JPRS ID: 9304 USSR REPORT METEORLOGY AND HYDROLOGY

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JPRS L19304 -
- 18 September 1980
USSR Re ort
p
METEOROLOGY AND HYDROLOGY
No. 6; June 19'~0
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JPRS L/9 304
- 18 September 1980
, USSR REPORT
METE~ROLOGY AND HYDROLOGY
No. 6, June 1984
. Translation of the Russian-language monthly journal METEOROLOGIYA
I GIDROLOGIYA published in Moscow by Gidrometeoizdat.
CONTENTS
. Modern Changes in Climate of the Northern Hemisphere
(K. Ya. Vinnikov, et al.) 2
Some Results of Joint Soviet-Polish Investigation in the Fie1d of
Numerical Short-Range Forecasting of Meteorological ~lements
(B. M. I1'in, et al.) 19
Correction of the Initial Field of Surface Pressure Trends in Numerical
Prediction of Pressure Field
(A. A. Mulyukov) 30
Method for Indirect Computation of the Mean Long-Term Precipitation
Duration Values
(E. G. Bogdanova) 39
Model Investigation of the Global P4ean Zonal Thermai Regime of the Earth's
Atmosphere
(L. L. Karol' and V. A. Frol'kis) 46
Application of the Teaching Model Method in an Investigation of the Piotion
of a Tropical Cyclone
(T, B. Rostkova and A. Ye. Ordanovich�) 61
Possible Mechanisms of Ice Formation of Silver Iodide Particles in a
Diffusion Chamber and in a Fog Chamber
(B. Z. Gorbunov, et a'l.) 71
Horizontal Water Circulation in the Somali Region of the Indian Ocean
(V. V. Pokudov, et al.) 80
One Method for Representation of Hydrological Maps for Analysis on an _
Electronic Computer
(L. P. Smirnykh) 94
-a- [III -USSR- 33S&TFOUO]
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Influence of Ivonlinear Effects of Changes in Streamflow on the Salinity
of the Sea of Azov
(N. P. Goptarev and I. A. Shlygin)............~............ 100
Correlation Between the Height of Sand Ridges and the Parameters of
I~iver Flow and Channel
(B. F. Snishchenko) 107
Numerical Evaluation of Change in the Thermal Regime of a Peat Deposit
= as a Result of Its Drainage
(N. M. Khimin and I. L. Kalyuzhnyy) 118
Prediction of the Air Temperature Anomaly Variation Over the Course of
a Month by Five-Day Periods
(R. I. Burakova) 130
Influence of Orography on the Surface Wind
(S. M. Kozik)............ 137
Change in River Runoff for Large Regions of the Earth
(P. P. Denisov) 14U
Ozonometric Apparatus for Creating Sample Ozone-Air Mixtures
(V. A. Kononkov and S. P. Perov) 144
- Fiftieth Anniversary of Radiosonde Observations in the USSR
(G. P. Trifonov) 151
Revie*a of Monograph "Odnorodnost' Meteorologicheskikh Ryadov vo Vremeni
i v Prostranstve v Svyazi s Iz~anen3.yem Klimata" (Homogeneity of
Meteorological Series in Time and Space in Relation to Climatic
- Change), by Ye. S. Rubinshteyn, Leningrad, Gidrometeoizdat, 1979,
80 pages
(A. Kh. Khrgian) 164
Book Review: "Gidrometeorologicheskiy Rezhim Ozer i Vodokhranilishch.
Bratskoye Vodokhranilishche" (Hydrometeorological Regime of Lakes and
Reservoirs. liratsk Reservoir), Leningrad, Gidrometeoizdat, 1978,
165 pages
(Me Sh. Furman) 166
Sir.tieth Birthday of Kirill Yakovlevich Kondrat'yev............~...... 168
Sixtieth Birthday of Nilcolay I1'ich Zverev ..............s............. 172
Sixtieth Birthday of I1'ya Zaynulovich Lutfulin 174
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A
High Award to Yevgeniy Konstantinovich.Fedorov 176
Awards at the USSR Exhihition of Achievements in the National Economy.
(M. M. Kuznetsova) 177
At the USSR State Coummittee on Hydrometeorology and Environmental
Monitoring
(V. N. Zakharov) 184
Conf erences, Meetings and Seminars
(K. M. Lugina and Yu. G. Slatinskiy) 185
Notes From Abroad
(B. I. Silkin) ........................................o..... 189
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UDC 551.524.34(215-1~)
MODERN CHANGES IN CLIMATE OF THE NORTHERN IiEMISPHERE
Moscow METEOROLOGI~YA I GIDROLOGIYA in Russian No 6, Jun 80 pp 5-17
[Article by Candidate of Physical and Mathematical Sciences K. Ya. Vinni-
kov, Professor G. V. Gruza, Candidates of Geographical Sciences V. F.
Zakharov and A. A. Ririllov, N. P. Kovyneva and Candidate of Physical and
Mathematical Sciences E. Ya. Ra.n'kova, State Hydrological Institute, All-
Union Scientific Research Ins`titute of Hydrometeorological Information-
World Data Center, Arctic and Antarctic Scientific Research Institute
and USSR Hqdrometeorological Scientific Research Center, submitted for
publication 15 January 1980]
' [Text) Abstract: The article presents empirical data
on the change of inean annual air surface tem-
perature in the northern hemisphere during the
period 1881-1978. The authors analyze the lin-
ear trends for different parts of the series.
The conclusion that during the period 1966-1975
the mean annual air surface temperature of the
extra-equa.torial part of the northern hemisphere
(17.5-87.5�N) h~s iacreased gradually is confirmed.
Materials are presented which characterize the
integral ice content of the north polar basin.
It is demonstrated that a peculiarity of the de-
velopment of the arctic ice cover during recent
years is its contraction.
Change in Surfa.ce Air Temperature
In many recent studies the mean annual surface temperature of the air,
averaged over the area of individual hemisplieres or wide latitudinal
zones, is used in characteri~ing changes in the global temperature re-
gime.
The longest uniform series of inean characteristics of air surf.ace temper-
ature for the northern hemisphere were obtained in the studies of Willett
[30, 31J, Mitchell [22, 23], Callendar [18], L. P. Spirina [13J, Ye. S.
Rubinshteyn [11], I. I. Borzenkova, et al. [1], Landsberg, et al. [21].
1
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In all these studies it was established that from the end of the ].ast
century to the 1940's a process of warming o� the northern hemisphere
developed which in the 1940's was replaced by a cooling. Both these
processes were e~cpressed most clearly in the high latitudes. ~
For a considerably shorter time interval, taking in the 1950's, l.'~60's
and 1970's, similar data were obtained in the studies of Angell and Kor-
shover [14, 15J, Yamamoto, et al. [32j, Brinkman [17], Kukla, et al. [20],
Walsh [28, 29] and Barnett [16].
Willett [31] was the ftrst to draw atCention to the fact that the cooling
trend, beginning in the 1940's, for the first time noted on the basis of
data for the high latitudes, had gradually shifted into the lower lati-
tudes. In the middle latitudes of the northern hemisphere i~t has been
observed only since the 1950's, and in the tropical and equatorial lati-
tudes considerably later. With the beginning of the 1970's Willett
has noted an incipient weak tendency to warming. This preli~r,inary con-
clusion found confirmation in a study by I. I. Borzenkova, et al., in
whj.ch thz conclusion was drawn that in the mid-1960's the cooling process
in the northern hemisphere had ended and had been replaced by a warming
process whose mean intensity during the period 1964-1975 was estimated
at about 0.3�/10 years for the mean annual air temperature at the surface
in the extra-equatorial part of the hemisphere (87.5-17.5�N).
Although the quantitative information contained in the mentioned studies
differs not only with respect to the scales of spatial and temporal averag-
ing, but also with respect to accuracy, there are virtually no significant
contradictions in the data of the principal studies. The contradictinns
in the interpretation of data are greater. In particular, in the studies
of Kukla, et 31. [20~ and Borzenkova, et al. [1] contradictory opinions
are ~;.pressed concerning the recently observed tendencies in change in
tne thermal regime of the northern hemisphere.
In this connection we note that it makes sense to retain the tr.aditional
use of the terms "global warming" or "cooling" relative to the processes
of change in the mean annual or seas~nal air temperature at the surface
over the greater part of a hemisphere. The desirability of such an applic-
ation of these terms is dictated by the fact that data on changes in the
air temperature at the surface over a sufficiently long period of time
could be obtained from materials obtained by relatively reliable instru-
mental measurements. This does not exclude the necessity for monitoring
ct~anges of the thermal regime of the free atmosphere.
During 1977-1978 specialists at the Al1-Union 5cientific Research Insti-
tute of Hydrometeorological Information-World Data Center created [5J
" ~i supplementary archives (on magnetic tapes) of anomalies of surface
mean monthly air temperature for the northern hemisphere for the period
1891-1978. The basis for the archives is the same sources of information
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[8, 12J as were used in a study by I. I. Borzenkova, et al. [1]. However,
the reading of data from the maps of monthly temperature anomalies was
accomplished anew using a somewhat differing latitude-longitude grid
with a spacing of 5� in latitude x 10� in longitude. With the use of
these data for the period 1891-1978 we obtained ti~e sPries of monthly
air temperature anomalies for the principal latitude zones of the north-
ern hemisphere (87.5-72.5�N, 72.5-57.5�N, 57.5-37.5�N, 37.5-17.5�N, 87.5-
17.5�N).
A comparison of the primary mean annual temperature anomalies obtained
using data in the new archives and averaged for the mentioned latitude
zones with the similar values obtained in carrying out study [1] does
not reveal the pr:~sence of significant random errors for any of the lati-
tude zones. The differences between the data in [1] and the data in the
archives of the All-Union Scientific RPSearch ~n~titute of Hydrometeoro-
logical Information-World Data Center for the 1960's and 1970's, for the
- zone 87.5-17.5�I~ in general reveal a systematic negative error for the
second half of the 1960's, being of the order of -0.05�C. These differ-
ences from 1960 through 1975 were equal to 0.00, 0.00, 0.02, -0.03, -0.03,
-0.05, -0.03, -0.06, -0.07, 0.03, 0.00, -0.01, 0.01, -0.01, 0.00 respec-
tively, The new data for the period 1961-1969 are more precise. In the re-
maining cases the nonclosures in the comparison of data are not great and
.the materials can be considered equally preciae.
The resulting time series of inean monthly air temperature anomalies are
not uniform because the anomalies for the period 1891-1940 and 1961-1969
were computed relative to the means for the period from 1881 through 1935
(40); the anomalies for the period from 1941 through 1960 relative to
the means for the period from 1881 through 1960, and the anomalies for
the period from 1970 through 1978 relative to the means for the period
from 1931 through 1960 [8, 12J.
Now we will discuss in greater detail the principles for restoring uniform-
ity of the considered time series.
In [1] Borzenkova, et al, developed a system of corrections making it pos-
sible to eliminate the n~nuniformity of series of air temperature anomal-
ies when using only the primary values of the,anomalies without making use
of information on the "norms." The corresponding corrections for t;~e mean
ir~tlnthly anomalies, averaged by latitude circles, were published in [4)
also for anomalies of the mean annual surface temperature of the principal
latitude zones of the northern hemisphere are given in Table 1. This sys- ~
tem of corrections is denoted by the letter A.
In order to apply the mentioned correction method to the data in the ar-
chives of the All-Union Scientific Research Institute of Hydrometeorolog-
ical Information-World Data Center it is necessary to take into account
the circumstance that the data in this archives begin in 1891, not in 1881,
as the data in [1].
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This circumstance is no obstacle to obtaining a similar system of correc-
tions for the data in the archives of the All-Union Scientific Research
Institute of Hydrometeorological Information-World Data Center if as an
additional condition use is made of the assumption that the sum of the
primary air temperature anomalies during the period from 1881 through 1935
or 194J is equal to zero. This condition is almost obvious since the pri-
mary temperature anomalies for this period of time were computed relative
to the "norms" for the period 1881-1935(40); some uncertainty in the end of
the period makes this condition approximate.
In order to ensure a comparability of these results to the materials in
[1], in correcting the data we will reduce them to the "norms" for the
period 1881-1975.
This system o.f. corrections will be denoted by the letter B.
A third independent system of correr_tions, C, can be obtained using infor-
mation on the "norms" for air temperature present in ~he archives of the
A1.1-Union Scientific Research Institute nf Hydrometeorological Informa-
tion-World Data Center.
Earlier, in [4], it was postulated that corrections of the C type, evaluat-
ed using the air temperature "norms" and relating to different intervals
of years, have a lesser accuracy. Computation of these corrections invalv-
ed reducti.on of air tempei~ature data to sea level, with plotting, drafting
of maps and visual interpolation of data at the points of intersection of a
regular grid. In computing the ~ifferences in the "norms" for the two per-
iods, that is, the corrections of interest to us, we obtain small differ-
ences of. high values, whose random errors are summed. These differences, -
even if they are caused by errors entering into the corrections, are in-
troduced into the series of observations, impairing their uniformity. How-
ever, having a lesser accuracy (in comparison with the systems of correc-
tions A and B) for regions well covered with observational data, the sys-
tem of corrections C can be less reliable for poorly covered regiens, es-
pecially for the areas of the world ocean.
Accordingly, henceforth in the representation and analysis of data we wi1l.
use the system of corrections B for the goints of grid intersection situ-
ated over the continents and the system of corrections C Eor the remaining
points of grid intersection.
Such a combined system of corrections will be denoted by the l.etter 1).
All the mentioned systems of corrections for correction of the time series
for mean annual air temperature at the surface in the northern hemisphere
are presented in Table 1.
The closeness of the corrections relating to systems A and B must not cause
surprise because these systems are virtually identical. The differences
between the systems of corrections A and B, on the one hand, and C, on
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the other, are especially significant for the latitude zones 72.5-57.5� and
_ 57.5-37.5�N. These differences can be considered as measures of the inhomo-
geneity of the series after their correction. For the mean annual surface
temperature in the extra-equatorial part of the North Atlantic (87.5-17.5�
N) the uncertainty in the evaluation of the jumplike disruption of homogen-
, eity ~f the series is 0.03-0.04�C b etween 1940 and 1941, less than 0.05�C
between 1960 and 1961 and a value of about 0.1�C between 1969 and 1970.
The problem of the forms of representation of the empirical characteristics
of the secular variation of climatic parameters was examined at a special
conference of the representatives of three institutes: USSR Hydrometeor-
ological Institute, All-Union Scientific Research In~titute of Hydrometeor- -
ological Information-World Dar.a Center and State Hydrological Institute in
February 1979. The conference adopted the following recommendations:
1. In the representation of the secular variation of climatic parameters
it is considered necessary that the following be given in tabular or
graphic form:
a) actual values of the parameters for i;ldividual years;
- b) results of five-yea.r moving averaging;
c) evaluations of linear trends obtained by the least squares method for
- 10-, 20- and 30-year periods for inteYvals of years ending with the last
year of a time series which is a mul tiple of 5 and also during the last
, decade and the entire observation period.
2. The following should be used as evaluations of trend:
a) the angle coefficient of the linear trend;
b) the relative contribution of the linear trend to the total dispersion
for the considered period.
