JPRS ID: 9621 USSR REPORT EARTH SCIENCES

• Document Type: CREST
• Collection: JPRS
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00850R000300090043-2
• Release Decision: RIF
• Original Classification: U
• Document Page Count: 40
• Document Creation Date: November 1, 2016
• Sequence Number: 43
• Content Type: REPORTS

APPROVED FOR RELEASE: 2047/02/08: CIA-RDP82-00850R000300090043-2
~ FOR OFFICIAL USE ONLY
JPRS t /9621
- 23 March 1 J81
: ~ . . _ . ~ _ .�N. _ ~
� " ~ ~ ~ ~ ~ ~ :
� � � = S ~~~5~~~ SS ~S = � Y ~SSS� p ~ SI S ~ ~ �
~ ~ ~ � b
� : ~s~ . ~ ?i : t:s ~ii ~:~s~ ~ ~ :
_ ,
US~R Re ort
p
: EARTH SCI~NCES
~FOUO 2/81)
.
F~I~ FOREIGN BROADCAST INFORMATION SERVICE
- FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047102/08: CIA-RDP82-00850R000300090043-2
NOTE
JPRS publfc:ations contain information primarily from foreign
newspapers, periodicals and books, but also from news agency
transmissions and broadcasts. Materials frnm foreign-language
$ources are translated; these from English-language sources
are transcribed or reprinted, with the or~ginal phrasing and
other characteristics retained.
Headlines, editorial reports, and material enclosed in brackets
are supplied by JPRS. Pracessing indicators such as [TextJ
or [ExcerptJ in the f irst line of each item, or following the
last line of a brief, indicate how the original information was
grocessed. Where no processing indicator is given, the infor-
mation was summarized or extracted.
Unfamiliar names rendered phonetically or transliterated are
- enclosed in parentheses. Words or names preceded by a ques-
tion mark and enclosed in parentheses were not clear in the
original but have been supplied as appropriate in context.
- Other unattributed parenthetical notes with in the body of an
. item originate taith the source. Times within ~.tems are as
giv~n by source.
- The contents of this publicatior. in no way represent the poli-
cies, views or at.titudes of the U.S. Government. -
COPYRIC~T LAWS AND REGULATIONS GOVERNING OWNERSHIP OF
MATERIALS REPRODUCED HEREIN REQUIRE THAT DISSEMINATION
OF THIS PUB?,ICATION BE RESTRICTED FOR OFFICTAL USE Oi~1LY.
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047102/08: CIA-RDP82-00850R000300090043-2
FOREIGAI BROADCAS`f INFORMATION SERVICE
- P. O. Boa 2604
Washington, D. C. 20013
Z6 February 1981
NOTE FROI~t THE DI RECTOR, FB I S:
Forty years ago, tlle U.S. Government inaugurated a new
service to monitor foreign public broadcasts. A few years later
a similar group was established to exploit tlie forei~,m press.
~ Prom the rrerger of t}iese organizations evolved the present-day
FBIS. Our constant goal t}iroughout Ilas been to provide our readers
witli rapid, accurate, and compreliensive reporting from tlle public
media worldwicie.
On belialf of ~11 of us in FBIS I wish to express appreciation
to our readers wli~ have guided our efforts throughout the years.
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047102/08: CIA-RDP82-00850R000300090043-2
- FOR OFFICIAL USE ONLY
~ JPRS L/9621
23 March 1981
USSR REPORT
EARTH SCIENCES
~FOUO 2/81)
CONSENTS
METEOROLaGY
Radiation Factors in Contemporary Changes in Global Climate 1
O~EANOGRAPHY
~ 'Model of the Limiting Spectr~ of Internal Waves 2
" Scattering of Radiation Incident on a Sector of the Sea Surface.
_ Statistical Appruach to the Evaluation of Accuracy 1~
TERP.ESTRIAL GEOPHYSICS
Relationship Between Inhomogeneities in the Upper Mantle ar.d Tectonics. 20
, . . ~
~ ~ - a - (III - USSR - 21K S&T FOUO]
F~R ~FFiC'reT. rr~E ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047102/08: CIA-RDP82-00850R000300090043-2
FOR OFFICIAL USE OML.Y
METEOROLO~Y
UDC 551.5
RADIATION FACTORS IN CONTII~ORARY CHANGES IN GLOBAL CLIMATE
Moscow RADIATSI~NNYYE FAK~ORY SOVREMEIJIJYKH I7�hiF1~I.NENIY GLOBAL'NOGO KLIMATA in R~~ssian
1980 signed to press 3,Iun 80 pp 2, 279
- [Annotation and table of contents from book "Radiation Factors in Contemporary
Changes in GZobaZ Climate", by I:. Ya. ICondrat'yev, Gidrometeoizdat, 1,350 copies,
280 pages]
[Text] [Annotatio~n] The most important external factors in contemporary changes in
- climate are possible variations of the solar constant and also the gas and aero-
sol composition of the atmosphere. 1fi is range of problems is the main content of
tt~.e book. Emphasis is on the properties of atmospheric aerosol and its possible
. influence on climate, which is manifested in changes ir. the r~arth's albedo and
_ the radiant heat influx in the atmosphere. Anthropogenic effects on the ozone lay-
" er are discussed (refarence is primarily to halocarbons and their producCs), as
- we11 as the consequences of these madifications from the point of view of varia-
tions of the radiant heat influx in the stratosphere.
