JPRS ID: 10558 METEOROLOGY AND HYDROLOGY NO. 2, FEBRUARY 1982

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JPRS L/ 10558
- 2 June 1982
US~R Re ort _
p
METEOR~LOGY AND HYDROIOGY
No. 2, February 1982 ~
FBIS FO~REIGN BROADCAST INFORMATION SERVICE
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JPRS L/10558
2 June 1982
USSR REPORT
METEOROLOGY AND HYDROLOGY
No. 2, February .1~82
Translation of the Russian-language monthly jou~:nal METEOROLOGIYA I
GIDROLOGIYA published in Moscow by Gidrometeoizdat.
CONTENTS
'kT~ieory of Anthropogenic Effects on Local Meteorological Processes in City....... 1
*Investigatioii of Stability of Regression Scheme for Pred~~t~.ng H50G r'ield for
Nort hern Hemisphere 2
*Statis t ics of L~rrors in Predicting Geepotential 3.
*Parame t ers of Statistical Monitorin~ of Vertical Wind Profile 4
*Spatia 1 Structure of Horizontal Flow of Atm:ospheric Moisture 5
*Parame terization of Fluctuations of Stratospheric Ozone Content 6
Effect of Water Temperature Anomaly in North�Atlantic on Circulatidn, Thermal
Regime and Moisture Cycle in Northern Hemisphere Atmosphere 7
Numerical Experiments With Model of Active Layer of Ocean 23
*Criter ia Characterizing Flow of rluids With Stable Stratification 30
Depend ence of Accuracy in Computations of Parameters ~f SEa Wind Waves on
Princ ipal Wave-Forming Factors. 31
*Disper s ion of Suspended Matter in Homogeneous Water Flow 38
*Sprin~ Snow Thawing and Evaporat ion in Central Yakutia 39
*Comput ing Optimum Density of Planted Fi,elds 40
~Comput ing Optimum Grids for Regional Short-Range Weather Forecasting Models.... 41
*
Denotes items which have been abstracted.
- c~ - [III - USSR - 33 S&T FOUO]
F/lA IIF~i!'T A i T?CF /lNT V
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* Applying Separating Function for Alternative Diagnosis or Prediction Using
Dependent Predictors 42
- * Meanders of Cromwell Current 43
* Problems in Meteorological Image Recognition 44
* Eightieth Birthday of Yelizaveta Luarsabovna Andronikova 45
* Awards at USSR All-Union Exhibition of Achievements in National Economy..... 46
* At USSR State Committee on Hydrometeorology and Environmental Monitoring.... 47
* Notes From Abroad 48
* Obituary of Yevgeniy Konstantinovich Fedorov (1910-1981) 49
*
Denotes ite~us which have been abstracted.
.
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UDC 551.588.7
THEORY OF ANTHROPOGENIC EFFECTS ON LOCAL METEOROLOGICAL PROCESSES IN CITY
Mosc~w METEOROLOGIYA I GIDROLOGIYA in Ruesian No 2, Feb 82 (a~nuscript received
15 Aug 81) pp 5-16
[Article by M. Ye. Berlyand, professor, and M. N. Zashikhin, Main Geophysical
Observatory]
[Abstract] A study was made of an urban heat island, with emphasis on formula-
tion of a theory of change in air temperature and humidity, as wel~ as wind
velocity and the radiation regime in a city, and also the diurnal variation
~ and interrelationship of these parameters. Allowance is made for the advective
influence of air flow onto an urban territory from its neighborhood. The mathe-
matical formulation of the problem of modeling urban microclimate is based on
solution of a syrstem of equations for the influx of heat and moiature in the
atmosphere, thermal conductivitq of the soil, continuity equation and equatior
of motion. The initial parameteYS for solving the problem are velocity o� the
geostrophic wind, mean daily temperatures of the underlying surface and the
gradient of vertical temperature decrease in the air and soil, the degree of
mo istening of the underlying surface, as well as the thermal conductivity and
heat capacity coefficients, both in the city and outside it. In solving the
radiation part of the problem it is necessary to stipulate the optical thick-
ness and certain radiation characteriatics of urban air basin contamination. A
series of 6 examples with different parameters was investigated. The computed
values of the intensity of the heat island, the nature of its change in the
course of the day in its annual variation, and also the dependence on wind vel-
ocitq, altitude, etc.. agree well with the known results of numerous observa-
tions. Among the factors taken into account in the model are air contamination,
the degree to which the city is built up, cn~nges in the characteristics of
heat and moisture exchange and release of heat due to economic activity. Such
computations and their analysis made it possible to examine differences in the
diurnal fluctuations of air temperature, wind velocity and exchange coeff icient,
as well as the development of radiation fogs in the city and outside it. Fig-
ures 3; references 19: 10 Russian, 9 Weatern.
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UDC 551.509.314+551.547.3(215-17)
INVESTI~ATION OF STABIZITY OF REGRESSION SCHEME FOR PREDICTING HSp~ FIELD FOR
NORTHERN HEMISPHERE
Moscow METEOROLOGIYA I GIDROLOGIYA in Rusaian No 2, Feb 82 (manuscript received
3 Jul 81) pp 17-25
[Article by V. A. Steblyanko, candidate of phyaical and matnematical sciences,
and A. A. Burtsev, USSR Hydrometeoralogical Scientific Research Center]
[Abstract] In moet statistical weather forecasting schemes there is an in-
crease in the prediction error with transition from a depend~nt to an inde-
pendent sample,because the evaluationa of the correlations between the pre-
dicted parameter and the set of predictors obtained empirically using a de-
pendent sample do not have adequate stability. The authors have attempted to
solve the problem of formulating a forecasting scheme which insofar as pos-
sible takes into account the limited nature of the sample and nonstationarity.
The scheme has an adaptive character (its parameters can be ad~usted in depend-
ence on newly arriving information). The problem is solved by a combination of
the "moving control" and "screening" methods. The example considered here is a
variant of prediction of the mean monthly H500 field, as the predictors tak-
ing some parameters characterizing the preceding months. As possible predic-
tors use was made of the expansion coeff icients for the OT1~88 f ield in the
latitude zone 40-75�13 on the basis of mixed polynomials (Chebyshev polynomials
along the meridian and trigonometric functions along the circles of latitude)
and the coefficients of expansion of the H500 field in polar region in
natural orthogonal functions. An algorithm is proposed for i~.vestigating the
asymptotic behavior of the parameters of the vector of regression coefficients.
This algorithm is based on the Robbins-Munro stochastic approximation proced-
ure. Evaluations of the quality of forecasts with choice of the predictors
only by the "screening" method and also by the "screening" method in combina-
ticn with "moving control" are given. Tablea 1; references: 7 Ruseian.
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UDC 551.509.313
STATISTICS OF ERRORS IN PREDICTING GEOPOTENTIAL
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 2, Feb 82 (manuscript received
25 May 81) op 26-32
[Article by A. M. Babaliyev and V. V. Kostyukov, candidate of phyaical and math-
ematical sciences, Karaganda State University and West Siberian Regional Sci-
entific Research Institute]
(Abstract] An attempt is made to study the errors in two spec.tfic pragnostic
models presently being used in the USSR on th~ basis of a seriea of statistical
characteristics. The first model ia a hemiapherical model based on primitive
eauations, making it possible to obtain forecasts for a hemisphere (Ye. Ye.
Kalenkovich, et al., CHISLENNYYE METODY RESHENIYA ZADACH :d~GNOZA POGODY I
OBSHCHEY TSIRKULYATSII ATMOSFERY, Novosibirsk, VTs SO AN SSSR, 1970). The fol-
lowing statiatical parametera were used: relative error, carrelation coefficient
between two random values, evaluation of similarity of evolution of fields of
predicted and actual trends, mean square error, mean arithetical error. "signal
noise," equal to the ratio of the dispersions of the field of errora and the
actual field, mean values Mat, Mpt and the standard deviations O'Ft and O'pt of
the actual and predicted trends. These eval~:ations were computed separately for
different physiographic regions. Six regions were defined: Table 1 gives the
~ mean values of the evaluations for two- and three-day predictions of geopoten-
tial at the 500-mb level. The success differed considerably for diff erent re-
~rions. The relative errors of two-day forecasts were minimum for Europe, and for
three-day forecasts for North America, whereae the greateat errors were for
the Pacific Ocean area. Also considered, on the same principles and employing
the same statistical criteria, was a model for a limited territory (regional
model) (G. R. Kontarev, IZV. AN 5~~~: FIZIKA ATMOSFERY I OvEANA, Vol 11, No 3,
1975). This model is also based on primitive equations and was developed for
the Novosibirsk region. A table gives evaluations of daily forecasts with the
regional model for the 500-mb surface. In both cases there is a discussion of
the problems involved in taking the errors into account in order to increase
the quality of forecasts. Figures 4, tables 4; referencea: 7 Ruasian.
