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ME i T i ' _OGT
< JULY 1980 NO. 4r Afifi I L 1980 1 OF 2
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JPRS L/9130
3 July 1980
USSR Report
METEOROLOGY AND HYDROLOGY
No. 4, April 1980
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3 July 1980
USSR REPORT
METEOROLOGY AND HYDROLOGY
No. 4, April 1980
Selected articles from the Russian-language journal METEOROLOGIYA
I GIDROLUGIYA, Moscow.
CONTENTS
Vertical Circulations in Jet Streams and Frontogenesis
(N. P. Shakina) 1
Seasonal Temperature Variations in the Southern Hemisphere Atmosphere at
Altitudes 25-80 km
(Yu. P. Koshel'kov, A. I. Butko) 10
Some Features of a Tropical Cyclone Over the Arabian Sea in 1977
_ (L. I. Petrova) 17
Influence of Atmospheric Condensation Nuclei on the Attenuation of Solar
Radiation
(V. I. Khvorost'yanov) 31
Improving Estimates of Atmospheric Aerosol Turbidity
(L. D. Krasnokutskaya, Ye. M. Feygel'son) 47
Investigation of Aerosol Fallout During Distant Transport of
Contaminating Substances
_ (T. N. Zhigalovskaya, et al.) 56
; Statistical Characteristics of the Vertical Structure of the Liquid Water
Content and Temperature Fields in Cumulus Clouds
' (V. S. Kosolapov) 63
Influence of Absorbing Properties of the Surface on the Diffusion of an
Impurity in the Atmospheric Boundary Layer
(M. A. Novitskiy) 73
- a - [III - USSR - 33 5& T FOUO] -
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Contamination of the Atmospheric Surface Layer Over the Atlantic Ocean
l,y Benz (a ) pyrene
- (A. I. Osadchiy, et al.) 80
Computation of Co:itamination of Surface WaterG of Some Regions in the
World Ocean by the Atmospheric Fallout of Strontium-90
(K. P. Makhon'ko) 90
Calculation of the Propagation of an Impurity in the Northeastern
Atlantic and in Adjacent Seas
(B. R. Zaripov, D. G. Rzheplinskiy) 100
Salt Balance in the World Ocean
(A. M. Gritsenko, V. N. Stepanov) 106
Short-Range Prediction of Autumn and Winter Ice Jam Levels on the Lower
Volga at Chernyy Yar Station
(P. I. Bukharitsin) 115
Application of the Coherence Function in Analyzing the Turbulent
Structure of a River Flow
(D. I. Grinval'd, M. P. Yekhnich) 124
Method for Predicting the Wintering of Winter Wheat
(V. A. Shavkunova) 130
Optimum Calibration of Remote Instruments Using the Results of Direct
Measurements in the Ocean
(S. V. Dotsenko and L. G. Salivon) 139
- Empirical Orthogonal Functions Method and its Application in
Meteorology
(M. I. Fortus) 148
Seventieth Birthday of Yevgeniy Konstantinovich Fedorov
(Yu. A. Izrael') 160
Soviet Awards to Workers in Field of Hydrometeorology 166
At the USSR State Committee on Hydrometeorology and Environmental
Monitoring
, (A. V. Kolokol'chikov) 170
Conferences, Meetings and Seminars
(A. A. Vasil'yev and. M. V. Rubinshteyn) 174
Notes from Abroad
(B. I. Silkin) 178
Letter to the Editor (from B. I. Silkin) ...................e.......... 180
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PUBLICATION DATA
English title . METEOROLOGY AND HYDROLOGY
Russian title : METEOROLOGIYA I GIDROLOGIYA
Author (s) ,
Editor (s) : Ye. I. Tolstikov
Publishing House ; Gidrometeoizdat
Place of Publication : Moscow
Date of Publication . April 1980
Signed to press ' . 21 Mar 80
Copies � 3790
COPYRIGHT � "Meteorologiya i gidrologiya", 1980
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UDC 551.(515.8+557.5)
VERTICAL CIRCULATIONS IN 3ET STAEAMS AND FRONTOGENESIS
Moscow METEOROLOGIYA I GIDROLGGIYA in Russian No 4, Apr 80 pp 5-11
[Article by Candidate of Fhysical and Mathematical Sciences N. P. Shakina,
USSR Hydrometeorological Scientific Research Center, submitted for public-
ation 25 July 19791
Abstract: The author gives a theoretical anal-
ysis of the dependence between the direction
of vertical circulation in a jet stream and
the nature of evolution of 4 high-altitude
frontal zone. It is shown that with accentua-
tion of the frontal aone the vertical circula-
tion in this zone and in the jet stream is
"thermally direct," whereas with blurring of
the frontal zone the vertical circulation is
"thermally invers2." In a quasigeostrophic ap-
proximation these movements are manifested as
compensatory. Ia the approximation of full
equatians the descending branch of circulation
in an accentuati:lg frontal zone occupies a re-
gion of maxlmi.im frontogenesis as a result of
ageosrrophic effects. The subsidence of strato-
spheric air occurring in this region is mani-
fested locally as a branch of "thermally in-
verse" circ ul3tion., acting as a regulator of
the sharpness of fronts.
[Text] In jet streame in the upper troposphere, associated with high-al-
titude frontal zones, tr,e trajectories of air particles are usually spir-
al, with ascent along one side of the jet stream aais and with descent on
the other. The results of experimental investigations made by different
authors (see review by V. A. Dzhordzhio [2]) show that the direction of
circulation in *_he vertical plane normal to the axis of the jet stream
can be both "thermally direct" (ascent on the side of the warm air) and
"thermally inverse" (the colder air ascends, the waimer air subsides).
The reasons for the complex mesoscale structure of the vertical movements
1
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ror. oFr� rr.rnt, irSr. Orri.Y
and wind fields in jet streams a.1d, in particular, the reasons for the
formation of any type of vertical circulation must be sought in the
large-scale dynamics of high-altitude frontal zones.
Proceeding on the basis of analytical and numerical results of investiga-
tions of atmospheric frontogenesis [4-6], it is possible to formulate some
regularit.ias in the development of thermally direct and thermally inverse
circulations in jet streams. At the same time it is possible to obtain a
physical explanation of "indirect circulations" observed in intensive
upper tropospheric frontal zones. Although the fact of existence of such
circulatia.zs was established rather long ago and has been repeatedly con-
firmed by an analysis of frontogenesis on the basis of real data (for ex-
ample, see [7]), a failure to understand the physical essence of this grQ-
cess until now has been leading some meteorologists to an incorrect inter-
pretation of the observed phenomena.
We will begin with an analysis of frontogenesis in a quasigeostrophic ap-
proximation. Usually the intensity of frontogenesis (or frontolysis) is
evaluated using a scalar frontogenetic function which in the case of a
plane adiabatic movement is described in the form [lJ
Q_ a eiax au a e- -ov a e j
F= d I~ e I- Iv 5 I f ax v.e - az., d)J
. ~1)
+ ~ .
a y~ay au a e at. a H
lr H il- o y ax -a y oy '

where j 8 is the horizontal gradient of patential temperature.
Now we will write an equation for the instantaneous distribution of ver-
tical movPments in a quasigeostrophic approximation (so-called omega
equation) in the form proposed in [61 :
. . -a,w (2)
N_ + 1' a:_ = 2 9� Ug.
Here
i1!'' = b
H, [1s
is the square of the Brent-Vaisala frequency (e p is the potential temper-
ature at the earth's sur�ace, e is the standard potent_ial temperature at
the level z), V h is the Laplace operator in the hori.zontal plane (z = h),
~.is the Coriolis parameter, assumed to be constant,. (~g is a vector, whose
divergence or convergence determines the sign of tt:e vertica l movements
and their value:
. ( avg g avR l (3)
Qg = l- b0 dX
y
. � g JVg ~
- A~~ a Qir
2
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~
- d dyg �c0 =Q:
(3)

(Vg is the vector of the geostrophic wind with the components ug, vg).
It is easy to see that the Qg vector is related to the scalar frontogenetic
function Fg, computed from the field of the geostrophic wind, by the ex-
pression
' An
Fg glcdi vd Qs' (4)
~ .
On the other hand, Qg can be regarded as a vector frontogQnetic function
in geostrophic movement. In actuality, if the ageostrophic components of
the wind are absent, it is easy to confirm that
do g dQ a o a
Qr = ar "0va = ar + ua aX ay � ~5~
Thus, we find that in a quasigeostrophic approximation the distribution
of vertical movements is determined by the divergence or convergence
_ of the frontogenetic vector function, in other words, by tha distribution
of frontogenetic effects horizontally. With sufficiently large scales of
movements in the free atmosphere, when the wind can be considered close
to geostrophic, equation (2) is useful not only for qualitative estimates,
but also for many computations. We will limit ourselves to an evaluaLion of
the direction of vertical movements in the sectors of the thermopressure
field of interest to us, proceeding on the basis of (2) and (5).
Usually in such evaluations as a first approximation it is assumed that in
the case
= k.~, .~.1 ~ m > 0
N Tthere is a descent of the air, whereas with a negative left-hand side of
_ (2) there is ascent. Now we will examine the conditions characteristic for
the jet stream "entry" and "delta" (Fig. la). In the "entry" region the
geostrophic movement should lead to frantogenesis, and in the "delta" re-
gion to frontolysis. The _~g vectors in the "entry" region are oriented as
indicated in the diagram and there is a divergence _~Tg to the left of the
flow and convergence at the right; these correspond to descending movements
(and generation of anticyclonic vorticity in the lower-lying layers) under
the left side of the "entry" region and ascending movements at the right
_ (with the generation of cyclonic vorticity). We see that the vertical cir-
culation is thermally direct. In the "delta" region, where the geostrophic
movement tends to decrease the horizontal temperature gradient (here front-
olysis occurs), to the right of the flow there will be convergence of the
Qg vector, and to the left divergence. Accordingly, the warm air will
descend and the cold air will rise, and thus the circulation will be ther--
mally inversE.
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y Cold XoaoB Cold
, xc~oa _ - -
j+`- ~�f � y- - -