Table 1
Systems of Corrections (�C) for Restoring the Homogeneity of Time Series
of Anomalies of the Mean Annual Air Temperature at the Surface in Various
Latitude Zones of the Northern Hemisphere
Ceaepxax I 13~31-1940. 1961-1969 1941-1960 1970-1978
wHpoTa, ~ ~ v I C I ~ A I B I C I D A B I C~ D
zpa~ A i i
i ;
8i,o-72,5 ~ O.Oa -Q, I�i-0,14 -O, l~l 0,05 0,0.` U,07 0.09 0,63 0,55 0.~6 l.i.~l
72,5-57,5 ~-U.O~ -u, I~ -U,08 -U.12 u,01 0,02 U.02 U,O~ 0,38 0,3E 0,21 0.31
:i7.5 37,5 ~-~).U9-�U.10-~,02-U,U7I-0,02-0,02-O,U1 -0.0~ U,16 O,lt U,u2 O,U~
37.0-17,5 i-O.Ui -U.(kil-0.01 -0,04 0,00-Q,UI -O,UI -0,01 0,12 0, I~ 0. I~} 0,1 I
8i.5-17,5 -U,Oi lU -0,03 -U.07~ 0,0~~ U,00 0,0( O,OI'~ U,21 0,2 0,14 (1,1~
KEY: -
A) North latitude, degrees
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Table 2
' Deviations of Mean Annual Air Temperature at Surface in Extra-Equatorial
Part of the Northern Hemisphere (Zone 87.5-17.5�N) frum Mean During Period
1881-1975
~ ! ~ I , ' 3 i 4 I ; I b I ; ' y I
t'~i.~~ i 0 , ~ j I ,
I
.
~ss~~ I ~_o. i.~ -o.~s -0.2~ -e.:~o ! -o.~o ~ _e.4s -o,a~ ~ -o.so ~ --o.~?a
i~~~u i- o, i;~ - 0.2; -~~,25 -~~.a~ -0,~4 _o. is -o, ts ' u.u,, _u. ' -o,o:;
i:wu ( t!.u~ U.03 --0.30 -u.2S -0.28 -U,32 ! -U,UB ' -U.3? , -0.16 ' -~~.1!~
191U ~--u,'?i -U,O6 -0,26 --0,'?1 O,Ut! : O.U4 --U,12 i-~~,s' -0,23 , -U,IU
192U ~-O.UI U.1 ~ 0.(~5 0,12 U,~19 , 0,1'i ~ 0,24 ! O, IIi ~ u.23 ~-0,1?4
I93G u,2~ u,29 0.20 -u,11 0,30 .(?,15 ~ u. t7 u.3~? n,;~3 . t~,33
I~-~U U,32 0,1~ 0,?6 0.35 0,3;3 0,07 ; U,18 ~ 0.2`.~ I U.2u (?,Ifi
19~0 0,0:, 0,2? (1,?1 ~~.41 I),12 i 0.09 I-0~ 12 0, I1 ' 0,22 ~ t),24
1960 U.21 I1,15 U.lt; U,13 -0,19 !-0.11 -U,Oi 0.1:~ - 0,(~5 I_~),~~t
KEY: 19i0 0.1~ -~U,Ot -0,2~1 u,17 U.1 I; U,14 i-U.12 ~ U, ' ~'~S
A) Years
In accordance with these recommendatians, in Fig. 1 for the five consider-
ed latitude zones of the northern hemisphere we have represented the sec-
ular variation of anomal.ies of the mean annual air temperature at the
surface. I:i addition, data on the mean annual air temperature at the sur-
face for the greater part of the norther.n hemisphere (zone 87.5-17.5�N)
are given in Table 2. In Fig. 1 and Table 2 the materials from the ar-
chives of the All-Union Scientific Research Tnstitute of Hydrometeorolog-
ical Information-World Data Center, relating to the period 1891-1978, are
supplemented by data for the periods 1881-1890 from (1].
Evaluat~.ons of the linear trend parameters far the mean annual surface tem-
pzrature for the princ ipal latitude zones of the northern hemisphere are
presented in Table 3. We use m to denote the number of years in time in-
tervals for which the angle coefficiei~t~ of the linear trend in �C/10 ~
years is evaluated, t�C is the mean value in this interval and p( % is the
r.elative contri.bution of the linear trend in the dispersion of the series
in the particular interval. The evaluation algorithm was described in de-
tail in [10).
On the left side of Table 3 we have given the recommended evaluations and
on the right side ane of the possible methods for piecewise-linear ap-
proxtmation of secular variation of air temperature at the surface in the
northern hemisphere.
An analysis of the evaluations for the extra-equatorial part of the north-
- ern hemisphere (87.5-17.5�N) shows that on the average for the period fr.om
1891 through 1978 about 20% of the dispersion of the series was attribut-
able to the positive trend.
After a more detailed examination of this series it can be concluded that:
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'0 '
1,5
1,0
0,5
0
-0,5 a7, S- 71,3'C. ut. :
N ~~,s `
-1,0 ~
,'0
,
-1,S
S
~
-?,0 ~
1
~ ~
J
J
~
7z, s- s~ s -~;3
0~5 ~-1,0
0 ' '
~ . ~
17,S-J7,S j
-0, 5
_i S
~
~ r
s' � s ~ -
' �~'C --,s
,
o '
a~,s-�s
n,s , , , ,
~ ~eeo 1690 1900 19f0 1920 ?9J0 1940 1950 ?960 1970 'S~0
Fig. 1. Secular variation of annual and five-year mean air temperature
anomalies (relative to the "norm" for 1881-1975) for different latitude
zones in the northern hemisphere. Correction system D.
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roR or~zcr.ai. us~ ~rn,Y
r
by the 1940's the intensive warming of the northern hemisphere which
had begun at the end of the preceding century had ended;
this warming was replaced by a cooling process which began in the 1940's _
and which ended in the 1960's;
since the mid-1960's tre changes in air temperature at the surface in
the northern hemisphere have been characterized by a positive trend of 0.1- -
0.2�C/10 years.
By combining the warming of the northern hemisphere during the last 10-15
years with the preceding cool ing, it is easy to arrive at the conclusion
that in the present period there is a continuation of the cooling which
began in the 1940's. In actuality, the evaluations of the linear trend
are negative for the periods 1946-1~75 and 1956-1975.
In this connection it aiust be noted that the authors evaluate the trends
only as a diagnostic procedure. In their opinion, the basis for any global
climatic predictions must not be a formal extrapolation of empirical data,
but an analysis of the physical mechanisms of climatic change.
By examining similar evaluations for the narrower latitude zones 87.5-72.5,
72.5-57.5, 51.5-37.5, 37.5-17.5�N we discover that:
the trend parameter ~ has the same sign for almost all the mentioned
latitude zones;
in absolute valiie the ~ evaluations reveal a clearly expressed tendency
to an increase from the low to the high latitudes.
Three evaluations of the parameter do not fit into these patterns. Two of
them for the intervals 1966-1975 and 1940-1964 for the zone 57.5-37.5�N are
not statistically significant because the linear trend for these periods
does not describe any appreciable part of the variability of the mean an-
nual air temperature at the surface. The third evaluation, relating to the
period 1969-1978 for the zone 87.5-72.5�N for this same reason has a low
statistical significance. Ho~ever, if we compare this period with the par- E
tially overlapping period 1966-1975 we discover an increase in the mean
air temperature values during these time intervals. It can be surmised
that a 10-year period is too short for a reliable determination of the lin-
ear trend sign for air temperature in the high latitudes.
In order to compare data published by different authors we will examine
evaluations of the trend parameter ~ for the mean annual air temperature
at the surface in the northern hemisphere for one and the same period 1964-
1975 (see Table 4). �
The first evaluation, based on the materials published in a study by I. I.
, Borzenkova, et al. [1], was obtained by M. I. Budyko and K. Ya. Vinnikov
[2] and was 0.31�C/10 years. The use of the refined primary data makes it
poss~ble to conclude that the real value of thie parameter falls between
0.28 and 0.15�C/year and is evidently close to 0.19�C/10 years.
9
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ruK urrl~iE~L u5t~ UNLIf
The use of data published in a study by Angell and Korshover [15] makes it
possible for mean annual conditions to obtain the evaluation 0.28�C/10
years, close to the first of the cited evaluations. The data of Yamamoto,
e al., presented in a study by Kukla, et al. [20], give the evaluation
0.12�C/10 years. Finally, tt~e materials published by Barnett give th~
least evaluation ~ = 0.07�C/10 years.
Evaluations of Linear Trend Parameter for Mean Annual Air Temperature aC ~
the Surface in the Northern Hemisphere for the Period 1964-1975
According to Data of Different Publications ,
_ Data source North latitude, � �C/10 years
Borzenkova, et al. [1] 17.5-87.5 0.31
Angell and Korshover [15] 0-90 0.28
Kukla, et al. [20] 0-90 0.12 :
Barnett [16] 15-65 0.07
This study
System of corrections:
B 17.5-87.5 0.28
C same 0.15
D same 0.19
All the evaluations cited above coincide in sign and their quantitative
differences can be attributed rather easily to the difference in the lati-
tude zones to which they belong. For example, the data of Barnett [16]
do not include the region of the high latitudes to the north of 65�N, where
the changes in air temperature at the surface are several times greater.
than in the low latitudes, as a result of which the ~ evaluation obtained
using his data are the lowest. The data of Angell and Korshover [15), re-
lating to surface temperature, are much inferior to the accuracy of the
data of Yamamoto, et al., cited in the study by Kuk1a, et al. [20]; the
latter evidently give the best evaluation for the entire northern hemi-
_ sphere. But the evaluation f3 = 0.12�C/10 years, according to the data of
Yamamoto, et al. for the entire hemisphere (0-90�N), agrees satisfactorily
with the evaluation 0.19�C/10 years obtained for the extra-equatorial
part of the hemisphere (87.5-17.5�N) according to the data cited in Table
2.
We also note the good correspondence between the materials in Fig. 1, per-
taining to the high latitudes of the northern hemisphere, and the data ob-
tained in a study by Walsh [28].
Thus, modern data characterizing modern changes in air temperature at the
surface in the northern henisphere virtually do not contradict one another, ~
and if its changes during the last 10-15 years are considered, it is dis-
cavered that during this period there was some warming of the northern
hemisphere as a whole, although unambiguous evaluations of the trends for
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i~~~r, ~~i~ t~ i r. i ni, i~:;i~: ~~Nt.~�
1966-1978, associated with the cooling beginning in 1975 in the zone of
the high latitudes, force one to exhibit care and refrain from categorical
conclusions~in the interpretation of the presented materials.
Evidently, due to the fact that the period of aerological observations is
relatively short and during this entire period there was a rapid improve-
ment of instruments and methods for obtaining information the data in the
� scientific literature on change in the global characteristics of the ther-
mal regime of the free atmosphere exhibit inadequate agreement. And the
differences no longer pertain to interpretation of materials, but the data
themselves.
The recent~changes in the mean temperature in the lower half of the tropo-
sphere, determined from the thiekness of the layer between the 500- and
. 1000-mb surfaces, are presented in the studies of Kukla, et al. [20J (mat-
erials obtained by Dronia), Painting [25] and Harley [~9].
_ An analysis of the data presented by Dronia in [20] show that the mean
temperature of the lawer half of the troposphere in the zone 35-90�N
is decreasing rapidly, beginning from the end of the 1950's, but in the
zone to the north of 65�N this decrease has slowed down or completely
stopped from the mid-1960's. Dronia does not discover any tendency to a
temperature increase.
The data of Painting [25] somewhat contradict the materials of Dronia. The
materials presented in [25] show that approximately from the mid-1960's ttte
tendency to a cooling changes to the opposite in the high latitudes of
the northern hemisphere (75, 80, 85�N). In the lower Iatitudes (50-60�N)
the cooling, beginning from the end of the 1950's, was continuing to the
mid-1970's.
Similar materials, relating to the extra-equatorial part of the northern
hemisphere for the period from 1949 through 1976, are presented in a
study by Harley [19]. These data show that on the average for the zone 25-
85�N the very intensive decrease in temperature in the lower half of the
troposphere, transpiring in the first half of the 1960's, in the mid-1960's
was replaced by a warming. This warming is clearly traced in the data for
the latitude zone 25-40�N. On the other hand, in the high latitudes (70-
85�N) Harley's data do not indicate any definite tendency to a change in
the temperature of the lower half of the troposphere for the period 19b5-
1976.
The contradictions in the data of Dronia, Painting and Harley cannot be re-
solved without a detailed analyeis of the measurement data used by the
authors and the methods used in their processing. '
As a more complete characteristic of the thermal regime af the atmosphere
in a hemisphere Starr and Oort [27] introduced a new parameter mean at- ~
mospheric temperature weighted by mags. In studies [27, 24] this tempera-
ture was computed for the periods 1958-1963 and 1968-1973. The first of
1i '
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rv~~ VPPLl.1NL uJ~ litvL7
these periods was characterized by a rapid decrease in the temperature of.
the entire northern hemisphere atmosphere by 0.6�C in 5 years. During
the second period the changes in temp~rature had a wavelike character in
the absence of an apparent linear trend.
Later Angell and Korshover [15] studied the change in mean temperature of `
the troposphere (the part of the atmosphere in the layer from the earth's
surface to the 100-mb surface) during the period 1958-1977 and drew the
conclusion that in the extratropical part of the northern hemisphere the
cooling noted in the first half of the period is continuing to the present
time, although on a somewhat lesser scale.
Everything saj.d above is evidence that at the present time the available
evaluations of change in air temperature at the surface in the northern
hemisphere are more reliable in comparison with the evaluations of change
in the thermal regime of the free atmosphere.
~volution of the Ice Cover in the Arctic Ocean in the Modern Period
Arc.tic sea ice is one of the most impartant links in the global climatic
system. ~
Recently steps have been taken in the direction of generalizing available
material on the distribution of ice in the Arctic Ocean for the gurpose
~f determining total ice content and analyzing its variabilitiy [6, 7J.
As a result it was established that from the beginning of the 1940's and
to the mid-1960's there was an increase in this ice contznt, amounting to
0.6 million square kilometers. Thereafter it:; decrease began and parallel
with this process there was an inerease in atmospheric temperature which
scme authors have been inclined to regard as the beginning of a long
epoch of warming, whereas others regard it as disruption of a normal cool-
. ing regime. _
The data on the basis of which conclusions were drawn concerning the natcire
of the changes in the area of the arctic ice cover during the last 30 ye:~rs
apply entirely t~ the three summer months: July, August and September. :~ue
to the fact that observations of the distribution of ice in a number af
regions in the Arctic Ocean began many years after culmination of the warm-
ing, and it is important to evaluate the change in the area of the ice
cover precisely from that moment, the research region was limited. This
region, with an area of ].0.9 million square kilometers (about 74% of the
area oE ttie entire ocean), included the Arctic basin proper and the Foll~w-
ing seas: Greenland, Norwegian, Barents, Kara, Laptev, East Siberian and
Chukchi. These circumstances, nr.!;urally, could not but cause questions can--
cerning the validity.of applying the conclusions drawn in general to in-
dividual years and the entire Arctic Ocean. -
Now we will make an attempt at generalizing and analyzing the available data
on. the development of the ice cover during the course of the entire annual
cycle and thus answer the first part of the question.
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1~Uh OFFCCIAI, l~til. t1NLY ~
106nrrZ
9,0- ,
m ~ The basis for the investigation
B,s ~ ~ ~ was primarily data from ice aer-
ial reconnaissanc~ surveys made
e,o- ~ ~ regularly in the marginal zone
es ; ~ of the ocean, beginning in 1946.
~ Unfortunately, the evaluation of
~ the accuracy of these data involv-
D~ o ' ~
~ ed great difficulties and for thjs
~ reason it was not do~e. Nevert-he-
~s ~ ~ less, they undoubtedly must be
e,0 I regarded as sufficiently reliable
p~ , for ~udging the trends in varia-
~s tions of ice area in the modern
; period. This is particularly cor-
~p ~ rect for the warm half of the
~ ~ ' year when the geographical posi-
~a ~ I tion of the boundary of the sea
~ ~ ice is surveyed with great detail
~
6,5 ~ ' - several times a month. Data on
the dietribution of ice in the
6,0 i Greenland Sea were taken from a
~p study by A. A. Kirillov and M. S.