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UDC 551.509.314+551.55
PARAMETERS OF STATISTICAL MONITORING OF VERTICAL WIND PROFILE
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 2, Feb 82 (manuscript received
26 May 81) pp 33-37
[Article by S. I. Gubanova and S. M. Olevskaya, candidates of F'iysical and math-
ematical sciences, USSR Hydrometeorological Scientific Research Center]
[Abstract] It is more diff icult to monitor the wind than geopotential or temper-
ature. However, due to the recent availability of new data on the statistical
structure of wind components the authors,undertook computations of the appro-
priate parametera for monitoring win:j components at nine isabarie levels from
1000 to 100 mb. In seeking the parametera for vertical statistical monitoring
by the optimum interpolation method used was made of the detailed data on ver-
tical statistical st:ucture of wind components in V. D. Kaznacheyeva, et al.,
"Generalized Characteristics of Vertical Wind Correlationa Over th~ USSR~"
PRIMENENIYE STATISTICHESKIKH METODOV V METEOROLOGII, Moscow, Gidrometeoizdat,
1978. Sin~~e there is a dependence of the interlevel correlatione of ~ind com-
ponents on season and latitude (the zonea 45-60�N, north of 60�N and south of
45�N are defined), computations were made separately for these latitude zones
for winter and sumaner. A table gives the computed monitoring parameters for
both components for January and July. This table reveals that the influence
_ of season on the values of the weighting factors ai, bi in the key formula is
insignificant, especially for the zonal component and can be neglected for all
zones and both components. However, there is a depende~ace of ai, bi on lati-
tude. If the zone 45� is excluded, for the two remaiaing zones it is pos-
sible to use the same interpolation weights. Yt is ahown that the ai, bi val-
ues can be employed in experimental computations in a vertical statistical
monitoring scheme. In a sample teat with use of actual data from 173 stations
in the Soviet Union it was found that the standard deviations of the zonal
and meridional wind components were from 4 to 20 m/sec. Vertically theae para-
meters change approximately identically; they increase with altitude to some
level near 200-300 mb and decrease aloft. Tables 2; references 8: 7 Rusaian,
1 Western.
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UDC 551.571(571.1)(574)
( SPATIAL STRUCTURE OF HORIZONTAL F:,OW OF ATMOSPHERIC MOISTURE
Moscow METEOROLOGIYA ~ GIDROLOGIYA ir. Russian No 2, Feb 82 (manuscript received
25 May 81) pp 38-44
[Article by L. P. Kuznetsova and N. P. Chernova, candidates of geographical sci-
ences, Institute of Water Problems]
[AbstractJ The authors have endeavored to apply the aerological method in com-
putin~ the water balance elements of river basine of different areas and eval-
uating the feasibility of the ob~ective interpolation method in studying the
spatial structure of the horizontal flow of atmospheric moisture in the basins
of the Ob' and Irtysh Rivera. Iri this article emphasis is on determination of
the space correlation functions for the flow of atmospheric moieture. Mvch of
the article is devoted to determination of the values of the correlation coef-
ficients fo.r the latitudinal and longitudinal space correlation function in
~ different distance gradations for the four seasons of the year. It was found
' that the f ields of components of the flow of atmospheric moisture have a clear-
ly expressed anisotropy caused by the seasonal characteristics of circulation
of air masses. It is further shown that the space correlation functiona, comput-
ed independently of dire~tion, provide no adequate information on the structure
of the spatial correlations in the moiature transfer field. They are suitable
only for very approximate computations and for short dietances. In the consid-
ered region this distance is 800-1000 km, approximately corresponding to the'
width of the zone of intensified westerly transfer. Correct computations of
the horizontal moisture flow require the uae of a system of space corYelation
~ functions computed for individual components of the moiature flow and for dif-
ferent directions. Figures 1, tables 3; referencea 9: 8 Russian, 1 Western.
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UDC 551.510.534
PARAMETERIZATIQN OF FLUCTUATIONS OF STRATOSPHERIC OZONE CONTENT
Moscow METEOROLOGIYA I G2DROLOGIYA in Russian No 2, Feb 82 (manuscript received
4 May 81) pp 45-50 ,
[Article by 0. M. Pokrovskiy, candidate of physical and mathematical sciences,
and A. Ye. Kaygorodtsev, Main Geophysical Observatory]
[AbstractJ In this study of the parameterization of fluctuations ot strato-
spheric ozone concentration the initial data used were the mean monthly fields
ef total ozone content during a 10-year observation period 1957-1967 in the
northern hemisphere in a regular grid. Then using the Bozhkov latitudinal-sea-
sonal regression method it was possible to reconatruct the mean ozone concen-
tration (to be more precise, its partial pressure) in nine atmospheric layers
situated between altitudes 5 and 45 km. Computations were made for a 10-year
sample for the northern hemisphere for two seasona winter and summer. Iu
summer the maximum concentration falls in the low latitudes in the middle
stratosphere where processes of photochemical reproduction of ozone are most
intensive. In winter there are two anomalous regions of maximum concentra-
tions. The first is the high-latitude region where a large quantity of ozone
is accumulated, transported by meridional circulation. The second is the trop-
ical zone where the processes of photochemical reproduction of ozone and its
transport from the southern hemiaphere are important. Maximum turbulent trans-
port is in the high-latitude region, whereas transport by stati~nary waves pre- ~
dominates in the temperate latitudes. Ozone is transported from the summer hemi-
sphere into the winter hemisphere by mean meridional circuJ.ation and toward the
poles by turbulent dynamics. Both the atationary and turbulent components of
ozone concentration fluctuations are approximated quite well by empirical or-
thogonal functions. The f irat three empirical orthogonal functions satisfactor-
ily deacribe the spectrum of natural variations in the m~ridional section.
Figures 3, tables 1; references 9: 1 Russian, 8 Weatern.
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~
UDC 551.465.7:551.513(261)(215-17)
EFFECT OF WATER TEMPERATURE ANOMALY IN NORTH ATLANTIC ON CIRCULATION, THERMAL
REGIME AND MOISTURE ~YCLE IN NORTHERN HEMISPHERE ATMOSPHERE
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 2, Feb 82 (manvscript received
27 May 81) pp 51-62
[Article by V. P. Meleshko, candidate of physical and mathematical sciences,
and A. P. Sokolov, Main Geophysical Observatory]
[Text] Abstract: A model of general circulation of
the atmosphere was used in investigating the
influence of the water temperature anomaly in
the North Atlantic on general circulation,
thermal regime and moisture c~?cle in the atmo-
sp'~ere. A positive anomaly is stipulated in
the zone of active thermal interaction between
the atmosphere and the underlying surface, sit-
uated in the northeastern part of the Atlantic
Ocean. The state of the atmosphere in the north-
ern hemisphere in January was computed by means
of integration of a system of equations for a
period of two months, with and without allowance
for the water temperature anomaly. The article
gives a detailed comparative analysis of atmo-
spheric charaeteristics for the northern hemi-
, sphere and individual regions on the European
continent.
Introduction. Recently a number of interesting investigations directed to study
of large-scale interaction between the atmosphere and ocean and evaluation of
~ the influence of water temperature anomalies in the upper layer of the ocean
on general circulation and thermal regime of the atmosphere have been carried
out.
Bjerknes [19, 20] established that the formation of a positive thermal anomaly
in the equatorial zone of the Pacific Ocean ia accompanied by an intensifica-
tion of the zonal current in the middle-latitude atmosphere in winter. In his
opinion, this correlation is governed by an increase in ascending movements
and water vapor condensation over the region of the anomaly, causing an intensi-
fication in meridional circulation in the Hadley cell gnd an increase in the
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transport of the moment of momentum from the low latitudes into the middle and
high latitudes. In the example of anomalous weather conditions over the north-
ern part of the Pacific Ocean and North America Namias [25-27] demonstrated
that there is a correlation between atmospheric processes over these regions
and water temperature in the northern and central re~ions of the Pacific Ocegn.
He also established that in a number of cases water temperature anomalies of a
considerable extent can persist for a period of several months and therefore
data on them are of def~nite prognostic value.
The problem of the influence of the North Atlantic on the formation of average
weather conditions over Europe and the territory of the USSR has been examined
in numerous Soviez and foreign studies. In most of these studies attempts have
been made to establish synchronous and asynchronous statistical correlations
between the thermal regime of the North Atlantic and atmospheric circulation, on
the one hand, and weather conditions over Europe and the European USSR, on the
other. For example, V. G. Semenov [15] established that during the winter months
when there is a negative temperature anomaly in the northern part of the Atlan-
tic Ocean (to the west and southwest of Iceland) a zonal circulation is observ-
ed over Europe, whereas when there is a pasitive anomaly there is an intensive
meridional transport of air masses. He noted the existence of a feedback between
water temperature anomalies in the northern regions of the ocean and air temper-
atures over the European USSR in winter and their relatively weak direct correl-
ation during the summer months. It was noted in a study by S. T. Pagava, et al.
[13] that in order to detect the correlation between the thermal state of the
North Atlantic and air temperature in Europe it ie extremely important to take
into account not only heat exchange between the ocean and the atmosphere, but
also informstion on the type of synoptic processes. In another study [14J, S. T.
Pagava formulated the conditions under which there are direct and inverse rela-
tionships between air temperature in Europe and water temperature in the North
Atlantic.
On the basis of observational data Ratcliffe and Murray [28] established that the
development of blocking anticvclones over Western Europe and Scandinavia is asso-
cfated with the appearance of negative anomalies over an extensive area of the
ocean to the south of Newfoundland and passage of active cyclones was associated
with the formation of a positive anomaly. Among the other studies in this direc-
tion here we should mention as well the investigations made by A. N. Kryndin
[8], A. L. Kats, et al. [6], N. A. Bagrov and N. I. Mertsalova [2], A. L. Duy-
tseva and D. A. Ped' ~5], A. I. Ugryumov and A. P. Krupyanskaya [lfi], L. V. Kli-
menko and L. A. Strokina [7].
