycle, sometimes seen 
in trees and in various phenomena, and 20 years, and possibly a 37 or 38-year 
cycle of variable amplitude that persisted for many centuries in Arizona tree 
records, are probably solar though not commonly in the spots. A 10-year 
cycle showed in the occasional spots during the great dearth near 1700. It 
has not, as far as known, come out strongly in recent years. There is some 
suspicion that a cycle of 5 years is influencing southern California rain to an 
increasing extent since 1900. 

The 14-Year Cycle — This cycle, often double-crested, takes a value near 
13.7 years in the last century. Its total range of amplitude is near 25 per 
cent. It must be studied in trees, since meteorological records do not go 
back far enough. There are slight alternative choices of exact value in the 
Flagstaff 500-year records through which it has lasted. Its dominance or 
intensity varies. A maximum perhaps came in the period 1933 to 1935. 
This cycle has been persistent since 1850 or so; it possibly changed phase near 
1820. In cyclograms it shows extensively by interference with other cycles, 
giving the impression that we may be dealing with a submultiple of a longer cycle. 

As to phenomena in the sun, a 14-year cycle was most evident in the 
smoothed annual numbers between 1788 (maximum) and 1837 (maximum), 
the last cycle in this interval being 7 years in length. 

The ll\-Year Cycle — This has appeared in a double-crested form in trees 
since 1850 or before with a total range in amplitude of 20 per cent; its maxima 
have come in the ring sequences about two years after the maxima and minima 
in the sunspot numbers. It has had various appearances in California ring 
chronology that suggest a 270-year recurrence cycle. At each appearance 
it has lasted a considerable period, of the order of 100 years. Thus at the 
present time we can cast this Hellmann cycle forward a half or whole 11 years 
length with the feeling that the length or intensity has a change in the not 
distant future. 

Probably other cycles both longer and shorter could be included in this 
list, but the various cycles mentioned, when assembled into a picture, give 
us at least an idea of the prediction mozaic. 



CYCLE PROBLEM AND LONG-RANGE FORECASTING 141 

The exact outcome of this mozaic is not important since we have not 
finished testing our hypothesis; but the advance of technique developed by 
carrying forward this process is most important. Such questions as these 
arise: In casting forward the observed cycles, should we give more weight 
to the latest cycle data than to past series of cycles? What is the practical 
rate of increase of weight from the past toward the present? How far can 
we rely on recognition of cycles that may be just beginning? What is the 
last word on the expected number of repetitions of each cycle operating? 
Is this number constant through history or not, and how does it change? 
We see a need for investigating dominating cycles: Should a subtraction 
process be used in isolating cycles; what value should be given to weak cycles? 
Why do some curves give most satisfactory sets of cycles and others not? 
Answering these questions in a more or less complete way will rest in further 
studies of the long chronologies which were largely developed for that purpose. 
We have even planned a definite method of attack on these questions in a 
process which we call "laboratory prediction." Experience has shown that 
as these methods go forward, further improvements will develop. These 
long chronologies also supply data which we believe will enable us to locate 
phases of the sunspot cycle in past history. We recognize also many studies 
to be made on the relation of solar changes to tree growth since the invention 
of the telescope in 1610. 

By outlining the process as done herein, we find the data that need to be 
observed more carefully. We shall gain knowledge and skill both from 
historical studies of the past and more intensive work on the present. In 
the course of time, the action of these climatic cycles will be known in more 
and more detail, and long-range forecasting will improve. It will not be 
good sense to look for accuracy at the start, and for some years verification 
of error must be taken as merely so much scientific information that merges 
into and improves the method. 



Studies of the Cyclograph — E. Schulman 143 

Summation Curves 155 

An Automatic Optical Periodograph — A. E. Douglass 164 

Bibliography 166 






142 



APPENDIX 

STUDIES OF THE CYCLOGRAPH 
By Edmund Schulman 
INTRODUCTION 

The cyclograph is an optical-mechanical instrument to aid in the detec- 
tion of cycles in variable phenomena. When plotted in a curve, data of this 
type are transformed by the cyclograph into a pattern whose interpretation 
by the observer represents a cycle analysis. This pattern is highly sensitive 
to changes in position of moving parts of the instrument and thus enables 
analysis over a continuous and large range of cycle lengths. The readable 
display in the pattern of complex and frequently hidden changes in the char- 
acter of cycles in natural phenomena makes cyclograph analysis not only a 
rapid but a highly powerful method, in solving many cycle problems such as 
those encountered in climatic studies. 

However, since the cycle results are obtained by interpretation of a pat- 
tern, it is relevant to inquire how much the personal element influences the 
results. The comparison of the analyses of two or more independent observ- 
ers is thus indicated. The following discussion is principally concerned with 
such an investigation; some studies which are in part supplementary to simi- 
lar material in Chapter II of this volume are also included. 

DESCRIPTION OF THE INSTRUMENT 

The cyclograph as used at present in the Tree-Ring Laboratory is sub- 
stantially the same as described by Dr. Douglass in 1915, 1919 and especially 
1928 (see Bibliography), although some minor modifications were introduced 
in 1931-32. In skeleton outlines, the instrument has three major parts. 

(1) The Light Source — This consists of a horizontal series of light bulbs, 
in back of which is a mirror, and in front of which is a diffusing screen. This 
screen forms a window, measuring 44 inches horizontally by 3 inches verti- 
cally, in which may be placed for analysis a cycleplot 1 of any curve. All 
the holes in the cycleplot therefore receive a uniform illumination. 

