Analysis By JEROME NAMIAS ‘Frets Revisep AND ENLARGED EpIvrION ; with CONTRIBUTIONS i by J? | TOR’ BERGERON _ _ BERNHARD HAURWITZ GRAHAM MILLAR _ ALBERT K. SHOWALTER ROBERT G. STONE j AND HURD C. WILLETT ay Edited by ROBERT G. STONE October, 1940 —E AMERICAN METEOROLOGICAL SOCIETY, MILTON, MASS. 1940 ny Price $1.25, postpaid Given in Loving Memory of Raymond Braislin Montgomery Scientist, R/V Atlantis maiden voyage 2 July - 26 August, 1931 KKK KK KK Woods Hole Oceanographic Institution Physical Oceanographer 1940-1949 Non-Resident Staff 1950-1960 Visiting Committee 1962-1963 Corporation Member 1970-1980 KKK KK Faculty, New York University 1940-1944 Faculty, Brown University 1949-1954 Faculty, Johns Hopkins University 1954-1961 Professor of Oceanography, Johns Hopkins University 1961-1975 i mn O 0301 0093827 9 An Introduction to the Study of Air Mass and Isentropic Analysis By JEROME NAMIAS FirtH REVISED AND ENLARGED EDITION with CONTRIBUTIONS by TOR BERGERON BERNHARD HAURWITZ GRAHAM MILLAR ALBERT K. SHOWALTER ROBERT G. STONE AND HURD C. WILLETT | WN UU Edited by ROBERT G. STONE October, 1940 THE AMERICAN METEOROLOGICAL SOCIETY, MILTON, MASS. Price $1.25, postpaid The Previous Editions of This Work Appeared Under the Title “AN INTRODUCTION TO THE STUDY OF AIR MASS ANALYSIS’’ First Edition : . wsept., 19384-May, 1935 Second Edition . : . september, 1935 Third Edition : : , August, 1936 Fourth Edition . ; 5 October, 1938 TABLE OF CONTENTS E\DITOR’S PREFACE ; : 3 : 5 INTRODUCTION ‘ 3 : i : is 4 : 5 lie CONDITIONS OF ATMOSPHERIC STABILITY: LAPSE RATES I) CONSERVATIVE PROPERTIES OF AIR MASSES III. THE RossBy DIAGRAM—PLOTTING ROUTINE IV. THE Rosspy DIAGRAM—INTERPRETATION We ELEMENTS OF FRONTAL STRUCTURE—THE WARM FRONT VI. ELEMENTS OF FRONTAL STRUCTURE—THE COLD FRONT. VII. ELEMENTS OF CYCLONIC STRUCTURE THE NORWEGIAN WAVE-THEORY OF CYCLONES, BY B. HAURWITZ FRONTAL WAVES, BY T. BERGERON . 5 5 SOURCES OF ENERGY FOR EXTRA-TROPICAL CYCLONES, BY T. BERGERON A NoTE ON DYNAMIC ANTICYCLONES AND CYCLONES, BY R. G. STONE THE ROLE OF THE TROPOPAUSE IN THE DYNAMICS OF EXTRA-TROPICAL DISTURBANCES, BY T. BERGERON . 5 6 VIII. THE TEPHIGRAM RADIOMETEOROGRAPH SOUNDINGS IN THE MIDDLE NortH ATLANTIC (after Durandin) . ‘ ; j A NOTE ON ESTIMATING CONDITIONAL AND CONVECTIVE INSTABILITY FROM THE WET-BULB CURVE, BY R. G. STONE . IX. Synoptic ASPECTS OF THE THUNDERSTORM AIRPLANE SOUNDINGS ILLUSTRATING CONVECTION (after Kochanski) THE IcE-NUCLEI THEORY OF RAINFALL, BY R. G. STONE . HAIL FORECASTING (after United Air Lines) . 5 ‘ ili iv CHARACTERISTIC PROPERTIES OF NORTH AMERICAN AIR MASSES, BY H. C. WILLETT Magsgor FRONTAL AND AIR MASS ZONES OF THE EARTH, BY T. BERGERON . FURTHER STUDIES OF AMERICAN AIR MASS PROPERTIES, BY A. K. SHOWALTER ILLUSTRATIONS :— Dust Storm (after Parkinson) FLooD RAINS (after Minser; Byers) FRONTS AND AIRCRAFT ICING (after Minser) . BERGERON’S MODEL OF THE WARM-FRONT-TYPE OCCLUSION SPRING SHOWERS (after Botts) WINTER CYCLONE WITH DUST STORM (after Parkinson) Maps AND CROSS SECTIONS OF FRONTS; AIRCRAFT ICING (after Minser) A SUCCESSION OF PoLAR AIR MASSES; WEATHER MAPS AND Cross SECTIONS FoR Nov. 30—Dsc. 2, 1988 (after George and Elliot) A RossBy DIAGRAM (after Tu) SYNOPTIC CHARTS SHOWING WINTER CYCLONES (after Pierce; Dorsey) . 