iMWl.
NAVAL POSTGRADUATE SCHOOL
Monterey, California
|
THESIS |
||
|
DETERMINATION OF LAND ELEVATION USING TIDAL DATA |
CHANGES |
|
|
by |
||
|
Francisco Antonio Torres Vidal |
Abreu |
|
|
September 1980 |
||
|
Th Th |
esis Advisor: W. C. esis Co-Advisor: D. P. |
Thompson Gaver, Jr. |
Approved for public release; distribution unlimited
UNCLASSIFIED
SCCUMITY CL ASSiriC ATION OW This »*r;C rl^Von Oa>« gnimtati)
REPORT DOCUMENTATION PAGE
T~SFFo*m7u3¥TB"
a. GOVT ACCCStlOM NO.
READ INSTRUmnNS BEFORE COMPLETING FORM
)■ MCCl^lCMT't CAT ALOC NOMSEN
4 TITLE r«<d Su*<ir(«)
Determination of Land Elevation Changes Using Tidal Data
»• Tv^e OF mt^omr * ^ewtoo cove hed
Master's Thesis; September 1980
«. PCnPOKMIMO ONG. nCPOMT NUMSCK
7. AuTMOI»f»j
■ . CONTRACT OM SHANT NUMMCnr*;
Francisco Antonio Torres Vidal Abreu
10. PAOSHAM £L£MCNT. PNOjECT TASK AACA • WORK UNIT NUMBCNS
• . PCWFONMINO OAOANIZATION N AM C AND AOOMItl
Naval Postgraduate School Monterey, California 93940
I I CnNTWOLLINC OFFICE NAME anO AODMCIS
Naval Postgraduate School Monterey, California 93940
12. NEPOUT DATE
September 1980
t3 NUMSKR OF PACES
124
U MONlTONiNG AGENCY NAME A AOONESS<'/« Httffmnt Irom Ctmtralltng OlUfi
Ift. SCCUMITY CLASS, (ot IM« tiport)
Unclassified
\%m. OKCLASSIFICATION/DOVNCnAOlNC •CHCOULE
l«. OlSTRIfluTlON STATEMENT (at thit Maparl)
Approved for public release; distribution unlimited
17. OISTHIBUTION STATEMENT Cot lh» «A*>rae/ Mi|«r»« In ffloflfc 20, II dlllmrmni Irmm Kmport)
SUPPLEMENTAHY NOTES
It KEY WOnOt (Ctmilnu* on r»w»r»» tid» II nacaaaarr "4 Identity kr bloek number)
Vertical Crustal Movements Land Elevation Changes Tide Time Series Trend Analysis Tide Station Elevation Changes
Pacific Coast Tide Stations Cumulative Analysis
20 ABSTRACT (Conlinu* an rmvaraa aMa II nacaaa^rr 1>^ Idmnlllr kr *!•«* maa*«0
The purpose of this thesis is to study the temporal pattern of vertical land movements at selected Pacific Coast tide sta- tions. The relative motion of the land at these stations is indicated by the relationship between monthly mean sea levels measured at pairs of stations. Examination of historical monthly mean sea level data by means of graphical and spectral analysis led to the use of an anomaly filter which adjusts for mean
DO /,°r,, 1473 (Page 1)
EDITION OF 1 MOV 8* IS OaSOUCTE S/N 0103*014> A«0 I
UNCLASSIFIED
fECUHlTY CLASSIFICATION OF THIS PAGE (Whan Dala Kniarad)
UNCLASSIFIED
g^emwrv eu Amyic-tTipw ot Tmt »»qK<'i»i<w n««« *<*ia«»4.
monthly differences. A cumulative analysis procedure of Wyss [1977] was adopted to the study of the relative movement of seven tide stations. Determination of the type of vertical movement between pairs of stations, the date of sudden move- ment, and the station responsible can be determined from analysis of the cumulative curve of monthly sea level difference. Results of the cumulative analysis show that tide stations, whether separated by short or long distances, experience frequent changes in relative elevation. Whether these are caused by land move- ments or changes in station datum, or both, is not known.
DD Form 1473
, 1 Jan 73 S/N 0102-0X4-6601
UNCLASSIFIED
»ICU«IT* CLAMI^ICATIOW Qf TWU l»*OKnw>«»» 0«f fwi»»<)
Approved for public release; distribution unlimited
Determination of Land Elevation Changes Using Tidal Data
by
Francisco Antonio Torres Vidal .Abreu Lieutenant Commander, Portuguese Navy Portuguese Naval Academy, 1965
Submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE IN OCEANOGRAPHY (HYDROGRAPHY)
from the
NAVAL POSTGRADUATE SCHOOL September 1980
ABSTRACT
The purpose of this thesis is to study the temporal pattern of vertical land movements at selected Pacific Coast tide stations. The relative motion of the land at these stations is indicated by the relationship between monthly mean sea levels measured at pairs of stations. Examination of historical monthly mean sea level data by means of graphical and spectral analysis led to the use of an anomaly filter which adjusts for mean monthly differences, A cumulative analysis procedure of Wyss [1977] was adopted to the study of the relative movement of seven tide stations. Determination of the type of vertical movement between pairs of stations, the date of sudden movement, and the station responsible can be determined from analysis of the cumula- tive curve of monthly sea level difference. Results of the cumulative analysis show that tide stations, whether separ- ated by short or long distances, experience frequent changes in relative elevation. Whether these are caused by land movements or changes in station datum, or both, is not known.
TABLE OF CONTENTS
I. INTRODUCTION 11
II. ALTERNATIVE ANALYSIS OF MEAN MONTHLY SEA LEVEL
DATA 21
III. THE CUMULATIVE PROCEDURE 31
IV. SUMMARY AND CONCLUSIONS 44
TABLES 48
FIGURES 54
APPENDIX A: COMPUTER PROGRAMS 99
1. Program Used to Perform Spectral Analysis 99
2. Program Used to Perform Least Squares Best Fit -10 2
3. Programs Used to Perform Filtering Action 104
4. Program Used to Perform Cumulative Analysis 108
5. Other Subroutines Called -HO
BIBLIOGRAPHY -118
INITIAL DISTRIBUTION LIST--- - -120
LIST OF TABLES
I. Time Series Used for Each Tidal Station 48
II. Differences Obtained for Long Term Trends
When Using Raw and Filtered Data 49
III. Comparison of Spectra for Seattle Derived from the Raw Data, 12 Month Running Means,
and Anomalies (16 Degrees of Freedom) 50
IV. Sea Level Trends Obtained for Three Stations
Using Different Lengths of Time Series 51
V. Trends of the Difference Data for Pairs of
Tide Stations for Specific Time Series 52
VI. Trends of Elevation Change Relative to
San Francisco 53
LIST OF FIGURES
1. Mean monthly sea level for Seattle (SE) ,
Crescent City (CC) , and differences (SE-CC) 54
2. iMean monthly sea level for San Francisco (SF) ,
San Diego (SD) , and differences (SF-SD) 55
3. Mean monthly sea level for Santa Monica (SM) ,
Los Angeles (LA), and differences (SM-LA) 56
4. Power density function of the spectra of Seattle
data (2 degrees of freedom) 57
5. Power density function of the spectra of Seattle
data (8 degrees of freedom) 58
6. Power density function of the spectra of Seattle
data (16 degrees of freedom) 59
7. Power density function of the spectra of
San Francisco data (2 degrees of freedom) 60
8. Power density function of the spectra of
San Francisco data (8 degrees of freedom) 61
9. Power density function of the spectra of
San Francisco data (16 degrees of freedom) 62
10. Raw data, 12-month running means, and anomalies
for Seattle 63
11. Raw data, 12-month running means, and anomalies
for San Francisco 64
12. Raw data, 12-month running means, and anomalies
for Santa Monica 65
13. Raw data, 12-month running means, and anomalies
for Los Angeles 66
14. Power density function of the spectra of 12-month running means --Seattle (2 degrees of freedom) 67
15. Power density function of the spectra of anomalies-- Seattle (2 degrees of freedom) 68
16. Power density function of the spectra of 12-month running means- -San Francisco (2 degrees of
freedom) 69
17. Power density function of the spectra of anomalies- -San Francisco (2 degrees of freedom) 70
18. Trends of the raw data for SM, LA, and (SM-LA)
using a 10-year window 71
19. Trends of 12-month running means for SM, LA,
and (SM-LA) using a 10-year window 72
20. Trends of anomalies for SM, LA, and (SM-LA)
using a 10-year window 73
21. Trends of anomalies for SE , SF, and (SE-SF)
using a 20-year window '^4
22. Trends of anomalies for SE, SF , and (SE-SF)
using a 30-year window "-
23. Trends of anomalies for SE , SF, and (SE-SF)
using a 40-year window ^^
24. Cumulative differences (SE-LA) using raw data and matching the station means ^^
'to
25. Cumulative differences (SE-LA) using anomalies
and matching the station means 7'
'to
26. Cumulative differences (SE-LA) using 12-month running means and matching the station means ^^
27. Cumulative differences (SE-LA) using raw data
and matching the first data points ^0
28. Cumulative differences (SE-LA) using anomalies
and matching the first data points SI
29. Cumulative differences (SE-LA) using 12-month running means and matching the first data points 82
30. Residuals for a second degree best fit curve
for SE-LA for 1924-1974 (using raw data) 83
31. Residuals for a first degree best fit curve
for SE-LA for 1924-1947 (using raw data)
32. Residuals for a first degree best fit curve for SE-LA for 1948-1965 (using raw data)---
84
85
33. Residuals for a first degree best fit curve
for SE-LA for 1966-1974 (using raw data) 86
34. Cumulative differences (SF-CC) using anomalies
and matching the first data points 87
35. Cumulative differences (SF-LA) using anomalies
and matching the first data points 88
36. Mean monthly sea level for San Francisco (SF) ,
Los Angeles (LA), and SF-LA (1944-1951) 89
37. Mean monthly sea level for San Francisco (SF) ,
Los Angeles (LA), and SF-LA (1957-1964) 90
38. Cumulative differences (LA-CC) using 12-month running means and matching the first data points 91
39. Cumulative differences (AV-SM) using 12-month running means and matching the first data points 92
40. Correlogram for Seattle data (anomalies) 93
41. Correlogram for San Francisco data (anomalies) 94
42. Correlogram for Santa Monica data (anomalies) 95
43. Correlogram for Los Angeles data (anomalies) 96
44. Correlogram for SE-SF (anomalies) 97
45. Correlogram for SM-LA (anomalies) 98
ACKNOWLEDGEMENTS
The author wishes to express his appreciation to Dr. Warren C. Thompson as thesis advisor for his guidance, knowledge, method and systematic assistance in the prepar- ation of this study and to Dr. Donald Gaver as co-advisor for his useful comments and collaboration.
The assistance of Lt. Dale E. Bre tschneider , NOAA Corps, of the National Oceanic and Atmospheric Administra- tion, Pacific Environmental Group, in the timely procurement and transmission of data is greatfully recognized.
Special appreciation is given to my loving wife and children whose understanding and patience enabled me to complete the necessary research.
10
I. INTRODUCTION
The determination of relative rates of land elevation change can be made using the resultant information from geodetic work. However, geodetic levelling is repeated very infrequently because it is time consuming and represents a high cost. In coastal areas tidal data, available for many sites, has been used for the same purpose. Its use is not an innovative idea; books and technical papers dealing with this subject have been written by Lisitzin [1974], Roden [1963], Hicks and Shofnos [1965a], Hicks [1972b], and several others. It was, perhaps, the reading of a paper by Balazs and Douglas [unpublished] of the National Geodetic Survey of the National Oceanic and Atmospheric Administration (NOAA) entitled "Geodetic Levelling and the Sea Level Slope Along the California Coast" that constituted the challenge point for the beginning of this thesis. These authors found a clear and large discrepancy between relative movement rates from repeated levellings and tidal observations, but were not able to explain the reasons for that situation.
In this thesis it was decided to use sea level data from several stations on the Pacific Coast of the United States of America aiming at possible establishment of a continuous history of differential vertical land movements among tide stations along this coast. In order to maximize the resolution
11
of the results it was decided to use mean monthly sea level data, rather than the mean annual data used in some past studies. The data, originated by the National Ocean Survey (NOAA) , was provided by the Pacific Environmental Group of the National Marine Fisheries Service (NOAA) located at Monterey, California, and all the computational work was accomplished on the IBM-360 computer at the W. R. Church Center of the Naval Postgraduate School. As some of the received data was not continuous, only periods without missing data were used to avoid the introduction of an un- controlled source of errors. Table I shows the time series used for each station.
The ocean level is constantly changing and its heights are recorded at long-term tide stations using automatic (analog or digital) methods. The recorded heights are related to the zero of a tide staff which is supposed to be connected by differential levelling to several nearby bench- marks. If the observations are averaged in a special way in order to filter out the short-term water level variations, a value for the mean sea level is obtained. The mean monthly data used here, which is derived from a direct average of all the hourly values during an entire month, can be con- sidered a close approximation to the mean sea level value for the site where it was collected for that averaging inter- val. But this mean sea level, so important to the hydrogra- pher, geophysicist , and geodesist, is not a constant value
12
from month to month. Short-term variations of duration less than one month, like oscillations in barometric pressure caused by daily temperature fluctuations, wind effects, seiches, and tsunamis, are some of the causes that give rise to the fluctuations or departures from the mean water level. But exactly because they are transient and of such short- term duration, when averaged over the period of a month they are not significant. Some of the causes of longer term water level variation that account for month-to-month sea level differences are:
(a) The movement of the axis of rotation of the earth (Chandlerian motion) with an approximate period of 14 months.
(b) The nodal cycle of the moon with a period of 18.613 years.
(c) The sun spot cycle with an approximate period of 11 years.
(d) Variations from the average meteorological conditions
(e) Variation of the average sea \\^ater density in the vicinity of the tide station.
(f) Dynamic effect of ocean currents (the last three causes are meteorologically and/or oceanographically induced, producing sea level changes with the following characteristics:
(1) Duration- - larger anomalies average about three months but may be as long as 10-34 months [Roden, 1966].
(2) Amplitude- -monthly variations from the mean are commonly 100mm but may reach 300mm [Bretschneider , 1980].
13
(5) Coastwise coherence- -very high over distances less than 200 km; significant over distances of the order of 1200 km for tide stations located in the same macro environ- ment [Roden, 1966],
(4) Tide station exposure- -within the same macro environment on the open coast and in bays, exposure is rela- tively unimportant but stations well inside estuaries and fjords where there is large fresh water runoff may be exceptions) .
(g) Eustatic changes in elevation of sea level due to the melting of the ice accumulated on the continents.
(h) Any kind of crustal movements, including natural isostatic movements (generally assumed as low and gradual with rates of change varying from zero on stable coasts to approximately 40mm per year [e.g., Hicks and Shofnos, 1965a] in areas of rapid crustal rebound), sudden movements associ- ated with earthquakes and faulting, and the very rapid movements induced by man resulting from oil and groundwater withdrawal, vibrations related with land use, etc.
The presence of long-term vertical movements of both water and land contained in a tidal data time series makes it impossible to determine with high precision the absolute rates of land change. Except for the case of large rates of crustal rebound, we never know with enough confidence if a long term increase of mean sea level was due to land sub- sidence, to a slow rise of mean sea level, or to both causes
14
Lisitzen [1973] and Hicks [1972] tried to estimate absolute rates of land change from single station tide data. The subjective assumptions used by both were not strongly convincing, though with scientific reasons behind them. The former concluded that the eustatic rise of the sea level began in 1891, and the latter simply applied the eustatic sea level rise rate of 1.0mm per year found by Gutenberg [1941] (using sea level data from 69 stations in 22 different regions around the earth) . This study deals only with rela- tive rates of change determined from time series data using pairs of tide stations.
Since vertical movement that can occur in the earth's crust is one of the components contained in each tidal time series, it would be a simple matter to quantify this compon- ent if all the others could be evaluated and removed from the data. However, this approach is not possible because of lack of data on some components, difficulties in quantifying the effects of other components, and also difficulties in isolat- ing the effect of astronomic tidal components of known period (e.g., the nodal cycle of the moon) from the data.
Using a different approach, it can be said that each monthly time series from a given tide station is composed of random fluctuations (short-term climatological variations are an example) , periodical fluctuations (the astronomical components that force the tides and the annual climatological cycle), and what can be considered, at least to a first
15
approximation, to be linear trends (the eustatic rise of sea level and the movements of the earth's crust). As random and periodic data have no long-term trends in themselves, any trend detected when analysing the data should reflect the latter factors.