(2) Movable Mirror Carriage — The mirror carriage is suspended from a 
two-rail track which is 7 feet above the floor and runs about 40 feet horizon- 
tally, beginning some 6£ feet from the window. The carriage holds two 
mirrors, 5.5 inches by 25 inches, each inclined 45 degrees to the vertical with 
the reflecting surfaces toward each other and facing the window. Since the 

1 A curve plotted on opaque paper, and maxima cut out. See pp. 44 and 149. 

143 



144 CLIMATIC CYCLES AND TEEE GROWTH 

top mirror is on a level with the light source, and the lower one is on a level 
with the object glass of the analyzing box, running the carriage out or in 
has the sole effect of changing the object distance without disturbing the 
optical axis. The carriage runway is calibrated in terms of standard scale 
(see p. 44). 

(3) The Analyzing Box — Facing the movable mirror is found the analyzing 
box, which contains most of the working parts of the instrument. The 
objective is a Tessar II B lens of 6 inches focal length, directly in front of a 
negative cylindrical lens of 12 inches focal length, whose axis is horizontal. 
Therefore all rays in the horizontal planes come to a focus at 6 inches from 
the objective, while rays in vertical planes focus at 12 inches. The image 
formed by this system at the 6-inch focal plane consists then of a reproduction 
of the holes in the cycleplot with respect to horizontal spacing of the centers 
of gravity of the holes, but with the images in the form of parallel vertical 
bars of light ; the width of any bar depends upon the width of the correspond- 
ing maximum and its light intensity upon the amplitude of the maximum. 
This image of parallel bars is called a "sweep" or a cylindrical pattern. 

In the focal plane there is placed an analyzing plate consisting of two 
glass plates having alternate transparent and opaque rulings, whose grating 
constant is 0.02 inch. Superposing the two plates makes possible any size 
of transparent line up to 0.01 inch, the total spacing of a pair of successive 
transparent and opaque lines being constant at 0.02 inch. As arranged at 
present, the width of a transparent line is closely 0.001 inch. The analyzing 
plate is inclined at an angle of 17 degrees to the vertical sweep lines. 
It is then easily seen that the analyzing plate breaks up every vertical bar of 
light into segments, some of which are permitted to pass through, and some of 
which are held back. The resulting pattern is a series of light images or dots 
in several duplicate horizontal bands or sets. With a total effective rec- 
tangular aperture behind the focal plane of 0.4 by 1.5 inches, the longer side 
horizontal, an inclination of 17 degrees, with the analyzing plate used, yields 
almost exactly five of these horizontal bands in the pattern. A thread is 
placed in the focal plane to indicate horizontal direction. 

Behind the analyzing plate is a condensing lens system consisting of two 
cylindrical lenses of 6 inches focal length with their axes vertical. Near 
this system is a small mirror set at an angle of 45 degrees, which throws the 
light to one side to an observer who views the pattern through an eye lens. 
The observer then has the cycleplot window to his left and the movable 
mirrors to his right, while he is out of the direct line of the rays. For photo- 
graphy, the small secondary mirror is swung out of the way and the light 
allowed to proceed directly to a camera compartment. 

When the mirror carriage is moved, the object distance changes and, of 
course, the focal plane will suffer a corresponding slight change. To keep 
the position of the focal plane constant, the lens system of the analyzing 
box, consisting of Tessar lens and negative cylinder, is mounted on a movable 
frame which receives a slight motion from an arm resting against a spiral 



APPENDIX 145 

wheel. This wheel turns by means of a gear meshing with a toothed runway, 
which in turn moves at a rate that is a small ratio of the motion of the mirror 
carriage. The resulting motion of the objective is then such that the change 
of object distance is exactly counterbalanced and the focal plane remains 
fixed. 

OPERATION 

Calibration — Periods in the cycleplot may be made to give a horizontal 
alignment of dots in the pattern by the simple process of changing the distance 
of the movable mirrors. With a series of artificial curves having regularly 
spaced maxima plotted on the normal scale of a unit every two millimeters, 
it is possible to calibrate a scale marked on the carriage runway so that the 
cycle length corresponding to any horizontal alignment may be read directly. 
The cy olograph is calibrated from 5.0 to 42.0, the smallest division being 0.1 
unit. 

Nature of the Pattern — If the cycle present in the data is not exactly periodic, 
that is, with all the maxima equally spaced, then since there exists a mean 
length of the cycle there will be a mean alignment in the pattern. Depar- 
tures from this mean horizontal position of the dots indicate a slight lag or 
advance in the occurrence of the maxima concerned ; hence, the term differen- 
tial was at one time applied to the pattern obtained. The closer the cluster- 
ing of the light-dots about the straight line, the closer the cycle approaches a 
perfect cycle or periodicity. It is analogous to the clustering of dots about a 
regression line in a scatter diagram as a measure of correlation, though the 
cyclogram pattern itself is more closely akin to the O-C diagram (in which 
positions of the dots along a horizontal line represent their theoretical or 
computed places, and the vertical displacements from this line the observed depar- 
tures from exact periodicity) } It is evident that a change of period in any 
interval will be represented by a different trend in the corresponding interval 
in the pattern, demanding a different position of the mirrors to bring that 
interval into horizontality. Logarithmically varying cycles will thus form a 
curved line pattern. 

