JPRS ID: 9929 USSR REPORT METEORLOGY AND HYDROLOGY NO.4, APRIL 1981

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JPRS L/9929
24 August 1981
USSR Report
METEOROLOGY AND HYDROLOGY
No. 4, April 1981
~
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, .
JPRS L/9929
; 24 August 1981
USSR REPORT
METEOROLOGY AND HYDROLOGY
' No. 4, April 1981
Translation of the Russian-language ::,onthly journal METEOROLOGIYA I
GIDROLOGIYA published in Moscow by Gidrometeoizdat.
CONTENTS
Some Features of the Energetics of Temperate-Latitude Cyclonic Formations....... 1
Formation of Moistlning of the Land Accompanying Climatic Variations............ 16
Effect of C02 on the Therma.l Regime of the Earth's Climatic System 24
' Numerical Modeling of the Diurnal Evolution of the Atmospheric Boundary Layer
' in the Presence of Clouds and Fogs 38
I
~ Modeling of an A Priori Ensemble of SoZutions of the Inverse Problem and
~ Stability of Optimum Plans for an Ozone Satellite Experiment 51
~ Evaluation of Accuracy in Determining Turbulent Fluxes Using Standard
; Hydrometeorological Measurements Qver the Sea 59
; Chlorinated Hydrocarbons in the Near-Water Atmospheric Layer Over the
North Atlantic 68
Methodological Problems in Measuring Temperature and Salinity in the Ocean
Boundary Layer 74
' Possibility of Seasonal Prediction of Water Temperature in the North Atlantic... 81
~ Delaying Effects in the Ocean-Atmosphere System and Their Modeling 89
Method for Computing the Thermal Diffusivity Coefficient of Bottom Deposits of
La-rge Shallow-Water Lakes (In the Example of Lake Kubenskoye) 98
Directions in Research for the Purpose of Supplying the National Economy With
i Agroclimatic Information 108
.
!
i
I
- a- [III - USSR - 33 S&T FOUO]
i
i Fl1R /IFFI!'i A i i 1CF. nNi b'
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Remote Sensing.-of the Atmosphere From 5ate31ites During the FGGE Period........ 121
Thermodynamic Conditions Accompanying Convective Cloud Cover and Precipitation
Near the Equator (According to Data From the Regional Monsoon Experiment
(MONEX)) 135
Optimum Measurement of Radar Parameters of Meteorological Formations........... 144
Review of Monograph by Yu. A. Izrael': 'Ecology and Monitoring the State of the
Environment' ('Ekologiya i Kontrol' Sostoyaniya Prirodnoy Sredy'),
Leningrad, Gidrometeoizdat, 1979 154
Seventieth Birthday of Georgiy Anisimovich Alekseyev 158
At the USSR State Committee on Hydrometeorology and Environmental Monitoring... 160
Conferences, Meetings, Seminars 161
Notes From Abroad 166
49
- b -
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UDC 551.515.1
SOME FEATURES OF THE ENERGETICS OF TIIMPERATE-LATITUDE CYCLONIC FORMATIONS
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 81 pp 5-16
[Article by N. Z. Pinus, professor, and `1. P. Kapitanova, candidate of physical and
mathematical sciences, Central Aerological Observatory, manuscript received
30 Sep 80]
[Text] Abstraci.: The article presents the results of
investigations of the budgets of kinetic, poten-
tial and internal energy, as well as the energy
of phase transformations, on the basis of the water
vapor budget in different stages of evolution of
temperate-latitude cyclones, making use of empir-
ical material. Quantitative estimates of the ener-
gy capacity of the mechanisms forming the budgets
are presented.
During recent years more and more attention has bepn devoted to study of the ener-
getics of cyclonic formations in the temperate latitudes. These cyclones are an
extremely important part of the general circulation of the atmosphere. Assodiated
iaith these are atmospheric f ronts and cloud systems, as well as precipitation
~ fields determining the state of the weather over large areas and being extrenely
important for man's economic activity.
The budget of any type of energy, like the other characteristics of cyclonic--form-
ations (moisture cycle, etc.) can be studied ii a moving coordinate system which
= moves along the trajectory of movement of cyclones or over a fixed area (polygon).
The first research method makes it possible to study the features of energetics,
taking into account different phases in the evolution of this synoptic formation.
In a fixed polygon it is possible to trace the course of the atmospheric processes
_ transpiring over it'and compare the peculiarities of the budgets of different'syn-
optic formations.
The nature and structure of the budgets of different types of energy in the atmo-
spheze are dependent on the temporal and spatial scales of averaging; with an in-
crease in these scales there is a smoothing of the values of the parameters making
up the budget. In this connection a factor of great importance is the choice of
' the extent (area) of the polygon.
1
= 1
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In our studies [1, 2, 4, 5, 71 we obtained preliminary evalua.tions of the role of
different mechanisms forming the budgets of kinetic, potential and internal energy
of different parts of a cyclonic formation and in different stages of itS evolution,
and also the role of the energy cf phase transformations of water vapor. In par-
ticular, in the study of the energetics of a deep cyclone penetrating into the
European USSR in November 1973 it vas possible to detect and evaluate the role of
horizontal advection through the lateral boundaries of a cyclonic formation (ex-
change with the external medium) anc.' internal vertical redistributions of energy
(and water vapor). It was establishecl that local changes in kinetic, potential
and intenzal energy are relatively smail against the background of major energetic
processes transpiring at diff erent altitudes in cyclones; they constituted approx-
imately 6-10% of the total changes of the corresponding budget. The law of compen-
sation between the inflow (outflow) of kinetic energy and the outflow (inflow) of
labile (the sum of internal and potential) energy is not oper.ative within a cyclone.
In a cyclc+ne, in addition, especially in its central part, the contribution of the
energy of phase transformations was substantial. It was important to check the de-
gree of universality of the results on the basis of independent material and make
a more precise evaluation af the energy capacity of temperate-latitude cyclonic
formations. In this article we examine the results of investigation of the energetics of indi-
vidual cyclones moving in different zones of the European USSR in a moving coordin-
ate system (Lagrangian budget), and also different parts of cyclonic formations
observed over fixed polygons (Eulerian budget). Figure 1 shows the trajectories
of the cyclones which we studied and the geographical position of three fixed poly-
-ons in which investigations were made of the atmospheric processes transpiring
there. We investigated the energetics and moisture cycle of five cyclones observed
in Ap ril (10-12) 1968, in October (22-25) 1973, in November (24-27) 1973, in Feb-
ruary (~8-21) 1978, in June (18-20) 1978, selected taking into account the nature
and clarity of the trajectory of movement (surface center) and intensity of their
evolution. The trajectories of these cyclones in general coincide well with the
mean long-term paths of cyclones in the territory of the Soviet Union [3].
In the Balkhash polygon a stuuy was made of the processes transpiring in May (13-
27) 1972, in the Perm polygon in December (12-25) 1973, and in November-December
[(11-18 November) and (29 November-9 December)] 1977, and in the Riga polygon in
rfay (16-27) 1979. .
The area of tlie moving and fixed polygons, equal to approximately (2-4)�1011 m2,
in all cases was a hexagon based on the six nearest stations for temperature-wind
saunding of the atmosphere with a seventh station at the center. Data from seven
such stations served in all computations as the initial aerological information.
The equaticns describing the budgets in a quasistatic approximation (for a unit
mass) are:
kinetic energy budget
~ oK .KV71t_ aWK -l~�~~+
a aP
2
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(1)
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potential energy budget
dt p� R V a~p g W+ '1z; .
(2)
internal energy budget
dl --~�IV- da�1 - ai -p�'D V -ad P ~ -{-V�`P -1a; (3)
P
water vapor budget
W
dy a q
ar = - p ' 4 V - dp ~i� (4)
The following notations were used in these equations: K-- kinetic energy of inean
motion, jTis potential energy, I is internal energy, q is specific humidity, p is
pressure, (J~is geopotential, cc)= d F/ a t is the analogue of vertical velocity in
a p coordinate system, W is the velocity of vertical movements, ~ is the wind vec-
tor, '
d d
Q = dx av
The line at top denotes averaging for area.
. o y,g C~
~
i
O
( r~ .
~ .
~ AFXAH:'Ef18C 9/ i )
t ~
~lIEHV?H(PAIl~!
1 1;; .~MN!iCKxK ~ Ic 7 1 L,/
' a H~WEB, 6AlIX '
rr S
K~1E~ _ o /~APbKOB ~ �
)'KNtllHHEe
l.
Fig. 1. Trajectories of cyclones and location of polygons. 1) October 1968; 2) Oc-
tober 1973; 3) November 1973; 4) February 1978; 5) June 1978.
In eq uat:ions (1)-(4) the terms at the lef t describe local changes in the energy
(moisture content), the first two terms at the right the changes due to hori-
zontzil inf.lows (outflows) through the la.teral boundaries of a column of the atmo-
spliere and the vertical redistribution, the third term in (1) at the right the
;;eneration.of kinetic energy due to the operation of the force of the horizontal
pressure gradient, the third term in (2) at the right the relative transforma-
tion of kinetic and potential energy, the third term in (3) at the right the
3
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relative transformation of the internal and potential energy (through the change
in kinetic energy in the ascending (descending) fluxes); the fourth and fifth
terms in this equation describe the relative transformation of internal and kin-
etic energy (with broadening (compression) by pressure forces at the boundary of
the volume), Q 1 includes the dissipation of kinetic energy into heat, nonlinear
interactious of movements of different scales, effects of errors of initial aero-
logical infornmation and computations on an electronic computer.
We note, as was demonstrated in [5, 7], that in the case of sufficiently great
scales of spatial averaging the Q 1 value has a negative sign and (with allowance
for the errors in initial aerological information) describes the rate of dissipa-
tion of kinetic energy into heat. With a decrease in the averaging scale the ef-
fects of nonlinear interaction of disturbances of different scales and disturb-
ances with a mean flux begin to exert an influence, as does the effect of therma.l
s.tratification of the atmosphere. In these cases Q 1 can be either a positive or
negative value and in addition, can attain large absolute values, QZ are subgrid
effects and the effects of errors of initial aerological information and comput-
ations on an electronic computer; Q 3= dQ/dt + Q'g are t:e nonadiabatic inflows
(outflows) of heat due to radiation heating (cooling), phase transformations of
water vapor (condensation, evaporation), turbulent heat transfer, and also the
effects (L53) of errors in initial aerological information and computations on
an electronic computer;
~4 - - (qcon - qevap) + Dq + a 41~
where qcon is water.vapor condensation, qevap is the evaporation of cloud par-
ticles and precipitation particles, Dq is the turbulent transfer of water vapor,
ZA~ are the effects of errors in initial aerological information and computations
on an electronic computer. If it is assumed that Dq and L~q are small, the 64
value is the total effect of condensation (sublimation) of water vapor and evapor-
ation of cloud particles and precipitation particles in the considered volume.
The -:-~4 value will be positive in the case of predominance of evaporation pro-
cesses or negative in the case of a predominance of water vapor condensata.on (sub-
limation) processes.
All the terms in equations (1)-(4), except Zk, ~z, 63 and 64, were computed on
an electronic computer using data from aerological observations. The 1, 62, A3
and L\4 values were obtained as residual values on the basis of the balance of
equations (1)-(4).
The mettiod and procedures for computing energy and the moisture cycle were describ-
ed in jl, 5]. These sources also give evaluations of the role of errors in initial
aer.olu4;ical information. Numerical experiments indicated that although the errors
in computations of energy and the moisture cycle due to the inaccuracy in aerolog-
ical information are rather considerable, this applies, in particular, to an evalu-
ation of the value of the residual terms in equations (1)-(4). They exert relative-
ly little effect on the general patterns of spatial and temporal changes in energy
and the moisture cycle and in addition, are numerically the smaller the greater
the thickness of the considered layer of the atmosphere. Satisfactory results are
4
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obtained with a thickness of the layers v p= 200 gPa. On the average the error
of the residual terms is 8-10%.
As indicated by investiKations, cyclonic formations have enormous energy reserves:
the kinetic energy in a column of the atmosphere is Psurf - 50 gPa, where Psurf is
the surface pressure, on the average being 4�106 J/m2, the potential energy is
about 6�108 and the internal energy is about 1.7�109 J/m2. The reserves of kinetic
energy increase with altitude and in the vertical profile of the distribution have
a maximum in the layer 400-200 gPa. The reserves of potential energy increase with
altitude, whereas the reserves of internal eZergy decrease. In the layer 200-50 gPa
the reserves of potential and internal energy ire approximately identical; the dif-
ference does not exceed S%.
- The horizontal distribution of the reserves of kinetic energy even over the rela-
tively small area of the golygon (2�1011 m2) is characterized by a definite nonuni-
formity. The degree of the horizontal nonuniformity of reserves was evaluated by
' us as the standard deviation of the reserves in a column of the atmosphere over
the area of each of the six triangles of the polygon from the total reserve over
the area of the entire polygon, normalized to this total reserve. This ratio var-
ied in the range from 10 to 60%. The degree of horizontal nonuniformity of the re-
- serves of kinetic energy is different in different stages of cyclone evolution. In
the generation period the degree of nonuniformity was relatively small and does
not exceed 10%. With the deepening of the cyclone it increases to 40-60%.