Although the important role of the ocean in the formation of weather on the con-
tinents, especially over Europe, has been confirmpd by ntunerous investigations
and a great number of different prognostic procedures have been proposed, the
basis for which has been the correlations between individual characteristics of
the ocean and atmosphere, the quality of long-range forecasts still remains un-
satisfactory. The reason for such a situation is evidently the extreme diver-
sity of the processes of thermodynamic interaction both in the atmosphere itself
and in the ocean-atmosphere system caused by the operation of inechanisms with
feedbacks.
. 8
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A number of hypotheses have been proposed in which the long-observed devel-
opment of anomalous weath~r conditions over individual regions of the earth
can be attributed to such factors as the development of stable anomalies in
the upper layer of the ocean, the anomalous extent of sea ice and snow cover
on the continents, etc. Among the investigations in which a study was made of
the influence of water temperature anomalies in the Pacif ic Ocean on atmospher-
ic circulation and certain hypotheses explaining the formation of anomalous
states of the atmosphere over the North American continent and other regions
of the earth were checked we should mention the studies of Spar [30, 31],
Chervin, et al. [21], Kutzbach [22], Rowntree [29J, Shukla and Bangaru [32].
The studies of G. I. Marchuk, et al. [9, 10] proposed a mathematical approach
based on integration of the conjugate equations of hydrothermodynamics of the
atmosphere and ocean which makes it possible to describe some asynchronous re-
lationships between the atmosphere and ocean and to determine thermally active
regions in the world ocean, exerting a considerable influence on the formation
- of macroscale air temperature anomalies over individual regions of the earth.
Che Soviet program "Razrezy" will be an important contribution to study of the
processes of interaction between the ocean and the atmosphere for the purpose
of establishing a correlation between thermal and dynamic anomalies in the
ocean and formation of anomalous thermal and circulation regimes in the atmo-
sphere. Implementation of this program has already begun. Our investigation
was carried out in accordance with the plan for work under the mentioned pro-
gram.
Model of Atmosphere and Formul.ation of Experiment
The objective of our investigation was an evaluation of the influence of the
water temperature anomaly in one of the regions o� active thermal interaction
between the atmosphere and ocean, situated in the North Atlantic, on general
circulation, thermal regime and moisture cycle in the atmosphere.
ico
~~�ev _ .
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,~yf .\yt' {~~1/ % ' 1~]~ l I . .y~
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tA ( I 'i ~ ~ '.f ~ 90 ( / r~- r~ -I Cl ~
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rec ~i ~ ~ .L' ~~-J�~.~i ~
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' 1 ' ~ ___l._-_-'
o .
Fig. 1. Distrfbution of total heat Fig. 2. Position of region with water
- flow (turbulent flow and heat loss- temperature anomaly (�C). The dashed
es in evaporation) computed using line defines three regions on the Euro-
atmospheric model for January (W/ pean continent.
m2). Regions in which heat flow is
over 180 W/m2 are shaded.
9
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Somc information on regions of an active thermal effect ^-an be obtained from
the HEAT B~~LANCE ATLAS [1], which gives the distributions of turbulent heat
flows and heat expenditures on evaporation, computed for different months of
the year. According to the maps cited in the atlas, during the cold season of
the year the greatest total heat flow values, including the turbulent heat flow
and expenditures of heat ~n evaporation, are situated along the eastern shores
= of the Asiatic and American continents, and also in the tropical zone.
Figure 1 shows the distribution of the mean total heat flow, computed by means
of a model of general circulation of the atmosphere for January conditions.
Figure 1 shows the distribution of heat flows to the atmosphere as a whole Lo be
in agreement with [1], although the region of great heat flows in the North At-
lantic in the model was displaced in the direction of the European continent.
Accordingly, for stipulating of ocean surface temperature anomalies we selected
a region situated in the northeastern part of the Atlantic Ocean in which the
computed total heat flows entering the atmosphere from the underlying surface
were the greatest (see Fig. 2).
The investigation was made using a model of general circulation of the atmo-
sphere developed at the Main Geophysical Observatory imeni A. I. Voyeykov. De-
tailed information on the model is given in [11] and therefore it will only be
described briefly.
The model has three layers of equal mass; the integration region is a hemisphere.
The geographical distribution of the continents and their relief is taken into
accouut. The mean horizontal grid interval is 425 km.
The model makes use of a full system of equations in hydrothermodynamics in an
CY-coordinate system. The principal physical processes operative.in the atmo-
sphere are taken into account: transport of solar and long-wave ~adiation, tur-
bulent exchange in the boundary layer, macroscale condensation and convection,
hydrological regime of the active soil layer and mesoscale diffusion. The flux
of solar radiation reaching the upper boundary of the atmosphere is computed
. taking into account the temporal change in mean daily solar altitude. The quan-
tity of two-level clouds is determined using empirical expressions on the basis
of the relative humidity values in the corresponding layers of the atmosphere
computed in the model.
An evaluation of atmospheric response to water temperature anomalies at the ocean
surface was made in two numerical experiments. In the first of these the water
temperature was assumed equal to its climatic value (with seasonal changes taken
into account). Henceforth for convenience in exposition we will call this experi-
ment the control (CE). In the second experiment the values of the anomalies were
added to the climatic water temperature values in the region shown in Fig. 2.
_ Both the value of the anomaly itself and the horizontal extent of the region of
its stipulation were considered constant during the entire integration time. We
will call these computations an experiment with an anomaly (AE).
In each experiment the system of equations was integrated for 60 days with the
use of real initial data, which corresponded to 1 December. The computations
were analyzed for the period from 31 to 60 days of the forecast, corresponding
to January.
10
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12
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~
In discussing the r~~sults it must be remembered that the differences between
the variables represented in the figures were obtained by subtracting the
~ values computed for the CE experiment from the corresponding values obtained
i in the AE experiment.
i
Change in Circulation, Thermal Regime and Moisture Cycle in Northern HemiP~,here
Atmosphere
In the formation of a positive water temperature anomt.ty the lower lay~ars of the
troposphere began to receive additional heat over the iagion with an anomaly due
to an increase in the vertical transport of turbulent heat and the latent heat
of condensation. The quantity of the additional heat influx is dependent on
changes in the vertical drop in temperature and specific humidity, and also on
stratification of the lower layer of the troposphere.
Table 1
Quantity of Turbulent Heat Flow H and Heat Losses
in Evaporation LE, Computed in AE and KE Exper-
' iments for 31-60 Days of Forecast Qver Region
With Water Temperature Anomaly
Heat flow, W/m2 CE AE
g 81 206
LE 139 195
~ Table 1 shows that as a result of the effect of these anomalies the total heat
' flow increased by a factor of 1.8. This change occurred for the most part due
, to an increase in the turbulent heat flow.
It is interesting to note that with an increase in water temperature by 1�C the
computed changes in the heat flows considerably exceed the corresponding changes
in the flows obtained in [22] for the northern part of the Pacific Ocean. This
is evidently attributable to the fact that the thermal interaction between the
atmosphere and ocean in the northeastern part of the Atlantic Ocean is more in-
~ tensive than in the northern and northeastern regions of the Pacific Ocean (see
Fig. 1).
The computed changes in some characteristics of the moisture cycle, and also the
thermal and circulation regime of the northern hemisphere as a result of the ef-
fect of ocean temperature anomalies,are shown in Fig. 3.
Although the general picture was quite complex, from a comparative analysis of
~ the cited fields it is possible to establish a number of interesting peculiar-
ities.
' Considerable changes in the total heat flow were obtained not only in the water
temperature anomalies, but also in other regions of the northern hemisphere.
The greatest changes in the heat�flows are concentrated in regions of active
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thermal interaction between the atmosphere and the underlying surface situated
in the Atlantic and Pacific Oceans (Fig. 3a).
A macros~ale cy~clonic eddy in the field of differences in the horizontal velo-
city vector, whose axis is somewhat tilted to the east with an increase in alti-
tude, is formed over the region with the anomaly (Fig. 3b). Macroscale eddies
with cyclonic or anticyclonic rotation in the field of differences in the hori-
zontal velocity vector are observed in other regions of the~northern hemiephere.
The most intense eddies are formed near the eastern shores of the continents,
that is, over regions of active thermal interaction between the atmosphere and
the ocean surface.
It can be noted from a comparison of Figures 3a and 3b that the formation ~f cy-
clonic eddies in zones of active thermal interaction is closely asaociated ;vith
the e;ign of the difference in total heat~flows: positive flow differences cor-
- respond to cyclonic eddies and negative flow differences correspond to anticy-
clonic eddies.
The air temperature in the lower troposphere inc~�eases to the southeast of the
region with the anomaly and decreases to the nor~:h of it (Fig. 3c). Air temper-
ature changes which are large in absolute value and different in sign are observ-
ed at considerable distances from the North Atl3ntic. It should be noted that the
regions of increase (decrease) in temperature egree well with the corresponding
regions of decrease (increase) in pressure, reduced to sea level. Large pressc~re
differences are observed primarily over the continents in the middle and high
latitudes. The Icelandic and Aleut~an Lows were somewhat transformed: the first
extended in the direction of Western Europe, the extent of the second decreased.
