JPRS ID: 8315 METEOROLOGY AND HYDROLOGY NO. 1, JANUARY 1979

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6 MARCH i979 ~ FOUO i OF 2
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JPItS L/8315
6 March 1979
~
METEOROI.OGY AND HYDROLOGY
- N0~ 1, ~ANUARY 19~9
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JPRS L/83~.5
6 March 1979
METEAROLOGY AND HYDROLOGY
No. 1, January 1979 -
Selected articles fram the Russian-language journal _
METEOROLOGIYA I ~IDFtOLOGIYA, Moscow. �
. CQNTENTS PAGE
Numerical Analyeis of Meteorological Fields With Use of Satellite -
Da.ta
(S. I. Gubanova, et al.) 1
Numericc~l Model of Atmospheric Dynamics on a Spherical Earth
- (V. V. Aenenko, N. N. Obraztsov) 10
~ Modelin~ oP $ydrostaticit~ of Iarge-Scale Atmospheric Processes -
V. M. Kadyshnikov 26
Automic Control of D~ta F~om Temperature Sounding of the
Atmosphere From Meteorological Sa~ellites ~
(L. S. Gandin, V. P. Tarakanova) 38 -
Activity of the Hurricane Season in the North Atlantic
(V. A. Vetroumov) ........e..~............e 48
Correlation Between Circulation Aeculiarities of the Northweatern
Part oP the Pgcific Ocegn an~ Weath~r Conditione in th~e
Southern Far Fast;
_ ' (V. F. Voronina) 59
Numerical Modeling oP Systems Por Observing and Analyzing
Ozone Field
(0. M. Pokrovakiy, et al.) 57
E~raluation of the Factors Fo~ming the Microclime~te oP Alma.-Ata
City �
(I4i. A. Akhmedzhanov, V. I. Degtyarev) 80
� - a- (III - USSR - 33 S&T Ft)UO]
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CONTENTS (Continued) ~6e -
r
Nonetationary Two-Parame~er Model of the Main Oceanic
- Thermocline
(P. S. Lineykin, A. V. F'rolav) 89
Variations in the Water Volumes in Rivera of the Soviet Union
(K. P, Voskresenskiy~ i~6
Calculations o~ ~he 5te,bility of Freshly Falling Snaw on a Slope
(V. A. Khalkechev) 114
Calculations of Accumulation of Mel.t Water by the Soi.:1
G. Pa,lagin) ].21
Relationship Betw~en Diatant Transmigrations of Insecte Aarmf~zl
for Agriculttu�al Crops and Atmoepheric Processes -
, (L. A. Ma.karova, et al.j i32
Self-Contained Radio Wave Meter for I~ydrological Support of
Marine Drilling
(Yu. F. Nlasterov) 138
ScientiPic-Operational $ydrometeorological Support for the
- Fishing Ixidustry
(F. S. Terziyev) 145
�Similarity, Self-Similarity, ?ntermediate Asymptotic Forms. -
Theory and Applicati~ns to Geophysical Hydrodynamics~ _
(Podobiye, Avtomodel'nost'. Promezhutuchnaya Aaimptotika.
Teoriya i Prilozheniy~ k GeoPizicheskoy Gidrodinamike).
Review of Book by G. I. Barenblatt (Leningrad, Gid~o-
- meteoizdat, 1978, 207 Pages)
_ (Ye. M. Dobryshman) 156
Review of Monogra~ph by I. V ~ Popov: ZAGADFff RF~CHNOGU RL~SLA
(Mysteries of the River Channel), I~eningrad, Gidrometeoizdat,
1977 -
(A. V..Plashchev) 1~9
Seventieth Birthday of Konstantin Pptro rich Voskresenskiy
(A. A. Sokolov, et al.) 161
~ZVenty-FSPth Birthday oP Aron Markovich Gindin -
(V. N. Zakharov) 164
Conferencea, Mee~ings and Semina~s
- (V. V. Koatarev, et al.) 165
= - b -
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CONT~I~iT:~ ( Continued) Page
r: ,
Notes From Abroad
(B. I. Stlltin) 171
Biographical Notes on Mikhail Andreyevich Velikanov (1879-1964) -
(Ye. G. Popov) 173
- Obitusry of Mileyko Georgiy Nikitich (1919-1978) i78 `
~ -
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PUBLICATION DATA
. English CiCle : N~TEOROLOGY AND HYDROLOGY
- No 1, J~an 79
Russian title : NIETEOROLOGIY~ I GIDROLOGIYA .