X
-----~t t +-------X
- - Warm + + - - - - - - - - ~,Iarm
Tenao Tenno
2 3
Fig. 1. Distribution of 4 and 0�Qg in entry and delta of jet stream (a)
and in flow with transverse shear (b). 1) isotherms, 2) wind velocity
-s
vectors, 3) Qg vectors. The signs on V�Qg are indicated.
We will direct the x-axis along the isotherm so that we will have Q1 = 0.
The forced verticv.l mnvements then will be determined by the value
o
dy Qt y ar I oe
If plane frontogenesis occurs (as in the entr.y region), then
dQ d a O
ae o y <
(since )e/d y 0) it is positive, and on the side of the warm air
_ (y < 0) it is negative. Accordingly, with y> 0 there is development of de-
scending movements and with y 0 there are ascending movements: the cir-
culation is thermally direct relative to the axis of greatest intensity
of frontogenesis. In the delta region the picture is the opposite.
In another special case, when the geastrophic motion causes only a turning
of the isotherms, not their squeezing together, it is also easy to show
that the forced vertical circulation always has a thermally direct charac-
ter relative to the axis of the maximum turning of the isotherms (ascent in
the region of heat advection, descent in the region of cold advection).
Such a situation is shown in Fig. lb; it can be considered characteristic
_ for a plane baroclinic wave. In order to determine the direction of circul-
ation in this case we note that j~g ={0, vg} and QZ = 0; everywhere dvg/a x
> 0, but the second derivative a 2vg/a x2 is positive in the left part of
the figure and negative in the right part. Therefore, when (a T/(9 y) = const
< 0 we obtain V �&g> 0 in the ri ht part of the figure, that is, in the
region of cold advection, and ~7�~g < 0 in the region of heat advection,
whereas at the point of bending of the vg(x) c rve at x= 0 we will have
~7�Qg = 0, although R1, and this means, also l have a maximum here. The
straight line x= 0 in our case is in actualitygthe "line of zero advec-
tion," to use the terminology employed by Pogosyan and Taborovskiy [3].
4
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We note that closed circulations (with a change in the sign c.f w) arise
only in the presence of maxima or minima of the functions describing the
squeezing together of the isotherms or their turning (that is, according-
ly the functions QZ and Q1, if the x-axis is directed along the isotherms).
Frontogenesis in the usual understanding of the word, evaluated using the
scalar furction Fg, at the time shown in Fig. lb is equal to zero, as
follows from (4). However, the horizontal shear mechanism, leading ini-�
tially only to a turning of the isotherms, already at the next moment cre-
ates a non-zero component of the temperature gradient along the x-axis and
with it, also non-zero Fg values; frontogenesis in the region of horizon- _
tal shear will be intensified, with a tendencq to the formation of a zone
of maximum 1791 - a frontal zone along the line of maximum Q]. (that is,
with x= 0). This mechanism leads to frontogenesis in developing baroclin-
ic disturbances.
Thus, vertical circulations, developing during quasigeostrophic movement,
actually are thermally direct during frontogenesis (Fg >0) and inverse in
the case of frontolysis (Fg < 0); in addition, they are thermally direct
in those cases when advection by the geostrophic wind leads to a turning
of the isotherms (regardless of the direction of the latter).
Does this conclusion agree with the observed facts ot subsidence of strat-
ospheric potentially warmer air in high frontal zones a phenomenon ob-
served in the case of intensive frontogenesis and perceived in the neighbor-
hood of the jet stream as a branch of thermally indirect circulation?
As we have already seen, the subsidence of air on the cold side of a high
frontal zone during accentuation of a front (like the ascent on the warm
side) is a compensatory circulation which should develop even within the
framework of a quasigeostrophic approximation. The fact that the descending
branch of this circulation intensifies and acquires a special character,
also taking in the zone of maximum frontogenesis, is a consequence of two
factors: first, nongeostrophic effects, taken into account by the quasigeo- `
strophic model only in part, and second, the presence of the tropopause as
a layer of change of the vertical temperature gradiente
Figure 2 shows a characteristic section of a tropospheric frontal zone and
a jet stream by a vertical plane normal to the axis of the latter. This
picture corresponds both to observations [7] and to the results of hydro-
dynamic modeling of frontogenesis along the axis of compression of the
horizontal deformation field [S]. As already mentioned, the tropopause 1ev-
el differs in that there is a break in the vertical temperature gradient
here and together with it, Ertel potential vorticity
q= ~ (!k ~ � L) A (6)
a conserved value in the system of so-called full (primitive) equations,
which we, after some additional assumptions, will use for an analysis of
the nongeostrophic effects playing an important role in forming the
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vertical structure of atmospheric frontal zones and fronts. As is well
known [4, 51, a changeover from quasigeostrophic to full equations makes
it possible to obtain the most significant refinements precisely with re-
spect to vertical structure, which for us is of the greatest interest in
this case. r6
I 1J5
200
100
400
600
800
'
1000
-1 -Z J y
Fig. 2. Characteristic sec tion of tropospheric frontal zone and jet stream
during intensive frontogenesis.l) tropopause, potential temperature iso-
lines, 3) isotachs, 4) bo undaries of regions I and II (see text).
The intensity of Frontogenetic processes differs greatly in different lay-
ers of the atmosphere. It has been demonstrated theoretically [5] that
sharp frontal discontinuities, where the vertical component of absolute
vorticity I in the course of a finite time can attain (in a nonviscous
examination) infinitely high values, can arise only near the underlying
surface Qr near such level s where there are "discontinuities" of potential
vorticity q or its first or second derivatives. In particular, sucti a
" level is the +_ropopause, which separates stratospheric air from tropospher-
ic air, having substantially diff erent patential vorticities. In the tropo-
sphere layer frontal zones cannot attain such a high iatensity as near its
~ boundaries. Accordingly, d uring frontogenesis vertical circulations are
most clearly expressed either in the lower layers or under the tropopause.
Within the framework of a quasigeostrophic approximation the vertical move-
ments change sign at the point of maximum frontogenesis. Accordingly,
the vorticity field is also found to be symmetric relative to this point,
which does not correspond to the really observed picture. However, within
the framework of models with full equations or even with a more limited
allowance for the ageostrophic components only in a direction transverse
to the front [5] the maximum of positive vorticity is obtained, in accord-
ance with observations, at the point of most intensive frontogenesis. The
increase in positive vorticity during frontogenesis, maximum at the lower
boundary or near the tropopause, is accompanied by a decrease in pressure
or a lessening of the altitudes of the isobaric surfaces. At the ground
this leads to the formation of a trough along the front. However, if such
a process occurs near the tropopause a moving internal discontinuity q
the pressure decrease in the region of the front leads to a"drawing"
of the tropopause into this region, situated on the cyclonic side of the
jet stream. The localization of the latter on the warm side of a high
6
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= frontal zone is also a result of the influence of essentially nongeostroph-
ic factors [5].
~ Positive vorticity, maximum in the zone of greatest horizontal temperature
contrasts, increases with time, and in addition, increases with altitude
with approach to the tropopause from below (since the tropopause is the
- level of the discontinuity q), and also with transition through the tropo-
pause. This leads to the appearance of the ageostrophic component uag, di-
- rected from the zone of maximum v at eac1i level to the zone of increase in
l(that is, in the direction of low pressure); uag will increase with al ti-
tude. As a result, a counterclockwise circulation develops in the jet stream
and on the cyclonic side of the latter, that is, in the zane of maximum
a descending branch of this circulation develops (Fig. 2).
Thus, the subsidence of air, and with it tha "drawing in" of the tropopause,
is a passive consequence of the distribution of vorticity and wind velocity
arising in the frontogenesis process; from this point of view the "thermally
indirect" circulation appears to be a result of dynamic, not thermal fac-
tors. _
There is a close relationship between the generation of vorti~ity in the
process of development of an upper tropospheric front and vertical circul-
ation. We will write a vorticity equation corresponding to full equations in
our two-dimensional model:
d ( dm dw dv
d a ' ax az � (7)
In Figure 2 it is possible to def ine two regions to the right and left
' of the center of the forming frontal zone. In region I d w/ a x? 0, d v/a z>
- 0; accordingly, the effect of the second term on the right in (7) will in-
volve a decrease in positive vorticity. Thus, lower3.ng of the tropopause
is an obstacle to formation of excessively great ("inf initely great" in
a nonviscous examination); this lowering is the more intense the more in-
tense is the frontogenesis process. However, in region II
~ tls < o' a~ > O'
and positive vorticity will increase under the influence of vertical circul-
ation. Here the lowering effect is frontogenetic because more potentially
warm stratospheri.c air subsides on the warm side of the high frontal aone.
Thus, the subsidence of stratospheric air acts as a regulator of the front-
ogenetic process, decreasing positive vorticity (and temperature contrasts)
in the zone of maximum frontogenesis and at the same time increasing vortic-
ity and temperature contrasts on the periphery of this zone. The subsidenc e
of potentially warmer air, caused by dynamic factors, can be regarded as a
branch of "thermally indirect" circulation only locally, in a limited
- sense. As was already demonstrated above in an analysis of a quasigeo-
strophic omega equation, subsidence on the cold side of a developing front
is a branch of a frontolytic thermally direct circulation; but the same
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descer.ding branch, taking in stratospheric air, appears tu be warmer than
the tropospheri.c cold air (situated to the left of it in Fig. 2).
Now we will define the principal results of the study made here.
1. Proceeding on the basis of the quasigeostrophic omega equation in the
form (2), it is demonstrated that the distribution of vertical movement s
in the free atmosphere, in particular, in j et stream zones, in a quasig eo- -
- strophic approximation is determined by divergence or convergence of the
frontogenetic vector function, or, in other words, by the horizontal dis-
tribution of frontogenetic effects. With an accentuation of the high
frontal zone the vertical circulation in the jet stream is thermally d i-
rect (in the sense that ascent occurs on the side of the warm air mass),
and during blurring is thermally inverse (ascent on the side of the cold
air) relative to the axis of the greatest intensity of frontogenesis or
Frontolysis r.espectively. If geostrophic movement lpads only to a turninR
of the isotherms (without their aiAnificant squeezing together or spread-
ing apart), then the developing circulation relative to the axis of maxi-
mum turning (line of zero advection) is thermally direct: ascent in the
- region of heat advection and descent in the region of cold advection. -
2. As demonstrated by an analysiu of the wind fields and vorticity within ~
the framework of the approximation of "fu11" equations, as a result of
essentially nongeostrophic movements in the neighborhood of the tropopa use
the descending branch of the circulation in an accentuating high frontal
zone is intensified and takes in the region of most intensive frontogen-
= esis. The subsidence of stratospheric air, potentially Taarmer, is local
ly perceived as a branch of thermally inverse circulation. This subsid-
ence, accompanied by the drawing in of the tropopause, is a result of dy-
namic (not thermal) factors an increase in vorticity and wind velocity
in the case of frontogenesis near the tropopause. Descent in the region of
maximum frontogenesis appears as a regulator of the sharpness of fronts,
constituting an obstacle to the formation of excessively sharp tempera- ~
ture contrasts and redistributing them horizontally.
BIBLIOGRAPHY
1. Vetlov, I. P., FRONTOGENEZ I PREOBRAZOVANIYE VYSOTNYKH DEFORMATS-
IONNYKH POLEY (Frontogenesis and the Transformation of High Deform-
ation Fields), Leningrad, Gidrometeoizdat, 1951.
2. Dzhordzhio, V. A., "JEt Stream," METECROLOGIYA I GIDROLOGIYA (Meteor-
ology and Hydrology), No 6, 1956.
3. Pogosyan, Kh. P., Taborovskiy, N. L., "Advective-Dynamic Principles
of Frontological Analysis," TRUDY TsIP (Transactions of the Central
Institute of Forecasts), No 7(34), 1948.
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4. kloskins, B. .T., "Atmospheric Frontogenesis Models: Some Solutions,"
QUART. J. ROY. METEOROL. SOC., Vol 97, No 412, 1971.
- 5. Noskins, B. J., Bretherton, F. P., "Atmospheric Frontogenesis Models: �
Mathematical Formulation and Solution," J. ATMOS. SCI., Vol 29, No I,
1972.
6. Hoskins, B. J., Draghici, J., Davies, H. C., "A New Look at the td -
Equation," QUART. J. ROY. METEOROL. SOC., Vol 104, No 439, 1978.
7. Reed, R. J., Danielssen, E. F., "Fronts in the Vicinity of the Tropo-
pause," ARCH. MET. GEOPH. BIOKL., A, Vol 11, No 1, 1959.
9
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UDC 551.524.73(215-13)
SEASONAL TEMPERATURE VARIATIONS IN THE SOUTHERN HEMISPHL'tE ATMOSPHERE AT
ALTITUDES 25-80 KM
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 12-16
[Article by Candidate of Geographical Sciences Yu. P. Koshel'kov and A. I.
Butko, Central Aerological Observatory, submitted for publication 7 July
1979]
Abstract: The amplitudes and phases of the an-
nual and semiannual variations were computed
on the basis of the mean monthly temperature
values in the southern hemisphere at altitudes
25-80 km. The authors give a comparison with
data for the northern hemisphere and describe
great interhemispherical differences in the
nature of the seasonal variations, confirming
the necessity for creating reference models
of the atmosphere separately for each hemi-
sphere.
[Text] As is well known, seasonal temperature variations in the lower
stratosphere in the southern hemisphere have been successfully investigat-
ed on the basis of ra3iosonde data (for example, see [1-4, 7, 14, 17, 21,
23]). The results of rocket sounding obtained at individual stations in
the southern hemisphere and some satellite data have been used by a number
of authors for an analysis of seasonal variations in the stratosphere and
partially in the mesosphere [3, 9, 16-20, 22]. The limited volume of data
gave these investigations a preliminary character. An empirical model of
the temperature distribution at altitudes 25-80 km in the southern hemi-
sphere [6], constructed recently on the basis of all available data from
rocket sounding (up to 1977), makes it possible, in generalized form, to
evaluate the peculiarities of temperature distribution in the upper atmo-
sphere of this hemisphere. The reliability of the mean temperature values
obtained in [6], at least to altitudes 50 km, to a definite degree is con-
firmed by the fact that the addition of supplementary observational data
(for a two-year period) and a change in the method for the analysis of the
data lead onl; to insignificant changes in mean temperature values (of
10
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about 1-2�C), as indicated by a comparison with earlier results [5]. It
- can therefore be assumed that the amplitudes and phases of periodic tem-
perature variations, computed using the data in [6], scarcely change sig-
nificantly with a further increase in the mass of data from rocket sound-
ing. Definite refinements (especially in the mesosphere) are possible,
however, with the accumulation of the results of satellite observationa,
ensuring global coverage.
Ja�~. latitude a ~c�~,, su�~.
sD 9 A I 2' VCIRATo %e~ 7J A II 1 1G 4 TaYJ 9 fi T N YC1RA
r?o _ BOKn_., -70 BO+~n
. ~s` �E 60en �f0 � BGKr. , _
'65 � Tn es! ~M :A - 7 .
�ea
7'~ -JO .J~q . 70 1,0-~ ._'~p . Tia
�SJ
40
,0110 � 0
70
.10 60 �1f - " �iOT~ �70 �60
: _ .?S 60___ �7 60 T2o 60 �10
-0
-JSSO` _ TlIjo ito'JO
` 0 SO 10�iC 10
' SO
0 SO
f 0
T~o �ID 7M 40. l0 p _ � 10
�15 y~ -S y~ �10 1 ' �~O.IC �f0
40 ~
FC ` rJD�1S Tj~�i~o ' Ja�ti ti0 r~a
-ij y0 JO �J5 '30 �t0 JO ' �y0
JO �
- �ti0 . JJ, ~ � 0
�fS .ys .6~ --2 �EO
] a/ Y l! !1 Il Aon. S I dl YJF Q D I p'i P P8 UJ79.11 I:0 1 Y!! Lf A710. R.
Fig. 1. Seasonal temperature variations in the southern hemisphere (1) [6]
and according to model CIRA-1972 (with allowance for annual variation [10]
at equator (2).
Figure 1 shows the seasonal variation of inean monthly temperature in the
southern hemisphere. As a comparison we have also shown (with a six-month
time shift) data from the International Reference Atmosphere COSPAR (CIRA
1972 [11]), based on data for the northern hemisphere (except for the meso-
sph2re of the low and subtropical latitudes, where data for both hemi-
spheres were used). Figure 2 shows the amplitudes and phases of the annual
_ and semiannual variations in the southern hemisphere. Similar data for the
northern hemisphere are available in the investigations of both Cole
[10J and Nastrom and Belmont [19].
As is well known [21], the lower stratosphere of the equatorial zone is
characterized by a similarity of the phase of the annual variation in re-
gions situa.ted to the north and south of the equator. As indicated in
Fig. 2, the temperature maximum in the annual variation to the south of
the equator is attained in the middle of the year, that is, in the same
period as in the northern hemisphere.
Superposed on variations with an annual period are semiannual variations
whose relative role is particularly significant in the low latitudes (Fig.
1). The amplitude of the semiannual variations in the stratosphere to the
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rui< uV t, it: 1, the vorticity will be negative when there is a
cyclonic circulation.
Such a Vcp distribution can be observed precisely in the boundary layer of
a hurricane (typhoon) at distances exceeding (excluding the periphery) the
radius of the maximum winds.
The authors of [3], in an analysis of data from the expedition "Tayfun-75,"
also pointed out the negative vorticity value (on the basis of polygon
measurements) in tropical lows. The noncorrespondence between the sign of
vorticity and the type of circulation disappears if vorticity is computed
along the contour taking in the center of circulation. We note that in
evaluating the Gray parameters over the course of a two-week period in
28
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the zone of potential formation of tropical cyclones on the basis of data
from the "Tayfun-78" expedition [31 it was found that the vorticity para-
meter (evaluated on the basis of polygon measurements) in many cases had
a negative value and in general was characterized by a very great disper-
sion.
The wind shear parameter was somewhat less (the shear was greater) than in
the investigations in [13]. The Coriolis parameter, naturally, differs
little and it can be regarded as a scaling factor. In general, the DP
value was lower and the TP value was higher than according to the data
in [13].
Thus, the investigation carried out in this section indicates that the gen-
eration potential for a tropical cyclone proposed in [13], which is well
confirmed on ;:he basis of climatological data, cannot be directly used in cor-
responding evaluations on the basis of local (polygon) measurements. Tn
particular, attention must be given to relative vorticity, and possibl--
a refinement should be maue in the region of its determination. A further
checking of potential in other individual cases of hurricane development
is necessary.
BIBLIOGRAPHY
l. Veselov, Ye. P., Bel'skaya, N. N., Petrova, L. I., Papezh, A.,
"Peculiarities in the Development of a Tropical Cyclone Over the Arab-
ian Sea During the Period of 'Bursting' of the Monsoon in June 1977,"
METEOROLOGICHESKIYE ISSLEDOVANIYA (Meteorological Tnvestigations),
Ido 24, 1979.
2. Zaytseva, N. A., "Spatial-Temporal Variability of Long-Wave Radiation
Fluxes and Heat Influxes Under Conditions of Monsoonal Circulation,"
METEOROLOGICHESKIYE ISSLEDOVANIYA, No 24, 1979.
3. Ivanov, V. N., Mikhaylova, L.A., Nekrasov, I. V., "Some Statistical
Properties of the Phenomenological Parameters af Cyclogenesis in the
Tropical Zone," TAYFUN-78 (Typhoon-78), Leningrad, Gidrometeoizdat,
1980.
4. Nesterova, A. V., Petrova, L. I., "Dynamics and Energy of the Tropo-
sphere According to Data from the 'Tayfun-75' Expedition," TRUDY IEM,
No 22(87), 1979.
5. Pal'men, E., N'yuton, Ch., TSIRKULYATSIONNYYE SISTEMY ATMOSFERY (Cir-
culation Systems in the Atmosphere), Leningrad, Gidrometeoizdat, 1973.
6. Petrova, L. I., Nesterova, A. V., "Inflow Layer on the Periphery of
Tropical Cyclones," TAYFUN-78, Leningrad, Gidrometeoizdat, 1980.
7. Plessing, P., Fayster, U., Peters, E., "Results of Ozone Radiosonde
Measurements in the International Experiment 'Musson-77'," METEORO-
LOGICHESKIYE ISSLEDOVANIYA, No 25, 1980.
29
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8. Khain, A. P., "Methods for the Parameterization of Convection Used in
the Modeling of Tropical Cyclones," TAYFUN-75, Vol 2, Leningrad,
Gidrometeoizdat, 1978.,
9. Chuchkalov, B. S,, "First Results of Experiment 'Musson-77'," METEOR-
OLOGTCHESKIYE ISSLEDOVANIYA, No 24, 1979. 10. Buuker, A. F., "Computations of Surface Energy Flux and Annual Air-
Sea Interaction Cycles of the North Atlantic Ocean," MON. WEATHER
REV., Vol 104, 1976.
11. Frank, W. M., "The Structure and Energetics of a Tropical Cyclone,"
ATMOS. SCI. PAPER, No 258, Colorado State University, 1976.
12. Gautier, M. C., "Cyclogenese Tropicale," METEOROLOGIE, No 6, 1976.
13. Gray, W. M., "Tropical Cyclone Genesis," ATMOS. SCI. PAPER, No 234,
Colorado State University, 1975.
14. Herbert, P. Y., Frank, N. L., "Atlantic Hurricane Season of 1973,"
MON. WEATHER REV., Vol 102, No 4, 1974.
15. Yamasaki, M., "The Rate of Surface Friction in Tropical Cyclones,"
J. METEOROL. SOC. JAPAN, Vol 56, No 6, 1977.
16. Kurihara, Y., "Budget of Tropical Cyclone Simulated in an Axisym-
metric Numerical Model," J. ATMOS. SCI., Vol 32, No 1, 1975.
17. Ramage, C. S., "Monsoonal Influence of the Annual Variation of Trop-
ical Cyclone Development Over the Indian and Pacific Oceans," MON.
WEATHER REV., Vol 102, No 11, 1974.
' 18. Rasmusson, E. M., "Mass Momentum and Energy Budget Equations for
. BOMAP Computations," NOAA TECHNICAL MEMORANDUM ERL, BOMAP-3, 1971.
19. Watts, D., "Severe Cyclones in the Arabian Gulf - June 1977,"
WEATHER, Vol 33, No 3, 1978.
20. Williams, K. T., Gray, W. M,, "A Statistical Analysis of Satellite-
Observed Trade Wind Cloud Clusters in the Western North Pacific,"
TELLUS, Vol 21, 1973.
21. Zipser, E. J., "On the Thermal Structure of Developing Tropical Cy-
clones," Nat. Hurric. Res. Proj. Preprint, No 67, 1964.
30
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UDC 551.(521.3:510.42)
INFLUENCE OF ATMOSPHERIC CONDENSATION NUCLEI ON THE ATTENUATION OF SOLAR
AND LONG-WAVE RADIATION
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 28-39
[Article by Candidate of Physical and Mathematical Sciences V. I. Khvorost'-
yanov, Ukrainian Scientific Research Hydrometeorological Institute, sub-
mitted for publication 27 July 1979]
Abstract: The microphysical model of condensation
nuclei proposed by L. M. Levin, Yu. S. Sedunov
and V. I. Smirnov is used in computing the aerosol
sections of attenuation and absorption of sular '
and long-wave radiation and also gpectral optical
thicknesses. It is shown that the dependence of
these characteristics on wavelength and relative
humidity is described by power laws and the para-
meters determining them are related to one another
and can be expressed through the microphysical
characteristics of the aerosol. The computed val-
ues agree well with the experimental data. By means
of averaging in the wavelength spectrum it was pos--
sible to derive expressions for the integral op-
_ tical thickness of the effective wavelength of aero-
. sol scattering and the aerosol part of the Linke tur-
bidity factor.
[Text] The determination of interrelationships between microphysical and
optical properties of atmospheric condensation nuclei is of interest both
for cloud physics and for atmospheric optics because it makes it possible,
_ using optical measurements, to investigate the characteristics of condens-
ation nuclei and processes leading to cloud formation and also makes it
possible to improve optical methods for monitoring atmospheric contamina-
L-ion.
Two of the most important optical characteristics of atmospheric aerosol,
making it possible to judge its microstructure, are the dependence of the
attenuation cross section O'and the dependence of optical thickness l~'on
radiation wavelength A and on humidity H. The c7 (1.) and --C
31