An example of the important role which is played by circulation factors in forma-
tion of the thermal regime of the atmosphere:is the temperature distribution
directly over the region of the ocean surface temperature anomaly. In the north-
ern part of this region, at altitudes of about 1.5 km, there is a rather consid-
erable decrease in air temperature which is associated, as indicated by Fig. 3b,
with the formation of the mentioned cyclonic cell, and as a result, with the
transport of cold air masses into the Atlantic Ocean area from the northern part
of the European continent.
The problem of why in the AE experiment there was a change in the circulation and
thermal regime of the atmosphere in regions situated at a considerable distance
from the North Atlantic is quite complex. Qne of the possible explanations of
this phenomenon is as follows.
The heating of the lower layer of the troposphere over the region w~th the water
temperature anomaly favored a decrease in air density in a column of the atmo-
sphere and a redistribution of mass in the northern hemisphere. This was the
reason for some change in circulation. Since the water temperature did not change
over other parts of the oceans in the AE experiment, the turbulent flows of heat
- and the expenditures of heat on evaporation could change only as a result of
a change in wind velocity, air temperature and humidity in the lower troposphere.
These changes to a great extent are dependent on stratification of the planetary
boundary layer. The greatest heat flow changes can be expected in zones of ac-
tive thermal interaction, where the stratification of the lower layer is
14
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~ unstable in comparison with other regions. As a result, the initially arising
changes in circulation and the thermal regime in the lower troposphere can in-
crease over the zones of active thermal interaction as a result of the influence
of inechanisms with positive feedbacks.
The fact that substantial changes in pressure and temperature are observed not
only near the region with the water temperature anomaly, but also at a consider-
able distance from it, serves as a confirmation of the well-known hypothesie
of the existence of a con~ugate character of atmospheric processes in indiv~dual
regions of the earth. For example, Spar [31] noted that in the modeling of glo-
bal circulation with a water temperature anomaly in the northern part of the
Pacific Ocean considerable pressure changes were discovered in the middle lati-
tudes of the southern hemisphere.
An analysis of the results of computations also reveals thzt in regions with the
greatest air temperature differences, which are situated primarily over the con-
tinents, the greatest temperature dispersion values also occur. These featur~s
are in qualitative agreement with the empirical investigations carried out earl-
ier. For example, on the basis of an analysis of the natural orthogonal func-
tions for the temperature and pressure f ields in the northern hemisphere M. I.
Yudin [18], A. V. Meshcherskaya, et al. [12] studied oscillatory processes on a
planetary scale. In the temperature and pressure fields there was found to be a
number of nodes of different sign which resemble standing waves in the atmosphere
of the thermopressure seiche type described by V. V. Shuleykin [17]. A study by
E. I. Girskaya [4] also revealed macroscale temperature variations in individ-
ual regions of the northern hemisphere for different months.
Figures 3d and 3e give the differences in the intensity of precipitation and the
vectors of horizontal transport of moisture in the atmospheric layer 600-1000
gPa. Figure 3d shows that the zone of a considerable increase in precipitation
in the AE experiment is situated along the southern regions of the European con-
tinent and over the greater part of the North Atlantic. It is noteworthy that
an increase in precipitation occurred not only to the east of the anomaly, but
also in a westerly direction as far as the North American continent, that is,
opposite the main west-east transport of air masses.
Fi3ures 3b and 3e show that in addition to the formation of a cyclonic eddy an
eddy of similar intensity was formed over the second region of active thermal
interaction between the atmosphere and ocean situated in the region of the Gulf
of Mexico (see Fig. 1). As a result, these two eddies formed an intercontinental
circulation cell whose northern branch carries cold air onto the North American
continent from the eastern regions of Europe and the polar basin, whereas the
southern branch transports warm and moist air from the region of the Gulf of
Mexico onto the European continent and then to the Caspian Sea. As a result of
intensification of the zonal wind component along the southern branch of the
circulation cell evaporation �rom the ocean surface also increased in this zone.
Extensive regions with considerable differences in precipitation are observed in
other regions of active thermal interaction between the atmosphere and ocean and
the continents adjacent to it. The sign of change in precipitation agrees quite
well with the nature of change in the horizontal transport of moisture in the
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lower troposphere. In particular, on the continents precipitation increases in
those places where the horizontal transport of moisture in the f ield of differ-
ences is directed from the ocean and decreases in those regions of the ocean
where the corresponding transport occurs from the continent.
.70 �t~ ~ l~~~~ ~ : t ~ ~i ,r d)
_3 1 ~ , ~ ~ ~ ~ ~ ~�:~y
40 ~ ~ rn , r : (l
~ o~ ' r ~ o ~ ~ ~ , ~F
SO ~ '%.F J, ' � ~ / ,o' ~ ? I
r ~ ~ ~f�J. ~ , ~ ov/~ V, ` 1
, ~ �
~t' tv
, ~ ' ~t,~ ~ ~ ~
e ~
days ~ ~ L.~ ~'Ur,.r,� p / , n
~
r ~ ~:.o ; J
40 : - ~ ~ i ~ ~ .
~ o; ',,.r,~ ~ t~ ~ ~ : ~ ~
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so
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1~'71 i rT''l, 1 IT^rrll' -
0'/ J d9 110 1B0 170 S9 ~ d. U G'D. d. 60 >?0 1B0 17U i0 t D. 0
Eurasia America Eurasia America
Fig. 4. Longitude-time distributions of deviatione of altitude of 500 gPa sur-
face (dam) from zonal values. a) wave numbers 1 and 2, CE experiment; b) wave
numbers 1 and 2, AE experiment; c) wave numbers 5 and 6, CE experiment; d) wave
numbers 5 and 6, AE experiment. ~
Table 2
Dependence of Square of Amplitude of Altitude of 500 gPa Isobari_c Surface on
Wave Number for Latitude Zone 50-60�N According to AE and CE Experiments
Wave Number
1 2 3 4 5 6 7 8 9 10
CE 37.5 50.6 21.0 18.6 14.7 11.0 9.0 4.5 2.4 5.3
AE 19.8 88.9 11.3 18.0 25.7 20.4 9.7 5.0 3.7 6.4
Changes in Amplitude and Velocity of Movement of [~~ave Disturbances
Now we will examine the influence of the water temperature anomaly on the velo-
city of propagation of wave disturbances in the atmosphere in the latitude zone
passing through the region with the anomaly.
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Table 2 shows that considerable changes were exhibited by the amplitudes of
planetary waves with the numbers 1, 2 and 3 which are determined by t~ie value
of the thermal contrast between the continents and oceans. The formation of an
anomaly in the North Atlantic favored an intensif ication of an ultralong wave
with the number 2 to a considerable degree at the exnense of waves 1 and
3. The energy of baroclinic waves with the numbers 5 and 6 also increased ap-
preciably.
The evaluations show that in the considered latitude zone the energy of all the
waves increased by 18% in the middle troposphere. The energy of planetary waves
with the numbers 1, 2, 3 increased by l0y (with an increase in the energy of the
wave with the number 2 by 80%), the energy of the baroclinic waves with the num-
bers 5, 6-- by 76%, and the energy of all the shorter waves by 8%.
Figure 4 gives the longitude-time diagrams (distributions of troughs and ridges)
for two groups of waves whose diameters were subjected to an appreciable change:
planetary waves with the numbers 1 and 2 and baroclinic waves with the numbers
5 and 6. These diagrams were constructed on the basis of data on the change in
the altitude of the isobaric surfac~ 500 gPa from 31 through 60 days for the .
latitude zone 50-60�N.
It follows from Figures 4a,b that an increase in the amplitude of the planetary
wave with the number 2 and attenuation of a wave with the number 1 in the AE ex-
periment caused an intensification of the ridge over the Pacif ic Ocean'and a
trough over the North American continent. With respect to the trough over Eurasia
its intensity almost did not change, but it became less mobile in the AE experi-
ment.
The intensity of the troughs and ridges, which correspond to baroclinic waves
with the numbers 5 and 6(Fig. 4c,d), increased over the Pacific and Atlantic
Oceans and North America in the AE experiment. Moreover, whereas in the CE ex-
periment the ridges and traughs over North America and the Pacific Ocean were
motionless or moved little, in the AE experiment they became deeper and more
mobile. The mean velocity of their movement to the east was about 130/km day at
all longitudes.
A similar spectral analysis of aititude of the 500 gPa surface was made for the
l.atitude zone 40-50�N~ that is, to the south of the anomaly, which also indicat-
ed that the amplitudes of the baroclinic waves with the numbers 5 and 6 somewhat
- increased, whereas the troughs and ridges became more mobile. If it is assumed
that the mentioned baroclinic waves correspond to large pressure formations in
the atmospheric model, it can evidently be assumed that in the formation of a
positive water temperature anomaly there is an intensification of cyclonic
(anticyclonic) activity and a meridional type of circulation in the middle lati-
tudes of the northern hemisphere.