An important parameter to a definite degree reflecting the dynamic activitq of a
cyclonic formation and weather-forming processes is the ratio of the kinetic ener-
gy value to the labile energy value. Whereas for the atmosphere in the northern
hemisphere this ratio averages 0.01-0.07%, in temperate-latitude cyclones, as in-
dicated by our computations, this ratio can attain 0.4-0.6%, and as an average
was 0.18%. The vertical profile of this parameter has a maximum in the layer 400-
200 gPa. This maximum is the more clearly expressed the greater are the energy re-
serves in the entire considered layer of the atmosphere (Psurf - 50 gPa).
The computations indicated that with respect to significance (contribution to
budget) the kinetic energy budget is determine3 by:
the generation of kinetic energy (Kgen) due to the operation of the pressure
gradient torce transforming the potential energy into kinetic energy (internal en-
ergy source);
the inflows (outflows) of energy (Kbound) through the lateral boundaries of a
coluum of the atmosphere (external source);
the vertical redistribution (Kver) of energy (in a cyclone there is energy
transfer from the lower half of the troposphere into the higher layers).
~ The budget of potential energy is determined by:
; inflows (outflows) of energy (Tfbound) through the lateral boundaries of a col-
-i umn of the atmosphere;
thP vertical redistribution of energy (TI-yer);
' the relative transformation of potential and internal energy.
5
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The budget of internal energy is determined by:
the inflows (outflows) of energy (Ibound) through the lateral boundaries of a
column of the atmosphere; the vertical~redistribution of ene'rgy (Iver);
the relative transformation-of`infernal and'potential energy; '
the relative transformation of iriternal and kinetic anergy;
the intensity, of nonadiabatic processes (phase transformations of water vapor,
radiation proresses, etc:): As an example, Figure 2 sKows tho- struct-ure of the budgets of kinetic and internal
energy for the central part of the February (1978) cyclone in the stage of its max-
imwn development. In computations of the structure the sum of the moduli of the
parameters entering' inm equatioiis (1) and, (3) was assigned the value unity. Yhe :
internal energy:budget (Fig.' 2b)' gives data only on'the contribution of It, Ibound,-'
Iver, dTT/dt and G_3; the''.telative` contribution of the remaining components of the ~
budget totals less than 2%. It can be seez that the' contribution 'of 'the local-changes of energy in both budgets:
is. relatively 'small; iri'`the P'surf - 800 gPa layer'it is 6%, but at' greater alti-
tudes it is less than 3% in the- budget of kinetic energy, whereas in the internal
energy budget at all levels it is less than 2%. .
The contribution of lateral effects and the vertical redistribution of energy is
zmportant. ln the kinetic energy budgefi their total contribution for the atmo- spheric boundary layer '(Psurf -$OO gPa) is about`25%, for the layer 800-600 gPa
about 12%, for the layer 600-400 gPa about 25%, for the layer 400-200 gPa
about 45%, and for the 1aqer 200-50 gPa'=- about 20%. In the internal energy
budRet these contributions~are stiTT more important arid constitute $7, 33, 61,
59 and 287.. . . , _
The contribution of the gerieration of kin'etic energy due to the operation of the
pressure gradient force and subgrid effects (L1) is decisive in the kinetic en-
ergy budget. In the internal energy budget a considerable contribution is from nonadiabatic factors, attaining almost'S0y of the budget in the layer 600-400 gPa.
The reTafive smallness of ttie coritribution of nonadiabatic factors to the internal
etiergy tiu8get `for the boundary layer' (about 8%) fis evidently -attributable to the -
fact that in this atmospheric layer the changes in the energy of phase transfor-
mations' of'wafer vapor"`aird chang'es due to:radiation factors are opposite in sign
and quantitatively to a considerable degree compensate one another. The contribu-
tion oF the relative transformatioris of internal and potential energy at differ-
ecit :l.evels attains 10-20%. It should be noted that although the relative contribu-
tion of the relative transformations of internal and kinetic energy to the budget
is not great (less than 1%), the quantity of tliis energy is extremely great
(see Tables 1 and Z).' -
The vertical redistribution of energy in cyclonic formations has the important
characteristic that iri tfiem there is a transfer of energy from the layer Psurf -
400 gPa into the layer 400-50 gPa, most sharply expressed in the leading and cen-
tral parts of a cyclone. On the periphery of an anticyclone, as demonstrated by
investigations in fixed polygons, the transfer of energy occurs from the layer
6
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- 50-400 hPa intc> tlw lower luyers of the atmosphere. As an example, Fig. 3 shows
the 3veraged profiles of tlie vertical redistribution of kinetic energy for the
periphery of cyclones and the periphery of anticyclones, constructed on the ba-
sis of data for Riga polygon. This figure shows that at the cyclone periphery
there was pumping of energy from the layer Psurf-400 gPa to the layer 400-50 gPa;
the greatest outflow occurs at- the layer 800-600 gPa (about 1 W/ml), whereas the
greatest infl.ow is in the layer 200-50 gPa (about 1 W/m2). At the periphery of an
anticyclone, on the other hand, there was a pumping of energy from the lower
stratosphere and the upper troposphere into the lower l.ayers; the greatest out-
flow was from the layer 50-200 gPa, whereas the greatest inflow was in the layer
400-600 gPa.
dPa d7a
.C
�00 r
4DU ~
G00~
COG~
P-
P3 I
S~
~
C"oo
4001
600
B00
.
. .

,
.

: .
\
: ~
~ ` .
, ~ , ' ' X.- , . , ,
.

' ~ , � 'i ~'I~,,
~,~:\~:�:,,j\;:.
.I;
~
~
. ~ \ 
-
Ii'
~
�

~
'
~ ~ ~
~
� ~
:
o 10 20 30 4!% 50 60 70 40 90 100 %
~
3
4
S
b
~
9
5
Fig. Structure of budgets of kinetic (a) and internal (b) energy. 1) Kt, 2)
Kboundv 3) l~ver; 4) Kgen, 5) 41, 6) It, 7) Ibound, 8) Iver, 9) dT7/dt, 10) 63.
Similar patterns of the vertical redistribution of energy are also characteris-
' tic for processes in other polygons. A distinguishing characteristic of the Bal-
khash polygon is that the maximum pumping of energy in the mechanism of vertical
~ :edistribution occurs here at great altitudes (in the layer 600-400 gPa).
It ali-Duld be r.oted th~:.t on the periphery of cyclones in the initial stage of
; their filling the pumping of energy upward from the layer Psurf - 600 gPa still
continues, but at the same time there is pumping of energy downward from the
7
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9
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layer 50-200 gPa, as a result of which there
ly in the layer 400-200 gPa. The patterns of
and internal energy have the same character.
1-17Q
gPa
is an increase in energy, especial-
vertical redistribution of potential
~ ~ ? U 9r!~: '
w/ m2
Fig. 3. Vertical redistribution of kinetic energy on periphery of cyclones (a) and
periphery of anticyclones (b). Riga polygon.
Thus, although the vertical redistribution of energy in itself does not change the
total energy reserves in the column of the atmospliere Psurf-50 gPa it exerts a
strong effect on the structure of the budget of relatively thin layers of the at-
mosphere (-/^Ap= 200 gPa) and determines tlie degree and character of the energy re-
lationsliip betcaeen different layers.
The energy processes in temperate-latitude cyclonic formations have an enormous
energy capacity. This is illustrated by the data given in Tables 1 and 2 for the
column of tlie atmosphere Psurf - 50 gPa (ground-approximately 20 km) with an area
of the base 2�1011 m2 450 x 450 km). Table 1 gives averaged estimates of the
energy capacity of the mechanisms forming the budget for different parts of cy-
clonic formations and the periphery of anticyclones and Table 2 gives similar
data for the central part of cyclones in different phases of their evolution. The
maximum values exceeded these means by a factor of 2-3.
Investigations confirmed that in the budget of both kinetic, potential and 3,nter-
nal energy small local clianges traced on the basis of data from scheduled aero-
logical observations are formed against the background of extremely active pro-
cesses of generation of kinetic energy, horizontal advection, vertical redistrib-
ution and also subgrid processes. This is attributable to the fact that active
internal and external sources and losses of energy as a rule mutually compensate
one anotFier and are manifestecl tof;etlier in the course of local energy changes.
Table 1 shows that lateral effects are expressed most strongly in the leading and
central parts of cyclones in which the horizontal influx of kinetic energy aver-
ages 8-1.0 bill.ion KLJ, witli the corresponding figures for potential and internal
energy heing 760-860 and 1150-2830 billion KW. It should be noted that in the
central part of a deep cyclone penetrating into the European USSR in November 1973,
rare with respect to the intensity of processes and rate of movement [6], the con-
tribution of horizontal advection to the kinetic energy budget exceeded by a factor
of 1 1/2 the contribution from the generation of kinetic energy [5].
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gPa
,-,7c
SO '
100
500
SO
B0~
P3
N %
El Z
fmJ
~ i 0 f0 20 JO 40 $O 60 70 BO 90 f0011e
I'ig. 4. Structure of water vapor budget.
1) 9t, 2) Qbound, 3) Qver, 4) d 4�
Now we will turn to Table 2. The data in this table show that the role of the mech-
anisms forming the energy budget to a considerable degree is dependent on the stage
o� cyclone evolution. All the energy transformations transpire most actively in the
maximum development stage.
Cyclones in general differ from one another both with respect to energy reserves
and with respect to the activity of energy transformations, but the structure of
the budgets of each of the types of energy for them in general is similar.
Table 3
Distribution of Kver, A 4 and AT/Pit Parameters by La.yers
_
OcraUel 1
973
Ilovember 19
73.
F
gPa
(
Kver
A4 ]02
~
A T
At
I,
, A~ 10~
4
A T
A!
$
`ver
g/
I
W/m2
m2�sec
R/hr
W/m2
(mZ�sec
K/hr
200-50 ~ 2.51
0.02
-
30,9 I
--0
22
400-200 l 621
-0,22
0,01
16,9 I
,
-1,49
0
072
600-400 ~ -4,94
-1,68
0,08
-6,2
-6,80
,
0
306
800-600 -0.92
-9.03
0,18
-20,6 I
-11,36
.
0
512
Pa-800 ~ -2.89
-2.89
0.13 I
-21.0
-6.34 '
,
0,285
I Q _
er
Pa I Kver � 10-, I 0 tT Kver AV 102
ar
~
' Td/mZ (m2. sec) I P/hr ~ W/m2 (m2gsec
~ - 1z/hr
200-50 -1,80 0,03 2,70 -0,52
900-200 I 8,90 -0.09 0,004 7,19 -2,19 ' 0,10
600-400 , -3,60 0,12 -0.005 -7,07 -11,68 0,53
800-600 I -0.80 -2,06 0,09 -0,43 -13,49 0,61
P3-800 i -2.70 -1.53 I 0.07 -2 39 -6,01 0,27
11
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The moisture cycle and the energy of tlie phase transformations of water vapor as-
sociated with it occupies a special place in the znergetics of cyclonic forma-
tions. 11s indicated in Tables 1 and 2, tlie energy of phase transformations in dif-
ferent parts o� a cyclone is evaluated as an average of 20-40 billion KW; in tlie
central part of cyclones in the stage of their deepening and maximum development
it attains an average of 70-75 billion KW. jdith respect to its quantity this ener-
- gy exceeds by several times the generation of energy due to.the operation of the
force of horizontal pressure gradients.
As indicated by computations, the water vapor reserves in the column of the atmo-
sphere Psurf - 50 gPa with an area of the base 2�1011 m2 on the average are about
2 billion tons; about 80% of the moisture reserves are contained in the layer
psurf - 600 gPa. The degree of horizontal nonuniformity' in the distribution of
moisture reserves over the area of the polygon is dependent on the stage of cy-
clone evolution. In the generation of a cyclone it is about 20%; in the mature
- stage it is aUout 50%.
The water vapor budget is determined by:
the inflow (outflow) of water vapor (qbound) through the lateral boundaries of
a column of the atmosphere;
the vertical redistribution of water vapor (qver);
the phase transformation of water vapor (0 4).
Table 4
Moisture Cycle in
Cyclonic Formations,
millions tons/hour
Mechanisms forming
Region
(part)
of cyclone
Stage
in cyclone devel
opment
water vapor budget
leading
cen-
southern waves
deepen- devel-
f illing
-
tral
periphery
ing opment
maximum
- Lateral inflow
57
71
26
18
43 110
14
Vertical re(iis-
tribution
25
41
27
15
33 55
25
Effective condensa-
,:ion
59
62
2
21
100 105
7
As an example, Fig. 4 shows the structure of the water vapor budget for the central
part of tiie T'ebruary (1978) cyclone in the stage of its maximum development. The
loczil clianges in the lower half of the troposphere are as follows: in the layer
i) surf ' 800 gPa their contribution was 19%, in the layer 800-600 gPa approx-
imately 27, ard at greater altitudes 5-2%. The horizontal inflow and the ver-
tical redistribution were: in the layer Psurf - 800 gPa total 61%, in the-lay-
er 800-600 gPa --,about 22%, and in the layer 600-400 gPa even 92%. Whereas in
the layer PsurP - 800 RPii the effective condensation contriUution was approximate-
ly 20% of the budget, in the layer 800-600 gPa it was already 50%. At greater alti-
tudes this contribution does not exceed several percent. It should be noted that in
the layer 200-50 gPa the moisture budget is determined primarily by the vertical
re:distribution (inflow from the lower layers of the atmosphere), constituting 50%
of the budget.