TABLE OF CONTENTS
Introduction.~~~~~~~~~~~~~~~~~~~e~~oooo~~~~~~~~~~~~~~~~~~aooooooa~~ooo~o~~~aa~ooo 3
Chapter I. Contemporary Changes in Global C],~mate and the Earth~s Radiation
- Ba].ance.~~~~~~~~~~a~~~uo~a~~~~~~~~~~~~~~~~~~oooo~~~~~~uoooo~~ooo~~� 7
1. Contemporary Changes in Climate According to Ohservational Data...oo.o..o0 7
2� SOlSr Constant~~~~~~~~~~~~o~o~~~~~~~~~~��~~~~~~~~~~~oooooo~~~~~o~~~v~~o~eo 32
3. Earth's Radiation Balance..,.ooa ....................oooo.o...ooo.o.....oo. 46
Chapter II. Gas Composition of Atmosphere and Rad~ative Heat InPlux.o.o........0 89
1. Parameterization of Radiation Processes in Numerical Modeling of General
- Circulation of the Atmosphereo ....................aooooo....oo......aooov 92
2. Atmospheric Greenhouse Effect..oo ...................o.oooo...o.....oa.o.. 107
3. Stratospheric Composition and FaGtors Determining Ito.a.....ooao...~.oo.0 126
4. Environment and Nuclear War.,,o.o.~ ................ooooooo..oooooooaoooo� 173
5. Solar-Stratospheric Relationshipso .............~...o.o..o..oooo..ooo.~aoo 181
' Chapter III. Influence af Aerosol on Radiation Transfer and Climate,o..o...aooo 189
1. Tropospheric Aerosol...........a ..................ooo.....ooooa..o...o.ao 191
2. Stratospheric Aerosol..........o...~ ...............ooo....ooooo......ooo0 224
S~.ry~~s~~~~~~~~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~~~~~~~~~o~~~aoooo~~~~~~~~~o~� 244
Bibliography .............~.....o.....o...................o..oo.oo.ooo....o.o... 247
Index ...............................,,..............o.......oooo..ooo..oaoooooo. 27'L
_ COPYRIGHT: Gidrometeoizdat, 1980
[68-5303]
5303
CSO: 1865
1
FOR OFFICIAL USE ONLY
i _
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047/02/08: CIA-RDP82-00850R000300090043-2
~OR OFF[CIAI. USE ONLY
OCEANOGRAPHY
~
UDC 5510466,81
MODEL OF THE LIMITING SPECTRUM OF INTERNAL WAVES
Moscow IZVESTIYA r1KADEMII NAUK SSSR; FIZIKA ATMOSFERY I OKEANA in Russian Vol 16,
- No 11, 1980 pp 1173-1178
[Art~cle by So P. Levikov, State Oceanograpr.ic Institute, manuscript submitted
12 Mar 79, resubmitted after revision 19 Dec 79]
[Text] Abstract: The author proposes a model of
the high--frequency part of the sp~ctrum
cf internal waves propagating in thin
stratified layers of the thermocline.
The f~Celd of internal waves is modeled
by an ensemble of algebraic solitones
with random ampl~tudes and phases. The
article gives a comparison of the prcpos-
~ ed theoretical curve with known evalua-
tions of the spatial spectrum of inter-
- nal waves in the ocean obtained on the
basis of observational data.
It is known that the heights of surface gravitational waves developing under the
inf luence of the wind are limited due to collapse. Some universal interval is form-
ed in the spectrum of wave heightso It is assumed that the form of the spectral
function in the spectrum can be obtained from an analysis of the dimensionalities
[1]. Assuming that the one-dimensional frequency spectrum is determined
only by the acceleration of gravity g and the frequency tc1, we obtain
m (c~) -rg`~-�.
The spectrum of wave n~nnbers ~(k) (we recall that the waves are two-dimensional)
in this case has the form
~ ~k) ~k-`,
- for sections of the wave field (plane waves) t~ (k) k-3. '
Internal waves can also attain states of destruction so that it is necessary to ex-
pect the formation of a similar equilibriunl interval in the spectrum of internal
waves. In this ~rticle an attempt is made tu derive an analytical expression for
such an equilibrium (limiting) spectr~. In examining this problem we will use
an analogy with a better studied process surf~ce waves,
2
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047102/08: CIA-RDP82-00850R000300090043-2
- FOR OFFICIAL USE ONLY ~
The correctness of the Phillips " W-5 law" for the equilibrium interval in the
spectrum of surface waves has been confirmed by numerous in situ nieasurements [2J.