Various methods have been used to study sea level changes but only four will be briefly described as a background neces- sary to introduce and better understand the work done in this thesis :
-Gutenberg [1941] used mean annual sea-level data col- lected at long-term tide stations around the earth. At that time the unavailability of computers made the use of the least square fitting technique very difficult. The author proposed and used a short-cut system of averaging the first x and the last X years, and dividing the difference between the two means by the number of years between the weighted midpoints of these intervals. His criterion for the selection of x was as follows: If the number of years of data was greater than 25, X should be 10, but if t < 25, x = t/3. Gutenberg does not speak about errors and the purpose of his paper was to deter- mine the eustatic rate of rise of the sea level.
-Roden [1963], studying sea level variations in Panama, used anomalies of mean monthly sea-level data obtained by taking the difference between the monthly sea level and the long-term mean for the same month. To find the trends, Roden assumes a record z(t) which is the sum of a deterministic
16
function of time and a stationary random fluctuation,
z(t) = a + bt + x(t)
where b is an unknown constant representing the long term trend in which we are interested. Here, x(t) is the sta- tionary random fluctuation with zero mean and known auto- correlation or spectrum. Roden uses the solution,
b = /J"K(T-t) z(t)dt
where T is the record length, and b is an estimate of the unknown constant b. The particular shape of the Kernel K(T-t) depends upon the autocorrelation of x(t) . The mean square error of the estimate of 6 used was
e' = 12 6VT3
where 5^ refers to the spike at the origin, assuming white noise.
In a later paper, Roden [1966] uses the expression,
b = ^ t^^^¥- l)^(t)
c^T^ + 6cT + 12 -^
where c is the constant decay of the autocorrelation of the sea level fluctuations. For the mean square error of the estimate the following expression was used:
2 4 cm
£2 = O.
TCc^T-" + 6cT + 12)
where m denotes the variance of the data o
17
-Hicks and Shofnos [1965a, 1965b] and Hicks [1972a, 1972b] used yearly mean sea level values weighted by a tri- angular array (1,2,3,4,3,2,1) and then computed the trends by fitting a least- squares line of regression. The formulas used for the computation of the slope, b, of this line as well as for the standard error of the slope, Sb, are:
Sxy - il20Slll b = -— ^
Ex'
(^x)
Sb =
Sy .X
Z.X - -^^ -
n
where n represents the number of yearly values. S^y.x is an estimate of the error variance around the assumed line relating y to x; Sy.x is an estimate of the error standard deviation, and given by:
c /~T~z rWP TTT (Zx) (Zy) , Sy.x = / Ey^ - ^-^ - b(Exy - -^^ ^^ ^ ^ )
__
-Merry [1980] also uses a least- squares fit but applies it to unfiltered daily mean sea levels in a study of secular sea level changes.
One important statement that must be made is that these authors, although using different types of sea level data (daily, monthly, and yearly) , different smoothing techniques.
18
and different methods to determine the trends contained in their data, all assume that both the eustatic rise of the sea level and the movements of the earth's crust can be considered linear to a first approximation. It should also be noted that all dealt with single-station analysis, that is, the data from each tide station was analysed independently of other tide stations to obtain rates of sea level change.
Because of the impossibility of making accurate determin- ation of absolute rates of land change using single station analysis, it was decided to eliminate or greatly minimize the effect of sea level changes in the tide data by comparing the tidal data from several pairs of stations separated by var- ious distances [Table I]. Subtracting from each mean monthly sea level value at station A the corresponding value for the same month and year at station B, we generate a new set of time series data which must contain within itself the rela- tive rate of land elevation change between the two stations, free of any eustatic related trend. Because of the principle on which it is based, we will refer to this procedure as "differential tidal levelling"; the procedure may be thought of as an analog of the method of differential spirit levelling used in geodetic surveying.
In this procedure we assume that the glacial -eustatic , the climatological , and the oceanographic "long term trends" do not significantly differ in themselves over distances on the order of hundreds of kilometers. These are therefore
19
eliminated in theory by the described differencing computa- tion. The difference between the two series also leaves some random and periodic information that should not introduce any trend. This method, besides allowing the detection of rela- tive rates of land elevation change between any two stations due to tectonic effects, has the advantage of largely removing the short term and seasonal variations, especially at stations separated by short distances. The method also provides a basis for calibration of an entire coast. Nevertheless, it should be used with care particularly when comparing widely separated station pairs, which is a common situation along the west coast of North and South America.
It was with this background that the computational phase began. The next section describes successive efforts to derive rates of land elevation change from sea-level differ- ence data at paired tide stations. Section III treats in detail the procedure introduced by Wyss [1977], and further developed in this study, to accomplish this objective.
20
II. ALTERNATIVE ANALYSIS OF MEAN MONTHLY SEA LEVEL DATA
The first step taken was to plot the mean monthly sea level data for all of the stations as well as the differences between several pairs of stations. For illustration, three examples are shown on Figures 1, 2, and 3 for the pairs Seattle-Crescent City, San Francisco-San Diego, and Santa Monica-Los Angeles, respectively. Only eight years of data are shown in order to avoid obscuring details. The upper and middle values on each graph represent the data for the first and second station of each pair, the lower values being the resultant difference. Each symbol represents one month (January through December) related with the year indicated, and is obtained from an average computation of hourly values recorded in units of feet. The vertical scale is relative and is the same for all the curves (1 foot/inch).
These three station pairs were selected to illustrate the effect of distance between the stations (note Table I) . Each set of station data shows a distinct annual cycle, and it is possible to detect visually a long term trend for a period as short as eight years for some of the stations. The difference data also show this long term trend; however, the annual cycle is not so evident and depends upon the dis- tance between the two stations. The variation of the differ- ences is smallest for the closest station pair due to similarity
21
of data, which creates a more effective cancellation. The differences appear to be much more random than the original data for each station. Taking differences has the effect of cancelling out systematic variations common to the two series.
The visual evidence of an annual cycle, despite being disguised in the difference data, oriented this work toward the need for a spectral analysis of station data in order to determine if other frequencies with significant energy are present. The occurrence of annual and other cycles would justify a filtering operation before treating the data for trends. The short length of some of the time series was a clear temptation to perform the analysis with a small number of degrees of freedom (with a correspondent lack of confidence in the results) , but stations like Seattle and San Francisco with at least 912 data points (76 years) allowed the use of 16 degrees of freedom. The spectral analysis was performed on several stations for 2, 8, and 16 degrees of freedom with the subroutine PREPFA, shown in Appendix A-1, using the prin- ciple of the Fast Fourier Transform (FFT) . Other subroutines called by PREPFA can be found in Appendix A-5, except PLOTG and RHARiM which are library subroutines of the W. R. Church Computer Center.
Figures 4, 5, and 6 show the power density function of the spectra for Seattle data for 2, 8, and 16 degrees of freedom, respectively (note different scales). Figures 7, 8, and 9 are the corresponding graphs for San Francisco.
22
For both stations the maximum detectable frequency is 0.5 cycles per month. This frequency, Fn = jj— , is determined by the time interval At between each data point, where Fn is the Nyquist frequency and At=l month. In all six figures noticeable sharp concentrations of energy (peaks) are seen to occur only in the low frequency part, with almost nothing at higher frequencies. The typical decrease of noise with increasing frequency may be seen best in Figure 7. Identifi- able by their high concentration of energy, only the frequen- cies of 0.083 and 0.167 cycles per month could be found. These correspond to the annual and semi-annual cycles. These prominant peaks, although coincident with the tidal constitu- ents Sa and Ssa, are essentially of meteorological and ocean- ographic origin. Thus, with so high a concentration of energy at these specific frequencies with a periodic origin (but not absolutely repetitive year after year) , it was decided to eliminate this interference from the station data before computing long-term sea level trends.
In order to remove the two prominent cycles appearing in the spectra, it was decided to experiment with two different types of filters. A principle to be adhered to was that the annual and semi-annual cycle should be removed without sig- nificantly modifying the proportionality of the energy exist- ing at the other frequencies. This requirement of maintaining the energy proportionality was adopted to guarantee that only the periodic components in the station data, which do not
23
contribute to the long-term trend, are removed by the filter- ing process.
The first filter used is a simple 12-month running mean, 12 months being the length of the averaging window needed to remove the effects of both the annual and semi-annual cycles. The operation of this filter is very easy. The first data point is obtained by averaging the first 12 data points from the raw data, the second is obtained by averaging the next 12 data points (2 through 13), and so on. It is obvious that with this method, so often used in practice, we are introduc- ing a "tail" effect. During the entire averaging process the first and the last (nth) data points were just called once, the second and the (n-l)th twice, ..., while all the data points between and including the 12th and the (n-ll)th were used twelve times. A subtle consequence is that the filtered data series is 11 months (11 data points) shorter than the raw data series, so that the sea level trends computed from the rai\f and filtered data may be expected to differ slightly. Nevertheless, it is a very effective filter for special applications .
The second filter used removes the long-term mean monthly sea levels from the raw monthly data to produce a time series of monthly sea level anomalies. This is accomplished by first averaging the sea level values for each month (i.e., first for January, then February, and so on) and then sub- tracting these 12 means from the respective monthly values
24
in the raw record. The result is a record of monthly sea level anomalies relative to the long-term mean monthly sea levels .
For all three sets of monthly station data, i.e., the unfiltered sea level values termed the raw data, the 12-month running mean data, and the anomaly data, the trend, the scatter of the monthly values, and the standard error of the slope were obtained using the conventional least-square for- mulas referred to in the introduction. Some comments will be made later about the errors introduced with the use of these formulas when the data are correlated. The computer program used to perform these calculations was subroutine LEASTS, found in Appendix A-2. Appendix A-3 gives the subroutines RMEANl and ANOMAL written to perform the two types of filter- ing just described.
An example, using four stations, of the effects of apply- ing these filters to the raw data is illustrated in Table II The table shows that for a given station, the sea level trend computed by the three methods agrees quite closely. The values that describe the scatter of the data and the standard error of the trend are what would be expected from the three methods, i.e., smaller values for the scatter of the 12-month running means than for the raw data or anomalies The reader should be cautioned not to compare the trends between stations because they are obtained from different series of years.
25
With regard to the variability of the filtered data compared to the variability of the raw data, a better feeling can be obtained through Figures 10, 11, 12, and 13. Each graph shows from top to bottom the raw data, the 12-month running means, and the anomalies for the first eight years of tidal series at stations Seattle, San Francisco, Santa Monica, and Los Angeles, respectively. These four figures, in conjunction with Table II, show that the trends and the variabilities of the anomalies are much closer to those of the raw data.
It was stated above that it was desired that the filters used should remove only the annual and semi-annual components and that the spectra of the filtered data should maintain the proportionality of the energy distribution with frequency observed in the spectrum of the raw data. The question of whether the two filters used satisfy these conditions will now be addressed. The transfer function for each filter is different, and so the results of the spectral analysis may be expected to differ somewhat. This study was done using four stations with the indicated 2, 8, and 16 degrees of freedom, but the results for only two stations for 2 degrees of freedom are presented. Figures 14 and 15 refer to Seattle and show the spectra resulting from the application of the 12-month running mean and the anomaly filters, respectively; these should be compared to the spectrum for the raw data shown in Figure 4. Similar spectra for San Francisco are
26
shown in Figures 16 and 17 and should be compared to Figure 7. The differences can be seen more quantitatively in Table III, which is discussed below.
From visual inspection of these figures it can be seen that both filters very effectively eliminate the annual and semi-annual components, but while the running window filter removes practically all the energy contained in frequencies greater than that of the annual cycle, the anomaly filter eliminates only the undesirable peaks of one cycle/year, two cycles/year, and multiples of these frequencies, leaving the energy at the other frequencies with the same approximate proportionality. To illustrate the effects of the filters quantitatively. Table III shows energy density ratios obtained from comparison of these spectra for Seattle (using 16 degrees of freedom) . By removing the values closest to the periods which we intend to eliminate (12 and 6 months) , the quotient (3)/(5) is seen to vary between the values of 1.272 and 0.888, while the quotient (3)/(4) varies between 1.330 and infinity. The same conclusion can be reached also by visual comparison of the plots.
After this examination the conclusion that all further work should be prosecuted using the anomalies was reached. Nevertheless, in order to further compare the filtering pro- cedures, the raw data and both sets of filtered data were used in the following investigations. The sea level trends for three tide stations computed for different time intervals
27
are shown in Table IV. The table shows that the trends are time dependent. These results were not unexpected because other authors [Gutenberg, 1941 and Roden, 1966] already- referred to the problem of the "instability" of the long term trends.
Although the trends of the sea level at one individual station are clearly shown not to be constant, there is reason to believe that the trend of the differences in monthly sea level between a pair of stations, particularly closely spaced stations, might be much more nearly constant. In order to inquire into this question the following experiments were performed. Programs were run in order to find and plot the running trends of the differences, where the trend was com- puted for a selected time interval or window. Thus, for a given time series of monthly sea level differences between two stations, the trend for the first x years is computed, where x is the window length, then the operation is repeated by stepping the window one month at a time and computing a new trend. The result is a graphical computation of a time series for an x-year trend for a given station pair. The selection of the window length was not arbitrary. Knowing the existence of long period tidal components expected to be contained in the tidal series, including the regression of the moon's node (18.613 years), the revolution of the lunar perigee (8.847 years), and the revolution of the solar perigee (20.940 years), the closest numbers of integer months to these
28
values were chosen. The results, which are not presented, did not show a constant value for the trend of differences within some reasonable standard error. It was only obvious that by increasing the length of the window the variability of the resultant trends was decreasing, which was expected.
In order to go further in this analysis, plots and computations were made for several pairs of stations using windows covering 10, 20, 30, and 40 years of data, when pos- sible. Also, raw and filtered data were used in all experi- ments. For illustration, Figures 18, 19, and 20 show for the station pair Santa Monica-Los Angeles (SM-LA) the trends for the monthly difference data; also shown are the trends for each station. The length of the window used is 10 years These three figures refer to the raw data, 12-month running means, and anomalies, respectively. The pattern presented using these types of data is almost the same. The yearly cycles are evident in the raw data computations (Figure 18} , and the degrees of smoothing obtained with the filters can be observed in Figures 19 and 20. An important observation relates to the variability of trends obtained for a close pair of stations. For the station pair of SM-LA the trends of the differences range between -2.5 and +7.0 mm/year for the period considered. This suggests that for this specific time-window (10 years) , time periods can be found during which Santa Monica rose relative to Los Angeles (or Los Angeles subsided relative to Santa Monica) while other
29
periods reflect the opposite. On the time ordinate in these figures "mean year" means the central year of the window used for the calculation of the trends. To show how the variabil- ity of the trends for each station and for the differences are smoothed with an increase of the window length, Figures 21, 22, and 23 show the trends of the monthly anomaly data using 20, 30, and 40-year trend windows. All refer to the pair Seattle-San Francisco (SE-SF) . The difference curve is the lowest one on all the graphs.
These demonstrations show that the sea level trend is determined, in part, by both the width and the mean position in time of the window used; accordingly, it was determined that the aim of this work should be modified. Instead of trying to refine or otherwise improve on the values already published by several authors using single station tide meas- urements to estimate rates of land change, the study was reoriented in order to find the evolution with time of the relative movement between two stations. This will be the topic of the next chapter.
30
III. THE CUMULATIVE PROCEDURE
Wyss [1977], in a study of land elevation changes asso- ciated with earthquake occurrence, introduced a method of cumulative analysis using monthly sea level differences be- tween two very close tide stations. In order to apply this technique, it is desirable to adjust the monthly sea levels at one station relative to the other so that their means are equal. Thus, if for stations A and B, all the data values of B were modified in order to make the average of B equal to the average of A, the differences between A and B would have values with a random variation around zero. The dif- ference values, (A-B), are then cumulated in a time series beginning with the earliest monthly difference value. The cumulative curve that results will be a random walk around the value zero if the sea level history at the two stations is identical. There will be swings up and down, but eventu- ally a return to zero will occur. If the elevation of one station relative to the other is different, this random plot will soon show an evident and pronounced trend. In this case, if the monthly differences are cumulated over many years, very large cumulated differences amounting to many feet may result.
Now, if the relative elevation changes suddenly instead of cumulating small positive or negative values around zero, values containing a constant increment (positive or negative)
31
are now added introducing a trend on the random data, and an inflection point will appear in the cumulative curve. The difference between slopes on each side of the discontinuity allows determination of the amount of relative elevation change. The inflection point, itself, allows the identifica- tion of the date for relative elevation change. In the case of a sudden elevation change or jump revealed by a cumulative curve, the station which is responsible cannot be identified. However, the latter can be determined when more than one station pair is used because a change in the slope of the cumulative curves must occur at the same time in all pairs of stations containing the common station.