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As indicated by an analysis of research data, there is a defin.it-e correlation be-
tween the profile of the vertical redistribution of kinetic eaergy and the profile
of effective water vapor condensation due to the energy of phase transformations
which is set free and atmospheric heating. Table 3 gives data on the vertical re-
distribution of kinetic energy (Kver), the effective condensation of water vapor
(6q) and the rate of atmospheric heating (6T/L1t) by the energy of phase trans-
formations (assuming that all the energy of phase transformations is expended on
the heating of air) for the central part of cyclones in the stage of their maxi-
mum development. This table shows that the maximum outflow of kinetic energy in
the vertical redistribution is in the layer 600-400 gPa and the minimtmm outflow
is in the layer 800-600 gPa. The maximum of the heating rate is in the layer
800-600 gPa, so that this atmospheric layer is heated to a greater degree than
the layers 1'sur� - 800 and 600-400 gYa. Accordingly, the layer 600-400 gPa in time
becomes thermally unstable and the ptunping of energy into the higher layers is
intensified in it.
- In actuality, in the underlying layer relative to the layer with the maximum rate
_of heating the vertical temperature gradient decreases and with time this layer
' becomes thermally more stable, whereas in the above-lying layer, on the other
hand, the vertical temperature gradient increases. This layer becomes thermally
' more unstable and convective movements can develop in it. These movements can be
; propagated upward and in turn favor the vertical transfer of water vapor. ihe rate
of generation of buoyancy, equal to ,T
ga at ~
' where g is the acceleration of f ree falling, and 0(- is the coefficient of volumet-
ric expansion of the air, can attain, as indicated by computations, 200-250 cm2/
sec2 per hour.
, Thus, the vertical movements of air, ensuring water vapor transfer, exert a sig-
nificant influence on the structure of the water vapor budget and the effective
condensation of water vapor, ensuring the release of the energy of phase trans-
' formations, in the feedback system exerts an influence on the intensity and ver-
tical distribution of the vertical movements of air themselves. This phenomenon
caas manifested with particular clarity in the Octob er (1973), February (1978) and
June (1978) cyclones. In the November (1973) cyclone this phenomenon was maskeii
by a strong horizontal inflow of kinetic energy in the layer Psurf '600 gPa, giv-
ing an intensification of the pumping of kinetic energy from the layer 800-600
gPa.
Quantitative evaluations oL- the role of each of th e meclianisms enumerated above,
rorming the water vapor budget (for the column of the atmosphere Psurf ' 50 gPa
with au area of the base 2�1.011 m2), are given in Table 4. The data in this table
; :,how that the moisture cycle is most intensive in the central part of a cyclone
~ � and in the stage of its maximum development. The effective condensation is maxi-
mun in the leading and central narts of cyclones (59 and 62 million tons/hour)
' and in the stage of deepening and maximinn development (100 and 105 million tons/
hour).
The data in Table 4 convincingly show that the water vapor budg'et is significant-
1y r.~lated to the dynamics (energetics) of the atmosphere (intensity and nature
of horizontal and vertical movements).
13
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I'OR ON'F1('LU. I1tiN: ONI.Y
In conclusion we will examine some results of the investigation related to the
moisture cycle and precipitation in cyclonic formations. Computations indicated
that effective condensation (condensation minus evaporation) of water vapor in
a cyclone in the wave stage, in the central part of a cyclone in the development
_ (deepening) stage, in the leading part of a cyclone occurs 55-90% due to tlie lat-
eral influxes of water vapor and only 15-10% due to the initial reserves. In the
central part of the cyclone in the stage of its filling and on the southern peri-
phery of a cyclone the effective condensation of water vapor occurs 70-100% due
to the initial reserves.
Thus, the initial reserves of water vapor in a cyclone in the wave stage, in the
central part of the cyclone in the development (deepening) stage and in the lr!ad-
ing part of a cyclone are almost not entrained into the phase transformation
processes and the formation of precipitation.
hours
B
i~
.~BIl.15v 19. OJ ~9. "5 2C. OJ 20.15 11. 03~
� hours
Fig. S. Pieasured and computed quantity of precipitation during period 18-21 Febru-
ary 1978. In central part of cyclone: 1) measured, 4) computed; in leading part of
cy clone, 2) measured, 3) computed.
Second, it must also be noted, as demonstrated by the comparisons in [1], that the
effective condensation of water vapor satisfactorily reflects the presence and in-
tensity of continuous precipitation (over an area) in cyclonic formations. This
was also confirmed in subsequent investigations. As an example, Fig. 5 shows the
(luantity of precipitation measured in the precipitation-gage network and also the
quantity of precipitation computed on the basis of the residual term for the lead-
ing and central parts of the February cyclone, from 18 through 21 February 1978.
If one takes into account the present-day accuracy in measuring precipitation in
the precipitation-gaging network, the density of this network and the accuracy of
radiosonde measurements of air humidity, the agreement between the curves can be
regarded as entirely satis�actory; the maximum quantity of precipitation was ob-
served at 1500 hours on 19 February at the time of the maximum development of the
February cyclone and it was confirmed by all the curves shown in Fig. 5.
13IBLIOGRAPHY
l. Kapitanova, T. P. and Pinus, N. Z., "Budget of Water Vapor and Precipitation
in Temperate-Latitude Synoptic Formations," METEOROLOGIYA I GIDROLOGIYA
(Meteorology and Hydrology), No 1, 1980.
14
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i'
2. Kogan, Z. N. and Pinus, N. Z., "Atmospheric Aeat Balance in an Extratropical
Cyclone and Over It," RADIATSIONNYYE FROTSESSY V ATMOSFERE I NA ZEMNOY POVERKH-
~ NOSTI (Radiation Processes in the Atmosphere and at the Earth's Surface), Lenin-
~ grad, Gidrometeoizdat, 1979.
3. Kryzhanovskaya, A. P., "Mean Long-Term Paths and Frequency of Recurrence of Cy-
~ clones and Anticyclones Over the Northern Hemisphere," SINOPTICHESKIY BYULLE-
}TEN' GIDROMETTSENTRA SSSR I VNII GMI (Synoptic Bulletin of the USSR Hydrometeor-
ological Center and the All-Union Scientific Research Institute of Hydrometeor-
. ological Information), 1977.,
' � 4. Pinus, N. Z. and Kapitanova, T. P., "Water Vapor Budget and Energy of Phase
'i Transformations in a Temperate-Latitude Cyclone," METEOROLOGIYA I GIDROLOGIYA,
No 10, 1978.
~ S. Pinus, N. Z. and Kogan, Z. N., "Budget of Kinetic Energy of Cyclonic Formations,"
METEOROLOGIYA I GIDROLOGIYA, No 3, 1976. -
6. Chelyukanova, S. V., "Unusual Cyclone," METEOROLOGIYA I GIDROLOGIYA, No 3, 1974.
7. Kogan, Z. N. and Pinus, N. Z., "Some Aspects of Energy Budget in Middle Latitude
; Cyclones," SECOND SPECIAL ASSEMBLY, JAMAP, Seattle USA, 1977.
15
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UDC 551.(571.34+583)
FORMATION OF MOISTENING OF THE LAND ACCOMPANYING CLIMATIC VARIATIONS
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 81 pp 17-23
['Article by 0. A. Drozdov, professor, State Hydrological Institute, manuscript
received 17 Jun 801
[Text] Abstract: Since an increase in temperature in-
creases the moisture content and vertical in-
s.tability of air masses, but weakens westerly
transfer and circulation in the temperate lat-
itudes, in the modern epoch moistening in the
temperate latitudes decreases during a warming.
With a change in temperature by more than t2�C
relative to the modern level the correlation
between temperature and precipitation becomes
direct. Similar phenomena are observed in the
annual variation of precipitation. The secular
and intrasecular temperature variations over sev-
eral centuries reveal an appreciable correlation
with the objective characteristics of volcanism
and reveal no correlation with Wolf numbers.
In preceding articles ([7] and others) studies were made of the correlation be-
tween the thermal regime and moistening. Although these correlations are complex
and locally ambiguous, they are decisive in characterizing the precipitation of ex-
tensive territories in the temperate latitudes. The complexity of these correla-
tions is attributable to a diversity of effects caused by temperature changes in
the moistening regime. Direct correlations between the quantity of precipitation
and an increase in temperature arise due to an increase ln moisture content and in-
stability of atmospheric stratification. They are clearly manifested with consider-
able changes in temperature: in the annual variation, in the variation of the quan-
tity of precipitation with latitude and in a change in precipitation in warm and
cold geological epochs.
On the other hand, since during warmings there is a decrease in the temperature dif-
ference between the poles and the equa.tor, there is a weakening of westerly trans-
fers in the temperate latitudes, which leads to a decrease in water vapor flows
from the oceans into the interiors of the continents. The possibility of compensa-
tion of the role of westerly flows by meridional flows is noted only with a very
16
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high temperature background (from the south in simmmer at the present time, from
the northern seas in the geological past). A weakening of westerly tr3nsfers
increases the intensity of the transfers along the meridians, which favors an in-
crease in the temporal and spatial variability of temperature and precipitation. In
addition, cyclonic activity attenuates over the continents and the temperature
contrasts decrease within the cyclones themselves, which has a negative effect on
the moistening of arid regions.
An analysis of the material shows that on the average for the temperate latitudes
under modern conditions the moistening decreases with an increase in temperatures.
Judging from the climatic variations in different parts of the spectrwn in the
Holocene and in the historical epoch this regularity persists at least with temper-
ature changes from -1.7 to +1.3�C in comparison with the modern epoch. Cold epochs,
including the "small glacial epoch," were relatively moist; the warm, including
boreal and subboreal epochs, were dry. However, with an increase in the temperature
level by 2�C the moistening was substantially increased (Atlantic epoch); during
coolings greater than 2�C the quantity of precipitation evidently decreases (Fig.
- 1). A complex dependence of the quantity of precipitation on temperature is also
obtained in the annual variation.
LJe examined the changes in precipitation in the annual variation with a change in
temperature for 10 stations in Europe and SiUeria situated to the north of the
A. I. Voyeykov "great continental axis." Such a choice of stations ensured at
them through the course of the year a predominance of winds with a westerly cum-
ponent, that is, relatively uniform conditions of atmospheric circulation. Among
these stations six were on the plain, two on the western slope of the Ural Range,
one to the east of the Sayan and one (Sverdlovsk) in the "saddle" of the Middle
Urals, at the beginning of the leeward slope. The stations near the ranges differ
somewhat from the others: the windward stations have relatively more and the lee-
ward stations have relatively lesser winter precipitation and therefore this pre-
cipitation thereafter had to be excluded from consideration. At Sverdlovsk the
annual variation of precipitation is similar to that observed at lowland stations.
~ 'Cendency to Atlantic epoch
r~
ro
Iiodern level ~
- ~ U
ciC mo i:; ten.in
~ Levcl oi boreal and
Tendency to ~ subboreal epociia
subarctic 'H
0
epoch ~
Temnerature devi�3tion from moderu ievel
-J -2 -1 9 2 3
_ Fig. 1. Diagram of changes in mean annual precipitation in the temperate latitudes
of the land with a change in temperature in comparison with the modern tempera-
ture.
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'
orrected)
~
n
S
with t
eInonp.;
c
(u
~
'
= 0
(6c'
~
1 (TCIi
, Yr.
r'JGT.J

At bottom: month-
~Z~T~
�
17
ly precipitation
CT =
station �
J_
_
sums (without cor-
~ o~
rections) for sta-
~ ffi
~ ffi ,
tions, at top:
2 a ~
�
p

~
~ ~
mean of indicated
g ~
1
g '
~ ip

_g ~ ~ ~
stations. 1) Sverd-
1 .
'
~ 1�

:
~
~

'-A,,7 ff ~
t
k
'I
r
lovsk; 2) Tomsk;
; o
~ �
,
~
-
~ fla~%
�
3) Kayani; 4) Cop-
i
ef � 2
�3, �4 , o�S
enhagen; 5) Berlin
-ZO -1
-12 -B
- 'r 0 4 B 12
16 .'0'C
Fig. 2. Change in monthly quantities of precipitation in annual variation relative
to the precipitation falling at 0�C as a function of temperature in regions with
small circulation-moisture diffe.rences in course of year.
The dependence of the actual quantity of precipitation, related to precipitation at
0�C, on temperature on the average indicated an increase in precipitation with an
increase in temperature, being interrupted in the interval from -8 to 0�C. This in-
terval evidently corresponds to a rapid change in interlatitudinal temperature dif-
ferences due to degYadation of the regime of snow-ice phenomena with an increase
in temperatures.
In connection with the change in the temperature level from year to year there is
also a change in the form of correlation.with the quantity of precipitation [8]. In
the warm season of the year the correlation between these parameters is negative
(as in the Brickner cycles); in the cold season of the year it is positive. This
circumstance in part is a consequence of the trivial fact that cyclonic activity,
forming precipitation, decreases in summer, whereas in winter the temperature in-
creases, but in part also reflects the regularities noted above.
In addition to the mentioned features of the correlation, during the cooling and
warming in both the long-term and annual variation latitudinal shifts occur in the
pressure-circulation zones (trajectories of cyclones, positioning of anticyclones,
- dislocations of atmospheric fronts, etc.). This circumstance has now already been
noted by many Soviet and foreign authors [3, 4, 6, 17y 18 and others].
The superposing of this process on the dependences noted above creates an ambiguity
in the changes in precipitation in dependence on the temperatures within large re-
gions and a fundamental curvilinearity of the mentioned correlations for each point
separately. The simultaneous effect of all the three above-mentioned correlation
factors creates difficulties for an analysis of the regularities of the considered
correlations.