Regional Changes in Precipitation and Thermal Regime Over European Continent
For a more detailed clarif ication of the mechanism of the influence of the water
temperature anomaly in the North Atlantic on the thermal regime of the atmosphere
over the Euro~ean continent this continent was broken down into three ma~or ~
~ 17
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regions (see Fig. 2): northwestern regions of the USSR and Scandinavia (region
1), Western Europe (region 2), central and southern regions of the European
USSR (region 3). These regions include 9, 12 and 12 paints of grid intersection.
Tabl'e 3 shows that temperature changes in diffzrent regions of Europe are not
identical. In Western Europe (region 2) and in the European USSR (region 3) the
temperature of the tropoaphere increased, especially significantly in the first
of the men~ioned regions. On the other hand, over the northwestern regions of
the USSR and Scandfnavia it decreased at all levels in the atmosphere.
As indicated by Figures 3b and 3e~, the main reason for the temperature increase
in the tropospnere over regions 2 and 3 was an increase in the horizontal trans-
port of heat and humidity from the Atlantic Ocean onto the continent by the
southern branc~. oi the intercontinental circulation cell, whereas the decrease
in temperature over region 1 was caused by an intensification of the horizontal
transport of cold air masses from the internal regions of the continent. With
respect to the insignificant decrease in temperature at the level 150 gPa over
all the regions, it was caused by a general attenuation of west-east transport
over Europe.
Table 3
Mean Differences Between Air Temperatures (�C) at Four Atmospr~eric Levels. Com-
puted Using Data From AE and CE Experiments for Three Regions in Europe for
31-60 Days of Forecast
Changes in air temperature Region
1 2 3
a T150 -0.4 O.Z -0.1
bT500 -2�4 1.2 0.4 ~
ST850 -2�~ 4.9 1.4
b T1000 -2�9 5.2 1.6
Table 4
Mean Intensities of Precipitation (in cm/day) Obtained in AE and CE,Experiments
for Three Regions for 31-60 Days of Forecast
Experiment Region
1 2 3
c;L 0.27 0.27 0.19 ~
AE 0.19 0.40 0.22
Table 4 gives the mean intensities of precipitation obtained in the AE and CE
experiments. In regions 2 and 3 precipitation increased by 48 and 16Y respec-
~ tively, whereas in region 1 it increased by 30y. With respect to surface pres-
sure, it decreased in all three regions: in the firat by 6.0 gPa, in the
second by 11.5 gPa, and in the third by 4.1 gPa. Thus, in the AE
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experiment over a large part of the European continent there was a warming in
the troposphere and an increase in the quantity of precipitation and only
over Scandinavia and the northwestern regions of the USSR did the temperature
drop and did the quantitp of precipitation decrease.
Statistical Significance of Changes in Temperature and Precipitation
The question of the extent to which these changes in the thermal regime in the
troposphere and precipitation are statistically significant is of definite
interest. As a significance test we will examine the ratio [24]
,
I ~ _ cT '
Here BA - BK is the difference in two sample means in which BA and BK are
the mean monthly values of the variable B in experiments with allowance for the
stipulated water temperature anoma].y and without allowance for it, CrT is the
mean square error in evaluating the mean.
The volume of the sample which is used in evaluating significance is very lim~t-
ed and therefore the evaluations obtained here must be regarded as extremely ap-
proximate. The evaluation of aignificance was made on the basis of 30 instant-
aneous states of the atmosphere with a time interval of one day. The mean
square error CJ'T was computed taking into account that the variables entering
into the time series are not random. First, on the basis of the resu~lts of numer-
ical experiments we determined the time autocorrelation function for temperature
at the level c3'= 0.833 and precipitation separately over the continents and
oceans in the middle and low latitudes. A comparison of the four normalized
functions for each variable indicated that the differences between them are in-
signif icant. Accordingly, in the,r0 evaluations we used one (but different for
temperature and precipitation) normalized autocorrelation function, which was
approximated by an analytical formula ensuring its positive determinancy. The
evaluations indicated that the changes in temperature in the lower troposphere
were significant ( Ir~ 1) over great regions of the northern hemisphere, in-
cluding Western Europe and the European USSR.
Similar evaluations were made for precipitation and indicated that for the north-
ern part of the Atlantic Ocean, Europe, Far East and Southeast Asia the computed
changes are also statistically significant.
Summary
The results of the numerical experiment and the model of general circulation of
the atmosphere indicated that the influence of the positive water temperature
anomaly in the ocean on general circulation, thermal regime and moisture cycle
in the atmosphere is manifested very complexly. In the formation of an anomaly
in the northeastern part of the Atlantic Ocean there is an appreciable iricrease
in temperature of the troposphere and an increase in precipitation over Weatern
Europe and a considerable part of the European USSR. On the other hand, a de-
crease in air temperature and decrease in precipitation occur in the northern
regions of Europe.
19
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Changes in the thermal regime of the atmosphere are also observed in other re-
gions of the northern hemisphere: air temperature increases in the Far East
and in Alaska and decreases over the polar basin and over the greater part of
the North American continent. Substantial changes in precipitation are discover-
ed in the low latitudes. Macroscale preasure formations became more intensive
and mobile in the middle latitudes in the AE experiment.
The additional heat flow entering the atmosphere over the region with the water
temperature anomaly causes a redistribution of atmospheric mass and a change
in circulation. This is evidently the principal factor favoring appreciable
changes in heat transfer to the atmosphere over other regions of active ther-
mal interaction. The value and the sign of these changes are determined by the
complex of physical processes with feedbacka, so that it is extremely difficult
to establish a cause-and-effect aequence for these processes.
In this connection it is worth noting further investigations directed to the de-
termination of the conditions under which the intensity of heat transfer from
the underlying surface to the atmosphere can change substantially in the re-
gions of active thermal interaction quite remote from the regions of formation
of water temperature anomalies in the ocean.
We note in conclusion that the results obtained in this investigation to a cer-
tain degree are dependent on the properties of the atmospheric model, in partic-
ular, on the presence of a boundary at the equator, methods for the parameteriza-
tion of physical processes, etc. For this reason it is desirable to carry out
similar investigations with other atmospheric models.
BIBLIOGRAPHY
1. ATLAS TEPLOVOGO BALANSA ZENIIQOGO SHARA (Atlas of the Earth's Heat Balance),
edited by M. I. Budyko, Moscow, 1963.
2. Bagrov, N. A. and Mertsalova, N. I., "Thermal Interac*ion Between the Ocean
and Atmosphere," TRUDY GIDROMETTSENTRA SSSR (Transactions of the USSR Hydro-
meteorological Center), No 64, 1970.
3. B~erknes, J., "Macroscale Disturbance of Atmospheric Circulation Caused by
the Possible Influence of the Pacific Ocean Equatorial Zone," DINAMIKA
KRUPNOMASSHTABNYKH ATMOSFERNYKH PROTSESSOV (Dynamics of Macroscale Atmospher-
ic Processes), Moscow, Nauka, 1967.
4. Girskaya, E. I., SOPRYAZHENNOST' TF�MPERAT[JRNYKH ANOMALIY SEVERNOGO POLUSHAR-
IYA (Con~ugate Nature of Northern Hemisphere Temperature Anomalies), Lenin-
grad, Author's summary of dissert+~tion, Leningrad, 1971.
5. Duytseva, M. A. and Ped', D., "Degree of Influence of Thermal State of Water
in the North Atlantic on Formation of the Temperature Field Over the Contin-
ent," TRUDY GIDROMETTSENTRA SSSR, No 93, 1972.
6. Kats, A. L., Morskoy, G. I. and Semenov, V. G., "Formation of Large Air Tem-
perature Anomalies Over the Territory of the USSR During Winter," TRUDY TsIP
(Tratlsactions of the Central Institute of Forecasts), No 29, 1957.
20
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7. Klimenko, L. V. and Strokina, L. A., "Correlation Between Change in Heat
Content of Waters in the North Atlantic and Air Temperature Over the Euro-
pean Territory of the USSR During Winter," TRUDY GGO (Transactions of the
Main Geophysical Observatory), No 249, 1969.
~I 8. Kryndin, A. N., "Role of the North Atlantic in Formation of Air Temperature
' Over the European Territory of the USSR," TRUDY GIDROMETTSENTRA SSSR, No 23,
1968.
9. Marchuk, G. I. and Skiba, Yu. N., OB ODNOY MODELI PROGNOZA OSREDNENNYKH
ANOMALIY TEMPERATURY (One Model for Predicting Averaged Temperature Anom-
alies), Preprint VTs SO AN SSSR, Novosibirsk, 1978.
10. Marchuk, G. I., "Modeling of Changes in Climate and the Problem of Long-
Range Weather Forecasting," METEOROLOGIYA I GIDROLOGIYA (Meteorology and
Hydrology), No 7, 1979.
11. Meleshko, V. P., et al., "Hydrodynamic Model of General Circulation of the
Atmosphere," TRUDY GGO (Transactions of the Main Geophysical Observatory),
No 410, 1980.
12. Meshcherskaya, A. V., Rukhovets, L. V., Yudin, M. I. and Yakovleva, N. I.,
YESTESTVENNYYE SOSTAVLYe1YUSHCHIYE METEOROLOGICHESKIKH POLEY (Natural Compon-
ents of Meteorological Fields), Leningrad, Gidrometeoizdat, 1970.