Before examining the results of the cumulative analysis, further explanation must be given about the kind of curves that can be expected when using the cumulative procedure. As was said before, there is strong reason to reject the assumption of long-term linear sea level changes, but there is no reason to avoid the assumption of linear relative ele- vation changes occurring over short periods of time. If we make this assumption, only two possibilities can occur. Either the two stations are stable relative to one another and the trend of the monthly sea level differences between them is zero, or there is elevation convergence (a negative trend) or divergence (a positive trend) between both stations In the first case, a straight line will be shown in the cumu- lative curve, with a positive or negative slope, depending on
32
whether the elevation of one station is higher or lower than the other; the linear segment will be horizontal if the means of the monthly sea levels are equal at the two stations for the time period represented. In the second case, if the monthly differences converge or diverge, the amount to be summed each time is different from the preceding value and follows a linear law of variation. The cumulative curve will then show a parabola with a negative or positive slope, respectively. Subroutine CUMMUL, (Appendix A-4), was written to perform this type of analysis.
To illustrate the above description of straight line seg- ments with different slopes, as well as branches of parabolas with positive and negative slopes, some of the cumulative graphs produced are presented. Figures 24, 25, and 26 show the cumulative differences for the pair Seattle-Los Angeles using raw data, anomalies, and 12 months running means (three sets of curves were produced for all pairs of stations because the different degrees of smoothing on each curve were helpful for identifying the inflection points). One interpretation of the cumulative curve in these figures is that they consist of three legs or segments, the first one between 1924 and 1947, and the other two between 1948-1965 and 1966-1974. This pattern in which the cumulative values become more negative and suddenly change toward more positive was not expected. These graphs show that the averaging procedure used to achieve an initial matching of the data for both stations was not the
33
most suitable because it caused a change in slope from nega- tive to positive, thereby suggesting a change in sign of the movement between the two stations. From the three figures we can see that the Seattle data was negative relative to the Los Angeles data during the first interval and became positive during the second and third legs. The absolute values of the slopes of the first and second legs strongly suggest that some event occurred about the end of the year 1947. Nevertheless, it must be noted that in 1947 a change in the sign of the slope also occurred. A change in the sign of the slope of a cumulative curve means that one data set crosses the other, so that the sign of the differences re- verses. If the cumulative curve is made by linear legs, then a symmetrical picture results in which the slope on either side of the crossing point has the same magnitude but is opposite on sign. In Figure 24, the character of the dis- continuity shows that not only did a "jump" occur between the two stations but the "jump" caused a reversal in the sign of the differences. In order to avoid misinterpretation of the cumulative graphs, the decision was made to recumulate the monthly difference values after first equating the initial data point of each station. The graphs presented in Figures 27, 28, and 29 show these results for the same pair of sta- tions, using raw, anomaly, and 12-month running mean data, respectively. Their appearance is seen to be markedly differ- ent from Figures 24-26. This group of six plots was helpful
34
in two ways; first, inflection points are easily identified, and second, the apparent differential station movements can be isolated from background noise. This procedure of produc- ing a set of six plots for each pair of stations was the routine used for all possible pairs among the seven stations dealt with.
The cumulative curves in Figures 28 and 29 never cross the zero line. Their relatively smooth appearance could lead to an alternative interpretation that instead of three straight line legs, the curves could be viewed as a long branch of a parabola. This interpretation could justify the computation of a single difference trend for the entire data series. From simple observation, there is no doubt that the long term trend between the two stations must be positive; the value of 2.13 mm/yr +^0.28 mm/yr is obtained for the entire raw data series (1924-1974) .
In order to test the hypothesis of these cumulative curves being composed of three straight line segments versus a branch of a parabola, two methods were used.
The first method, assuming the curves to be composed of three linear segments, was to calculate the differential sea level trends from the monthly difference values for each leg. The results obtained for SE-LA are given in the upper part of Table V. The three values for the trends are very close to zero, indicating similar movement at both stations during each period, but also that "jumps" occurred between each leg.
35
The measure of a "jump" can be obtained (as already explained) by computing the difference between the slopes of the adjacent legs on the cumulative curve.
The second test was to perform a least-squares best fit to obtain the hypothetical parabola represented by the cumu- lative data of Figures 24 through 29, and then to compute and plot the residuals obtained by taking the differences between the cumulative curve and the best fit parabola. For this purpose subroutine LSQPL2, a library subroutine of the Com- puter Center of the Naval Postgraduate School, was used. The residuals between the cumulative curve of Figure 27 and the best fit parabola are shown on Figure 30. It is clear that the variation of the residuals is not random, and some struc- ture can be observed such as would be expected from fitting a parabola to straight line segments. The next step was to fit each one of the three segments of the cumulative distri- bution with first degree curves (straight lines) and again compute the residuals. If the hypothesis of three linear legs is reasonable, the variance of the residuals should show a significant decrease and should display a more random dis- tribution around zero. Figures 31, 32, and 33 illustrate these residuals for the first, second, and third legs, respec- tively. The randomness around zero is evident, at least for the periods shown in Figures 32 and 33, and a decrease of the extreme values can also be observed. Thus, if the cumulative curve for SE-LA indicates three intervals of constant elevation
36
difference between stations, the jumps indicated about 1947 and 1965 amount to 4.6cm and 4.4cpi , respectively. Another conclusion can also be extracted from this analysis of the residuals. Both Figures 31 and 30 clearly show a unique structure in the data between the end of 1927 and 1934, sug- gesting that something of geological significance may have happened between these dates.
Similar tests were performed for several pairs of stations where the cumulative curve suggested the possibility of a single long term difference trend. Figure 34 is an example. This curve was initially chopped into three pieces. The first branch of parabola included the period from 1950 to 1959, the second from 1960 to 1964, and the last from 1964 to the end of the series. The values for the trends of the partial series as v\^ell as the entire series, computed from the monthly differences, are shown in the lower part of Table V. The test of the residuals was also applied, this time with three second- degree curves for the best fit of each branch. The results were similar to those for the SE-LA station pair. Again, the analysis of all pairs containing SF and CC not only allowed the identification of the inflection points, but also allowed identification of the station whose movement was responsible for it.
An example of station identification can be observed in Figure 35, where a change of movement occurred near the end of 1960. This figure refers to the pair SF-LA where the
37
movement which occurred in 1947 can also be seen. By compar- ing the plots for SE-LA (Figures 24-29) with the plot from SF-LA (Figure 35) , it is seen that an inflection point occurs on both plots for 1947. Therefore, Los Angeles must be the station responsible for this inflection. Near the end of 1960 a similar movement appeared on plots SF-CC and SF-LA. Using the same logic, SF is the responsible station. Figures 36 and 37 show plots similar to Figures 1, 2, and 3, but in- clude the periods containing the inflections of 1947 and 1960 for the pair SF-LA.
Cumulative analyses were made of the 21 possible station pairs for the seven stations analysed. Two plots are pre- sented in Figures 38 and 39 which illustrate some of the typical situations that were found. By disregarding small features, Figure 38 shows three distinct periods. The first one ends in 1959 and has a positive trend. The second one extends from 1959 to 1963 with a negative trend, and a third leg (almost linear) has a trend close to zero. Figure 39 shows six distinct straight line segments with different slopes and a small part of a parabola (between the end of 1951 and the end of 1952) . All of the cumulative distribu- tions appear to show only segments of straight lines and branches of parabolas. Therefore, it can be assumed that the difference data represents dominantly linear sea level trends .
38
At this point it is of interest to present the results of cumulative analysis applied to the seven tide stations studied. The method chosen to do this is to reference the relative vertical motions to a single station on the coast. San Francisco was chosen as the reference station because of its long time series without missing data (1899-1978) and also because only two vertical movements were ascribed to it during this long period. Table VI shows, for the time inter- vals listed, the sea level trends and errors in the trends for SE, CC, AV, and LA relative to SF. Assuming that San Francisco experienced discontinuous movements only in 1931 and 1960, all the other movements indicated by the boundaries between the time intervals shown are attributed to the other four stations. Although the sea level trend history for each station relative to the reference station could theoretically be determined directly from linear and parabolic segments fitted to the cumulative plots produced, time did not permit this. Trends shown in the table were instead computed by fitting linear curves to the station difference data for each of the many intervals betiveen the identified inflection points. Identification of the inflection points was found in some cases to be quite subjective. It should also be noted that the cumulative curves of nearly all station pairs that include SF appear to consist of parabolic segments.
Additional comments regarding the data in Table VI are necessary. The first one is that very short-term trends,
39
which cover a length of time like one year or two, must be looked upon with suspicion because they are dominated by the assymetry of the annual cycle still present in the difference data. Second, the stations of Santa Monica and San Diego were not included in the table because all cumulative plots including these two stations show a complicated pattern with continuous and aperiodic waves. The other cumulative graphs show generally well defined patterns leading to easy identi- fication of movements. Some dates of relative sea level rate change at these stations are suspected, e.g., Santa Monica in 1941, 1945, 1955, and 1956 and San Diego in 1942, 1950, and 1959, but it is impossible to define these discontinuities with the same confidence as for the other five stations. Also, it is evident from Table VI that as the length of each period under analysis decreases, the standard error of the slope increases. This is a price that must be paid when using cumulative analysis. The detection of apparent inflec- tion points results in chopping the entire time series into shorter segments, with the corresponding reduction in con- fidence in the trends obtained.
Some comments must be made about the computations of the trends as well as about the corresponding errors. The standard least-squares formulas used by other investigators in this field and also used in this thesis are not the most appropriate if the data to which a curve is to be fitted is not independently random. High correlation between the
40
monthly sea level values can be observed in the correlograms in Figures 40, 41, 42, and 43, prepared for Seattle, San Francisco, Santa Monica, and Los Angeles, respectively. Nevertheless, if the length of the series is large and it is assumed that for each time segment the trend of the data is smooth, a reasonable approximation is obtained for the value of the slope. But a poor approximation of the standard error of the slope results if the time series is short and the data fluctuations are not independently random. In order to obtain a representative standard error a corrective factor must be applied to the conventionally calculated standard error. This factor [Bloomfield, 1980] is:
1+ 2 Z P^
T=l '■
where x is the time lag in months and p is the autocorrela- tion function at lag x. This factor is positive, greater than one, and multiplicative; accordingly, it introduces an amplification of the value of the standard error of the slope If, for simplification, a geometric decay of the correlogram is assumed (and that is not always the case) this formula can be simplified to
where p, is the value of the autocorrelation function for a time lag equal to one.
41
Figures 44 and 45 show the correlograms for the differ- ences (using anomalies) between the pairs SE-SF and SM-LA. From these two examples it can be seen that the variability of the trend found with the ordinary least- squares formula should be increased for the first case by a factor of 1.3, using p-. = 0.26, and for the second case this factor is 2.17, using Pt = 0.65. Thus, the calculation of the corrective factor is different for each pair of stations and must be computed separately for each case. The values obtained for SE-SF, CC-SF, SF-AV and SF-LA, are 1.83, 1.69, 1.91, and 1.91, respectively. As the confidence limits for some of the trends are relatively large, the associated trends can be largely disregarded. Thus, care must be taken with the contained information, even knowing that it represents the most probable values .
As an example of the interpretation of Table VI, the positive relative trend shown for SE (2.34 mm/yr) for the period 1899-1910 means that sea level was rising at Seattle relative to San Francisco or that the Seattle tide station was subsiding relative to San Francisco during that period of time.
The question should be raised as to the cause of the relative vertical motions between tide stations determined from the application of the cumulative analysis. There are two plausible causes for the sea level differences:
42
(1) Occasionally or steadily occurring real land eleva- tion changes. It should be pointed out here that the occur- rence of sudden movements as shown on the cumulative plots agrees with results found from on-going studies using Very Long Baseline Interferometry to the effect that crustal plate motions in California may be characteristically jerky at regional scales of hundreds of kilometers and not continuously slow and smooth [Whitcomb, 1980]. Differential tidal level- ling in the Salton Sea reported by Wilson [1980] also indi- cates jerky crustal movements.
(2) Occasionally occurring changes in the station datum. These may be due to tide staff displacement, replacement of the staff or gage, moving the gage, displacement of the in- strument datum, construction work at the pier, etc. These kinds of changes are likely to be very small, although they appear to be detectable by the cumulative analysis technique.
Insufficient time and information precluded this study from determining which of the above phenomena was responsible for the movement for each disturbance data at each station.
43
IV. SUMMARY AND CONCLUSIONS
This thesis investigated the problem of determining the rate of land elevation change from monthly mean sea level data. The techniques used by different authors are surveyed as well as the different types of data and methods used for the calculation of trends. The assumption of linearity of the sea level trend used by previous authors in estimating absolute rates of land elevation change is also discussed. In addition, causes of water level variation contained in monthly sea level time series are enumerated. Because of the impossibility of separating the many components, it is concluded that absolute values for the rates of either sea level change or land elevation change cannot be found. Accordingly, the use of a differential tide levelling pro- cess was proposed in which the elevation of one tide station relative to another is determined.
In the experimental phase, mean monthly sea levels at seven tide stations on the Pacific Coast of the United States were chosen for study. Spectral analysis was first performed, and this showed peaked concentrations of energy around the annual and semi-annual cycles for all stations. Except for these frequencies, the spectrum up to the frequency of 0.5 cycles per month contained only noise, showing a typical decay with increasing frequency. These concentrations of energy,
44
essentially of meteorological and oceanographic origin, were then filtered out of the monthly station data using two fil- tering processes, a 12-month running mean filter and an anomaly filter. Descriptions of these filters are given in the text. The effect of each filter on removing the annual and semi-annual cycles without otherwise altering the prop- erties of the monthly sea level data was then tested by com- paring the power density spectrum of the filtered time series with that of the raw monthly data. The results obtained favor the use of the anomaly filter for future work because it eliminates the concentration of undesirable energy in all other frequencies found in the unfiltered data.
Several experiments were performed in computing sea level trends from sea level difference data, both filtered and un- filtered, using running intervals or windows with arbitrary and non-arbitrary time lengths. It was found that the sea level trend determined for a given station is dependent on the window length used, the chronological location of the window in the time series, and whether the monthly sea level values used are unfiltered (raw) data, 12-month running mean data, or anomaly data. Because of these totally time depend- ent results obtained for sea level trends, attention was redirected to the use of a new technique introduced by Wyss [1977] involving cumulative analysis of time series data. The method, termed here the cumulative analysis procedure, which is further developed in this thesis, involves cumulation
45
of the monthly values from beginning to end of a tide series. For this purpose, the monthly sea levels for the seven tide stations studied (Seattle to San Diego) were combined to yield 21 station pairs. The cumulative plot for a typical station pair appears to be composed of straight line segments and branches of parabolas. The linear segments represent time intervals during which the elevation of the two stations remains constant, while parabolic segments indicate a linear rate of change in elevation occurring between the stations. The segments vary in length up to 17 years. The fact that each cumulative curve consists of several segments indicates that differential vertical movements between tide stations, whether separated by short or long distances, occur frequently.
Also noted in some of the cumulative curves are inflec- tion points. These indicate a sudden vertical displacement of one tide station relative to another. The cumulative curve containing an inflection does not reveal at which sta- tion the movement occurred, but the responsible station can be identified from examination of two or more cumulative curves containing the station.
The process of chopping the cumulative curve into seg- ments (and of determining whether each segment is linear or curvilinear) was found in some cases to be quite subjective. Accordingly, tests were devised, and applied to selected cumulative curves, to determine whether each segment iden- tified is best represented by a linear or a parabolic fit.
46
The first test compares the residuals obtained between a best fit parabola and the cumulative curve with residuals obtained between a best fit line segment and the same cumu- lative curve. The other test compares the sea level differ- ence trend for each well defined segment of the cumulative curve with the long term difference trend obtained for the entire time series.
The cumulative procedure, although limited by subjective interpretation of the cumulative curve, is sensitive to very small sudden or continuous changes in the elevation of one tide station relative to another. In addition, in contrast to conventional geodetic methods, application of the proce- dure produces a continuous history, month by month, of dif- ferential elevation changes between two stations (over the period of common tide measurements) . It is recommended that the cumulative procedure be used in future analyses of tidal data time series, although further investigation should be done to refine the analysis techniques. It should also be determined whether, for the tide stations studied, the changes in elevation of one station relative to another are caused by real land elevation changes or by changes in station datum, or both.
47
/
TABLE I TIME SERIES USED FOR EACH TIDAL STATION
c^ ^- c u 1 Number ~. ^ • Approximate Distance
Station Symbol ^^ ^ears ^^"^^ Series ^^^^^^en Stations
Seattle SE 76 1899-1974
Crescent City CC 25 1950-1974
San Francisco SF 80 1899-1978
Avila AV 14 1946-1959
Santa Monica SM 33 1933-1965
Los Angeles LA 55 1924-1978
San Diego SD 31 1931-1961
68 5 Km 481 Km 333 Km 2 44 Km 38 Km 153 Km
Note: The data format for all the stations was mean
monthly sea level values in feet on computer cards.