Procedure in Analysis — Two complete analyses of each curve are made, one 
with the movable mirrors at successive settings from 5 to 42 units, and the 
other with the mirrors returning from 42 to 5. The items usually noted are 
cycle length, duration (dates of beginning and ending), emphasis or cycle 
strength, fractionization or splitting of cycle into one or more series of sub- 
ordinate crests, phase changes, changes in length or amplitude and any 
special characteristics. 

The matter of cycle emphasis needs particular consideration. The im- 
portance or strength of a cycle is indicated by underlining the figure repre- 
senting the cycle length, very good cycles receiving two or even three under- 
lines (see page 147). The factors determining the assignment of underlines are 

1 In the cyclogram, departures from exact periodicity are also indicated by displace- 
ments from a horizontal alignment, but maxima are plotted in their observed places in the 
time scale. 



146 CLIMATIC CYCLES AND TREE GROWTH 

regularity of period, number of maxima, regularity of amplitude, strength of 
amplitude, kind of fractionization if any, and freedom from ambiguous 
maxima and alternative settings. 

CYCLOGRAM FORMULAE 

A cyclogram pattern may show harmonics arising from two fundamentally 
different causes. In one case the harmonic is only apparent and arises from 
a fractionization of the pattern due to a fractional setting ; in the second case 
the harmonic actually exists in the data under analysis. 

Harmonics Due to the Cyclograph — The following criterion may be used for 
judging the fractionization of a setting. If the movable mirrors are set at a 
point on the scale, i/j of a cycle length existing in data plotted at normal scale, 
i/j being a simple ratio, then there will be i times the normal number of 
horizontal rows in the pattern, every row consisting of a series of light dots 
located one to every j successive lines of the analyzing plate. 

It has been found in practise that with the exception of settings at \, 
\, \, and rarely \ and ?, the effect of harmonics and multiples is negligible, 
and these when they occur can easily be recognized. It is possible that 
the less simple harmonics determine to some extent, however, the apparent 
presence in real data of subordinate, weak cycles which may not be real. 

Harmonics in the Data — Consider an arrangement, with a 12.0 unit stand- 
ard cycleplot in the window, the mirrors set at 12.0 ; then the pattern consists 
of five horizontal rows of light dots. 

Suppose we replace the 12-unit standard with any other cycleplot, which 
also contains a 12-unit cycle and, in addition, a set of secondary maxima of 
smaller amplitude spaced half-way between the major maxima. We now 
find double the number of rows of light images in the cyclogram, every other 
row being relatively faint. Two secondary maxima will give two fainter 
companion rows of images. The departure from a straight alignment of 
the rows of dots of course measures the departure of the cycle from a per- 
fect cycle or periodicity. 

It is important to note that the secondary maxima will not be of as great 
a mean amplitude as the fundamental. They may exactly divide the space 
between the fundamental crests into 2, 3, 4, ... n parts depending on the 
number 1, 2, 3, . . .(n-1) of secondary maxima, in which case there will be 5n 
equally spaced rows in the pattern, or they may directly follow or precede 
the fundamental, in which case there will be 5 similar sets of rows, the arrange- 
ment of rows within the set depending on the positions of the secondary 
maxima. Again, departure from straight alignment will depend upon de- 
parture of the maxima from exact spacing. 

Alignment Formulae — Since cyclograms may be observed at all scale set- 
tings between 5 and 42 units, the inclinations of cycle alignments in the pattern 
change with the setting. Let origin of coordinates be at intersection of a 
sweep line, analyzing line, and a horizontal cross-hair. Consider the rec- 
tangular coordinates of the adjacent light dot in any alignment with reference 



APPENDIX 147 

to the cross-hair as axis. Then it is easy to show that the angle of inclination 
6 of the alignment is given by 



H) 



(1) tan0 = (1 — £J tani 

where i is the inclination of the analyzing lines. 

p is the period length of the mirror setting. 

c is the cycle length represented by the alignment. 
From (1) we have 

(2) c= ptani 



tan i — tan 



If the sweep lines are inclined at an angle <j> to the horizontal cross-hair 1 
we have the more general case 

(3) tan t - (C - P) sin * sin ! 



p sin (0 — i) + (c — p) sin <j> cos i 
and 

(4) c - p (l + tanflsin(0-i) \ 

\ (1 — cot i tan 0) sin <f> sin i/ 

With <j> = 85° and i = 102° as in cyclograms in this volume (4) becomes 

/r . 1—0.09 tan 

(5) c = p 

v ' v 1-O.21tan0 

CONSTRUCTION OF FREQUENCY PERIODOGRAM 

To produce a periodogram summarizing the analyses of a number of curves, 
the procedure is first to make up a cycle diagram (see fig. 57). Each cycle in 
every analysis of the series is entered in the diagram with its weight, the 
numerical value of which is that given in the following table. To expedite 
the formation of the diagram, the cycle weights are sometimes represented by 
symbols as follows : 



Type 


Underline 


Weight 


Symbol 


Poor 


X 


1 


- dash 


Normal 


no 


2 


. dot 


Good 


1 


4 


x cross 


Excellent 


2 


6 


e circled cross 



A plot is made on the standard 2-mm. graph paper used in the Labora- 
tory; cycle lengths, one scale unit per centimeter, are plotted as abscissae, the 

1 An apparent inclination of the sweep lines to the vertical will arise when the cross- 
hair is not precisely horizontal. 