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dependences, determined by the empirical Angstrom law c)"( il) , i.( ,A A-Q -
were experimenLally investigated in [4, 6, 7, 22], In [22] the Angstrom
law was theoretically related to the existence of the Junge aerosol spectra
(see also [8, 18]), but with such an approach it is not possible to de-
scribe the dependences cr (H) , 'L,::H) , al though these parameters, according to experimental data 4; 6, L'.nj, with an increase in humidity, can in- F.
crease by a factor of sei-p�:al times, In [19-21] the C7'(H) dependence =
was computed using empirical formul�s correctly describing the growth of
nuclei with an increase in humidity, but not relating it to the microstruc- -
ture of an aerosol, and in [l] with an allowance for microphysical pro- -
cesses. In these cases the Mie function was assumed to be equal to two,
- but numerical computations do not always make it possible to detect func-
tional dependences between radiation and microphysical properties of
nuclei.
In an earlier communication [17] there was a brief exposition of the re-
-.ults obtained when using a microphysical model of condensation nuclei
formulated by L. M. Levin, vv. S. Sedunov [11, 131 and V. T. Smirnov [15]
for computing the optical attenuation cross sections. In this article, in
addition to the optical cross sections, this model is used in computing
the spectral optical thicknesses and the coefficients of absorption of
long-wave radiation. It is shown that the dependences of these parameters
on wavelength and on humidity are described by power "laws; a correlation
is established between them and the parameters determining them are ex-
pressed through the microphysical characteristics of the aerosol. By means
of averaging in the wavelength spectrum it was possible to derive expres-
_ sions for the integral optical thickness, the effective wavelength and
the aerosol part of the Linke turbidity factor.
Short-Wave Radiation Attenuation Cross Sections
The process of formation of the aerosol spectrum is essentially dependent
on relative humidity H. With H> 707 (only such a case is considered in
this article) the supersaturation value a= eoo - er/e, , regulating the
rate of growth of particles, is determined by the hygroscopj.city and sur-
face tension effects (13:
o (r) - 1 - (1 - ~o) eXP ( B Xt - ru (1)
where er and e,-.,o are the vapor pressures over the surface of a droplet of
the radius r and at infinity, B= 20'/RvTpW;: 1.2�10'7 cm is the Kelvin
parameter, C7'is surface tension, Rv is the gas constant of vapor, C=
brP+O`' ) is the activity of the nuc:leus, rp is the radius of a dry nuc-
leus, ~ p is supersaturation over the plane surface of the water.
The mass of the soluble part of the nucleus is proportional to its activ-
ity, that is, with x= 0.5 to the volume of the nucleus and with aC= 0
to its surface [9].
32
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The equilibrium size of the particle is determined from the condition
b(r) = 0. If the spectrum of dry aerosol is deacribed by a Junge dis-
tribution f(rp) = aro'' , then, as indicated in [11, 13, 151, with H> 70%
the size distribution function for aerosol particles f(r) will be as
follows: - -
1+2 a-} 1
a 6~'�-~~/^ V++) 2 r-�~ ~i+~~ r l - ~ fi s
IfP=grl f(r)7=3 r~v/ ll--~~alr.. ' (2)
~
2B 1-~�
!'rp
The attenuation cross section 6j~t and the absorption coefficient aA
can be computed using the known formulas
rmax
aat = r. I' drr=f (r) Kar (2 -r,).),
(3)
rmin
rmnx '
aR = r, f drr= f(r) Kans (2 - r: X). (4)
. . � rn.+n . . . .
The distribution (2) is not a power-law distribution and the dependences
Q' CT'(H) obtained using it, employing (3), also must no t be power-
- law dependences, as in [l, 19-21]. But it is found that in this problem
it is possible to use the power-law approximations (2). In actuality,
when H< 100Z rgr < 0 and in the humidity range 70-97% the ( rgrI value
falls in the range 2�10-7-2.6�10-6 cm. As indicated by numer3cal comput-
ations with the use of (2) and the K(2n' r/,l ) values computed using the
Mie theory, the maximum of the integrand V_ in formula (3) for U1at with
0.5 � m is near r- 0. 2 � m (curves 1, 2 in Fig. 1), and more than 95%
of the contribution to the integral (3) for Lr~t is from the region r} 0.06
jtm. But in this region in the indicated range of humidities r~>Jr r( and
by analogy with [151 with an accuracy to f irst-order terms for Irag l /r and
taking into account the expression (1 O)/jS O _(H - 1)-1) the f(r)
function can be represented in the form
b ' '~'2�-' (5 )
f ~r) = 2 I f a ~I -H)R[I - (R 3 )rf (1 -IY)-'1 r
1
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ryl 1 trT 6 KH' 9
;2s - e
t ~
6
,5 Zi^~
0 ` S
r ~ -
~
~ 0,5 1 1,5 rMKM
Fig. l. Dependence of attenuation cross sections Crat on the upper integra-
- tion limit making computations using (6)-(10) and integrand Y/ in (3), com-
puted using (2) with H= 70% (curve 1) and H= 90% (2). Curves 3-6: y= 4
and H corresponding to 70, 80, 90 and 95%; curves 7-9: H= 97% and Y cor-
responding to 4.5, 4 and 3.5.
6 Kn'~.
-�1
1,25 : ~ y
1 . 6 t
0,75
0,0 Q9 H
47
Fig. 2. Dependence of experimental cross sections Clat and those computed
using (6)-(10) on humidity. 1, 3) experiment [4] and computations with T=
0.5 � m; 2, 5) experiment [16] and computations with /k = 0.59 1j.m; 4, 6)
computations with 1= 0.59 ~im, oc.= 0.5 and y corresponding to 3.5 and 4.5.
34
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The a value can be determined from the condition of normalization to the
concentration of dry aerosol:
f r-1
Q-4A ~v - I~ rmin I I rmin ~ 1.
L ` rmax J
Substituting (5) into (3), for Clat we obtain
a,at (H) _ Di (Y, a) Ni.-4 (1 - M-R -
(6)
- D: (v, a) Ni.-(Q+i) (1 _ j-j)- (R+V~
where D1, D2, R, Q are constants dependent on aerosol microstructure:
D, 1Y a~ = 3'2Q �-..Q+l bR r~_1 ~i _ r~min lr-~
min l rmax ~ ~ RI�
D�: o' a) = 3.2Q-FI rG+l bR tmin I I- rrmin R I R -F- (8)
~ s /
(9)
R = (Y - 1),'? (1 x). Q = (3 y - 4 ac - 7),'2 (1 a
I1, IZ are dimensionless integrals:
Xmax Xm~x
dx z- ' lQ-r)
Kae (X). f: = dx x- rQ+�
-1 Kabsf Xmin. mac rmin, mexilk. (10)
Xmin Xmin
Figure 1 shows that the integrand (3) for the visible region of the spec-
trum decreases rapidly outside the region 0.06 < r: 0.6 �m; thPrefore, we
can accomplish the transition xmin-'O, xmax-'C>O , after which the inte-
grals are not dependent on the limits. Computations indicated that this
exerts no influence on the results.
Formula (6) shows that the dependence of oat on wavelength (Angstrom law)
and on relative humidity are expressed by power laws; as can be seen from
(9), the corresponding exponents are linearly related: Q= 3R - Z. The Q
and R values for different y, Qc are given in Table 1.
Tab1e 1 shows that in the Junge model of dry aerosol y= 4 in the case of
the soluble part, proportional to the volume of the nucleus, a = 0.5 (and
also for V= 3, x= 0), Q= R= 1, d(H) (1 - g)-1, This
case evidently is encountered most frequently in the atmosphere. We made
computations of dat using (6)-(10) with ol = 0.5, b= 0.25 [11, 13] and
the mean values of continental aerosol rmin = 10-5 cm, N= 103 cm 3[18].
The results are presented in Figures 1 and 2. Figure 1 shows that the
principal contribution to the attenuation of solar radiation is from par-
ticles in the range of radii 0.1-0.6 �m, which agrees with the observa-
tional data [4, 6]. This interval is broadened with an increase in H and -
a decrease in V. Figure 2 illustrates the dependence O'(H). The theoret-
ical curves are close to the experimental curves with V= 4.
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rux urrlulpil ubr, UiVLT
The good agreement of the curves indicates the
turbidity with H> 70% is due to an increase of
measuring 0.1- l�m; 2) although atmospheric a,
component mixture [7, 12, 18], the dependences
can be described using one or two distribution
tive v , oc , N.
following: 1) atmospheric
cloud condensation nuclei
arosol is a complex multi-
Ct ( /A), c7 (H) with H> 70%
functions with some effec-
Table 2 gives the Dl, D2 values, by using which, with formula (6) it is
easy to compute 0'at with different V, ;k and N. In this case [ a] = cm-l,
[N] = cm-3 and [d'atl = cm 1.
The contribution of the second term in (6) attains 8% with H= 90% and 18%
with H= 95%, that is, in evaluations of CSat with the corresponding error
this can be neglected. In the case H4 100%, when I rg I is great, expres-
sion (5) loses sense and for f(r) it is possible to use (2) with the
neglecting of r/I rgrI . Substituting it into (3), we obtain
Xmpa: /
, ~t - p3 i.- P; D3 - 1+ Q(~ 1R '~P nP+l ; 13 c J Cl~X X- (P-f-1) Kah 111 ~ -
- - / Xmin
where p=(V - 2a- 3)/(1 +oC), that is, with H->100% v'at does not tend
to infinity, but tends to a finite limit a"1. As can be seen from (9) and
(11), p= 2R - 2, p= Q- R and since in all cases R,>0, p>I le-1'. .
The results of computation of '15otT for this case, using (20), with Q= 1 km,
v= 4, cx = 0.5, No = 103 cm 3 are given in Table 4.
The last line gives the Rayleigh optical thicknesses from [8]. As indicated
by Table 3, except for the case~= 0.4 ~L m, HCOM0 00
7CO0 CC 000�. V O e' = ~ - Q>c')c")chiGCVI~
~ I t1; t'~ht~trQ) Ol
N O C C O C C C C p-
~
~ M~ h o0 1~ tp y w R) co
_ ~ 1m n0 ~ 00 N 7 a!' f, Cy T1
tlt tC^O O mtDOC9~DI~NN L~i C+
O ~ COOOCC OC�~-� (1) ~ -OommoO^t~
L: tO C:1 fC h I-00 Q1 rn ~
W
y.~ ^ CCCCO000--~
~ 00 cm cD 00 Cl; 1, m w
cOOt- a0aOL7 C
~ - N C'7 N~~t tD f-1
I 41 N
I. I i. IdI I I r i~ Q~ o ' N M~ tD ~ F~ ~ 04
~ tcnn~aoopw
~ N o000000.-
N rl
D t C+ e--I ~rl ~O
~ Ncz~- M~ N
O ~ q~Q~l~tOh Q c0L1la0MOfM
O ooocoo c~ g ~oeva~er
C.,) O ^ 0 oD a0 aO a0 Oi
$4 v OOCOGO.-.
1 ~
~ a~MC ~ oo~ � c~d c0
d
N LqLqcq
~ OOCOO~.~ { ~3: N h~~0~ ~ :j
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of the corresponding eigenvalues to the spur of the matrix (n is the or-
der of the matrix), that is
~
~ IAi
r-~
Ek = n ~
I=1
Elk is the so-called total dispersion of the expansion caafficients w'(zj)
into a series for Yi(zj).
Table 5 gives the eigenvalues for four groups of clouds and the values of
the dispersions Fii, whereas Fig. 2 gives the vertical variation of the
first three eigenvectors of clouds of the first and second groups. We
note that the f irst eigenvectors of all groups of clouds do not pass
through zero. The vertical variation of the first vectors resembles the
vertical profile of its standard deviations.
It is known that as a rule the first eigenvector describes tne most charac-
teristic vertical distribution of deviations of ineteorological elements
from their mean profile. Physical allowance for only the first eigenvector
for the liquid water content profile can be interpreted in the following
way: if a deviation of the liquid water content profile from the mean de-
veloped, it will be everywhere of the same sign, changing only in value
with altitude. The second and subsequent vectors characterize the finer
, structure in liquid water content variations. The second and third vectors
of all groups of clouds accordingly once and twice pass through zero. Phys-
ically their presence in the expansion of variations means that in the
cloud there are regions of an excess or deficit of liquid i�oisture relative
to the mean profile. Thus, each eigenvector is indicative of localizatiun
of liqu�.d water content in definite parts of a cloud.
It is evident that if for any group of clouds the correlation coefficients
- more or less smoothly decrease with altitude, for this group allowance for
the eigenvectors, beginning already with the second or third, is unimpor-
tant. Mathematically this is also expressed in a more rapid decrease in the
- eigenvectors with an increase in the number. And this makes it possible to
accomplish an optimum approximation of the random functions (or vectors)
_ by one, two or a maximum of three of the first eigenvectors.
Figure 3 gives an example of optimum approximation of the arbitrary func-
tions f' (z~ *
I' (z;) ee ?i (Zj), ci = I f (zi) rel (zi),
j_i
with n = 3, E3 99%.
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It can therefore be seen that already the first three eigenvectors approx-
imate quite well random vectors of diff erent types.
In conclusion we will briefly formulate the principal results.
In order to investigate the vertical structure of liquid water content
and temperature of cumulus clouds all the experimental material was col-
lected into four groups in dependence on cloud thickness. The mean profiles
oE liquid water content and temperature of these groups indicate a number
of differences of both a quantitative character (for example, an increase
in the maximum liquid water content of clouds from the first to the fourth
groups) and a qualitative character (different number of liquid water con-
tent maxima with altitude in the groups).
For all these groups we computed the correlation matrices of the profiles
of liquid water content and temperature and for these matrices their
eigenvalues and vectors. It was found that on the whole there is a rather
high correlation between the deviations of liquid water content at all
levels. There are also regions (for different groups at different alti-
tudes) of rapid decrease in the correlation moments, indicative of local
or absolute maxima and deficitc of liquid water content and temperature.
The eigenvalues and eigenvectors of different groups of clouds indicated
the possibility of an optimum approximation of the profiles of liquid
water content and temperature in dependence on the required accuracy
(Table 5) by two or three eigenvectors, which have a deep physical sense:
the first eigenvector indicates the most characteristic universal increase
or decrease in liquid water content or temperature relative to their mean
value, whereas the second, third and other vectors emphasize a finer struc-
ture in variations of liquid water content.
The expansion of the unknown random profiles of liquid water content into a
series of eigenvectors can be used in radiometric methods in restoring
these profiles [7].
In conclusion I regard it as my pleasant duty to express deep appreciation
to N. I. Vul`fson and V. I. Skatskiy for the furnishing of factual material
from aircraft measurements of lj.quid water content and temperature of
clouds and to M. S. Malkevich for valuable consultations ar.d discussion of
the results.
BIBLIOGRAPHY
1. Bagrov, N. A., "Analytical Representation of a Series of Meteorolog-
ical Fields by Natural Orthogonal Representations," TRUDY TsIP (Trans-
actions of the Central Institute of Forecasts), No 74, 1959.
2. Voyt, F. Ya., Mazin, I. P., "Liquid Water Content of Cumulus Clouds,"
IZV. AN SSSR, FIZIKA ATMOSFERY I OKEANA (News of the USSR Academy of
Sciences, Physics of the Atmosphere and Ocean), Vol VIII, No 11, 1972.
71
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3. Gavrilenko, N. M., Yashovskaya, Z. M., "Liquid Water Content and Thick-
ness of Convective Clouds in Different Synoptic Processes," TRUDY
UkrNIGMI (Transactions of the Ukrainian Scientific Research Hydro-
meteorological Institute), No 61, 1966,.
4. Malkevich, M. S., OPTICHESKIYE ISSLEDOVANIYA ATMOSFERY SO SPUTNIKOV
(Optical Investigations of the Atmosphere from Satellites), Moscow,
Nauka, 1973.
5. Obukhov, A. M., "Statistical Orthogonal Expansions of Empirical Func-
tions," IZV. AN SSSR, SERIYA GEOFIZ. (News of the USSR Academy of Sci-
ences, Geophysical Series), No 3, 1960.
6. Popova, N. D., "Parameterization of the Vertical Distribution of
Liquid Water Content of Clouds Using Natural Components," TRUDY GGO
(Transactions of the Main Geophysical Observatory), No 395, 1977.
7. Popova, N. D., "Determination of the Vertical Distribution of Liquid
Water Content in Clouds Using Natural Components," TRUDY GGO, No 411,
1978.
8. Skatskiy, V.I., "Investigation of the Liquid Water Content of Cumulus
Clouds," TRUDY IPG (Transactions of the Institute of Applied Geophys-
ies), No 13, 1969.
72
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UDC 551.551.8
,
INFLUENCE OF ABSORBING PROPERTIES OF THE SURFACE ON THE DIFFUSION OF AN
IMPURITY IN THE ATMOSPHERIC BOUNDARY LAYER
- Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 60-65
[Article by Candidate of Physical and Mathematical Sciences M. A. Novits-
kiy, Institute of Experimental Meteorology, submitted for publication
20 Tune 1979]
Abstract: The article gives the results of an
analysis of the absorbing properties of the
surface on the diffusion characteristics of a
cloud of impurity in the atmosphPric boundary
layer. The scattering of the impurity from an
instantaneous poinr source was computed by
numerical solution of a system of equations for
the concentration moments and equations describ-
ing the stationary horizontally homogeneous
boundary layer of the atmosphere. It is shown
that the trajectory of the center of gravity of
the cloud and the longitudinal integral disper-
sion are essentially dependent on the absorption
of the impurity by the surface.
[Text] A quantitative analysis of the diffusion of contaminating substances
in the atmosphere is becoming more and more important with an increasing
contamination of the environment. In computations of propagation of impur-
ities a complex problem is determination of their interaction with the un-
derlying surface. Difficulties in determining the absorbing properties of
the surface more and more make it necessary to assume that the underlying
surface completely reflects the impurity falling on it. It is evident that
the results of computations of the scattering of an impurity obtained us-
ing such an assumption cannot be adequately correct. In addition, it must
be remembered that the absorbing properties of the-surface are not constant
but are dependent on the season, the falling of precipitation and other
factors. Accordingly, it is of unquestionable interest to ascertain to
what extent the diffusion characteristics of the scattered impurity are
dependent on the absorbing properties of the underlying surface.
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llr2'1c'1A1. itST:. ONT.1'
The interactioti between the impurity and the earth's surface is usually
described by the following boundary condition with z= 0:
k(Z) a: w C=PC,
(1)
where C is the concentration of the impurity, k(z) is the coeff icient of
turbulent diffusion, w is the rate of gravitational precipitation of the
impurity, ~ is the coefficient of absorption of the impurity by the under-
lying surface [1].
The process of turbulent scattering will be described by the semi-empir-
ical equation of diffusion in a parabolic form
_ _ x_ r a r ac N a3 c
a~c 1
d~ +U, a + v a~ 't771~K.9 +KE d;, + K;-at_ j' (2)
where T=tf/i2, S=xf/r, u
~=yf/x u,,, 11=zf/x u*,
f is the Coriolis parameter, X-is the Karman constant, u* is dynamic velo-
city, U, V are the dimensionless components of wind velocity, K,t , Kt , K S _
are the dimensionless coefficients of diffusion in the corresponding direc-
tions.
In solving the formulated problem it is desirable to limit ourselves to an
analysis of the behavior of the several first moments of the concentration.
This is justified because in practical applications we are most frequently
interested preci.sely in the integral characteristics of the cloud of impur-
ity, such as the coordinates of the center of gravity and dispersion. In
addition, the problem is substantially simplified because it is possible
to transform from a three-dimensional diffusion equation to a system of
one-dimensional equations for the concentration moments. We will multiply
equation (2) by ~ in a corresponding power and integrate for ~ and I.
Then we obtain [4] the following system of equations:
aq : a aq
. . d : = x d,, (K aY, ~ (3)
! U
a , (Kri d,~ ) + 9 ' (4)
t~~ l aT, ~K*, 0~)~'2Kiq}-~2m,U, (5)
where q, ml, sl are the concentration moments
:9= JCdEdt, ' (6) ,
m, = JcCdEdC, (7)
s, - f c=Cdcd;.
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Equations similar to equations (7) and (8) can also be written for the i~ -
components of m2 and s2. By means of the eoncentration moments the dis-
persions are computed in the folZowing way:
�2 - f S'd'q - C? E: C� (9)
- j 9~ 1 9d ri '
where C� and CS are the coordinates of the center of gravity of the cloud,
C -jm, dr C._Jm:d~
a f qd-ri ) , - J qd.~ � (lp~
In order to determine the wind velocity profiles entering into equations
(4)-(5) we used a model of a stationary horizontally homogeneous boundary
layer [6]. The system of equations for the model has the following form:
d2X Y - O,
d Y,= Kf�
where
d= Y X _ p (11)
d r~= '
- Ap d0~ u - ufi
il ~~m dr~' Y -Km d ~y .
~
_ X f/ - L e L~ m
Q- Re u~ i
�
u&, vg are the components of geostrophic wind velocitv, km is the eddy vis-
cosity coefficient.
The x-axis of the coordinate system is directed along the surface friction
vector.
For closing the system of equations (11) we used the hypothesis of the
Prandtl displacement length
K. = x JX a-{- p}',4 r
(12)
where L= L(Yj, L,,,) is the displacement length, L a, is a parameter making
it possibl e to stipulate the thermal stratification. In the computations the
displacement length was determined by an expreasion from [6]
I' - - "I (13)
�
1 * x ~
r
where Y~o is the dimensionless roughness of the underlying surface.
The boundary conditions fo:� equations (11)-(13) were as follows:
T1=r10 X=1, Y=O;
?l-00. X-0, Y-.0.
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In solving the system of equations (3)-(5), describing the scattering of
the impurity, the coefficient of vertical diffusion K rZ was assumed to be
equal to the coefficient of eddy viscosity Km; the coefficients of hori-
zontal diffusion K~ and K S were proportional to Km,
/(E = u K,n, I( I _ Wm, (14)
where a and b are some constants (possibly dependent on stratification).
Unfortunately, the presently available data on the values of these con-
stants and their dependence on stratification are contradictory. The com-
putations were made with a= 4.5 and b= 13, which corresponds to the es-
timates cited in [3].
It is understandable that the use of the constants obtained for the snr-
face layer is not entirely correct for the entire boundary layer. However,
the computations made indicated that beginning with some moment in time
shear diffusion introduces a definite contribution to the horizontal
scattering of the impurity and the horizontal dispersions cease ro be de-
pendent on the values of the constants a and b. (In this case the center
of Rravity of the cloud is still in the lower part of the boundary layer)..
Therefore, the use of the values of these constants cited above does not
lead to the appearance of appreciable errors in the entire boundary layer.
The components of geostrophic wind velocity Ug and Vg were computed using
the functions X and Y by use of the expression U010) = V(qo) = 0; then _
we determined the U(rj) and V(1l,) profiles. Since we examined the dif-
fusion of a weightless impurity from an instantaneous point source, the
initial condition for equation (3) was stipulated in the form
9(y), 0) =9ob(q-h), (15)
where h is the height of the impurity source. -
The initial conditions for equations (4) and (S) were zero conditions. The
boundary conditions are easily obtained from expression (1). Since a weight-
less impurity was considered, then w= 0. Integrating (1) for ; and
for equation (3) we obtain the condition
aq _ a
9'
K�. d r, - x u,
(16)
The boundary conditions for equations (4) and (5) have a similar form.
The cited equations (3)-(5) and (11)-(13) were solved numerically: the
boundary layer equations were 3olved by the iteration method proposed in
[51; the equations for the concentration moments were solved by an im-
plicit second-order method [2].
Figure 1 shows the trajectories of the center of gravity of the cloud of
impurity for cases of ideal reflectican of an impurity by the surface (1)
and complete absorption (2) with different stratification. Variant a--
slight instability, L co= 0.1, Ro = 6.7�106, variant b-- neutral
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stratification, L., = 0.015, Ro = 7.5-106, c-- weak stability, LOO = 10-3,
Ro = 1.2�107
. The impurity source was at the height h= 10-4, the roughness
of the underlying surface was r70 = 10'5. It can be seen that in the case
of total absorption of the impurity by the surface the deviation of the
trajectory from the direction of the surface wind is greater than in the
case of total reflection of the impurity. With an increase in atmospheric
stability the trajectories become increasingly more distant from one
another. This is attributable to the fact that in the case of instability
the intensity of mixing is greater, the impurity is more rapidly raised
upward and the influence of the lower boundary condition is less. We will
proceed in the following way in order to explain the large angle of de-
viation of the trajectory in the case of total absorption of the impurity
at the boundary. We will integrate equations (4) for Y1. Then, taking (3)
into account, we obtain the following equations for the total moments M1
and M2: _
d M, m i(ro) f q Ud 1,
d: -
-;cz'o m:(Yw)+S 9Vd(17)
where
M,= f nitd'i+ M.:= Jm, clri.
The second terms on the right-hand side of these equations have the sense
of the mean velacities of transfer of the impurity in the corresponding
directions. It can be seen that in the case of total absorption of the
impurity the contribution of the lower layers leads to a relative increase
in the contribution of the V-component of velocity to the total transport
of the impurit-,, as a result of which there is a greater angle of devia-
_ tion of the trajectory of the center of gravity of the cloud in the case
of total absorption of the impurity at the boundary.
_ � o : zo 40 so so 100