However, up to the present time this law has not been derived from any rigorous
theoretical model. The results in [3] give the dependence ~(ce1)NliJ'4 far the
equilibrium interval in the spectrum of the slightly turbalent fi~ld of surface
gravitational waves. The di~ference from the Phillips "cJ'S law" is associated
with the fact that the authors of [3] e.xamined slightly nonlinear processes of
, interaction of random wave :Eields; highly nonlinear interactions of the collapse
= type were not taken into account.
For an explanation of th~e equilibrium interval V. A. Krasil'nikov and V. Ie Pav-
lov used a model of interaction between gravitational and capillary waveso Using
as a point af departure some stigulated form for turbulence in the near-water
layer of the atmosphere; they obtained the following dependence for the fre-
quency spectrum of sur�ace gravitational waves in the equilibrium interval:
~ (w)
which is close to the Phillips law, but nevertheless differs from it.
For the time being no theoretical expression has been derived for the equilibri~
interval in the spectrum of surface waves and therefore it is necessary to limit
- ourselves to less rigorous solutions, for example, th~se based on an analysis of
dimensionalities.
- However, it is imposstble ta use an analysis of dimensionalitl.es for obtaining the
spectrum of internal waves of interest to us. Phillips [5] proposed another ap-
- p roach based on the assuraption that the ~ncrease in amplitudes of the spectral com-
ponents in the field of the lower mode of internal waves is limited due to shear
- instability. The limiting amplitude of some spectral component as is determ~ned
- by the critical Richardson nu~nber, which, as for steady plane-parallel flows, is
assumed equal to 1/4
ary2 4 c~' N~ k-1 for short waves (cJ 2~-k),
ksj~m k~ for long waves (u1~k),
where W is frequency; k is the wave number; Nm is the maximum V~ais~la frequency; it
- is assumed that cJ/Nm ~ 1. The spectral density is determined as the square of wave
amplitude per unit area in wave number spsce. We obtain
:
- S(k) Qk1~kZ ~ k~ for short waves,
k- for long waveso
, The model of a limiting spectrinn of internal waves proposed by Phillips [5] is lin-
- ear and has li.mitations follow3ng from its linearity the entire solution is
stipulated in the form of the superposing of independent spectral components. This
assumption evidently ceases to be correct for waves close to collapse. Accor.:ingly,
in this case rigorously coupled sets of spectral componenCs arise which in pitys-
ical space correspond to a real nonlinear wave.
The model of the limiting spectrtmm of internal waves proposed in [6] has similar
limitations associated with linearity.
3
- FOR U~FICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047102/08: CIA-RDP82-00850R000300090043-2
= FOR OFFICIAL USE ONLY
We will not discuss the results obtained hy Garrett and Munk [8,9], who proposed
an expression for the "climatic" spectrum of internal waves, correct in the low-
~i'equency range, wtzere the assumptions made concerning the linearity of the
field of internal waves are soundly validated.
We will use arsnther approach: for compu~ting the limiting spectrum of internal
waves we wi11 select a solution in the form of some superposing of nonli.near for-
mations, each of which is a solution of the nonlinear problem corresponding to a
wave with a limiting amplitude.
_ S~ectrum of internal waves propagating through density layers. We will derive an ex-
pression for the high-frequency part of the spectrum of internal waves propagating
in sharply defined layers o~ the thermocline. As is well laia~rn, it is precisely in
thin stratified layers where there is an i*~crease in the nonlinea~ effects favor-
ing wave collapse [9, 10].
Now we will turn to an equation describing the dynami;.s of unsteady slightly non-
linear internal waves propagating through a stratified thin layer bounded abo~e
and below by a homogeneous deep fluid [11, 12]:
~ �
A,=-C,A=+aAA;+~ ~
2 HjA], HjA]~- ~ f z~~~ d~. . ~1~
Here A(x,t) is the horizontal velocity component in the wave field or the devia-
tion of the isopycnic line from the position of equilibrium; Cp is the velocity
of wave propagation (in a linear approximation). The coefficients aC and p are de-
termined from the solutions of the ~.inear boundary-value problem relative to the
- vertical coordinate and are thus dependent on the ct:aracteristics of stratifica-
tion and tiie vertical velocity shear in an undisturbed stateo Equation (1) was de-
= rived on the assumption of ~ong waves relative to D-layer thickness, that is, the
ratio D/J~, is a small value (,Q, is the characteristic wave length), According to
the generally accepted classification these internal waves are "high-quality"
short waves (their lengths can be from several meters to several hundreds of
meters). The effects of the earth's rotation and viscosity are not taken into ac-
count.