148 



CLIMATIC CYCLES AND TREE GROWTH 



smallest interval recognized being one-tenth unit. It is then easy to sum up 
the columns, mentally transforming symbols into numbers, and obtain a set 
of periodogram numbers. These when plotted form a weighted frequency 
periodogram. 

It is evident from the optical nature of the cyclogram method of cycle 
analysis that there is a logarithmically decreasing exactness in assigning a 
cycle value with increasing length of the cycle. Hence, the abscissae of 
the periodogram are taken to represent a logarithmically increasing range 
from 5 to 42 ; in practise a range of 5 per cent is used, successive intervals over- 
lapping by one-half the range. 

It is often of value to plot the individual cycle lengths in other ways than 
the one described above and called a cycle diagram. For instance, a long 
sequence of data may be segmented into several equal time intervals for each 




Fig. 57 — Construction of a frequency periodogram from ten groups 
in the Central Pueblo area. 



of which a cycleplot is prepared; if the sets of cycle lengths obtained by 
analysis are plotted in suitable symbols with the ordinates corresponding to 
the successive time segments equally spaced, then slant alignments from one 
segment to another may become evidence of cycle flow, i.e. gradual change of 
cycle lengths. Again, by using time on a vertical scale and cycle lengths as 
abscissae (or the reverse), it is possible to represent graphically the exact range 
of occurrence of the cycles in any data. An example of this may be found in 
figure 3 Id where it is called a chrono-periodogram. 

ERRORS OF THE INSTRUMENT 

The errors of the instrument fall into two classes, those involved in the 
building of the cycleplot and those due to manipulation of the optical ele- 
ments of the cyclograph. 



APPENDIX 149 

Preparation of Curves — Measuring of specimens is now done almost exclu- 
sively with the standard measuring engine, a modification of the cathetometer 
method described in Climatic Cycles and Tree Growth (Douglass, 1919, pp. 
58-59). A subordinate scale on the instrument checks decade sums and 
eliminates serious errors in measurement. 

Many growth curves show trends due to aging of the tree, sudden favor- 
able or unfavorable change in environmental factors and the like, which are 
meaningless in terms of cycles, and hence are removed by standardizing. 
This process is accomplished by transforming the actual measured values 
to percentage departures from a mean or standardizing line (run through the 
data by estimation) containing the trends it is felt should be removed. It 
has been found that standardizing lines drawn by Dr. Douglass when com- 
pared with lines through the same data drawn by the writer differ in only 
a small degree; however, it is evident that even a relatively large difference 
will have practically no effect on the lengths of the cycles found and only 
a small effect on the amplitudes. This is particularly true in light of the 
desirable practise of keeping the standardizing line as free from bends or 
"kinks" as the data permit. 

Cutting Line — After a curve is smoothed, it is transferred by carbon tissue 
to a strip of brown opaque paper called cycleplot paper, some 48 inches long 
by 4 inches wide, and therefore slightly larger than the window of the cyclo- 
graph. A base line is then drawn on the curve; this is called a cutting line, 
and the maxima that it isolates are cut out with a razor blade. The present 
practise of the Laboratory is to use a cutting line that approaches or is a 
straight base line, usually parallel to the horizontal axis and at the approxi- 
mate height of mean minimum. On the margins of a deep minimum, the 
straight cutting line is slightly modified downward, to avoid displacing the 
center of gravity of the maximum. Those minor maxima which lie below 
the cutting line are taken care of by cutting out only the very tops; those 
minima which lie above the cutting line are extended downward by means of 
narrow tongues. Tests show that cutting lines of different observers yield 
no definite difference* as far as cycle lengths are concerned ; the amplitudes of 
those cycles if determined optically from the cycleplot would, of course, be 
affected by cutting lines departing from the usual procedure. At present 
amplitudes are obtained by arithmetic summation of the data and are thus 
independent of the cutting line. 

We may therefore conclude from a study of the errors in the cycleplot 
building process that, when the standard methods of the Laboratory are 
used, the resultant extraneous effects introduced into the derived cycle ele- 
ments are too small to be of any consequence. 

The most important of the errors involved in the actual manipulation 
of the instrument is the occasional slight change in the focus correction due 
to the convenient use of cords connecting the focusing device to the carriage 
on the track above. The practise in cycle analysis is, however, to test the 
calibration both before and after every analysis or short series, with the 



150 



CLIMATIC CYCLES AND TREE GROWTH 



regular standard cycleplots, any scale error becoming immediately evident; 
the instrument is then adjusted, or if the error is small it is applied as a 
correction to the results. 

Since the scale is calibrated in tenths of units, cycle values are at best 
correct only to the nearest tenth unit. In rare cases only, of outstanding 
cycles or in special study, is interpolation to hundredths of a unit made. 

ERRORS IN CYCLOGRAM ANALYSIS 

The matter of precision in assigning cycle lengths has received much 
attention. The material used consisted on the one hand of a large number 
of cycle analyses of the 42 Western Groups carried through by Dr. Douglass 
in 1926-28, and on the other hand of a considerable series on the same 42 
Groups and also on the California Coast Redwoods made during 1933-34 
by the writer. An intensive study of this material over a period of some 
months resulted in a set of statistical "constants" and is summarized in 
table 1. 

Table 1 — Variations in cycle settings 



Tests 


CaBes 


P. ct. Av. 
Diff. 


1. Differences between Out and In Settings, same obser. 

(a) 42 Groups, unkn. scale, using Max. AED. Jan. 1928 

(b) 42 Groups, unkn. scale, using Min. AED. Jan. 1928 

2. Differences between two analyses of same material, same 

observer. 