~ ; i Khromteova~[9]. The authors used
' ~ all available data characterizing
6,s ! I the state of ice in this sea con-
tained in the Danish Ice Yearbooks
6,~ ~ , (period 1946-1962), in the ~ournal
~ I MARINE OBSEItVER (period 1959-1968),
s,s ~ ' and finally, on British maps of
ice conditions in the North Atlan-
e,s~ ID ; tic, the basis for which was ob-
servations from artificial earth
e,o ~ ~ satellites (period 1966-1977). In
, I ~ giving a general evaluation of the
~S ; ~ ; I data used in this study it must be
said that their rel3ability within
o,o ~og ~ ~ the year increases from winter to
i summer, but within the investigated
75 ~ period from its beginning ~o the
f9JS 1945 1955 1963 1975 1985 end .
Fig. 2. Changes in area of ice cover FigurP 2 shows the long-term vari-
of Arctic Ocean in individual months ation of area of the ice cover in
and as average for year. Thick curves the Arctic Ocean during the course
result of five-year moving averaging. of Marcli, June, July, August, Sep-
tember, December and as an average
for the year. Each of the cited
- monthly curves is characteristic
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, v~. vr, ~..xn., uoc, virLi
for its season, but taken together they give a fu11 idea concerning the
intra-annual characteristics of long-term changea.
]D6 MH~
i, ~
6,5
" I
~i -
6,a , i
~
1915 1935 19f5 '955 .`.�6~5 1975
_ Fig. 3. Change in area of ice cover in Arctic Ocean in second half of Aug- _
ust. For annotations see Fig. 2.
We note that the nature of the long-term changes in area of the ice cover
within the year for the most parti remains constant. After a period of
lessened ice content in the n;:id-1950's the ice area begbn to increase and
ir~ 1967 attained maximum values during the entire investigated period. In
the late 1960's the area of the ice cover began to decrease. This process
also continued in the 1970's. As a result, the extent of the ice cover in
the Arctic Ocean approached close to that which was observed prior to its
expansion.
~ The conclusions drawn by V. Yu. Vise [3] concerning the scales of change
in the area of occurrence of arctic ice during the warming epoch were
based, as is well known, on data on the ice conteut of arctic seas, in-
cluding an earlier period 1924-1939. In discussing these data, the author
mentioned their low quality and the extremely approximate nature of the
] evaluations obtained using them. Nevertheless, it would be incorrect to-
day, under condj.t~ons of increasingly recognized need for studying pro-
longed trends in the development of natural conditions in the past, to
ignore these data completely, without making use of them in the anatysis.
Despite shortcomi7gs, it must be admitted that they give a true idea can-
cerning the priiicipal tendencies in development of the ice cover in the
1920's and 1930's. This is confirmed by numerous types of evidence con--
cerning the behav~or of other environmental elements during this period.
It is therefore desirable to supplement the data of V. Yu. Vize and ~btai.n
a picture of continuous evolution of the .'~ce cover in the course of the
l.a~t 50 years. This picture is presented in Fig. 3.
It can be seen that the area of the ice cover in the course of a half-cen- ~
tury has experienced considerable changes. The curve of five-year moving
averages from the end of the 1920's drops steeply downward; in the 194~'s
and in the first half of the 1950's it does not exhibit any significant
tendencies and then moves upward. As indicated by V. Yu. Vize, the reduc-
tion in the area of the ice cover in the first stage was abo;it 1 million
square kilometers. An expansion of the ice cover in ~he I950's and 1960's
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resulted in an increase in the area by 0.8 million square kilometers,
that is, almost reduced to zero the prPCeding improvement in ice condi-
tions. In the years which followed the area of the ice again began to de--
crease and by the middle of the 1970's had decreased by 0.4 million sqLa_re
kilometers in comparison with the maximum in the 1960's.
It is interesting to know whether the curve reproduced in Fig. 3 reflects
the nature of the change in the mean annual area of the ice cover in the
Arctic Ocean or whether it is correct only for August. A positive answer
to this question would make it possible to ~udge the nature of the long-
term changes in t.he mean annual area of the ice cover on the basis of reg-
ular observations in one of the summer months.
For this purpose we evaluated the correlation between the mean annual and
August ice areas in the investigated region. The result was entirely sat-
isfactory: the correlation ce~fficient was 0.82. The presence of correla-
tion with such a coefficient can serve as an adequate basis for drawing
the conclusion that the curve shown in Fig. 3 correctly reflects the main
characteristics of the long-term variability of the mean annual area of
the ice cover. Taking this into account, an attempt was made to determine
the mean annual extent of the ice cover in the mid-1920's on the basis ~f
the August ice content. This extent was close to 8.2 million square kilo-
meters. Figure 3 shows that by the mid-1950's the extent had decreased
to 7.6 million square kilometers. It musC also be noted that the carrela-
tion coefficients characterizing the closeness of the correlation between
the mean annual area of the ice and its area in other months were approx-
imately the same as for August. This makes it possible, with a greater as-
su~ance than before, to apply the conclustons drawn on the basis of sea-
sonal or monthly data concerning prolonged tendencies in the development
of the ice cover to the entire year period.
The striving to esamine the sea ice cover as a whole for the Arctic Ocean
or for the entire hEmisphere inevitably res~sl.ts in a loss of part of the
valuable information: the volume of the useful material will be determin-
ed by the length of the shortest series of observations taken into account
in reckaning total ice content. Nevertheless, comparing the data presented
above on the change in the area of polar sea ice in the Arctic Ocean, the
preliminary estimates of the total quantity of palar sea ice in the north-
ern hemisphere made at the Arctic and Antarctic Scientific Research Insti-
tute and similar data published by Sanderson [26] and Walsh [29], we dis-
cover that all these materials indicate that a general characteristic of
the development of the arctic ice cover during recent years was its con-
traction.
BIBLIOGRAPHY
1. Borzenkova, I. I., Vinnikov, K. Ya., Spirina, L. P., Stekhnovskiy, D.
I., "Change in Air Temperature in the Northern Hemisphere During the
Period 1881-1975," METEOROLOGIYA I GIDROLOGIYA (Meteorology and Hy-
drology), No 7, 1976.
I5
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- . va? ~a ? a.~ii[~u V?L V~~L?
2. Buclyko, M. I., Vinnikov, K. Ya., "Global Warming," METr,OROLOGIYA I
GIDROLOGIYA, No 7, 1976.
_ 3. Vize, V. B., OSNOVY DOLGOSROCHNYKH LEDOVYKH PROGNOZOV DLYA ARKTICHESK-
IKH MOREY (Principles of Long-Range Ice Forecasts for Arctic Seas),
Mosco~w, Izd-vo Glavsevruorputi, 1944.
4. Vinnikov, K. Ya., "On the Problem of the Method for Obtaining and In-
terpreting Data on Changes in Air Surface Temperature in the Northern
Hemisphere During the Period 1881-i975," METEOROLOGIYA I GIDROLOGIYA,
No 9, 1977.
5. Gruza, G. V., Ran'kova, E. Ya., DANNYYE 0 STRUKTURE I IZMENCHIVOSTI
h'I.IMATA. TEMPERATURA VOZDUKHA NA UROVNE MORYA. SEVERNOYE POLUSHARIYC
(Data on the Structure and Variability of Climate. Air Temperature at
Sea Level. Northern Hemisphere), Obninsk, 1979.
6. Zakharov, V. F., "Cooling of the Arctic and Ice Cover of Arctic Seas,"
TRUDY AANII (Transactions of the Arctic and Antarctic Scientific Re-
search Institute), Vol 337, 1976.
7. Zakharov, V. F., Strokina, L. A., "Recent Changes of the Ice Cover of
the Arctic Ocean," METEOROLOGIYA I GIDROLOGIYA, No 7, 1978.
KART~' aTKLONENIY TEMPERAiURY VOZDUKHA OT MNOGOLETNYKH SREDNIKH SEVER-
NOGO POLUSHARIYA (Maps of Deviations of Air Temperature from Long-Term
Means for the Northern Hemisphere), Nes 1-4, GGO, 1960-1967.
9. Kirillov, A. A., Khromtsova, M. S., "Long-Term Variability of tha Ice
Content of the Greenland Sea and a Method for Its Prediction," TRUDY
AANII, Vol 303, 1971.
10. Polyak, I. I., METODY ANALIZA SLUCHAYNYKH PROTSESSOV I POLEY V KLIMAT-
OLOGII (Methods for Analysis of Random Processes and Fields in Climat-
ology), Leningrad, Gidrometeoizdat, 1979.
11. Rubinshteyn, Ye. S., STRUKTURA KOLEBANIY TEMPERATiJRY VOZDUKHA I~TA SEVER-
NOM POLUSHARII (Structur~ of Variations of Air Temperature in the
Northern Hemtsphere), Part I, 1973, ~'art iI, 1977, Leningrad, Gidro-
meteoizdat.
12. SINOPTICHESKIY BYULLETEN'. SEVERNOY~' ~OLUSHARIYE (Synoptic Bulletin.
Northern Hemisphere), 1961-1978, Gidromettsentr SSSR-VNIIGMI-MTsD, Ob-
ninsk.
_ 13. Spirina, L. P., "Secular Variation of Mean Air Temperature in the
Northern Hemisphere," METEOROLOGIYA I GIDROLOGIYA, No 1, 1962.
14. Angell, J. K., Korshover, J., "Esti~r~ate of the Global Change in Temper-
ature, Surfac~ to 100 mb, Between 1958 and 1975," MON. WEATHER REV.,
Vol 105, No 4.~1977.
16
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1 15. Angell, J. K., Korshover, J., "Global Temperature Variation, Surface-
100 mb: an Update Into 1977," MON. WEATHER REV., Vol 106, No 6, 1978.
16. Barnett, T. P., "Estimating Variability of Surface Air Temperature in
the Northern Hemisphere," MON. WEATHER. REV., Vol 106, No 9, 1978.
17. Brinkman, W. A. R., "Surface Temperature Trend for the Northern Hemi-
- sphere Updated," QUATERN. RES., Vol 6, 1976.
18. Callendar, G. S., "Temperature Fluctuations and Trends Over the Earth,"
QUART. J. ROY. METEOROL. SOC., Vol 87, No 371, 1961.
19. Harley, W. S., "Trends and Varfations of Mean Temperature in the Lower ~
Troposphere," MON. WEATHER REV., Vol 106, No 3, 1978.
20. Kukla, G. J., Angell, J. K., Korsho~~:r, J., Dronia, H., Hoshiai, M.,
Namias, J., Rodewald, M., Yamamoto, R., Iwashima, T., "New Data on
Climatic Trends," NATURE, Vol 270, No 5638, 1977.
21. Landsberg, H. E., Groveman, B. S., Hakkarinen, I. M., "A Simple Method
for Approximating the Annual Temperature of the Northern Iiemisphere,"
GEOPHYS. RES. LETTERS, Vol 5, No 6, 1978.
22. Mitchell, J. M., "Recent Secular Changes af Global Temperature,"
ANNAL~ OF THE NEW YORK ACADEMY OF SCI., Vol 95, Article 1, 1961.
23. Mitchell, J. M., "On the Worldwide Pattern of Secular Temperature
Change. Changes of Climate," ARID ZONE RESEARCH, XX, UNESCO, Paris,
1963.
24. Oort, A. H., "Structure of Atmospheric Variability on a Global Scale,"
SYI~OSIUM ON THE STRUCTURE OF THE PRESENT CLIMATE AND ITF VARIABILITY,
Leningrad, USSR, 1977.
25. Painting, D. J., "A Study of Some Aspects of the Climate of the North-
ern Hem~.sphere in Recent Years," METEOROL. OFFICE SCIENTIFIC PAPER,
No 35, London, Her Ma~esty's Stationery Offic~, 1977.
26. Sanderson, R. M., "Changes in the Area of Arctic Sea Ice 1966 to 1974,"
METEOROL. MAGAZ., Vol 104, No 1240, 1975.
27. Starr, V. P., Oort, A. H., "Five-Year Climatic Trend for the Northern
Hemisphere," NATURE, Vol 242, No 5396, 1973.
2$. Walsh, J. E., "The Incorporation of Ice Station Data into a Study of
Recent Arctic Temperature Fl~xctuations," MON. WEATHER REV., Vol 105,
No 12, 1977.
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i~ui< ui~ r~~: i ni, u;,i~: ~?vi.v
29. Walsh, J. E., Johnson, C. M., "An Analysis of Arctic Sea Ice Fluctua-
tions 195:-1977," J. PHYS. OCEANOGR., Vol 9, No 3, 1979.
30. Willett, H. C., "On the Present Climatic Variation. Centenary Pro -
ceedings. Roy. Meteorol. Soc., 1950.
31. Willett, H. C., "Do Recent Climatic Fluctuations Portend an Imminent
Ice Age?" GEOPHYS. INT., Vol 14, No 4, 1974.
32. Yamamoto, R., Iwashima, T., Hoshiai, M., "Change of the Surface Air
Temperature Averaged Over the Northern Hem#sphere and Large Volcanic
Eruptions During the Years 1951-1952," J. METEOROL. SOC. JAPAN, Vol
53, No 6, 1975.
18
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UDC 551.509.3
SOI~IE RESULTS OF JOINT SOVIET-POLISH INVESTIGATIONS IN THE FIELD OF
NUMERICAL SHORT-RANGE FORECASTING OF METEOROLOGICAL ELII~NTS
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 6, Jun 80 pp 18-26
[Article by Candidates of Physical and Mathematical Sciences B. M. I1'in
and L. V. Rukhovets, Doctor J. Parf iniewicz, G. A. Kobyshev and J. Nemec,
Main Geophysical Observatory and Institute of Meteoro?ogy and Water Man-
agement Polish People's Republic, submitted for publication 30 October
~ 1979]
[Text] Abstract: A study was made of problems relat-
ing to improvement of a model of short-range
numerical forecasting used by the Main Geo-
physical Observatory. Theae improvements are
a result of joint investigations carried out
at the Main Geophysical Observatory and at the
Institute of Meteorology and Water Management
� by way of bilateral cooperation between the
USSR State Committee on Hydrometeorology and "
the Hydrometeorological Service of the Polish -
People's Republic. The article gives a brief
description of a new three-parameter model.
Test results indicated that the success of pres-
sure field predictions for 24 and 48 hours under
the new model is substantially higher than when
using the Main Geophpsical Observatory model.
Investigations carried out at the present time within the framework of
direct cooperation between the USSR State Co~ittee on Hydrometeorology
and the Hydrometeorological Service of the Polish People's Republic, in
addition to other work, provide for ~oint work in the field of numerical
~ short-range weather forecasting. Some of this work is related to i~-
provement of the short-range forecasting model developed at the Main Geo-
physical Observatory, employed in the routine practice of some prognostic
centers of the USSR State Committee on Hydrometeorology. This same model
~ is the operational model used by the forecasting service of the Polish
People's Republic.
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r~x Urrlt,tA1, u5~: ~NLY
Without dwelling in detail on a description of the Main Geophysical Observ-
atory model [lJ, we will note only its principal features. Two fundamental
ideas were used in the model. The first of these (belonging to M. I. Yu-
din) is use of the base of eigenfunctions of a 1 inearized differential op-
erator of a prognostic equation ~ointly with the base of empirical ortho-
gonal functions. This idea served as the basis for the quasigeostrophic
forecasting model with few parameters developed in [6J. Recently this
same idea was used in [5] i.n developing a model with few parameters tn full
equations.