In addition to the long-term climatic changes, in whose creation fluctuations in the
elements of the earth's orbit, and possibly some other factors apparently particip-
ate, in the long-term variation of precipitation there is evidently a whole series
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of relatively regular fluctuations in which it is possible to detect approximate-
periodic components by correlation and spectral analysis methods. True, due to the
nonstationary character of many of these fluctuations they are perceived by many as
variants of "red noise" (for orders of the Markov process substantially higher than
the first). The longest of these (about 1500-2000 years) are usually related to
tidal phenomena [15], less frequently to solar activity. Neitlier such explanation
fully agrees with the actual material. In solar activity fluctuations there is re-
liable determination only of rhythms not longer than 90 years and more prolonged
rhythms are only postulated, frequently with an examination of the actual variation
of climate (the tie-in between tlle variation in climate and shorter solar cycles,
as will be demonstrated below, is also not ideal).
v ~
o
2;
~ ~ i ; ~ ~ ; ;
,
;o~~. ~^c' t79: '5~~ f91�� ;9ii~~ ;,�Ji� ~c.
'rP~ 1F.. 190P� 1910- 19~
7f7~ 1B5'v 1904 1914
Fig. 3. Secular variation of ice content near Iceland (according to Koch) (1) in
comparison with IJolf numbers jJ (five-year moving averages) (2).
The tie-in o� long-term temperature and moisture fluctuations with an 1850-year .
tidal cycle, in addition to some unclarity in the physical scheme of its influ-
ence on climate, is also inadequately satisfactory. In analyzing the variation of
these fluctuations from the present day into the past we find that already their
first realizations in the historical past diverge from the tidal cycle up to two
centuries (lagging or outpacing it in phase). Then into the depth of the past cen-
turies the tie-in becomes still poorer. The temperature and moistening fluctuations
themselves also in different parts of the hemisphere are not entirely synchronous;
the phase differences can attain several centuries.
_ Ttie tie-in of temperature and precipitation fluctuations is also not very rigorous.
l:vidently, even if the tidal phenomena are related to the considered fluctuations
the syncllronism of the effect is impaired by autooscillations in the atmosphere-
ocean-polar ice system. According to the computations of V. Ya. and S. Ya. Sergin
[13], the latter can vary in a considerable range of spectra.
The reasons for the shorter fluctuations (300-500 years [6], according to [16] 360
years; 200 years [14], according to [16] 180 years) are unclear. This was also
true for secular cycles (60-120 years) [1, 7, 8] (dissimilar with respect to dura-
tion and phases in different parts of the hemisphere, and also varying with time)
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and numerous sliorter cyctes (intrasecular, Brickner, and others). Many of these
are traced on the basis of ice and isotopic indicators, and also on the basis of
fluctuations of water bodies and deposits of silts in lakes over the course of sevr
. eral millenia [1, 7, 9, 10, 14, 16 and others]. Secular and more prolonged cycles
since the time of tlieir discovery have been manifested in different geophysical
series more or less regularly.
Attempts at explaining intrasecular, secular and multiple (with respect to dura-
tion) fluctuations on the basis of the influence of solar activity meet with for-
mal difficulties of a statistical nature. The spectra of secular fluctuations of
different geophysical parameters are not identical to one another and do not coin-
cide with the solar cycles (including for an average period up to 10 years or
_ more [9]); in sufficiently long series the increasing difference in the phases of
the fluctuations of helio- and geophysical factors becomes quite appreciable.
Since for the time being no jinnplike changes in phases in the fluctuations of geo-
physical parameters or time gaps have been discovered in tlieir manifestations up
- to the time of restoration of the correspondence in phase with secular and other
solar cycles, any phase difference can be accumulated between the fluctuations of
- geophysical parameters and the solar activity cycles.
Such, in particular, was found to be the case in a comparison of the Wolf cycles
with the variation of the ice content of the sea near Iceland (according to the
Koch index) (Fig. 3), although in both series there are fluctuations with a dura-
tion of 10-12 years.
A number of scientists (M. I. Budyko [2], H. H. Lamb [21, 22],'H. Flohn [17, 18]
and others) have attempted to establish a correlation Uetween decreases in trans-
parency caused by eruptions of groups of volcanoes (or, on the other hand, pro-
longed increases in transparency) with climatic fluctuations. As long as the ef-
fectiveness of eriiptions was determined on the basis of indirect criteria, includ-
ing on the basis of temperature anomalies in the northern hemisphere, it was pos-
sible to doubt the objectivity of such comparisons, at least during the time prior
to the development of actinometric observations. Even in recent studies with the
use of information on eruptions substantially refining and prolonging 2000 years
backiaard the statistics cited by Lamb [19], the correlation between volcanic activ-
ity and climate left much to be desired. However, the precipitation of soluble
products of eruption onto the glaciers of Greenland (I12SO4, (N11412SO4), some of
which make a substantial contribution to the formation of turbidity, created change
in the conductivity of ice persisting for many hundreds of years and detected in
cores during drilling.
For the time being these data have been obtained only on the basis of drilling in
c:reenland for a period of 350 years; it is desirable that such refinements be ob-
tained for other regions of the earth. And nevertheless the results of drillings
make it possible to conclude that short climatic fluctuations are tied into vol-
canic-induced atmospheric turbidity considerably better than could be demonstrated
Uefore. For example, the last three secular warmings, which were separated by in-
tervals of about 100 years (1930-1940, 1840-1860, 1730-1740), confirmed by the
paleotemperatures of Creenland, a decrease in the volume of ice near Iceland
and cin increase in the growtli of wood at the northern boundary of the forest in
the Taz ftiver basin, were accompanied by a sharp decrease in the conductivity of
the cores.
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Similar warmings in 1650-1660 and 1530-1540 can be established only on the basis
of the indirect data mentioned above and the virtually zero values of the dust
curtain index, according to Lamb, in the years 1514-1550, 1552-1564, 1573, 1588,
1590-1661. Most of the years wi.th increased transparency either precede or occupy
the yearG of warming mzixima.
Thus, the liypothesis for the first time expressed by M. I. Budyko [2] concerning
the reasons for the secular warmings is confirmed, although for the time being on
the basis of limited material. With respect to climatic fluctuations of higher
frequencies, they are relatively well dated on the basis of increases in ice vol-
ume near Iceland (by a value greater than 20 Koch units [20]). These coolings al-
so agree satisfactorily with the temperature of long-series-stations in Westsrn
Europe [22], F:uropean USSR [12] and the growth of wood at the northern boundary
of the forest in [Jestern Siberia [14]. Piore than 75% of these fluctuations during
the period of adequately complete information (from the second half of the 18th
century) correlate with the group eruptions of volcanoes. In one case (the erup-
tion of Armagora in 1846) Lamb exaggerated the volcanic component of temperature
variation. (Because of the year preceding the eruption, characterized by an anom-
:ilously high temperature for some undetermined reason. This initial level should
not be taken into account and the subsequent cooling must be reckoned from the
- mean level of temperatures for the group of precedinf; years).
After correction of this variation in accordance with data on conductivity, the
agreement with the variation of temperature indicators is restored. In three
cases (1865-1869, 1885-1892, 1938-1942) the coolings were unrelated to volcanism
and according to the information available for the two latter cases the coolings
! had either a local character (1938-1942) or were noted in the American sector of
the Arctic with a relatively high temperature in the Eurasian sector, which in
~ Eurasia formed winter colds of a monsoonal character.
~ Ear.lier we made the assumption that such coolings, usually local, are associated
witli circulation conditions forming in the Arctic and in all probability caused
by tile distribution of polar ice in periods when i-Ls volume was relatively small.
This increases meridional transfers, at definite longitudes creating advection
~ Erom t11e Arctic, and at others either advection of heat, or at the longitudes
of sectors with a small quantity of ice, an intensification of monsoonal phenomena
' on the temperate-latitude continents in winter. For the cansidered cases this is
in general confirmed.
Tltus, secular and intr.asecular fluctuations of climate are frequently, although
not :lw is the
scattering asymmetry factoi, ~Cx is spectral optical thickness,
~
[B = air] ~9 P~� ~ zX L yi. P�) dz. (3)
I As thz boundary condition for F~~ at the underlying surface we used the reflection
1 condition, at the upper boundary (10 km) the equality of the descending flux to
the value I,>, cos M, where I is the solar constant, cos � is the solar zenith
angle, which was computed as a function of latitude, season of the year and time
of day.
' In [13] the spectrum of absorption of solar radiation by vapor was broken down into
two sectors with large and small vapor absorption coefficients. The coefficients of
' absorption and scattering of droplet water were not dependent on time. In this com-
munication spectral computations were made for 32 wavelengths, taking into ac-
; count the eight principal absorption bands in the interval 0.4-4 � m(see Table 1).
For the coefficients of scattering U'AL and absorption �CAL we used analytical ex-
pressions obtained in [12) for the spectra of droplets in the form of gamma dis-
tributions. For this purpose the computed droplet spectra in each time interval
were approximated by gamma distributions whose signif icant parameters were then
siibstituted into the formulas from [12]. The intensity and profile of the effective
fluxes of solar radiation, computed by this method, were close to those observed
under cloudy conditions with corresponding solar altitudes [5, 6, 8].
As in [2], the initial relative humidity in the boundary layer was considered con-
stant and temperature was considered as decreasing linearly with altitude; droplet
water was absent. If at some altitude humidity for the first time attains satura-
tion, Nm of condensation nuclei is activated and the droplet phase is formed.
Evolution of Clouds Over Snow
In modeling the albedo of snow was considered equal to 80%; solar altitude was com-
puted for the latitude of Kiev for 21 March and 21 December. Qualitatively both
cases arP similar; in the first of them the amplitude of the diurnal variations
is greater. The initial conditions are as follows: geostrophic wind 10 m/sec, rela-
tive humidity in the boundary layer constant and equal to 90%, surface temperature
5�C and decreases with altitude with a gradient 6�C/km. Humidity at the surface
was equal to the saturating humidity over ice. Calculations begin at 0350 hours.
Tlie evolution of tlie t'1BI. i.s illustrated in Fig. 2. Due to long-wave radiazion
cooling the surface temperature decreases by 6�C.at 0400 hours, the turbulence
coefficient k decreases (maximum value from 9 to 4 m2/sec) and relative humid-
ity increases. At 0810 hours at an altitude of 300 m a cloud is generated and the
long-wave radiation balance at the surface decreases sharply. At 0820 hours (here
and in the text which follows the time is astronomical) the sun rises, but the
total radiation balance Ro remains negative for a period of a half-hour (cooling
cantinues). At 0855 Ro changes sign, the surface temperature rises, the thickness
of the ALL and ttir.hulent exchange increase, the k maximum at 1200-1400 hours is
at an altitude 200 m and increases by a factor of almost 10, attaining 35 m2/sec.
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The increase in the solar and total radiation balances continues to midday; the
temperature increase continues to 1400 hours. This is followed by onset of surface
cooling, although Rp is still positive. The reason is that now the soil surface,
covered with snow, is warmer than the deeper soil layers. Such a temperature gra-
dient arises in ttie soil that with these solar altitudes the radiation balance no
longer can compensate for the flux of heat from the surface into the depths of the
soil. Beginning at this moment turbulent exchange again begins to decrease.
zM
750
60C
callcm2�sec
450 J Kan
Ro:P.,,Rs10 CMt,C
300 F 2
950 1 S
4, 0
0 T 6B 0 '
6 B
166 2
~ 764
~ 262 2 � -
10'---
1
lp
9
term tdays
18 20
Fig. 2. Evolution of ineteorological parameters in ABL. Computations for latitude
of Kiev, 21 December. 1) long-wave balance RL; 2) short-wave balance Rg: 3) total
balance RO; 4) surface temperature TO; 5z altitude of maximum of turbulence coef-
ficient, the figures are its values in m~/sec; 6 and 7) altitudes of the lower
and upper cloud boundaries; 8) altitude of maximum liquid-water content, the fig-
ures represent its value in g/kg.
r1n i.ncrease in cloud thickness occurs during the course of the entire day, for the
most part clue to upward incrFase. The linuid-water maximum is in the upper part of
_ the cloud, which is caused by radiation cooling. Beginning with 1700-1800 hours
there is a stabilization of the ABL and clouds. This quasistationary state is as-
sociated with the blocking effect of the inversion over the upper boundary and
' the fact that the total heat balance at the surface is close to zero.
The effect of heating and additional turbulence of the ABL in winter over the snow
is observed only in the presence of a cloud. jdith the modeling of cloud dissipation
by descending vertical movements [4] under these same conditions it was discovered
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that after tY:e disappearance of a cloud even at the midday hours the negative
long-wave balance is greater than the solar balance so that the total radiation
baiance is negative (high albedo and low sun), a temperature inversion develops
and turbulence decreases.
a) ZN b) z,a
600 600
ari r
~~~r~
.SG
V "r z d
~ � ~
L ~ t
~a'~~.oa 1G9 �i.~~ ;'Q~
I � \1 , . , u ~ I \_1'r . 'r , -1
0 J SN,10lt~' J 1 J,~I.IOt
16 1,8 Z,0 0 01 0,1 q, z/Kt;q:lRz g/kg J Q1 QZq t/Ra $~tg
-1 -0,5 0 2 f 6rMRn,("t~ OC/sec G 1 4 PHNM m
~611E1 T64 T'C 161 16G
, .2 0 1 Z J 9 d,10'`r1"KZ g/kg -z 't;c 6C/sec
:~1.k8 -~,o -o,s ~ ~ 1,..~p� cis �C/sec
9,6 1,0 g/kg
Fig. 3. Vertical sections of cloud after two hours of development. a), without al-
lowance for solar radiation; b) with allowance for solar radiation (latitude of
Kiev, 21 March), T is temperature; q is humidity; qL is liquid-water content; N and
r are the concentration and mean radius of the droplets;,6 is supersaturation;
(d T/d t) t , (d T/d t)g, (d T/d T)rad
are the rates of long-wave, solar and total radiation changes of temperature.