(a) 42 Groups, using Max. lst-direct; 2d-unkn. scale AED. 
1926-8 


216 
271 

190 
178 
326 

46 
95 

166 
241 


0.8 
1.0 

2.4 
2.5 
1.9 

2.5 
3.0 

2.8 
2.0 


(b) 42 Groups, using Min. lst-direct; 2d-unkn. scale AED. 
1926-8 


(c) California Coast Redwoods, using Max. lst-direct; 2d- 
unkn. scale. ES 1933 


3. Differences between two analyses of same material, different 
observers. 

(a) 42 Groups (part), AED. vs. ES, principal cycles 

(b) Same all cycles 


4. Effect of inverting curves for analysis. 

(a) 42 Groups, AED, lst-Max; 2d-Min., Norm. Scale, 1926. . 

(b) 42 Groups, AED, lst-Max; 2d-Min., Unkn. Scale, 1928. . . 



1. Standard procedure in cy olograph use demands an analysis over the 
entire range not only when the mirrors are moved out, but also when they are 
brought in. As far as possible, the second analysis is made independently 
of the first. Some remembrance of the pattern may, however, influence 
the assignment of a horizontal setting the second time, in many cases, and 
for that reason differences were expected to be small. 

As in the other cases discussed below, differences are chiefly due to 
confusion in the pattern because of weak cycles which make one setting 
hardly better than several others in the immediate vicinity. Sometimes only 
one or two dots (crests) will determine a significant alternative setting. When 
the pattern contains a strong cycle, alternative settings sometimes depend on 
the accepted duration of the cycle. Ambiguity arises in part also from the 



APPENDIX 



151 



placing of emphasis on different portions of the cycle at different times. In 
many cases, two distinctly alternative settings may be made, only a portion 
of the individual dots being common to each. The average difference of these 
alternative settings was found in 31 cases to be about 5 or 6 per cent. 

2. The second kind of difference is that resulting when the same material is 
subjected to analysis at two different times by the same observer. To make 
the test as rigorous as possible, the original analysis was compared with a 
second set in which the same data had been replotted on an unknown scale. 
Extensive analyses of this type in the 42 Western Groups by Dr. Douglass 
and in the California Coast Redwoods by the writer were available. After 
applying the proper correction factors to the second set, the average differ- 
ence when using the maxima was almost exactly the same as that when 
the plots were inverted and the minima were used. The total number of 
cycle pairs compared was 694. An average difference of 2.5 per cent, the 
largest found, is not very great when we consider that we are dealing with 
highly variable phenomena containing fluctuations due to some minor ex- 
tent at least to random causes. 

Table 2 — Anomalous cycles 



Type of test 
(see table I) 


Total cycle lengths, = y 


Anomalous cycles, = x 


P. ct. - 100 x/y 


la 


507 


75 


15 


lb 


625 


83 


13 


2a 


506 


126 


25 


2b 


450 


94 


21 


2c 


841 


191 


23 


3 


250 


60 


24 


4a 


443 


111 


25 


4b 


665 


183 


28 



3. The third kind of difference considered, that between two observers, is 
the most important. The only available data that could be used were in 
the 42 Groups; the analyses had been made some eight years apart and were, 
of course, quite independent. The average difference of 3 per cent is grati- 
fyingly small; in this value there are included cycles, the identifications of 
some of which, as corresponding to the ones paired with, were highly doubt- 
ful. When only the strong cycles were used, the average difference is no 
larger than the difference of the second kind (see number 2 above). 

4. In ordinary procedure the maxima of a curve are isolated for analysis. 
What happens when the minima are isolated instead? Comparison of 
analyses using maxima with those using minima shows that the average dif- 
ference is of the same order as before. The total of 407 pairs of cycles is 
certainly large enough so that the result may be viewed with confidence. 
No apparent change was found in the number of emphasized cycles. There 
was also no evidence for any systematic increase or decrease in cycle length 
on inversion. 



152 



CLIMATIC CYCLES AND TREE GROWTH 



Frequently an observer finds weak cycles which another observer, or even 
the same observer at a different time, does not find. Such cycles (called 
anomalous and not included in our lists of weak cycles) constitute a serious 
matter for investigation. The amount of these cycles present are given 
in table 2. 

It is significant to note that the out-in tests contain a much smaller per- 
centage of anomalous cycles than the remaining kinds of tests; there is evi- 
dently a dependence of one set on the other, as suggested already. The 
similarity in the size of the remaining percentages indicates the absence of any 
systematic factor; but an average of one anomalous cycle in every four seems 
at first glance serious. It was found, however, that these are almost all weak 
cycles of little weight, and random length, which largely cancel out when the 
analyses in which they are found are summed into a periodogram. 

Another question which may be considered here is the difference in the 
lengths of cycles analyzed at different times, as a possible function of the 
length of the cycle. The available data are summarized in table 3. When 

Table 3 — Cycle differences with cycle length 



Range — Years 


No. of Cycles 


Av. Diff. — Years 


Obs. 


5.1-10.0 


112 


0.173 


ES 




77 


0.195 


AED 


10.1-15.0 


97 


0.259 


ES 




105 


0.323 


AED 


15.1-20.0 


45 


0.336 


ES 




76 


0.389 


AED 


20.1-25.0 


44 


0.445 


ES 




58 


0.502 


AED 


25.0-and over 


30 


0.480 


ES 




37 


0.638 


AED 

,, ... 



plotted there is evident a straight line relationship for each observer which 
may be expressed as 

An = kn 
where An = difference in cycle lengths, 
k = constant for observer, 
n = cycle length. 