Beginning in 1964 a model with few parameters has been used in the routine
praccice of the Northwestern Administration of the Hydrometeorological Ser-
vice ([3]). The second idea (belonging to I. Z. Lutfulin), serving as the
basis for the Main Geophysical Observatory model, is the use of data on
the three-hour surface pressure trends for the purpose of refining the
surface field forecast. This idea was used in [2] for creating first a
two-level model of a forecast and then for forecasting the surface field
~ in a model with few parameters. Such a combined model already for more
than 10 years has been used in the operational practice of the Northwest-
ern Administration of the Hydrometeorological Service, and in recent years,
after some improvements made by A. B. Simanovskiy, this model has been in-
cluded in the BTGMTs (Baltic Territorial Hydrometeorological Center), Mur-
mansk and some other administrations of the State Committee on Hydrometeor-
ology. Since 1974 the Main Geophysical Obser.vatory model has been used in
the operational practice of the Institute of Meteorology and Water Manage-
ment of the Polish People's Republic.
In 1978 the Central Asian Regional Scientific Research Hydrometeorological
Institute carried out comparative tests of a number of models used in the
operational practice of the State Committee on Hydrometeorology [4J. These
tests indicated that the Main Geophysical Observatory model gives better
results than other models in the prediction of the surface field. With re-
spect to the quality of forecasts of high-altitude charts, here it is dif-
ficult to give preference to any one model; several models have virtually
identical eval �ations for the probable success of forecasts. At the same
time, the Main Geophysical Observa[ory model is extremely economical both
with respect to computation time and with respect to the volume of the
necessary computer memory. This is attributable to the fact that the Main
Geophysical Observatory model involves the use of two parameters and for.
computation of the predicted fields at sia levels in the atmosphere it is
necessary to have approximately an equal memory an~l computation time as in a
similar two-level ~�aodel. Accordingly, the Main Geophysical Observatory model
can be used at forecasting centers not having high-capacity electronic com-
puter.s. In particular, it is easy to use with the M-220 and Minsk-32 elec-
tronic computers.
However, for centers having higher-capacity electronic computers (such as
the BESM-6) the economy factor is no longer so significant. However, the
use of only two parameters for the purpose of economy is naturally reflected
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in the accuracy of the resulting forecasts. Accordingly, in the ~oint in-
vestigations~made at the Main Geophysical Observatory and the Institute
of Meteorology and Water Management specialists have developed a three-
parameter model [8, 9). In this model a third parameter has been added;
like the other two it is an eigenfunction (vector) of a linearized opera-
tor, differentiated in the vertical coordinate, entering into the prognos-
tic equation. In addition, as in the two-parameter Main Geophysical Ob-
servatory model, the right-hand sides of the prognostic equation, ea-
pressing the nonlinear terms, are represented by empirical orthogonal func-
tions. The changeover from the eigenfunctions of the differential operator
to empirical orthogonal functions is based on the least squares method with
use of information on the vertical statistical structure. It can be assum-
ed that this changeover stage introduces definite errors into the results.
Accordingly, it was decided that in the model no use be made of the base
of empirical orthogonal functions and that a model would be formulated
which makes use only of the eigenfunctir~ns of the mentioned differential
operator.
' As the initial equations of the model we will use the equations for vortic-
ity and heat influx in quas igeostrophic and adiabatic approximations:
v"-4-}-lA�=l= a~~ , (1)
. a9 + RAT d:
~ W= 0. (2)
.
Here ~ is geopotential,
' Po '
p is pressure, pp is standard pressure at the earth, `
dq d ' ~
- dt ' q - pt '
2~ sin~ is the Coriolis parameter,
d, _ ( YQ Y) R= T
g(9
is the statistical stability parameter, being a function only of the ver-
tical coordinate, T is t-.emperature, R is the gas constant,
A_, J~~, o~ 2); A T= R~ J(~, a~
. ~
a.- + y= ~ ~~A~ B~ ~ aX oa _ a~a a~,a
�
The vertical boundary conditions are:
W-~ when ~=0, (3)
w=~ 9-' g~ Werror when 7i = 1- 8, ~4 )
P~, Po
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rvn Vrr t.~Lr~i. U~ts UIVLT.
where ~ is air density, ~ is the thickness of the boundary layer, werror
is the vertical velocity at the upper boundary of the boundary layer.
~
After replacement of the vertical derivatives by finite differences i~ a
system of equally spaced points of intersection with the interval
0.075 (~~~2 = 0, ~ 1= 0.075, S1 1/2 = 0.15, I 2= 0.225, S 2 1/2 = 0.3,
~ .975) and use of the Fourier method we obtain a system of equa-
tions for the eigenvectors ~ ;
X i= 4 Xlk qk'
k~l
,~~i ~ /.i.kr - Fj ~l = ~ ~ . . ~ ~ ~5~ -
Here ~
e
F~ x'r (,~1 i~ RA~ j C~~ i 1+~ aj, l~j) lA: (:~l -
r. ~ ~ - 1
(6)
~~p~~
0,45 po Werror~
~
where
, ,i i for j= 1, 2, 3, 4;
( ~ r 2 Q xt~ ~ ~ Q~ '~~~T~
J+~,- 1-ry
z'r ) - 5 ~x~ r - Xr s - x~ ; ~~3)rd~~~
x~ ( ;6 ) _ (8 .rj - - 3 x; - ~i di;~
r ~ �
" a~, ,1=-x~
"~r~ j ~OT 1, 2~
~ i are the eigenvalues, xi~ are the cou~ponents of the eigenvectors, repre-
sented in Table 1, d~.~.1~2 are the values of the statistical stability para-
meter in the layer ( ~�+1), computed on the basis of climatic data.
These values, taken ~rom [6~, are cited in the last column of Table l.
The values of the coefficients pL T( ~ i+ 1/2~ are given in Table 2.
In order to obtain the initial values of the Xi parameters, using the val-
ues of the heights of the isobaric surfaces 200, 300, 500, 700, 850 and
1000 mb, we employ information on the statistical structure of the vertical
geopotential profiles.
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TaU1 e 1.
Values of Components of Eigenvectors xi~, Eigenvalues a y and Statistical
' Stability Parameter d~ + 1/2
y'poeeH~, ~ I d~ t
.s~6 z, ~ .r�: ~ xs ~ .r, ~ x�, ~ ~ .r.~ ~ .r; ~
- Level, mb ~ ( ~ lu-~=.~r
75 O,~ti 0,3~ti 0,146 -0,016 -U,U01 -O,U00 -0,000
225 U,4U!~ -(),l~J~# --0,854 0,~334 U,078 -(1,01~! 0,001 !.3
:375 0,390 -~0,223 -O,ill -O,G9�i --Q,c~ti9 0,199 -O,U`?3 O,~i
525 f1,368 -U,245 O,l2i -0,354 U,;:~iG -U,632 U,136 U,;i
~i75 O,:i.i8 -Q,25i U,264 9,U91 U,~4:3 0,712 --0,435 U,6
975 0,1'?5 -O,U95 0,129 0, l~ t-Q,208 -U,12i -0,~461 U.~3
~ l0'=.K-~ 0, Itil U,3 it 5,251 16,217 ,937 80,~102 132,585 I,~~
Table 2
Values of Coefficients ~i r( ~ 1� In~:
r
.
'1 1
t
I50 ~ 300 I 450 I 600 I i74 ~ 9~0
~ -0.083 -O.Oi2 -0,072 -0.06i -O,Ofi7 -0,06~
-0,733 -0,323 -Q,150 -0,060 --O,Olri -0,0�8
3 --0,769 1.858 1.~428 Q.913 0.~l5Q U.U3i
4 0,2Ei9 -0,5; 3 ?,046 2,967 ?,079 0,~l2U
5 O,U61 -1,618 6,870 -0.887 -0,~423 -1,338
6 -0,011 0,533 -~}.986 8.960 -0.?8;1 -2,917
7 0,001 -0,060 0,95~4 -3,807 8,~85 -g,g32
Table 3 gives the factors for conversion from the geopotential values for
the mentioned isobaric surfaces for conversion to the Xi values obtained
by the least squares method.
For conversion from the Xi values to the geopotential values at standard
levels an inverse matrix i~ employed. This conversion is accomplished at
the end of the forecast for obtaining the prognostic values at standard
levels.
On the right-hand sides of (6) the vertical derivatives are represented by
f inite differences, after which in place of ~i, entering under the signs of
the horizontal differential operators, we introduce the X~ values with the
23
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coefficients cited in Table 3. We will limit ourselves to the first three
vectors (corresponding to the three minimum eigenvalues).
Finally, the difference equations in a grid with a 300-km interval, serving
for determination of the three parameters X1, ~2, X3,assume the following
form:
9
X, - 1,449 � 10-=' X, ~ 1~ (0,206 Js (X� X:) -
-0,258 Je (�~'i, a -{-0,634 J6 (a'2, �l':~) -
-1,067 J6 (.l',. .~5 �a~i)-O,169 Je (-~~i, c~k �~~s) +
-}-~,024 Je I, ~B ~3~-1,2~7 ~6 1~2~ a8 .~y~-
-0,169 J6 ~!e ,1,)-0,066 Js (as, ~a ~~a) +
-}-0,024 1s (~t~s, 9e ,l' ~ ) -0,06C Js (~'s, .~s ~ s ) -
1,028 J~, (h,s ~~X~)) - o,o2s ~a',. 1~') +
] 0-3 (-4,028 X,-{-0,062 aB ~"2-0,085 ~8 .t 3) ;
X, - ~,704 � 10-~~ X~ - ~o-~
~ (1,8`?9 J,: (,1',, ,Y_,) -f-
-~-Q,C22 .~6 I. ~3~ T3,~fl3 ~g ~.~q~ ~3~'-
-0,169 Js (a',, ~~e Xi)-1,2071s (Xi~ r~e �k~:)-
-~,066 f6 1'k l, ~8 ~ 3~ - 1 ~`Z~7 ~6 IX4, .~'8 X1 ~
-1,367 ./e (Xs, ~a ~'z) -0,383 !6 {Xs, t1s ~'s) -0,066 J6 (X3, ~a X, ) -
. - 0,3~3 J, ,t'; 0,303 J a'_, ~ X)_ o.o?ti / x., 1=~~ +
, ~ ) t- e~ i h y~ ~ i, ~ r
_ T~Q-3 ~n,~~2 ~g l ~--~,~~7.~5 ~,2~{'~,~64 !~p i13~ r
X ; - -~,72F � 10-' .~1'~ = ~~l ~ 0,012 J~; I~,,
+ 11,K48 Js (1~~, .l's) --3,213 J6 (Xs, :1'~) -}-0,024 J~ (X OK ,1'~ ) -
-0,06C J6 (,t~,, ~e .~'I)-1.028 Js '~e ~~as 0.99 and
the standard deviation of the experimental points from the correlation line
was ~1g y = t0.13.
The formula for determining the value in accordance with the graph in
Fig. lb has the form
0,:,1 D'.s e= ~ 100 - r) 10'
(3)
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l~o~t ~FFZCr.nL usr: orr~Y
where ~ is the mean long-term monthly duration of falling of precipitation
(in hours); D is tha mean number of days with precipitation during the
month; e is absolute air humidity, mb; r is relative humidity, X; t is
air temperature, �C, the mean long-term values during this same month;
pG and ~ are constants; oL =-0.355, ~_-0.0699.
t~ 4
20d~ " .
~ ~
. . ~ '
~son ' P x
.
. ,
� v � � ~ %
� . ,!1 D 2
1000 ~ ' ; S 1
~
~ ' ~ -10~ �60 -10 0 10 6Q ~
S00 a. '
' ~1
hours
0 S 00 f000 1500 r, v
Fig. 2. Comparison of actual ~act and Fig. 3. Probability distribution
computed 'Ccomp values of annual precip- curves Py of monthly values A=
itation duration. 1) USSR, 2) Indonesia 'G ~o~p -'Gact~ ti act 100X in
10% intervals of these values.
1) USSR; 2) Indonesia
It should be noted that in different publications the number of days with
precipitation means different things. Depending on the accuracy with which
precipitation is measured in different countries and the form in which
- these data are published, this may refer either to the number of days with
a quantity of precipitation 0.1 mm or 7 0.01", that is, ~ 0.25 mm, or
even ~ 1.0 mm. In formula (3) the value D? ~.1 ~ is used and when em-
ploying other D values they must first be reduced to the necessary value.
1'he method for performing such a reduction is given in [1].
Formula (3) was checked for the purpose of determining the accuracy of
the'~ values computed from it; this was done on the basis of independent
material using data from 54 stations in the USSR not employed in construct-
ing the graph in Fig. 1. In addition, the formula was checked using data
for 18 stations in Indonesia, which publishes information on the duration
of precipitation registered using a pluviograph [3J. Since the precipita-
tion in this region is usually very heavy, its duration according to
pluviograph data virtually does not differ from the visual observations
and it can be used for the checkin~ of formula (3). Unfortunately, it was
impossible to find any other published data on the duration of precipita-
tion and therefore we had to be content only with the mentioned data.
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r~n urrl~.lrw uaG uivLt
Figure 2 shows the results of comparison of the actual "~!act and computed
(using formula (3)) comp aranual durations of precipitation for both the
Soviet Union and Indonesia. The standard deviation between 'Cact and 'Ccomp
in this case should be characterized by the value
� ^c r - t~' lU0
~ ~ ( 4 )
=1, n_i ,
/
which for the USSR was Equal to �21%, and for Indonesia �24%. The some-
what greater value for Indonesia is attributable to the limited stat-
istical sample and the lesser accuracy of the initial parameters the
numbers of days with precipitation and the air humidity characteristics.
The accuracy in computing the monthly values of the duration of precipita-
tion is characterized by Fig. 3, which gives the probability distribution
curves for the values A= '~~omp -~act~ ~act 100%, computed for each
month for the same stations in the USSR and ~ndonesia. (I~t is infeasible
to construct such curves for the annual '~comp values due to the smallness
of the sample.) The curves presenCed in Fig. 3 indicate that the error in
computing the monthly values of the duration of precipitation using formula
(3) in 70% of the cases is not more than 30% both for the USSR and for In-
donesia.
Thus, formula (3) makes it possibie to obtain the computed values of the
mean long-term monthly and annual durations of precipitation with an accur-
acy of f30% and t(20-25)%, having data only on the number of days with pre-
cipitation, on air temperature and humidity, and in case of necessity
also on the precipitation sum. These data are represented sufficiently com-
pletely in the world reference literature for the entire territory of the
land (except, perhaps, for Antarctica). Accordingly, it seems possible to
compute the monthly and annual durations of precipitation and map them on
a planetary scale. In addition, after obtaining maps of the duration of
precipitation and after constructing a world map of the annual sums of pre-
cipitation [5~, for the f irst time it will be possible to obtain a map of
the mean annual intensity of pre~ipitation for the entire territory of the
land.
BIBLIOGRAPHY
1. Bogdanova, E. G., "Computation of the Number or Days With Precipitation
of Different Gradations," TRUDY GGO (Transactions of the Main Geophys-
ical Ubservatory), No 404, 1978.
2. Drc~zdov, 0. A., "Duration of the Falling of Precipitatiun as a Climatic
Characteristic," TRUDY 2-go VSESOYUZNOGO GEOGiir'1FICHESKOGO S"YEZDA
(Transactions of the Second All-Union Geographical Congress), Vol 2,
Moscow, Geograf izdat, 1948.
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, -
3. KLIMATICHESKIY SPRAVOCHNIK ZARUBEZHNOY AZII (Climatic Handbook of For-
eign Asia), Leningrad, Gidrometeoizdat, 1974.
4. Lebedev, A. N., PRODOLZHITEL'NOST' DOZHDEY NA TERRITORII SSSR (Dura-
tion of Precipitation Over the Territory of the USSR), Leningrad,
Gidrometeoizdat, 1964.
5. MIROVOY VODNYY BALANS I VODNYYE RESURSY ZII~I (World Water Balance and
the Earth's Water Resources), Leningrad, Gidrometeoizdat, 1974.