5 : . : ; : X. ISENTROPIC ANALYSIS 5 3 d F : ISENTROPIC ANALYSIS OF A THUNDERSTORM SITUATION, JUNE 22-27, 1937 (after J. Namias) . ANALYSIS OF THE RAINFALL SITUATION OVER THE WESTERN STATES, May 6-7, 1938, By MEANS oF AIR MASS AND ISENTROPIC CHARTS (after Weightman) EXAMPLES OF Upprer-AIR CROSS-SECTIONS SHOWING INTERPRETATIONS OF THE TROPOPAUSE, ETC. A BIBLIOGRAPHY FOR SYNOPTIC METEOROLOGISTS, BY R. G. STONE ADDENDA TO BIBLIOGRAPHY GLOSSARY OF ELEMENTARY TERMS USED IN ARTICLES INI TO IX . Pages - 73-108 108. 109-113 113-135. 114-115 116-117 118-121 122-124 125 126-127 128 129-131 131 131-135 136-161 . 161-167 168-171 172-175 176-226 227 228-232 Corrigenda for “An Introduction to the Study of Air Mass and Isentropic Analysis,” by J. Namias and others, 5th ed. Page 5, table at bottom of page, lines under “Condition” and “Type of equi- ) librium”, should be deleted and the following should be substituted (the preferred terminology is italicized :— a
3.42°100 m Mechanical instability, or auto-convective gradient
(self starting; hence this is not an equilib-
rium) J
Page 6, col. 2, line 8 of footnote, “J.-J. Jang” should read or
Page 14. col. 1, line 11, “T/P2*” should read “T/p: Cs Te NAAN CINE SWS Fa
Page 14, col. 1, line 18, “wet-bulb temperature” should read eet pels poten-
tial temperature.”
Page 69, line 7, “Su” should read “Sc.”
Page 71, top, line 4, delete “warm.”
Page 150, col. 2, line 4, “stream function” should read “isentropic accelera-
tion potential” (see BULLETIN A. M. S., Jan. 1941, p. 45).
Page 172, line 18 (in fine print) “frontal at” should read “frontal topogra- _
phy at.” .
Page 174, line 9, “15 km” should read “18 km or higher.” —
Page 174, line 10, “by 10 mb” should read “by 9 mb.”
Page 175, line 1, “In Fig. 6, shown above is” should read “Fig. 6 above is”. . .
Page 175, line 3, “tions shows” should read “tions. It shows.” ; Me
Page 228, 2nd col. line 34, “to dry air” should read “to saturated se te ue
33, after “entire” insert “originally stable”. ,
Page 229, 2nd col., lines 2 and 3 from bottom, “decreases? should read
“increases.” | i et
Page 282, 2nd col. 3rd line from dovowt Fuge “equal”. Pa wea
[Supplement to the June 1941 Bulletin of the American Meteorological Society) =
Editor’s Preface to 5th Edition
NCEASING demand has again
U induced the Society to extend
this convenient booklet into
a 5th revised and enlarged edition. The
text of the 4th edition is reprinted with
numerous secondary annotations and
changes to indicate some of the present
attitudes or practices that depart from
those stated or implied in the previous
editions. The practices in other coun-
tries are so diverse that no special note
of them could be taken, but extensive
citations of foreign literature are
given in the Bibliography.
At the time the 4th edition appeared
(Oct. 1938) a new technique and point
of view, known as isentropic analysis,
was under promising experimental de-
velopment and it was anticipated by
the authors and editor that any future
edition of this “Introduction” would
have to take account of the new method.