AuChor (s) :
,
Editor (s) : E. I. Tolstikov
Publishing House : GIDROMETEOIZDAT
' Place of PublicatiAn ; Moscow
s Date of Publication ~ 1979
Signed to press ' : 16 Dec 78
Copies : 387~ _
COPY~tIGHT : "Meteorologiya. i gidrologiya",
- 197~ ~
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+
, .
UDC 551.509.313 ~
NUMERICAL ANALYSIS OF MET~OROLOGICAL FIELDS WITH USE OF SATELLITE DATA
Moacow METEOROLOGIYA I GIDROLOGIYA in Russian No 1, Jan 1979 pp 5-10
[Article by Candidate of Physical aqd MaChematical Sciences S. I. Gubanova, '
Profeasor S. A. Mashkovich and Ye. L. Metelitsa, USSR Hydrometeorological
5cientific Reaearch Center, submitCed for publication 22 May 1918]
Abatract: A atudy was made of the effect of ~oint
~ise of aerological and satellite data in a four-
dimensional analyais model [9]. The model is based
on spatial-temporal optimum interpolation. The -
authors give the quantitative characteristics of _
the contribution of satellite measurements in �
four-dimensional analysis for Che northern hemi-
sphere in specific situaCions. There is an anal- _
ysis of the influence of asynchronicity of observ- -
ations. Evaluations of a refinement of analysis of
. OT1~g0 charts are given.
[Text] The problem of initial information is one of the most important in
- the numerical forecasting problem. There are different approaches to solu- _
~ tion of this problem. The most natural way to solve it is Co obtain addi-
tional infarmaCion on the sCate of the atmosphere obtained using new ob-
:~ervational me,~ns, such as the method of remote sounding of the atmosphere
from artificial earth satellites. The usQ of satellite data in a numerical
;inalysis of ineteorological fields is associated with solution of a number
c~f problems. One of them is computation of the vertical distribution of
temperature, relative topography and humidity on the basis of radiation
measurements from a satellite. Another equally important problem is the
development of effective methods for taking into account data on these ver- -
tical profiles ir~ numerical analysis. This ~roblem is the subject of this
;irticle. `
Datn an the vertical distribution of temperature and relative topography,
ubtained on the basis of such sou~.ding, constitute that form of informa-
cion wi~ich, it would seem, can be used directly in numerical analysis. In -
~?ctuality, however, definite difficulties axise here. In contrast to trad-
itional aerological measurements, as a rule rigorously tied in to definite
1
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geogruptiical po:inCa ~nd observation Cimes, satellite daCa can be arbiCrar-
_ ily d:ta triUuted in time and space. Therefore, allowance for them involves
changeover f.rom ordinnry epaCial (three-dimensional) ob~ecCive analysis
tn fc~ur-dlmen~innnl. iinal.y~.iH. tt is important thnt Che ~rrors in sate111Ce
_ LnE~rmatian ure considerably greaCer than in aerological data snd also Chat
rhese errors may be correlated (for example, see [10]). In this connection
there is no clear idett as to whether the mentioned satellite data are ade-
quately reliable and to what extent Chey can be used effectively in numer-
' tcal analysis and forecasting: opinions on this score are exCremely conCra-
dictory [2, 11-13].