Thus, under winter conditions cloud cover exerts a warming effect (greenhouse ef-
fect), screening long-wave radiation and transmitting solar radiation.
The influence of solar radiatfon on cloud development is illustrated in Fig. 3. The
extremal values of the long-wave and solar influxes are attained almost at the same
al.titude, SO m below the upper cloud boundary, but the second of them is much less.
A positive solar influx partially compensates radiation cooling in the upper part
of the cloud; here there is a decrease in the condensation rate, liquid-water con-
tent maximum and total influx. Solar radiation exerts the most important influence
on the lower part of ttie cloud. As a result of a temperature increase and a de-
crease in undersaturation at the snow surface the lower boundary of the cloud drops
down. Radiation heating in the lower part of the cloud, caused by the total effect
of long- and sliort-wave radiation, is now twice as great; its maximum is close to
0.2 degree/hour and is attained at an altitude of 120 m over the lower cloud boun-
dary. The lower two-thirds of the cloud exist in an undersaturation state because
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greater heating causes more intensive evaporation in the lower part of the cloud.
Since small droplets evaporate more rapidly, this leads to an increase in the
mean size of droplets by 20-30%. Zdhereas in the absence of the sun the mean radi-
us of the droplets has a tendency to an increase with altitude (Fig. 3a), in the
presence of solar radiation the mean radius has a distinct maximum in the lower
part of the cloud (Fig. 3b), caused by more intense evaporation. Due to turbulent
mixing, in the upper part of the clo ud the size of the droplets increases by 10-
15% and their concentration decreases.
Thus, solar radiation intensifies the pattern of existence of a cloud in a state
of dynamic equilibrium: in its upper third condensation transpires, whereas
evaporation transpires in the lower two-thirds. The close correlation between ra-
diation and microphysical characteristics leads to the following: in the presence
of solar radiation a cloud over snow is somewhat "drawn" downward; the liquid-
water content in it decreases and it is redistributed from small to larger drop-
lets.
Such a change in the microstructure of a cloud causes a change in its radiation
characteristics. Table 1 gives the, spectral coefficients of scattering and ab-
sorption obtained using the formulas from [12] using the spectra of droplets
computed at an altitude of 300 m at two moments in time.
The decrease (almost by a factor of 2) in the scattering coefficients in the en-
tire spectral region and the absorption coefficients in the bands X and 3.2 was
caused by an increase in the mean radius of the droplets at this altitude from
- 4.4 to 9.8~cm and emphasizes the need for joint computation of the radiation and
microphysical characteristics. The constancy of oeXL in the case of weak absorp-
tion is attributable to their nondependence on the spectrum of droplets [2, 121.
An interesting problem is that of the contribution of the radiation factor to the
energetics of a cloud, especially in connection with the recently arising discus-
sion of the role of radiation in the dynamics of cloud formation [7, lO]. Table
2 represents the temporal variation of the rates of temperature change due to the
heat influxes: long-wave (a T/J t),t , solar (aT/J t)s, phase (d T/ dt)cond, tur-
bulent (3 T/3 t)ed and 'total velocity (3 T/ a t)tot at the altitude z, where radi-
ation cooling is maximum (under the upper boundary). In the morning hours long-
wave cooling and the negative turbulent influx caused by a temperature inversion
- are compensated hy only 20% by the heat of condensation so that the total rate of
cooling is greater than 3�C/hour. By midday the heating of the surface and the re-
structuring of temperature stratification lead to a change in the sign.of the tur-
b�lent influx, whicli together with the phase and increasing solar influx to a con-
siderable degree compensates long-wave cooling. At 1400 hours the total rate of
cooling is less than 0.4�C/hour, that is, an order of magnitude less than the long-
wave cooling. Table 2 is also an answer to the question raised in [10] concerning
the mechanisms of smoothing of the powerful "thermal well" formed by a cloud rela-
- tive to long-wave radiation. [Jith a decrease in solar altitude and surface temper-
ature the turbulent heating decreases and the total rate of cooling increases We
note that in the modeled situation ttie role of solar radiation is reduced for tiLe
most part to an increase in the radiation balance at the surface; the direct ab-
sorption of solar radiation in a cloud is small in comparison with other types of
influx.
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I
Table 1
' Coefficients of Scattering (Numerator) and Absorption (Denominator)
; of Solar Radiation by Droplets in cm2/g
~ R7nrl
r ~ u I
0.8 E, I
pa- (
Qi (
4' I
Q I
,l' I
3,2
I
362
=
2364
2364
2367
2353
2314
1281
1184
0850 h r
0,018
0,0~15
0,22
0,8i
l~,y
69
l149
1180
1401
1401
1401
1402
13b9
1336
711
701
1250 hr:, 0,018
i
0,018
i
0.22
0,87
1S.S
tib
7W
7tk1
Table 2
Temporal Variation of Different lieat Influxes (�C/hour) at Level of Maximum
Radiation Cooling
8.5
~ 10
aaly n
~ 12
rs
~ 14
I 18
zAc
(dTldl),
300
-3.96
950
-3,56
540
-3,04
630
-3,93
840
-3
19
(dT;dt)s
0,08
0,34
0,45
0
36
,
-
(t7T/dt)cnna
1.21
1,01
0,68
,
1,15
88
0
(aTid!)ed
-0,94
-0.23
0,61
2.04
,
1
23
(c7T!d1)lor
-3,11
-2,44
-1.30
-0.38
,
-1,08
Table 3
Temporal Variation of Temperature (�C) and Its Rate of Change (�C/hour) at Lower
Cloud Boundary
I 8.5
~ 10
I2
~ 14 ~
IS
~ 16 (
18
Tlow bound �C I
(dT, Jt );,,t
-10,38
--0.96
I-10,03
1 ,12
I7,28
0.952
I-6,07 I
0.312
-5.91 I
-0.02~1
6,06 I
-0.264
-6.4I
-0. I I 4
We note that the maximum value of the solar influx in a cloud of 0.45�C/hour (Table
2) for the variant of 21 December with a solar altitude hs = 15.5� and a maximum
value 0.74�C/hour, obtained in the variant tor 21 March with hg = 30�, agree fairly
well with the measured values 0.63�C/hour with hS = 40� from [5] and 0.8-1�C/hour
with hs = 26� from [8]. This agreement is evidence of a satisfactory accuracy of
the method used for computing solar radiation.
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Changes in the temperature of the lower cloud boundary are determined for the most
part by variations of tlic radiation balance at the surface. Tliis is illustruted by
Tabl.c 3. In thc morning hours Tlow bound drors down, wliich is associated with a
a temperature inversion in the layer below the clouds. An increase in Tlow bound
begins with heating of the surface at the time cif sunrise. According to our com-
putations, the total rate of heating due to long- and short-wave radiation (which
" is attained at 50-70 m above the lower boundary) does not exceed 0.15�C/hour, that
is, the increase in temperature at the lower boundary is almost completely attrib-
utable to the turbulent heat influx from the surface.
Table 3 shocas that it is maximum at 1000 hours when the temperature gradients iri
the surface layer are ma.ximum and decreases with an evening-out of temperature in
the layer below the clouds. After 1500 hours, up to the next sunrise, Tlow bound
drops down.
In [7], on the basis of data from aircraft sounding, it was demonstrated that the
correlation of temperature change after 12 hours at the upper Q TuP and lower
,6 Tlow bound boundaries of St-Sc is positive, although it is known [8] that the
radiation changes of temperature near the upper and lower boundaries have differ-
ent signs and the conclusion was drawn that radiation plays a small role in com-
parison with advection and vertical currents.
In our case, as can be seen from a comparison of Table 2 and 3, the signs on dTuP/
3 t and d Tlow bound/a t in the first hour after cloud generation are identical,
before 1500 hours are different and after 1500 hours are again identical. As fol-
lows from what was stated above, the different signs on a Tlow bound and d TuP
at the near-midday hours are related to the turrulent influx of heat near the
lower boundary from the underlying surface, and not to an increase in radiation
heating caused by solar radiation.
Thus, different signs apply to ,6TuP and 6 T only in the course of 20% of the day
and therefore with the use of sounding data each 12 hours, as in [7], the proba-
bility of positive correlations of 6Tlow bound and Q Tup is greater than the
probability of negative correlations.
In addition, some time after the formation of a cloud there will be relative stabil-
ization of the ABL and the diurnal variations of temperature caused by short- and
long-coave radiation are relatively small, as is indicated by the surface tempera-
ture curve in Fig. 2, after 1100-1200 hours, i.e., af ter 3-4 hours of cloud devel-
opment when the ABL has been transformed from cloudless conditions to cloudy condi-
tions. Table 3 sliows that from 1200 to 1500 hours L1Tlow bound is less than 1.40C,
- and from 1500 to 1800 hours 6Tlow bound =-0.5�C. The temperature difference after
12 tiours c:!n be still less since the signs on 4 Tlow bound to the time of attain-
ing the maximum Tlow bound (1400-1500 hours) and thereafter are opposite. Accord-
ingly, the changes of Tlow bound, identical i.n sign with the changes Tup and
caused by advection and ascending vertical movements, as was noted correctly in
[7], can be greater than the changes caused by diurnal variation.
These computations siiow that at least in the absence of vertical movements the ex-
istence of a positive correlation between 6Tup and ATlow bound by no means is
evidence of a negligible role of radiation in the formation and energetics of
stratified clouds (Table 2).
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We note further that the role of radiation in the formation o� a temperature in-
version over lower-level clouds is entirely comparable with the role of vertical
movements. An inversion is formed due to radiation and in the absence of ver-
tical movements (Fig. 3). The modeling of the evolution of clouds with allowance
for radiation and vertical movements [11] indicated that in the absence of ver-
tical velocities the intensity of the inversion is 6T= 2.5�C when there are
descending movements (-1 cm/sec) LT = 5.5�C. Ascending movements in the absence
of radiation should lead to complete disappearance of the inversion, but with al-
lowance for radiation the inversion persists (Fig. 2 in [111).
z
,o
a~
cal
c � 6
S e ran
9
,
%,0
ZBd
1
0-US �
.
Ob/10 0630 0650 hrs
Fig. 4. Dispersal of fog over dry soil after sunrise (latitude of Kiev, 21 Sep-
tember). Solid curves isolines of liquid-water content, the figures near them
represent the liquid-water content in g/kg; T is soil temperature; Rp is the ra-
diation balance at the surface; hg is solar altitude.
Table 4
Rates of Temperature Change (�C/hour) Radiation (Numerator), Total (Denominator)
at Altitudes 10 and 50 m
.i
,
0 1
0620 hrs 10630 hrs 0640 hr:
10 ( ~JT `Jt )r:id ;
-I.-4:i
-I.0$ Q.?? ~ 0.10
~(!)T
-0,05
0.41
''.UG 3.85 ! ;3,92
50 ! (dT;Jt)rad ~
-1.82
~ -3.:.~?
-3.40 i -3.81 j -1.42
' (dTldt)t�, ~
-1,74
-0.95
' 0.27 1.83 2,99
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It follows from everything stated above that the radiation factor exerts a very
significant influence on the dynamics of at least lower-level clouds and that it
must be taken into account in numerical models together with other factors in-
volved in cloud for.mation, the importance of wlrtch i.s mentioned in [7]: turbulcnt
exchange and vertical currents.
Dispersal of Radiation Fog at Sunrise
The computations were made when there was a geostrophic wind of 3 m/sec, an in-
itial humidity of 90%, over dry soil (albedo 25%) for a solar altitude at the
latitude of Kiev on 21 September. The calculations began at a time corresponding
to 0300 hours. Under these conditions the formation of a fog begins an hour after
the onset of the calculations and after three hours of calculations its thickness
is 60 m. The sun rises at this time, corresponding to 0600 hours. Evolution of the
fog is illustrated in Fig. 4. The dispersal begins from below; the detachment of
the lower boundary (isoline "0") from the earth occurs after 20 minutes, the fog
is transformed into a cloud, which thins out, both its boundaries move upward
and after 30 minutes come together at an altitude of 75 m, that is, full dispersal
occurs 50 minutes after sunrise when the altitude is 7�. In this process there is
a predominance of evaporation from below, whereas for some time cooling and con-
densation continue near the upper boundary and therefore in the process prior to
fog dispersal it rises by 15 m. T-he solar influx in the fog layer is extremely
small and constitutes less than 7% of the long-wave influx.
An interesting effect is observed in the behavior of the radiation balance (Fig. 4).
Its increase, caused by sunrise, when t= 0630 hours, is replaced by a dropoff. The
reason for this is that by this moment there is a great decrease in the optical
thickness of the fog and an increase in the negative long-wave balance. Then, when
the sun rises above the horizon, the short-wave balance increases more rapidly than
the long-wave balance and the total balance again inereases.
The contribution of the radiation factor to the energetics of fog dispersal is
illustrated 4 n Table 4. It follocas from tliis that at an altitude of 10 m after 10
minutes and at an altitude of 50 m 20 minutes after sunrise heating will begin,
that is, the positive turbulent heat inFlux from the surface will be greater than
the sum of radiation cooling and the expenditures of heat on evaporation.