13. Pagava, S. T., et al., VLIYANIYE SEVERNOY ATLANTIKI NA RAZVITIYE SINOPTICH=
ESKIKH PROTSESSOV (Influence of the North Atlantic on the Development of
Synoptic Processes), Leningrad, Gidrometeoizdat, 1958.
I 14. Pagava, S. T., "Nature of the Correlation Between the Thermal State of the
North Atlantic and Air Temperature in Europe," METEOROLOGIYA I GIDROLOGIYA,
- No 1, 1962.
15. Semenov, V. G., VLIYANIYE ATLANTICHESKOGO OKEANA NA REZHIM TEMPERATURY I
OSADKOV NA YeTS (Influence of the Atlantic Ocean on the Temperature and
Precipitation Regime in the European USSR), Leningrad, Gidrometeoizdat,
1960.
16. Ugryumov, A. I. and Kupyanskaya, A. P., "Some Correlations Between Tempera-
ture of the Ocean Surface and Atmospheric Circulation in the North Atlan-
tic," TRUDY GIDROMETTSENTRA SiSR, No 147, 1975.
17. Shuleykin, V. V., "Macroscale Interactions Between the Ocean, Atmosphere
and Continents," PROBLEMY SOVREMENNOY GIDROMETEOROLOGII (Problems in Mod-
ern Hydrometeorology), Leningrad, Gidrometeoizdat, 1977.
18. Yudin, M. I., "Study of Factors Governing Nonstationarq State of General
Circulation of Atmosphere," DINAMIKA KRUPNOMASSHTABNYKH ATMOSFERNYKH
PROTSESSOV (Dynamics of Macroscale Atmospheric Processes), Moscow, Nauka,
1967. ~
~ 21
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- 19. Bjerknes, J. A., "A Possible Response of the Atmospheric Hadley Circula-
tion to Equatorial Anomalies of Ocean Temperature," TELLUS, Vol 18, No 4,
1966.
20. Bjerknes, J., "Atmospheric Teleconnections From the Equatorial Pacific,'~
MON. WEATHER REV., Vol 97, No 3, 1969. .
21. Chervin, R. M., Washington, W. M. and Schneider, S. H., "Testing the Statis-
tical Significance of the Response of the NCAR General Circulation Model to
North Pacific Ocean Surface Temperature Anomalies," J. ATMOS. SCI., Vol 33,
No 3, 1976.
22. Kutzbach, J. K., et al., "Response of the NCAR General Circulation Model to
Prescribed Change in Ocean Surface Temperature. Part I: Mid-Latitude
Changes," J. ATMOS. SCI., Vol 34, No 8, 1977.
23. Laurman, J. A. and Cates, W. L., "Statistical Con:3iderations in the Evalu-
ation of Climatic Experiments With Atmospheric General Circulation Models,"
J. ATMOS. SCI., Vol 34, No 8, 1977.
24. Leith, C. E., "The Standard Error of Time-Average Estimates of Climatic
Means," J. APPL. METEOROL., Vol 12, No 9, 1973.
25. Namias, J., "Seasanal Interactions Between the North Pacific Ocean and
the Atmosphere During the 1960s," MON. WEATHER REV., Vol 97, No 3, 1969.
26. Namias, J., "The 1968-1969 Winter as an Outgrowth of Sea and Air Coupling
During Antecedent Seasons," J. PHYS. OCEANOGR., Vol 1, No 2, 1971.
27. Namias, J., Negative Ocean-Air Feedback Systems Over the North Pacific in
the Transition From Warm to Cold Seasons," MON. WEATHER REV., Vol 104, No
9, 1976.
28. Ratcliffe, R. A. S. and Murray, R., "New Lag Associatiozs Between North
Atlantic Sea Temperature and European Pressure Applied to Long-Range
Weather Forecasting," QUART. J. ROY. METEOROL. SOC., Vol 96, No 408 [year
not given}.
29. Rpwntree, P. R., "Statigtical Assessment of Sea," SER., Vol 1, No 22, 1979.
30. Spar, J., "Some Effects of Surface Anomalies in a Global General Circula-
~ tion Model," MON. WEATHER REV., Vol 101, No 2, 1973.
31. Spar, J., Transequatorial Effects of Sea Surface Temperature Anomalies in
a Global General Circulat~_on Model," MON. WEATHER REV., Vol 1D1, No 7,
1973.
32. Shukla, J. and Bangaru, B., "Effect of a Pacific Sea Surface Temperature
Anomaly on the Circulation Over North America: A Numerical Experiment
With the GLAS Model," GARP PUBL. SER., Vol I, No 22, 1979.
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UDC 551.46.01.001.57:551.5
NUMERICAL EXPERIMENTS WITH MODEL OF ACTIVE LAYER OF OCEAN
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 2, Feb 82 (manuscript received
9 Apr 81) pp 63-68
_ [Article by V. A. Ryabchenko, candidate of physical and mathematical sciences,
Institute of Oceanology, USSR Academy of Sciences]
[Text] Abstract: An integral model of the active layer
of the ocean [4] for taking into account the
feedback between the heat flow at the water-
air boundary and temperature of the ocean,sur-
face is given. Results of computations of the an-
nual variation of temperature in the upper
quasihomogeneous layer in the region of
weather station N agree well with observation-
al data. The results of numerical experiments
are given. These illustrate the sensitivity
of the solution to variations in parameters
of the model. It is shown that the reaction of
the solution is substantially greater with the
variation of the external (atmospheric) para-
meters and weaker with the variation of the in-
ternal parameters.
The authors of [4] proposed an integral model of the active layer of the ucean
based on the assumption of a proportionality between integral dissipation and
the production of turbulent energy of inechanical and convective origin. At the
same time it was assumed that mechanical turbulent energy dissipates complete-
ly within the limits of the Ekman boundary layer. The model was used for comput-
ing the seasonal evolution of characteristics of the active layer in the region
of weather station N in the Pacific Ocean. The results of computations of the
annual variation of temperature and thickness of the upper quasihomogeneous
layer (UQL), although *.hey do not contradict the observational data, neverthe-
less differed appreciably from them. Suffice it to mention that the computed
values of temperature of the UQL during the period of the maximum of summer
heating were 2-2.5�C higher than the observed values. One of the possible ex-
planations for the noted discrepancy is the absence of allowance for a feedback
between the heat flow at the water-air discontinuity and the temperature of the
ocean surface (we recall that in [4J the heat flow values at the ocean surface
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were considered stipulated). In this article we will attempt to eliminate
this limitation and we will cite the results of numerical experiments illus-
trating the sensitivity of the solution to variations of different kinds of
parameters of the model.
The seasonal evolution of the active layer of the ocean in the case of weak hor-
izontal advection and diffusion can be described using the following system of
equations for temperature Ts in the UQL, temperature Th at the upger boundary
of the seasonal thermocline, thickness h of the UQL and turbulent heat flow qh
at the lower boundary of the UQL (see [4]): ~
h = 90 - 9n+ � (1)
Q~'' _ ( d~ - W~th ( ~h ~:~hl > o, .
, ,
' /,;h c2~
2'(' / Ah - iC~h~ ~ rs l,~n) !it with I dt - i~'h~ ~ ~i
T~~ = ~.,c~ - h, I ~ d! `
\
,C
a - 4c~h Ts Tn f l- Ci Ri`~ F( ~h 1 1 with ~f C~ F'
~ \ /J
1~ C with r~h .
0~ (3)
hR ~ 1-- ar RF - 0~ ~ ac
~
( r., T~~~ ( - t:'~~) with ( ~t - ~
1
~7 r~ = dh
~ with ( ri~ - ze~hl ~ U. ~4 ~
/
Here q~ is the specific (normalized to the volume heat capacity of sea water)
turbulent heat flow at the ocean surface, wh and'Y are vertical velocity and
the temperature gradients at the upper boundary of the seasonal thermocline,
( (1 - lr;'!t~) with It < h~,
r ''l
i~,-~ 1-~ p with lt ~ 1r~;
he = u*/(C3 If~) is the thickness of the Ekman boundary layer, u* is dynamic wind
velocity, f is the Coriolis parameter, x'~"~~t
Ri - -
is the Richardson flow number, O~T is the coefficient of thermal expansion of
sea water, g is the acceleration of free falling, C1, C2 and C3 are numerical
constants, t is time, the subscript "0" denotes the values of the character-
istics of the active layer at the time t= t~ of change in the sign on q~ fall-
ing at the beginning of the heating period. The temperature gradient 'Y in the
seasonal thermocline is determined at the time t= tI of cessation of the ris-
ing of the lower boundary of the UQL
/dh
( Jt - ~~Ir ~ 0
~
using the formula
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r~
Tdi - rth
z~h ~TS- Tso) dt
Ir~ � li� - ~k, N~~)' ~u( ~tt
and then is considered invariabl.e during the entire period of deepening of the
lower boundary of the UQL
~ 1
( >
,
up to a new annual cycle.
The sqstem of equations (1)-(4) is closed and can be solved by stipulating the
heat flow q~ at the ocean surface, dynamic wind velocity u* and also vertical
velocity wh. In [4J the q0 values were stipulated on the basis of observation-
al data in the form of a periodic function of time. There, as already noted,
no allowance was made for the feedback between qp and the temperature of the
ocean surface (by definition the latter is equal to TS). In order to take this
~ correlation into account we will turn to the heat balance equation for the
ocean surface, in accordance with which
90 = Q~ ~Q~ -4- Qn �F Qe)~ ~S~
where Qs is the flow of direct and scattered short-wave solar radiation, Q is
the effective radiation, Qh and Qe are the flows of apparent and latent heat.