`6=0,1
I{
, ~ ~ B=~
~ ~ d = ~0
~
,
Fig. I. Form of algebraic solitones for different values of amplitude parameter ~ o
It is known that equation (1) has solutions in the form of stationary solitary
~
waves, so-called algebraic solitones. In a moving cocrdinate system x= x- COt
~ 4~ ~ ,
A (z) = a a=~-8z . ~2~
4
FOR OFFICIAL US1E ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPR~VED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2
FOR OFFICIAL USE ONLY
Figure 1 shows the shape ~f the wave for different values of the ~ parameter. I~t
can be seen that the lesser the ~ value, the higher and narrower is the solitone. _
The slightly nonlinear theory allows the existence of solitones with an arbitrary
- antplitude (although it must be remembered that equation (1) was derived on the se~
sumption of a small amplitude of the waves, it foZlows from the restrictions of
slightly nonlinear theory). It was impossible to derive an expression for the
limiting amplitude of the wave in this approximation; it must follow from the
theory of strongly nonlinear waves. Such an evaluation, for example, was obtain-
ed for waves in rarefied plasma propagating across a magnetic field [14]. It was _
established in this case that a stationary wave exists with H~X < 3H~, where H~
- is the magnetic field in imdisturbed plasma, H~X is the naxim~m magnetic field
in the solitone (here Ii~X is similar to the height of a wave of the limiting am-
plitude and HQ is similar to the depth of the undisturbed fluid).
_ We wil~ estimate the limiting height of a solitone, using an analogy with soli-
- tones, on the surf ace of the fluid. For example, for the latter the following
expression is correct for the relationship between the depth h of the fluid and
the maximum height ~~X of the solitone [15J:
~,~.M~0,78h ~3~
(similar estimates are also given in other sources). We will also assume that
the height of the internal solitone is of the order of the thickness of the strat-
ified layer D. In di:nensional variables equation (1) assumes the form
~
~1, D� ~l~l=+C,sD ax= H ~~1~=0� ~4) _
where ~ is the height of the internal wave. (Conversion from (4) to (1) is accom-
plished by replacement of the variables 1~= DA, x= Dx', t= Dt'/C~). The solu-
tion (2) is transformed to
4$ ~ a
' '~~x~'~ r D x'+Sz ~ (5)
2
From the condition ~(x = 0)^~ D we have 4r D, that is
a ~n D. (b)
We will estimate the spectral density of a one-dimensionai record (series) formed
from the superposing of algebraic solitones with random amplitudes and phases.
The total one-di~ensional wave field is stipulated in the form
4~ 6,
_ ~ ~z~ ~ a ~x~-r~) =-~-b~~ ' ~ 7)
where r~ is a random phase. The Fourier transform of expression (7) wi11 have
the form
F~ ~~z) ya J~(z-h a' j~-g~=e~~ dz s 4a ~ J y:+d 2 e~?,eu�~ da=
~ ~ _m ~
~ /A:
~ = 4~ ~~u.! a~e dz= 4~ ~ CIAr~~-ne-~a1~
ct ~ a'-f-8~= a
- ~ ~
We multiply by the complex-con~ugate expression
S
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPR~VED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2
_ FOR OFFICIAL USE ONLY
- FF�- 16~ ~~~~~r~-?~~)(~!e-AE~e_AOp~.
: ~
a
>
Now we will average it for the random phase, which we assume to be uniformly dis-
tributed in the interval (0.2?i). The spectral density can be evaluated using the -
formula ~ ~k~ = 16~=~ k'e-="a.
a , (10)
Fig. 2. Compzrison of experimental eval-
uations of the spatial spectrum of in-
ternal waves [17] with model curve S(k).
The straight lines represent the corres-
ponding power-law dependences,
~ ~
The schematic function S(k) is represented in Fig. 3. The spectral density S(k)
has a maximwn at the wave nimmber kp~s-1. For solizones with a large amplitude
_ (lesser S parameter) kp is shifted into the region of higher k. For solitones of
a maximum amplitude, correspnnding to S~n, we obtain
k0 b min~ D_l �
Thus, in the spectrum of fluctuations of vertical velocity measured in the field
of algebraic solitones with a maxi.miun amplitude it is necessary to expect a maxi-
- mtmm with kp~D-1, where D is the characteristic thickness of the layer with a
sharp stratification.
_ 7
- FOR UFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPR~VED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2
NOR OFFICIAL USE ONLY
We note in conclusion that the equation used in the study, which is now usually
called the Ben~amin- Ono equation, has recently attracted the attention of re-
searchers. For esample, quite recently a precise N-solitone solution [17, 18]
was found for it, from which it follows that in the case of interaction of two -
solitones their phases do not change (in contrast to solttones of the Cortevega~
- de Vries equation). In addition, with the interaction of two solitones their
heights in the interaction region decrease substantially. Thus, the assumption of
_ a random distribution of phases made in this study is correct if there was such a
' distribution at some initial time. With respect to the contribution due to waves
situated in the interaction region, it i~ evidently small. However, this problem
requires investigation.