Already in 1939 isentropic analysis was
so generally practiced in U. S. A. that
plans were laid to add an introductory
chapter on the technique. Mr. Namias
was engaged by Prof. Sverre Petter-
ssen to prepare such a chapter for his
excellent book “Weather Analysis and
Forecasting” recently published. We
are able to offer a slightly modified
form of this chapter in our 5th edi-
tion, through the kind permission of
Prof. Petterssen and of the McGraw-
Hill Book Co., Inc., of New York.
The Bibliography in the 4th edition
has been so widely appreciated that an
effort is made to improve it materially
in this new edition. Besides bringing
it down to date, a great many more
entries are added and the whole ar-
ranged conveniently by _ subjects.
Finally, additional illustrations are
provided in the appendix.
This opportunity has been seized to
correct a few typographical and other
errors which unfortunately passed in
the 4th edition; the editor wishes to
thank the numerous individuals who
have kindly called our attention to
errors and offered suggestions for
improvement. The basic part of this in-
troduction remains rather elementary,
but many more technical annotations
are provided for the numerous stu-
dents who have the background to
enter a little deeper into the subject.
However, we have not attempted to
enlarge the work into a textbook of
synoptic meteorology. It is assumed
that the reader is familiar with the
elements of meteorology and with the
general conception of the weather
map as given in numerous and readily
available textbooks, to which this
booklet is only an adjunct of certain
newer topics not particularly well-
treated outside a few technical and
expensive works.
The material available for direct
analysis of upper-air conditions has
lately reached a new high. There are
now 34 regular aerological stations in
the U. S., mostly using radiosondes,
the largest network of its kind in the
world and in history. The adequate
use of such data in forecasting is being
tried here for the first time anywhere
and will call for an increasingly quan-
titative and physical approach.
The editor wishes to acknowledge
the very generous assistance in read-
ing proof and valuable advice on
many points given by Prof. Charles
F. Brooks, Secretary of the Society,
who has handled the arrangements
for publishing this work. Thanks are
due Miss Edna Scofield for aid in
editing and reading proof.—Robert G.
Stone, Sept. 1940.
vi
From the Preface
When these sketches were first pre-
pared it was thought that the sub-
ject would develop so rapidly that
any attempt to simulate a_ well-
rounded and comprehensive treatise,
even for beginners, would not be
justified nor feasible. Needless to say
the continued warm response and wide
influence which the work has had has
left the authors and editors with a
sense of responsibility for which they
had not bargained. The authors feel
that most of the early principles of
air mass analysis still bear a funda-
mental value for synoptic practice, so
that extensive revisions have not been
necessary in this new edition, though
references are made here and there to
some of the points that have been
particularly altered or questioned in
light of more recent developments.
From the practical point of view,
the beginner in America now has
much better opportunities to “pick up”
experience through his own efforts
than when this “Introduction” first
appeared over three years ago, when
no competently analyzed air-mass
weather maps were available outside
of a few institutions and special serv-
ices and none to the public. At pres-
ent, thanks to the remarkable changes
in U.S. ‘Weather Bureau _ practice
since 1934, such maps may be in-
spected by anyone at a large number
to the 4th Edition
of airport and city offices of the
Bureau, and many of their personnel
can now produce or interpret analyses
acceptably, while at the Central Office
in Washington competent and funda-
mental research is being carried on.
(The problem of rapidly training a
large organization in such a different
technique is admittedly difficult).
The present “Introduction”, how-
ever, should not be regarded as one to
the whole field of synoptic meteor-
ology. For such a serious ambition
one should study physical meteorology
as well, and there are excellent gen-
eral texts such as Humphreys’ “Phys-
ics of the Air’, Brunt’s “Physical and
Dynamical Meteorology’, Taylor’s
“Aeronautical Meteorology”, “Byers’
“Synoptical and Aeronautical Mete-
orology”’, [and now (1940) also Pet-
terssen’s “Weather Analysis and
Forecasting”, Sutcliffe’s “Meteorology
for Aviators’, and “The Admiralty
Weather Manual’’,] to lighten the
road. But to that large audience
which desires only a brief, authorita-
tive, and inexpensive “first reader”
in this fascinating concrete way of
looking at the weather, this booklet
is offered again in the hope that
it will continue the instrument for
wide dissemination of modern me-
teorological principles which it has
been.—Robert G. Stone, Oct. 1938.