ZO
4
Fig. 1.
Figure 2 shows the dependence of height of the center of gravity of the
cloud of impurity on time. These variants correspond to the same values
of the parameters as the similarly denoted curves in Fig. l. In the case
of total absorption of the impurity by the surface there is a more rapid
rise of the center of gravity. This is attributable to the fact that the
absorbing surface eliminates the impurity from the lower part of the
boundary layer. The rate of ascent of the center of gravity increases with
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an increase in instability due to an increase in the intensity of mixing.
t
zc

Cq
0,6
04
0,1
n
S
101
5
~ I
~I
~ i
i ~
i ~
i
6
~J---f-- / t
1011 i I
2�10� S 10, ~
Fig. 2 Fig. 3
An analysis of the behavior of the vertical dispersion ~ n indicated that
the change in the boundary condixion exerts a very weak influence on its
value.
Fi ure 3 shows the integral dispersions of concentration of the impurity
also for cases of t._-tal reflection of the impurity at the boundary
(solid curves) and total absorption (dashed curves). The variants a, b, c
correspond to the same boundary layer characteristics as in Fig, 1. A com-
parison of the illustrated curves reveals that absorption of the impurity
at the boundary Ieads to a decrease in the longitudinal dispersion. With
an increase in stability the iniluence of the boundary condition becomes
stronger. In contrast to this, it follows from computation of the behavior
of the transverse dispersions F2 that in the considered time interval with
a change in the lower boundary conditinn they virtually do not change. Such
a behati�ior cf the dispersions can be explained in the following way. Tl-ie
longitudinal scattering of the impuri.ty is determined to a considerable
degree by the wind shear. Since the shear is greatest at the surface,
78
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the absorption of the impurity by the surface leads to a decrease in the
contribution of the lower layers to longitudinal scattering. However,
transverse scattering of the impurity at the surface is determined by
eddy diffusion and therefore the change in the lower boundary condition
- exerts no appreciable influence on
Thus, our analysis reveals that in computations of transverse dispersion
the nature of the interaction or the impurity with the underlying surface
_ plays no significant role. At the same time, a knowledge of the absorption
coefficient is entirely necessary in computations of longitudinal- disper-
sion and the trajectories of movement of the center of gravity of the
cloucl of impurity. The cited graphs in actuality determine the corridor
in which the curves d escribing the behavior of the corresponding parameters
fall in the case of a real underlying surface.
BIBLIOGRAPHY
1. Krotova, I. A., Natanzon, G. A., "Influence of an tlnderlying Surface
on the Propagatio.z of a Weightless Impurity in the Atmospheric Sur-
face Layer," TRUDY IEM (Transactions of the Institute of Experimental
Meteorology), No 21(80), 1978.
2. Samarskiy, A. A., WEDENIYE V TEORIYU RAZNOSTNYKH SKHEM (Introduction
to the Theory of Diff erence Schemes), Moscow, Nauka, 1971.
3. Yaglom, A. M., DIFFUZIYA PRIMESI OT MGNOVENNOGO TOCHECHNOGO ISTOCHNIKA
V TURBULENTNOM POGRANICHNOM SLOYE. TURBULENTNYYE TECHENIYA (Diffusion
_ of an Impurity from an Instantaneous Point Source in a Turbulent Boun-
- dary Layer. Turbulent Currents), Moscow, Nauka, 1974.
4. Saffman, P. G., "The Eff ect of Wind Shear on Horizontal Spread from
an Instantaneous Ground Source," QUART. J. ROY. METEOROL. SOC., Vol
88, No 378, 1962.
5. Wipperman, F. K., "The Planetary Boundary Layer of the Atmosphere,"
DEUTSCHEF WETTERD IENST. OFFENBACH a. M., 1973.
6. Wipperman, F. K., "Eddy Diffusion Coefficients in the Planetary Boun-
dary Layer," ADVANCES IN GEOPHYSICS, Vol 18a, Academic Press, 1974.
79
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UDC 614.71:551.510.42(261/264)
CONTAMINATION OF THE ATMOSPHERIC SURFACE LAYER OVER THE ATLANTIC OCEAN
BY BENZ(A)PYRENE
Moiscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 66-72
[Article by Candidate of Geographical Sciences A. I. Osadchiy, Candidates
of Physical and Mathematical Sciences A. I. Shilina and S. G. Malakhov,
Institute of Experimental Meteorology, submitted for publication 1 Aug-
ust 1979]
- Abstract: An experimental evaluation of the
latitudinal distribution of benz(a)pyrene
is presented. A decrease in the concentra-
tion of benz(a)pyrene in atmos Pheric air
toward the equator to 10'3-10"+ ng/m3 was
discovered. In the ragion of the temperate
- and subtropical latitudes the relative co-
eff icient of enrichment of lead and the
relative concentration of benz(a)pyrene (rel-
ative to the value near the ICZ) were close
in value, which can be evidence of the Fresence
of a common source of their emission.
[Text] Benz(a)pyrene (BP) is of particular interest among the anthropo-
genic atmospheric pollutants. It is a by-product of many types of human
activity. BP enters both into the lower layers of the atmosphere (surface
layer) and into the higher layers (middle and upper troposphere, lower
stratosphere). As a result of persistence the BP in the forn of passive
aerosols can be transported for many thousands of kilometers from the
site of entry into the atmosphere. Facts concerning the transport of BP
over great distances are given in [5]. There is every basis for assuming
that BP is propagated globally.
In this connection it is of considerable interest to estimate the BP con-
centration in the atmosphere of the least cc;ntaminated regions on the
- earth over the ocean in the northern and southern hemispheres and also
in the Antarctic region, where the BP sources are considerably less tban
_ in the northern hemisphere. The levels of concentration of BP obtained
80
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in this way could characterize the present-day global background of con-
tamination in the atmospheric surface layer. The paper gives the results
of ineasurement of the aerosol component of BP in the near-water air layer
over the Atlantic Ocean in the latitude range 57'N-74�S, and also in the
region of the Antarctic coast between 52�W and 46�E. The observations were
made during the work of the 22d Soviet Antarctic Expedition from aboard
the steamer "Estoniya" during the period from 25 January through 7 Anril
1977.
25 76 ~ 21
2 ~
,
, 6
I ~
I ! I
21
~ . I 20 ~
;7 (
19
~ I
1J~
10 i 11
\
Fig. 1. Sketch map of sampling sites.
The sampling was carried out from the deck of the steamer at a height of
~ about 15 m above the sea level using a FW apparatus of the centrifugal
type using FPP-15 filters with a rate of air throughput of about 200 m3/
hour. The duration of the sampling varied from 10 hours to several days
[2]. The air sampling was accomplished under conditions precluding thr:
possibility of their contamination by shipboard effluent. During thF.
sampling, on the basis of an analysis of synoptic weather charts and the
press.ure pattern charts, regularly received aboard the ship, an allowance
was made for the synoptic sitiiation and the nature of the transport of air
masses for the purpose of obtaining samples representative for definite
- circulatory conditions in this region of the ocean. A quantitative deter-
mination of BP was made by the method of quasilinear luminescence spectra
, 81
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using the Shpol.'skiy effect [4]. The filters with the samples were sub-
jected to extraction using purified n-hexane in air-flow columns with a
rate of outflow of the extract 0.2 ml/min. The extract was frozen at the
- temperature of the liquid nitrogen (-196�C) and irradiated by a flux of
W radiation with a wavelength of 365 nm. The intensity of the analytical
BP quasiline with a wavelength a= 402.4 nm was measured using an FEP-1
nhotoelectric attachment for an ISP-51 spectrograph.
Table 1
Benz(a)pyrene Concentration in Different Regions of Atlantic Ocean
lpo6a 1
I
aTa
JZZ
_3 KoopuFtHarbt yvacTKa oT6opa npo6 ~
4
---HaHano KOHCII 7 _
wHpora I uo~roTa wEipora~ I ao.irora 6
K0xt1esirpa-
nUNA f,c113(a)-
Hpex~
1
27 I
57046'c 9
40�45'alpl
51042'c I
02�22's
0,12
2
28
5142
02 22
43 02
09�23' e
0,15
3
30
41 34
1015
37 40 l
12 04
0,01
4
02 II
13
CaHra-Kpyc Ae TeHepiiq)
.
0,01
5
02
27�44' c
16�37' s
27�44' c
16�37' a
0.003
6
03
27 40
16 35 12
01 10
2830
0,0004
7
08
0510
31 00
23�00' ro
39 00
0,0003
8
14
3405
52 30
47 02
42 16
0,0003
9
20
51 30
36 00
74 46
26 50
0.0002
10
26
7400
2500
6737
36�18' e
0,0003
11
04 111
6700
45�30' a
67 40
45 50
0,0006
13
07
6700
44 00
50 00
26 00
0,0005
14
10
5000
2600
34 30
18 10
0,0004
18
16
28�30' ro
13 24
26 10
1140
0.005
ig
17
261011
1140
18 30
07 10
�
'
0,003 ,
30
18
18 30
05 10
06 35
04
42
s
0.001
21
21
04 45
06� I 5' a
l I�00' c
11 30
0,0005
32
24
11�10' c
17 30
27 44
16 30
0,003
- 33
38
13
CaEira-Kpyc
Ac TeHepiicp
0.17
' 24
29
28�30' c
16000'3
44`00' c 1
09�00' 3
0,002
- 3.5
01 IV
4615
0700
5130
00�03'a
0.001
26
03
51 30
00 05
57 15
0830
0,15
27
04
57 15
0830
57 50 ,
22 40
0,04
KEY:
1. Sample
2. Date
3. Coordinates of sampling sector
4. Beginning
5. Latitude
6. Longitude
7. End
82.
8. BP concentration, ng/m3
9. N
10. E
11. S
12. W
13. Santa Cruz de Tenerife
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The limit of BP detection is 1�10-9 mol/liter and the reproducibility
of the analytical results was f15%.
Figure 1 shows the track of the steamer "Estoniya" during the voyage as
part of the 22d Soviet Antarctic Expedition. Data on atmospheric contam-
ination by BP along the ship's track and in some ports are given in Table
1. Tq e atmospheric contamination by BP is maximum in ports 0.06-0.6
ng/m (Table 1). Fluctuations of the BP concentrations in the near-water
air layer in ports are very great and evidently are determined primarily
by the wind direction and weather conditions. The data in Table 1 make
it possible to estimate the BP concentration in the principal climatic
zones of the Atlantic Ocean (except for the polar regions of the northern
hemisphere).
Table 2 gives the mean and extremal BP concentrations in the principal
climatic zones of the Atlantic Ocean. Table 2 indicates that the highest
BP concentrations are observed in the temperate latitudes of tile north-
ern hemisphere, in the English Channel, Strait of Dover, in the Baltic
and North Seas. The lowest BP concentrations are observed in the western
regions of the Atlantic Ocean in the temperate latitudes of the southern
hemisphere.
Figure 2 shows the latitudinal variation of the concentrations of benz(a)-
pyrene in the near-water air layer over the Atlantic Ocean. The solid
curve represents measurements on the route to Antarctica; the dashed
curve represents measurements during the return of the ship. The gaps cor-
respond to measurements made in ports (see Table 1) or sectors of the
track on which samples were not taken. Figure 2 shows that in the north-
ern hemisphere the general variation of change in the concentrations of BP
in the near-water layer of the atmosphere over the Atlantic Ocean was re-
tained during movement of the steamer to Antarctica and back. In the
northern hemisphere the BP concentrations decrease relatively rapidly from
north to south to the meteorological equator (ICZ).
In the southern hemisphere in the western regions of the Atlantic Ocean
the BP concentrations decrease with an increase in latitude. In the east-
ern regions of the Atlantic Ocean the BP concentrations are substantially
higher than in the western regions, evidently due to the stronger influ-
ence of the continent, caused by the peculiarities of atmospheric circula-
tion in these regions and the heavier shipping than in the western regions.
In the latitude region 0-30� in the eastern regions of the Atlantic Ocean
in the southern hemisphere the BP concentrations are equal to or are some-
what greater than the BP concentrations in the northern hemisphere in this
same latitude range. Along the shores of Antarctica there is an increase
in the BP concentrations in comparison with the BP concentrations in the
temperate and subantarctic latitudes of the southern hemisphere.
An interesting peculiarity of the distribution of BP concentrations over
the Atlantic Ocean is that within the limits of one and the same regions
in the temperate and subtropical latitudes of the northern hemisphere
83
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KEY TU iABLE 2
1.
Hemisphere
10.
Value
2.
Observation region
11.
Northern
3.
Atlantic Ucean region
12.
North Sea, Baltic Sea, straits
4.
Western
13.
Temperate and subtropical lati-
5.
Eastern
tudes
6.
Average in both regions
14.
Trades zone
7.
Mean value
15.
ICZ and equatorial zone
8.
Number of ineasurements
16.
Southern
9.
Range of changes
17.
Subantarctic and Antarctic lat-
itudes
18.
African coast region (subtrop-
ical latitudes)
4,7 Nz/m-'
BP ng/m3
?6 I
W
~
~I
I
S
~I
~r
aJK
J
271
.
~
ICZ
Q
I
I
90?
I
I
~
d
S
~
i
n
Z
~ I 1f
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j
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V
i 2~~ ~
_
15
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13 n
S
~ 14 r"ri
J
1rr
s
~ -g
07 8
-
2
9
N so'c.a. 20 0 20 yo so en - taw S
Fig. 2. Distribution of concentrations of benz(a)pyrene (BP) over Atlantic
Ocean by latitude. The figures on the graph correspond to the numbers of
samples.
85
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the BP concentrations can vary substantially (the differences between
the minimum and masimum values attain two orders of magnitude). In the
- tropical and equatorial regions the changes in BP concentration are con-
siderably less. For the purpose of clarifying the reasons for such con-
siderable variations in BP concentrations in the temperate and subtrop-
ical latitudes of the northern hemisphere in these regions of the Atlan-
tic Ocean we analyzed the conditions for the transport of air masses
at the level of the 700-mb isobaric surface, describing the distant
transport of a passive atmospheric impurity in the lower troposphere.
Fig. 3. Reverse trajectories of air masses, drawn from sampling sites. 1)
on route to Antarctica, 2) with movement in opposite direction, 3) long-
term mean monthly trajectories of transport of air masses. The figures
_ correspond to the numbers of the samples in Table 1.
Figure 3 gives the trajectories of movement of air masses at the 700-mb
level corresponding to the middle of the period of sampling (due to the
fact that when taking samples ar_ allowance was made for the synoptic sit-
uation and the nature of the transport of air masses the trajectory is
representative for the entire sampling period) and also the long-term
mean trajectories of movement of air masses within the limits of this
_ region, constructed on the basis of the data in [1]. An analysis of the
nature of the transport of air masses makes it possible to note that the
maximum BP concentrations in air samples were observed during the trans-
- port of air masses from the territory of Europe (samples Nos 2, 3). These
concentrations were close to the BP concentrations in cities [5]. The
relatively low BP concentrations were observed in the case of transport
of air masses from the subtropical and temperate latitudes of the western
and arctic regions of the Atlantic Ocean (samples Nos 5, 22, 24, 25).
An analysis of the trajectories of air masses during the sampling period
and the mean long-term (climatic) trajectories of transport of air masses
make it possible without a great volume of observational statistics to
86
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obtain some idea concerning the background BP concentrations in these re-
gions of the Atlantic Ocean under typical conditions of atmospheric cir-
culation by means of exclusion of the data obtained under anomalous con-
ditions of transport of air masses. Figure 3 ahows that samples Plos 5,
22 and 24 are representative samples, reflecting the background concentra-
tions of BP in the near-water air layer over the Atlantic Ocean in the
temperate and subtropical latitudes of the northern hemisphere. Thus, the
- background concentration of BP in the eastern regions of the Atlantic
Ocean in the region of the temperate and subtropical latitudes of the
northern hemisphere can be assumed equal to 0.002 ng/m3.
Also of considerable interest is the increase in BP concentrations along
_ the shores of Antarctica in comparison with its concentrations in the
temperate and subantarctic latitudes of the southern hemisphere. A sim-
ilar effect was registered earlier along the shores of Antarctica in an
investigation of the concentrations of global radioactive products of
nuclear explosions in the surface air layer. The increase in the concen-
tratiQns of global radioactive products of nuclear explosions in the re-
gion of the coast of Antarctica is attributable to the presence in this
region of intensive vertical transport of air masses from the upper tropo-
sphere (lower stratosphere) into the lower layers [3]. This makes it pos-
sible to postulate that in the process of transport of global aerosols
_ of benz(a)pyrene into the Antarctic region a factor which can be of sub-
stantial importance is the transport of sir masses containing BP in the
upper layers of the troposphere (possibly also in the stratosphere) and
their subsequent subsidence into the lower layers in the region of the
_ Antarctic coast. Observational data on the concentration of BP in the
interior regions of Antarctica and an increase in statistics of ineasure-
ments of the BP concentration in the temperate and subantarctic lati-
tudes of the southern hemisphere will assist in the final solution of
this problem.
Table 3
Distribution of the Relative Concentrations of BP and the Coefficient of
Lead Enrichment in the Near-Water Layers of the Atmosphere in the Eastern
Regions of the Atlantic Ocean in the Principal Climatic Zones of the
Northern and Southern Hemispheres
Hemisphere Observation region BP Lead
- Northern North Sea, Baltic Sea and straits 230.0
Temperate and subtropical latitudes 8.0 7.9
Trades zone 3.6 1.2
Equatorial zone and ICZ 1 1
_ Southern Trades zone 2.0 2.3
Region of African coast (subtrog-
ical Iatitudes) 8.0 5.6
81
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In connection with the increased BP concentrations in the near-water
layer of the acmosphere in the neighborhood of the African coast of the
Atlantic Ocean it is of interest to compare them with measurement data
for lead in this region, cited in [6]. It is desirable to examine the
relative (for examnle, in relation to the content in the air masses of
the ICZ) BP concentrations and coefficients of lead enrichment which we
computed on the basis of the data in [6] in different climatic regions
of the Eastern Atlantic (Tabli 3).
Table 3 gives the relative (in relation to the concentration in the ICZ)
BP co:7centrations and the lead enrichment coefficients in the regions of
_ the temperate and subtropical latitudes (regions of westerly transport)
and the Northeast Trades of the northern hemisphere, and also the Trades
zone of the southern hemisphere.
Table 3 shows that the relationships between the BP concentrations and
the coeff icients of enrichment of atmospheric aerosols with lead in these
regions are rather close, as a result of which it can be postulated that
the BP and the lead in the near-water layer of the atmosphere in these
regions have a common source of origin.
Conclusions
1. In the Atlantic Ocean it is the near-water layers of the atmosphere in
the temperate and subtropical latitudes of the northern hemisphere and the
eastern regions of the southern hemisphere which are most contaminated
with BP.
2. The BP concentration in the near-water layer of the atmosphere in the
northern hemisphere in the Atlantic Ocean region increases with an in-
crease in latitude, whereas in the southern hemisphere there is a de-
crease. Along the shores of. Antarctica the BP concentration is higher than
in the temperate and subantarctic latitudes of the southern hemisphere.
3. The BP concentration in the near-water air layer in aerosol form in the
most remote clean regions of the Atlantic Ocean is 10-3-10'4 ng/m3. ~
BIBLIOGRAPHY
1. ATLAS KLIMATICHESKIKH KHARAKTERISTIK TEMPERATURY, PLOTNOSTI I DAVLEN-
IYA VOZDUKHA I GEOPOTENTSIALA V TROPOSFERE I NIZHNEY STRATOSFERE
SEVERNOGO POLUSHARIYA (Atlas of Climatic Characteristics of Air Tem-
perature, Density and Pressure and Geopotential in the Troposphere
and Lower Stratosphere of the Northern Hemisphere), No 4, Moscow,
Gidrameteoizdat, 1974.
2. Davydov, Ye. M., Malakhov, S. G., Makhon'ko, K. P., Mashkov, F. T.,
"Filtering Apparatus for Determining the Concentration of Radioac-
tive Dust in the Atmospheric Surface Layer," TRUDY IEM (Transactions
of the Institute of Experimental Meteorology), Ne 2, 1970.
88
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3. Zhukov, V. A., "Radioactive Contamination of Surface Air Over the Ant-
arctic Continent," METEOROLOGIYA I GIDROLOGIYA (Meteorology and Hydrol-
ogy), No 11, 1976.
4. ^'eplitskaya, T. A., KVAZILINEYCHATYYE SPEKTRY LYUMINESTSENTSII KAK
r:ETOD ISSLEDOVANIYA SLOZHNYKH PRIRODNYKH ORGANICHESKIKH SMESEY (Quasi-
linear Luminescence Spectra as a Method for Investigating Complex IL
Natural Organic Mixtures), Moscow, Izd-vo MGU, 1971.
5. Shabad, L. M., 0 TSIRKULYATSII KANTSEROGENOV V OKRUZHAYUSHCHEY SREDE
(Circulation of Carcinogens in the Environment), Moscow, Meditsina,
1973.
6. Chester, R., Stoner, Y. H., "Pb in Particulates from the Lower Atmo-
sphere of the Eastern Atlantic," NATURE, Vol 2815, 1973.
89
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� va va a aV itlL VJL VI~L<
"1
UDC 551.464 (260) (100)
CQMPUTATION OF CONTAMINATION OF SURFACE WATERS OF SOME REGIONS IN THE
WORLD OCEAN BY THE ATMOSPHERIC FALLOUT OF STRONTiUM-90
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 73-78
[Articl e by Candidate of Physical and Mathematical Sciences K. P. Makhon'-
ko, Institu:e of Experimental Meteorology, submitted for publication 3
July 19791
~ Abstract: T:ie author examines anticyclonic sub-
tropical macrocirculatory systems in the South
Atlantic, southern part of the Indian Ocean and
northern part of the Pacific Ocean, within which
the advection of water masses is difficult and in
the first approximation can be neglected. The
concentration of Sr90 in the surfz.ce waters is
_ computed for the period 1954-1979 in its temporal
variation on the basis of the fallout of this iso-
tope from the atmosphere onto the underlying sur-
face and with allowance for its penetration into
the deeper layers of the ocean. A satisfactory
agreement of the results of computations and ob-
servational data is observed.
[Text] The author of [9] computed the cnntamination of the surface waters
of the North Atlantic by Sr90 in the region of an anticyclonic subtropical
macroc irculatory system within which the convection of water masses is
diffic ult and in the first approximation can be neglected. In the com-
putatio ns this made it possible to take into account only the fallout of
" Sr90 f rom the atmosphere onto the ocean surface.
Computations of the concentration of the isotope in the quasihomogeneous
surfac e layer of the ocean with the thickness h were made in [9] by a
numerical method using the formula
~
1
' C= e-A' I r ~ p (q) r e-`'' d 0,
where P(t) is the fallout of the isotope from the atmosphere, t is time,
_ A' _-A+ T is the sum of the constant of removal of the isotope from
the quasihomogeneous layer into th- depths of the ocean and the constant
of rad 3oactive decay.
90
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It is interesti_ng to attempt to carry out similar computations of contam-
ination of the surface waters with Sr90 for other similar regions in
the oceans. As is well known, in the world ocean there are a whole series
of macrocirculatory systems, the most powerful of which are five anticy-
clonic subtropical circulations in the North and South Atlantic, in the
northern part of the Pacific Ocean and in the southern parts of the Pac-
ific and Indian Oceans [17]. In the Atlantic and Pacific Oceans the south-
erly anticyclonic systems are characterized by a lesser intensity of cir-
culation of waters than in the northern hemisphere. In the southern part
of the Pacific Ocean the general pattern of circulation is not expressed
so clearly. In the northern part of the Indian Ocean the circulation of
waters in general is characterized by a greater complexity and seasonal
variability as a result of monsoonal shifting of the winds and the high
- degree of disruption of the ocean by land mass. Accordingly, we will lim-
it ourselves to an examination of contamination of the surface wate:s
only in the southern parts of the Atlantic and Indian Oceans and in the
northern part of the Pacific Ocean, where it is possible to discriminate
regions within which the advection of radioactive water masses in the
first approximation can be neglected and it can be assumed that the contam-
ination of waters was caused only by radioactive fallout from the atmo--
sphere.
South Atlantic. A southerly subtropical anticyclonic circulation is form-
ed by the Bengal Current on the northeastern periphery, the Brazilian
Current on the west and the Circular Antarctic Current on the south. De-
spite the fact that it, in turn, is subdivided into quasistationary eddies
having dimensions an order of magnitude less, the general macroscale cir-
cularion is expressed qui.te clearly. Its period is approsimately three
years, which is more than two times greater than the period of circula-
tion in the North Atlantic; the exchange of surface waters across the
- equator is difficult. All this makes it possible to discriminate in the
South Atlantic a region having a closed circulation of water masses ap-
proaimately limited by the coordinates 5-40�S, 10�E-35�W, within which
the advection of Sr90 with ocean waters from other regions with a certain
degree of approximation can be neglected [1, 10, 11, 18].
Then [he Sr90 concentration in the surface waters of this region in the
ocean will be determined by the entry of the isotope from the atmosphere
onto the ocean surface P(t) and the simultaneously transpiring process
of its outflow inta the deeper water layers [9]. The data in [24, 251
will be used in determining the Y(t) values in the considered latitude
zone necessary for computations using formula (1). Fibure la shows the
pattern of temporal change of fallout of Sr90 from the atmosphere; Fig.
lb shows the concentration of this isotope in the surface waters of tl:is
region of the Atlantic, computed usinR formula (1), for a mean thickness
of the quasihomogeneous layer h= 40 m and A' = 0.3 g-1, which corres-
ponds to a residence time of Sr90 in the quasihomogeneous layer Z= 1/A -
= 3.6 years. The dots represent measurements of the Sr90 concentration in
the surface waters of this regian of the ocean, cited in systematized
91
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3. ~~LY 19t7~~
~i-
NO. 4r AP'RI L 1980
_OGT
t OF 2
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form in monograoh [10] and supplemented by the results in [5]. The ver-
_ tical lines represent the values of the mean square scatter of data and
_ the figures over the dots correspond to the number of observations enter-
ing into the averaging. The A' value was selected in such a way as to
obtain the best correspondence between the experimental data and the
computed curve. _
' P mKi/(km2.yr)
Pnlfu/(K~ to~ C, 10'"Xu/n 75
101 loz Ki/liter
zv
qs s 5
o,i 2
r . ~ x2
'05 1933 /JtiS 1913 r a31933 fl65 1915
Fig. 1. Temporal change in the fallout of Sr90 from the atmosphere in the
latitude zoiie 5-40�S (a) and its concentration in the surface layer of
the ocean within the zone of the subtropical anticyclonic circulation
of the South Atlantic (b). 1) [10]; 2) [5].
Unfortunately, the number of observations of the Sr90 concentration in the
_ waters of the South Atla:itic is substantially less than in the northern
hemisphere, which makes the estimate of residence time of Sr90 in the
quasihomogeneous layer 'G = 3.6 years less reliable. Nevertheless, we can
note the satiGfactory agreement of the shape of the computed curve with
_ observational data and draw a qualitative conclusion concerning the less-
er intensity of the vertical exchange of water masses in the southeril
part of the Atlantic than in the northern part.
Indian Ocean. The southerly subtropical anticyclonic circulation is f.ormed
in the north by the Southern Fquatorial Current which passes along 10�S
from the Sunda Archipelago to the shores of Africa, on the west by the Mad-
agascar Current, on the south by the South Indian Ocean Current; the east-
ern boundary of the circulation is the West Australian Current. Within the ~
- limits of this macrocirculatory system there is a series of anticyclonic
circulations formed by the southern periphery of the South F.quatorial Cur-
_ rent. The surface homogeneous layer in the entire central pzirt of the ocean
is about 30 m. The transport of waters from the Pacific Ocean into the In-
_ dian Ocean through the Indonesian seas is 2.12�103 m3/sec, which is
_ negligible. The existence of a closed circulation makes it possible to dis-
criminate a region of the ocean approximately bounded by the roordinates
20-40�S, 50-110�E within which in the first approximation it is possible
to neglect the advection of water masses [8, 221.
92
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PmKi(km2.yr)
C,1019Bu/n Ki/liter
eo
6~ e
io
~
s
z

:3
F +4
1935 1965 1975 99s5 .3ff5 11915
Fig. 2. Temporal change in fallout of Sr90 from atmosphere in latitude
zone 20-40�.S (a) and its concentration in the surface layer of the ocean
within the zone of the southerly subtropical anticyclonic circulation of
the Indian Ocean (b). 1) [13, 14], 2) [26], 3) [30], 4) [16].
With respect to radiation conditions, the southern part of the Indian ~
- Ocean is one of the least investigated regions of the world ocean. The
- eRtreme ccantiness of observational data on the concentrations of long-
lived isotopes in the waters of this ocean makes it possible to draw
only qualitative conclusions concerning the patterns of their behavior.
Earlier, on the basis of ineasurements of the Sr90 concentrations in the
equatorial part of the Indian Ocean the conclusion was drawn that there
is an anomalously high reserve of this isotope. It was postulated that
the rate of self-purification of the surface waters does not differ from
that in other regions of the world ocean. The transport of more radioac-
tive waters from the Pacific Ocean is too sma1l to change the general pat-
- tern of contamination in the Indian Ocean [12]. It was therefore postulat-
ed that this effect was caused by the maximum of annual precipitation in
the equatorial Zone [14) or the fallout of the produets of nuclear ex-
plosions transported in the troposphere from the Pacif ic Ocean region [12J. _
However, the trajectories of radioactive masses propagating from explosions -
_ in the Pacific Ocean over the Indian Ocean lie for the most part to the
north of the equator with a deflection onto the Arabian Peninsula [29],
that is, in the direction away from the region of interest to us.
We will den;onstrate that the radioactive contamination of the surface waters
in the considered region of the Indian Ocean can be attributed only to the ~
radioactive fallout onto its surface.
For the computations we will use data [24, 25] on the fallout of Sr90 from
the atmosphere in 1954-1978. Figure 2a shows the pattern of temporal change
in the fallout of this isotope in the latitude zone 20-40�S, and in Fig.
2b, the concentration of Sr90 in the surface waters of the considered re-
gion of the Indian Ocean, computed using formula (1), with A' = 0.2 year-1
corresponding to = 1/A = 5.7 years. The determined residence time for
93
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;on,rof.iMt cca,

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Sr90 in the surface waters of the southerly subtropical anticyclanic cir-
culation in the Indian Ocean is entirely realistic with respect to order
of magnitude. It is true that the extremely limited number of observations
of the Sr90 concentration in this region of the ocean forces us to use
the results with great caution and regard the conclusion about a lesser -
rate of vertical exchange in comparison with similar regions in the At-
lantic as only purely qualitative. Data from observations of the Sr90 con-
centration in the waters of the considered region are cited in (13, 14,
16]; reference [26] gives data on the concentration of Cs137 which we re-
computed into the Sr90 concentration taking into account the Cs137/Sr90
= 1.6 ratio obtained in [26] on the basis of a great volume of statistical
data for the Pacific Ocean. This exhausts the observational data for tre
_ particular region and therefore for orientation Fig. 2b also gives observ-
ational data on the Sr90 concentrations in the entire latitude zone 20-40�
S in the Indian Ocean. Figure 2b shows that these data do not contradict
~ the determined general picture of contamination of surface waters in the
considered region of the ocean by Sr90. It follows from this that the role
of advection of Sr90 in this latitude zone of the Indian Ocean in general
is small.
_ Pacific Ocean. In the northern part of the Pacific Ocean the surface cir-
culation of waters in general does not change from season to season and
from year to year. The subtropical anticyclonic circulation is formed in
the southern part by the North Trades Current, in the west - by the Kuro-
shio Current, a continuztion of a branch of which is the North Pacific
Ocean Cur.rent, running to the east and on its path sending branches to the
south. The most continuous is the circulation zone bounded approximately
_ by the coordinates 20-35�N and 140-180�E (without the northwestern corner)
[2, 3, 32]. The depth of the upper quasihomogeneous layer of the ocean in
- this region averages 60 m[23].
. A peculiarity of the Pacific Ocean is the presence of intensive local
sources of radioactive contamination of waters: for the most part poly-
gons for the testing of nuclear weapons and also the dumping of the wastes
of atomic industry, the sites of their burial, etc. [6 7, 27]. As indi-
cated by estimates [6], about 70% of the reservz of Sr�O in the waters of
the Pacific Ocean as of 1961 must be attributed to the direct introduction
of this isotope into ocean waters directly at the site of nuclear shots and
in the form of local fallout from the atmosphere. However, the slowness ~
and the spatial nonuniformity of processes of mixing and circulation of
waters in the ocean do not make it possible to evaluate the contribution -
of local contaminations to the total contamination of waters in individual
regions of the Pacific Ocean. Accordingly, it is already impossible to ap-
ply the computation scheme employed above to the region which we invest-
igated: on the basis of data from observations of the Sr90 concentration
in the surface waters using formula (1) find A and then, on the basis
of the fallout P(t), restore the pattern of changes in concentration during
the years when there were no observations.
94
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r
In such a situation it remains only to attempt to estimate the A' value, -
proceeding on the basis of indirect data.
We will assume that vertical water exchange in the considered region of
the Pacif ic Ocean is similar to the water exchange in the similarly situ-
ated region of the Atlantic. Then in the region as the exchange constant
we use the value found in [9] for the anticyclonic circulation in the :
North Atlantic Jt, = 0.5 yr-1. Since the water exchange in the subtropical
anticyclonic circulation must evidently be somewhat more intensive than
in the tropical zone, this value does not contradict the value ' = 0.4
Yr-1 (2 = 1/A = 2.7 yr), found fn [31] for the equatorial abyssal region
near Bikini atoll on the basis of ineasurements of the Pb210 concentration.
_ Figure 3a shows the fallout of Sr90 from the atmoaphere in the region 20-
35�N [24, 25], whereas Fig. 3b, with a solid curve, showa the temporal
change in the concentration of Sr90 in the surface waters of the consid-
ered region of the Pacific Ocean,-computed using formula (1) for the value
n.' = 0.5 yr'l, corresoonding to = 2,1 years. The dashed curves in
this same figure represent the concentrations computed for values A ' -
0.3 and 0.7 yr-1 (t = 3.6 and 1.5 years), which we feel are still real-
istic, but less probable. This same figure shows data from observations
[S, 15, 19-21] of the concentration of Sr90 in the surface waters of the
considered region and data [26, 28] which we computed on the basis of the
observed Cs137 concentrations. Unfortunately, all the observational re-
sults relate only to two short time intervals: 1961-1962 and 1965-1968,
and therefore the data have been supplemented by information for 1974 oii
the Sr90 concentration in another region of the ocean situated nearby with
the coordinates 20-28�N and 150�E-160�W [4].
Figure 3b shows that the solid curve (-A..' = 0.5 yr-1) coincides with the min-
imum values of the Sr90 concentration observed in the described region.
Most of the points on the graph fall above this computed curve. This may
be related to the presence of a slow exchange of water masses between the
inner part of the anticyclonic circulation and the outer part of the ocean
area, whose waters were subjected to the effect of local contamination
sources. The upper dashed curve (A' = 0.3 yr-1) in general coincides quite
well with the experimental points. Thus, within the framework of available
observational data with a residence time of Sr90 in the surface waters of
'G = 3.6 years there.is no need fur using the hypothesis of the existence of
an appreciable water eachange between the inner part of the ring of circul-
ation of waters and the outer ocean area for explaining the real picture
of ocean contamination.
t'.owever, as time passes, the gradual quasidiffusional evening-out of the
- Sr90 concentrations in the entire ocean should nevertheless come about,
which in subsequent years leads to a deflection of the computed curve down-
ward from the observational data. In this case the curve computed using data
_ on the global fallout of Sr90 can be regarded as the lower limit of the pos-
sible concentrations of this isotope in the surface waters of the ocean.
95
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PMKuMInt tod)
10
S
1
1
c,tQ"rruln s Ri/liter
r
ft7
'o 6) �1 WN
2
0 yb ~
?
J
9935 ~965 1975 1133 1965
.
.
.
~
~