6. SPRAVOCHN~K PO KLIMATU SSSR. CH. II I IV, VYP 1-34 (Handbook of USSR
Climate. Parts II and IV, Nos 1-34), Leningrad, Gidrometeoizdat, 1965-
1970.
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I ~/1\ \JI i' 1~~ ~ 111.� IIJ~i llltl~l
UDC 551.513.1
MODEL INVESTIGATION OF THE GLOBAL MEAN ZONAL THERMAL REGIME OF THE
EARTH'S ATMOSPHERE
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 6, Jun 80 pp 38-48
[Article by Doctor of Physical and Mathematical Sciences I. L. Karol` and
_ V. A. Frol'kis, Main Geophysical Observatory, submitted for publication
24 September 1979]
[TextJ Abstract: The article presents a semiempir-
ical simplified model of the thermal regime
of the atmosphere belonging to the Budyko- ,
Sellers class of models. A study is made
of the relative influence of the northern
and southern hemispheres and the effect of
exclusion of horizontal transfer. An allow-
ance is made for the change in the vertical
distribution of temperature and the latitud-
inal change in the temperature of ice forma-
tion and their influence on the model regime.
Numerical experiments were carried out for
studying the effect of a change in the solar
constant on a model climatic system.
1. In the investigations of changes in climate carried out at the present
time by use of so-called semiempirical models, based on the equations
for heat balance of the earth - atmosphere system, a study is usually
made of the thernial regime of one isolated hemisphere (usual.ly the north-
ern hemisphere) and no allowance is made for interaction between the
northern and southern hemispheres [2, 10, 11, 13]. However, the differ--
ences in the mean characteristics of the radiation and dynamic factors
forming the climat~ of these hemispheres and the relationship of their
temperature distributions (deviation of the mean annual thermal equator
from the geographic equator) are well known. Accordingly, it is important
to take into account this difference of the hemispheres in the parameters
of a model and include the thermal relationship between the hemispheres
in the model, and also trace how this difference in the reaction of the
model thermal regiide is reflected in the change of an external factor (the
solar constant Sp).
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In this article we present some results of such an investigation for a
variant of a model close to the Sellers-North model [10, 11, 1 3] in whi.ch
use was made cf several meridional distributions of radiation factors
which differ somewhat from one another. The response of a model tempera-
ture regime to these differences is e~camined, as well as the effect of the
influence of the meridional temperature gradient in the atmosphere at the
mean level T on the intensity of heat transfer between the tropical and
polar zones. For evaluating the role of this heat transfer we computed the
distributions of radiation-equilibrium temperature with the exclueion of
heat transfer, which are compared with the principal distributions with
these same values of the solar constant S~. An attempt was also made to
take into account the influence exerted on the model regime by another
inverse relationship: the dependence of T and the temperature of the sur-
face layer of the atmosphere TO on T, reflecting the change in the ver-
tical distrit+ution of temperature and not taken into account, for example,
in [3].
2. Following [3], we will use the heat balance equation at the level z
~ H-rF =-c c T' �r (1)
oz ( ) p,c(KC ) ~
where H and F are the vertical macroturbulent and radiant heat fluxes (pos-
itive, if directed upward), cp = 0.24 cal/(g��C) is the heat capacity of
the air at a constant pressure, P[g/m3) is air density, K[m2/sec] is the
coefficient of macroturbulent thermal conductivity in the horizontal
plane, is the two-dimensional first-order ~perator, T' is air tempera-
ture, r is the flux of latent heat.
Equation (1) describes the steady mean annual temperature distribution.
The heat transfer is parameterized by macroturbulent heat exchange.
Following [3J, we integrate (1) for the entire thickness of the atmosphere:
_ (H + F): _ ~ - (H + F):-~, = c (7c T) + R~~ ~2~
where p�
T= ~ ~ T'dp
Po ~ (3)
is the temperature of a vertical column of the atmosphere of a unit cross
section averaged for pressure; p~ = 1000 mb is surface pressure,
R, _ ` rdz, ; = cp PuK g~ ; _ .tit-!c�. sec
~4 )
D=(H~--F);_o-(N+F)~_x rR, '
is the total heat influx to a vertical column of the atmosphere of a unit
cross section.
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r~~ vrrl~lew UoG vtvLi
We will express (H+F)Z=~ through the heat balance equa~ion for the under-
lying surface:
(H F):_o , k: Ci = ~l, (5)
where G is the flux of " evident" and R2 is the flux of latent heat into the
soil. At the upppr boundary of the atmosphere
(/~1:= m = 1) (6)
and there is satisfaction of the radiation balance of the earth-atmosphere
system
- S F)r=:: = 5 ~ l - - x~,) -
(7)
where S is the flux of solar radiation at the upper boundary of the atmo-
sphere, I is the flux of outgoing long-wave radiation, ~ p is the albedo
of the earth-atmosphere system.
Substituting (5)-(7) into (4), we finally obtain
c(~cT)=-~~. D=St1-z~)-~+(R~-R.~-r. ~s)
Henceforth we will assume that all the fields are zonally homogeneous.
The outgoing thermal radiation I, according to Budyko [2], is a bilinear
ft~nction of the surface temperature TD (in �C) and the tenths of effec-
tive cloud cover n.
f-/~ To~ 1~ = x, - x~ n, r= 6, - b: n,
(9)
where n is clou~i cover in fractions of unity (in tenths), al, a2, bl, bZ
are empirical coefficients.
3. In order to relate the temperature T in (8), approxim.ately coinciding
with the temperature of the 500-mb surface, with T being the mean for a
vertical column of the atmosphere, and the surface temperatur.e T~ in for-
mula (9), we ohtain the empirica~ relationship between T and Tq = T~ -
T fer d~.fferent latitudes [4].
We will examine two variants of this relationship. In the first T~1 =
T~(~) - T(~) is determined from mean zonal climaCic data [S-7]. It is
regarded as an empirical functio n and is no t dependent on external para-
meters. It is possible to use T 1 for computations of modern climate,
but with a change of any external parameter s such T 1 values can substan-
tially distort the T changes. In the second variant~we will represent Tq2
in the form '
. 7~~ s=~ 7'n = a ~ T'~' n s~
(10)
8
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~
FUR OFFICIAL USE ONLY
where gl and g2 are determined from a linear regression equation on the
basis of these same data on Tp and T. This equation was derived for the
entire northern hemisphere and separately for the zone from the equator
to 60�S. In Antarctica the hi~h level of the surfac e does not make it
possible to include the local values for the southern hemisphere Tp - T
and T in the general correlation.
The following values of the coefficients in (10) were obtained:
g', = 0.57/0, t 2 i: g~=;~,76/33.03-}-9 (c~) ,
where the numerator applies to the northern hemisphere and the denomina-
tor applies to the southern hemisphere, q(~) is an empirical function
equal to zero to the north of 60�S, whereas to the south of 60�S q(cp) is _
selected in such a way that with the present-day value of the soiar con-
stant S~ formula (10) is satisfied everywhere in the southern hemisphere,
that is
4(V) _ (To-TI-(g~T-6'z). 60� g ~c~~ 90�S., (11)
where Tp and T are the climatic temperature values [S, 7]. Tq2 approx- .
imately takea into account the influenc~ of the inverse relationship be-
tween the averaged temperature T of a vertical column of air and the sur-
face air temperature Tp.
The mecha.nism of this inverse relationship is particularly significant
in those experiments where the changes in T are considerable.
Substituting (10) and (11) into (9), we obtain
~
1=t~-}-;;T, (J~ ~ ~~=J~~+ ; ~ 12 ~
~ )
,
~ ' gi ~ 8:
where the upper line applies to the variant Tql and the lower line to the
variant Tq2.
The mean zonal albedo of the earth-atmosphere system O~p is respresented
in accordance with Budyko and Cess [2, 8] in the form
2,~ = ae n~' ~ rt), ~13~ .
where a~ is the albedo of clouds, GYS is the albedo of the earth-atm~-
sphere system in the case of a cloudless sky.
We introduce the dependence of OC~ on solar zenith angle Z and on ~ ~
[8, 9] in the form
- A, -}-A~as- A:{cos;,
(14 )
49
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t~UK UH'r'LI:IAL 1151s (JNLY
where Al, A2, A are dimensionless empirical coefficients and the depen-
dence of O~S on3temperature, as in the Budyko and North models [2, 10,
11], is -
a; , 7~� < 1 j
xs= ~ (a~ a�1 '2, Tu = T; (jg)
l x~ , T~, > T~,
where ai, a~ is the albedo of the earth-atmosphere systern in the cases
of surfaces with and without a snow and ice covered surface, Ti is *he
temperature of the surface air at which the surface is covered with ice
and snow.
The mean zonal a~ and ~i values are represented in the form
2~r = xf, L p~ zo tr� l 1- P~)~ x1 = 7;~ P~ xilY. ~ 1 - P~~. ~16 ~
~ 0 L~ ~ iL p~,7~ ~ i W are the and ~ i values for the land and
ocean respectively, PL is the latitudinal distriburion of the fraction of
the area of the land to the area of the zonal "belt."
In a steady mean annual zonal homogeneous atmosphere Rl and RZ cornpensate
one an~ther and the heat flux to the underlying surface is G= 0.
4. As a result, the considered thermal regime of a zonally homogeneous,
vertically averaged atmosphere is described by the equation
vl'i~T)=-S~1-x,,~r~,~?t)]~-f~(~t)+'(~l) T, (17)
= where a'P, I~, ~ are determined from expressions (10)-(16) . The coeffic-
ient K, entering iz~to Y, is determined from the condition: temperature
T~(~) at the latitudes of the boundaries ~N and ~S of the northern
and southern polar caps should assume values Ti(~). _
7~n~=,v)= Tt~~,v~~ T~~~?~~) =r,l=~). (18)
W-Lth the present-day level of the solar constant S~ we have approxi.n~ately
~N = 72�N ~nd ~S = 60�S. As follows from (10) and (11), TD(C~) is re-
lated to T( by the formula
( )
7~0 - ~((+)g~)TT~(~?))rt- g:. T~:� 19
The coefficient K=(KN, KS) is considered constant within the limits ot
each of the hemispheres and its valu~s wi11 be determined below,
50
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z~
I
i
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FCIR OFT''[CIAL USr nNLY
We will examj.ne two variants of the Ti values . In the i ir~ variant
Ti 1( = cohst in the limits of each of the hemispheres is equal
to -10�C in the northern hemisphere [2] and -1.9�C in the southern hrmi-
sphere, that is, the temperature of ocean freezing. It_ the second varilnt
Ti 2(~) is a variable and approximately takes i~nto account that the
surface air temperature at which a snow-ice cover is formed changes with
latitude.
_ ,p P~ ~Y)' 0,3
- T 1~~ = - 1,9 - gl (P~ (f) --~.2), 0,`? _ P~ _ O,3 -
- - ~'y ~ Pc ~ 0,?.
If interlatitudinal heat transfer is neglected, the thermal conductivity
coefficient in (17) will be equal to zero and the thermal regime of the -
earth - atmosphere system is determined only by radiant equilibrium from
the heat balance equation (17). Then we have
S[I - ap l7'u. ~11 ln~ (20)
T~(?) _ ~ ~n~ .
In this study we make use only of the data from Cess, obtained as a result
~ of processing of satellite measurements with the f~llowing values of the
empirical coefficients in (9) and (14) [8, 9]: al = 257/262; a2= 91/81
' (W/m2); bl = 1.63/1.64; b2 = 0.11/0.09 (W/(m2��C)); A1 = 0.641/0.691;
A2 = 0.258/0.219; A3 = 0.494/0.619. Here the numerator applies to the
northern hemisphere and the denominator to the southern hemisphere,
whereas in (16): ~0 L= 0.43/0.275; ot~ W= 0.43/0.103; 0!i L= 0.43;
�li W- 0.43. The numer.ator applies to Antarctica, where it is assumed ~
that to the south of 64�S the contin~ntal ice does not thaw; the denomin-
ator applies to the remaining part of the earth's surf~ce. For example,
the author of [12] gl.ves other values of the coefficients al, a2, bl, b2.
However, with the use of a cioud cover value equal to 0.5 different values
of the coef.ficients in (9) give close results. The cloud cover value is
assumed to be constant within the limits of the hemisphere and is equal
to nN = 0.51 in the northern hemisphere and ns in the southern hemisphere
[8J. The lntitudinal variation of the solar radiation flux was taken from
[8J for a value of the solar constant S~ = 1360 W/m2.
5. The tempsrature T(x) of the considered thermal regime is determined
_ from the zonally homogeneous equation (17). Since the coefficients y and
}3 are conatant withiz the limits of each of the hemispheres, it is pos-
sible to find T(.c) for each of ;:hem and "splice1' them at the equator for
the thermally interacting hemispheres.
Using a Green's function of the clifferential operator
~
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r~tt vrrl~.~~u., u~n u?vLi
d t d
dx ~ - x') d.r
the conditions of continuity and limitation on temperature and the heat
flux within the .limits of a hemisphere, and also the equality of the
flux at the poles to zero
1~ dT _ Q when x= t 1,
~ ~ ~ dx
f rom (17 ) we obtain
~
T,~� (x) G,~. (,r, y) ~S ~ 1- a.,,) to~ dy CN P~. 0_ x~ 1, -
u (21)
TS.(~)- f G.~~~~,Y)IS~1-x~)-l~~~d~~+Cs.l~s(-x),--1,x~0. r
Here G (x, > ) = R ~ P~ p~ < x
~ ~ ~ i ~ Pf x) p1 ~Y), > x,
P; (x) = P.,f (x), P~ x) - P.,~ x)
are linearly independent Legendre functions of the first kin:d [1)
x - Sin 1 2 i = j~=/ - ~,25, 'i - t~~R~~~/, W~ = l~ -1 Ch (*~~~1,
R= 6.37�108 cm is the earth's radius, C. is an arbitrar~ int~;ration con- '
stant which is determined from the condi~ions at the eq~ator, j= N, S is
the index for the northern or the southern hemisphere, T1= 3.14159.
We will examine two types of conditions at the equator.
The condition G is for thermally interacting hetnispheres:
dTN (x)
~',v (-r) _ ~'s 'i,v ll l - x~ dr -
' ~ 1 -,r~ `lT,, (x) when x = 0. (22)
_ ~ ti ~.r ~
The condition H is for thermally isolated hemispheres:
v~ 1- x'~ ~T N~ Y~ = 0, l~~ 1- X= dT~X(.r) _ 0, when x= 0. ~23)
d.r
The condition H is used in the Budyko and North models [2, 10, 11].
As follows from (13)-(15), OC P in expression (20) is dependent on a can- ~
tinuously distributed temperature Tp(~). If we determine the latitudes
~ N and ~ S of the boundaries of t'~e "polar caps," for which (18) is
satisf ied, in (20) OC P is a function of the argument ~ and the parameters
52
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I~UR Ot~riCtAt, trSl~, ~~KI,1'
~N and ~g, that is, in place of (15) we have
x~ , ~ < ros ~r ? ~
- ~s = ~~i * xo);~Z, ~ _ ~S or ~ _ N (24)
' z~ , ~S < ~ <
In the ~odel it is assumed that the boundaries of the polar caps with the
present-day values of the solar constant and other parameters are known.
Substituting (19), (21) and (24) into (18), we obtain a system of two
transcendental equations, from which, as it can be shown, it is possible
to make an unambiguous determination of the coefficient of macroturbulent
thermal conductivity K=(K , KS). Substituting the determined K values
into (Z1), taking (19) and ~24) into account, we find the T~(cP) profile
corresponding to the present-day value of the external parameters. Then,
investigating the changes of the thermal regime with variation of the
solar constant or other external narameters, the thermal conductivity coef-
ficient K can be considered either constant or. variable in a known way.