48
TABLE II
DIFFERENCES OBTAINED FOR LONG TERM TRENDS WHEN USING RAW AND FILTERED DATA
Seattle (1899-1974)
San Francisco C1899-1974)
Santa Monica (1933-1965)
Los Angeles (1924-1978)
Record length: 76 yrs
76 yrs
33 yrs
55 yrs
Raw data: b 1.922609 1.911846 2.814878 0.590955
Sy.x 84.77 59.263117 63.338516 60.829502
Sb 0.127954 0.089446 0.334117 0.149132
12 Month b 1.912255 1.886021 2.541461 0.510632
running Sy.x 30.506815 29.897564 29.283841 26.579253
means Sb 0.046890 0.045953 0.161142 0.066826
Anomalies: b 1.927965 1.905879 2.718758 0.555566
Sy.x 62.328436 50.409106 42.951712 39.328127
Sb 0.094073 0.076083 0.226574 0.096418
where: b is the slope of the long term trend in mm/yr; positive values indicate a rising sea level trend for the entire record.
Sy.x is an estimate of the error standard deviation in mm.
Sb is the standard error of the slope in mm/yr about the long term trend. It was calculated as if the fluctuation of the monthly values are independent. These estimates of the standard error are almost certainly too small.
49
TABLE III
COMPARISON OF SPECTRA FOR SEATTLE DERIVED FROM
THE RAW DATA, 12 -MONTH, RUNNING MEANS, AND
ANOMALIES (16 DEGREES OF FREEDOM)
|
(1) Period (months) |
(2) Frequency (eye. /mo. |
Energy Density (feet sq. x month) (3) (4) (5) Raw 12 mo. Anomalies ) Data r.m. |
Quotients (3)/(4) (3)/(5) |
|||||
|
64.000 |
0.016 |
0 |
.173 |
0.130 |
0. |
177 |
1.330 |
0.977 |
|
21.333 |
0.047 |
0 |
.091 |
0.024 |
0. |
079 |
3.791 |
1.151 |
|
12.800 |
0.078 |
1 |
.324 |
0.002 |
0. |
112 |
662.000 |
11.820 |
|
9.143 |
0.109 |
0 |
.214 |
0.004 |
0. |
098 |
53.500 |
2.183 |
|
7.111 |
0.141 |
0 |
.103 |
0.001 |
0. |
067 |
103.000 |
1.537 |
|
5.818 |
0.172 |
0 |
.188 |
0.000 |
0. |
070 |
00 |
2.685 |
|
4.293 |
0.203 |
0 |
.084 |
0.002 |
0. |
066 |
42.000 |
1.272 |
|
4.267 |
0.234 |
0 |
.072 |
0.001 |
0. |
080 |
72.000 |
0.900 |
|
3.765 |
0.266 |
0 |
.043 |
0.000 |
0. |
034 |
oo |
1.264 |
|
3.368 |
0.297 |
0 |
.075 |
0.001 |
0. |
069 |
75.000 |
1.086 |
|
3.048 |
0.328 |
0 |
.059 |
0.000 |
0. |
053 |
00 |
1.113 |
|
2.783 |
0.359 |
0 |
.052 |
0.000 |
0. |
053 |
CO |
0.981 |
|
2.560 |
0.391 |
0 |
.030 |
0.000 |
0. |
027 |
00 |
1.111 |
|
2.370 |
0.422 |
0 |
.048 |
0.000 |
0. |
054 |
00 |
0.888 |
|
2.207 |
0.453 |
0 |
.062 |
0.000 |
0. |
060 |
00 |
1.033 |
|
2.065 |
0.484 |
0 |
.033 |
0.000 |
0. |
030 |
oo |
1.100 |
|
2.000 |
0.500 |
0 |
.025 |
0.000 |
0. |
024 |
oo |
1.041 |
Note: Only alternative values of frequencies are shown (Af= 0.0155 cycles/month).
50
TABLE IV
SEA LEVEL TRENDS OBTAINED FOR THREE STATIONS USING DIFFERENT LENGTHS OF TIME SERIES
|
Station |
Time Period |
Tre Raw data |
nd 12 |
(mm/yr) mo.r.m. |
Anc |
)malies |
||||
|
Seattle |
1899- |
■1974 ( |
'76 |
yr) |
1. |
92261 |
1. |
91226 |
1. |
92796 |
|
Seattle |
1899- |
■1968 ( |
'70 |
yr) |
1. |
80475 |
1 |
74807 |
1. |
81080 |
|
Seattle |
1924- |
•1973 ( |
'50 |
yr) |
2. |
73895 |
2. |
71548 |
2. |
74963 |
|
Seattle |
1924- |
■1947 ( |
'24 |
yr) |
2. |
44849 |
2. |
79119 |
2. |
50428 |
|
Seattle |
1948- |
■1965 ( |
:i8 |
yr) |
1. |
83066 |
1. |
77530 |
1. |
89668 |
|
San Francisco |
1899- |
■1978 ( |
'80 |
yr) |
1. |
83336 |
1 |
81182 |
1, |
82822 |
|
San Francisco |
1924- |
■1973 ( |
'50 |
yr) |
2. |
36677 |
2. |
348 99 |
2. |
35055 |
|
San Francisco |
1899- |
■1968 ( |
'70 |
yr) |
1. |
87412 |
1. |
84081 |
1. |
86713 |
|
San Francisco |
1924- |
■1978 ( |
'55 |
yr) |
2. |
11264 |
2. |
06595 |
2. |
09943 |
|
San Francisco |
1899- |
■1974 ( |
76 |
yr) |
1. |
91185 |
1 |
88602 |
1. |
90588 |
|
Los Angeles |
1933- |
-1962 ( |
:3o |
yr) |
1. |
06396 |
0. |
85891 |
0. |
94343 |
|
Los Angeles |
1924- |
■1973 ( |
:5o |
yr) |
0. |
63811 |
0. |
61212 |
0. |
59517 |
|
Los Angeles |
1924- |
■1947 ( |
:24 |
yr) |
2. |
41874 |
2 |
39378 |
2. |
23160 |
|
Los Angeles |
1948- |
■1965 ( |
:i8 |
yr) |
1. |
47915 |
0 |
90488 |
1. |
14511 |
|
Los Angeles |
1924- |
■1978 ( |
:55 |
yr) |
0. |
59096 |
0. |
51063 |
0, |
55557 |
51
TABLE V
TRENDS OF THE DIFFERENCE DATA FOR PAIRS OF TIDE STATIONS FOR SPECIFIC TIME SERIES
c^ ^ • T^ • n • J Trend fmillimeters per year) Station Time Period ^ .. ^^„ . „ ^^ -.-^ . ^
Partial Series Full Series
SE-LA 1924-1947 (24 yr) 0.0297 2.1375
SE-LA 1948-1965 (18 yr) 0.3513 (1924-1974)
SE-LA 1966-1974 (9yr) -0.0953
SF-CC 1950-1959 (10 yr) 7.1997 3.2682
SF-CC 1960-1964 (5 yr) 12.7439 (1950-1974)
SF-CC 1965-1974 (10 yr) 3.4339
52
TABLE VI TRENDS OF ELEVATION CHANGE RELATIVE TO SAN FRANCISCO
Stations Time Period Trend (nun/yr) Standard Error of the Slope (mm/yr)
SE-SF 1899-1910 2.34497 1.993378
1911-1927 1.01102 1.089108
1928-1931 -3.92303 8.252379
1932-1934 3.86056 19.600630
1935-1945 0.27098 2.021985
1946-1952 -7.65468 4.130359
1953-1960 -4.05034 3.501000
1961-1965 -12.63590 6.847633
1966-1974 -0.87969 2.938892
full series 1899-1974 -0.01075 0.119488
CC-SF 1950-1954 1.01228 4.633611
1955-1959 -10.63333 5.191369
1960-1960 -49.87460 46.494390
1961-1963 -15.23740 9.759881
1964-1974 -2.48234 1.627356
full series 1950-1974 -3.26817 0.455462
SF-AV 1946-1947 25.50820 12.868782
1948-1952 -7.61081 2.991260
1953-1959 -0.16552 2.754739
full series 1946-1959 -0.14199 0.862576
SF-LA 1924-1931 -2.19510 1.909139
1932-1947 1.75783 0.758469
1948-1960 1.21958 1.011479
1961-1970 3.62779 1.557846
1971-1978 -3.91764 2.136735
full series 1924-1978 1.52172 0.121347
Notes: 1. The trends were calculated from the raw monthly data.
2. Discontinuities at San Francisco were found to have occurred in 1931 and 1960.
53
.Q
Q Q
P-'-
-e
! O
Q
^
;:^::
■■■■■o
■■■■!--tLr- '■■ -co ;-
:$r
CD
#;
0
<i
-0-
:1q
asi
:n:;::rn::::::€J..Q:;:::
O ^ !
.0.
©^
-e-+-
.0.
.as
+ iT + «F!
e.:0l:;:t::tj:i::j:::i;i ::::|:Q^::±:ttt;:;ti:
:::|:;-^:g::t:::t:m::|::
-e-
i€r
:e;:i:t:H::m
..( .1 ..J... .;.... !....(. ..I.,.. I..
..I .. ..|....|....f...r ■ i>->.i»
1%
LO
' cn
4
:«
ti
<
4
-0-
■+^
■i< ■
:|^:
■ i LO I LO
':■ CD
■t
•T-f-:
fi^:
^
ilES:^'-
, 7=S±mSi
:::±:r:m:;:::;t:
ti
••«■
4
,^... .,....!...,(. ...l....|....| 1. ...!....,... .|....j....|, ...,._{_ ,....,....,....,....,....,....,....,,
CD
CO LD CD
il
-^
..[■....i..
+
;■-{-
i:::; cm
ji;::;:::;:::!;:::;:: cd
-■•4f-:-i-|-;
■+■
*
■+!■
•■!•■•■!■'•<<»
..I....1....I.. ..i....i,...i..
..<|..i
..l....i . ..!...;.. .,l....i .
■•!•+■
.Hi"
-f
iii
-H
LD CD
O LD CD
o o o o o
O LO O LO O
o r- LO CM o
-^ CD CD CD CD
i33i
o o o o a o in o LO o o r-- LO oj o
'-• o o o o
54
ia3d
o I
LU
o
LU LU
Q
O
o
>-
»— I
LU
LU
cr:
LU
LU
oo
o
_I
LU
> LU
_J
ca:
LU LO
>-
LU
O)
cn
^■■i-4-:-i"r-f't"T-f-
J,....,..
•H--!-
,,....,. ...,...,...., -ifj-.^.- ■;»-|.-i— 1.-1.-.-1.-1-1..
•••i—i—i-* f- j 4-^-
;;::;::rx:;:;::::^^;::;:
«/)■•'■■■' <!■'■•■■ !■■•■!■•■
::p::::;:::;!::±#:o.
e^
©
a
..i....i....i...X...i....i..
■i-i--!-4-!e-
•ei-
e
e
G-i-i-i-i-i-H-i-i-
2i....|."y".j— j"";--;""j""j."
,^ ,.|...i....j....^...|....j...^....|....i...
-B
t:::;:i-,::^:::i::t:;!::::i::;x;:i:;:t:x:;:
e:g"m4#
t-j-i-iO-
•G-
Oi
....:0i........................
Q.,
■■\--\-r iQ
m
.0
: I : : ; ; : ^f >- .J...J...^...J....J....,....;._J..Q
.4....i...4...^....j....j...i,...j..Q -i...^....i...4...^....j....^...i.......
..i....i....i.„.i....i....i5;Q...i.,
=>iri--H-i-r-l-t-i" ■©■■••■••••••■■••r-i-r-i-r
...r:..i....i....l....i-...i.i —i-.i-
^....l..
r^-
•••■■ ea-i-!" i-
■■:-xri-r-r -r- ■•! ••■•1-! ■■!"■•+•■
■• LU--4- •■• ■•^•■■■0^■■■■l-^■■■i■■
4
<
%
■:^:
t
.,^..
•■i--i--!-i--i--|;<J-
:;p:::r;r:!::^;::
..4,
:r^:;
:tr::g;i
:i*
-l-r
:;;::i::¥ii:::t:;;i::i;:::;:;:|oo L±;:!::!::::i:;;:!:;:i::i:::i;j- ^
X!-t-!-t-!-i-i-t-
s
•i 00 en
i-t-i"
:r;^::;;|::;:;:tr::;: co 7!-fi-i-"i-i-i-:- on
.4jl:::t::i:::tixi::::;:::i;:; en
+
...L...!$,..i,...:....i....i;:..L..::..'Ln J::::iti::::!::j:::r:t:::::::!::::lori
^
^:;;
i:|-
+
«
....j....j....|....;....,....:.^....j....;....j....i....:....i...,i...H....i ■■■^■'■■■■t ■■]■■■■■■■■•■■
■4
,■■■■■■+
I--!- ■ 1 ■ -I
i-l-i-i t. :: = : = :
•■!-iJT-rT-!-T-rr-
:;p#::p::;::|:;:;;::;:: :;:i^;::r::;:::t::i;:i::!::i::
t::rt:;#-tz::r:a
-t::p=i~mm:r
..^..
!■<•
:<••
jjzxFS,;::::::::
^
3iis
....|.X.,...;,.,4....i....|....,.......j VJ>
...,|.-l...i....j....l...H....|....!....i.... .,_,
5
^...;,...|,..,i....i,.
■'^•--''--'■'■-^ W
..4.
14-
<
..j....i....i...,i....|...;^ !....;....:
••!■■••!•• i< :•! •
.,(....;....(. ...i....i....i....i. ..,;..
:mmn:
CM
en
:tH::::i:::f:r::|;:;::
liii
00 CD
00000 O LO O LO O
o r- LO oj o -^0000
i33d
55
00000
O LO O LD O
o r- LO c\j o -^ C) o o o i33d
00
c/0
o
UJ
cr
LU LU U. I— I O
Q
00
o
UJ
I— H
o
C/1
00
|
00 |
0 |
|
m |
0 |
|
00 |
|
|
*— ^ |
»— » |
|
0 |
|
|
z: |
|
|
<a: |
|
|
q; |
|
|
LL- |
|
|
en |
|
|
(D |
00 |
|
CD |
d: |
|
'— ' |
0 |
LU
CNJ
O)
..i....i.....*rf.i€i...i....;....:....i....i
•■■■■■■■■■ ^Q-r-r-i--
''W'-^ ^^^
</>
-i-i ••«£
:lx^ ^^-rx:^
e
:t:i:r;:;:;::i;i:::i;::t:i:::i;;
Q
\§:
0
o
d
.,...i....|....|..^q:!....!....!....i...+...!.. ,.,....,..|..0^..;....|....i....i....|....i..
Xi;:a:±::;..:t
#
■■••- •i""i--f—i- j-i
^^
ieSi-i-i-l-i-l-!-
,....,Q...|....,....j....,....,....|...
j^r-
"fH™! ^..~ ■••:•■ -• -Q-' ■ ■••■!—!-i--!-t"i ■•■
:::;::4:::i::;;::;::::;::::i..;:::::n:g
..i....i....i....i....i..,.i..
i.».r*«4.-xi.«>t*— i>«<t>»*t.<..t<*.
!?^
^ •■■■4 + '*4H-
Qi.,.i....i....i....|..
..,..,£,
.4.4..i.4-4-4-r4 ■^■■" ■ i !^-r-f 4-4--T-4'
I^l0fy-"f4-
..|...
"T'tf •>*■'■:
..;...^...4,...).,..i...j....i..,.i....i... |....i.^ ,.i... i... i.. i....i.. ..{...
^ ^ : ■ ^ i ^ ' ^ I '^ ^ ■ ■ : i i i
^„,,.,
WSBn-Sl^'S^
A
,l::i:
WSSSEEtB
■■'sii f — i.-i.-H-4-i--i
■■t/3|- ; "T-'l--!--! ■■■•■■•••I---I
o on
H-
!<l
.1,::
4
flEEEEEE
.«■!
;:i|::
4
:J::
::i:::i±l:::t:T:::: ;/
■•••:■•■•!•-*—'•■■■!■••!■••■ !■ -
•:-r-i
! 00
4
I en
.<
::;t
*
..i....i....i....f....i....i-.i-..|^.;...' j..,.i....i....i....i..
<..
:S::.::;::i:i:::;::i:; r-
..|...,.....,....,......,,...<J.,^...,....,....,...,....,...,...,......
■•4
..^..
..!.. .i.-^..(....i....|....t....|....i....
±-
oo
;:t;|:i:i:Ex3:;:E:j CD
:i:::±i,::!::::!:r:a:;:r:l 2
:::;::::4^!;:;:i:;:i:::i::::!::::!;:::i ^ ...,..^,..,.,.,..,..,...1....,...,
i
3sa^^^^^^^^^^^^^^^^^^^^^
;fcm±r
LO
cn en
..^,,
*■
•T-l -I— 'r'T"!'
-4
..,....J....,....J.......
i±i^ = — ^ ^
itmx
:ft
rr
: +"|-!-f4-!--i CO
....;.„^.,..;...,....,.......,...,....