(
Fi 3. Temporal change of fallout of
Sr~0 from atmosphere in the latitude
zone 20-35�N (a) and its concentration
in the surface layer of the ocean with-
in a northerly subtropical anticyclonic
circulation in the Pacific Ocean (b). I)
A' = 0.3 year'1, II) A ' = 0.5 year-1,
III)A' = 0.7 year-1; 1) [28], 2) [15],
3) [19-21], 4) [51, 5) [4], 6) [28].
96
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_ . ,
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What has been said applies to an equal degree to the other oceans as
well. The diff.erence between observational data and the computed curve
in principle will make it possible to evaluate the role of such quasi-
diffusion in the dqnamics of bontamination of waters in the consider-
ed regions of the world ocean.
BIBLIOGRAPHY
1. Bulatov, R. P., Barash, M. S., Ivanenkov, V. N., Marti, Yu. Yu., AT-
LANTICHESICIY OKEAN (Atlantic Ocean), Moscow, Mysl', 1977.
2. Burkov, V. A., OBSHCHAYA TSIRRULYATSIYA VOD TIKTiOGO OKEANA (General
Circulation of Waters in the Pacific Ocean), Moscow, Nauka, 1972.
3. Burkov, V. A., "Structure of Currents in the Pacific Ocean and Their
_ Nomenclature," OKEANOLOGIYA (Oceanology), Vol 4, No 1, 1966.
4. Vakulovskiy, S. M., Vorontsov, A. I., Katrich, I. Yu., Koloskov,
I. A., Roslyy, Ye. I., Chumichev, V. V., "Sr90 and Tritium in the Sur-
face Waters uf the Northern Part of the Pacif ic Ocean in 1974," OKEAN-
OLOGIWA, Vol 18, No 2, 1978.
5. Vdocenko, V. M., j:olesnikov, A. G., Spitsyn, V. I., Vernovskaya, R. N:,
Gedeonov, L. I., Gromov, V. V., Ivanova, L. M., Nelepo, B. P.., Tikho-
mirov, V. N., Trusov, A. G., "Radioactivity of Waters of the World
Ocean and Behavior af Some Fission Products in the Ocean," ATOMNAYA
ENERGIYA (Atomic Energy), Vol 31, No 4, 1971.
6. Zudin, 0. S., Nelepo, B. A., STATISTICHESKIY ANALIZ INFORMATSII 0
RADIOAKTIVIdOM ZAGRYAZNENII OKEANA (Statistical Analysis of Information
on Radioactive Contamination of the Ocean), Leningrad, Gidrometeoizdat,
1975.
7. Zudin, 0. S., Nelepo, B. A., Spiring, A. N., Trusov, A. G., "Distribu-
tion of the Cs Concentration in the Surface Waters of the Pacific
Ocean," ATOMNAYA ENERGIYA, Vol 32, No 4, 1972.
, 8. Kort, V. G., "Water Exchange Between the Oceans," OREANCLOGIYA, Vol 2,
No 4, 1962.
9. Makhon'ko, K. P., "Computation of the Contamination of Surface Waters
in the Central Region of the North Atlantic by Atmospheric Fallout of
Sr90," METEOROLOGIYA I GIDROLOGIYA, No 3, 1979.
10. Nelepo, B. A., YADERNAYA GIDROFIZIKA (Nuclear Hydrophysics), Moscow,
Atomizdat, 1970.
11. Ozmidov, R. V., Popov, N. I., "Some Data on the Prop:igation of Soluble
Impurities in the Ocean" (Disposal of Radioactive Wastes into Seas,
Oceans and Surface Waters) PROC. SYMP. IAEA, Vienna, 16-20 May 1966,
IAEA, Vienna, 1966. 97
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rux urTlc;lAL uSE UNLY
12. Patin, S. A., "Regional Diatribution of Sr90 at the Surface of the
World Ocean," OKEANOLOGIYA, Vol 5, No 3, 1965.
13. Popov, N. I., Orlov, V. M., Patin, S. A., "Sr90 in the Deep Waters
of the Indian Ocean," TRUDY INSTITUTA OKEANOLOGIYA (Transactions of
the Institute of aceanology), Vol 82, 1966.
14. Popov, N. I., Orlov, V. M., Patin, S. A., Ushakova, N. P., "Sr90 in
the Surface Waters of the Indian Ocean in 1960-1961," OKEANOLOGIYA,
Vol 4, No 3, 1964.
15. Popov, N. I., Patin, S. A., Polevoy, R. I., Konnov, V. A., "Sr90 in
the Waters of the Pacific Ocean. Communication 2: Surface Waters of
the Central Region, 1961," OKEANOLOCiYA, Vol 4, No 6, 1964.
16. Petrov, A. A., Ovchinnikova, S. S., Komagurov V. Ye., "Present-Day
Radioaetive Contamination of 5ea Waters by Sr~~ and Cs137," TgUDy
VNIRO (Transactions of the All-Union Scientific Research Instituti! of
Fishing and Oceanography), Vol 117, 1978.
- 17. Stepanov, V. N., MIROVOY OKEAN. DINAMIKA I SVOYSTVA VOD (The World
Ocean. Dynamics and Properties of Waters), Moscow, Znaniye, 1974.
13. FIZIKt1 OKEAIr'A. T. l. GiDROFIZIKA OKEANA (Physics of the Ocean. Vol 1.
Hydrophysics of the Ocean), edited by V. M. Kamenkovich, A. S. Monin,
Moscow, Nauka, 1978.
19. ChwnYichev, V. B., "Sr90 Content in the Waters of the Pacific Ocean
- in 1962 and 1964," TRUDY INSTITUTA OKEANOLOGII, Vol 82, 1966.
20. G`humichev, V. B., "Sr90 in Waters of the Northwestern Part of the _
- Pacific Ocean During 1966-1978," TRUDY IEM (Transactions of the In-
stitute of Experi.mental Meteorology), No 1(32), 1972. -
21. Chumichev, V. V., "Sr90 in Pacific Ocean Waters During 1964-1966,"
TRUDY IEM, No 3(42), 1974.
22. Shcherbinin, A. D., STRtJKTURA I TSIRKULYATSIYA VOD INDIYSKOGO OKEANA
(Structure and Circulation of Waters in the Indian Ocean), Leningrad,
Gidrometeoizdat, 1976.
23. Bathen, K. H., "On the Seasonal Changes in the Depth of the Mixed
Layer in the North �acific Ocean," JGR, Vol 77, No 36, 1972.
24. ENVIRONMNTAL QUARTERLY, Appendix, EML-353, 1979.
25. FALLOUT PROGRAM, Appendix, HASL-329, 1977.
26. Folsom, T. R., Mohanrao, G. J., Pillai, K. C., Sreekumaran, C., "Dis-
tributions of Cs137 i.n the Pacific," HASi,-197, 1968.
r 98
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27. Folsom, T. R., Mohanrao, G. J., Winchell, P., "Fallout of Cesium in
Surface Sea Water Off the California Coast (1959-1960) by Gamma-Ray
Measurements," NATURE, Vol 187, No 4736, 1960.
28. Folsom, T. R., Sreekumaran, D., Hanaen, N., Moore, J. M., Criamore,
R., "Some Concentrations or Cs137 at Moderate Depths in the Pacific
_ 1965-1968," HASL-217, 1970.
29. Machta, L., List; R. Y., Hubert, L., "World-Wide Travel of Atomic
Debris," SCIENCE, Vol 124, No 3220, 1956.
30. RADIOACTIVITY IN THE MARINE ENVIRONMENT, Nat. Acad. Sci., Washington,
1971.
31. Schell, W. R., "Concentration, Physicochemical States and Mean Resi-
dence Times of Ph210 and P0210 in Marine and Estuarine Waters," GEO-
CHIM. AND COSMOCHIM. ACTA, Vol 41, No 8, 1977.
32. Tully, J. P., "Oceanographic Regions and Processes in the Seasonal -
Zone of the N. Pacific Ocean," STUDIES ON OCEANOGRAPHY, Seattle, 1965. \

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UDC 551.465.7(261)
CALCULATION OF ThE PROPAGATION OF AN IMPURITY IN THE NORTHEASTERN
ATLANTIC AND IN ADJACENT SEAS
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 79-83
[Article by B. R. Zaripov and Candidate of Physical and Matheamatical Sci-
ences D. G. Rzheplinskiy, All-Union Scientific Research Institute of Fish-
eries and Oceanography and Institute of Oceanology TJSSR Academy of Sci-
ences, submitted for publication S March 19791
Abstract: A study was made of the propagation
of impurities in. the boundary regions of the
Atlantic and Arctic Oceans. In the computations
use was made of the characteristics of currents
obtained by the diagnostic method. The authors
give prognostic mean long-term maps of the con-
tamination level, taking into account the loca-
tion of the principal sources of dumping of
wastes and the processes of decay of the impur-
ity.
[Text] The present-day level of contamination of the world ocean is quite
high and this can lead to a considerable decrease in its bioproduc tivity
[6, 9, 12, 131. There is a special danger for bioproductivity from petrol-
eum contami.nations [6, 9, 12]. According to available data [7], the world
ocean annually receives from 5 to 10 million tons of petroleum. In the
North Sea alone there are more than 1,000 wells which yield more than 50
million tons of petroleum annually [9]. The contamination of the invesC-
igated region, which includes the Northeast Atlantic, and also the highly
productive Norwegian, Greenland and North Seas, is extremely great [8, 12-
141.
The amount of observational data on contamination of the ocean is con-
stantly increasing, but for the time being they are inadequate for eval-
uating the contamination of large-scale ocean areas over long periods of
time. For this purpose it is promising to make use of numerical modeling -
methods. In this case the well-known semi-empirical turbulent diffusion
equation is used for computing the propagation of an impurity. We examined
some theoretical and practical aspects of use of this equation for such
purposes in earlier studies [3, 4]. .
100
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In order to compute the propagation of an impurity it is necessary to
have data on currents. But there have been virtually no measurements of
currents at the spatial-temporal scales investigated here and therefore
the authors first carried out computatioas of the mean long-term hori--
zontal and vertical circulation of waters with the use nf the diagnostic
method described in [10]. This method takes into account the principal
factors involved in the formation of currents the water density field,
bottom relief and wind and gives reliable results [11]. The station-
ary mean long-term winter circulation of waters is stipulated in comput-
ations of propagation of the impurity [5].
The turbulent diffusion coefficients were assumed to be constant in time -
and space and were determined from the well-known "four-thirds" laws for-
mulated by Richardson and Obukhov. For horizontal and vertical diffusion
these values were 0.2�108 and 0.2�101 (in cgs) respectively. As the boun-
dary conditions we stipulated the impurity flux through the boundary sur-
face.
The available data on the quantity of contaminating substances entering
the ocean and their physicochemical transformation are extremely scanty.
Accordingly, the magnitude and direction of the impurity flux at the boun-
daries was stipulated on the basis of the following qualitative considera-
tions. The runoff of the rivers of Western Europe and Great Britain is
- highly contaminated; in addition, along the shores there is a great number
of large cities with a considerable volume of runoff of industrial and
household wastes. Accordingly, the time-constant impurity flux directed
into the ocean through the "solid" boundary the shores of Europe and
Great Britain is stipulated. Since the volume of contaminated water
entering the ocean from-the shores of Iceland and Gieenland is small, in
these sectors of the "solid" boundary the impurity flux was assumed equal
to zero.
Observational data [9, 12] show that the Gulf Stream, and then the North
Atlantic Current, carry contaminated waters and therefore in the southern
and western sectors of the "fluid" boundary the flux of impurity directed
into the computation reRion is stipulated (see Fig. la). South of Green-
land, in the region of transport of waters by the East Greenland Current,
the impurity flux is directed from the computation region. The flux in the
northern sector of the "fluid" boundary is directed from the computation
region since in the eastern part there is transport of contaminated waters
by the Norwegian Current, whereas in the western part there is "dilution"
by the purer waters of the East Greenland Current. At the ocean surface -
there is stipulation of a small impurity flux, uniform over the entire
ocean area, directed from the ocean into the atmosphere; such transport,
according to data in [7], occurs due to evaporation and spray accompanying
waves. A settling of the impurity occurs at the bottom [7]; this is also
taken into account in the computations.
101
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rUK urrLLiA. uSL UNLY
f4 t f t t 1
;o a 10 ~ 20 U
13
10~

I
60r / � ~ ..i~

r~ 4 t~ f f~
L-- - -
'+0 30 20 10 0 70
10
6j 13
~ b Zn V
~10 70~
~ y J%
7 6 G 5 S .
~y V y~411`:'...
2
90 30 20 10 D 10 _
DI y) :
20 JD y
70 c I70 ~ 15 O.. 70 a,.::.~',^1S G90 s~ ,f0
LL1/
' . ~ ZS 15 i .
75 JO 10
_ ss~. � . `'v~ ~ ~ . ~ r,2
0
1S ,
IV ~10 ZS
v
60~~~~ ~ 1o,

~o ~2o S ~
Zs~
~ o =
~ ~
Fig. l. Distribution of impurity six months after onset of computations
in arbitrary units (the arrows indicate a stipulated direction of trans-
port of the impurity through the boundaries). a) at surface; b) at 50-m
horizon; c) at 100-m horizon; d) at 200-m horizon.
The rate of decay of contaminating substances in the ocean is extremely
different, and in particular, decreases with a decrease in water tempera-
- ture. Here we assumed a uniform absorption of impurity with a rate
of 0.3% per day. As the initial conditions it was assumed that the inves-
tigated ocean area is free of the impurity. The correctness of such ini-
tial conditions was examined in [2] for computing the distribution of a
nonconserva.tive impurity� The turbulent diffusion equation was there
numerically using the "directed differences" method (for example, see
[10]). T_he interval of the computation grid was 1� in latitude and 2� in
lungitude; in the North Seh the interval was reduced to 0.5� and 1� re-
spectively. The time interval was 3 days. The computations were made for
a period of six months and indicated that the distribution of the impur-
ity three months after the onset of the computations assumes a"quasista-
tionary" character and thereafter remains virtually constant.
The results of the computations were used in constructing maps of the dis-
tribution of impurity at the horizons 0, 50, 100, 200 and 590 m. The en-
tire layer 0-500 m(see Fig. 1) is characterized by a higher content of
the impurity in the Norwegian-Greenland basin. This is determined by the
' peculiarities of circulation of these waters. In the layer 0-50 m the
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impurity, entering through the southern boundary of the computation re-
- gion, is transported quite rapidly into the Norwegian Sea together with
the waters of the North Atlantic Current, whose velocity is high. At the
50-m horizon the isolines of concentration of the impurity were directed
approximately along the main f'ow of the North Atlantic and Norwegian Cur-
rents. In the central part of the Northeast Atlantic a local zone of in-
creasF.d concentration (up to 6 arbitrary units) is formed, associated with
reduced current velocities. In the western part of the Northeast Atlantic
the increase in the concentration of the impurity is associated with the
cyclonic circulation of waters, which in turn is determined by the Ice-
. landic Low. In the Norwegian-Greenland basin there is an accumulation of
the impurity and it is possible to discriminate two zones of increased
concentration (up to 20-25 arbitrary units) to the northeast of Iceland
and in the eastern part of the Norwegian Sea on the periphery of the cy-
clonic circulation of waters. There is an increased concentration in the
central part of the North Sea, associated with the cyclonic movement of
waters and ascending movements in this region.
Zones of increased concentration of the impurity in the western part
and to the south of Iceland begin to be formed at the 100-m horizon
(Fig. l,c,d) in the Northeast Atlantic. An increase in the concentration
is observed in the eastern part of the North Sea. In the southern part of
the Northeast Atlantic the isolines have a zonal direction. At the 200-m
horizon there is an appreciable increase in the level of contamination
of the Northeast Atlantic, which especially in the west and southeast be-
- comes comparable with the level of contamination of the Norwegian-Greenland
basin. The reason for this is evidently that the current velocity at this
hor~zon is lower than at the surface and as a result the impurity is not
so rapidly transported into the Norwegian Sea. A zone of increased concen-
tration up to 30 arbitrary units is formed in the western part of the North-
- eastern Atlraatic; its center coincides with the region of water upwelling.
In the southeast, in the region of an increase in the concentration of the -
impurity, the directions of the currents are unstable [5]. There is a high
level of contamination in the Norwegian-Greenland basin. To the northwest
of Iceland, in the region of the East Greenland Current, the waters are
purer. On the basis of the results of these computations we will examine the prin-
cipal peculiarities of distribution of the impurity in the investigated
water area. In the considered Iayer the contamination level increases with
depth. The horizontal distribution of the impurity is essentially nonuni-
form and for the most part is determined (with stipulated boundary condi-
tions) by the peciiliarities of water circulation. In general, the level
of contamination in the Norwegian and Greenland Seas is greater than in
the Northeast Atlantic. The North Atlantic Current transports impurities
into the Norwegian-Greenland basin, characterized by a cyclonic movement
_ of waters. Zones of less mob ile waters ("stagnant" zones) are formed in
which there is an accumulation of impurity. The impurity concentration
is increased in the central part of the North Sea, but in general it is
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rva vrriA,lAL UOr. v1VLY
lower than in the Norwegian Sea. This can be associated with the stipu-
lated settling of the impurity on the bottom (the North Sea is a shallow-
water basin) and with a quite intensive water exchange between the sea
and the Atlantic. The impurity concentration in the zone of the Norwe�ian
Current is increased; this current carries contaminated waters which en-
ter from the North Sea and which are transported by the North Atlantic
Current. In the Norwegian-Greenland basin there are two zones of increased
concentration: in the eastern part and toward the northeast of Iceland. To
the west of Iceland the waters are purer because this region is remote
from the pz�incipal sources of contamination.
The maps of the distribution of impurity cited here are prognostic maps
of the mean long-term (winter) level of contamination of the investigated
water area. They can be used for different purposes precisely in this way.
We note that in many cases the zones of increased concentration of the im-
purity coincide with the regions of increased biogroductivity. The contam-
ination level of the Norwegian-Greenland basin is increased and this is
one of the most productive regions in the world ocean. Computations indi-
- cated that the system of water circulation in this region, in combination
with delayed processes of decay of contaminants favors the accumulation
of the impurity, which can lead to a decrease in its bioproductivity. The
coincidence of regiuns of increased contamination and high productivity
is not random. As is well known, the basis of primary bioproductivity is
the supply with biogenous substances and the water circulation favors the
accumulation in one and the same regions of both biogenous and contaminat-
ing substances. We also note that these maps can be used as the background
level in computing mesoscale processes of transport of the impurity (for
example, in determining the consequences of tanker accidents or damage
to oil wells).
As noted above, observational data on contamination, averaged for the spa-
tial-temporal scales considered here, are virtually unavailable. A compar- -
- ison of the computed maps with data from individual surveys is not entire-
ly correct. However, comparison of our maps with data from some surveys
[l, 9] in general indicated their fair qualitative correspondence. We note
_ in conclusion that the development.of the theory of sea currents in the
near future should lead to the possibility of preparation of quite precise
forecasts of currents with different times in advance [11], which in turn
will make it possible to prepare prognostic maps of the contamination
level both for the entire world ocean and for its individual regions.
BIBLIOGRAPHY
1. Buyanov, N. I., "5r90 and Cs137 in the North and Norwegian Seas,"
MATERiALY RYBOKHOZYAYSTVENNYKH ISSLEDOVANIY SEVERNOGO BASSEYNA (Mat-
erials of Fishery Investigations in the Northern Basin), No 21, Mur-
mansk, 1974.
2. Galkin, L. M., RESHENIYE DIFFUZIONNYKH ZADACH METODOM MONTE-KARLO
(Solution of Diffusion Problems by the Monte Carlo Method), Moscow,
Nauka, 1975.
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= 3. Zaripcv, B. R., "Modeling of the Distribution of Matter in Water Bod-
ies LTSing the Turbulent Diffusion Equation," EKSPRESS-INFORMATSIYA
- Tst?7.ITEIRKh (expansion unknown), 5eries 9, No 9, 1977.
4. Zaripov, B. R., Rsheplinskiy, D. G., "Use of the Diffusion Equation
- for Computing the Distribution of Oceanological Characteristics,"
EKSPRESS-INFORMATSIYA TsNIITEIRKh, Series 9, No 10, 1977.
5. Zaripov, B. R., Rzheplinskiy, D. G., "Mean Long-term Seasonal Cir.cul-
ation of Waters of the Northeast Atlantic, Norwegian, Greenland and
North Seas (Diagnostic Computations)," OKEANOLOGIYA (Oceanology),
Vol XVII, No 5, 1977.
6. Mironov, 0. G., "Biological Aspects of Contamination of Seas by Pet-
ruleum 3nd Petroleum Products," IZV. AN SSSR, GEOGRAFIYA (News of the
US5R Academy of Sciences, Geography), No 2, 1972.
- 7. Mironov, 0. G., "Concise Description of tne Physical Factors Exerting
an Influence on the Fate of Petroleum in the Sea," TRANSPORT I KHRAN-
ENIYE NEFTl: I NEFTEPRODUKI'OV (Transport and Starage of Petroleum and
Petroleum Products), No 10, 1975.
8. Oradovskiy, S. G., Simonov, A. I., Yushak, A. A., "Investigation of
the Nature of the Distribution of Chemical Contaminants in the Gulf
Stream Zone and Their Influence on the Yrimary Productivity of Ocean
Waters," METEOROLOGIYA I GIDROLOGIYA (Meteorology and Hydrology),
No 2, 1975.
9. Ryabchikav, A. M., "Environmental Coutamination by Petroleum," VESTNIK
MGU (Herald of Moscow State University), GEOGRAFT'YA (Geography), 1974.
10. Sarkisyan, A. S., OSNOVY TEORII I RASCHET OKEANICHESKIKH TECHENIY (Prin-
ciples of the Theory and Computation of Ocean Currents), Leningrad,
Gidrometeoizdat, 1966.
11. Sarkisyan, A. S., CHISLENN'IY ANALIZ I PROGNOZ MORSKIKH TECHENIY (Numer-
ical Analysis and Prediction of Sea Currents), Leningrad, Gidrometeo-
izdat.
12. Simonov, A. I., Oradovskiy, S. G., Yushak, A. A., "Present Status of
, Chemical Contamination of Waters of the North Atlantic," METEOROLOGIYA
I GIDROLOGIYA, No 3, 1974.
13. Terziyev, F. S., Norina, A. M., "Scientific and Practical Aspects of -
the Problem of Contamination o.f the Northern Seas," PROBLEMY ARKTIKI I
ANTARKTIKI (Problems of the Arctic and Antarctic), No 25, 1977. 14. Roll, H. V., "Die heutige Verunreinigung der Meere," UNIVERSITAS, Vol
26, No 7, 1971.
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UDC 551.464.38(260) (100) -
SALT BALANCE IN THE WORI.D OCEAN
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 84-89
(Article by A. M. Gritsenko and Professor V. N. Stepanov, Institute of
Oceanology USSR Academy of Sciences, submitted for publication 3 July 19791
Abstract: A study was made of the principal com-
ponents of exchange of the total content of salts,
including exchange between the oceans, the ocean ~
and the atmosphere and land. For the first time
an attempt has been made to determine the balance
of salts in the world ocean. Available data and
indirect computation methods are used for evalu-
ating the components.
[Text) Significant concepts in this field are extremely limited. The most
thorough investigations have been made on the exchange of salts between
= the ocean and the atmosphere and the land. Relatively recently a very valu-
able study was published by V. N. Ivanenkov and A. N. Gusarova [8], devoted
_ to the excrange of dissolved oxygen, silicic acid and inorganic phosphorus.
With respect to the transfer of salts i.n the waters of the ocean an article
has been published by Yu. A. Grigor'yev [6], which examines exchange be-
tween the Atlantic and Indian Oceans, and also the Indian and Pacific
Oceans. In addition, computations have been made of the transfer of salts
in individual small regions.
Our objective was to estimate the receipt and loss components of the salt
balance in the werld ocean. The intensity of exchange of salts, like indi-
vidual chemical elements (judging from data published by V. N. Ivanenkov
and A. N. Gusarova), are determined primarily by water exchange between
the oceans. Their cancentration in ocean waters plays a secondary role.
The exchange of salts between the ocean and the atmosphere is three orders
of magnitude less than in the waters of the ocean.
Exchange of salts between the oceans. According to the computations in [10]
rhe total content of salts in the world ocean is about 46.5�1015 tons. Al-
most 7�1014 y.:ons (Table 1) or 1.5% of their quantity _s drawn into
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the exchange between the oceans. Accordingly, the total eacharge of salts
in the world ocean can occur in approximately 70 years. -
Table 1
Exchange of Salts Between Oceans
KEY:
6
7
9
10
Iipxxo,u
-
Pacxo,�
Paa~iocrb
� OKeaH
jp1z
1 %
1012
~p -
1
r/zoO 5
r/zoa
I x
r/zod
I%
ariaitTiNechuii
232,7
33
235,3
34
-2,6
1
1
I'IN111lHCKIfA
TnxNff
249,9
36
249,2
36
+0,7
,
0,3
CeeepHwH AeAOanTdR
199,9
13,0
29
2
197,5
13,1
28
2
+2,4
-0,1
1,2
0,8
Bcero: I
695,5
100
695,1
100
+0,4 I
0,06
1.
Ocean
6.
Atlantic
2.
Receipt
7.
Indian
3.
Loss
8.
Pacif ic
4.
Difference
9.
Arctic
5.
tons/year
10.
Total
Most of the salts are transported into the Antarctic part of the oceans
(Table 4), where the water eachange is particularly significant. Its volume
in the Atlantic and Indian Oceans differs little 33-36% relative to the
global exchange; here total exchange can occur in 40-45 years. In the
Pacific Ocean it is substantially less; the reason is the barrier created
by the narrow Drake Passage and this is also reflected in the Atlantic
Ocean. Constituting about 1/3 of the salt exchar_ge in the entire world
ocean, the total exchange in the Pacific Ocean with its enormous water
mass can take place in approximately 125 years. The smallest role in the
planetary exchange of salts is played by the Arctic Ocean only 2% of
their total mass transported in the world ocean. The rate of exchange of
waters in the oceans is virtually the same [11].
It should be emphasized that the cited estimates can be regarded as ex-
tremely approximate. They were made without allowance for the different
intensity of movement of waters, determined by the peculiarities of strat-
_ ification and the related nonuniformity in the rate of transfer of energy
and matter. And nevertheless the determined values are as small as those
given by other authors (in particular, as given by Ivanenkov and Gusarova
[81). At the same time, estimates of a completely Ifferent order of mag-
nitude are also known; for example, A. Poldervart [9] points out that
during the last billion years of existence of the world ocean the sodium
chloride, constituting 77% of all the dissolved salts, has been exchanged
roughly only 9-10 times.
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run urr lUltu., UJt UtVLY
Estimates of components of exchange of salts through ocean surface. Par-
ticularly thorough investigations in this field have been made by S. V.
Bruyevich and Ye. Z. Kulik [5], then by S. V. Bruyevich and V. D..Korzh
[4], and finally S. V. Bruyevich and V. N. Ivanenkov [3]. Among the studies
of foreign authors we should note a study by E. Eriksson [12]. ihe mention-
ed studies give a review of the main literature, which makes it possible -
to limit ourselves here only to those highly important conclusions which
were drawn with respect to the considered problem.
The transfer of salts from the ocean into the atmosphere occurs in the
process of evaporation and 3s a result of the spraying of water during
- wind waves, constantly occurring in the ocean with greater or lesser force.
N. N. Zubov has proposed that the loss of salts in the presence of waves
be called "mechanical evaporation," whereas L. I. Belyayev has proposed
that it be called "mechanical loss of salts." The appearance of salts in
the air as a result of evaporation is called "physical evaporation," and
only for it is there a. quantitative estimate based on field and laboratory
- experiments. According to S. V. Bruyevich and his colleagues, 0.5 g of
salts is lost from 1 m2 of ocean surface.
- In the literature we were unable to find data on how much salt can enter
the atmosphere as a result of the spraying of water when waves are present.
It is very difficult to obtain such estimates, primarily due to the extreme-
ly great variab ility of the wind waves and the complexity of the process of
_ salt ejection. S. V. 3ruyevich and V. D. Kcrzh [4] examine a considerable
number of Soviet and foreign studies devoted to the mechanism of formation
and destruction of air bubbles and water droplets arising when waves are
present. When the bubbles burst a small streamlet is ejected from their
surface and this gives rise to individual tiny droplets so that the larg-
er of them enter the ocean, whereas the tiniest ones become condensation
nuclei.
Indirect computation methods were employed in order to ascertain the pos-
sible volume of the salts entering the atmosphere. For example, E. Eriks-
son [12], on the basis of the quantity of salts transferred across 1 km
of shore per day (5.4 tons) and a total length of the shore line of the
world ocean (250,000 km), determined that during a year 0.5�109 tons is
carried onto the land from the ocean in a year. Estimating the magnitude
of transfer of salts onto the land at 10% of their total quantity entering
into the air, E. Ericsson obtained a total value for the entire tnass of
~ salts in the atmosphere equal to 5�109 tons/year. These computations were
confirmed by S. V. Bruyevich on the basis of the fact that the salts
transported onto the land are then returned to the ocean with river run-
off; he determined the magnitude of chemical runoff at 0.5�109 tons/year.
Assuming that river runoff -Ls about 10% of the entire evaporation from the
surface of the world ocean, the transfer of salts into the atmosphere was
found to be the same as found by E. Eriksson, equal to 5�109 tons/year.
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r�oR OFFrr.iAi, tTSr oNr.Y
Proceeding on the basis of available estimates of individual components
of the exchange of salts through the ocean surface, we made an attempt
to determine their budget for individual oceans and the world ocean as a
whole (Table 2). In order to ascertain the quantity of salts which is re-
leased to the atmosphere by each ocean we used the earlier-computed evapor-
_ ation; for the world ocean it was 496�103 km3 annually [11].
Table 2
Exchange of Salts Through Ocean Surface in 109 tons/year
2 OtceaH
Corrae,~Abuuie o6Wetia AraaHTErve-
- 1 Mupoooii I CKIIII I NH',{IIIICKIIff,
-
= 9
OHsNVecKOe Eicnapeiiite
BwnaAeHNe coneH c ocan-
lO
Ke)1N
- 11
XHMN4ECKIIH CTOK PCK
06Wee xonNyecTeo conefi,
-
~NacTeyauiHx e o6weHe
12
4epe3 nosepxHOCrb oKea-
N8:
109 TI20a
13
�o
KEY:
1.
2.
3.
4.
5.
6.
7.
8.
-4,752
-1,140
-0,248
-0,060
4,500
0,980
0,500
0,220
5,0
1,2
100
24
Exchange components
Ocean
World
Atlantic
Ind ian
Pac if ic
Arctic
Spraying by wind waves
Ceee HWII
T31%1i16 JlCAO Hthll} 7
-1,044 I
-2,471
-O,CSE
-0.129
110;i?
� 2,440
0,063
0,160
I , I
2,6
22
52
-0,097
-0,003
0,043
0,057 `
0,1
2
9. Physical evaporation
10. Salts falling in precipitation
11. Chemical runoff in rivers
12. Total quantity of salts partic-
ipating in exchange through
ocean surface
13. Tons/year
Physical evaporation was computed, taking into account that according to
the estimates made by S. V. Bruyevich, et al. during this process 0.5 g
of salts enters the air from 1 m2 of water. It is therefore found that
0.248�109 tons of salts annually are carried from the surface of the world
ocean into the atmosphere. Since this is 5% of the total transfer of salts,
their total quantity participating in exchange through the surface of the
world ocean is the same as given by the authors mentioned earlier, equal to
5�109 tans/year. The relationship of the salts released by each ocean
will naturally be proportional to the evanoration value (Table 2).
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The quantity af salts sprayed by wind waves in the first approximation
evidently can be obtained from the difference between the total mass of
- salts entering the air and their transport in the course of physical
evaporation. Accordingly, this is 95% of all the salts carried into the
- atmosphere or 4.752�109 tons/year for the entire world ocean. Somewhat
- more than 1�109 tons/year can come from the Atlantic and Indian Oceans and
almost 2.5�109 tons/year from the Pacific Ocean.
The "receipts" part of the balance of salts drawn into the exchange be-
tween the world ocean and the atmosphere consists of the quantity of salts
falling with precipitation and the chemical runoff of rivers. On the basis
of determinations of the content of chlorine made by S. V. Bruyevich and
a number of other specialists, 0. A. Alekin [1] estimated its magnitude
with an annual river runoff at that time assumed to be 36�103 km3. Since
according to present-day data [2] it is 44.7�103 km3/year, the quantity of
chlorine transported into the world ocean is 2.83�108 tons. With a chlorine
coefficient for the ocean assumed to be 1.8, the total mass of salts carried
into the world ocean is 0.5�109 tons/year. For the individual oceans the
chemical runoff was assumed to be proportional to the river runoff (Table
2). Thus, it was found that not even half of all the salts are carried into
the Atlantic Ocean (44% of its total quantity), 32% are carried into the
Pacific Ocean, 13% into the Indian Ocean and 11% into the Arctic Ocean.
Table 3
9
10
11
KEY:
Estimate of Exchange of Salts Between Ocean and Land
OKeatt
1
CocraenFib-
LItHO 06\1CH8
MupoRO~i
3
Ar.iaEirN-
4CCKN{1 4I
-
Nx~tnticKUii5