Substituting known K into (21), which, in turn, is substituted into (18)
and (19), we obtain two transcendental equations for the perturbed values -
and S. After determining s0'N and ~'S and substituting them in-
to ~24), from (19) and (21) we find the perturbed temperature profile
TD'(C~).
T~(Sp) is similarly determined in the absence of ordered heat transfer.
Expressions (20) and (24) are substituted into (18). By solving the de-
. rived system of two transcendental equations, we find ~N and SPS. Sub-
stituting the determined ~N and ~S values into (20), we determine the
surface temperature T~(fO), correspon~ing to the radiatior. equilibrium
with selected values of the external parameters. However, condition (18),
used for obtaining a solution of equations (17), is not unique. The SP N
and CP S.valucs~can be a solution; these are determined by the condition
'?v = ?s - ~ when Tu (~1 < 7'! l~)~ ~25~
~N = 90�N., ~g = 90�S when T~, > T!
The routs of all the considered transcendental equations are determined
numerically by the successive approximations method.
6. The numbers of the different model v~riants for which the computations
were made and the value of the fitted paramgter the coefficient of
macroturbulent exchange K=(RN, Kg) (in lObm2/sec) are given in Table
.
The mean annual zonal profiles of surface temperature T for variants 1,
_ 2, 4, 5 are given in Fig. 1. The discrepancy between vaQiants 1 and 2
- in the equatorial latitudes is attributable to the different conditions
at the equator. The heat insulation of the equator in the condition H
53
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~'UK UPCI.I.Ir\1, ltJl: UIV1~1
leads to an excessive accumulation of heat in the northern hemisphere in
comparison with the southern hemisphere, and in the condition G the ex-
cess heat from the northern hemisphere is transported into the s~uthern
hemisphere. Accordingly, in the equatorial latitudes of the southern hemi-
sphere it is warmer in variant 1 than in variant 2. Figure 1 shows that
the conditions at the equatnr do not exert an influence on the temperate
and polar latitudes. The difference betwEen variants 4 and 5 from variants
1 and 2 is attributable to the inaccuracy of parameterization when using
the function Tg 2, especially in the northern hemisphere. In the equator-
ial latitudes T~ in variants 4 and 5 is similar to Tp in variants 1 an~
2. The break in the T~ profile in variant 4 is a result of the "discontin-
uity" of the function T 2 at the equator. As a comparison, Fig. 1 shows
the climatic values T~ ~rom [5-7], which are denoted with the letter k.
~a o
. o
~ ~i'~ o
m ~a~' � ?
o �
�
~ * {@
20 0. '
~ ~
.
.
, ~
m
~
10 :
m
s
� ~
6Q'ro.ur S 60'c.m. N
~ ~ 40 1D 0 20 y0 `
? -J
- i
-10 � ..4'
c
o
� � � 7 F'
�
. 1 ~ p
-20 � 4 "
. .
` o c o 5
~ a~ ~ T n
~
t
Fig. l. Mean annual mean zanal surface air temperature T~�
5
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F(1R 0~'~'iCiAL DSL ~~NLY
Table 1
Variants of Model and Corresponding KN and KS Values
~
1 ~'c.~a-2' ~'cno3 q
F ?ae G ~ ~~Ne R c~ 7~ Q
' ti S c _ G-
~'A f TQ ~ I TQ' ITq T~~' > 6 x x
~
Tj, 1 4 2 3 ~
T1: 3 G i -
hN ~4,09~3,70I3,9iI3,7Q U
3,5iI3.~0I3.7013.611 ll
s ~
i
KEY:
1. Variant of model
2. Condition G
3. Condttion H
4. Condition of thermal equilibrium
Note. With use of the variants Ti 1 or Ti 2 the values of the corres-
~ ponding coefficients KN and Kg coincide because for present-day ~N
and ~S values the variants Ti 1(~) and Ti 2(fA) coincide.
Tabl e 2
Change in Solar Constant in Percent With Complete Thawing of Ice Cover
of the Northern Hemisphere L~S', With Formation of "White Earth" Q S" With
Corresponding ~ N and fPg Values for Different Variants
M~d 1 varian BapNaHr ~~oxe:ut
i
~ I ? I 3 I 4 I 5 I 6 I i i 8
I
I
' ~S' !5 ~4.5 �I.~ 9,5 I I,3 ; O.J K.ti 9.5 I I,i
~ S" -G -12.5 -6 I -7 - I 2 -7 - I?,7 ---27
N 4,5 , 3,5 , .-4,5 -?3
~ ~ c. iu. 5~ 34 i-4 ~ 43 26 43 34 Q
~c'x,. m. 34 34 ' 29 ~ 37 ~ 29 34 ~ 0
S ~ I l ~
KEY:
1. Variant of model
2. N/ S
Note. In variants 2, 5, 7, 8 the LLS" value in the numerator corres-
ponds to *_he northern hemisphere and the Q S" value in the denomina-
tor corresponds to the southern hemisphere.
55
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rvi< 11 'G ~ J5~
< 11'C
5 ~ ~~~f1 d5,?
11 ~ ~JS,1 5
~ . JS,1~
tie so ae eo ~e so SS ~2
Fig. 3. Temperature distri3ution in May-July 1977 at horizons 0(a), lOC
(b), 400 m(c) and salinity at horizons 75 (d), 100 (e) and 400 m(f).
_ The above-menti.oned anticyclonic ctrculation of waters on the maps of hor-
izontal circulation is detected extremely clearly in the layer 0-100 m.
As can be seen from the maps, the western periphery of this circulation
is not the Somali Current, but a current running to the northeast parallel
_ to the Somali Current. Figure 3a,b,d,e shows that the current on the west-
ern periphery of the circulation in this layer transports warmer and more
83
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rvn vr?� i~~.rw u~~ vivi.i
saline waters than the Somali Current. The clearest differences in these
currents are detected to the south of Socotra Island in the region 10-11�
N, 54-56�E. Here the current on the western periphery of the circulation
turns to the ehst and then to the south and southwest; in the region 3-5�N,
50-52�E it closes the considered circulation. To the south of Socotra Is-
land it is also possible to trace the main flow of the Somali Current,
whose easterJ~~ direction along 10�N (Fig. 2a,c) at the surface again
changes to northeasterly, northerly and then passes to the east of Socotra
Island. The exis'.Ence of these two parallel currents is also confirmed by
the horizontal distribution of temperature and salinity and their differ-
ences are represented especially clearly in the vertical structure of the
waters (Fig. 4). The boundary separating these currents passes between
stations 108 and 109, as is indicated by the great horizontal ~radients
of temperat~:re and salinity. Between these statinns the isohalines run
vertically downward from the surface to a depth of 150 m.
' ,3
' ~u4 �os ~cs ~or~ae �~9 �o ~
~ l,l' u' /
n r , 1'
rpo ~ f
1a Z3-~
. �
I 16 ~
.GU~~15
I ~'`~6~
Lro~ ~ 1
_~`,s ^ /
/ v
JOOr~-1J~.~`~''~~y ~
U J
'r00 '1~ 1 ~
e
J'OJ 'C4 'OS '06 1071p! "09 ft,~ Itl 1I1 '1� ;IS
S
y~5� ) 4~J5,: �6 JSc~
~JS.! 1
'OC Jf.d JS�i J6 jfa rJ40~
1`\\oN~T1 ~ ~
J~ ~J JS,S J~~ Jf0
~ ~ `-J3 4"
:00 ~JdS~~
.~v I ~~~rss /
J00 Vy\
400 1 __L~1_
. .
FiR. 4. Vertic~l distribution of temperature (a) and salinity (b) 10-13
July 1977 on section to south oF Socotra Island.
~ This same Fig. 4 shows that the lower boundary of the upper isoth~rmic lay-
er tn the Somali Current is sitUated at depths 40-50 m(temperatures 23.0-
23.5�C), and in the other, warmer current (26.0-27.0�C) at depths 100-
120 m. In addition, there is a marked difference of salinity at the "cores"
of these currents: 35.40-35.50�/0o in the "core" of the Somali Current and
84
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l~OR OcFICIAL USE ONL.Y
36.10-36.20�/0o in the ~~urrent an the western periphery of the circula-
tion (here this is already the northern periphery).
Differences in the structure of waters of these currents were also dis-
covered on the basis of the distribution of dissolved oxygen. In tha
Somali CurrenC (to station 108) the surface quasihomogeneous layer to a
depth of 40-50 m contains 4.5-5.0 ml/liter of oxygen, and in the current
on the western periphery of the circulation this laqer with an oxygen
content of 5.0-5.5 ml/liter occupies a depth of 100-120 m. In addition,
th~ layer of maximum vertical gradients of dissolved oxygen under the
Somali Current is situated at depths from 40 to 120 m, and under the ad-
~acent current from 120 to 200 m.
The above-mentioned characteristics of the vertical distribution of hydro- ~
lopical elements confirm a significant upwelling of waters in the Somali
Current to the south of Socotra Island which is evidently observed in the
entire extent of this current.
Figure 4 shows that in the region of stations 114-115 there is also a
"core" of increased salinity (mnre than 36�/00), but already at greater
depths, about 120-160 m. This, evidently, is in fact the very same flow
of waters of the anticyclonic circulation, but here is has reached greater
depths and now has a southerly and southwesterly direction (eastern peri-
phery of the circulation).
A third detail of the circ;ilation of waters in the surface layer of the in-
vestigated region is a local cyclonic eddy to the southeast of the strait
between Socotra Island and Cape Guardafui (Somalia).
The waters emerging through the mentioned strait, flowing southeastward
along the shores of Somalia, on their path encounter the flow of the Somali
_ Current, turn northeastward and run parallel to this current; then at
Socotra Island they divide into individual currents. Figure 4 shows that
between stations 104 and 105 there is a boundary between the Somali Current
and the flow of waters forming the considered cyclonic circulation. The
salinity of the latter in the "core" of the flow at depths of 120-150 m
is about 35.70-35.80�/oa; at the surface about 36.00-36.10�/00.
Figure 2e,f shows that at the horizons 200 and 400 m the general pattern of
the horizontal circulation of waters changes absolutely to the opposite,
except for th~� strait between Socotra Island and Cape Guardafui, where the
cyclonir. eddy persists at all depths.
In the region of the anticyclonic eddy, which forms the character of cir-
culation of waters in the surface layer, at~ depths beginning with the hor-
izons 150-200 m it is easy to trace a"two-core" cyclonic eddy (Fig. 2e),
which by the 400 m horizon is already divided into two independent, also
cyclonic eddies. The waters of these eddies are relatively homogeneous
(Fig. 3c,f). In the north of the inve~tigated region the current at the
horizons 200-400 m also had an opposite northwesterly direction.
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- ruic ~irri~,,~u, uat. uivi~r
An interesting peculiarity at the considered horizons 200 and 400 m is the
absence of ttie S~mali Current over the entire ocean area. Moreover, at
these horizons indicatorc of the subsurface Somali l:ountercurrent appear
~it ttle~;~ hori zons . Ttiis counterciirrenC is formed, for the most part, by
the western periphery rf the c}~clonic circulation 1nd apparently by the
alungshore transport of waters in a southwesterl.y direction �rom the al-
ready considered strait. It follows from Fig. 2e, and also Erom the con-
sidered vertical distribution of hydrological elements, that the Somali
Current does not even reach depths of 200 m.
The considered g~ostrophic circulation of waters quite reliably reflects
the movement of waters over the entire area, but give~ no idea conrerning
tt~e current velocities and their temporal variability. This requires cur-
rent observations. However, the organization of a network of autonomous
buoy stations adequate for constructing a map of currents is virtually
impossible even for such a small region.
In 1973, 1917 and 1979 the ships of the Far Eastern Scientific Research
Hydrometeoralogical Institute in the investigated region occupied eight
stations with a work duration from 7 to 12 days (Fig. 1). Although the ob-
servations were made at individual points, together with geostrophic maps
they refine the r_rue picture and help to give some quantitative estimates
and current patterns.
In actuality, at all points in the first stationary polygon of the "MONEX-
Summer ~xpe~ition the directi~n of the vectors of. current velc~cities at
the hari.zons 200 and 400 m, averaged fo�r the observation period, coincid-
ed with the directjon af the geostrophic flows which existed in May-July
1.977 (F.ig. 2e,f). 'I1~e presence of a deep cyclonic circulation is evident-
ly a ctiaracCeristic feature of the deep circulation of waters in the Arab-
L~.~n SE~a.
In the upper layers there was also sume s~milarity in the direction of the
Keostrc>phic curr~.~nts in 1977 and the averaged velocity vectors of the cur-
rents measured hy instrumental methods in :lay 1979. This fact indicates a
constancy of the cnaracteristLcs of surface water ci.rculati~n constan[
presence of zn ~nticyclonic circul.ation of waters. Its existence is noted
hy all researchers; It is traced quitQ clearly even from satellite phato-
Rraphs (7, 8].
f3ut the ~~ositinn of this :~urface anticyclunic circulation ~f water~, hav-
inK a Kec~slrophic nature, r.hanges from year to year; it is evident.ly de-
pendent on thr intensity of the Somnli Current. For examplc. iil May 1979.
in ~i yccir of rinomalousl.y weak development of the Soma.li Current, it was
~;~~mewtiat di.splaced eastward. Thc:'width of this flow on its western peri-
~hery was Kre~Ger tt~an in 1977 and che intensity of transpc~rt of waterti
was s~~mewhat less (F'ig. 5) .
'I'li~ first statianary polygon of "MONEX-Summer" was situated precisel.y at
the center. of the surEace circulat~ion of waters. The westc~rn and northern
auton~~tnous buoy stations werF situat~~~3 in the nurtli~~ri;;t~~r]~� fluw :~nd the
3G
I'OR (?I~ 1~ Tc;1 ~11. IISI, clvl.,ti'
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rc,iz c~r~zc;rn~, ~rsr. ~)Ni.Y
eastern and southern buoy stations were situated in the southwesterly
ftnw, canstitutinK the surface Somali Countercurrent. :he position of the
current velocity vectors at the autonomous buoy stations rigorously cor-
~ respond~ to the direction of the geostrophic flows (Fig. 5).
,e ~o
a , .
a No data;
p ~ai~
~0`~ ~
~ ~~d`~ ~ ~50
o~ ' ~
~ o~~a~~' ~ % yp0 95
5~4 / s
~ ~ 9'0
_ a
Fig. 5. Map of geostrophic currents in 1979 at the surface, computed from
a depth of 500 m, and averaged vectors of residual currents at the 25-m
horizon,
riere it should be noted that the direction of the velocity vector at a
western point reflects the direction of the flow after 22 May 1979. Up
to this time the transport of waters to all intents and purposes occurred
in the reverse direction. This indicates that at the western periphery of
the anticyclonic flow there was also its intensification due to intensif-
ication of the Somali Current, which, according to "MONEX-Summer" data,
occurred during the period 20-22 May. Some traces of the variability of
the structure of currents correspanding to this intensification were dis-
covered in the surface Somali Countercurrent.
According to d~1ta from instrumental measurements of currents, the thickness
c~f the la;er occupied by the Somali surface countercurrent decreases from
ISU m at 8�N t~ 75 m at the equator (Fig. 6). The velocity of transport of
waters in its :;ystem at 6�16'N, 59�10'E in the layer 0-150 m varies from 35
to 19 cm/sec and at 4�N, 57�E it decreases to 15-22 cm/sec. But the current
here or_.cupies a layer of 75 cm (see Table 1).
It w;i>; extrem~ly interesting that at 49�E the velocity of water transport
in the layer f)-i5 m across the equator in a southwesterly direction (and
it can be interpreted as a continuation of the Somali Countercurrent) in-
creases sh3rply in comparison with the extra-equatorial flow. Here it must
be pointed out that the current in the surface layer in May 1979 was di-
rected a~zinst the wind, whose velocity from 16 through 26 May increased
from S to 10 m/sec.