■■"!""'^""i""'""!""f"'T" "!"■■
3|;:Effi::i:t:
•14-
■•+-r-!-i-i-!-|-
..i....i..4:.i....i....i....i....i....i..
•■■44^1- ■■!••• if4f
cn cn
CD
o o o o o
(o in CD in CD
o r^ LO c\j o
^ O CD O O
i33d
56
o o o o o
O LO O LO O
o r- LO c\j o
-^ C3 CD CD CD
i33d
-J I
1/1
00
UJ
o
LlJ
a
a
z:
UJ
-J
LU
o
cyo
o
o:: o
LlJ
LJ C/1
LU
CO
s- cn
LP
V O
o o
03
U3
OJ
|
^ |
0.^ |
o |
|
4; |
1— |
I/? |
|
, ^ |
LU |
|
|
rn |
||
|
LlJ Q CO |
||
|
7^ |
a. |
|
|
eP ■ |
<C |
|
|
^1 o |
O |
|
|
•si |
CT' |
LU |
|
Si |
ixJ |
_l |
|
^f |
1— |
|
|
iij |
! |
1— |
|
C_J |
LU |
|
|
>- |
W) |
|
|
^' |
Lu O |
|
|
^' rv, |
z |
CXI 1— o |
|
^ • |
LU |
|
|
^4'^ |
>- |
00 |
|
1 |
(_J |
|
|
?=' |
LU |
(HINDN'OS 133J] NDIlDNnd iilSN^Q y^MDd
57
LU ZD CZ) LU QZ
o
o I— I
I—
Ll.
>- I— I— I to
UJ
o
Q-
cn
r-,*^.
in
I —
on
C_1
LiJ ID
LiJ C~
in
OJ
a
LP
o
Ln o
o a
o
Q
q:
LU LU
UJ
Q
CO
I—
o
t/0
Ll. C
< UJ
u.
o
o
I— (
u.
>- »—
UJ
a
UJ O
o.
U)
O)
s_ en
HINOW'OS i33J] NOIlDNnd AilGNdQ ydMHd
58
o
ID
O
LD O
-I
i CO
o
H
o
o o
|
o |
|
|
O |
|
|
LiJ |
|
|
LU |
|
|
C£ |
|
|
Li_ |
|
|
J |
U_ |
|
O |
|
|
._ . |
OO |
|
^ |
UJ |
|
tJ |
UJ |
|
^>~ |
o |
|
UJ |
|
|
o |
|
|
cc |
KO |
|
'■-ij |
r— |
|
Q_ |
|
|
< |
|
|
1— |
|
|
on |
Q |
|
tJ_J |
UJ |
|
1 |
-J |
|
'■-J |
1— 1— |
|
^ — |
«5C |
|
UJ |
|
|
''_J |
00 |
|
u. |
|
|
21 |
o |
|
1 — 1 |
,a; |
|
Q£ |
|
|
1— |
|
|
y- |
o |
|
UJ |
|
|
( i |
a. |
|
__ |
oo |
|
^z. |
|
|
LiJ |
UJ 3= |
|
' |
1- |
|
a |
U- |
|
UJ |
o |
|
QI |
z: |
|
o |
|
|
Li_ |
t— < |
|
1— |
|
|
o |
|
|
z |
|
|
ID |
|
|
u. |
|
|
>- |
|
|
h- |
|
|
HH |
|
|
CO |
|
|
z: |
|
|
UJ |
|
|
o |
|
|
ex: |
|
|
UJ |
|
|
3 |
|
|
O |
|
|
Q. |
|
|
• |
|
|
<u |
|
|
s. |
|
|
3 |
|
|
o> |
59
a'^"*' ^^1 "?^l
o
JZ
O
iJJ
Q_
cn
LJ >—
O
UJ
liJ
Ul
LU
o
o o
C/1
ea: to
•a:
O
LP
o
LP
o
|
o |
||
|
- . |
LlJ |
|
|
- 7- |
D_ |
|
|
*■ |
OO |
|
|
'■- |
UJ |
|
|
' |
:r. |
|
|
czi |
1— |
|
|
LU |
u. |
|
|
o |
||
|
i-i_ |
||
|
Ll_ |
o 1— « |
|
|
'^^ |
||
|
CD |
2: u. >- 1— 1 — 1 CO UJ cc UJ 3: o |
|
|
r^ |
Q- |
|
|
O |
OJ i- |
(HINOWOS 133d] NOIIGNHJ AlISNdQ UdMOd
60
o
o
LU UJ
o
o
m
O
o
o
i o
5 O
O
o
[HINDN'OS i33d} NQIlDNild AlISNda ddMOd
61
CJ
LJ_I
o
00
LU LU
q::
LU
o
00
o o
I— <
ex:
q::
O-
oo
LU
IE
J—
U-
o
o
I— I
I—
>- I—
l-H
OO
2:
LU Q
c:
LU
O
Q_
CO
a>
s_
13 CD
•r~
Lt-
o
o
o
o a
Cl_
en _J
UJ ZD
a
IxJ CII
o
o
LU UJ
u.
o
in
on
CD LU
o
Q O
o
CO I— I
<_>
<c a:
C>0
•a: a: I— o
UJ
t/)
UJ
o
l-H
o
00
UJ
o
o o.
o^
CT>
(HiNOWOS i33d) N0Ii3Nnd iiISN3Q y3MGd
62
-€^
&
0
^-o~~
0
Q
■■S=-
S'
Q
^
■e
G
0
e
%
© 0'
o^:
%
0,
• 0 0
■s>-
;;,;:%
CD CD CD CD CD CD \S) CD ID CD
o n- i_n <\j o
^ CD CD CD CD
i33d
00000
O in O LD o
o n- LO oj o — ^ o o o o i33d
LU
LU
CO
o:: o
LlI
s: o
2: <c
o
LlJ
2:
CJ3
cc:
|
0 |
|
|
0 |
|
|
cj- |
z: |
|
, |
0 |
|
2: |
|
|
CVJ |
|
|
»— " |
|
|
M |
|
|
< |
|
|
(T) |
1— |
|
cn |
< Q |
|
en |
|
|
3 |
|
|
.— < |
< |
|
cn |
|
|
. |
|
|
0 |
|
|
' — |
|
|
OJ |
|
|
S- |
|
|
3 |
|
|
cn |
63
o o o o o
O LO O LD O
o r- i_n oj o — I o o o o
i33J
|
o o o |
o o o LO O LO r>- LD C\J |
o o o |
|
^ |
o o o i33d |
o |
o
I— «
<_) cc
tn c
UJ
o
<
•a:
(/I
:^ <:
LU
Z3
o
o
a:
CD
64
o o o o o
O LO O LO O
CD r- Ul CM o
—« o o o o
i33J
o o o o o
CD m CD in CD
O r- LO CM o
-H o o o a
65 i33d
o
< to
cc: o
00
LlI
I— I
_J •a: s: o
z: •a:
Q
<:
I— o
C\J
Q
•a:
CJ
s-
d
G —
wm
p
n
CD CD CD CD CD
CD in CD Ul CD
O r- LO C\J O
— o o o o
i33d
CD CD CD CD CD
CD in CD LD CD
o r^ LO c\j o
— • o o o o
i33d
en en
o
en
CD
|
cn |
|
|
C\J |
00 |
|
m |
UJ |
|
_J |
|
|
< — 1 |
LU |
|
O |
|
|
< |
|
|
to |
|
|
o |
|
|
oo |
-J |
|
C\J |
Oi |
|
cn |
o |
|
■» H |
|
|
t/) |
|
|
LU |
|
|
t— 1 |
|
|
_l |
|
|
^ |
|
|
:s~ |
|
|
r- |
z: |
|
(\j |
< |
|
cn |
Q |
|
<— t |
•^' |
|
•=C |
|
|
to |
|
|
z: |
|
|
< |
|
|
CD |
LU |
|
CM |
|
|
cn |
z: |
C\J CD
rr
OJ
d
o
CM
I—
CO
s-
OJ
66
GD
a
o
CD
o
3* O
CM O
o
■
o
ED SI
cc
UJ Q_
in
_j
LJ
>- LJ
ZD C3
CC Ll.
o o
UJ UJ
o
UJ UJ
a:
UJ OJ
UJ
UJ
o
(XI
o.
C/1
o
o
J— <_)
U-
>-
I— I
{/)
UJ
o
o
Q.
<u
s-
3 CD
(HiNOWOS 133J] NOIlGNHd AilSN^Q y^MDd
67
^
^i
CD
o
CD
o
3" o
o
o a
[HINOWOS 133J} NOIiONnj iilSN^Q UBMOd
68
O 2:
QZ LU Q_
Ul LU _J CJ
>-
U
LU ZD
a
LU
o o
o
o
LU Q
CO
LxJ
LU
! 1/5
o
U-
o
en
H- (J LU
o_
LU
O
o
K- <
t—
o
u.
>- I—
I— 1
LU Q
cc:
o o.
IS)
s- cn
.BL
CD
a
CD CD
o
m
O
o
■
az
UJ Cl_
ui
LU _J CJ >—
CJ
CJ
:z: a
LU QZ Ll_
o a
LU UJ
u. o
CO
UJ
o
CM
o
(-0
I
o
CM
a. oo
UJ
I—
u. o
2:
o
o
z
>- I—
to
a
UJ
3: o
Q.
s-
ZJ
(HINON'OS i33d} NOIlGNnj J.lISN3a U3M0d
69
oo o
CD
a
a
■
■
cc
LxJ Q_
cn
LU
__j
CJ
>—
>- CJ
:z.
LU
ID CZ)
uu
o
o
LU LU
LU LU
o:
C3 LU Q
O
;/) I— I
o
UJ
o
a:
H- O UJ Q. 00
O
o 1—1
I— o
z
LU O
Of:
LU
o
o.
(U
(HiNOWDS i33d)N0Ii3Nnj AiISN3a y3M0d
70
LP
IS
J
0)
"a; en
c
(/)
o
1
o
CO
en
LiJ
LO
LD
O
I
O I
o a
a:
UJ
>-
I
o
<: ■z.
-J I
o
<:
C/1
o
■a:
UJ
o
o^
00
<u
Zi C71
yX/WW NI SQNByi
71
CD
cn
|
V) |
|
|
(U |
|
|
fM |
|
|
OJ |
|
|
o> |
|
|
c: |
|
|
<C |
|
|
(/) |
|
|
0 |
|
|
-J |
|
|
(C |
fO |
|
u |
00 u |
|
•I— |
OJ •!- |
|
c |
1— c |
|
o |
O) 0 |
|
2: |
CDS: |
|
c |
|
|
(T3 CC (O |
|
|
-M |
+J |
|
c |
00 c |
|
<o |
0 TO |
|
oo |
—1 LT) |
XN >
' ' I \ \ L_J.
J I I L
J L_JL
-1
in
-I LH
cn
o
CD
cn
cn
CD
cn
Ln m
CD
LD
in
LD I
O 1
o a
<c
UJ
>-
I
o
CD »— I
|
<: |
||
|
_j |
||
|
«r" |
||
|
CC |
u-> |
|
|
CE |
Q |
|
|
^ |
UJ |
2: |
|
0 |
>- |
<: |
|
LD |
• |
A |
|
cn |
«a: |
|
|
'~' |
2: CE |
|
|
UJ |
CO |
|
|
5: |
0 Li- |
|
|
2: |
||
|
U) |
el |
|
|
zr |
LU |
C5
ZS O
s:
CM
CO O
UJ
a>
(U
cn
yjl/NN NI SQN^yi
72
|
1/) |
||
|
V |
||
|
1— |
||
|
<u |
||
|
en |
||
|
c |
||
|
<: |
||
|
w |
||
|
0 |
||
|
-J |
||
|
ra |
»o |
|
|
u |
t/) |
0 |
|
•r— |
a; |
•f— |
|
c |
r— |
c |
|
o |
<u |
0 |
|
2: |
CDS: |
|
|
c |
||
|
<0 cC |
fO |
|
|
+-> |
+-> |
|
|
c |
</) |
c |
|
rt3 |
0 |
OJ |
|
OO |
_J |
t/1 |
J L
J ' ' I '
1_J i L.J I ' i I «
LT-
-1 ^
I CD
O -J <^
i 1
|
0 |
||
|
0 |
||
|
J |
:z |
|
|
HH |
||
|
u~ |
"^» |
|
|
o'- |
||
|
er) |
<C LU >- 1 0 |
|
|
Qc: |
«=c |
|
|
(X |
0 |
|
|
■ |
LU |
1— 1 |
|
0 |
:^ |
oo |
|
in |
:=i |
|
|
en |
||
|
^ |
z: |
<" |
|
CE |
1 |
|
|
lU |
||
|
s: |
D5 0 |
LP IT
en
o
00 o
U- LlJ
in
LO
|
<^ — ' |
•=3: |
|
CD |
0 |
|
^H |
z: |
|
< |
|
|
u. |
|
|
0 |
|
|
C>0 |
|
|
Q |
|
|
■z. |
|
|
UJ |
|
|
CC |
|
|
lo |
\- |
|
PO |
, |
|
en |
0 |
|
♦—4 |
CM |
|
OJ |
|
|
s_ |
LO
O
CD
y^/WN NI SGN3yi
73
J 1 \ L
J L.J.
in
J I \ I I L.
t I I I I
ul
in I
yx/ww NI SQNByi
74
o en
i
J
o
o in en
i o
-I ^ en
|
o |
|
|
a |
|
|
^ |
|
|
1— I |
|
|
3 |
|
|
Q^ |
|
|
<c |
|
|
UJ |
|
|
>- |
|
|
o |
|
|
cc |
CM |
|
CE |
<: |
|
LU |
o |
on
|
« |
CE |
U- |
|
o on |
LU |
1 |
|
en |
2: |
Lul |
|
U- |
||
|
t |
to |
|
|
o |
||
|
CM |
LU |
|
|
O u. 1— 1 |
||
|
• |
_J |
|
|
o |
g |
|
|
en |
o |
|
|
•— • |
o o |
|
|
, |
LU |
|
|
o o |
1— |
|
|
en |
• |
|
|
s- |
en
o
CO
en
w
I
J L
J I { L
) I I I I ( 1 I I I I I I t t I I
If)
irt
I
J
o
CD
|
0 |
||
|
Q |
||
|
Z |
||
|
»— 1 |
||
|
3 |
||
|
01 |
||
|
<C |
||
|
lU |
||
|
• |
>- |
|
|
o |
1 |
|
|
rr |
0 |
|
|
en |
CO |
|
|
r— 1 |
QI |
•sC |
|
d |
CD |
|
|
LU |
1— 1 |
|
|
>- |
00 |
|
|
2: |
U- |
|
|
cr |
1 |
|
|
UJ |
UJ |
|
|
O |
2: |
oo |
|
CO |
||
|
Ol |
Q z: |
|
|
*"* |
«c |
^
o en
o en
o
I
00
UJ
(/>
o
1/1
UJ
o
UJ
CM OJ
s-
=3 Oi
yi/ww Ni 9aN3yi 75
o
(.O
J
-i
J ! L
m
J I I I I L
I I t
in
in
I
-1
i °
_J Ln en
" -^
i
i
C
rr en
o cn
o en
o
CE LiJ
o
o
<:
LlJ
>-
I
o
o
oo
|
■GI |
1 |
|
|
■ o |
l_L_i |
to |
|
CD |
Q |
oo
LU
o
CO
UJ I— I
-J <C 2; o
00
o
La
CO
CM
s_
y;,/NN Ni saN3Ui
76
o
CD
J I I I L-J I I I \ 1— J I I I I I L-J I I t ' I '
(i33d) b1-3S
ddlQ 3AIibinNn3
77
C3
cn
-4
«
I
|
o |
o |
o |
o |
|
«— • |
CVi |
CO |
=r |
|
1 |
1 |
1 |
1 |
LU
J—
00
|
o |
||
|
(S3 |
1— |
|
|
cn |
||
|
1— I re o |
||
|
"^ "^ |
J— |
|
|
CO |
< |
|
|
CO |
s: |
|
|
CE |
Q |
|
|
o |
LU |
<C |
|
LD |
>- |
ca: |
|
cn |
- . |
h- |
|
aJ |
2 |
|
|
21 |
o
oo
|
o |
|
|
rr |
|
|
cn |
— 1 1 |
|
LU |
|
|
CO |
|
|
</) |
|
|
liJ |
|
|
o |
|
|
z |
|
|
uu |
|
|
• |
a: |
|
o |
LU |
|
CO |
Ll. 1— 1 |
|
*"• |
o |
|
LU |
|
|
5> |
|
|
l-H |
|
|
1— |
|
|
< |
|
|
-J |
|
|
ID |
|
|
s: |
|
|
• |
=) |
|
o |
o |
|
rvi |
• |
|
CD |
«!l- |
|
>-< |
CSJ |
|
a; |
|
|
&- |
|
|
=j |
|
|
cn |
J \ L
J I 1,1
o I
o
CM
I
o
en
t
(133d] U1-3S 'JJIQ 3AIlUinwn3
78
o
_ OD CD
1 s
-1 J
1 ° J CD
3 en
o en
J I L
o m
07
o
CM
cn
o
I
t/1 UJ
I— <:
UJ
I—
CD
|
n: |
||
|
o |
||
|
.^_y |
f- |
|
|
CO |
< 2: |
|
|
cc |
Q |
|
|
cn |
Z |
|
|
o |
UJ |
<. |
|
Ln |
>- |
LU |
|
o^ |
»— <■ |
1— 1 |
|
"-• |
-J |
|
|
LU |
§ |
|
|
21 |
< |
|
|
1 — 1 |
C3 |
«yo
I
LlI
00
LU
UJ OH
o
UJ
>
I— I
I— <i: _J 3>
o
CM CD
J L
o
OD
cn
o
o
CD
cn
I ' « I ' ' ' ' ' ' ' ' i ^
cn
00
z:
LU
3=
|
2: |
||
|
CO |
||
|
cc |
< |
|
|
CE |
s: |
|
|
o |
ii 1 |
|
|
ID |
)— |
oi |
|
cn |
V— ^ |
|
|
'-' |
o |
|
|
UJ |
s: |
|
|
s: |
CSJ |
|
|
•— 4 |
||
|
f— |
||
|
■ |
3 |
|
|
o |
||
|
=r |
||
|
Ol |
<" |
|
|
•— • |
1 LU 00 OO LU O LU |
|
|
• |
OC |
|
|
o |
LU |
|
|
ro |
Ll. |
|
|
CD |
•—4 |
|
|
LU > |
o
o
o cn
I
O
CM <U
s-
(139d] U1-3S 'Jdia 3Aiiuinwn3
79
' ' ' '
1 > t I I I I
I 1 1 I I 1 I
I I » I
o
o
CO
o rvi
a
o
CD CD
O
cn
o
CD
en
o en
o
o
(M
I
(Jl
az
CE LU
m
o o.