All the flow values were normalized to the volume heat capacity of sea water.
We will examine each term entering into (5) in greater detail. The expression
for the total flow of solar radiation absorbed by the ocean can be written in
the form
_ = n,u ~1 = (/J)~~1 ao)~ (6)
where QSD is the total flow of solar radiation incident on the ocean surface
in the absence of a cloud cover, 0~~ is the albedo of the ocean surface;~~,
like Qs~, are known tabulated functions of latitude and season of the year
(for example, see [3J), ~(n) is an empirical function characterizing the de-
pendence of Qs on the mean tenths of cloud cover n(specific form of ~p(n) can
be found in [1, 2]).
Adhering to [7], we will represent the dependence of the effective radiation
of the sea surface on its temperature in the form of a Taylor series in powers
TS - TA) (here TA is air temperature in the near-water layer of the atmosphere).
Limiting ourselves to the first two terms of the series, we obtain
Qe =~Q*o TA 4 Q' Q TA (TS - T,t)J/Po~o~
where Q* = 0.985 (0.39 - 0.05 e~~2)(1 - 0.6 n2) is a dimensionless empirical
coefficient taking into account the influence on effective radiation by cloud
cover and air humidity, eA is water vapor elasticity (in millibars) at the
~ standard altitude of ineteorological measurements, 6 is the Stefan-Boltzmann
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constant, P~c~ is the volume heat capacity of sea water.
The TA and TS temperature values are given in (7) in K.
'1'he sum of turbulent flows of apparent and latent heat, as usual, are parameter~
ized in the form
Qh ~ Q~ = P
~o Co' u� ! (T~ - T� ) + p ~9s - 9A)
where qA is specific air humidity at the'height of standard measurements, qs is
saturating specific humidity at the temperature TS, P A c is the volume heat
capacity of air, CD is sea surface drag, L is the latent ~ieat of evaporation.
If it is now assumed that qz a-~A and the Clausius-Clayperon equation is used,
as a result we obtain
eo L 1 1
q_ a pA eXP j_ X~ - To~}' (9)
l \
where pA is atmospheric pressure at sea level, RW is the specific gas constant
of water vapor, e~ = 6.11 mb is water vapor elasticity.at a temperature TD =
273 K, a~ 0.622 is a numerical constant.
Thus, if the dynamic wind velocity u*, air temperature TA, dew point temperature
Tr and the cloud cover tenths n are functions of time, equations (1)-(4) togeth-
er with expressions (5)-(9) and the initial conditions unambiguously determine
the temporal evolution of the thickness and temperature of the UQL, temperature
at the upper boundary of the seasonal thermocline, and also the heat flows at
the ocean surface and at the lower boundary of the UQL.
Below we give the results of computations of the seasonal evolution of the ac-
tive layer for the conditions at weather station N in the Pacific Ocean _
30�N, .7~ = 140�W). All the necessary initial information was taken from [6J. In
that study it was shown that for the se~ected point in the ocean it can be as-
sumed that wh = 0, n= 0.75, QS = QS + QS sin (G! t-'R/2),
u� = u� rc,~ sin t~ 2), Ta = T,~ +T~ sin (wt - a),
wher~
T, - T, T, sin (~ut - r,), r~e Q~ c 34,1,~ 10-8ac~�C/c, sec
~s - 13,4 � 10-~M��Cfc, - 0,'?32 ,+c/c, u,~ - 0,052 ~t/c, m/sec
n n ,
T~ - 18,5�C, T, - 14,5�C, TA = T, - 3�C,
the line at top corresponds to the mean annual values; the sign corresponds
to the amplitudes of oscillations of the considered characteristic.
The values of the numerical constants C1, C2 and C3, figuring in expressions
(4), are stipulated in accordance with [4] equal to:
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1 q0~
Co = 1, l� 10-', C, ~~2 with > 0,
~ with q0< 0,
~ U,29 � lU-3 with u*~ 0.25 m/sec,
C' - 0,38� 10-' with u* ~ 0.25 m/sec, C3 = 60.
! As the initial values of the thickness of the UQL and temperature we assume h
= 120 m and TS = Th = 18�C. ~
~ , o_fc?n��c% aec
u, M/e ' ~ 6 ~
Jb',
~J u) a )
.
� 0 , ~
. ~
gY i \
i ~~`�y
. _Z �
~ 8 ~ ~ i ~ b'c
o ~
~ e~ ~ ~ P1 a) t;
, c ) d )
sa ~ ' ;f ~
Y
~a - -�-�-a
~~o '
I1M
~ ~ ~ ~ a ~
Fig. 1. Annual variation of dynamic wind velocity (a), heat flow at the surface
(b), thickness (c) and temperature (d) of upper quasihomogeneous layer at weath-
er station N in Pacific Ocean. 1 and 2) results of computations with determina-
tion and stipulation q~; 3) observational data [6].
The results of co~nputations of the annual variation of the principal character-
istics of the UQL are represented in Fig. 1. As a comparison, here we have giv-
~ en the results of computations with a stipulated heat flow qp. It can be seen
that agreement with the observational data in the first case is appreciably
better than in the second. With stipulation of the surface heat flow the dis-
crepancies between the computed and observed temperature values at individual
times in the annual cycle can attain 2-2.5�C, whereas when determining the sur-
face heat flow in the process of solution of t~e problem they do not exceed
0.6�C. The second maximum in the seasonal variation of aurface temperature, ob-
served at the beginning of October, is absent in both computations. This in all
probability is associated with the exclusion of the salinity effect and the ap-
proximation of the external parameters by only two terms of a Fourier series in
time. With respect to the thickne~s of the UQL, the model ensures only a quali-
- tative similarity of the computed and observed h changes. The reason for this
is both the limitations of the model iiself and l~nown difficulties in determin-
ing h on the basis of experimental data. In actuality, on the one hand,
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tl~~~ jump layer, whoae thickness under real conditions is not lese than 10-30
m, Is replaced in the model by a layer of zero thickness; on the other hand,
the accuracy in determining the lower boundary of the quasihomogeneous layer
on the basis of experimental data does not exceed 5-10 m(see, for example, [5]).
T, JT� T~ /T,.~~ ~ max T~w min ~
4~ ~ ~
l \ r
L. r ~ C, ~y C
1,0 - ~ ~ ~i a,
~ r
Qy n ~ n
li~~l~ ' ~M/I/nMM./ ~IIN/nN~/ .
n j
~ ~a
Ct \ C~ G.
1, ~ ~i ~ ~
f,P � ~r - ~ ~t ~r
n
n
u,
4s ~ ~
~ q3 f,0 ,c f,; f,0 is QS 1,0 d/d,
Fig. 2. Relative changes in mean annual and extremal values of temperature and
thickness of UQL as function of variations of external parameters of model. The
values of the normalization factors, noted by the subscript "0", correspond to
the conditions of the main experiment (Fig. 1). 0~ is any of the model parameters
c ited in the f igure.
For the purpose of investigating the sensitivity of the solution to the accuracy
in stipulatin� the internal parameters of the model (numerical constants C1, C2,
C3) and atmospheric characteristics (TA, u* and n) we carried out a number of
numerical experiments. It was found that the variations of the indicated para-
meters did not lead to any substantial changes in the phase relationships be-
tween the sought-for variables. Accordingly, here we will limit ourselves only to
a discussion of their mean and extremal values.
Figure 2 shows that variation of the conatants C1 and C2, corresponding, all oth-
er conditions being equal, to the change in the contribution of thermal convec-
tion* and mechanical mixing to the heat flow at the Lower boundary of the UQL
(see first of the equations (3)), leads to insignificant changes in the tempera-
ture and thickness of the UQL. A decrease in the constant C3, equivalent, all
other conditions being equal, to an increase in the thickness of the Ekman lay-
er he, has little influence on the T8 value and at the same time causes an ap-
preciable increase in the mean value and amplitude of h variations. However,
even in this case the relative changes in h are less than with a change in the
*
Here reference is to the C1 value with q0 < 0.
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dynamic veloc~ty of the wind u*, air temperature TA and the tenths of cloud
cover n. The same can be said with respect to changes in temperature of the
UQL. With an intensification of the wind and an increase in cloud cover tenths
. as might be expected, there is a decrease, whereas with a temperature increase
there is an increase in the mean annual value and amplitude of the TS variations.
Thus, the reaction of the solution to changes in the external and internal para-
~ meters of the model is not the same: it is substantially stronger with a varia-
tion in the external and weaker with a variation of the internal parameters.
This circumstance is evidence of the reliability of the model and the possibil-
ity of its use in mass computations of the seasonal evolution of temperature
and thickness of the U2L.
The author expresses appreciation to S. P. Smyshlyayev for assistance in carry-
~ ing out the computations.
BIBLIOGRAPHY
1. Berlyand, T. G., "Methods for Climatological Computations of Radiation,"
METEOROLOGIYA I GIDROLOGIYA (Meteorology and Hydrology), No 6, 1960.