Thus, in the dispersal of a fog by the sun the main role is played by an increase
in the radiation balance, heating of the soil and turbulent transfer of heat up-
ward and the direct absorption of solar radiation by droplets plays a secondary
role. This circumstance is confirmed by observational data [14].
1'he authors of [31 made computations of
fluence, wliich was modeled by adding to
to the short-wave balance and close to i
fog evolution is qualitatively similar t
' principal stages are the same as in Fig.
its rising, thinning and evaporation.
the evolution of a fog under a thermal in-
the heat balance equation a term similar
t in value. In this case the pattern of
o the evolution of a fog at sunrise. Its
4: transformation of a fog into a cloud,
48
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For dispersal the minimum value of the additional (short-wave) balance should ex-
ceed the value of the long-wave balance by a factor of 3-4; otherwise there will
be a restructuring of the fog without dispersal [3]. This condition can be used in
predicti.nK the f.act of Eog dispersa]. after sunrise when there are measurement dr:tn
far the long- and short-wave balances. If the initial thickness of the fog is suf-
ficiently great 100 m) and the short-wave balance is small, after its transform-
ation into a cloud the rising of the lower cloud boundary, caused by solar heating,
and the rising of the upper boundary, caused by long-wave cooling, occur with an
identical rate [3]. Thus, the appearance of the sun in the morning hours in autumn
or spring may not lead to fog dispersal, but its transformation into low stratiform
cloud cover, as agrees with observational data.
BIBLIOGRAPHY
1. Buykov, M. V., CHISLENNOYE MODELIROVANIYE OBLAKOV SLOISTYKH FORM (Numerical
Modeling of Stratiform Clouds), Obninsk, 1978.
2. Buykov, M. V. and Khvorost'yanov, V. I., "Formation and Evolution of a Radia-
tion Fog and Stratiform Cloud Cover in the Atmospheric Boundary Layer," IZV.
AN SSSR: FIZIKA ATMOSFERY I OKEANA (News of the USSR Academy of Sciences:
Physics of the Atmosphere and Ocean), Vol 13, No 4, 1977.
i
; 3. Buykov, M. V. and Khvorost'yanov, V. I., "Modeling of Fog Modification by a
~ Thermal Method," TRUDY UkrNIGMI (Transactions of the Ukrainian Scientific
~ Research Hydrometeorological Institute), No 161, 1978.
I 4. Buykov, M. V. and Khvorost'yanov, V. i., "Modeling of the Process of Restora-
tion of Stratiform Clouds After Artificial Dispersal," TRUDY UkrNIGMI (Transac-
tions of the Ukrainian Scientific Research Hydrometeorological Institute), No
j 185, 1981.
5. Goysa, N. I. and Shoshin, V. M., "Experimental Model of the Radiation Regime
of an 'Average' Stratiform Cloud," TRUDY UkrNIGMI, No 82, 1969.
~
6. Kondrat'yev, K. Ya., Gayevskaya, G. N. and Nikol'skiy, G. A., "Influence of
Cloud Cover on Short-[Jave Radiation Fluxes in the Troposphere and Strato-
sphere," RADIATSIONNYYE PROTSESSY V ATMOSFERE I NA ZEMNOY POVERKHNOSTI. MATER-
IALY X VSESOYUZNOGO SOVESHCHANIYA PO AKTINOMETRII (Radiation Processes in the
Atmosphere and at tlie Earth's Surface. Materials of the Tenth All-Union Con-
ference on Actinometry), Leningrad, Gidrometeoizdat, 1979.
7. Matveyev, L. T., "Reasons for the Formation of Clouds," METEOROLOGIYA I GIDRO-
LOGIYA (Meteorology and Hydrology), No 8, 1978.
8. POLNYY RADIATSIONNXY EKSPERIMENT (Full Radiation Experiment), Leningrad, Gidro-
meteoizdat, 1976.
9. Feygel'son, Ye. M. and Krasnokutskaya, L. D., POTOKI SOLNECHNOGO IZLUCHENIYA
I OBI,AKA (Solar Kadiation Fluxes and Clouds), Leningrad, Gidrometeoizdat, 1978.
49
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10. Feygel'son, Ye. M., "Role of Radiation in the Formation of Stratiform
Clouds," METEOROLOGIYA I GIDROLOGIYA, No 8, 1979.

11. Khvorost,yanov, V. I., Feedbacks Between Turbulence, Vertical Currents and
Cloud Cover in the Atmospheric Boundary Layer," IZV. AN SSSR: FI7.IKA ATMOSFERY
Z OKEANA, Vol 15, No 8, 1979.
12. Khvorostlyanov, V. I., "Approximate Computations of the Scattering and Absorp-
tion Coefficients for Short-Wave Radiation by Clouds," RADIATSIYA V OBLACHNOY
AITSOSFERE (Radiation in the Cloudy Atmosphere), Leningrad, Gidrometeoizdat,
1981.
13. Herman, G. and Goody, R., "Formation and Persistence of Summertime Arctic
Stratus Clouds," J. ATMOS. SCI., Vol 33, No 4, 1976.
14. Jiusto, J. E. and Garland, L. G., "Thermodynamics of Radiation Fog Formation
and Dissipation," J. RECH. ATMOS., Vol 13, No 4, 1979.
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UDC 551.(510.534+507.362)
MODELIilG OF AN A PRIORI ENSEPIBLE OF SOLUTIONS OF THE INVERSE PROBLEM AND STABILITY
OF OPTITNM PLANS FOR AN OZONE SATELLITE EXPERIiIENT
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 81 pp 45-51
[Article by M. S. Biryulina, Leningrad State University, manuscript received
s .rui so ]
[Text] Abstract: The article gives computations of the
optimum plans for an ozone satellite experiment
for different latitudes and seasons for the pur-
pose of checking their stability. The basis for
the computations was model a priori covariation
matrices of the ozone profiles, the method for
iihose construction is described and substantiat-
ed. It is shown that optimum two- and three-chan-
nel schemes for an ozone satellite experiment
must not have appreciable seasonal and latitud-
inal variations.
Satellite methods for obtaining information on the atmospheric content of ozone have
become especially timely during recent years, in particular, in connection with pos-
sible variations of the ozone layer as a result of natural and anthropogenic changes
in atmospheric composition [8, 11]. The need for obtaining global information on the
characteristics of the ozonosphere associated with this has stimulated the develop-
ment of special satellite methods for determining ozone content based on the inter-
polation of data on outgoing atmospheric radiation in different spectral ranges.
_ In earlier studies [6, 7] we evaluated the theoretical possibilities of indirect
methods for restoring the vertical profile and total content of ozone for different
satellite schemes: IR method (band 9.6[,1.m), W method (backscattering), joint use
of the IR method with the heterodyne or UV method. These very same studies gave
recommendations for creating the corresponding specialized satellite instruments
based on optimization of the scheme for measurements in the IR spectral range by
the V. P. Kozlov method [2, 3]. Computations of the designs of these instruments
were made using a priari statistics for ozone profiles for the conditions prevailing
in Berlin [10]. However, it is known [4, 5] that the optimum conditions for satel-
lite measurements for other meteorological parameters, computed by the Kozlov meth-
od, are dependent on the statistics used. In this connection it seems important to
clarify the applicability and effectiveness of the proposed optimum schemes of an
uzone experiment for other sounding conditions other latitudes and seasons.
This article is devoted to this subject.
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The lack of a sufficient quantity of information on the statistical characteris-
tics of ozone distribution in the atmosphere for different regions of the earth
makes solution of the formulated problem difficult. Under these conditions a solu-
tion was obtained by using model a priori covariation matrices of the ozone pro-
files Kqq,
- One of the well-known methods for modeling covariation matrices is constructing ele-
ments of the matrix using a formula from [1]
KQ, = 3, (9) (4) exf) I Z,. l
(1)
where Kii is an element of the matrix with the superscripts i, j; C_i(q) and O"j(q)
are theQgtandard variations of ozone content at the i-th and j-th levels in the at-
mosphere; zi and zj are the altitudes of the i-th and j-th levels; r is a parameter
of the model.
It can be shown rigorously that the use of a priori covariation matrices of such a
type in the algorithm for the statistical regularizatioi; method is equivalent to
application of the first-order Tikhonov regularizstion n2thod to soiution of the
inverse problem. Thus, the proposed method for modeling the Kqq matrices is to.an
adequate degree theoretically substantiated.
[de selected the following criterion for a correct evaluation of the r parameter:
dispersion of the total ozone content ensured by a model matrix in accordance with
the formula
- zn zo
`K,,q (zt, zj) dzt dsj (2)
(C~rU is the dispersion of the total ozone content; Kqq(zi, z~)= K1J) coincides with
the real dispersion of ttie total content at a given point on the garth for a par-
ticular season.
The modeling method which we selected (formula (1) plus the criterion of evaluation
- of the r parameter) was checked for the conditions prevailing in Berlin, for which,
as we have already mentioned, we had natural covariation matrices.for ozone. In this
case equation (2) for evaluating the r parameter assumes the form
(Ii+ zi) dzf dzj k'qo (zi, 21) dz; dsi,
(2a)
~
c.llere I:qq is the real covariation matrix of ozone and KQq is the model covariation
mz3tris of ozone.
[1s an evaluation oE experimental accuracy, as usual [6, 7], we used the value
~,,1. 1~~ (3)
pwhere "f'y(p) is the natural standard variation of ozone concentration at the level
1) (corresponding to the a priori matrix Kqq), cTq(p) is the mean square error of
restoration at this same level (corresponding to the residual covar.iation matrix
A
_ Kycl).
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~g p
,
~
i
_ ~T
Fig. 1.. Vertical variation of parameter
5pq(p )(p in millibars ) fo r simnmer con-
ditions in Berlin region.
c?~
Fig. 2. First (a), second (b) and third
(c) eigenvectors of Kozlov informational
operator for summer in tne Berlin region.
(real a priori sLatistics).
In the case of use of so-called "extraneous" statistics (in our case the model
- statistics Kqq) a formula is known [6, 71 for the residual covariation matrix
which is transformed to the form
n "
Ky,, - K,~~r �4T ~aK~nr AT ~ S)-1 AK~~v - 9 K,~Q, . (4)
where j K�q (1- ,Y.41T A K,l,, - ICA).
(4a)
Here A is an operator of the direct problem; R is a decision operator of the prob-
lem; Z is the covariation matrix of ineasurement errors; I is a unit operator; Q Kqq
_ is the deviation of the used a priori statistics from the true statistics
K,i,, = ti qq - Kqv) i

L~K is the correction to the residual covariation matrix caused by inadequacy of
theqa priori statistics; T is the transposition symbol.
Figure 1 shows the vertical variation of ?q(p) for three cases: 1) the true
a priori statistics; 2) model a priori covariation matrix; 3) same as (2), but with-
out allowance for the correction dqq for the inadequacy of the a priori statistics.
The curves are shown for a level of inean square measurement error O'I erg/cm2�spe�
sr�cm 1).
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The closeness of all three curves in the figure indicates that a model covaria-
tion matrix of the type (1) quite well represents the real a priori statistical
ensemble of ozone profiles (the 4a correction is small) and can be used with a
good degree of accuracy without taking this correction into account.
Now we will discuss the informational content of the experiment. In the V. P. Koz-
lov method it is determined by the information volume, which characterizes the
number of states of the object distinguishable in the experiment:
V n;.i
,_i
(5)
where Ai are the eigenvalues of the Kozlov informational operator C= Z'1 AKqqAT
and are greater than unity (k is the number of the last of such eigenvalues).
- The computations indicated that for all schemes of the IR experiment ("full" ex-
periment, optimum two- or three-channel instrument see [6]) the V value (for
any persists well when using in the iiiformational operator C the mode], matrix
Kqq. Moreover, as indicated by Table 1, the eigenvaiues a i themselves, and not
only their product, persist with a good accuracy. At the same time, the eigenvec-
tors of the C operator, on the basis of which the optimum plan of the experiment
is computed by the Kozlov method [3], also virtually do not change. Figure 2 shows
the first three eigenvectors of the C operator for summer conditions in Berlin
with the use of a real covariation matrix. The corresponding vectors for the model
matrix within the limits of accuracy of the figure do not differ from those shown.
The optimum plans, computed on the basis of these vectors, completely coincide.
Their configuration is illustrated in [6].
Table 1
Comparison of Eigenvalues of C Operator (rJ'I = 1) erg/(cm2�sec�sr�cm 1))
- and Values of Information Volume for Real and Model A Priori Statistics for
Berlin, Summer, m is the Number of Sounding Channels
~
~
I
SttltiS-
%.x
~
' %..v

C~
roi
U
m I
bD U~
U) V: 1
I
U
t1CS
I
-
N
N
~
i II
~
�
U
~
n
20
KIN I
41.35
0.3694
0.3161� 10-=
6
391
%,I,,
92.46
O,a 10:i
0,3211 � I U-=
6
417
I
&
1945
10.53
0,2913� 10-1
193
24430
'
h'qq I
1975
11.75
0,3603 �10-1
152
24580
We limited ourselves to a discussion only of the first three eigenvectors of the
Kozlov informational operator on the basis that the optimum scheme for an ozone
satellite experiment in the IR spectral range with the modern level of ineasure-
ment errors includes not more than three registry channels [6]. If one continues
the comparison of the eigenvectors and the numbers of the C operator for real and
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model a priori statistics, it is possible to confirm their close coincidence to
~ the sixth number inclusive (we did not examine eigenvectors and numbers at higher
~ levels). This f act once again confirms the representativeness of the model covari-
ation matrix (1) and the reliability of the optimum plans for an ozone satellite
experiment determined on its basis.