87
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rvi. .~cr .~..ni. u.~i'. v~ri.i
~ ~ .cu OO sa O
~ .5 ;c~ ~ ,rao r.
:~~;~s~~'io�a ~ooo t~o,
~p0 ~ t3J
~ ~Su 10 ` ` dJ0 ~
~ 30 Jc~ G0 1^D'OOC
.rT ~
ZO 0 ? b' G :0
~~ol r
~ r
C~'J r ~
~ C L
s~Q~~r~j;1~~ O O
~ -:s - sao' ~sa
SJ~�~ f00 ~;SOJ00 r00S00 ~p9~
0 10 40 D TO ~~~15 10
YOO,'
4 ,
i
^l.^C~ ~ 1
~ L
~ . 1 'GJ
~ :J^ O
� r
j~ J -
~
~'J'l
�C~ ~~Y~
O~V~
1~.' J
Fig. 6. Roses and curves of maduli of residual currents averaged during
the period of observations. 1-7 numbers of observation points.
Equally surprising was the complete similarity of the current r�oses in
the eqilatorial region at 41�E and 53�E in the layer 0-500 m. Observations
at 53�E were already made in 1966 by Taft and Knauss t9] almost during the
same period oF rhe year. In both cases in the layer 0-75 m there was a
sc,utherly flow, (n the layer 100-300 m-- westerly, deeper easterly
f1ow. Rut the ubserva~_ions of 1979 mad e it possible to demonstrate that
this e;i5terly f.low in tile l.ayer 700-1, 000 m also is agai.n replaced by a
w~~stc~rly fluw with vel.octties 30-35 cm/sec (Fig. 6). However, these val-
?ies characterize tt~e mean diurnal flow velocity, whereas its instantaneous
values in individual time intervals exceeded SO cm/sec. Thus, at the equa-
~or in the regton 49�E there was a four-layer structure of currents which
is evidently ch:~racteristic f~r the period from l~irch thro~igh June.
Such a pattern of Che distribution of f1owS at autonomous buc.~y station
poi.nts was ohtained as a result of the averaging of current velocity over
a c~uite prolonged time interval (7-12 days). The use of the mPan daily ~
88
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i
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Components of Residual Currents
~ I ~ T'opu3c,Hr~
C~�1i+o~ lata 2~i ~p I :
A_ B ' ii~ ~ 10f1 la0
i ~ � , t' i� I c' I u! r u r I u
' ~ ~ I
i ,
1 I Hr~c ~t0. nt. lllu~
ha.~bc~:Niis ?7 ~�i~
U81'tl I97i r. - - 0+21 I~-~2~t2 +~+32 +lfi -~23
~ 2 }-Il1C :IU. ~1] Wo� .I
~:a.i~c~;uiir 1f1-17 \'i
lQ-i r. _ ~
- -S� - 19�~+21 -14 - , - +8 -19
~ ~ H11C(1 ~~u.~Nai i- I
29 1979 r 1 �
+ 2� l0 I - - ~12 ~4 +4 -i
HNC ~.~na,qeMUn ~ I
Ill~tptuon~ 17-39
1979 r. - 4 ~ 10 i- - i- - ~�3 - 2 f i + l
~ HIiC =.ahalc~~NS ho� ~
pu.~ee~ 1 i-25 ; I I i
19i9 r. I(? -2-1 - lfi -28 - - ~-1~-21 -1~ -2 i
G HIICfI ~I7pii.i~iB,l
1i-39 \ 197U r. ~ -?I ; +I -ld -2 - - -3 --5 -7
~ ~ I
7 FI11C(7 ~f]pnGnii'I I - ~
I lyi9 r. - "ai -8 -fi~ : ?I -S -10 ~ -:i0 ~
~
H' Ucpc~He~ine ~~eii~uie, ~ie~i 3a 7 r~ron
values (after filtering only of tidal oscillations of current velocity)
does not give a complete idea concerning residual currents in the equator-
ial latitudes. At these latitudes the inertial oscillations of current
velocity, occurring at any point in the world ocean, attain extremely
high v~lues. Both the period and the amplitude of the oscillations in-
crease. The latter circumstance for the time being is completely inexplic-
able.
In the Equatorial latitudes of the Indian Ocean fluctuations of current
velocity are detected on the basis of the above-mentioned observations.
Figure 7 shows the variability of the residual velocities of currents at
different latitudes and depths at individual points of the first station-
ary polygon of "MONEX-Summer."
As in (1, SJ, the represented variability of the residual currents occurs
in circular orbits with rotation in a clockwise direction and with a period
close to 2T!/f. The fluctuations of. current velocity undoubtedly have an
� ~ 89
~
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ruK ut~ri~.~:~i, i~~r. uai,~
Tah] e 1
Averagtd for ObGervation Periods
C ~',~~~E?~o~:rtr ~ D
_i
?UO ~1UU + "~UO ,`S(lp IUItU I:~,oQaurt~Tu
I i ~ ~
I ~ , I - , ~
t r ' u t, u, c~ ~ u I v ~ u c~ ~ u t~ i a~ -
i ~ ~
I ~ ~
~ ~
I ~ I ~ e
~ --~n _i~~ - i~ _i-~ ; .~~u -aa _ ~ ~~s - - ~-~~o ii�~ uo ~?,.F
~ ~ I i ~ ;:;�t u i. g
~ I i
_ ~ -lU -I1 iy , ---II ' ~ _t:i -19 i -I; - I _ I_.13 ~09�~I:i, ui.
~ ~ ~ ~ ~S:i�1~ ~ i
I i I I I ~ I
~ - ; i ---IU i - 3 ' -21 I 2~ +I '?i. -~S'-2:.' ! -~;-ll 08 ~6' c ni
~ ~ I ~ j j I .i7�01' s i.
I ; I i ~
i ,
i ~
~ ~ ~ ; i _ ~ ~ ; ~ -2 ~~)ti.'b' ~ ~ii.
~ i i ' ' I I:i}�3~' _t
I I i '
~ ~ ; I ~ I I ~y i I ~ _
- ~ i-~~~ I t'~0 ' I.�~} --i~I 2'~ ~ iU~i Ib" r ut
~ ~ ~ ~ i ~ ~ ~ ~;9`!0~ n
I I , ' - , :'I i I
--li ~ ' ~ I -i i - ~ - ~ ~ -�1 -fl ~ ~ ~~I ~ I~~S�i~~ C. ;II
i ; ~ ~ ~ ~ I I ~~)7' ~ ~ n 1.
j ' ~ ~ ~ ~ I j ~ ~ ~)0 01 ' iu u i
1 ~ j - i ~ j ; I t ' t ~ ?li I -~i ~ - 23 .;1 i - ~ ~~i - �11 ; ~K`:iR o .l. C'
RE~':
A) No (see i~i~;. 6)
B) Ship, date
C') Horizons
D) C~cirdinates
F. ) N
F) I;
S
!I) AveraKinf; for tes5 than 7 days
I) Scient~fic research ship "Yu. M. Shokal'skiy"
2) S1me
3) Scienttfic research weather ship "Volna"
. Scientific research ship "Akademik Shirshov"
~ij Scir.ntific research st-,ip "Akademik Koro?ev"
6) 5cientific research weather ship "Priliv"
7) Scientific rese.~rch weather ship "Priboy"
9U
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~~~~i< urr r~:i~~i. iitii~: ~~tv~.~�
inertial nature. There is no doubt of this because with 24-hour averaging
of the current velocity components the probable error in the readiregs of
BPV current meters (and ali the buoy stations registering the pertinent
movements were outfitted specifically with these current meters), compar-
able with the amplitudes of the inertial oscillations, is of no practical
significance [6].
SOM Y SOM y S~~
r
: 1? ?d ?9 !g
16 te n
n J ?J 19 Ie ~
~ 6 1 ~
J
1J ~D
y ~ ?J f7 ps ?y 11
9 ,
e ~1.
100 r' 900 H G04r.. ~y ~
14 ~ ~ptnJt
p ~ Z1
~ ~t5 124 j 1S;
~ 1 tt ~
~ 1 0_.'-~ , 1S~-
~ 11 ~ 1l 1 `
fl 11 77�S
l b 1E
N E
4�~4't.u+. 66�~e'e.a rsy'~~ srr,~a. ~�~6~~~ sQ~~o'i.a..
1-1J ~ 79 11�19Y 19 ' ~1�19Y 7S
Fig. 7. Inertial oscillations of inean daily currents at individual points
in the Indian Ocean. Near the density 3ump layer the maximum of the ampli-
tude of the inertial oscillations of current velocity attains 60 cm/sec.
Figure 7 shows that these oscillations can be interrupted for 24 hours or
more, that is, they can be absent for a definite time interval.
Inertial osciliations of current velocity are characteristic for the entire
layer from the surface to 1,000 m, that is, the layer in which instrumental
~observations were made. After the amplitude m~ximum in the thermocline lay-
er they slowly attenuate and retain high values even at a depth of 1,000 m.
The amplitude of the inertial oscillations evidently is somehow dependent
on the mean current velocity of the general flow, averaged over a quite
prolonged time interval, taking in at least two or three cycles of rotation -
of a fluid particle in a circular orbit. It is also dependent on the stab-
ility and frequency of recurrence of the residual currents. Even at depths
of 800-1,000 m with a mean current velocity of about 20 cm/sec dur;ng the
observation period the amplitude of the inertial oscillations is commensur-
able with the current velocity with its frequency of recurrence within the
limits of one direction from 30 to 40X. It becomes two or three times less
with a frequency of recurrence of velocity from 50 to 80X. Here it is
91
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~
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Iht ~ ' ~~~L~C`i~
~EP'TEM~E1~ ~1~. ~t~t~E ~ t~F ~

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I~l)l~ UI~P'l.C1AL USh: ~)NLY
interesting tu nale that the amplitude maximum was observed somecahat t~
the north of 4�N. lvTear this parallel within the conEines of the Indic~n
Ocean the water flows w~re leasl stable. sinr_e the limit of propagation
of zonal equatorial currents runs here and accordingly a zune of
slightly stable flows.
Conclusions
1. The anticyclonic circul~3tion of waters in the Arabian 5ea oc.rupies the
surface 2GU-m layer.
- 2. In the subsurface and intermediate l~iyers of the Arahian Sea to the -
south af Socotra Island there i.s an extensive two-cenr_ered cyclonic ctr-
cu.lation. Its western periphery is possibly the deep Somali Coutitercurrent. ~
To the east of the island it is possible to trace an anticyclonic circula-
tion giving deep ma.sima of current velocity on the vertical discribution
c urve .
: 3. A vertical. multilayer systPm of curreuts is the dist~.nguishing charac-
t~ristic of the Arabian Sea. The most consistent chang~ in the signs of
current �:elocities is traced in the equatorial region where, exe~pt fc~r
the surface layer, the currents have a zonal d.irection; in the layer 100-
300 m water transport is to the westward, 300-600 m-- eastward, deeper
again we.stward.
4. The ampl itude of the inertial oscillations of current velocity in the
equatorial latitud~s of the Indian Ccean can exceed one knot. 1n order tc~
obtain reliable data on the residual curren ts it is necessary to averaqe
the velocity values in a time interval which is a multiple af the p~riod
of the inertial oscillations and the period of Lhe tidal currents.
BIBLIOGRAP HY
l. ~rekh~vskikh, L. M., et al., "Some Results of a Hydruphysical FxPeri-
= ment in a YoLygon in the Tropical Atlanti.c. " IZVBSTIYA AN SSSR, FI7IKA
9Th10S~ERY I nKE.ANA (Ne~~~s of the L'SSR Academy of Sciences, Physics af
the Atmosphere and Ocean), Vol. 7, No 5, 1971..
- C~lovastov, V. A., "Uceanographic In~~estigations :in the Er.perimenl 'M~n-
sn~n-77;" METEOROLOGIYA I GTDROLOGIYA (Meteorology and Elydro:togy), Nc~
~
9, 1978.
3. Golc~v~~stov, V. A. ,"Variability of the Heat Conter.t of Waters in the _
Monsoonal Region of the Indian Ocean and the Factors Delermining It,'~
RKSPRESS- INFORMATSIYA . OKEAN'OLOGIY~`. (Express Informat: ~on. Oceanology) ,
Nn 3 (~~6) , 1978 .
w
~ 92
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FOR UFFLCIAL USG ~NLY
4. Golovastov, V. A., Tunegolovets, V. P., "Large-Scale Interaction Be- -
tween the Ocean and the Atmosphere in the Example of the Pacific and
Indian Oceans and the Problem of Long-R~nge Weather Forecasting (Re-
view)," TRUDY DVNIGMZ (Transactione of the Far Eastern ScientiEic Re- ~
search Hydrometeorological Institute), No 87, in press.
5. Monin, A. S., Kamenkovich, V. M., Kort, V. G., IZMENCHIVOST' MIROVOGO
OKEANA (Variability of the World Ocean), Leningrad, Gidrometeoizdat,
19~4.
6. Rebayis, E. A., "Characteristic M~otions of Anchored Buoy Stations and
Their Influence on the Registry of Currents," TRUDY MEZHVEDOMSTVENNOY
EKSPEDIT~'ZI TROPEKS-74 (Transactions of the Interdepartmental Expedi-
tion TROPEX-74), Volume II, OKEAN (The Ocean), 1976.
7. Tarasenko, V. M., "Investigation of the Somali Current," GIDROLpGIYA
INDIYSKOGO OK~ANA (Hydrology of the Indian Ocean), Moscow, Nauka,
1977.
8. Duing, W., "The Monsoon Regime of the Current in the Indian Ocean,"
E. W. Center Press, Honalulu, 1970..
9. Taft, B. A., Knauss, G. A., " The Equatorial Undercurrent of the Indian
Ocean as Observed by the Lusiad Expedition," BULL. SCR~PPS INST.
OCEANOGR., Univ. of California, Vol 9, 1967.
10. Swallo;a, G. J., Bruce, G. J., "Current Measurements Off the Somali
Coast During the Southwest Monsoon of 1964," DEEP SEA RES., Vol 13
(s), i966.
11. Woaster, jd. S., Schoefer, M. B., Robinson, M. R., ATl.AS OF THE ARABIAN ~
SEA FOR FISHERY OCEANOGRAPHY, Univ. of California, 1967.
- 93 '
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1'VL~ VL'1'L~.1l1L UJG VL'IL�
UDC 551.46.06:681.3.01+556
ONE METHOD FO1~ R~PRESENTATION OF HYDROLOGICAL MAPS FOR ANALYSIS ON AN
ELECTRONIC COMPUTER -
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 6, Jun 80 pp 74-77 -
[Article by L. P. Smirnykh, Institute of Automation and Process Control,
Far Eastern Scientific Center USSR Academy of Sciences, submitted for pub-
lication 3 September 1979]
[Text] Abstract: The author describes a method for rep-
resenting hydrological maps in isotherms for an-
alysis on an electronic computer. Each hydrolog-
ical map is stipulated by a set of isotherms d+e-
scribed by elements of the map coding grid. Meth-
ods are proposed for a comparative analysis of _
hydrolo~~i~:al maps on an electronic computer, the
results ~~f which are quantitative or qualitative
evaluations of changes in the position of individ-
ual isotherms or their sets. An archives of hydro-
logical maps of the northwestern part of the sur- -
face of the Pacific Ocean has been created for
such a representation, as well as a complex of
programs for a YeS computer operational system for
its processing with the use of graphic terminals. `
The use of the proposed method in commercial ocean-
ography problems reveaLed its high promise and
ef f ec tiveness .