From the above table we find the differences in cycle values, in per cent, 
to be as follows: 

Pet. Av. Diff. 



Mean Cycle 


AED 


ES 


7.5 


2.6 


2.3 


12.5 


2.6 


2.1 


17.5 


2.2 


1.9 


22.5 


2.2 


2.0 


29.5 


2.2 


1.6 



The value of k is found to be 0.024 for AED and 0.020 for ES. 
In summarizing this study of differences, we find that in spite of oppor- 
tunities for disagreements the results of different observers are closely alike 



APPENDIX 153 

and we conclude that we are dealing with real cycle phenomena and a reliable 
method of analysis. 

PROBABILITY TESTS 

We now take up such matters as the tendency of an observer to favor 
certain cycle lengths (resulting in spurious emphasis on special values in the 
periodogram) and the recognition of real and unreal cycles. To investigate 
such problems by means of probability curves is illuminating. 

A general method, used in the Tree-Ring Laboratory, for obtaining a 
lot-drawn or random curve is the following. Each year represented in a 
sequence of measurements of ring widths of a specimen or group to be used is 
marked on a slip of paper. All slips are then thoroughly mixed in a container, 
and drawn out at random without replacements. The values corresponding 
to the years drawn are put down in the order of drawing, and a curve is made 
from the series. This represents a quite accidental or probability arrange- 
ment, whose frequency distribution, however, is of course identical with that 
of the original curve. Each curve is then put into the cycleplot form. 

Recognition Tests — A test was made with four 500-year lot-drawn curves, 
to which were added two 500-year real curves of northern Arizona tree-growth, 
and the analysis carried through by the rack method of simultaneous or con- 
current analysis, every curve appearing for a moment in front of the cyclo- 
graph window and then giving place to its neighbor. Both real curves were 
recognized at once, by their evident similarity in the cyclograms. 

A second and more extensive recognition test was made with a group 
comprising 27 lot drawings and 6 genuine curves. They received simultane- 
ous analysis, five and six at a time, with two real curves for comparison; one 
was put in rack at the top, the other at the bottom, and the unknowns in 
between. The analysis was made in six sets. It is to be noted that the real 
curves among the unknowns were from the same geographic area (and hence 
contained approximately the same cycles) as the two comparison curves. 
Nevertheless, the results were quite gratifying: 
Of 6 called genuine, 5 were genuine. 
Of 2 called possibly genuine, 1 was genuine. 
Of 25 called false, 25 were false. 

We may conclude from this that when the curves are subjected to simul- 
taneous analysis as above, the probability of picking out the real from the 
false is quite high. 

Cycle Preference Tests — To test whether there was any preference in the 
matter of assigning particular cycle lengths and to test for characteristics of 
cycles in random sequences, a group was made up with considerable care 
consisting of 37 cycleplots of which 6 were genuine. All were individually 
analyzed without knowledge as to which were genuine and thus all received 
treatment as if they were real. 

The periodogram values of the first 15 of the lot-drawn curves were 
compared with the values for the remaining 16. A correlation coefficient 
of 0.016 ± 0.117 was found, indicating completely random distribution of 



154 CLIMATIC CYCLES AND TREE GROWTH 

the cycles in lot-drawn curves. As a comparison, the periodogram numbers 
of the analyses of 22 dated Coast Redwood specimens were correlated with the 
numbers for 19 undated specimens. The correlation coefficient was 0.56 
± 0.08, strong evidence then that the cycles found are present in the trees 
concerned and not accidental in origin. The correlation coefficient for a 
similar comparison of the more homogeneous Central Pueblo Area curves 
was 0.76 ± 0.05. As a check, the correlation coefficient was obtained be- 
tween the periodogram numbers representing analysis of two additional 
random groups. The value was 0.05 ± 0.11, again indicating random dis- 
tribution of cycles in lot drawings. 

THE PRESENTATION OF CYCLE DATA 

In mass presentation of cycle data, as given in the lists of Chapter V, it 
is impossible to represent all the peculiarities of the individual cycles. The 
summation curves following this section supplement the lists but often do 
not reveal significant detail seen in the cyclogram. It is hoped that it will 
eventually be possible to publish cyclograms to accompany all cycles men- 
tioned. The column titles in the tabular matter referred to are explained 
below. 

Number — The numbers in this column refer to the summation curves 
(pp. 156). The latter are placed in order of increasing cycle length, which is 
the arrangement of the long chronology lists. 

Cycle — This column gives the exact cycle length used in the amplitude 
computation. Since values of the cycle observed are subject to the inaccura- 
cies already discussed, differences between two cycles of 2 to 3 per cent may 
not mean that they are different ones. For example, 13.6 and 13.8 may really 
represent the same cycle. Often a change in cycle length of 2 per cent or 
more will be found when the assigned duration is changed somewhat. 

Occasionally a cycle is seen as two-crested, that is, with one set of subor- 
dinate intermediate maxima; the notation in the lists, oc\, follows the cycle 
length. Two subordinate crests are noted as oc\, and so on. If every other 
maximum in an alignment is especially strong, indicating the presence of 
the double-length cycle, it is noted in the lists as x2 (times 2). This para- 
graph refers particularly to the cycle tables of the monthly sunspot numbers 
and the geological material. 