; 2. Budyko, M. I., TEPLOVOY BALANS ZEMNOY i'~JVERKHNOSTI (Heat Balance of the
~ Earth's Surface), Leningrad, Gidromete~izdat, 1956.
3. Ivanov, A., "Absorption of Solar Energy in the Ocean," MODELIROVANIYE I
PROGNOZ VERKHNIKH SLOYEV OKEANA (Modelinp and Prediction of the Upper Layers
~ of the Ocean), Leningrad, Gidrometeoizdat, 197~.
I 4. Kagan, B. A., Ryabchenko, V. A. and Chalikov, D. V., "Parameterization of
the Active Layer in a Model of Macroscale Interaction Between the Ocean and
Atmosphere," METEOROLOGIYA I GIDROLOGIYA, No 12, 1979.
I 5. Kalatskiy, V. I., MODELIROVANIYE VERTIKAL'NOY TERMICHESKOY STRUKTURY DEYAT-
EL'NOGO SLOYA OKEANA (Modeling the Vertical Thermal Structure of the Active
Layer in the Ocean), Leningrad, Gidrometeoizdat, 1978.
6. Dorman, C. E., Paulson, C. A. and Quinn, W. H., "An Analysis of 20 Years of
Meteorological and Oceanographic Data From Ocean Station N," J. PHYS. OCEAN-
OGR., Vol. 4, No 4, 1974.
7. Haney, R. L., "Surface Thermal Boundary Condition for Ocean Circulation Mod-
els," J. PHYS. OCEANOGR., Vol 1, No 4, 1971.
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UDC 532.517.4
CRITERIA CHARACTERIZIHG FLOW OF FLUIDS WITH STABLE STRATIFICATION
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 2, Feb 82 (manuscript received
25 May 81) pp 69-76
~(Article by A. N. Shabrin, candidate of technical sciences, Hydromechanics Insti-
tute, Ukrainian Academy of Sciences]
[Abstract] A study was made of a model of a current in which a flow of fluid with
a free surface and the density P1 flows into a water body filled with a fluid
with the density /0 2(with /~Z~P1). An example of such a situation would be when
fresh water flows into the sea or some water bo dy f i l le d w i t h s a l i n e w
a t e r. T h e
author seeks an answer to these two questions: 1) what are the conditions for
the penetration of saline water into the fresh water flow? 2) what is the nature
of the interaction of fresh and saline water when fresh water flows into the
sea? In solving these problems no effort is made to take wind-induced and tidal
phenomena into account. Solutiona are sought for the case of stable stratifica-
tion. Different approaches used in the past in arriving at stability criteria
are reviewed and a new method is proposed for analyzing atability conditions for
the interface of fluids of different density. Experimental and theoretical inves-
tigations made by the author both reveal that there ia a clearlq expressed and
unambiguous interrelationship between interface stability and the ratio of flow
frequency and buoyancy. Knowing this, it is possible to employ parametera which
are quite easy to obtain experimeatally for an analysis of interface atability
conditions not only when there is a uniform density gradient in the entire thick-
ness of the layer, but also when the interface layer is divided into parts. Fig-
ures 3, tables 2; references 10: 8 Ruasian, 2 Western.
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UDC 556.535.6
DEPENDENCE OF ACCURACY IN COMPUTATIONS OF PARAMETERS OF SEA WIND WAVES ON
PRINCIPAL WAVE-FORMING FACTORS
i
~ Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 2, Feb 82 (manuscript received
~ 20 Apr 81) PP 77-81
I [Article by R. A. Dal in, candidate of naval sciences, Leningrad Hydrometeorolog-
i ical Institute]
[Text] Abstract: On the basis of use of the method
of linearization of the random arguments
~ function a study was made of the change in
accuracy in computing the mean heights and
periods of wind waves in deep water as a func-
i tion of the errors in initial values o� the
principal wave-forming factors: wind velocity,
~ its fetch and the duration of the effect. The
' article gives the accuracy characteristics of
! the principal wave-forming factors, which make
; it possible to compute the parameters of wind
waves with an accuracy satisfying practical
i requirements. It is shown that the main influ-
ence on the accuracy in computations is from
errors in wind velocity. There is a consider-
; a'oly lesser influence on the results of com-
i putations even of considerable errors in de-
~ termining the fetch and duration of exposure
to the wind. .
~ Methods for computing the parameters of wind waves which are recommended for
application in off icial documents [3, 5] are now used in the practice of hydro-
meteorological support of the transport and fishing fleets, in hydraulic con-
struction and in other work at sea. The basis for the mentioned methods is the
expressions derived by a group of Soviet researchers [2]. According to [3], for
~ deep-water conditions these expressions have the form
I -�'~-h, = O,W42 ( ~,)~~a, (1)
~ e
; _ 0,0013 ( )b~12 , (2)
8 t _ ~g~~ (RV~j'~5 (3)
i ~ - ~ .
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}{ere h and x are expressed in meters and ti and t are expressed in seconds.
If the dependence of the mean height h and the mean period t of wind waves is
expressed in explicit form on the principal wave-forming factora wind velo-
city V, fetch x and duration t of exposure to the wind and x and t are convert-
ed into kilometers and hours respectively, expressions (1)-(3) assume the fot'm
1:-9,1�10-'~xV' ~ ' (4)
'h-1,04�10-~~~ taV''', ~5~
6 i
z - 7,5 ~
(6)
The last expression, with (4) and (5) taken into account, can be represented
by the formulas
o,4s y'x v~ , ~ ~
~ _ o,~s i/rv.? . (8)
We note that the finding of the parameters h and ti by the use of formulas (4),
(5), (7) and (8) when modern microcalculators are available requires only a
few seconds and is considerably less fatiguing and more precise than when using
the nomograms cited in [3, 5]. At the same time, these formulas mak~ it pos-
sible to establish the dependence of the errors in determining the parameters
of wind waves on the errors in the initial values of the wave-forming factors.
In actuality, if the method of linearization of [1] is applied to expressions
(4), (5), (7) and (8), it is possible to obtain the following relationships:
using expression (4) ah~v~ = 1,21 � 10-~~ o~,
a ~9~
�hcx) = 3,~~' 10-3 ~
X~ Q.~~
~1~ ~
using expression (5)
oh~~~ = 1,G5 � 1(1-'- ~{~1~V7 0~~ (11)
ad�~ = 0~43 ~ 10-= V~� o~~ (12)
from expression (7)
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R z
. ot~~~=p,27 ~-V~ov, (13~
s
' Q~~.r~ _ ~
z aX+ ~14 ~
from expression (8) 4~ ~
i ot~?'~ p,361 / V ov~ (15)
V
a=rr~ _ ~,12 j~, at� O
y 16
In formulas (9)-(16) ~h and dti~v~ are the mean square errors in computing
h and t respectively in dependence on the mean square error in wind velocity
CIV; cTh~X~ and o.~ (X~ are the mean aquare errora in computing h and t re-
spectively in dependence on the mean square error in the fetch ~X: a'n(t). ~i(t)
are the mean square errors in computing h and t~respectively in dependence
on th~ mean square error in the duration of exposure to the wind U't.
In the considered case the legitimacy of applying the linearization method is
justified by the fact that as a result of the smallness of the errors in the
V, x and t values in comparison with their absolute values the functions de-
scribing the dependence of h and t on these values, not being linear in the
entire range of change in their arguments, are almost linear in a narrow range
of their random changes.
Using expressions (9)-(16) for conditions close to those which are usually en-
countered in practical computations, that is, for wind velocities 5, 10 and
15 m/sec, a fetch of 200 and 300 km, duration of exposure to the wind of 6
and 12 hours, we computed the evaluations of the possible errors in determin-
ing the mean height and mean period of wavea as a function of the errors ~y,
O'X and Clt .
The computed data are given in Table 1. An analysis of the table shows that the
errars in computing the wave parameters can attain conaiderable values. These
errors are particularly sensitive to the errors in initial wind velocity values.
Thus, even an insignificant error in wind velocity 1 m/sec results in an
error in computing the mean height of waves attaining more than 20 cm. It must
be noted that a mean square error in determining wind velocity of 1 m/sec is
entirely possible since the methods for determining wind velocity by use of
weather maps ensure a higher accuracy.
The errors in initial durations of wind action, especially wave fetch, exert a
lesser influence. However, in these cases as well, they can attain values
which to some degree are capable of distorting the final result of the computa-
tions.
However, it should be mentioned that the value of the Qh and ~ti parameters is
not adequately indicative. In actuality, one and the same error o'h, for ex-
~mple, with great wave heiQhts, can legitimately be considered inaignificant,
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but in the case of low heights inadmissible. In order to take this circum-
stance into account it is desirable to proceed to a relative characterization
of the error the variation coefficient [4], that is, in our case
(1~)
kh = h ' 1 ~�/o
and
k. _ ~ Ipp~~u, (lg)
- t
Then, taking expressions (4) and (9) into account, it can be written that
0
kR~~> = 3 -G' 100�~0~ � (19)
It follows from expressions (4) and (10) that
k"~'~ - 3 X ' 100�/0~ . (20)
from expressions (5) and (11)
kh~~~ = 1,5~3 ~ � 1~�/0+ (21)
from expressions (S) and (12)
kk~~~ = 0.42