An Introduction to
The Study of Air Mass and Isentropic Analysis
By JEROME NAMIAS
INTRODUCTION TO THE 5TH EDITION
HE SYSTEM of weather analysis
developed chiefly by the Norweg-
ian school of meteorologists and
referred to as “Air Mass Analysis” in
the United States, has received wide-
spread adoption throughout the me-
teorological services of the world. In
addition to the group of professional
meteorologists who employ’ these
methods as the foundation of their
activities in synoptic meteorology,
there has developed a large group of
people whose interests are so intimate-
ly associated with meteorology that it
is necessary for them to possess more
than a fragmentary knowledge of the
physical processes of the atmosphere.
The increasing number of aviation
enthusiasts is only one of these groups.
Many such people, and indeed, many
practicing professionals at present en-
gaged in meteorology, have not had the
time nor the opportunity to carry on
an organized collegiate program of
study in modern synoptic meteorology,
and for this reason have felt the need
for some simplified presentation of the
fundamentals upon which the science
rests. It has been the purpose of this
series of articles to fulfill this gap in
such a manner that these students may
be able to obtain a physical picture of
basic weather processes without first
having to possess a mastery of ad-
vanced physics and mathematics. Since
weather forecasting is still quite re-
moved from the quantitative stage,
and since a qualitative evaluation of
the various entering factors consti-
tutes a large share of the forecaster’s
technique, it is possible to develop a
moderate degree of forecasting ability
with an understanding of the physical
processes as described in these articles.
The actual technique of air mass and
isentropic analysis can hardly be im-
parted adequately by written material.
It requires a more personalized guid-
ance by an experienced analyst.
While textbooks in modern synoptic
meteorology have been vastly improved
since many of these articles were first
written, notably by the works of Byers,
Taylor and Sutcliffe, there has con-
tinued a demand for these articles, and
more recently for some similar presen- ~
tation dealing with the new method of
upper-air analysis along the surfaces
of constant entropy. Professor S. Pet-
terssen (of M.I. T.) and the McGraw-
Hill Company have been so kind as to
permit me to publish here, with some
small alterations, the chapter on
isentropic analysis originally prepared
for his textbook on Weather Analysis
and Forecasting (McGraw-Hill, N. Y.,
1940).
I. CONDITIONS OF ATMOSPHERIC STABILITY: LAPSE RATES
A. VERTICAL DISPLACEMENT OF
A PARTICLE
It has long been known that verti-
cal motions in the atmosphere are of
great significance in that practically
all precipitation may be ascribed to
the condensation brought about
through expansional cooling of rising
air. It can be shown that the amount
of precipitation possible through the
mixing of currents of air possessing
different temperature and moisture
characteristics is very small, and
that the precipitation resulting from
2 AIR MASS ANALYSIS
this cause must be negligible in com-
parison with other causes. Further-
more the theory of fronts and air
masses is based upon atmospheric
discontinuities, which, are simply
zones of rapid transition of the vari-
ous meteorological elements. It is
assumed that these zones of transition
are comparatively free from large
scale mixing, the individual large
scale air currents flowing side by side
or above one another without appre-
ciable mutual drag.
Granting the importance of vertical
motion in the atmosphere a discussion
of the factors which tend to aid or
hinder such motion is in order. This
leads to the problem of stability.
Here the term stability is used in its
physical sense; if an air particle
tends to remain in, or return to, its
former position following a displace-
ment, the condition is termed stable;
if displacement results in a tendency
to further movement of the particle
from its original position, the origi-
nal condition is designated as un-
stable; and finally, if the particle
neither resists nor assists displace-
ment, the condition is one of neutral
equilibrium.
B. TYPES OF EQUILIBRIUM
In the case of the atmosphere there
are four principal types of equilibri-
um to be considered when we are con-
cerned with the vertical displacement
of a selected particle through a layer
of the atmosphere having known
characteristics. These types of equi-
librium are:
il, Stable
a. With respect to dry air*
b. With respect to saturated air
2. Unstable
a. With respect to dry air
[1. Mechanical]
b. With respect to saturated air
8. Neutral
a. With respect to dry air
b. With respect to saturated air
4. Conditional
Another case, that of convective
equilibrium, will be treated inde-
pendently in a future article, since it
concerns the displacement of layers
of the atmosphere rather than the dis-
placement of individual particles of
air through a given layer.