In the processing of hydrological maps of surface temperatures of the ocean
for the needs of commercial oceanography the problem arises of determining _
changes in the position of the isotherms of definite nominal temperatures
during some observation period.
A direct comparative analysis of Che isotherms for obtaining qualitative
or quantitative evaluations of the change in their position is complex and
time-consuming as a result of the specifics of plotting of hydrological
maps (arbitrary configuration~of isotherms, theiY nonuniform distribution
over regions of the map, validity of the graphic description) and the
great volume of information sub~ect to simultaneous processing.
94 ~
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One of the possible means for solving the problem of a comparative anal-
ysis of the isotherms is the development of inethods for transforming the
_ initial description of a hydrological map into some other form in accor-
dance ~rith the conditions of the practical problem to be solved (reple-
sentation), for which it is possible to use known comparison measures. In
this case there is a need for automating some elements of processing of
hydrological maps with the use of modern computers (graphic terminals).
Our objective is to construct a representation of hydrelogical maps with
retention of a description in the form of isotherms for input and com- -
parative analysis in an electronic computer. This representation must
afford the possibility of comparison of individual isotherms and hydro- _
logical maps with one another witfi respect to the isotherms and also of
obtaining evaluatians of the results of the comparison.
In this article we. propose that the maps be prepared in the form of a
set of isotherms registered by a sequence of elements of the coding grid
through which�they pass. In this case with an accuracy to ttie dimensions
of a grid element there is retention of the position of isotherms on the
map. The concepts of regions of determination of isotherms, singularities
and characteristics used in the preliminary analysis stage are introduced.
- Algorithmic methods of comparative analysis of isotherms and isotherm maps
_ based on different comparison measures are being developed. Methods for
minimizing the initial representation of maps or groups of maps are can-
sidered.
The language of the theory of ratios is used for a formalization of descrip-
tions of representations and algorithmic methods of comparative analysis.
We will use F=(F1, F2,...,Fk) to denote a set of hydrological maps; S
Tsl, s2,...,sN) is used to denote a set of elements of the coding grid;
_(tl, t2, t~) is a set of isotherm nominals, where s~~i~} , t~'. tf~;
i= 1,...,n; j= 1,...,m; f= 1,..., N= n x m, m is the number of rows
- ir. the coding grid, is the number of isotherm nominals.
1Y 25 1B 1~ ZB 19
' . . ~ ~
09 � ~
~ - ' -
98
, --------T~-r----
07 . 6 �
OS ; .
OS ' . - - - �
. ~ L a_1 .i._ L_ .~J
95
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.
For each map Fi it is possible to discriminate the subset Si~ S and T.j ~T;
then the ratio S 1~ Ti x Si is the formal registry of the map; (t, s)E Ei
means that the isotherm of the nominal t passes through an element of the
coding grid s, tETi, s~ Si.
The figure shows a fragment of a hydrological map. The grid S=(2405, 2505,
2810, 291~) and the isotherms T=(5, 6) are stipulated. Then
~(5; 2409, 2410,...,2810, 2910); (6; 2405, 2406,..., 270;, 2807)} .
The list of elements of the coding grid through which the isotllerm of tlie
nominal t passes is written as t~ _{s; (t, s)E then the map is
represented by the combination of the list of isotherms
~>~,
~
where (g*~, V*~) are the coordinates of the lower left corner; (g i, V ~i.)
tie coordinates of the upper right corner of the commoa region of ldefinitl.on
M .
~ The comparative analysis procedure ha~1 three principal aspects:
comparison of the isotherms of one nominal from several hydrological
maps;
comparison of hydrological maps with respect to a group of isotherms;
comparison of groups of hydrological maps with respect to one or more ~
isotherms.
As the basis for iche procedure it is possible to describe two measures of ~
isotherm comparison: one is related to discrimination of identical elements
in the description of isotherms and the other is related to computation of
the distance between isotherms. Both measures are used as an explanation of
the concepts of similarity, the difference of the compared ob~eces.
Definition 1. Ttao isotherms will be considered ~-indisCinguishable if the
intersection of their regions of definition contains not less than ~-ele-
ments:
I ?~'~flw:l
Definition 2. lfao isotherms will be considered ~-close if the distanc.e be-
tween them is not greater than~:
R (S,, S~) ~
The distance between isotherms is determined by the number of coding gric!
elements situated between them.
The general comparative analysis scheme is identical for both measures and
differs in the nature of the computations:
a) Comparison of the isotherms of one nominal from s.everal hydrological
maps.
Assume that the set of isotherms ~Sf~ is stipulated, where f determines
the nominal and i is the number of t e map, i= 1,...,k.
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In order to discrimj.nate identical elements in the description of iso-
therms we will consider all possible intersections of the elements Sf.
We obtain the set of numbers determining the number of elenents
entering into the intersections. In dependence on the purpose of the
comparison of the isotherms it is possible to obtain the following re-
sults:
ordering of the isotherms of relative similarity -indistinguisha-
bility) with any pre-stipulated isotherm;
breakdown of the maps into groups with respect to the compared iso-
therm with stipulation of some indistinguishability threshold
breakdown of the maps with respect to the compared isotherm with
max ~ -indistinguishability within the group.
The second measure is used in determining how much higher (lower) the
isotherms pass relative to one another or ~?~hat the distance between
them is; in this case it is necessary to discrimir.?te some sectors in
the Sf set where these evaluations are possible.
Using the resulting set of threshold niunbers ~ it rP~ains possible to
obtain results similar to those en~erated abov~.
b) Comparison of the hydrological maps with respect to the group of iso-
therms.
A set of hydrological maps F=(F~,.F2,...,Fk) is stipulated; each map is
described by a set of isotherms; f SfJ, i= 1~...,k; f= l,.o., Q,.
Definition 3. Ztao maps F1 and F2 will be called o(-indistinguishable if
they are ~-indistinguishable not less than according to thePC-isotherms.
By varying the a and ~ thresholds, it is possj.ble to obtain th~ following
results:
ordering of the maps with respect to prestipulated degree of similar-
ity (difference);
breakdown of maps into groups with respect to stipulated thresholds;
breakdown of maps by groups with respect to groups on the basis of
max criteria of Ot - and ~-indistinguishability.
Both comparison measures are used.
c) Comparisons of groups of hydrological maps on the basis of one or more
isotherms.
Assume that in the F set there is a priori sti ulation of a breakdown in-
to groups (equivalence ratio) E0,
(6)
dT (o. tl ~ 0 T(H -T- h(t)] = T~ ~t)~ T~z+ ~1 = T: ~Z).
dz
The last term in equation (5) is the heat influx into an elementary soil
volume as a result of the crystallization of inelt water entering into the
frozen soil during the spring snow melting, minus the heat expended on the
part of the freezing bound water which is beginning to thaw. We neglected
the heat flux of the percolating.melt water, because, as indicated in
[8J,'the magnitude of this flux is small in comparison with the flux of -
latent heat.
We have simplified the process of absorption of inelt water into the froz-
en soil ta the greatest extent possible because we are interested only in
the therma.l effect as a result of crystallization of infiltrating water.
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- HUR UH'FI(:1.AL U5E l)N1,Y
After excluding the dynamics of absorption from consideration, we will
assume that during the autumn-winter period, up to the time of onset of
snow melting, the moisture content profile in the drained peat bog is in
equilibrium. Below the level where the drainage system is laid the mois-
ture content of the deposit can be considered equal to the maximum mois-
ture capacity Wm. ~
~y We will denote the moisture content at the soil surface by means of Wp.
= This value can be determined experimentally. The equilibrium moisture
content prof ile is parameterized using equation (7).
(~V,,,~ l)~z~H-~o
~ = J -z~. =
H-z.,~z=H.
. I ~m - ~ - Wp~ (H- Z~~ '
~
The curve corresponding to this equation is in satisfactory agreement with
the experimental curve.
Assume that during the time Q t from the moment of onset of snow melting
the moisture reserves in the snow have decreased by h. It is assumed
here that until the aera~ion zone is completely filled with water all
the melt water is expended in replenishing the m~oisture suppli~s of this
layer; otherwise surface runoff occurs. The parameterization of the mois-
ture content profile for the upper layer in the form given below corres-
ponds to the assumption
~i' - ~ - - ~i .1h z-z�
~ ~~m W~ H- s~, H z~; if (8>
W ( z ) = lyl~n _ !Y o , 3 ~ h ( r-f - z~ ) .
lk~,n, if Wm Wo ~ 3 a h(H - z~~)�
In our model the discharge of water into a drainage network begins immed-
iately after disappearance of the snow. In the parameterization of dis-
charge we take into account the experimentally established fact that the _
moisture content in the drained sector decreases exponentially with time
to its ~quilibrium value Wequil in accordance with the dependence
W(t) = Wequil ~Wonset - Wequil~e~'aG t~ (9)
where Wonset is the moisture content correspvnding to the moment of onset
of discharge. The parameter OC is determined by the characteristic time
of the discharge, which for the zone of intereat to us is approximately
20 days. It is obvious that if there is ice in the drained layer the dis-
charge will occur more slowly. This can be taken into account by making
the parameter OC variable in time, dependent on the phase state of the
soil. Assume that ice is the mean ice content for the drained layer; ice
= ice(t). We will determine the dependence p~(t) using the expression
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- FOR OFFICIAL US~ ONLY
a (t)=zo (1 -
m ~1~~
After the substitution of (10) into (9) we obtain a formula describing the
dischar.ge of inelt water.
We will complete description of the model by determining the boundary con-
ditions (6). It is known that the influence of the initial condition on
solution of the parabolic equation decreases eaponentially with time. Ac-
cordingly, any plausible function can be taken as T2(z) in (6). We assumed
T2(z) = T~ = const and confirmed that the influence of such an initial
condition on the solution is completely annihilated after three-four years
the solution enters a periodic regime. This occurs for both drained and
undrained swamp areas.
It is known [2] that there is a rather close correlation between the tem-
perature of the surface of the swamp area and the air temperature at a
standard height, which is expressed by the regression equa.tion
Tsurface = 1.1 Tair ' 0.5. (11)
An exception is the period of snow melting when positive air temperatures
correspond to a temperature of the snow surface equal to zero. Thus, as -
the function T1(t) it is possible to take the following
' Tl ~t~ _ 0, if Tsurf ~ h~t~ 7~
Tsurf ~ if Tsurf x h(t) < 0,
where Tsurf is determined using equation (11).
Numerical Application of Model
Solution of a problem of the Stefan tvne bv the smoothed coefficients meth-
~ od is reduced to the crue solution when the smoothing interval tends to
zero [9]. However, a ntunerical solution gives good results when the
smoothing interval covers not less than 4-6 points of intersection of the
difference grid [3]. In order to make the smoothing interval sufficiently
narrow, placing a suff icient number of points of intersection of the
difference grid within it, and at the same time keeping the total number
of points of intersection quite small, it is necessary to use a nonuniform
grid having a region of increased density of points of intersection in
the neighborhood of the point of discontinuity of the coeff icients of the
thermal conductivity equation. In our problem the smoothing is carried
out in the neighborhood of the point z= H at the boundaries of contact
between the thawed and frozen zones. Under ordinary conditions a frozen
zone is formed in the upper part of a peat deposit, that is, with z val-
ues close to H. Therefore, we selected the following construction of a
spatial grid:
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rvi~ VL'1'1V1L1L u~n VIYL1
z~,=0; z,~~z, -N(r- 1)/(r~-1)
~ zt zr= ~ X r: z; = z,= ~ t~ zt; i= 2, 3, , N
Oz,,a., ~ h~t)~9 - 1)(9L- l) H (12) -
~ ez:=~z?_~ Xq; ~;=zr_~+~z~, i=N+2, N+B, N+L
t N= H; ZN 1 L= h( t) H
With r< 1 and q~ 1 the grid (12) has an increased density of points of
intersection in the neighborhood z= H, that is, at the soil surface.
By changing the r and q values it is possible to regulate the maximum
and minimum values of the interval in the z coordinate.
The grid (12) is time-movable. For scaling the grid solution to new points
of intersection with transition to the next time layer it is necessary
to carry out the interpolation as in [1]; we did this using the cubic
spline method [10J.
In applying the model we also use a nonuniform time grid. The most rapid
transformation of the temperature profile is characteristic of the snow
melting period, when a great quantity of heat is released as a result
of crystallization of inelt water. The use of a long time interva] during
this period can result in blunders. During the entire snow melting per-
iod the time interval in our case was 2 hours; otherwise the time was 1
day.
As information for determining the function T1(t) we used materials from
_ direct observations of air temperature published in [12]. Scaling to
points of the time grid was accomplished by interpolation by the cubic
spline method. Similarly we determined the temporal variability of the
depth of the snow cover and snow density.
Equation (5) was approximated in the grid (12) by a system of algebraic
equa.tions using a purely implicit, nonlinear model
T'"+~ - T" 1 T"`-~"t - T'R+~ Tm--t _ T!n+i
em~-1 i / _ ( Q~7 i 1 i _~t r i-1
' ~m-} t_ 7'n~ J=t z"~+~ 1 z'~'lt ,
~ J41 1
W'"~1 - lC/'�"
o T;"-'~ ) % (N - .zt) ~o L ~m+~ _ im , 1 ~ i ~ ~V + L - l ~ ~13~
cm-~ = c( W^~+1, Tm~~' i~.Zt Zmtl 'L 0~m~- 2;
~ ~ ~Jm-t 7'm~-~ ~m~1 7'm . I
a! _ ~ ~ t ~ 1 ) ~ ,
The boundary conditions have the form
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I~OR OFFICIl11. USE ONI.Y
7u = Ti~; 7'N+c = T~ ~tm): 7� = T~~~ n~ i~.`~ ~14~
~e used 1 September as the beginning of time reckoning (at this time a
snow cover is absent). The initial ~emperature distribution ~!n the snow
thickness immediately after falling of the snow was stipulated by a
linear function
smi - H
7~"'~-~ _ ~N~'1 [T'~ ~tm~)- TN~-t~ 'h~~ , 1V -1 1 ~ iN-{-L~ ~15~
,
ml
where t is the moment af onset of a snow cover, hml is the initial
thickness of the snow cover, assumed to be equal to the mean 10-day
thickne~s of the snow cover during the first 10 days after the onset of
its existence.
System (13)-(15) wa~ solved by the traditional iterations method in com- r
bination with fitting.
Results of Computations
On the basis of the mathematical model cited above we carried out com-
putations of the temporal variability of the temperature regime of drained
peat bogs for 15 places in the northern part of the Nonchernozem zone in
. the RSFSR. It was assumed that the depth of the drainage system zp is 1
m; the sea.sona.l variation of ground temperature is completely absent at
a depth of 6 m; the characteristics of the meteorological regime of the
atmospheric surface layer correspond to the observed mean 10-day values
[12] and the thermophysical properties are identical for all the peat
bogs in this zone:
It was established as a result of ma~hematical~modeling that under the
conditions prevailing in the northern part of the Nonchernozem zone of
the RSFSR the drainage of swamp areas leads to a substantial decrease in
the temperature of the upper layer of the peat deposit. The table gives .
the mean temperatures of the upper meter layer of the peat deposit at
the end of each month before and after drainage. An analysis of the
table shows that the mean monthly temperature of the active layer during
the growing season is 1-2�C lower in the drained swamp areas. A tempera-
ture decrease is observed during the entire year.
An increase i.n the depth of snow in drained swamp areas at the sam~ air
temperatures as before drainage leads to,a decrease in the tempe:ature
difference of the active layer in the peat bog before and aftez~ drainage.
Thus, the mean monthly temperature of the meter layer of the deposit in
January, February and March, computed using observational data for the
Verkhniy Shugor meteorological station, is positive, whereas during these
same months the similar temperatures computed for Nar'yan-Mar station are
negative. This is a result of~the fact that the snow depth in the region
125 I
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