Underlines — The significance of cycle underlines is discussed on page 146 
and on page 147. 

Duration — The dates just preceding the first maximum and following the 
last one were obtained at time of analysis. Dates were subsequently altered 
by as much as three or four years at beginning or end, to permit an integral 
number of rows in summation for amplitude. It is important to remember 
also that many cycles do not appear or disappear suddenly; hence caution 
is necessary in considering these dates as precise. 

First Maximum — The position of first maximum as given is that of the 
highest part of the summation curve. Many cycles have two or more crests, 



APPENDIX 155 

non-symmetrical but often not widely different in height. It is evident that 
if one should force these curves into such artificial form as a sine curve with one 
crest, the position of maximum might be changed somewhat. It was felt 
that there was not sufficient justification for this final smoothing, and the 
summation curves were simply Hanned (Chapter II). 

Rows — As stated above, usually only an integral number of rows or repe- 
titions of the cycle were considered for amplitude. In a few cases of longer 
cycle lengths, half-rows were also permitted in order to make full use of the 
data. 

Per cent Amplitude — The block method of summation for amplitudes, 
using for fractional periods rows not all containing exactly the same number 
of elements, has been discussed on pages 30 and 97. The difference between 
maximum and minimum of the Hanned summation curve is the total range of 
amplitude. Half this quantity, divided by the mean ordinate for the summa- 
tion interval, is the per cent amplitude given. Here also, as in the case of the 
position of first maximum, further smoothing, and elimination of the effect of 
interfering cycles, might alter the results. It should be remembered that the 
summation method will yield the true amplitude only with an indefinitely 
large number of sets; the value obtained from the limited number of sets is an 
approximation. 

A. D. Ratio — This test for cycle reality is discussed on pages 58 and 98. 
The values, while significant statistically, are not in themselves decisive for 
any individual case. 

Vertical Scale — This refers to the summation curves: See discussion 
following. 

CYCLE SUMMATION CURVES 

The accompanying curves show the mean cycle forms derived in comput- 
ing the amplitudes given in the tables of Chapter V. These curves become 
part of the reduction process and should be made clear to the reader, because 
the cycles may take forms quite different from the easy flow of the sine curve. 

Identity of the curves will be recognized by the number attached to each 
curve which refers to a corresponding number given in the tables of Chapter V, 

Exactly one cycle length is plotted and, if necessary, the curve is slightly 
smoothed by the usual Hanning process. In most curves the left end repre- 
sents the date of beginning as indicated in the "duration" in the tables (the 
phase may be checked by referring to date of first maximum), and the hori- 
zontal scale is two years to the division. In the 5-year means it is, of course, 
10 years per division. In laying out the curve for its repetitions the frac- 
tional year at its end, if any, must be taken into account. 



156 



CLIMATIC CYCLES AND TREE GROWTH 



The ordinates in the summation curves are related to the data given in 
Vol. II, Appendix, in the following way: 

R 



M = 



2 AV 



where M = mean value of data in II used in amplitudes'. 

R = total range in summation curve, taken at 10 per cent change 

per division. 
A = per cent amplitude in tables. 

V = vertical scale value in tables; a value of unity being taken where 
no entry is made in that column. 
For SVI cycles, M will give the actual mean ring size. Data for the 42 
groups and CPC were largely standardized and some groups were measured 
in different units. For comparison purposes it might be added that the 
approximate mean ring size in the 42 groups as a whole is 1.35 mm. It is 
proposed to publish the mean ring sizes in a forthcoming article. 

42 Western Groups 




10 12 14 



APPENDIX 

42 Western Groups 



157 




2 A 6 8 10 12 14 



42 Western Groups 




158 



CLIMATIC CYCLES AND TREE GROWTH 
42 Western Groups 



78 


































































































79 




































































































60 
























/ 


• 
























61 










































































































62 


















/ 
















































































83 








































































































































































































85 
86 
























































































































■ 












































































87 



















































2 4 6 8 10 12 14- 16 18 20 22 24 26 

Years 



42 Western Groups (Cont'd) 




2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 

Years 



APPENDIX 

42 Western Groups 



159 





































































































97 






































































































S 
















































38 




































• 


/ 
















































































































yy 




\~*~" 






















V 


































































































































100 


\^> 


s 




































































































































































































IUI 























































































































































2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 

Yeans 

42 Western Groups (Cont'd) 




2 4 6 8 1 



160 



CLIMATIC CYCLES AND TREE GROWTH 

42 Western Groups 




42 Western Groups 




2 4 6 8 10 



12 14 16 18 20 22 24 26 28 30 32 34 

Years 



APPENDIX 

Sequoia Chronology 



161 




176 



2 4 6 



Sequoia Chronology 




223 



2 4 6 8 10 I 



162 



CLIMATIC CYCLES AND TREE GROWTH 
Central Pueblo Chronology 




















Central Pueblo Chronology 


















269 












/ 


\ 














































, / 


' 












































































^ 












270 
























276 














V^ 


S \ 










271 












/ 


A 


































































t 
























J 


























/ 




















272 


<^- 


J 




















277 






/ 
























/ 


~N 


y. 


