- S ( k) ~
_ ~
I
kp k -
Fig. 3. ~chematic f~rm of spectrum of fluctuations of vertical velocity in the field
of internal waves of a limiting amplitude. _
The s:im~~le model of the spectrum constructed above can be considered the first step
en the path of creation of models of internal waves as a solitone gas, There are
natural means for its further complication and improvement: u~e of a precise N-
solitone sc>lution, allowance for interaction in the set of solitones and examina-
tion of a set of two-dimensional solitones.
BIBT~IbGRAPHY
1. Phillips, 0. rf., "The Equilibrium Range in the Spectrum of Win3-Generared ~
- Waves," Jo i~I.,UID MECH., 4, 426-434, 1958.
2. Hasse.tmann, K., "On the Spectral Dissipation of Occan Waves Due to White Cagp-
ing," I30ITNDARY-LAYER METEOROL., 6, No 1-2, 107-127, 1974.
3. Zakhai:ov, V. Ye., Filonenko, N. N., "Spectrum of Energy for Stochastic Fluc-
tuations of a Fluid Surface~" DOKL, AN SSSR (Reports of the USSR Academy of
Sciences), 170, No 6, 1296-1299, 1966.
4. Krasil'nikov, V. A., Pavlov, V. I., "Nonlinear Mechanis~ of Formation of the "
Equilibrium of the Spectrum of Waves at the Ocean Surface," IZV, WZOV, RADIO-
FIZIKI~ (News of Higher Institutions of Educa~ion, Radiophysics), 19, No 5-6, -
. 880-8$2, 1976.
5. Ptiillips, 0. M., DINAMIKA VERKHNEGO SLOYA OKEANA. (Dynamics of the Upper Layer
of the Ocean), Moscow, "Mir," 276, 1969,
6. Orlanski, I., "Energy Spectrum of Small-Scale Iuternal Gravity tidaves," JGR, 76, -
No 24, 5829-5835, 1971.
_ 8
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2007/02/48: CIA-RDP82-44850R000300094443-2
- FOR OFFIC(AL USE ONLY
7. Garrett, C. J. R., Munk, W, H,, "Space-Time Scales of Internal Waves," GEO-
PHYS. FLUID DYN., 3, No 3, 225-264, 1972.
8. Garrett, C. J. R., Munk, W. H., "Space-Time Scal~es of Internal Waves: A
= Progre~s Report," JGR, 80, No 3, 291-297, 19750
4. Woods, J. D., "Wave Induced Shear Instability in the Summer Z'hsrmocline,"
= J. FLUID I~CH. , 32, No 4, 791-800, 1968.
10. Floods, Jo D., Wiley, R. L., "Billow Turbulen~e and Ocean Microstructfire,"
DEEP-SEA RESs, 19, No 2, 87-121, 1972.
11. Ono, Ho ,"Algebrzic Solitary Waves in Stratified Fluid," J. PIiYS. SOC. JAPAN,
_ 35, No 4, 1082-1091, 1975.
~ 12. Levikov, S. P., "Unsteady Slightly Nonlinear Internal Waves in the Deep
- Ocean," OKEliNULOGIYA (Oceanology) , 16, No 6, 968-974, 1976.
13. Karpmazs, V. I., NELINEYNYYE VOLNY V DISPFRGIRUYUSHCHIKH SREDAKH (Nonlinear
Waves in Nondispersive Media), Moscow, "Nauka," 176, 1973.
- 14. Sagdeyev, R. Z., "Collective Processes and Shock Waves in Raxefied Plasma,"
� VOPROSY TEORII PLAZMY (Problems in the Theory o~ Plasma) , No 4, Moscow, Atom-
_ izdat, 24-80, 196~s.
15o Longuet-Higgins, M. S., Fenton, Ja D., "Qn the M~ss, Momentum, Energy and
Circulation of a Solitary Waveo II," PROC. ROY. SOC. LONDON, A340, 471-499,
1975.
16. Miropol'skiy, Yu. Z., Filyushkin, B. N., "Investigatj.on of Temperature Fluc-
tuations in the Upper Layer of the. Ocean at the Scales of Internal Gravita-
tional Waves," IZV. AN SSSR, FAO (NewG of the USSR Academy of Sciences, Phys-
ics of the Atmosphe~.re and Ocean), 7, 778-797, 1971.
17o Case, K. M., "The N-Solitone Solution of the Benjamin-O~o Equation," PROC.
NAT. ACAD. SCI., USA, 75, No 8, 3562-3563, 1978.
18. Satstuna, J., Ishimori, Y., "Periodic Wave and Rational Solitone Solutions
of the Ben~amin-Ono Equation," J. PHYS. SOC. JAPAN, 46, No 2, 681-687, 1979,
COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR, Fizik.~ atmosfery i okeana",
1480
[ 38-5303]
5 303
CSO: 1865
= 4.