It is obvious that if a particle of air
is lifted it must expand against the
decreasing pressure so that the pres-
sure within and surrounding the par-
ticle must be equal; if it sinks it must
be compressed. It is assumed that
these changes take place without the
transfer of heat either from the mov-
ing particle to its surroundings or
vice versa. Such a thermally insul-
ated process is termed adiabatic. If
the particle expands it does work; if
it is compressed work is done upon
it. Thus there must be a conversion
of mechanical energy into realized
heat if the particle sinks, while heat
must be converted into mechanical
energy if the particle rises. By
means of thermodynamics it can be
shown that the relation between tem-
perature and pressure in an adi-
abatic displacement of an unsaturat-
ed particle is as follows:
T ( pr ) +288
T» a p2
where 7; is the original temperature
of the particle at the pressure pi, and
T, is the temperature it assumes at
the pressure p2. This is Poisson’s
equation.
It is generally more convenient in
aerological studies to refer to the adi-
abatic changes in temperature with
respect to changes in elevation. From
1The term “dry air” in synoptic meteorol-
ogy simply means unsaturated air.
LAPSE RATES =}
Poisson’s equation and the hydro-
static equation (expressing the rela-
tion between pressure, density, and
height), it is possible to obtain the
rate of cooling of a rising air parti-
cle owing to its change in elevation.
The result is the convenient rate of
1 C deg. per 100 m. This rate is not
strictly constant; it depends upon
the amount of moisture within the
unsaturated air particle as well as
the temperature of the surrounding
air through which it is displaced.
However, these effects are relatively
small and tend to counteract each
other. Hence, for all practical pur-
poses, they may be neglected, the adi-
abatic rate of change of temperature
being taken as 1 C deg. per 100 m.
change in elevation. This is com-
monly known as the dry adiabatic
ALTITUDE km
- ter condensed.
lapse rate, or dry adiabat. (Lapse
rate is defined as the rate of change
in temperature with respect to height.
Unless preceded by the qualifying
term “adiabatic,” lapse rate refers to
the existing difference of temperature
per unit of height within a selected
layer of the atmosphere.)
Thus far -we have considered the
vertical displacement of an unsatur-
ated particle of air. Once the parti-
cle becomes saturated the latent heat
of condensation must be taken into
account, for it supplies heat to the
rising mass and therefore lessens the
rate of cooling due to expansion. The
lessening of the adiabatic cooling ef-
fect depends upon the liberated heat
of condensation, which in turn de-
pends upon the amount of liquid wa-
But as the particle
to)
TEMPERATURE C
Gale
TYPES OF LAPSE RATES
4 AIR MASS ANALYSIS
continues to rise, its temperature
falls, so that the total quantity of wa-
ter vapor possible within the volume
of rising air becomes less and less.
Therefore the rate of cooling of the
saturated mass becomes greater and
greater, until at high levels, where
the moisture content of the rising air
is almost negligible, its “rate of adi-
abatie cooling is practically the same
as that for dry air.
We are now prepared to deal with
the types of equilibrium as outlined
above.
1. Stable. The rate of cooling for
an unsaturated particle of air rising
through the surrounding atmosphere
is given by the broken line y in fig.
1. This is a straight line since the
rate is 1 C deg. per 100 m. Lines
drawn parallel to would represent
other dry adiabats at different tem-
peratures. If we assume the ob-
served vertical temperature distribu-
tion (the lapse rate) above 1000 m to
be represented by the line qi, it is at
once clear that a particle of air taken
from any position on the line g: and
brought up or down will immediately
find itself of a different temperature
and hence different density from its
surroundings. It will consequentiy
tend to return to its original position.
For example let us take a particle at
1000 m. where the temperature is 20°
C. If we bring this particle up to
2000 m., it will follow the line y and
at 2000 m. will assume the tempera-
ture 10° C. The surrounding air at
2000 m., however, has the tempera-
ture 14° C., or 4 deg. warmer than
the rising particle. Under this con-
dition the particle must return to its
former position, coming to rest at
1000 m, where its temperature is the
same as the surrounding air. In a
similar fashion it is easily shown that
downward motion of individual parti-
cles originally lying along the line
ai are hindered, the tendency being
always to make the particle return
to its original position. It is clear
then that the line g: represents a
stable lapse rate. In other words if
the lapse rate is less than the dry
adiabat the layer is stable for un-
saturated air.