Fig. 3. First (a), second (b) and third (c) eigenvectors of Kozlov informational
operator for northern part of western hemisphere. 1) 50�, summer; 2) 50�,
winter; 3) tr = 20�, summer; 4) ~0= 80�, winter.
Similar computations made for other seasons iti the Berlin region gave similar re-
sults.
The results of study of the possibility of modeling of the covariation matrices of
ozone on the basis of formula (1) for the conditions prevailing at Berlin made it
possible to proceed to modeling of the a priori statistics for other regions of
the earth for the purpose of checking the stability of optimum schemes for an
ozone satellite experiment.
For tliis purpose we used data in [12], which gives the latitudinal variation (with
a 10� interval) of the mean seasonal vertical ozone prof iles for the northern part
of the western hemispliere with the corresponding standard variations. On the basis
of these data, and also data on the total ozone content taken from [9] (by means
oE statistical processing of a sample of values of the total content it was pos-
sible to ascertain tlie C'U value), using the scheme described above we computed
the eigenvalues and eigenvecto rs of the operator C= Y-,-1 AKqq AT for SP= 20�N,
(summer), 50�N (summer and winter) and 80�N (winter) (in our opinion, the most rep-
resentative situations). Figure 3 shows the first three eigenvectors of the C
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� � ~,l f
a )
. /
,

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operator for the mentioned conditions. The figure shows that they are extremely
close with respect to the nature of the change and the vectors for the middle lat-
itucies (summer) virtually do not differ from tlie cor.responding Berl.in vectors (r;ee
FIg. 2). Tlie ltpL1.I1111I11 I,.lrm:;, comj)uLcd Cqr .i1l four considered siluarIons, coLnc(cle
witli one zinotlier LlI1CI with the optimum plans obtained earlier for the conditians
prevailing in Berlin [6]. [The author expresses appreciation to V. P. Kozlov, who
undertook these computations.]
Table 2
FUR OFN7CIA1. USE ONLY
Values of Informational Volume of Ozone Satellite
Experiment for Different Latitudes and Seasons
for Two Levels of Measurement Errors
(Three-Channel Optimum Instruments)
North latitude, season I VUI = 1
erg/(cm2�sec�sr�cm 1) V oi _
.92
177
240
133
0.1 erg/(cm2�sec�sr�cm 1)
20�, summer
50�, sununer
50�, winter
80�, winter
30910
28110
30860
26400
Table 2 gives the values of the corresponding informational volumes of the satel-
lite experiment for two levels of ineasurement error with the use of an optimum
_ three-channel instrument. The table shows that the informational content of the
experiment has an insignificant latitudinal and seasonal variation (which is de-
pendent on the measurement error); the values of the informational volumes for the
middle latitudes of the northern part of the western hemisphere (summer) are close
_ to the corresponding values for Berlin (see Table 1).
The observed latitudinal and seasonal stability of the optimum plans for an ozone
satellite experiment (at least for the considered conditions) is directly related
to the circumstance that, as already mentioned, with the present-day level of
measurement error in the IR spectral range the optimum scheme for an ozone experi-
ment contains not more than three registry channels (the method makes it possible
to determine not more than two or three independent parameters of the ozone pro-
file). Already the fourth vector of the C operator has insignificant seasonal but
well-expressed latitudinal variations. However, the eigenvalue corresponding to
this vector has a value of about 10'4-10-5 with a measurement error O'I = 1 erg/
(cm2�sec�sr�cm 1). Thus, the inclusion of a fourth channel in the optimum scheme
is reasonable accordin to the Kozlov criterion with a measurement error level
not worse than 10'2-10'1 erg/(cm2�sec�sr�cm 1), which in the spectral region s-iz �m
cannot be realized at the present time. It follows from this that a three-channel
optimum scheme is some limiting case of an optimum scheme for the registry of
radiation in an ozone experiment, with respect to which one can hope for its sea-
sonal and latitudinal stability. With respect to a two-channel scheme, it is
known that it should not have significant seasonal and latitudinal variations.
Now we will concisely formulate the conclusions from the results of this study:
1) The mettiod for modeling of a priori covariation ma.trices of ozone proposed in
this study is theoretically substantiated;
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2) Model covariation matrices of the proposed type with a good accuracy describe
the a priori statistical ensemble of ozone profiles;
3) The known positive determinancy, symmetry and good conditionality of these
matrices and the small number of parameters by which they are described make it
possible to use them in the operational processing of satellite information;
4) Computations of the optimum plans for an ozone satellite experiment, carried out
on the basis of such matrices for different latitudes and seasons, indicated that
the optimum two- and three-channel schemes for an ozone experiment obtained in [6]
should not have significant seasonal and latitudinal variations.
In conclusion the author expresses appreciation to Yu. M. Timofeyev for consulta-
tions and attention to the work.
BIBLIOGRAPHY
1. Gandin, L. S., STATISTICHESKIYE METODY INTERPRETATSII METEOROLOGICHESKIKH
DANNYKH (Statistical Methods for the Interpretation of Meteorological Data),
Leningrad, Gidrometeoizdat, 1976.
2. Kozlov, V. P., "Numerical Restoration of the Vertical Temperature Profile From
the Spectrum of Outgoing Radiation and Optimization of the Measurement Method,"
IZV. AN SSSR: FIZIKA ATMOSFERY I OKEANA (News of the USSR Academy of Sciences:
Physics of the Atmosphere and Ocean), Vol 2, No 12, 1966.
3. Kozlov, V. P., "One Problem in the Optimum Planning of a Statistical Experi-
ment," TEORIYA VEROYATNOSTEY I YEYE PRIMENENIYE (Theory of Probabilities and
its Application), Vol 19, No 1, 1974.
4. Koslov, V. P., Timofeyev, Yu. M. and Kuznetsov, A. D., "Optimization of Condi-
tions for the rleasurement of Outgoing Radiation in the Problem of Indirect
Restoration of the Vertical jJater Vapor Profile," IZV. AN SSSR: FIZIKA ATMO-
SFERY I OICEAtdA, Vol 12, No 5, 1976.
5. Kozlov, V. P. and Timofeyev, Yu. M., "Optimum Conditions for Measuring Outgo-
ing Radiation in the C02 Absorption Bands and the Accuracy of the Method of
Thermal Sounding of the Atmosphere," IZV. AN SSSR: FIZIKA ATMOSFERY I OKEANA,
Vol 15, No 12, 1979.
6. Timofeyev, Yu. M., Biryulina, M. S. and Kozlov, V. P., "Accuracy in Determi:ning
the Atmospheric Ozone Content Using Data From Measurements of Outgoitig Radia-
tion," METEOROLOGIYA I GIDKOLOGIYA (Meteorology and Hydrology), No 3, 1980.
7. Timofeyev, Yu. M. and Biryulina, M. S., "Joint Use of Measurements of Outgoing
UV and IR Radiation for Restoring the Vertical Profile and Total Content of
Ozone," IZV. AN SSSR: I'IZIKA ATt�fOSFERY I OI'.EANA (in press).
, 8. Ilidalgo, H. and Crutzen, P. J., "The Tropospheric and Stratospheric Composition
_ Perturbed by NO Emission of High-Altitude Aircraft," JGR, Vol 82, No 37, 1977.
9. 0'LONE DATA FOR THE WORLD, Fish and Environ., Canada.
57
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10. Spankuch, D. and Dohler, [d., "Statistische Charakteristika der Vertikalpro-
file von Temperature und Ozon and Ihre I:reuzkorrelation uber Berlin," GEOD.
GEOPHY. VEROFF., R II, H 19, 1975.
11. Vupputuri, R. K., "Seasonal and Latitudinal Variations of CFXCLy (Freons) and
C1 (C1, C10, HC1) in the Stratosphere and Their Impact on Stratospheric Ozone
and Temperature," Downsview, Atmos. Environ. Service Contr., 1976.
12. Wilcox, R. W. and Belmont, A. D., "Ozone Concentration by Latitude, Altitude
- and Month Near 80�W," Contr. Data Corp. Res. Division, Rept. No FAA.-AEQ-77-13,
Aug 1977.
58
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UDC 551.510.522
EVALUATION OF ACCURACY IN DETERMINING TURBULENT FLUXES USING STANDARD
HYDROMETEOROLOGICAL MEASUREr1ENTS OVER TIIE SEA
Moscow PIETEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 81 pp 52-59
[Artic]_e by A. S. Gavrilov, candidate of physical and mathematical sciences, and
Yu. S. Petrov, Leningrad Hydrometeorological Inst:itute, manuscript received
21 .Ju 1 80]
[Text] Abstract: A quite simple model is proposed for comput-
ing the turbulent fluxes of heat, water vapor and mo-
mentum on the basis of data from standard shipboard
hydrometeorological measurements. It is based on the
use of experimental dependences for the universal func-
tions of similarity theory in the near-water layer. On
the basis of this model a quantitative analysis is made
of the relative errors in determining turbulent fluxes.
Three principal sources of errors are considered:
errors in standard measurements, inaccuracy in stipul-
ation of universal f unctions and incorrectness in the
parameterization of heat and moisture exchange in the
immediate neighborhood of the water surface. Analytical
expressions are derived for the corresponding weighting
coefficierts and computations are given for some mean
conditions.
The use of data from standard shipboard hydrometeorological measurements for com-
puting the turbulent fluxes of momentum, heat and water vapor in the near-water
layer is of great importance for the solution of many problems in-climatology and
weather forecasting, since only these data are available in a volume adequate for
statistical analysis. The successful use of mass material from standard measure-
ments requires a clear understanding of the accuracy with which at the present stage
information can be extracted from these data on the values of the mentioned turbu-
lent fluxes. One of the possible approaches to solution of this problem is develop-
ed in this investigation. .
The-basis for modern methods for computing turbulent fluxes of momentum, heat and
water vapor on the basis of ineasurements of wind velocity (u), potential tempera-
ture (T) and specific humidity (q) at two levels in the near-ground (near-water)
layer is the Monin-Obukhov similarity theory [2], asserting that the dimensionless
gradients of wind vel.ocity, temperature and humidity
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~z du ~s dT iz dq
dz ' 'I T ds , '4 - 0- (l)
Q R'
are universal functions of only one dimensionless variable
%z.T;Nf
' U-
.
(2)
Here 0.4 is the Karman constant, U* is dynamic velocity, T* _-Hp/U* is the
temperature scale, Q* _-Ep/U* is the humidity scale (Ho and ED are the vertical
kinematic turbulent fluxes of heat and specific humidity), )a = g/T is the buoyancy
parameter, M= 1+ 0.07/Bo is a factor taking into account the influence of humid-
ity stratification on the stability of the near-water layer, BO = cPHp/(L Ep) is the
= Bowen number (cP and L are the specific heat capacity of the air at a constant pres-
sure and the specific heat of vaporization respectively).
The universal functions ~Pu, 5'T, 4vq (C, ) have been repeatedly determined from ex-
perimental data (for example, see the reviews in [3, 4]). The general scatters of
experimentai values obtained by different authors under the most diverse conditions
approximately correspond to the discriminated regions in Fig. 1. The reason for
this scatter is not only possible measurement errors, the peculiarities of the
- employed instrumentation and the methods employed in carrying out the experiment,
but also, as is more important, the deviations from the main postulates of Monin-
_ Obukhov similarity theory, always existing under real conditions, caused by the
joint effect of the most different mechanisms, such as the nonstationary character
of the situation, radiation heat exchange, horizontal inhomogeneity and some others.
It goes without saying that in principle it is possible to formulate a similarity
theory for the surface layer taking into account at least the most important of the
enumerated factors by means of the introduction of some set of new dimensionless
parameters, but for all practical purposes for the use of such a theory there
must be additional extensive information exceeding the framework of data from stan-
dard measurements. Along these lines it is natural to examine this sort of devia-
tion as random and to assume that the universal f unctions of similarity theory CPu,
~PT and Yq are stipulated with some error.
For the universal f unctions we will use simple expressions adequately well approx-
imating the experimental data,
- f < 0

l 1 + 0;
(3)
- J x.; ( 1 - 20) =/-13 _L 14 , : % 0
~y _ .yT T 1 l ,
l 2:1 + 2i + a~') 0� (4)
The equality of the universal functions ~ and 50T follows f rom the usually surmis-
ed similarity of the temperature and humidity profiles in the near water layer, as
is confirmed in general by measurement data [3].
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~
~ The cited approximations for ~Pu, `f T and in the case of free convection
satisfy the "-1/3" law, following from Monin-Obukhov similarity theory.
In this sense they differ from the frequently used power-law expressions obtained
by different authors [3,4] on the basis of formal considerations.
The integration of (3) and (4) leads to quite simple expressions for the dimension-
' less functions of wind velocity and temperature:
; U 1 n z~ +z-~ 1+~arctg 2 x 3 1-~ C, C< 0
~ 1nC +�;2~;~C~~, C_0; (5)
a3 [ l n y~ j,'3 arctg 2y~3 I 1+ a4 ln 4
j 1~=
+
T�
+ Cy, ~ < 4 ( 6 )
~
� a3 a4 ln : a~-~ C:, ~ =0~
where C1, C2, C3, C4 are integration constants, x = (1 -a~~:)'~3 y
The determination of dynamic velocity, the turbulent fluxes of heat and humidity
requires data on wind velocity ua, potential temperature Ta and specific humidity
qa at some altitude za (the level of standard measurements). As the second measure-
ment level it is possible to use the water surface at which the temperature Tw is
stipulated and humidity is considered saturating. The procedure for determining the
fluxes is reduced to solution of the following equations which together with (5)
and (6) form a closed system:
U _ xua ~I
dUn ~ . .