o
LlI
C3
a: o
o
< I—
Q
CO
|
o |
' |
|
zr |
|
|
en |
< |
|
.-* |
^ |
|
1 |
|
|
Ul |
|
|
CO |
|
|
oo |
|
|
LU |
|
|
O |
|
|
z |
|
|
LU |
|
|
• |
oe: |
|
o |
UJ |
|
fn |
Ll. |
|
07 |
LL. |
|
»-H |
I-H o |
CM
u
(133^) U1-3S "ddlQ 3AIlbinwn3
80
i I I , I I I I I I I i I I I I , I I t ,1 t
C/1
O a.
•a: I—
<c o
o
a: o
^ S
on cr
LU
LU •—I
_J
<: o ca: e3
I
LU
LU O
LU
q:
LU
o in
CM
o o
CM
o in
o o
o
LD
|
• |
ZD |
|
o |
t_> |
|
ru |
|
|
OJ |
OD |
|
•— « |
CM |
|
<u |
|
|
i- |
|
|
3 |
|
|
O) |
(I33zlj U1-3S 'Jdia 3AIiUinwn3
81
o
-1 CD
cn
J L
I I > 1 I t t I I I I I I
o o
in
o in
in
(133d) U1-3S 'dJia 3AIlU3nwn3
82
o
CD
o
CD
cn
to
o
o
I— to
Ixl
CJ
|
T— t |
o 1— |
|
|
• — ' |
Q |
|
|
CO |
z: |
|
|
£!1 |
«sc |
|
|
CT |
• |
|
|
o |
LU |
|
|
LO |
>— |
q: |
|
cn |
■v^ |
|
|
«— « |
• o |
|
|
UJ |
s: |
|
|
21 |
CSJ |
|
|
t— i |
CO |
|
|
\— |
1— 1 |
CO
CO LU CJ
LiJ
O
CVJ (U
t3»
a
-. OD
I 1 ( I 1 I I 1 } I t 1 I I 1 I I I I I I 1
to
o I/)
in
CM
O
in
I
LP I
[122A) U1-3S lid iS3a yod'iS3y
83
o -I r-
i CD
4 .
cn
i
I I I 1 I
o
o m cn
o cn
I
CO 01 CE UJ
LU
Q
CD
oo
CTi
CTi
o
I
UJ
o
UJ
>
UJ
CQ
UJ UJ
a:
UJ
a
o
z: o
UJ
cC
q: o u.
CO
_j •a:
=3
a i—t «/>
UJ
o
CO
s- cn
1
o
LO
(D
r\j
(I33zl} U1-3S ilJ iS3G y0d'IS3y
84
-i ^
en
o en
1
f LO
m en
I
CO
g:
LU
CO
CTi
o
_] I
LU
tn o
Ll- UJ
>
Od
ID O
|
oo |
|
|
■ |
LU |
|
o |
ca |
|
en |
|
|
en |
LU LU |
|
•— 1 |
q: |
|
o |
|
|
LU |
|
|
a |
|
|
1— |
|
|
oo |
|
|
q; |
|
|
t— < |
|
|
Li. |
|
|
LO |
<: |
|
CM en |
o |
|
.— • |
LL. |
|
to |
|
|
_j |
|
|
<c |
|
|
Q |
|
|
1— 1 |
|
|
CO |
|
|
LU |
|
|
• |
£ae: |
|
o |
|
|
OJ |
^ |
|
en |
CO |
|
«.^ |
|
|
0) |
|
|
S- |
|
|
3 |
|
|
CD |
e-B=^-^
I I I 1 I 1
■ ' ' I L
,1111
CO
Oil
o
I
|
o |
|||
|
en |
|||
|
« — ( |
|||
|
^ |
|||
|
1 |
|||
|
- |
■ in |
CD •— 1 |
|
|
)_ |
OD |
CO |
|
|
CD |
«««,x |
||
|
- |
IT) t CO St |
||
|
q:: |
|||
|
o |
|||
|
, |
Lo- |
||
|
O |
se |
||
|
« |
U3 |
—1 |
|
|
CD |
^ |
1 |
|
|
U) |
UJ |
||
|
cc |
LO |
||
|
CL |
o |
||
|
UJ |
u. |
||
|
>- |
UJ |
||
|
> , |
> |
||
|
LU |
o |
||
|
■ |
s: |
1— l-H |
|
|
LO |
1— 1 |
U- |
|
|
LP CD |
H- |
||
|
•—1 |
UJ |
||
|
CO UJ UJ |
|||
|
Ol |
|||
|
I |
o |
||
|
UJ |
|||
|
- |
|||
|
oo |
|||
|
- |
Oi |
||
|
• |
1— 1 |
||
|
O |
U- |
||
|
J in en |
«a: |
||
|
—• |
d; |
||
|
™ |
o U- |
||
|
CO UJ |
|||
|
- |
oc: |
||
|
LD |
CvJ |
||
|
CO |
|||
|
CD |
|||
|
. .— • |
<u |
||
|
C\J |
$- 3 |
||
|
1 |
cn |
(i33J)
bl-3S ilJ iS39 U03-IS3y
85
CM
|
-1 |
en ^ — 1 |
||
|
o |
|||
|
• |
z: |
||
|
i ^ |
1— 1 |
||
|
-d r~ |
oo |
||
|
en |
ZD |
||
|
T— t |
cr> CD |
||
|
CD cn o |
|||
|
• |
u. |
||
|
C\J r- |
, |
—1 1 |
|
|
^ |
Ul |
UJ |
|
|
cc |
cn |
||
|
en |
a: |
||
|
LJ |
o Ll_ |
||
|
)^ |
UJ |
||
|
> on |
|||
|
LU |
CJ |
||
|
o |
21 |
I— t— < |
|
|
cn |
h- |
h- |
|
|
UJ |
|||
|
CQ Ul UJ on |
|||
|
<3 Ul o |
|||
|
■ |
1— 1 |
||
|
00 |
u. |
||
|
^ |
. CD |
||
|
CD |
<a: |
||
|
on o U- </> -J |
|||
|
C to Ui |
|||
|
a: |
|||
|
ICD f 1 ,n |
CO CO |
||
|
CD |
|||
|
• .—1 |
(U |
||
|
1 |
s- 3 |
||
|
a> |
(i33J) B1-3S ilJ iS3a yo3-is3y
86
o in
o
o
o
o
o I
(i53d) 33-dS
ddlQ 3AIldinwn3
87
u^
O
O-
o
a:
C5
|
in |
it: |
|
|
CD |
CJ |
|
|
cn |
• '"- |
1— |
|
Ul |
«a; |
|
|
cn |
2: |
|
|
cc |
o |
|
|
LU |
< |
|
|
>— |
00 |
|
|
LlI )— 1 _l |
||
|
LU |
s: |
|
|
■ |
51 |
o 7=* |
|
o |
1 t |
cC |
|
rn |
||
|
CD |
^— |
C3 |
to
o
I/?
Ul LU
a:
LtJ
o
CO
Qi
s-
3
cn
I t > I
±.J I I I I I L..J I i I I I I L
o o
CM
O
in
o o
o in
J L
(i33d) Ul-dS 'ddlQ 3Aiiuinwn3
88
o
CD
en
o r- cn
s
I o
CD CD
-1
J
O 07
-
O
en
o m
;2
o
in
I
cc
CE
LU
00
o o.
o
I/)
nr o J— <: s:
o
2: ex.
oo
LU t— I
-J <
o
z: ■=C
2: »— I oo
Z3
"^
_J
I
U-
oo oo
LU
;z
LU
ct:
LU Ll.
u_
►—I Q
LU
|
0 |
ID 0 |
|
CD •— 1 |
m en |
|
S- C71 |
or
P'd ! ! !
. .° O.
e
::.§.:
.;;§
.0
t I
i '
e®
a
:§■;
7^
■ ■ ' '0>> ■•■••• Q
. . . ■ Q. .
J > ■ I iQ .
:^
: o^ :
' ' ]^'0
. . .6' I i
■ 1 I r I I
• I I I '
J I
> -1 ■! I i
4
I
<
::^
<j
<}
:^:^
4-
'i
^
<
m
i^i
^
^
-«
^
I-
'it
■■f
it
T ' ■
i
: .-++.
1 . 4- 1^1
|
o o o |
o o o LO O LD r^ ID C\J |
o o o |
o o o |
CD CD CD \T> CD in r- LO CM |
o o o |
|
|
• |
o o o i33i |
o |
89 |
w—4 |
o o o i33d |
o |
LO CD
O LO CD
LO ZT CD
IT
ZT
in
en
I
on
o
oo
|
UJ |
|
|
oo |
CD z: |
|
rr |
< |
|
O) |
oo |
|
•-H |
o |
00
|
r- |
|
|
ZT en |
o o oo |
|
•— 1 |
*— 1 |
|
o |
|
|
z: |
|
|
•=C |
|
|
q: |
|
|
u. |
|
|
^r» |
|
|
CO |
cC |
|
rr |
OO |
|
OT |
d: |
|
o |
UJ
-J <c
UJ
oo
>-
UJ
CO
-e
...|...!....i... j.,..i....i...4^^..|. ;...|...K. .;.4...|....i....i..
1^..
Q
ttrxtgb-;
•iO
...........
0
e
^i
■i-!-l"f0:
;.^
4+4H- ■+■«■;
:;!:::i±::!::±r%:
BSM:
..i....j....i..4...i....i....j....j....i..
■r-Q
..................................
..j._.i....i....i....i....j.„.|...^....;.. ..j...j....i....j.-.i....j....|....Q .
^„i....i...^....i...4...^..
■••i-O
••i--i-i-l-!"0i:-l- ..i....i....i....i...j..?rcli..i..
:t:i::i::.i::;&
±J§:;
-i,.0-
e
mi
•■i-i-f©'i-r-i-i"
..J....1....1....1....1....1..
..;....j._.;....j...j....i....|....i..
...j...^...^.».i....p.
'i'**T"T"T"T*"!""i""i"
|....,....,....|....I....,....,....,....,....j....l....l..
-!••■■!•■•!•■
i j »
..4_j...i •••i-i-i
iti
ra
.H....^€>::;:: ri::fc>;-:
••••••i-i-i0^--
..i..+.j„...:H...Q +™i..+...i....i0...
^...j....|.„^.. ..;....,....
' fi-t-ie !-rii
..J....i...y..y..^.,..J..
O'
••i--h"T-!-t-i-T'
■l-f-t-i- ■••!••■■!■• .....„,,...,....,....(.........,..
I ■ r T
;;!::;iiac:;:;!::
•<}■■
^
rt
■■i-i<l
:ti:::i:::H::::|:;:4i::i:;
L-^-
i
i-4.
N-
•■|-!-!-i«
«
f
■H^J
.^....,....;...,....,....,.........^q..|...
..j„.,....;....j....j....j....,....j..j^
•i-t"!-l-l:j--l-:<l
•l-r-H-j-f-i-i-
..l...J....;....l.^....I....l...J...
■1— j'-i-i—! ■• j^i-j-
•r-fr-! -0 fr-r
i....i.i..i..^ i....i....i....i....i..
i<l
<
..;....,....J^..^|....,....|
H'
M^
i I....l...+...i...
..j...<..
■t-i"t-t"t-!- <;•!•••■!■■
..!..,. !....».... I. ...|....1....9^l<--l-
i ^ ' i - = ■ • :
i::!::t:;:ft;:j:|:::!;:
|- • ■■!■ ■!■;•■•+•:•■•■!■■
- +
,...,.. ..,....,,..,|.......
...;..,.. ■.,.., li, , , , , ,4;'.i....;....i....;,.
..;....;...;. :....vo.„
-i-t4i-
tt
tl
.]....)....!....
:tt;+i-
■I....l....l....l..
4
^
J....I... J.. ..!....;. ...I..
...^....,....,„.^....;....,....,....,..
■!■•••!■•••!••••!—!••••!■•••!••
.j....j.„.i....j....i....i....j..
..I....i..„l....i....i....i....l....i....l..
■i-l-r-»-!
..,....,....,....,..,.]..
..(.... I. ...I»-I'»>l>.
■*
i
; !.l: ! i
m
+,
n
::;:::m:ft:
r-T-i-"-i-r-"—!—i"
!■+
]#:;
•i-ffi-
:!:;tt
!4^^
lis
:tj:;ft
tt
ttttti:
■l-H-i-
|
o o o |
o o o in o LP r- LD CM |
o o o |
|
•-H |
o o o 133d |
o |
o o o o o
O LD O LD O
o r- LO c\j o
-^ o o o o i33d
90
CD CD
CO CD CD
CO CD CD
•51-
I
-J
I
U-
00
Q
|
oo |
|
|
— « |
|
|
CD |
LU |
|
CD |
|
|
-^ |
•sC |
|
t/1 |
|
|
o |
|
|
-J |
|
|
M |
|
|
O |
LL. |
|
CD |
00 |
|
O) |
|
|
, |
o |
|
c_> |
|
|
00 |
|
|
t— 1 |
|
|
o |
|
|
:z. |
|
|
CD |
U- |
|
LD |
z: |
|
O) |
<: |
|
«-H |
oo |
|
cc: |
|
|
o |
|
|
Ui. |
|
|
_j |
|
|
LU |
|
|
CD |
>■ |
|
LO |
UJ —J |
|
CD |
|
|
»-H |
•a: |
|
oo |
|
|
>- |
|
|
_i |
|
|
zn. |
|
|
1— |
|
|
r- |
•z. |
|
LD |
o |
|
CD |
|
|
•ZL |
|
|
«~^ |
< |
|
UJ |
|
|
SL |
|
|
• 1^ |
|
|
CO |
|
|
<u |
|
|
s. |
|
|
3 |
|
|
o> |
J \ L
J L
J I L
J— J L— J L
o
CD
O
o
(i33d) 33-U1 'ddlG 3AIibinwn3
91
m
4
1
m
CD
en
CD
cn
in in cn
a
IT)
cn
o
I
CO GC CE LU
LU
I—
o
I— <
Q
H- I/)
or I—
cs
31
C_3
I—
<a:
s: o
<c
s:
o
CvJ CD
z:
1/1
o I
00 LU O
LU
O
LU
>
I—
CO
cn
<u
s-
3
|
o |
|
|
CD |
|
|
cn |
|
|
C/1 |
|
|
\— |
|
|
■21 |
|
|
>— 1 |
|
|
o |
|
|
o. |
|
|
<t |
|
|
1— |
|
|
• |
<x. |
|
oo |
o |
|
in |
|
|
CD |
h- |
|
t/l |
|
|
cc |
(S!
|
CD LO cr> |
■z. 1—1 a: o o |
|
|
CO |
s: |
|
|
cn .-H |
a: CE |
cL |
|
LlJ >- |
o |
|
|
*~^ |
CM |
|
|
in CD |
UJ 1 — 1 |
O ■Z. I-H 1 > |
|
o LD on |
UJ o |
q;
CO
CD
C7>
(i33d) N9-AU 'jjiQ 3Aiiy~inwn3
92
CO
o
CD 00
LU
O
UJ
o
■a:
o
_j
LlI
cc o o
o
cu
s-
13
en
|
m |
C\i |
|
• |
• |
|
0 |
0 |
o o
o I
i\cii3Nrj Noiiui3yyo3cinu
93
01
z:
o
CD CE
LU
CO
o
3*
OJ
■
o
CD
o
rvi
o
I
LU
_i
•a; o
o o
CO
I— I
<
Lu
C/)
a: o
Lu
cc ca o
-J
1x1
a: oc o o
s-
C7)
NDIlGNnd N0IlU13yyD30inu
94
iT)
O
CT
UJ
CO
o
CO
o
o
o
o o
■
a I
LxJ
O
o o o
CO
a: o
LU
O
o:: on o
CSJ
(U
s.