The rate of adiabatic cooling for a
rising saturated particle of air is
represented in fig. 1 by the line B
Note that 8 is a curved line, since
the rate of cooling is dependent upon
the heat of condensation as well as
upon the expansion. Also note that
the curve @ tends to straighten,
gradually approaching the slope of y
at upper levels, where the moisture
content becomes smaller and smaller.
If we now assume a lapse rate of gq
from 1 to 3 km. it is clear that a ris-
ing particle of saturated air will fol-
low the line 8, and will at every stage
in its ascent be colder than its sur-
roundings. Thus it will tend to re-
main at its original position and the
layer between 1 and 38 km. will, by
definition, be termed stable with re-
spect to saturated air. A lapse rate
less than the saturated adiabat may
be termed absolutely stable since it is
stable whether the rising air be dry
or saturated.
2. Unstable. Let us assume that
the lapse rate between 1 and 2 km.
has the form g; as in fig. 1. A parti-
cle of air displaced upward from any
position on the line g3 would follow
parallel to the dry adiabat y and ob-
viously would be warmer than the
surrounding air, level for level. There-
fore it would continue to rise. The
layer possessing the lapse rate q3 is
then unstable with respect to dry air,
and since the saturated adiabatic
lapse rate is always less than the dry,
it is clear that this condition is even
more unstable for saturated air. The
line g3 has been constructed to rep-
resent a special case of instability in
which the density remains constant
LAPSE RATES 5
with elevation. The density, of course,
is a function of the temperature and
pressure, and is slightly affected by
the moisture content. In the atmos-
phere the pressure decrease with ele-
vation is such that it nearly always
overbalances the increase in density
caused by the usually observed drop
in temperature with elevation. If the
temperature falls off sufficiently rap-
idly with elevation, however, a state
will be reached wherein the density
of the air is constant with height. If
the lapse rate exceeds the value 3.42
C deg. per 100 m there must be an
increase in density with elevation—
obviously a very unstable condition.
This particular case has been given
various names, the best one probably
being mechanical instability. gs rep-
resents a state of mechanical insta-
bility. This condition is never ob-
served in the upper atmosphere, since
it is such an unstable state. It is,
however, frequently observed imme-
diately overlying flat regions which
become greatly heated during the
summer daytime hours.
In the case of instability with sat-
urated air the lapse rate must be
greater than the saturated adiabat.
In fig. 1 the line q: represents such
a lapse rate between 1 and 3 km. It
should be noted that the layer above
3 km. is not unstable for saturated
air, since the rate of change of the
temperature along gi above 3 km. is
less than that along B:
38. Neutral equilibrium. With dry
air this state is reached when the
lapse rate is equal to the dry adiabat.
Under this condition the rising parti-
cle will possess the temperature of
the surrounding air at every stage in
its ascent. Thus it will neither as-
sist nor resist displacement. If the
rising air is saturated then the con-
dition for neutral equilibrium re-
quires that the lapse rate equal the
saturation adiabat.
4. Conditional equilibrium. It was
pointed out that the lapse rate given
by the line gq: is stable for rising air,
while between 1 and 8 km. it is un-
stable for saturated air, because the
lapse rate qi: lies between the saturat-
ed and the dry adiabat. When this
state obtains the layer is said to be
in conditional equilibrium. The con-
dition is simply that the layer is un-
stable if saturated, but stable if un-
saturated. This lapse rate is fre-
quently observed in aerological sound-
ings, and has been found to be impor-
tant in the development of thunder-
storms and showers. It should be
noted that the conditional instability
in the case of fig. 1 extends through
the layer between 1 and 3 km., and
no higher. Beyond 3 km. the lapse
rate g: does not lie between the dry
adiabat and the saturated adiabat for
the temperatures at these elevations.
The rate of change of temperature
along the line @ (above 3 km.) is
greater than along the line q:.
A summary of the above conditions
is presented in algebraic form be-
low: where q represents the existing
rate of change in temperature with
elevation (the lapse rate) ; y the dry
adiabatic lapse rate; the B, the satur-
ated adiabatic lapse rate.
Condition Type of equilibrium
a