N 


\J 


f 




















273 


k 4 


/ 




\ 




















































L_ * 














27^ 








\ 








/ 


' 


















"\ 
























\ 




S 


/ 










274 








/ 




v 












































N 


1 




V 


y 












/ 


■ \ 


























/ N ^ 






















/ 
























?7S 


/ 




\ 


















279 


f 
















































280 













































































2 4 6 8 10 12 14 



2 4- 6 8 10 12 14 16 

Years 



APPENDIX 

Central Pueblo Chronology 



163 




2 4- 6 8 10 I 



















Central Pueblo Chronology 












































































\ 














301 




































\ 




















A 






















294 








\ 
















/ 


y 




I 


f\ 




















/ 


~s 




















/ 






Kj 




\ 
















295 


/ 




\. 
















302 














— 














296 


■"N 




















303 






























' 


s. 


, 


/' 














304 


/^ 


\ 












J 


^ 


y 


































\ 






, / 




/ 


y 












297 










k_ 


















V/ 


/ 




1 


































































298 






















305 




















































































J 


"\ 








































?9<( 


/ 


' ■ 








\ 










306 


































/ 


\ 


*S 


\ 














/ 




\ 




















300 


| 


./ 


/ 






\ 










307 




/ 




\ 




/ 


\ 


{ 


X 


/ 










L 


/ 




















\ 


/ 






V ' 




V 


J 













10 20 30 40 50 



10 20 30 40 50 60 70 80 90 100 110 120 

Years 



164 



CLIMATIC CYCLES AND TREE GROWTH 



AN AUTOMATIC OPTICAL PERIODOGRAPH l 

VARIABLE STAR TESTS 

In all the previous work which had been done with the periodograph, a 
continuous series of observations was used. The test of discontinuous ob- 
servations was made on variable stars. In order to avoid prejudices and to 
get a fair sample of variable stars, my assistant selected a certain number 
from the table given in volume 37, in the Annals of the Harvard College 
Observatory, page 202. They comprised the 10th, 20th, and 30th star, etc., 
in the list. The accompanying table will give the results of the test and the 
time taken to obtain each one. One must remember, of course, that this 
was the first application of that instrument to these interrupted periods, and 
one can say confidently that the average time to solve a variable star period 
(after the plot is made) would be five or ten minutes. The columns in this 
table marked "Curve Period" and "Computed Period" are from Harvard 
Observatory Annals, volume 57, page 182. The "Curve Period" was ob- 
tained directly from a plot. The "Computed Period" was obtained after 
an application of the method of least squares. It is seen that the periodo- 
graph results agree very well with the least square solution. The solution 
of X Virginis, as seen in the table, was obtained after a very long study. The 
period of 52 days seems applicable if the observations of J. D., '2815, are 
omitted. 







H.C.0.ANN. 57: 182 


Periodograph 
Period Days 


Time taken to 
reach solution 


Number 


Name 


Curve 


Computed 






Period 


Period 










Days 


Days 






R 


021024 R Arietis 


181.7 


186.6 


186=bl 


19 m. 


V-l 


042309 S Tauri 


392.5 


365.0 


186±1 
372±2 


52 m. 


V-2 


115609 X Virginis 


(No solution) 


52 


4 h. 35m. 










omitting 












2815 J.D. 




V-3 


134440 R Can. Ven. 


317.2 


333.0 


332±3 


34 m. 


V-4 


163137 W Herculis 


287.0 


280.2 


282±2 


45 m. 


V-5 


201647 U Cygni 


470.9 


461.3 


463±3 


43 m. 



The method by which the solution was obtained consisted in placing a 
strip of slightly tinted yellow glass behind the minima of the curve in which 
all the observations were plotted by their distance from a mean line. This 
made a mixture of yellow and white spots on the differential pattern. When 
this mixture of spots resolved itself into alternate yellow and white rows, 
then a period was indicated. This could be done very readily. In the period- 
ogram the alternate beads or corrugations come down in different colors. 
Such a periodogram of R Arietis is shown in Plate 12b. 2 The marginal marks 

1 Presented at astronomical meetings, Pasadena, June 20. 1919, and Ann Arbor, 
September 3, 1919. See abstract in Pub. Ast. Soc. Pac, Vol. XXXI, 188, June 1919. 
Introduction omitted here. 

2 The reference to plates applies to this book but the photographs here are repro- 
ductions from the original article. 



APPENDIX 165 

in this figure correspond to a period of 150 days, 160 days, etc. There are 
two places in the figure where the corrugations are especially evident; one 
had about 157 and the other had about 187 days. In the instrument the 
latter is immediately recognized as the true period, because the lines are 
alternately yellow and white. 

Plate 24 shows a differential pattern of SS Cygni, so taken that vertical 
lines of dots show a period of about 110 days. The predominant periods 
may easily be worked out from this diagram. For the first four years, begin- 
ning about 1896 the double-crested 117-day period was the most prominent. 
Then for six years a double-crested asymmetrical period of 107 days was the 
most prominent. Then there was nearly a year of readjustment followed by 
two years of 110-day double-crested periods. This was followed by three 
years of 125-day double-crested periods, returning finally to four years of 
117-day double-crested asymmetrical periods. This alignment of dots is 
best seen by looking at the figure from a low angle rather than from the 
perpendicular position of ordinary reading. 1 

1 In considering this pattern eighteen years after it was first made and comparing 
it with cyclograms of solar records and of climatic data, we note that it shows the type 
of persistence, of bisection and of somewhat irregular changes that appear, for example, 
in the magnetic character figure C. In this analogy we have a suggestion that this 
type of variation might have its origin in the rotation periods of a large body like 
our sun. 



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