TuxEiii
6

Cesep+wi~
Jle,%osFirmii"I
-
I09 T/20~)
I qp I
109 TI20vI
I
109 T/20I
% i 109 TI20(3I
9rj
109 Tl20vI
%
fIepeHOC co-
-0,5
100
-0,12
24
-0,11
22
-0,26
52
-0,01
2
ncfi Ha cywy
XNNN4CCK1111
0,5
100
0,22
44
0.063
13
0,16 .
32
0,057
11
croK peK
�
Pa3xocrb
0
0,1
-0,047
-0,10
0,097
1.
Exchange component
7.
Arctic Ocean
2.
Ocean
8.
tons/year
3.
Wor.ld
9.
Transport of salts onto land
4.
Atlantic
10.
Chemical runoff of rivers
5.
Indian
11.
Difference
6.
Pacific
110
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Salts, returning to the oceans with precipitation, wiil correspond to
their total mass carried into the air, except for what is returned with
river runoff, since in the first approximation a balance should exist.
We should note a specific peculiarity of the salt balance in the Arctic
Ocean. In contrast to the other oceans, where the chemical runoff of ~
rivers is much Iess than the fallout of salts with precipitation, in the
Arctic it is substantially higher (Table 2). This is attributable to
the great river runoff but a particularly small amount of precipita-
_ tion. It would seem that thereby there should be an accumulation of sul- -
fates, predominating in river waters and precipitation. However, the con-
stancy of the salt composition in the Arctic Ocean, it must be assumed,
is maintained by the inflow of a considerable mass of chlorides with At- Iantic and Pacific Ocean waters. _
Exchange of salts between the acean and the land. In particular, it must
be noted that the balance between the transport of salts from the ocean
to the land and their return with chemical runoff occurs only with respect
to the world ocean as a whole. The budget is different for the individual
oceans (Table 3). For example, in the Atlantic and Arctic Oceans the chem-
ical runoff of rivers exceeds the transport onto the land, whereas in the
other two oceans the picture is the reverse.
The most interesting peculiarity of exchange of salts between the oceans
and the land is, as demonstrated by the investigations of S. V. Bruyevich,
et al., that during the spraying of salts when wind waves are present the
chlorides for the most part remain in the ocean, whereas the siilfates for
the most part pass into aerosols determining the salt composition of pre-
cipitation. This takes place at the moment of direct detachment of micro-
droplets of ocean water. There-is a redistribution of ions of saline compo-
sition [5]. This evidently thereby determines the difference in the chemical
composition of ocean and river water. The latter, flowing into the'ocean,
compensates that shortage of sulfates which is formed in the process of
salt exchange with the atmosphere.
Balance of salts in the world ocean. It has already been stated above that
the transport of waters in Antarctica is of fundamental importance. Since
exchange through the ocean surface is three orders of magnitude less than
the quantity which is propagated in the water layer, in the balance of
salts in the world ocean it is possible to limit ourselves to deter.mina-
tion of their transport between the oceans (Table 4). In this respect the
salt balance differs considerably from the balance of water and heat. For
example, the fraction of moisture exchange between the ocean and the at-
mosphere is 2-4% of the total circulation of water [7]. However, in the
heat balance eachange with the atmosphere plays a leading role, on the
- average for the world ocean attaining 77% [11].
111
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Table 4
Balance of Salts in the Oceans
I7pHxoA gI Pacao3 3; Y ipfuo~t2 Pacxo,43
Cocrae:tAiniuiie o6Me~~a
1 1012 r/Zor) 41 to'= r;zod 4 F !'y %
5 AT7a I1TIt4�CKtI{I oKcax
10
0610x C l41i;t1iiicKua+ otceaFtoM
52,7
218,4
11
OSHeH C Tiixi+H oxeaxoH
164,9
3,4
OGajett c CeBepHUH Jle,qoenTdM
13,1
11,9
12
oxeattoy
13
OciMeH r.o Cpea113e+1Haa1 MopeM
2,0
2,0
14 1'lroro:
232,7
235,3
15
p33HUCTb Me:uAy npttxoAoM N
-2,6
pacxoAoK
fj
I'INRNFICKFlA OKC
88
16
06NCN C AT:I2HTII4ECKN\1 OK28-
218,4
52,7
HOX
11
06MEH C TIiX{11f OHEBNOM:
17 a) npoijmw 30xACKOro apxii-
28,1
-
nenara u 6accoe nponne
18 61 o. TacHamipi - AHrapKreaa
3,4
1965
14 1�iTOro:
249,9
249,2
1 S
P83HOCtb xeacAy npNxoAoM H
pacxoao.m
7
Tnxitti oKCax
00HCII C MHAIIIiCK{IN OK28NOY:
10
8) IIpOAiIBN 30HaCKOfO 8pX{I-
-
28,1
17
nc.iara u 6accos npoans
18
6) o. Tantaanm - AHrapKrIi�
'
196,5
3,4
aa
16
OG-%ieH c:1t.iaHTmiecKnW oKCa-
3,4
164,9
nuu
12
ObNicH C CCDCPHW.tiI ,'IcAOeFiraM
-
l,l
mcaHOx
14 liroro:
199,9
197,5
15
p83HOM Me)cRy ITPNXOAOU( N
2.4
pacxoAOM
8 CeBep
1606Me� C AT78H1H4CCKNM OKEB-
HOM
1106meH C Tl17CNM OKCBHOM
14 Nroro:
~
15Pa3NOCrb NcwAy npnaoamM u
pacxo,qom
Haf+ neAOaxrwA oxeax
11,9 13,1
, 1,1 -
13,0 13,1
-0,1
23
70
6
I
100
88
ll
1
100
99
1
100
92
8
100
93
I
5
1
100
ij
21
?9
100
0,3
14
2
83
I
100
100
100
0,
9 MHPOBOII OKtBN
19 hontivecTeo coAei, YqBCTBYIO� 695,5 I 695,1
IuIix e o6!~cNe Mc;r,uy oxea-
118NH
15 p83HOCTb MCNSA)' IlpllXOj[OIM N 0,4
pacxoaoW . 112
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100 I 100
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KEY TO TABLE 4:
1. Exchange components
2. Receipts
3. Expenditures
~ 4. Tons/year
5. Atlantic Ocean
6. Indian Ocean
7. Pacif ic Ocean
8. Arctic Ocean
9. World Ocean
10. Exchange with Indian Ocean
11. Exchange with Pacif ic Ocean
12. Exchange with Arctic Ocean
13. Exchange with Mediterranean Sea
14. Total
15. Difference between receipts and expenditures
16. Exchange with Atlantic Ocean
17. Straits of Sunda Archipelago and Bass Strait
18. Tasmania-Antarctica
19. Quantity of sal,ts participating in exchange between oceans
In the case of the Atlantic Ocean exchange with the Arctic Ocean is of
considerable importance (5-69' of the receipts and expenditures). For the
Arctic Ocean this exchange is decisive not only in the balance, but also
in its entire nature. In the Pacific and Indian Oceans the salt exchange
through the Sunda straits exerts a considerable influence. The "nonclos-
ures" of the salt balance were very small.
The attempt made here to evaluate the principal components of the balance
- of the total content of salts in the world ocean and the contribution of
exchange with the atmosphere and land, despite their small role, is of
unquestionable interest for understanding the peculiarities of the planet-
ary redistribution of salts.
BIBLIOGRAPHY
1. Alekin, 0. A., KHIMIYA OKEANA (Ocean Chemistry), Leningrad, Gidro-
meteoizdat, 1966.
2. Alyushinskaya, N. M., Ivanov, V. V., "Water Inflow from the Land,"
MIROVOY VODNYY BALANS I VODNYYE RESURSY ZEMLI (World Water Balance and
the Earth's Water Resources), 1974.
3. Bruyevich, S. V., Ivanenkov, V. N., "Problems in the Chemical Balance
of the World Qcean," OKEANOLOGIYA (Oceanology), Vol XI, No 5, 1971.
113
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4. Bruyevich, S. V., Korzh, V. D., "Salt Exchange Between the Ocean and
the Atmosphere," OKEANOLOGIYA, Vol TX, No 4, 1969.
5. Bruyevich, S. V., Kulik, Ye. Z., "Chemical Interaction Between the
Ocean and the Atmosphere," OKEANOLOGIYA, Vol VII, No 3, 1967.
6. Grigor'yev, Yu. A., "Study of Water, Heat and Salt Flows on the Pro-
f iles Africa-Antarctica and New Zealand-Antarctica," BYULLETEN' SAE
(Bulletin of the Soviet Antarctic Expedition), No 59, 1966.
7. Gritsenko, A. M., Stepanov, V. N., "Water Balance of the World Ocean
and its Role in Planetary Processes," iZV. AN SSSR, SERIYA GEOGRAF.
(News of the USSR Academy of Sciences, Geographical Series), 1979
(in press).
8. Ivanenkov, V. N., Gusarova, A. N., "Annual Exchange of Dissolved Oxy-
gen, Silicic Acid and Inorganic Dissolved Phosphorus Between the
Oceans," KHIMIYA MOREY I OKEANOV (Chemistry of the Seas and Oceans),
Moscow, Nauka, 1973.
9. Poldervart, A., "Chemistry of the Earth's Crust," ZEMIJAYA KORA (The
Earth's Crust), Moscow, IL, 1957.
10. Stepanov, V. N., Burenin, V. V., Galerkin, L. I., Gritsenko, A. M.,
Moiseyev, L. K., "Heat Content of Waters of the World Ocean,"
OKEANOLOGIYA, Vol XVIII, No 3, 1978.
11. Stepanov, V. N., Gritsenko, A. M., "Heat Balance of the World Ocean,"
OKEANOLOGIYA, 1979 (in press).
12. Eriksson, E., "T'he Yearly Circulation of Chloride and Sulfur in Na-
ture," Pt 2, TELLUS, Vol 12, No 1, 1959.
114
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UDC 556.535.5.06(282.247.41+470.46)
SHORT-RANGE PREDICTION OF AUTUMIN AND WINTER ICE JAM LEVELS ON THE
LOWER VOLGA AT CHERNYY YAR STATION
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 90-95
[Article by P. I. Bukharitsin, Astrakhan Zonal Hydrometeorological Observ-
atory, submitted for publication 3 September 19791
Abstract: The article briefly examines the hydro-
meteorological and ic- conditions on the Lower
Volga during the autumn-winter period of 1978-
1979. The author describes the largest and most
unusual ice jams observed during this period
in the neighborhood of Kamennyy Yar, Chernyy Yar
and the mouth of the Yenotayevka channel. A prog-
nostic dependence is proposed for use in the prep-
aration of short-range forecasts of autumn and
winter ice jam levels at Chernyy Yar station.
[Text] Autumn and winter ice jams and the accumulation of water under snow
on the Lower Volga under conditions of regulated runoff (beginning in 1959)
have been observed annually. Theq are associated with a change in the ice
- and thermal regime of the Volga and also the regime of water discharges
and levels following the construction of the Volga Hydroelectric Power
Station imeni XXII Congress CPSU and the formation of the Volgogradskoye
Reservoir.
The studies of many researchers have been devoted to investigation of aut-
umn and winter ice jams on USSR rivers. Extremely important studies with
a description of the hydrometeorological conditions for the development
of ice jams and processes preceding and accompanying the formation of
ice jams, the geomorphological features of river reaches with ice jams and
also an examination of the state of study of the processes of ice jam for-
mation and making recommendations on preventing and contending with ice
jams and the accumulation of water under ice have been made by R. A. Nezh-
ikhovskiy [15], A. M. Filippov [23], R. V. Donchenko [6, 9], A. V. Shcher-
- bak [25], P. M. Lur'ye [12], G. N. Ustinov [22], Z. A. Genkin [4], V. V.
Lebedova and P. L. Medres [11], P. P. Angelopulo [1] and other authors.
115
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Great attention has been devoted to the development of inethods for pre-
dicting ice jams and computing the maximum ice-jan levels. These include
the studies of R. A. Nezhikhovskiy, G. V. Ardeaheva, N. P. Sakovskaya [13,
14, 16-19], R. V. Donchenko, A. M. Filippov [8], V. N. Karnovich [10], _
A. N. Chizhov and A. G. Deryugin [24].
The studies of V. V. Perzhinskiy [S, 20, 211, R. V. Donchenko, M. I. Bayu--
sova [7] and A. K. Barabash [2, 3] were devoted to study of ice jams and
the accumulation of water under snow on the Lower Volga.
- The article by A. K. Barabash [2] is one of the first investigations de-
voted to study of maximum ice-jam induced levels during the autumn-winter
period on the Lower Volga and in the delta. This study gives an analysis
of the process of formation of ice Jams under natural conditions and under
conditions of regulation on the Volga River below the Hydroelectric Power
Station imeni XXII Congress CPSU-and a dependence is proposed for the
short-range forecasting of the height of autumn ice-jam induced levels at
Chernyy Yar station.
Recently, in connection with the problem of lengthening the navigation sea-
son on the internal water bodies of the USSR during winter the interest of
' scientists in study of the ice-thermal regime on the Lower Volga has con-
siderably increased: .
The unusually high water volume in the Volga River basin in the autumn of
1978 and the related grea* discharges from the Volgogradskoye Reservoir,
about 9-11 thousand m3/sec or more, caused a considerable increase in
thelevel on the Lower Volga and in the d elta. The mean 10-day levels at
Astrakhan' at the end of October and November were 130 cm higher than the
corresponding mean long-term levels under regulated conditions and 150-160
cm higher than in 1977. Such high autumn 1 evels were observed for the first
time during the entire period of observations since 1881.
Sharp temperature drops during the period of ice formation in December 1978
from +6 to -20�C, together with a high water level held back the time when
an ice cover was formed. The prolonged go ing-out of the ice in individual
river reaches resulted in major winter ice jams such as had not been ob-
served earlier on the Volga.
An unusual ice jam was formed in late Dec ember at the mouth of Yenotayev-
ka channel. The packed ice cover in the main channel of the VoZga created
a backwater and some of the Volga water bypdssed it, going through the
channel. A level rise and also a thaw at the very end of December favored
the freeing of the channel of ice. The iniriated going-out of the ice con-
tinued for more than half a day. The floating ice was concentrated at the
channel mouth, since its further advance was impeded by the ice cover in
the main channel. An ice jam was formed. The considerable level.rise in
the channel led to inundation of the floodplain between the channel and
the main river channel. After 3 or 4 days the ice jam in the Yenotayevka
channel was destroyed. 116
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Table 1
Extremal Values of Winter Ice Jam and High Water I.evels at Stations on
the Lower Volga
7
8
9
1
n}rBKT H
M2KCN-
N8116NYi1
3aropgat~
Msoro:erHee axa-
3 9CNN51 33TOPHWX
3IIS1HfiX YPODH2{(,
C.K
Meoro.ieTaiic
3H3y2HFlA IlO.lq-
BOJ[NW7C ypon-
~ HC}!, C.U
nepxoA
xa6nioAeHnM
Ypoeexb
Ha6n. ax-
^
a
6
a
5
;