NOIlDNnj N0IiU13yU030inu
95
z:
o
UJ
CD O
CD
■
3*
■
O
o
o o
o I
LU t— I
_i
s: o
o
UJ
—I
LU
(/I
o
o
o o
_j
UJ
cc o
CD
NOiiDNnj Noiiui3yyo30inu
96
CO
o
CD CE
UJ
UJ
I— (
_1
O
00 I
t/O
O
o
LU
q:
o o
m o
o
■
o
NCIiONfld N0IiU13yy03DinU
97
en
o
CD d
|
C\J |
|||||
|
CO |
CD |
ZT |
C\J |
o |
. |
|
• |
> |
• |
• |
• |
o |
|
o |
a |
a |
o |
o |
1 |
LlJ
<: o
ct: o
C3 O _J LlJ OC
a: o
in
(U
CT!
NDIlGNnd NQIlU"13yy03Di.nU
98
APPENDIX A-1
PROGRAM USED TC PERFORM SPECTRAL ANALYSIS
SUBROUTINE PREPFA( M, MS ,DT , YYY, Fl , PERI OD, FREQUE,NF ) C C
C MEANING OF THE PARAMETERS
C C
C MdNPUT) IS THE INTEGER POWER OF 2 ON THE EXPRESSION
C 2*2**M
C MS(INPUT) IS THE NUMBER OF WINDOWS (ONE HALF OF THE
C NUMBER OF DEGREES OF FREEDOM)
C DT(INPUT) IS THE X-INTERVAL BETWEEN DATA POINTS
C YYY( INPUT) IS THE ARRAY TO BE ANALISED
C Fi (OUTPUT) IS THE ARRAY CONTAINING THE ENERGY VALUES
C PERIOD AND FREQUE ( OUTPUTS ) ARE THE ARRAYS CONTAIMING
C THE VALUES OF THE PERIODS AND FREQUENCI ES, RESPECT I VELY
C NF(OUTPUT) IS THE NUMBER OF FREQUENCIES TO BE ANALISED
C PLUS ONE
C C
DIMENSION YYY (1250), I NV(12 50) , S(I250) , FIS (1250) ,C( 1250 1),F1(1250) DIMENSION ART (1250), PERIOD (600), FREQUE (6C0) 240 FORMATCl',' POWER SPECTRUM IS CALCULATED •,/ • TOTAL NU ♦MBER OF SAMPLES=' ,T5,/1X,»THE TIME INCREMENT =',F5.3,/ *1X,«THE NtMBER OF DEGREES CF FREEDOM FOR EACH SPECTRAL * ESTIMATE =• ,15,///) 250 FORMAT(«0S 'STATISTICS OF SAMPLE NUMBER =SI4) 260 FORMAT ( 'C, 'MEAN VALUE =• , F12.3, 3X, • VARI ANCE =«,F12.3, *3X,'SKEWNESS =• ,F12. 3 ,3X, • KURTOS IS =• , F8 .3,3X , 'STD DEV
99
♦lATION =• ,F12.3)
270 F0RMAT(«0«,T10,F12.3,T25,F12.3,T40,F12.3) NM=2*2**M NM1=NM-1 N=NM*MS NF=2**M+1 NFREDM=MS*2 T=NM*OT
WRITE(6,240) N, DT, NFREDM DO 510 1=1, NF 510 F1(I)=0. IZ=0 K=0
CO 21 127=1, N ART(I27)=YYY(I27)
21 CONTINUE
CALL AVER/i(ART,N,AMEAN) DO 22 128=1, N C(I28)=ART(I28)-A^iEAN
22 CONTINUE
DO 520 MI=1,MS
K=K+1
DO 530 JJ=1,NM
IZ=IZ+1 530 F1S(JJ)=C(IZ)
WRITE (6,250) K
CALL TREND(F1S,NM,DT,U11,U21,U31,U41,URMS1)
CALL SPEC(F1S,M,INV,S,IFERR}
WRITE (6,260) Ul 1 , U2 1 , U31 , U41 ,URMS1
00 540 1=1, NF 540 F1(I)=F1S(I)+F1(I) 520 CONTINUE
DO 550 1 = 1, NF
F1(I)=F1(1)*T/(2.*MS)
100
IFd.EQ.DGC TO 23 PERI0D(I)=FL0AT(NM)/FL0AT(I-1) FREQUE( I)=1.0/PERI00(I) GO TO 24
23 PERIOD(I)=FLOAT(NM) FREQUE(I)*0.0
24 V»RITE(6,270)F1(I) , PERI GD ( I ) , FREQUE { I ) 550 CONTIMUE
CALL PL0TG(FREQUE,F1,NF, 1,1, I, 'FREQUENCY IN CYCLES PER * MONTH* ,29, •
IPOWER DENSITY FUNCT ION ( FEET SQ .MONTH) •, 37, 0 . 0, 0.0, 0.0, *G.0,7.5,5.0)
CALL PLOKO. 0,0.0, +999)
RETURN
END
101
APPENDIX A-2
PROGRAM USED TO PERFORM LEAST SQUARES BEST FIT
SUBROUTINE LEASTSC LLFIN, XX, YY, TREND, ERREST, ERRTRE ) C
c
C WEANING CF THE PARAMETERS
C
C
C LLFIN( INPUT) IS THE NUMBER OF DATA POINTS
C XX AND YYdNPUT) ARE THE ARRAYS CONTAINING THE X AND Y
C VALUES OF THE DATACY VALUES ASSUMED IN FEET)
C TRENO(OUTPUT) IS THE SLOPE OF THE REGRESSION LIN IN MM
C PER YEAR
C ERREST(OUTPUT) IS THE STANCARO ERROR OF THE ESTIMATE
C IN MM
C £RRTRE(OUTPUT) IS THE STANDARD ERROR OF THE TREND IN
C MM PER YEAR
C
C
DIMENSION XX(999),YY(999)
DOUBLE PRECISION SUMMX, SUMMY, SUKMXX, SUMMYY ,SUMMXY , TREN *D, ERREST, ERRTRE 210 FORMAT CO*) 220 FORMAT( 1X,3D24,15/)
C0NST1=3657.6
CONST2=30A.8
SUMMX=0.0D0
SUMMY=0.0D0
SUMMXX=0.0D0
SUMMYY=0.0C0
SUMMXY=0.0D0
00 10 LS = 1, LLFIN
102
SUMMX=SLNMX+XX(LS)
SUMMY=SUMMY+YY(LS)
SUMMXX=SLN',MXX+XX( LS) **2
SUMMYY = SlJMMYY+YY( LS ) **2
SUMMXY=S(jMMXY+XX(LS)*YY(LS) 10 CONTINUE
TREND=(SUMMXY-SUMMX*SUMMY/FLOAT(LLFIN) ) / ( SUMMXX-( SUMMX ***2)/FL0AT(LLFIN))
ERREST=DSQRT( {SUMMYY-SUMMY**2/FL0AT( LL FIN)-TREND*( SUMM *XY-SUMMX«SUMMY/FLOAT( LLFIN)) ) /FLOAT( LLFIN-2 ) ) ERRTRE=ERREST/DSQRT(SUMMXX-SUMMX*«2/FL0AT(LLFIN)» TREND=TRENC*C0NST1 ERREST=ERREST*C0NST2 ERRTRE=ERRTRE*C0NST1 KRITE(6,220)TREND,ERREST,ERRTRE WRITE(6,210) RETURN END
103
APPENDIX A-3
PROGRAMS USED TO PERFORM FILTERING ACTION
SUBROUTINE RMEANl (NPER, LCOM,LF IM,DXREDT, OYREOT,NDI i,X, *Y»XB,YB,LCATA) C C
C MEANING CF THE PARAMETERS C C
C NPER(INPUT) IS THE NUMBER OF PERIODS CF CONTINUOUS DA- C TACMORE THAN 12 POINTS) WITHOUT MISSING VALUES TO BE C ANALISED
C LCCM AND LFIM(INPUT) ARE THE ARRAYS CONTAINING THE IN- C FORMATION CF THE BEGINING AND ENDING POINTS OF EACH C PERIOD
C DXRECT AND DYREOT( INPUT) ARE THE ARRAYS CONTAINING THE C X AND Y VALUES TO BE FILTERED
C NDIM(INPUT) IS THE DIMENSION THAT SHOULD BE GIVEN TO C DXREOT AND DYREOT
C X AND Y( INPUT) ARE DUMMY ARRAYS FOR SCALING PURPOSES C IF SOME PLOT IS INTENDED TO BE DONE WITH THE OUTPUT C ARRAYS
C XB AND YB(CUTPUT)ARE THE ARRAYS CONTAINING THE X AMD Y C VALUES ALREADY FILTERED
C LDAT(OUTPLT) IS THE NUMBER OF DATA POINTS CONTAINED IN C THE CUTPLT ARRAYS C C
DIMENSION X(4),Y(4)
DIMENSION LC0M(20) ,LFIM( 20)
DIMENSION DXREOT { NO I M ), DYREOT (NO I M),XA( 1000) ,YA(1000)
104
OIMENSICN XB(IOOO) ,YB(1000)
LCOUNT^l
DO 62 L=1,NPER
LBEG=LCC^(L)
LSTOP=LFIM(L)
LEND=LBEG+11
SUM=0.0
DO 60 L1=LBEG,LEN0 SUM=SUN+0YRE0T(L1)
60 CONTINUE N0ATA=LST0P-LBEG-10 00 61 L2=1,NDATA
YA(L2)=SUM/12.0
XA(L2) = DXRE0T(LBEG)-^4.5+FL0AT(L2) YB(LC0UNT)=YA(L2) XB{LCCUMI=XA(L2) LC0UNT=LCCUNT+1
SUM=SUM-DYRE0T(LBEG-1+L2)+DYRE0T(LBEG+11+L2)
61 CONTINUE
62 CONTINUE LDATA=LCCUNT-1 XB(LDATA+1)=X(3) XB(LDATA+2)=X(4) YB(LDATA+1)-Y(3) YB(LDATA+2)=Y(4) RETURN
END
105
SUBROUTINE ANOMAL( NY ,NMO, YYY, WWW ) C C
C MEANING CF THE PARAMETERS C C
C NY(INPUT) IS THE NUMBER OF YEARS OF DATA C NMO(INPUT) IS THE NUMBER OF MONTHS OF DATA C YYY( INPUT) IS THE ARRAY VALUES TO BE FILTERED C WWW(OUTPUT) S THE ^RRAY VALUES AFTER BEING FILTERED C
c
DIMENSION YYY (1250) , YYU 12 50) , WWW( 1250 ) DIMENSION ARRTRA(12) 210 F0RMAT(1X,F12.3) 220 FORMAT(«0S3F12.3) CO 05 1 = 1, NMC YYl(I)=yYY(I) 05 CONTINUE
CALL TREND(YY1,NM0,1.0,U11,U21,U31,U41,URMS1)
DO 20 11=1,12 ARRTRA(I1)=0.0
J = I1 DO 10 1 2=1, NY
ARRTRA(I1)=ARRTRA(I1)+YY1(J)
J=J+12
10 CONTINUE
ARRTRA( I1)=ARRTRA( ID /FLOAT(NY) WRITE(6,210)ARRTRA(I1) 20 CONTINUE
CO 30 13=1, NMO MM=M00(I3,12) IF{MM.EQ.C)MM=12 WWW(I3)=YYY(I3)-ARRTRA(MM)
106
30 CONTIMUE RETURN END
107
APPENDIX A-4
PROGRAM LSEC TO PERFORM CUMULATIVE ANALYSIS
SUBROUTINE CUMMUL( NY , YEAR IN) C C
C MEANING OF THE PARAMETERS C
c
C NY(INPUT) IS THE NUMBER OF YEARS OF MEAN MONTHLY
C VALUES TO BE ANALISED
C YEARIN(INPUT) IS THE FIRST YEAR OF DATA
C
C
DIMENSION X(4),Y(4)
DIMENSION XNB(IOOO) ,XAS(IOOO)
DIMENSION YNB(IOOO) ,YAS(1000)
DIMENSION DYNBASdOOO) , DXNBAS ( 1000 )
DIMENSION CUMCIOOO)
DIMENSION WNB(IOOO) tWAS(lOOO) 201 F0RMAT(«0«t3F10.2)
NM0=NY*12
CALL PAGE
CALL REACCT(NY,X,Y,YNB,XNB,NP)
CALL READCT(NY,X,Y,YAS,XAS,NP)
DO 05 1=1, NMO
WNB(I) -YNB(I)
WAS(I)=YAS(I) 05 CONTINUE
DO 30 III=lf3
CALL AVERA(YNBtNP,AMEANl)
CALL AV£RA(YAS,NP,AMEAN2)
108
DIFF=AMEAN1-AMEAN2 OR D IFF=YNB ( 1 )-YAS ( 1 )
WRITE(6,201)AMEAN1,AMEAN2,DIFF
CO 10 1=1, NMO YAS(n=:YAS(I)+DIFF 10 CONTINUE
CALL DIFFER(0,NMO,YNB,YAS,X,Y,DYNBAS,DXNBAS,ND)
DELTAT=1./12.