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2007/02/48: CIA-RDP82-44850R000300094443-2
_
- FOR OFFICIAl. USE ~NLY
UDC 551.463:538a566
_ 3CATTERING OF RADIATION INCIDENT ON A SECTOR OF THE SEA SURFACE.
STATISTICAL AP1'ROACH TO THE EVALUATION OF ACCURACY
Moscow IZVESTIYA AKADEMII NAUK SSSR: FIZIKA ATMOSFERY I OKEANA in Russian Vol 16,
Pdo 11, 1980 pp 1189-1197
- [Article by M. Kh. Rafailov, manuscript submi.tted 3 Jan 80]
[Text] Abstract: When using the Kolm~gorov statistical
- test, taking into account the finite divergence
of incident radiation, it is possible to asceri
tain the dependence bat~reen the area of the sec-
- tor of the wave-covered sea surface scattering ~
radiation and the statistical parameters of the
spatial structures ma.king up the surface. IC is
demonstrated that if the area of the sector of
interaction of incident radiation with the sur-
face for a given divergence of the incident radi-
~ ation is greater than or equa~ to the definite
area of th~ sector of surface s~ationarity given
in the article there will be no distortions of
the parameters of the scattered field in comparison
with the scattering an a similar (from the statis-
tical point of view) surface of infinitely great -
area. An evaluation of the accuracy of the para-
meters of radiation scattered by the wave-covered
sea surface in a case when the area of the sector
of interaction is less than the area of the sector
of surface stationarity was obtained. Within the
framework of correlation theory it was possible to `
derive expressions for the a~ea of the sector of
stationarity of the wave-covered sea surface for the
individual spatial structures making up th~ surfaceo
Numerical estimates of the area of the secto-r of -
stationarity for a number of cases are given.
At the present time there has been extensive development of theoretical methods
for determining the parameters of the field of radiation scattered by the wave-
covered sea surface. The basis of these methods is the use of statistical models -
of the wave-covered surface, by means of which, with allowance for the spatial
structure of the incident radiation, it has been possible to determine the para-
meters of the scattered field [1-3]. There is also a great volume of experimental
10
- FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047102108: CIA-RDP82-00850R000300090043-2
FOR OFFICIAL USE ONLY
data on the scattering of the radiation incident on the wave-covered sea sur-
_ fac~, taking into account interaction with different components of the spec-
ttum of sea wavesp These data are used extensively when sounding the sea sur-
face for the purpose of determining wave parameters. It is assumed that the
scattering surface is quite representative in a statistical sense, that is, in
a sector of interaction between radiation and the surface all the scattering
elements of the surface whose probability of existence is greater than zero
participate in the scattering process. In other words, the scattering surface
in the sense of its statistical representativeness is equated to the surface of
an infinitely great area [4].
Under real conditions the interaction of radiation with the surface occurs in
- a sector of limited area. This sector is oriented in a definite way relative to
the general direction of propagation of sea wavesa In this case the represent-
ativeness of the statistics of sc:attering elements is limited and frequently
is too small for the results to be correct for the entire surface, and not only
~ for the considered sector.
Al1 this in a number of cases results in substantiai discrepancies between the
theoretical and experimental results in a~ investigatian of the radiation scat-
- tered by the sea surface and errors in determining the parameters of sea waves.
Factors of this sort are particularly important when during sounding of the
sea surface on the basis of the results of one or more experiments it is neces-
sary to obtain reliable information on the state of the sea surfacea
~
~ The problem of the relationship between the spatial structure of the radiation
field and the change in wave parameters in a finite sector of the sea surface
was examined in [5] from the point of view of hydrodynamic conditions for the
development of sea waves, taking into account the bottom profile in shallow
waters. However, the problem of changes in the structure of the scattered field
in dep endence on the area of the sector of interaction of radiation with the sea
surface in the case of a real three-dimensional random structure of the sea sur-
face when waves are present has not been solved.
The purpose of this study was a determination of the conditions under which the
parameters di the radiation scattered on the wave-covered sea surface, with al-
lowance for the properties of the radiation and the statistical characteristics
of the surface, are not dependent on the position of the scattering sector at
the surface. [Or the conditions of nondependeace of the parameters of the scat-
tered radiation on time if the surface moves relative to the interaction sector].
A result of the study was the derivation of formulas giving an evaluation of the
accuracy of the parameters of the scattered field in the case of a definite sur-
face area int~racting with radiation. The inverse problem was also solved: the
requirements on the area of the sea surface ensuring determination of the stat-
istically stable characteristics of the scattered field were determined under
conditions of a diff.erent state of the wave-covered sea surface.