E
slott
1978-
~
~
$
ca
-
79 rr., cm
= a
~
a
= 2
CZ'-
2
x
~to
i _
;;m
KamexNwii Sip
842
547
764
736
864
(1974-78 rr.)
qepHdFi Rp
60S
380
641
700
860
( 1959-78 rr.)
.
ExoTaeecK
589
260
484
556
744
(1959-78 rr.)
KEY:
1. Station and observation period
2. Maximum ice-jam induced level observed in winter of 1978-1979, cm
3. Long-term ice-jam induced winter levels, cm
- 4. Long-term high-water levels, cm
. 5. Minimum
_ 6. Maximum
7. Kamennyy Yar
8. Chernyy Yar
- 9. Yenotayevsk
A large winter ice jam was formed during the first 10-day period of Janu-
ary 1979 below Kamennyy Yar. It caused a sharp (more than 3 m) level in-
� crease and movement of water into the Volga-Aktubinsk floodplain (Tab1e 1).
At the same time, but more smoothly, a level rise began which was caused
by a second ice jam forming below Chernyy Yar. Here the level increased
by 1.5 m and almost attained the ma.ximum winter ice-jam induced level
during the entire period of regulated runoff which was observed in 1977
641 cm (Fig. 1).
The formation of such large winter ice jams at Kamennyy Yar and Chernyy Yar
was preceded by the going-out of the ice on the Volga River, continuing for
23 days. After it had poured into the floodplain the water found a round-
about course, bypassing the ice jams; the ice jam levels were stabilized
and remained without significant changes until opening-up of the river.
117
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4 -
^ti ~.,~6L, ~ �~y t~~�~y /!/WN
i ! , ~ ~ r,r : . EO(!D
j ; t i j �i
' ~ ~ ' i ~ 6000
; r f .
15 JO S 10 15 20 25 JO S 10 y~
preo6pb 1 AeDapA' 2 ~COpOp~
3.
4
Fig. 1. Curves of level changes at stations on the Lower Volga and the mean
daily discharges from the Volgogradskoye Reservoir during the winter of
1978-1979. 1) level variation at Kamennyy Yar, 2) level variation at Cher-
nyy Yar, 3) 1eve1 variation at Yenotayevsk, 4) level variation at Sero-
glazovka, 5) discharge from Volgogradskoqe Reservoir.
KEY:
1. December
2. January
3. February
4. Q m3/sec
Table 2
Change in Travel Time from Volgograd
to Chernyy Yar in Dependence on Mean
_ Daily Discharges in Lower Pool of the
Volgograd Hydroelectric Power Station
ts
to
ts
10
i
a
Q m3/sec
Mean daily discharges Travel time, - at Volgograd Hydroel- sec
ectric Power Station,
thousands m3/sec
5 3 Fig. 2. Dependenc e of maximum levels
5.5-6.5 3-4 at Chernyy Yar on water discharges
6.5-7.5 4-5 in lower pool of Iiydroelectric Pow-
7.5-8.5 5-6 er Station imeni XXII Congress CPSU
9 6 and duration of go ing-out of the
ice in days.
The formation of winter ice jams in the reach Kamennyy Yar - Yenotayevsk
was confirmed by the results of aerial reconnaissance carried out in Jan-
uary-February by the Astrakhan Zonal and Volgograd Hydrometeorological Ob-
servatories and observations from the icebreaker "Kapitan Krutov," made
118
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during an experimental voyage of the icebreaker along the reach Astra-
khan'-Volgegrad during February 1979. The thickness in the ice jama was
85-90 cm, locally attaining 140 cm. At the aitea where the ice jams were �
formed there was much frazil ice in the channel. The layer of frazil ice
beneath the main ice cover was 3.0-4.0 m; the hummocks were 1.5 m high. _
_ During the period preceding and accompanying the fornation of winter ice
jams the mean daily discharges of the Volograd Rese.rvoir on work days
were about 8-9 thousand m3/sec; on days off 5-6 thousand m3/sec, which
corresponds to the level at Chernyy Yar, equal in the case of an open chan-
nel to 280-300 cm. The high water volume and also the marked fluctuations
of air temperature were responsible for the prolonged period of going-out
of the ice on the Luwer Volga and created the prerequisites for the forma-
tion of major --ce jams.
The dependence between the maximum autumn-winter ice-jam induced levels
at Chernyy Yar on the water discharges in the lower pool of the Volgograd-
skoye Reservoir
.14
Kmax ice jam - f(R)
examined in a study by A. K. Barabash [2] unfortunately cannot be employed
in routine work in the represented form for a number of reasons:
an inadequate series of observations;
no allowance is made for such an important factor as the influence of -
ice conditions (for example, the duration of going-out of the ice);
- travel time from Volgograd to Chernyy Yar, taken from [2], equal to
4 days, is not a constant value; it is dependent on the water discharges
and on ice conditions in a particular river reach.
Proceeding on the basis of these considerations, the author has proposed
that a third variable be introduced into the dependence, namely the dura-
tion of go ing-out of the ice, and that the 8-year series of observations
be extended to 20 years (1959-1979):
Hice jam - f(4; Tice),
where Q is the mean daily water discharge in the lower pool of the Hydro-
electric Power Station imeni XXII Congress CPSU, Tice is the duration of
going-out of the ice at Chernyy Yar from the date of the level rise, as-
= sociated with formation of the ice jam, to the date of onset of a solid
ice cover.
In constructing thf_s dependence it was possible to establish a correlation
between travel time and water discharge (Table 2).
Thus, it was now possible to use the actual travel time, corresponding to the
the volume of the discharge and dependent on ice conditions, nut the mean
traval time, adopted in [2], equal to four days.
119
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0
r�uK or'r�iclAL usE orrr,r
" The regression equation for computing ice-jam induced Zevels at Chernyy
Yar has the form
Hice jam = 0,058,,+ 4,636 y- 29, (1)
where x is the mean daily water discharge in the lower pool of the Hydroel-
ectric Power Station imeni XXII Congress CPSU on the day of the forecast in
m3/sec, y is the duration of going-out of the ice at Chernyy Yar from the
date of the level rise associated with formation of the ice jam to the
- date of preparation of the forecast in days.
The correlation coefficient of the derived dependence (Fig. 2) is equal to
0.85. The guaranteeLyrobability of the method was 100% with an admissible
error Sadm= 0.6740'0 = 53 cm. The ratio of the mean square error to the
standard deviation ia S/(xo = 0.37. The condition of applicability of the
dependence (1) in operational practice
.15< n30cx
~
a
~A
a
ci;
1
2
=vosa~
aa
o
o
c
~
~
.
~ FC~DiC
.
Lrq R
.
u
7~S
,
u
~
2
9
10
9
lu
11 Tx6pxA-173
�
14
BxHxeua
ecxoAw 3
-5 1 Aexalta 2
24
13
40
18
44
15
$OAxos
3�R axct 4
AAeapa 2
-7 y
16
0
0
0
0
16
Maxcarqxa
2,0
-1 3liex8ua 2
2
13
29
36
30
37
17
KawE1x
1,4
AeKa6pa
--4 3.
24
9
15
11
I 13
12 Xapbuoacxas-60
lg
Fiomxap�Ona
2,2
-4 3 Aexaua 2
50
5 I
11
5
6
1
Aexa6pA 2
I
1
1
(
19
'qY~oKa
3-i~ nxcT
24
-T .
50
2
6
0
0
13 5eara .
� %
20 $8p8HOBN4H
2,8
-5
2lietcaAa 2
50
0
0
0
0
AHHBpA 2
~
21 Bpecr
1,2
-5
3.
50
6
t0
2
7
22 Naaueelt4tt
3,0
-6
1 1teKaAa 2
50
1
~ 3
2
4
axeapa
KEY:
1. Station
2. Development phase Ko
3. Minimum soil temperature at
depth of tillering node, �C
4. 10-day period of setting-in
of snow cover > 30 cm
5. Depth of soil freezing, cm
6. Thinning-out of winter rye, %
7. January
8. February
9. mean
10. maximum
11. Gibrid-173
12. Khar'kovskaya-60
13. Belta
14. Vinnitsa
15. Volkhov
16. Maksatikha
17. Kashin
18. Yoshkar-Ola
19. Chukhloma
20. Baranovichi
21. Brest
22. Ivatsevichi
23. sprouts
24. third leaf
25. lst 10-day period
26. 2d 10-day period
27. 3d 10-day period
28. January
29. December
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during the second ten-day period in January. Equations (3), (4) can be
used for Bryanskaya, Kalininskayar Moskov..'kaya, Ryazanskaya, Tul'skaya
and Yaroslavskaya Oblasts and the Ma.riyskaya, Mordovskaya and Chuvashsk-
aya ASSRs.
Table 3
Dependence of Area of Death of Winter Rye (Sdamp % of Sown Ar;�z) on Mean
Oblast Minimum Soil Temperature at Depth of Tiilering Node (t3),
Bushiness of Plants (KD) and Area With Poor State of Plantings
(So% of Sown Area) in Regions of Winterkilling
Cpe1tHRR 3
1
I
BNA ypflBH@HNR
2
K
2A OIllN6K2
K03~(~1Hi(NEHT 4
yp28RCHHR
hOPPeAAuxe
pcrpeccxN
6
SBp a2,273 ta+0,173 3+12,538
6,48
0,841�0,038 i
7
SAp= 0,555 S;,+6,023ta1-~,296t3 -f-
3,50
O,R48�0,056
+35,916
8
SBp-4,033 t3-}-0,215 73-4,211 Ko+
4,00
0
796�0
073
+0,521 Ro+31,451
,
,
9
SBp=0,539 SO-0,1891ta+6,005 t3+
'
�
283 t3+35
+0
152
3,49
0,899-!-0,056
,
,
KEY:
1. No
2. Form of equarion
3. Mean square error of regression equation
4. Correlation coefficient
5. BP = damp(ing)
During individual years the main reason for the death of winter rye in the
investigated territory may be winterkilling.
The winterkilling of plantings occurs in years with an inadequate snow
cover with a decrease in soil temperature at the depth of the tillering
node below the critical temperature at which SOY of the plantfngs perish.
Regression and correlation analysis of long-term data.on winter rye enabled
us to derive a number of dependences for computing the area of the death of
winter ryes in years when the main raason for death was winterkilling
(Table 3).
The equations are valid at a soil temperature below -10�C.
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The value of the mean error of these equations is less than the admissible
forecasting error 0.67 O', where CJ'ia the mean square area with plant-
ings of winter crops killed in percent of the sown area in an oblast. Ac-
cordingly, these equations, especially (6) and (8), can be used in prepar-
ing a forecast of the wintering of winter rye in years with the winterkill-
ing of plants. However, the best results are obtained when computing the
expected area of death of winter rye using equation (8).
All the cited equations, both in regions with thick and in regions with an
inadequate snow cover, make it possible to prepare forecasts of the state
of winter rye in spring for 2 or 3 months in advance. Knowing in advance
the reasons for the damage of winter crops and the extent of the area in
which it is expected, by the application of a number of agricultural en-
gineering measures, including the undersowing and resowing of dead winter
crops in spring by spring crops, it is possible to reduce considerably
the losses of grain yield. In the Nonchernozem zone the death of winter
crops can be completely eliminated or considerably reduced far more suc-
cessfully than in any other zone in the country when there is proper cul-
tivation and good care for the plantings during the autumn and wlnter-
spring periods.
**~t
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BIBLIOGRAPHY
- 1. Beletskaya, Ye. K., "Comparative Resistance of Winter Crops to Inunda-
tion at Different Temperatures," USTOYCHIVOST' RASTENIY K NEBLAGOPRI-
YATNYM TEMPERATURNYM USLOVIYAM SREDY (Resistance of Plants to Unfavor-
able Environmental Temperature Conditions), Kiev, Naukova Dumka, 1976.
2. Beletskaya, Ye. K., Ostaplyuk, Ye. D., "Growth and Formation of Frost
Resistance of Winter Crops in Dependence on Water Supply Conditions,"
USTOYCHIVOST' RASTENIY K NEBLAGOPRIYATNYM USLOVIYAM SREDY, Kiev, Nauk-
ova Dumka, 1976.
3. Kuperman, F. M., Moiseychik, V. A., VYPREVANIYE OZIMYKH KUL'TUR (Damp-
ing of Winter Crops), Leningrad, Gidrometeoizdat, 1977.
4. Moiseychik, V. A., AGROMETEOROLOGICHtSKIYE USLOVIYA I PEREZIMOVKA OZIM-
YKH KUL'TUR (Agrometeorological Conditions and Wintering of Winter
Crops), Leningrad, Gidrometeoizdat, 1975.
_ 5. Moiseychik, V. A., "Agrometeoxological Conditions for the Wintering of
Crops and Methods for Preparing Long-Range Forecasts of the State of
Winter Grain Crops in Spring," AGROMETEOROLOGICHESKIYE ASPEKTY PERE-
ZIMOVKI RASTENIY (Agrometeorological Aspects of Wintering of Plants),
- Leningrad, Gidrometeoizdat, 1977.
6. Moiseychik, V. A., "Agrometeorological Conditions for the Wintering of
Winter Crops," AGROMETEOROLOGICHESKIYE USLOVIYA I PRODUKTIVNOST' SEL'-
- SKOGO KHOZYAYSTVA NECHERNOZEMNOY ZONY RSFSR (Agrometeorological Condi-
tions and Productivity of Agriculture in the Nonchernozem Zone of the
RSFSR), Leningrad, Gidrometeoizdat, 1978.
7. Moiseychik, V. A., SOSTAVLENIYE DOLGOSROCHNOGO PROGNOZA VYPREVANIYA
OZIMYKH ZERNOVYKH K[JL'TUR (Preparation of a Long-Range Forecast of
the Damping of Winter Grain Crops) METODICHESKIYE UKAZANIYA (Methodo-
logical Instructions), Moscow, Gidrometeoizdat, 1971.
8. Moiseychik, V. A., SOSTAVLENIYE DOLGOSROCHNYKH AGROMETEOROLOGICHESKIKH
PROGNOZOV PEREZIMOVKI aZIMYKH KUL'TUR NA TERRITORII OBLASTEY, RESPUB-
LIK I V TSELOM PO SSSR: METODICHESKOYE UKAZANIYE (Preparation of Long-
Range Agrometeorological Forecasts of the Wintering of Winter Crops in
the Territory of Oblasts, Republics and the USSR as a Whole: Systematic
Instructions), Leningrad, Gidrometeoizdat, 1978.
9. Tiunov, A. N., Glukhikh, K. A., Khor'kova, 0. A., OZIMAYA ROZH' (Winter
Rye), Moscow, Kolos, 1969.
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UDC 551.46.08
OPTIMUM CALIBRATION OF REMOTE INSTRIJMENTS USING THE RESULTS OF DIRECT
MEASUREMENTS IN THE OCEAN
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 107-112
[Article by Candidate of Physical and Mathematical Sciences S. V. Dotsenko
and L. G. 3alivon, Marine Hydrophysical Institute, submitted for publica-
_ tion 24 April 1979]
Abstract: A study was made of the possibilities
of calibrating remote instruments on the basis
of direct measurement instruments for the case
of a"nonfrozen-in" field and models of fields
and instrument functions close to real fields
and instrument functions. It is shown that the
relative calibration error ia considerably re-
duced if the direct measurements are subjectPd
to time averaging with some optimum weight.
[Text] Instrumentation for remote noncontact sounding is coming into in-
creasingly broader use in the practice of physical measurements at sea.
Remote instruments, in comparison with direct contact measurement instru-
ments, have a number of advantages. One of the most important is the pos-
sibility of ineasuring the physical characteristics of the ocean at points
situated at a great distance from them. This makes it possible to install
remote sounding instrumente both on ships and on aircraft, affording new
possibilities for studying the ocean at the most different spatial and tem-
poral scales.
The use of remote instruments can be adequately effective only when they
ensure the required measurement accuracy. The differences between the
readings of a remote instrument and the readings of a direct contact meas-
urement instrument, intended for measuring the same physical parameter and
situated at the center of a resolution element of a remote instrument sen-
sor,are due to the following factors:
l. Characteristic noise of the remote�instrument. This is reduced by employ-
ing special sensing elements and measurement circuits.
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2. The influence of hydrometeorological factors for whose measurement the
particular instrument is intended (influence of physical parameters of
the atmosphere on the results of ineasurement of all the physical character-
istics of the ocean, influence of the state of the sea surface on the re-
sults of temperature measurement, etc.). A decrease in these Pactors is
achieved by the proper choice of the spectral windows of remote instru-
ments, appropriate processing of the output signals of the latter and cali-
bration of remote instruments on the basis of ineasurements of the physical
characteristics of definite regions of the ocean (polygons) made by direct
direct methods.
3. Differences in the averaging scales of the measured field of the com-
pared instruments. Any direct-measurement contact instrument used under
sea conditions in measurements both from a ship and from autonomous craft
or buoy has an incomparably lesser field averaging scale than a remote in-
strument. A remote instrument carries out~spatial averaging of the measur-
ed field with some instrument function h(r), describing the contribution
- of each volume of the measured field to the total instrument output signal.
The instrument function h(r) is determined by the directional diagram of `
the measuring instrument sensor, the orientation of this diagram relative
to the sea surface and the height at which the instrument is positioned -
above sea level. The broader the instrument directional diagram and the
higher it is situated above sea level, the larger is the resolution ele-
ment of the remote instrument used in field averaging. For example, the
noncontact devices used in measuring temperature which are carried aboard
artificial earth satellites can have radii of the resolution elements of -
several kilometers [1]. Accordingly, on the basis of signals from direct
measurement signals containing a very broad spectrum of high-frequency
_ field fluctuations it is impossible directly and with the required accur-
acy to evaluate the behavior of the low-frequency signal at the output of
the remote instrument, considerably smoothed by its instrument function. In
order to increase calibration accuracy it is necessary to carry out pre-
liminary averaging (smoothing) of the signals of polygon instruments.
It is evident that the closer the scale and the weighting function in aver-
aging of signals of direct measuring detectors to the scale and instrument
function of the sensors of remote instruments, the higher will be the cal-
ibration accuracy, and accordingly, the greater will be the accuracy of
remote measurements as a whole.
We will find methods for the optimum averaging of signals of direct measure-
ment contact instruments intended for calibration of remote instruments and
we will evaluate the calibration errors observed in such cases. The para-
meters of the field obtained by some optimum averaging of the signal of a
direct-measurement contact instrument will be used as the standard (Yst)�
There are three possible methods for such averaging: spatial, temporal and
spatial-temporal. The authors of [4] investigated a method for the optimum
spatial averaging of the signals of a set of different numbers of direct
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measurement instruments and it is demonstrated that a high accuracy in
finding the standard field parameters for comparison of the resu].ts of
remote measurement with it, even with an optimum configuration of the
network of direct -.easurement instruments relative to a resolution ele-
ment of the remote instrument sensor, requires the simultaneous use of
a great number of direct measurement instruments distributed over a con-
siderable area of the polygon. Such an organization of an experiment for
determining the standard field parameters can be technically difficult
to implement. Spatial-temporal averaging is accomplished by temporal aver-
aging of the signals of several direct measurement instruments and also
requires considerable technical means.
We will investigate the temporal averaging of the signal of a contact in-
strument, requiring the use of only one instrument, and we will find the
optimum method for such averaging ensuring the best calibration accuracy.
We will assume that the tollowing conditions are satisfied:
1. The measured field is centered, uniform, isotropic and "nonfrozen-in."
The model of anisotropic "nonfrozen-in" fields was examined in detail in
studies [3,5,6]. In describing them it is sufficient to know the multi-
dimensional spectra Gn(oZc.); the spectra with n> 1 can be found from the
known one-dimensional spectrum G1(a). Under isotropicity conditions these
fields are characterized by the following values: spatial correlation in-
terval rX, correlation time interval 'Gc and mean velocity vp of field
movement relative to the contact instrument sensor. The degree of "freez-
ing-in" of the f ield is characterized by the dimensionless parameter Yj =
vp ti C/rX, and it is the greater the greater the q value.
2. The instruments for both direct and remote measurement are inertialess.
The contact instruments have point sensors.
Now we will examine the following scheme for obtaining the standard value
of a field by a direct measurement instrument intended for calibration of
a remote instrument. Assume that a direct measurement instrument registers
field values X(r, t) at some point in a polygon used as the origin of coor-
dinates r= 0. It is evident that the changes in these values are related
to both the movement of the field relative to the fixed instrument and
its temporal evolution, determined by the "nonfrozen-in" properties [19].
Accordingly, applicable to a direct measurement instrument it is necessary
to take into account both the velocity of field movement vp and its "non-
frozen-in" properties. Using some weighting function U(,C), whose optimum
form will be determined below, at each moment in time t it is possible to
obtain a mean weighted signal at the output of the direct measurement in-
strument
(TC p = d irect ] Y�p (t) X [vo x (t t - U (T) d
~l )
We will assume that at the time t= 0 it is necessary, using the transform
(1), to obtain the best evaluation of that signal value at the output of
the remote instrument which the latter would have in the absence of
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distorting factors (for example, the atmosphere). Since the remote instru-
ment is usually mounted on rapidly moving carriers, the field for it can
be considered "frozen-in" and the strength of the undistorted signal at
its output at the time t= 0 is
[ ~7( = remoteJ YA= ~X (-P; D) h (P) dP� (2)
Thus, optimum calibration of a remote instrument essentially involves ob-
taining the mean weighted va1u�: of the signal at the output of the direct
measurement instrument _
~
Y�p (0) X(- vpt; U(s) d t, (3)
['?T p = direct ]
differing least from the Yremote value determined by formula (2) and its
use �or comparison with the real signal value at the output of the remote
instrument at the time t= 0.
The mean square error in comparison of the Yremote and Ydirect(0) values
is
E' = l Y�p (U) - YA)1.
[Tt"p = direct; .71, = remote]
It was demonstrated in[7] that the optimum weighting function U(-G), en-
suring the minimum of the E 2 value, should have the spectrum
Y~
( ) l + Z
[ORT = Opt]Uom G, (71 2e J G3+Crx)~`~"~v~~� (4)
~
l + r~' W
Fx ~
N ~
where h(,8) is the spectrum of the instrument function h(r). The square of
the absolute error in optimum calibration is
_ [11r.crxa- f~ 1Gsa12~'~ rX~ J~llorcr~~-Favo)-h(a)~~dad~. ~5~
x
However, if the calibration is accomplished on the basis of one instantan-
eous reading of the output signal of a direct measurement point instru-
ment without averaging of the registered data, then th.e square of the abso-
lute calibration error is
~~=J02-h(a)12 da
and is not dependent on the degree to which the field is "frozen-in."
The gain in accuracy of optimum calibration in comparison with calibration
on the basis of a single point measurement has the value
[OTTT = opt] z' ,
'oar
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(e/o)2
Fig. 1. Error in measuring a field Fig. 2. Optimum weighting function
with a remote instrument with p= 0.5. for p= 0.5; 2) 0.5; r?= 4; 1.5
1) v= 1.0; 2) y= 2.0; 3) y= 3.0; 4)
)l = 4.0 -
~
~ al a b
e
6
4 /
T
0 0 0.8 Z 0 i 0 n
s,o e) c Z~ d
~s
0 2 4 v 0 1 Z p
Fig. 3. Dependence of gain in accuracy in optimum calibration on different
field parameters and instrument sensor with p= 0.5. a) on relative radius
of insi:ranextt resolution element z with y= 1.5; y?= 1; b) on "frozen-in"
parameter rj with z= 0.5; 1.5; c) on sensor par.ameter Y with z= 0.5;
Y7 = 1; d) on field parameter p with y= 1.5; Y?= 1.
~
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Z rc