7.*_ - "T (8)
aT '
n
Fig. 1. iJniversal functions in
similarity theory for surface
layer. 'fhe solicl ciirves approx-
imately limit the region of scat-
ter of experimental values using
clata f rom [ 3, 4]. Tlie da stied curves
zire for computations of the uni-
versal functions using (3) and (4).
Qw = A Tn ~

_cp~T
~o -
,
(10)
A
LAq
A T=TQ -Tw,
(11)
a 9 = 9a
(12)
A T" � Tn C~a) - TR (Co
(13)
A Un = Un \~J - Un (Cn),
(14)
CQ = zarl., ;n = z$:'L, V= Co/aT,
(15)
U; 0,07
L= x~ T* MI 1'I = 1~- Bo ~
(I~)
[H&C = sat]
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HOR ONFICIAL USF: ONI.Y
U=
zo=m g. (17)
Here the qsat(Tw) value is saturating specific humidity when T= Tw and is com--
puted usir.g one of the psychrometric formulas; the roughness level of the sea sur-
face zo is determined using the well-known Charnok formula (17) [1]', aT is some
correction factor, equal to the ratio of the roughness level for wind velocity to
the level at which the air temperature coincides with the temperature of the water
surface and humidity is saturating. The aT value can be regarded as a universal
constant only with a certain degree of approximation. It is possible to achieve a
greater accuracy in the description of the processes of heat and moisture exchange
near tle water surface by using finer methods for the parameterization of transfer
processes in this region, but for the purposes of this study the employed approach
is entirely acceptable.
Proceeding on the basis of the general formulation of the problem, it is possible
to discriminate three principal sources of errors arising in the computation of
turbulent fluxes in the near-water layer. First, these are ordinary errors in de-
termining ua, Ta, qa and TW in the process of carrying out standard shipboard ob-
servations, second, the inaccuracy in stipulating the universal functions SAu, 9T'
and third, ttie incorrectness of parameterization of the processes of heat and mois-
ture exchange directly at the water surf ace. Assuming that the latter two types of errors to a definite degree can characterize
the errors in stipulating the universal constants of the employed model, we will
write the following expressions for the relative variations of the sought-for tur-
bulence characteristics:
- ''U ~ - F~ + F;' F;,
t (18)
~H� = FT+ FT+Fa0
E� = F; + F� F3, (20)
E~
where for = u T ~u T %
� , , n : Fi = �9; u A-' T ~ A3 ~'9 q tif
4 Al'
S ba
fjZ
F1 =D.1 am DT.
z; - m aT
- t=t
tiere as a simPlification it was assumed that
a T = -i ; (A T), 9 9)�
Tlie F1 functions correspond to the first group of errors, FZF`-- to the second, and
F3 to the third. The determination of the weighting coefficients Ai Bi and Di
on the basis of whose value it is possible to judge concerning the relative contrib-
ution of different measurement errors and errors of the model to the total error of
the computed turbutent flux,is the principal goal of the reasonings which follow.
62
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FOR OFFIC'IAL USE ONI,ti'
! These coefficients, as functions of the stability parameter ~a and the To and IC T
parameters can be determined as a result of solution of a system of linear algebraQc
~ eqiiations derived by varying all the variables in the initial equations of the modei
(5)-(17), including the paxameters ua, Q T, 6q, M, cY i(i = 1,...,5) m and ar. Af-
ter some transformations it is thus possible to obtain:
; qu _ ~ T T�), A" _ ~ uR
,qu= 0, A4 = ~ A`;, B~ ,4i 1C,,
 B; =-.4a X, (i-2,. . 5)9
j - a
~ Tr
Du-~Y~~L' D2=-Aq9Tn'
I ~ n
o ~
K=[ 1+ a T,j - D Urt `'11 o T�
Here the following notations were used:
c~T = c~T (0) = a3 -f-aa,
:
o�
~
1 t'n a d r
M
X, = J Tn rfQ
d al>,
xj 4 Tn J' 5),
T [ 1 ]
Cp
wiiere i= 1 corresponds to unstable stratification, i= 2 corresponds to stable
stratificat:ion. The functions 50u, VT, 4 Un and L1Tn entering into the expres-
sions cited above are computed using formulas (3)-(6), (13) and (14). Quite
simple analytical expressions can be cbtained for the Xj parameters.
_ Similarlv it is possible to obtain the coefficients in expressions (19) and (20):
A~ =A~ -9Tn (3c?j.-~;T-{-AT~), A9=A?'-2,
A?'= (1-~AU�-3~~), A~=~~~, A3=1,
n
I- U � 2
_
Av a -'4~r -K a(/R ~Al Tn`1T .+..9UnOT~~~'y.-~TZu~ ,
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13y =8; =-ATX,,
Bq = BT = - AT
? Xt (l = l, . . . ~ 5),
Di -Di -~1 oU TRTA Un-F3 ~~T - :%Tnu)~~
n n
Do = Dz = _ A2 Fr
2
The weighting coefPicients are evaluated using some optimum values of the constants
Lx i, determined on the basis of the experimental data cited in Fig. 1. These values,
together with their relative errors following from an analysis of Fig. 1, are given
in Table 1. This table also gives the mean value of the m constant recommended in
[1] and its relative error.
~ a) ~ f��7.
a
) ~
?,0 - 3
C
3
P'ig. 2. Contribution of different mechanisms of generation of errors to total rel-
ative error in computing the parameters u* (a), Hp (b) and Ep (c) as function of
stability parameter 4 . 1) contribution of errors in standard measurements, 2)
contribution of errors in determination of universal functions, 3) errors as a re-
sult of incorrectness in description of the processes of heat and moisture exchange
directly at water surface.
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-O,B -0,6 -0,4 -0,2 0,0 41,2

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NUR OFFI('lAl. USI? ON1N
12 'toY_ O t-- t~ O M O S O
~ ri o o i i- i o o i
rn oo rn cl t.- o 00 ~4
^ Q C; -r o ~o o o
ro ~ ~I; ~ I I CO O O O O O
H
N
~
t~
N
04
~
~

~--I

.L~
Cd
1.1
cn
W
O
W
N
zi
~
4-1
G
~
~
41
~11
44
.H
Q
~
O
W
N
JJ
C.'
N
~
U

W
4-1
N
O
U
~o
~

JJ
.C
00

N
3
I
C
. ~ 1
X sin "H X.
With a known value aeff and def'_nite initial and boundary conditions solution (7)
determines the temperature field T= f(x, t) in the bottom deposits in dependence
on the depth of the layer x and time t.
Expression (7) can also be used for solving the invetse problem of determining
the coefficient of effective thermal diffusivity of the bottom material. The di-
rect purpose of this study is a determination of aeff� For this it is first neces-
sary to stipulate the temperature distribution in the bottom material f(x) in the
initial condition (4) and the temperature variation at the surface of the bottom
- deposits (t) in the boundary condition (5), or, as is the same, the variation
of the mean mass water temperature in the lake.
The function f(x) was determined in analytical form on the basis of direct measure-
ments of temperature in the bottom material of Lake Kubenskoye, carried out by one
of the authors of this study in the course of expeditions of the Limnological In-
stitute USSR Academy of Sciences [4].
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The function 5P (t) was stipulated on the basis of the known variation of inean
ten-day temperatures of the water mass in Lake I:ubenskoye [1]. �
With stipulated initial and boundary conditions, and also with a distribution of
temperature at the end of the considered period of time, also known from direct
measurements, using expression (7) it is easy to determine the aeff value.
0 5
0) Z" 1'" I 4)
Z
.T1P R6d7d . I ~ 11D-10~7l~
Fig. 1. Temperature profiles in bottom deposits of Lake Kubenskoye. a, b) periods
of heating, c, d) periods of cooling.
In actuality, the left-hand side of expression (7) in such a case is known and the
- aeff value with any prestipulated error is found by trial and error and by com-
- parison of the right- and left-hand sides of equation (7) by solution of the direct
problem.
For the purpose of clarifying the possible seasonal change in the thermal diffusiv-
- ity coefficient of bottom deposlts we will determine aeff in periods of heating and
cooling of Lake Kubenskoye arbitrarily selected taking into account available ex-
perimental data: for 1973 we examined the period of Ixeating from 31 May through 26
July and then a period of cooling from 12 August through 9 September; during 1974
the period of heating from 11 June through 10 July and.the period of cooling frcm
29 July through 28 August. In order to evaluate the possible influence of free con-
vection on the intensity of heat transfer in the bottom deposits the periods of
cooling were selected in such a way that in one case there was a temperature maxi-
mum in the bottom deposits situated at some depth from the surface (period of cool-
ing 12 August 1973 -9 September 1973), and in the ather case the maximum tempera-
ture was situated near the surface of the bottom (period of cooling 29 July 1974-
28 August 1974).
Figure 1 shows the results of direct temperature measurements in the bottom deposits
of Lake Kubenskoye during the above-mentioned periods of time in dependence on the
depth x at which the layer is situated. The x coordinate is reckoned from the surface
of the bottom material into the depths of the mass. The index 1 denotes the initial
temperature distribution and 2 denotes the final temperature distribution in the
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bottom deposits in each of the considered per3oda.
Fot each of the peri4ds we will determine in analytical form the initial tempera-
ture distribution in the ground f(x) and the variation of water temperature ip (t).
Period of heating (31 May - 26 July 1973)
f (x) =14,8-8 x+2,4 z'; 0-'GO'1).
However, the following problems arise here: up to what point is it possible to
widen the band wittiout there being a considerable decrease in receiver response?
Adhering to the traditional approafh, we will analyze the dependence of the sig-
nal-to-noise ratio at the output of the meteorological radar receiver on the band-
width of the amplitude-frequency characteristic.
As the radiometeorological signal-to-noise ratio we will examine the ratio of the
r:iean power of the incoherent component of the echo signal to the mean noise level:
[BbIX= out(put);
LLi (-IV IP PW' (8)
noise]
~
~
scr~h�( j);=dj
- k7, nW
where k is the Boltzmann constant; Te is the equivalent noise temperature, noise
is the noise bandwidth of the amplitude-frequency characteristic.
For a rectangular sounding pulse and a Gaussian amplitude-frequency characteristic,
taking (6) into account, and als.o that ITnoise - 1.061(, we obtain
�i= kT~~Yfaa~l J-
\ (9)
a(1-e � )J
where a2 is the mean square of echo signal amplitude.
The function (9), normalized to
a
(S/N)P,max � (SIN) n
a,ln~o�o-kfP
~ . 0
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is shown in Fig. 2(curve 2). The same as for the CCL, with Tr'ro > 1 (9) can be rep-
resented approximately in the form
;7.-,.
k fe
(9a)
The resulting dependences �l = f('frto), computed usinR formulas (7) and (9),
accurately coincide with ttie results of numerical computations of the similar
parameters in [15], whereas the approximate formulas (7a) and (9a) are far simpler
than the expressions proposed in this study.
It follows from the cited data that a widening of the bandwidth by more than Tf* _
'Co-1 leads to a considerable decrease in the signal-to-noise ratio. However, its
narrowing to a value below Tr* leads to an increase in the spatial correlation radi-
us of the output signal, which worsens the range resolution of the meteorological
radar station [15, 161 and increases the error in reproduction of echo signal shape
(see (4)) with an insignificant increase in the signal-to-noise ratio. Thus, the
optimum method for measuring the mean power of the echo signal involves a compari-
son of the amplitudes of the echo signal and the calibration pulse of a known power,
whose spectrum is close to the spectrum of the sounding pulse, whereas the duration
corresponds to the extent of the meteorological formation.
It is of interest to clarify whether there is some optimum (ff'Gp)opt value which
caould be a compromise choice between the requirements of an increase in the radio-
taeteorological signal-to-noise ratio, on the one hand, and a decrease in the incre-
t,ent of the spatial correlation radius of the echo signal, on the other. In [15] for
this purpose the authors examined the ratio � 2=(S/N)p/r6 = f(T1"-GO), where r6 is
the increment of echo signal. duration in space coordinates at -6 db. The indi-
cated function had a maximum with (1Tfp)o t= 0.72. However, the considered para-
meter carries little information because when going on the basis, for example, of
the results in [8] it can be shown that with levels below -6 db the (n20)opt val-
ues change and with a level -3 db and above the (N/S)p/rn function in this case in
general does not have a maximum as a result of the well-known phenomenon of accen-
tuation of the wide-band signal with passage through a narrow-band filter. There-
fore, it is better to analyze the increment of the correlation interval, determin-
ed as
~
~~cal - ~'cal out - Iccals,
where
S( f ) df
.
ti = ~.I,q,~,' ~I9~p~~ = I. Jt,
[K = cal(ibration);
BbzX = out(put;
34P - eff (ective) ]
~
"K eaa ewx,
_ ~ Sl~)Ihn(f)I1 d/
~f9q,v eWZ - - S, .
_ o,
S0_S(f )Il-f"'
(10)
Using the already cited results of computation of the corresponding integral, for
a rectangular sounding pulse and a Gaussian amplitude-frequency characteristic we
obtain
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~tK _ ~laa
~ [K = cal; HOP = nor] *P.HOp
, where (S/N)P~ nor is the normalized radiometeorological signal-to-noise ratio. Us-
ing the dependence of the relative increment of the correlation interval on oc('TT