1. Statistical Analysis of Scattering Conditions
11
FOR OFFIC[AL USE ONLY
~
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047102108: CIA-RDP82-00850R000300090043-2
FOR OFF(CIAL USE ONLY
We will examine the wave-cnvered sea surface, representing it in the form of
several spatial structures of different scale sup~rposed on one an~other. In a
general case the scattering of radiation on such a surface is determined by the
ratio r,t the radiation wavelength T to the characteristic dimension ,Q. of a scaY~~
- tering nonuniformity of the surface. If ~1 ~,Q, the principal contribution to scat-
teriug is from reflection in accordance with the laws of geometrical optics; how-
ever, if the dif.fraction mechanism of radiation scattering predominates�
_ We will assume that both mechanis~s of radiation scattering existo Our task is to
evaYuate the influence of the finite dimensions of the sector of interaction of
the incident radiation with the surface on the characteristics of the scattered
- field. For its solution it is necessary to examine the statistically least repre-
s entative (in the sznse of presence of scattering elements) structure of the sur-
_ face components. A macroscale structure on which ripples, in turn, are already
s uperposed is such a critical structure from the point of view of statistical rep-
resentativeness. Accordingly, in our problem the mechanism of reflection from the
surface in conformity to the laws of geometrical optics will be decisiveo
In reflection the most im~,ortant surface characteristic is the distribution of
slopes. ~de will assume that a wave with the divergence [~a is incident on the sur-
f ace. Then L~Ptwill determine (Figa 1) the ambiguity measure Qp in the value of thp
integral distribution function F(oc)
a+ Aa ,
9
~'10 = S ~ ~a) da = F (a 2a) - F (a _ Dal ~ ~ 1)
e~ ~ 1
- a- -
t
where f(oc) is the differential distribution function for surface slopes, regard-
less of azimutho
f (a) � f~~~
, ft~~~ e
f~(a)
da Aa a
a 6
Fig, 1. Appearance of ambiguity in determining the integral distribution function
with a finite angular divergence L1a of incident radiation; a) differential dis-
t ribution law, b) integral distrib ution law.
For practical purposes the two detexmined distribution funetions of slopes will
not differ if with the angular divergence Qa their integral distribution functions -
differ from one another by a value less than Qp. As the ambiguity measure it is
possible to use the maximum possible value of the difference of two integy~.7. dis-
tributicn functions, one of which F1(~) corresponds to the integra~ dis-
tribution function for the entire general set of slopes, that is, for an infinite-
= ly great area of the scattering surface, whereas the second F2(oC) corres-
ponds to the integral distribution function for the considered samp.le set of ,
12
FOR OFFICIAL USE ON~LY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2007/02148: CIA-RDP82-44850R000300094443-2
FOR OFFIC[AL USE ONLY
slopes, that is, the really irradiated sector of a finite area: Q~ = sup ~IFL(oC)
-F2(a ) I}.
- Thus, it is possible to determine the volume of the sample set ensuring determina~
tion of distribution of slopes whose difference from the distribution for the gen-
_ eral set for a stipulated slope aC does not exceed (with a prestipulated probabil-
ity) the anbiguity measure Q~ for the integral distribution function of slopeso
= The Q~ value can be regarded as a parameter of the Kolmogorov statistical test of
agreement between two integral distributions F1(oC) and F2(a Using this test,
for the volume of the sample N~ the number of the independent observations of
- surface slopes we obtain
NO=v'(u)Qo f (2)
where '?(u) is the argiunent of the Kolmogorov distribution, having the form [6]:
r
_ A (v) _ ~ (-i)' eap (--2r'v')
r~-w
with a definite significance level u corresponding to the condition A(v 1- u.
We will consider the sea surface in the presence of waves as a random surface whose
y-coordinates have a normal distribution with zero means. Since the surface is
statistically symmetric relative to the mean level f(~ f(- the density of
the maxima n.~X f or the surface is equal to the density of the minima and the total
number of the stationary surface points is nst = 4n~~�
A continuous gently sloping random surface can be represented as 4 set of plane
_ microareas tangent to the surface; the distribution of slopes of these microareas
coincides with the distributian of surface slopes. With such an approximation of
the random suY�Face the density of the microareas, having the slopes will
' be equal to
~ ~y) =4?~.~ eap r - mo:+~~'m� ~
,
� ~ mo:m:o
or, dividing and
~mu~lti~ lying the right-hand side of this expression by the normal-
izing factor 2~1 2Jm ~m02, we obtain
R~~=, ~.)=4nm.~2nYm:omo:/~~=, (3)
where mdq is the initial moment of the spectrum of surface rises, of the orders
d and q, and is equal to
a a
- md� - J J W~k, ka+a sin� ~ cosa ~ dk dq~, ~4~
.
k is the wave number; ~ is the azimuthal angle relstive to the general direc:tion
of wave propagation; W(k,~) is the spectrum of surface rises; f(~ X, ~ y) is~ the
_ differential distribution function of slopes.