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The authors of [7], on the basis of the derived expressions, investigated
the calibrat ion of a remote instrument with a sensor having an axially sym-
metric bell-shaped instrument function, using a field whose spectrum also
has a bell shape. Such models of the field and sensor made it possible to
carry out computations in analytical form to a full extent and confirm the
high effectiveness of the considered method.
The field and instrument models considered in this study reflect the ade-
quately broad classes encountered in practical work. Thus, it is postul-
ated that one-dimensional field spectra have the form "
/ x ~ (P + 112)
Gi (a) _ I I+I x l~ (6)
l. ~
where Q'2 is field dispersion, p is a parameter characterizing the degree
of dropuff of its spectrum, (x) is the gamma function and the X.P coef-
ficient has the form -
1
'r r pt 2 /
A change in the p parameter makes it possible to examine a broad class of
fields. With p= 1/2 an exponential autocorrelation field function corres-
ponds to the spectrum (6), that is, the field in this case is not differ-
entiable. An increase in the p parameter leads to an increase in field
smoothness. With p -aoo the spectrum (6) acquires a bell-shaped for.m, that
is, the field has all the derivatives.
The instrument functions of the sensors of remote instruments are described
by the expressions x2
/
h r V-1/' r-1/1r 2
2 (2 v-1) ~ r r,0 _ 2 R)v-112
~ K~_t j2 I x,_'~` Rx l (7 )
\ 2)
where v`1/2, Ka(x) is a Macdonald function, and RX is the characteristic
radius of a sensor resolution element. Using them, with an appropriate
choice of RX and V, it is possible to approximate many real monotonically
decreasing instrument functions. In particular, with V~oo the function
h(r) acquires a beli shape. The spectra of the functions (7)
h (a) - + \ . RX a (�+l')
1/2
with large oC decrease as GY -(2 v+ 1), that is the U parameter characterizes
the degree of their decrease.
No analytical solution of the formulated problem is possible under the con-
dition that the field spectrum is given by formula (6) and the instrument
function is g iven by expression (7). Accordingly,, we prepared a program for
computing the above-mentioned parameters on an electronic computer. The
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program was difficult to develop due to the necessity for computing *he
triple integrals with infinite limits and the presence in formula (5) of
the spectrum of the weighting function U(cj) with a biased argument. The
required computation accuracy was ensured by replacement of the variables
in the integrals, leading to the possibility of integration in finite
limits, and by use of the Gauss quadrature formulas.
As already mentioned, the simplest method for calibrating a remote instru-
ment is calibration on the basis of one instantaneous reading of a point
contact measurement instrument. The dependence of the square of the error
arising in this case on the ratio z= Rx/rX of the characteristic radius of
a resolution element to the characteristic scale of the field for p= 1/2
and different v is represented in Fig. 1. The /0r)2 value increases
monotonically with an increase in z, assuming lesser values with larger
that is, with a greater degree of smoothing of the field by the sensor. If
the calibration accuracy is considered acceptable with &/d = 0.3, the
simplest calibration is accomplished with z= 0.15. An increase in the
necessary calibration accuracy still further reduces this value. Accord-
ingly, using one point reading it is possible to calibrate instruments
the radius of whose resolution element is small in comparison with the
characteristic scale of the measured field.
Now we will turn to optimum calibration with temporal averaging. A typical
optimum weighting function U('C), whose spectrum was computed using for-
mula (4), and then subjected to a Fourier transform, is shown in Fig. 2
for 0. This function is symmetYic relative to thE point = 0 and de-
creases with an increase in 'G . Thus, in accordance with the procedure (3)
in the optimum calibration proces,s there is an averaging of data from meas-
urement of the field by a point instrument with the weight U('G), which has
considerable importance in some finite region, which corresponds to low-
frequency filtering of direct measurement data. Accordingly, in order to
bring the values of the data from direct contact measurements closer to
the values of remote measurements, spatially averaged due to the presence
of a finite spatial resolution element, the data from the contact measure-
ments, obtained at one field point, were subjected to temporal averaging.
Such a procedure is optimum if the spectrum of the weighting function has
the form (4). It cannot lead to a complete exclusion of calibration error
because in remote sounding there is two-dimensional spatial averaging of
the fiel.d, whereas in contact measurements one-dimensional averaging in
time. A:, a result of the different number of ineas urements of the averaging
functions the signals of the remote instrument and the smoothed signal of
the contact instrument on the average will always have some differences
from one another.
The effectiveness of use of the optimum smoothing procedure in calibration
can be evaluated from Fig. 3, which represents the dependence of the gain
in the accuracy of this calibration on different field and instrument para-
meters.
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Figure 3a indicates that optimum calibration is the more effective the
greater is the radius of a resolution element of the remote instrument in
comparison with the characteristic f ield scale, that is, specifically in
the region where calibration on the basis of a single reading gives a
high error. This, for example, makes it possible, with rj= 1, to carry
out calibration with the above-mentioned accuracy to z= 1. Accordingly,
in this case there can be calibration of remote instruments having a large
resolution element on the basis of physical fields in the ocean. However,
it gives an anpreciable accuracy gain also with small resolution elements.
With an increase in the degree to which the field is "frozen-in" the ac-
curacy gain increases. This increase occurs particularly sharply with
I " 4; as can be seen from Fig. 3b, saturation sets in from the time Y? = 0.
Accordingly, it is best to carry out calibration using "frozen-in" fields,
that is, those fields which experience weak evolution with time.
The gain increases with a decrease in the parameter v characterizing the
shape of the instrument function for the remote instrument sensor (Fig. `
3c). For instruments with instrument functions of an exponential shape
the gain is greater than for instruments having a bell-shaped instrument
function. �
With an increase in the coefficient p, determining the degree of field .
smoothness, the gain decreases, but remains quite high. Therefore, the ef-
fect of use of optimum calibration is higher when it is carried out using a
field with an exponential autocorrelation function than when using a field
with a bell-shaped autocorrelation function.
Now we will illustrate the possibility of increasing calibration accuracy
when measurements are made by remote instruments with the assistance of
the described optimum calibration method, employing the instrument func-
tions of wide-angle and five-channel radiometers aboard the TIROS II and -
the radiometer aboard the Cosmos-149 satellite. tiThen these instruments
are installed on artificial earth satellites with an orbital altitude
h= 500 km the radii of the resolution elements RX of their sensors [8]
are 240, 27.8 and 12.8 km respectively.
Taking into account that the characteristic spatial correlation radius of
surface temperatures in the Black Sea [2] is rx = 130 km and that for the
enumerated radiometers the z parameter has values 1.85, 0.214 and 0.0985, we
find that the calibration errors for these instruments based on a single in-
stantaneous reading have values 84, 33 and 27%. As indicated in Fig. 3,
the use of optimum calibration gives a gain }k in measurement accuracy which
is equal to 12, 3.25 and 3 respectively (with rj = 1), which reduces the
calibration error to values 24.3, 18.3 and 15.6%.
Thus, the optimum processing of signals at the output of direct neasurement
instruments considerably increases the accuracy in calibrating remote in-
struments. The greatest gain is noted for wide-angle instruments, whereas
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the greatest calibration accuracy is for instruments with a narrow angle. ~
Optimum calibratian gives a considerable accuracy gain in comparison with
calibration on the basis of a single reading and is the more feasible the
greater the ratio z of the radius of a resolution element of the instru-
ment sensor to the characteristic field scale.
Similar computations made for an altitude of lifting of the sensor h= 10 -
km (which occurs when the remote inst?-uments are carried aboard an air- -
craft) will make it possible to reduce the measurement error from 6 to
4.3%, from 7 to 5% and from 1.7 to 1% respectively. The gain for low al- -
titudes is considerably lower, but as indicated by the comparison, the
abgclute calibration error for these altitudes is relatively small.
BIBLIOGRAFHY
1. Astkheymer, R., Vaard, De R., Dzhekson, Ye., "IR Radiometers on the
- TIROS II Satellite," RAKETY I ISKUSSTXTENNYYE SPUTNIKI V METEOROLOGII _
(Rockets and Artificial Satellites in Meteorology), Moscow, IL, 1963.
2. Belyayev, V. I., OBRABOTKA I TEORETICHESKIY ANALIZ OKEANOGRAFTCHESKIKH
NABLYUDENIY (Processing and Theoretical Analysis of Oceanographic Ob-
servations), Kiev, Naukova Dumka, 1973.
3. Gusev, V. D., "Correlation Method for Investigating Large Ionospheric
Inhomo gene it ies, " VESTNIK MGU. SERIYA MATEMATIKI, MEKHANIKI, ASTRON-
OMII, FIZIKI, KHIMII (Herald of Moscow State University. Series on
Mathematics, Mechanics, Astronomy, Physics and Chemistry), No 6, 1959.
4. Dotsenko, S. V., Ryzhenko, V. A., "Optimum Calibration of Remote In-
struments from Readings of Direct Measuremert Instruments," MORSKIYE
GIDROFIZICHESKIYE ISSLEDOVATTIYA (Sea Hydrophysical InvestigatioBS),
No 4(71), 1975.
5. Dotsenko, S. V,, "On Mathematical Description of Random Scalar Aniso-
tropic Fields," MORSKYYE GIDROFIZICHESKIYE ISSLEDOVANIYA, No 1(51),
1971.
6. Dotsenko, S. V., "Spectra of Random Scalar Anisotropic Hydrophysical
Fields," MORSKIYE GIDROFIZICHESKIYE ISSLEDOVANIYA, No 3(53), 1971.
7. Dotsenko, S. V., Salivon, L. G., "Optimum Calibration of Remote Instru-
ments Using Time Averaging," MORSKIYE GIDROFIZICHESKIYE ISSLEDOVANIYA,
No 4(75), 1976. -
8. Dotsenko, S. V., Nedovesov, A. N., Poplavskaya, M. G., Ryzhenko, V. A.,
"Spatial-Spectral Characteristics of Remote Sensors," MORSKIYE GIDRO-
FIZICHESRIYE ISSLEDOVANIYA, No 2(65), 1974.
9. Monin, A. S., Yaglom, A. M., STATISTICHESKAYA GIDROMEKHANIKA (Statis-
tical Hydromechanics), Part 2, Moscow, Nauka, 1967.
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UDC 551.509.314
EMPIRICAL ORTHOGONAL FUNCTIONS METHOD AND ITS APPLICATION Ii1 METEOROLOGY
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 80 pp 113-119
[Ar ticle by Candidate of Physical and Mathematical Sciences M. I. Fortus,
Institute of Atmospheric Physics, submitted for publication 26 June 1979]
Abstract: This is a brief review of studies
carried out for the most part af ter 1970 in
which the empirical orthogonal functions meth-
od is used for the purpose of an analysis or
prediction of ineteorological f ields and al:o
studies in which there is a discussion o� tl:e
methods for evaluating empirical orthogonal
functions on the basis of empirical data.
Particular attention is devoted to some theor-
etical problems related to the specifics of
application of the empirical orthogonal func-
tions method in meteorology.
[Text] Since the time of the studies of Lorenz, Bagrov and Obukhov (see
[1]) the empirical orthogonal functions method has become popular in meteorol--
ogy; hundreds of studies have appeared in which this method is used as _
one of the principal methods for drawing statistical r_onclusions from
meteorological information. A monograph [5] appear ing in 1970 presented _
and analyzed the results of the investigations mad e up to that time in
which the EOF method was used for studying thp statistical structure of
meteorological fields and also in forecasting problems, the interpretation
of data from indirect measurements, etc. [A quite detailed bibliography is
also cited there.1 During the time which has elapsed since 1970 the number
of studies in which the EOF method is used has inc reased still more. In
this connection it seems to us that the time has come to examine some of
these studies in detail, devoting particular attention to some theoretical
problems related to the specifics of use of the EOF method in meteorology
which have either not been discussed at all or which were not covered suf-
fic iently campletely in monograph [5]. We will diacuss for the most part
st:-.dies published after 1970; this review article can be considered a sup-
plement to the book [5].
148
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Assume that the field of
ordinates x and the time
bers {F(xi, t), i = 1,..
orthogonal functions are
al vectors 5GJ = [cPj, i
of covariations
FOK OFi'1c:TAi. 11SE. ON1,1'
some element F(x, t), dependent on the spa.cP r:o-
t, at the time t is described by a set of uum-
mi Fi (t) 3 . Most frequently the emFirical
determined as the normalized base of m-dimension-
= 1,...,mI , being the eigenvectors of the matrix
Bik = B (Xi, xk) = Fj (f) FR (l), 1. R 1, . . . . nt. (1)
where the line at top denotes time averaging (in actuality on the basis
of the available sample) and the prime denotes deviation of the Fi(t) val-
ue from its mean value Fi(t). It is important that these eigenvectors are
numbered in decreasing order of the corresponding eigenvalues aj (which
are non-negative because the B matrix is always non-neqatively determined).
The vector tFi(t)j can be represented precisely in the form of an expan-
sion of m vectors of a base of natural orthogonal functions (as for any
other orthonormalized base in m-dimensional space). The advantage of an
expansion in empirical orthogonal functions is that if we limit ourselves
~ to a number of terms p 0). Proceeding to the first differ-
ences for the most part filters out the largest-scale components, uic;ich
leads to a decrease in the characteristic sca12. It is desirable, even
necessary, that in all cases when such an inversion of the f irst empir-
ical orthogonal functions arises as a result of the computations that
there be a physical justification for this similar to that cited above.
When this justification is not found, especially in the case of a small
sample, thP conclusicr-L that an inversion is present is usually not stat-
_ istically significant. 152
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Using the empirical orthogonal functions method in general it is possible
to detect any field component in which the predominant fraction of energy
falls. In [14] the authors computed the empirical orthogonal functions
of the H500 8eopotential field over the northern hemisphere. The covaria-
tion matrix was determined by averaging in time, but without prior sub-
traction of the mean field H(x, y). As a result, as might be expected,
the first empirical orthogonal function was very similar to the mean
field H(x,y). The first main component al(t) of the temperature field
obtained in a series of studies virtuallq coincides with a sine curve
whose period is equal to one year due to the fact that the correlation
matrices were computed for deviations from v-alues averaged for all sea-
sons. A considerable fraction of the energy (80-90%) falls on such com-
ponents. However, it is scarcely feasible to discriminate this sort of
component by such an unwieldy procedure as computation of empirical
- orthogonal functions. It is better that this be done prior to computa-
tions of covariations using linear operations.
The stability of empirical orthogonal functions is noted in many studies
[7]. On this basis it sometimes makes sense to use one and the same sys-
tem of empirical orthogonal functions for different seasons and observ-
ation points, for several first main components of one and the same
field and even for different meteorological elemants.
In many cases for the description of ineteorological structure it is feas-
ible to use data on several meteorological elements. In this case the
state of the atmosphere will be described by a vector with the dimension-
ality s�m, consisting of s m-dimensional vectors, where s is the number
of elements and m, as before, is the number of observation points. The
empirical orthogonal functions method can also be applied to the total-
ity of such composite vectors, but first th2 components of the vec-
tors must be made dimensionless, for example, by dividing by the corres- ponding standard deviations. In constructing the empirical orthogonal
functions the cross correlations between the considered elements will
also be taken into account. -
Until now reference has been to the eigenfunctions of the empirical co-
- variation matrices. It is natural to raise the question: is it possible
to find empirical orthogonal functions on the basis of equations describ-
ing general circulation of the atmosphere? The problem is formulated as
follows: for the random field F(x, t) satisfying the system of equations
_ in hydrothermodynamics on a sphere or a part of a sphere, find the spatial
covariation function B(x,y) corresponding to a stationary distribution
of probabilities and construct an "eigenbase01 for this covariation func-
tion. It is well known how complex this problem is in such a general for-
mulation. However, it makes sense to examine it at least in simple special
cases. In a study by Monin and Obukhov [6] use was made of a very simple
model of the following type:
dF,;d1= LF,
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 vi. va a Lv.icw 1101:. vuLt
where L is a linearized "dynamic" operator dependent only on space coor-
dinates. It is shown that under the energy conservation condition (L* _
-L) the eigenfunctions (analogues of empirical orthogonal functions) of
the synchronous spatial cova:-iation matrix of the F field, corresponding
to a stationary probabilistic distribution, coincide with the eigenfunctions
of the L operator. It can therefore be understood why empirical orthogonal
functions are far more stable characteristics than the dispersions ~,j; the
empirical orthogonal functions are related to the dynamic operator, where-
as the dispersions are established as a result of nonlinear interactions
[6].
Without being able to discuss in detail the results obtained during recent
years for the empirical orthogonal functions of real meteorological fields,
- we will enumerate the principal directions in which the empirical ortho-
gonal functions method has been used in meteorological investigations. We
note that the extensive use of this method in the USSR began earlier than
abroad.
Most investigations have been devoted to an analysis of the fields of sur-
face pressure, H500 and H700, air temperature at sea level, temperature
of the ocean surface and precipitation both for the entire northern hemi- �
sphere and for its individual parts. In particular, special attention is _
being devoted to processes transpiring over the Atlantic and Pacific Oceans
and attempts are being made to establish correlations between them. Study
of the vertical structure of ineteorological fields is continuing [8].
Many attempts have been made to apply the empirical orthogonal functions
method for forecasts both for intermediate times and long-range fore-
casts. In such cases as the predictors it is customary to use the iirst
main components of the principal meteorological fields carrying the most
impurtant information concerning the course of long-period processes.
Then, using linear regression equations, an evaluation is made of the val- '
ues of the main components of the predicted field and these are used in
restorlnq the field in the future [5]. We note [3], in which the predic-
tor for a f.ive-day forecast of precipitation over the western half of the
USSR was the H500 field obtained as a result of a hydrodynamic forecast.
The type of circulation is taken into account. In [13], for the purpose -
of predicting the mean seasonal temperature over North America, informa-
tion on the totality of inean seasonal H700 and OT10700 00 fields and the fields
of surface temperature, temperature of the ocean surface and the precipita-
tion field was represented in the form of a 12-dimensional "climatic" vec-
tor close to the vector of the main components and then in place of the
regression equations use was made of the analogues method. In [4] the
breakdown of the geopotential fields in the northern hemisphere in seven "
levels was used for constructing a hydrodynamic model of the atmosphere
with few parameters which was used in making a forecast for six days.
It can be seen from what has been set forth above that the use of the em-
pirical orthogonal functions methad in meteorology leads to the necessity
for computing empirical orthogonal functions for matrices of very great
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dimensionalities. This gives rise to a number of problems, both purely com-
putational and those related to the complexity of rigorous validation of
statistical conclusions relative to empirical orthogonal functions evalu-
ated using small samples. With respect to computation algorithms, in ad-
dition to [5] it is possible, for example, to mention [15], which pro-
poses an economical iteration method, and also a number of others, cita-
tions to which can be found in reviews and monographs, some of which are
given in the bibliography.
A procedure used for the first time in the meteorological literature xn
[16] was very useful in 1969 for computing empirical orthogonal functions
in cases when the dimensionality m of the covariation matrix is greater
than the volume n of the sample. This procedure is based on the fact that
the nonzero eigenvalues of a matrix of the m-th order Z=jIZijjj, determin-
ed from Some rectangular matrix F= II Fiqll , i= q= 1,..., n;
n< m:
n'
Zij _ Y. F,, FlQ = FF*, t, ! = 1. . . . . m(14)
. y=t
coincide with the eigenvalues of a matrix of tho n-th order Y=� YqsII '
. m
YQs= ~FrvFts=F*F. q, s = 1, . . . , n, (15)
r_t
and the eigenvectors of the matrices Z and Y, z and y respectively, corres-
ponding to one and the same eigenvalue, are expressed through one another:
y=F"z
(16)
_ (the asterisk is the transposition symbol). In general, the y and�z vec-
tors do not have to be normalized simultaneously to unity. The remaining
(m - n) eigenvalues of the Z matrix are equal to zero. -
As Fi we take the values F'(xi, tq). It is easy to see that the spatial
covariation matrix B is related to Z by the expression
8;j= (lln) FF" _ (iJn) Zt1 (17)
(compare with (1)). We will show that with the additional condition of
statistical spatial homogeneity the Y matrix is proportional to the time
covariation matrix R of the F(x, t) field:
Rqs= R(tQ. ts) = = t m F'"F= im YQs; s. 9= I, rt. (18)
Here the " symbol denotes averaging for m points xj. In (18) it would
be necessary, strictly speaking, to take the deviations from the means,
which for each moment t can be evaluated by averaging for m poirits xi.
Here we will assume that for the field of deviations from the means in
- time F' the spatial deviations from the means are close to zeri, which is
probable under the conditions of statistical homogeneity with respect to
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1'VR UPP1l.1NL uJt UIVLY
t and x. We will denote the coinciding nonzero eigenvalues of the matrices
Y and z by �j, j= 1,...,n. It follows from (17) and (18) that the eigen-
values of the matrices B and R are related to lAi by the expressions
-vj = �)im, (19)
respectively, and the eigenvectors by a formula similar to (16).
Now we will turn to the representation (2), which with t= t, q= 1,...,n
and p= min (m, n) is transformed to equality. Instead of aj~tQ) we intro-
duce the normalized vectors
n
�I (ta) = al (rq)1(n Xj)l 12; (Iln) Y. aj (rQ) = 1 (20)
v=1
- (compare with (4)). Using (19), we rewrite (2) in a form symmetric relative
to x and t :
' min (m, n)
Fl4 = v 1,1112 4I (xI) (21)
Using the orthonormality of the spatial eigenvectors ~~(xi) and equation
(18) it is easy to show that oC~(tq) is th'e "eigenbase" of the time covaria-
tion matrix R. The question as to what in (21) should be considered the
main components and what should be considered the empirical orthogonal _
functions must be answered in dependepence on the relationship between m
and n.
In actuality, if, for example, n41m, and the field values are weakly cor-
related spatially, it can be hoped that the time covariation matrix R, its
first eigenvalues V 3 = 1,/m and the OCj vectors are evaluated using for-
mula (18) quite reliably. is means that it is possible to use the con-
siderations which led us to the formulas (10)-(12), from which we conclude
that with sufficiently large m?>n the Vj (and �j) values and the aCj vec-
tors describe the energy distribution in the time spectrum. In actuality,
in many cases the main components aj(t), evaluated using real data, are
not similar to the realizations of the random functions, but instead are
close to the trigonometric functions (and the first main component is close
to a constant or to a cosine with a large period), which corresponds to
formula (10) for empirical orthogonal functians p4 j �(t). It is therefore un-
' derstandable why the spectra of "random" functionsai (t) in these cases
have sharp peaks in the neighborhood of one or two frequencies. On the
other hand, when m,)-n the dispersions of the evaluations of the spatial
covariation matrix B and its eigenvectors can be great and comparable to
the dispersions of evaluations of the initial f ield.
Taking into account everything which has been said above, it is natural to
call the Gtii vectors (time) empirical orthogonal functions and call the
� 112~0j, being functions of space coordinates, the main components. Thus,
J
the O~j vectors (and this also means the aj(t) functions) can be considered
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determined (that is, nonrandom), and the ~Pj(x) functions random, whose .
fluctuations for each x reflect the individual peculiarity of the time real- `
ization of the Eield at the point x. Therefore, the 99J(x) functior.a cannot
be regarded as reliable characteristics of the spatial statistical structure.
With respect to the eigenvalues ~ of the B matrix, they are proportional
to the eigenvalues of the R matrix~
k) _ (min) yi, (22)
and therefore have no relationship to the spatial structure.
If m