CUM(li=DYNeAS(l)
IF(III.EQ.3)YEARIN=YEARIN+0.5
XAS( D^YEARIN
DO 20 1=2, NMO CUM(I)=DYNBAS(I)+CUM{I-I) XAS^ I ) =XAS( I-1)+DELTAT 20 CONTINUE
CALL PLOTG(XAS,CUM,NMG, 1,1,1, 'TIME ( YEARS )», 12, 'CUMMUL ISM-SD (FEET) ',30, 0.0, 0,0, 0.0, 0.0, 7. 5, 5.0)
IF(III.EG.2)G0 TO 77
IF(III.EQ.3)G0 TO 30
CALL ANOMAL(NY,NMG,YNB,YNB)
CALL ANCNAL(NY,NMO,YAS,YAS)
GO TO 30 77 CALL RMEAM(01,01,NM0,XNB,WNB,10C0,X,Y,XNB,YNB,NP)
CALL RMEAN1(01,01,NMO,XNB,WAS,1000,X,Y,XAS,YAS,NP)
NMO=NP 30 CONTINUE
CALL PLOT(0. 0,0.0, +999)
RETURN
END
109
APPENDIX A-5
CTHER SUBROUTINES CALLED
SUBROUTINE /SVERA (A,NPTS, AMEAN) C C
C MEANING CF THE PARAMETERS
C
c
C A( INPUT) IS THE ARRAY OF Y VALUES TO BE AVERAGED
C NPTS(INPUT) IS THE NUMBER OF DATA POINTS OF A
C AMEAN(OUTPUT) IS THE AVERAGE OF THE Y VALUES OF THE
C INPUT ARRAY
C
C
DIMENSION A(NPTS)
SUM=0.0
CO 100 I=1,NPTS
SUM=SUM+A(I) 100 CONTINUE
AMEAN=SUM/FLOAT(NPTS)
RETURN
END
110
SUBROUTINE TREND( FX ,NTS, DT,FMEAN ,U2, U3 t U4,URM S) C
C SUBROUTINE TREND EDITS ,CAL IBRATES AND DETRENDS DATA
C
c
C MEANING CF THE PARAMETERS
C
c
C FX(INPUT) IS THE ARRAY OF Y VALUES, (OUTPUT) IS THE DE-
C TRENDED ARRAY OF Y VALUES
C NTS( INPUT) IS THE NUMBER OF DATA POINTS
C DT(INPUT) IS THE X-INTERVAL BETWEEN DATA POINTS
C FMEAN,U2»U3,U4,AND URMSC OUTPUTS) ARE THE MEAN, VAR lANCE
C SKEWNESS,KURTOSIS AND STANCARD DEVIATION OF THE INPUT
C
c
DIMENSION FX(NTS) C EDITING CATA
C C
FNTS=NTS C COMPUTING THE LINEAR TREND
SUMF=0.0
DO 101 1=1, NTS
101 SUMF=SUMF+FX{I) SUMF1=0.0
CO 102 1=1, NTS XI = I
102 SUMF1=SUMF1 + XI*FX{ I)
XNM1=NTS-1
XNP1=NTS+1 XM=(1.0/CT)«(12.0*SUMF1/(FNTS*XNM1*XNP1)-6,0*SUMF/(XNM
*1*FNTS)) B=SUMF/FNTS-XM*XNPl*DT/2.0
111
FMEAN=SUMF/FNTS
WRITE (6,9) FMEAN,XM,B 9 FORMATOX, 'MEAN-S F 10 .5, 3X, • SLOPE = • , FIO .5, 3X, • I NTERC
*EPT =• .F10.5,//)
DO 103 1 = 1, NTS
XI = I 103 FX(I)=FX(I)-(B+XM*XI*DT)
C SUBROUTINE FOR CALCULATING VARIANCE, STO DEV, SKEWNESS C *, KURTOSIS
U2==0.0
L 3=0.0
L4=0.0
SUMU2=0.0
SUMU 3=0.0
SUMU4=0.0
00 151 1=1, NTS
U2=FX(1)*FX(I)
U3=U2*FX(I)
U4=U3*FX(I)
SUMU2=SUML2+U2
SUMU3=SUMU3+U3
SUMU4=SUMU4+U4 151 CONTINUE
FNTS=NTS
L2=SUMU2/FNTS
URMS=SQRT(U2)
t3=SUMU3/(FNTS*U2*URMS)
L4=SUMU4/(FNTS*U2*U2)
RETURN
END
112
SUBROUTINE SPEC ( Fl, M, INV, S, IFERR) C
C SUBROUTINE TO CALCULATE THE POWER SPECTRUM OF A SIGNAL
C *USING RHfiBt*,
C C
C MEANING OF THE PARAMETERS
C C
C FKINPUT) IS THE DETRENDED ARRAY OF Y VALUES. A MODIFI-
C ED ARRAY APPEARS AT THE OUTPUT
C M( INPUT) IS THE INTEGER POWER OF 2 OF THE EXPRESSION
C 2*2**M
C INV(ARRAY) ,S(ARRAY) ,AND I FERR (OUTPUTS ) ARE OUTPUTS OF
C SUBROUTINE RHARM
C C
DIMENSION INV(515),S(515) ,Fl(515)
CALL RHAPM(F1,M,INV,S,IFERR)
NP=2*«M-1
NF=2**M+1
NM=2*2«*M
NL=NM+1
F1(1)=F1(1)*F1(1)
CO 500 I=1»NP
J= 2*1+1
L=I + 1
XR=F1{ J)*F1(J)
XI=F1(J+1)*F1(J+1)
F1(LJ=XR+XI 500 CONTINUE
F1(NF)=F1(NL)**2
RETURN
END
113
SUBROUTINE READOT ( MUMYEA, X, Y, YNB, XNB, NP ) C C
C THIS SUBRCLTINE READS AND PRINTS THE DATA
C C
C MEANING CF THE PARAMETERS
C C
C KUMYEA(INPUT) IS THE NUMBER OF YEARS OF DATA TO READ
C X AND Y( INPUT) ARE DUMMY ARRAYS FOR SCALING PURPOSES
C IF SOME PLOT IS INTENDED TC BE DONE WITG TflE OUTPUT
C ARRAYS
C YNB AND XNE(OUTPUT) ARE THE ARRAYS CONTAINING THE DATA
C VALUES AND THE GENERATED ABSCI SSAS, RESPECTIVELY
C NP(OUTPUT) IS THE NUMBER OF DATA POINTS
C C
DIMENSION X(4),Y(4)
DIMENSION YNB (1250) , XNB (1250), I YEAR (105) 100 FORMAT(A4,7X,I4,12F5.2) 200 F0RMAT(1X,A8,2X,I4,I2F5.2J 210 FORMAT COM
ISTART=1
I£ND=12
DO 10 I1=1,NUMYEA READ (5, 100) NAME, I YEAR (ID ,(YNB( INB) , I NB= I START, I END)
WRITE(6,200)NAME,IYEAR(I1) ,(YNB( INB) , INB=ISTART, I END)
ISTART=ISTART+12
IEND=IEND*12 10 CONTINUE
NP=:IEN0-12
NUMM0N=NUMYEA*12
114
DO 20 I2=1,NUMM0N XNB(I2)=FL0AT(I2I 20 CONTINUE
XNB(NP-»-l) = X(3)
XNB(NP+2J=X(4)
YNB(NP+1)-Y(3)
YNB{NP+2)=Y(4)
WRITE(6«210)
RETURN
END
115
SUBROUTINE CIFFER ( I DELAY , I COM , YNB» YAS, X , Y , DYNEAS, OXNBA C C
C THIS SUBROUTINE PERFORMS DIFFERENCES BETWEEN TWO DATA
C SETS, PRINTING THE RESULTS C
c
C MEANING OF THE PARAMETERS C
c
C IDELAYdNPUT) IS THE NUMBER OF MONTHS OF DELAY BETWEEN
C THE FIRST AND SECOND TIME SERIES ( POSI T IVE IF THE SEC-
C CIMD TIME SERIES BEGINS EARLIER THAN THE FIRST ONE)
C ICOMdNPUTJ IS THE NUMBER OF COMMON MONTHS TO BE
C SUBTRACTED
C X AND Y( INPUT) ARE DUMMY ARRAYS FOR SCALING PURPOSES
C IF SOME PLOT IS INTENDED TO BE DONE WITH THE OUTPUT
C ARRAYS
C YNB AND Y/S( INPUT) ARE THE ARRAYS CONTAINING THE DATA
C POINTS TC BE SUBTRACTED
C OYNBAS AND DXNBAS ( OUTPUT) ARE THE ARRAYS CONTAINING
C THE RESULTS FROM THE DIFFERENCE COMPUTATION AND THE
C COMMON ABSCISSAS, RESPECTIVELY
C ND(OUTPUT) IS THE NUMBER OF DATA POINTS CONTAINED IN
C THE OUTPUT ARRAYS DYNBAS AND DXNBAS
C NCTE-THIS PROGRAM ASSUMES THAT THE MISSING VALUES OF
C THE CATA ARE REPRESENTED BY 99.9 OR 00.0. IF
C SOME MISSING VALUES OCCUR, ND WILL BE LESS THAN
C ICCf'
C
C
CIMENSION YNB(I250), YAS(1250)
DIMENSION DXNBAS{999) ,DYNBAS(999)
116
DIMENSION X(4),Y(4) 210 FORMAT CO') 220 F0RMAT(1X,2F6.2, 110) NN-1
lNIC=(IABS(IDELAY)-IDELAY)/2^-l A6C=FL0AT(INIC) IST0P=INIC-1+IC0M DO 20 JN80=INIC,ISTOP
JNBA=JNBO+IDELAY
IF{YNB( JNB0).GT.90.0.0R.YNB(JNB0) .LT.O.DGO TO 2000
IF(YAS(JNBA).GT.90.0.0R.YAS(JNBA) .LT.O.DGO TO 2000
DYNBAS{NN)=YNB(JNBO)-YAS(JNBA)
DXNBAS(NN)=ABC
WRITE(6,220)DXNBAS(NN),DYNBAS(NN) ,NN
NN=NN+1 2000 ABC=ABC+1.C 20 CONTINUE ND=NN-1
DXNBAS(NC+1)=X(3) DXNBAS(ND+2)=X(4J CYNBAS(NC+1)=Y(3) DYNBAS(ND+2)=Y(4) WRITE(6f210l RETURN END
117
BIBLIOGRAPHY
Balazs, E.I., and B.C. Douglas, "Geodetic Levelling and the Sea Level Slope Along the California Coast," National Oceanic Survey, NOAA (unpublished).
Bloomf ield. P., "Trend Estimation with Autocorrelated Errors, with Physical Application," lectures delivered at the Naval Postgraduate School, Monterey, California, July 1980.
Bretschneider , D.E., Sea Level Variations at Monterey, Cal- ifornia, M.S. Thesis, Navy Postgraduate School, Monterey, California, March 1980.
Gutenberg, B. , "Changes in Sea Level, Postglacial Uplift, and Mobility of the Earth's Interior," Bulletin of Geological Society of America, Vol. 52, p. 721-772, 1 May 1941.
Hicks, S.D., and W. Shofnos, "The Determination of Land
Emergence from Sea Level Observations in Southeast Alaska," Journal of Geophysical Research, Vol. 70, No. 14, P. 3315- 3320, 15 July 1965a.
Hicks, S.D., and W. Shofnos, "Yearly Sea Level Variations for the United States," Journal of the Hydraulics Division - Proceedings of the American Society of Civil Engineers, HYS, p. 23-32, September 1965b.
Hicks, S.D., "On the Classifications and Trends of Long Period Sea Level Series," Shore and Beach, April 1972a.
Hicks, S.D., "Vertical Crustal Movements from Sea Level
Measurements Along the East Coast of the United States," Journal of Geophysical Research, Vol. 77, No. 30, p. 5930-5934, 20 October 1972b.
Lisitzin, E. , Sea Level Changes, Elsevier Scientific Publish- ing Company, 1974.
Merry, C.L., "Processing of Tidal Records at Hount Bay Harbour," International Hydrographic Review, Monaco, LVII (1), p. 149-154, January 1980.
Roden, G.I., "Sea Level Variations at Panama," Journal of Geophysical Research, Vol. 68, No. 20, p. 5701-5710, 15 October 1963.
118
Roden, G.I., "Low Frequency Sea Level Oscillations Along the Pacific Coast of North America," Journal of Geophysical Research, Vol. 71, No, 20, p. 4755-4776, 15 October 1966
Smith, R.A. , and R.J. Leffler, "Water Level Variations Along California Coast," Journal of the Waterway Port Coastal and Oceanic Division, p. 335-348, August 1980.
Smith, R.A. , "Golden Gate Tidal Measurements: 1854-1978," Journal of the Waterway Port Coastal and Ocean Division, p. 407-410, August 1980.
Whitcomb, J.H. , "Regional Crustal Distortion Events in Southern California; A Confirmation of Jerky Plate Motion?, EOS, Vol. 61, No. 17, p. 368, 22 April 1980.
Wilson, M.E., "Tectonic Tilt Rates Derived from Lake-Level Measurements, Salton Sea, California," Science, Vol. 207, p. 183-186, 11 January 1980.
Wyss, M., "The Appearance Rate of Premonitory Uplift,"
Bulletin of the Seismological Society of America , Vo 1 . 67, No. 4, p. 1091-1098, August 1977.
119
INITIAL DISTRIBUTION LIST
No. Copies
Defense Technical Information Center 2
Cameron Station Alexandria, Virginia 22314
Library, Code 0142 2
Naval Postgraduate School Monterey, California 93940
Chairman, Code 68 1
Department of Oceanography Naval Postgraduate School Monterey, California 93940
Chairman, Code 63 1
Department of Meteorology Naval Postgraduate School Monterey, California 93940
Department of Oceanography, Code 68 3
Naval Postgraduate School Monterey, California 93940
Professor Warren C. Thompson, Code 68 Th 5
Department of Oceanography Naval Postgraduate School Monterey, California 93940
Professor Donald P. Gaver, Jr., Code 55 Gv 1
Department of Operations Research Naval Postgraduate School Monterey, California 93940
LCDR Francisco V. Abreu, Portuguese Navy 3
Instituto Hidrografico Rua das Trinas, 49 Lisbon-2, Portugal
Director 1
Naval Oceanography Division
Navy Observatory
34th and Massachusetts Avenue NW
Washington, D.C. 20390
120
10. Commander
Naval Oceanography Command
NSTL Station
Bay St. Louis, Mississippi 39529
11. Commanding Officer
Naval Oceanographic Office
NSTL Station
Bay St. Louis, Mississippi 39529
12. Commanding Officer
Naval Ocean Research 5 Development Activity
NSTL Station
Bay St. Louis, Mississippi 39529
13. Commanding Officer
Coastal Engineering Research Center
Kingman Building
Fort Belvoir, Virginia 22060
14. Commanding Officer Waterways Experiment Station U.S. Army Corps of Engineers P.O. Box 631
Vicksburg, Mississippi 39180
15. California State Lands Commission 1807 13th Street
Sacramento, California 95814
ATTN: Mr. William Northrop, Executive Officer
Mr. F.D. Uzes, Super. Bdry. Det. Off.
Mr. James N. Dov\rden, Bdry, Det. Off.
16. Director (Code PPH) Defense Mapping Agency
Bldg. 56, U.S. Naval Observatory Washington, D.C. 20305
17. Director (Code HO)
Defense Mapping Agency Hydrographic/
Topographic Center 6500 Brookes Lane Washington, D.C. 20315
18. Director (Code PSD-MC) Defense Mapping School
Fort Belvoir, Virginia 22060
19. RADM Herbert R. Lippold, Jr., Director (C) National Ocean Survey
Washington Science Center, Building 1 6001 Executive Boulevard Rockville, Maryland 20852
121
20. Mr. Carrol I. Thurlow 1 Assistant to the Chief Scientist (CX4)
National Ocean Survey- Washington Science Center, Building 1 6001 Executive Boulevard Rockville, Maryland 20852
21. CAPT John D. Bossier, Director (CI) 1 National Geodetic Survey
Washington Science Center, Building 1 6001 Executive Boulevard Rockville, Maryland 20852
22. Mr. Bernard H. Chovitz, Director (C12) 1 Geodetic Research and Development Laboratory National Geodetic Survey
Rockwall Building 11400 Rockville Pike Rockville, Maryland 20852
23. Vertical Network Branch (C132) 3 National Geodetic Survey
Rockwall Building
11400 Rockville Pike
Rockville, Maryland 20852
ATTN: Mr. Charles T. Whalen, Chief
Mr. Emery I. Balazs
Mr. Sandford Holdahl
24. Office of Oceanography 6 National Ocean Survey
Washington Science Center, Building 1 6001 Executive Boulevard Rockville, Maryland 20852
ATTN: CAPT Wesley V. Hull, Associate Director (C2) Mr. Steacy D. Hicks, Physical Oceanographer
(C2X6) CDR Ralph J. Land, Chief, Tides Division (C23) Dr. JohnM. Diamante, Technical Advisor (C23) Mr. James R. Hubbard, Chief, Water Levels
Branch (C234) Mr. Raymond A. Smith, Water Levels Branch (C233)
25. Chief, Program Planning and Liaison (NC-2) 1 National Oceanic and Atmospheric Administration Rockville, Maryland 20852
26. Chief, Marine Surveys and Maps (C3) 1 National Oceanic and Atmospheric Administration Rockville, Maryland 20852
122
27. Director
Pacific Marine Center NOAA 1801 Fairview Avenue East Seattle, Washington 98102
28. Director
Atlantic Marine Center NOAA 439 West York Street Norfolk, Virginia 23510
29. LCDR (NOAA) Gerald Mills, Code 68 Mi Department of Oceanography- Naval Postgraduate School Monterey, California 93940
30. Chairman, Oceanography Department U.S. Naval Academy
Annapolis, MD 21402
31. Commanding Officer
U.S. Army Corps of Engineers Los Angeles District Office Los Angeles, California 90053
32. Commanding Officer
U.S. Army Corps of Engineers San Francisco District Office San Francisco, California 94111
33. Director of the Portuguese Hydrographic
Institute Rua das Trinas, 49 Lisbon-2, Portugal
34. Direcqao de Instru9ao Ministerio da Marinha Lisbon-2, Portugal
35. Mr. Max Wyss
Cooperative Institute for Research
in Environmental Sciences National Oceanic and Atmospheric Administration University of Colorado Boulder, Colorado 80309
36. National Fisheries Service Monterey, California 93940
ATTN: Dr. Gunter Seckel , Director Lt. Dale E. Bretschneider
123
37. Lt. Kenneth W. Perrin NOAA Ship Mt. Mitchell 439 W. York Street Norfolk, Virginia 23510
38. Ms. Penny D. Dunn P.O. Box 158
Long Beach, Mississippi 39560
39. LCDR Donald D. Winter Naval Postgraduate School SMC 1745
Monterey, California 93940
40. Lt. (NOAA) Don Dreves 5713 145th PI. S.W. Edmonds, Washington 98020
41. Lt. Luis Leal Faria Instituto Hidrogrdfico Rua das Trinas, 49 Lisbon-2, Portugal
124
189906
Abreu
Determination of land elevation changes using tidal data.
Thesis
AI725
cj
189906
Abreu
Determination of land elevation changes using tidal data*
thesA1725
Determination of land elevation changes
illliiililliililllll 3 2768 001 90890 8
DUDLEY KNOX LIBRARY
m^^
■^