The niunber of microareas whose slopes fall in the intervals from ~ to ~X +d~X
= and from ~y to ~y +d~y, in a unit area of the random surface is
13
_ FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2007/02148: CIA-RDP82-44850R000300094443-2
FOR OFFIClAL USE ONLY
?~~~~,eg)=4n~.:2nY~oma~ f f ~~~=,$w)d~=d~~�
e s! (5)
In the surface area SD the total number of points of definite slopes is equal to
Nc~, DE)~n'(~, ~~)So� c6)
The N value can also be determined from the total number of mi.croareas on the
random surface taken from the condition that their number is statistically repre-
sentative for ensuring the stipulated degree of aecuracy
N~~, d~)=N~~~, (7)
where N~ is determined in accordance with formula (2); F(r� Q~,) is the proba- _
bility of appearance of slopes in the intervals from ~X to ~ X+Q ~ and from
~ y to ~y +L~zT~,.
Taking expressions (2), (6), (7) into account, for the area of a sector of sta-
tionarity the sector of minimum area ensuring the obtaining of a distribution
- within the framework of a stipulated accuracy not dependent on the movement of the
sector over the investigated surface we obtain
va
So = ~8~
~ Q,'4nmu 2rcymo~n+~o
If the area of the surface sector with which the radiation interacts is less then
Sp, due to a decrease in the volume of the sample set thEre will be a distortion
of the determined experimental distribution in comparison with the distribution '
for a general set with these same Al, Q ot values. When the quantity of reflec-
tors in a sector of interaction of radiation with the surface is ~ 1 it can be as-
sumed that the change in the experimental distribution is determined by the change _
in the sample dispersion m2' with retention of Lhe theoretical form of the distrib-
ution law.
The relationship between the change of the experimental integral distribution func-
tion F(m2') in comparison with the theoretical distribution F(m2) can be expressed
through the ambiguity measure Qes that is ~F(UC, m:2) - F(OC, m2')I = Q~. In this
case Qe is determined from formula (8) with the surface area Si
Q.=v (81[.S'tnm~) (rn'o:m:o)''h�
Hence, knowing the form of the distribution law, we determine the value of the
sample dispersion parameter from the equation F(m2') = F(m2) + Qe(Si).
The value of the possible deviation of the experimental value from the theoretical
value will be
- b = ~ Cf~a, m:~)-1~a, m:) ]da
a,sa ~9~
with the confidence coefficient A(~?).
2. Correlation With Statistical Parameters of Wave-Covered Surface
14
FOR OFF[CIAL USE ONLY
I
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2007102/08: CIA-RDP82-00850R000300090043-2
FOR OFFICIAL USE ONLY
A Gaussian random error has a law of distribution of slopes not dependent on azi-
muth in the form [7] '
cx a'(mso+mos) a=~m:o-mo~)
~ f (a) = eap [ 1 I [ 1 ' (~0)
Ym�m:~ 4m�m,: 4mo=m10
where I(z) is a modified Bessel function of a zero order.
In examining the wave-covered sea surface it must be noted that the individual
components of its structure have different statistical properties, Thus, there
are isotropic or nearly isotrop ic structures [8]. There are also highly aniso-
tropic structures consisting of waves having an approximately identical length
and direction of propagation.
The energy in the spectrum of such structures is grouped around one wave number -
on the spectral plane, that is, the spectrum is narrow-band.
For isotropic structures m02 = m2~ and the distribution of slopes conforms to the _
Rayleigh law
f~a) = m= exp L 2m: J~
(11)
~ If the structure has a narrow-band spectrum, that is m20 ~ m02, the distribution
of slopes has the form
:
f~a~ ~nm2o eXP L 4moz J ~12) -
The density of the maxima of the statistically isotropic surface is equal to ~
~ 1 m~ -
(13)
~mu 6ny3 m,,
- and for a surface having a narrow-band spectrum
- n~='~k'C~a), (14)
where y=~/m0~20 is the index of three-dimensionality of the surface; k= ml/
- mQ is the mean wave number around which the narrow-band spectrum is grouped; C(a)
- is the function of the parameter of spectral steepness [7].
With smallL~avalues and with a considerable slopeoC the uncertainty value is Q~ _
f(aC)QoC. In this case formula (8) for the area of the stationaxity sector for a
statistically isotropic structure is equal to
~ So_ 3Y3vzm=expla'/m,] (15)
4a2m~Da' '
and for a structure with a narrow-band spectrum
v= exp [ az/2m� ) (16 ) -
s�c 16k'C (a)'~c~'~' '
15
- FOR OFFLCIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/08: CIA-RDP82-00850R000300090043-2

APPROVED FOR RELEASE: 2047102108: CIA-RDP82-00850R000300090043-2
FOR OFFICIAL USE ONLY
in this case for a structure with a narrow-band spectrum the stationarity sector
has the form of an ellipse whose area is Sp =~trlr2, where rl and r are the
semiaxes of the ellipse, determined w~.tn the levels oc/~ and cff~ respective-
~ lp for the general direction of wave prcpagation and the direction perpendiculgr
to it.
In order to determine the values of the initial moments of the spectrim and the
character.istics of the sea surface related to them we will use the spectrum of
rises of the wave-covered ~urface in the form W(k) = Wt~k), kt_1