Below we presenC the results of numerical experiments on the ~oinC uRe of
aerological and saCellite data in numerical ob~ective analysia; an evalua-
tion is made of the conCribution of satellite information to Che resulte
_ of tihe analysis and an attempt is made to clarify whether this contribution
gives a positive effect.
As was already mentioned above, reference is noC to computati~n of verrical
ciistrib utions on the basis of s~itellire radi~tion measurements, but on the
- ~?se of already reconstructed vertical profiles of ineCeorological elements. ~
Specifi cally, we were concerned wiCh Che problem of assimilaCion of satel-
Lik~ da ta on the relaCive topography of the isobaric surfaces. The corres-
- ~~onding information at Che present tin:~ is being disseminated through the '
- IJMO global telecommunicaCions system in the form of SATEM summaries (earlier
SIRS summaries were transmitted). ~
'lhe data assimilation meChod is based on spatial-temporal optimum interpola-
tion. The effectiveness of use of this approach to solution of the four-di-
mensional analysi~ problem was demonstrated in [8]. Different aspects of op- ~
rimum assimilation of various kinds of information were discussed in [3,
G, 7].
, The numerical experimenCs were carried out on the basis of the four-dimen-~
sional analysis method and model developed at the USSR Hydrometeorological
Center. This model is based on the snatial-temporal optimum interpolation
method. It ensures 3oint processing of data obtained using different observ- _
:ition systems and having different levels of errors and it takes the correla-
l�ton of ineasurement errors into account. More detailed information on the
Cour-dimensional analysis model can be found in [9J.
'Che computations were made both for cases when only aerological data were
used (variant A) and for cases of joint u~e of aerological and satellite
- n?easurements (variant A5). In each case use was made of aerological infor-
nation for one ouservation time and satellite measurements made not more
than 12 hours from this t:!me. Satellite information was taken from SIRS
summaries received at the USSR Hydrometeorological Center. As is well known,
th~s information was received only for ocean areas. The number ~f satellite
soundin g points in the northern hemisphere for a 24-hour interval averaged
about 230 and varied in the range from 190 to 336. The number of aerological
- 2 -
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~
tele~rame tor onc obRervntion time, uaed in the computations, averaged
~bout 44A and varied from 411 to 680. In the computations it was as~umed
Ch~C the mean relaCive square errora in serological and satellite data on
rhe relative geopoCenCial H1~gg r~re equal to 0.02 and 0.10 reapecCively.
't'his means thAt in the middle troposphere of zhe temperaCe la~itudes the
error is about 2 and 5 dam. It was also aeaumed that the errors in satel-
lite information were correlated and horizontal correlaCion is deacribed
by the formula
- v (r) - ,,~~r~.
In Che analyais we used the values a 0.7; r~ ~ 200 km.
_ The analyais was made f~r a r~egular geographic grid with 5� intervals along -
the meridian and 10� intervals along the parallel (a toCal of 648 points on
- the map of the norChern hemisphere). The results of the analysis of the
_ relaCive topography H1~00 presented below were obCained using daCa for the
' {~eriod from 26 through 29 April 1977, 13 and 14 January 1977, 23 June 1974.
For evaluating the differences between the two fielda fl and f2 below we
use the values -
I f~ ("i~ -f~ (A~~ i.~)~ ~
_ d~ ~ f! ~ J:~ ,~r '~r. r./'(fl - f=~+ a"111 a f~ b(t
�I
~
The d2 value is the mean square discrepancy between Che fields of the meteor-
ological element, computed for the hemisphere. If the field of the meCeorolog-
ical element is approximated by a series in spherical functions
~
Fm e~m a f~m e n~ - Am jBm
fR / R. n n~ fA~ n k. n R, n'
n~ n
_ then the expressions for d2 can be written in the form
d~=~d~;
~
~ 1 when m = 0
- d~+ - 2 a ~ ~~f~m ~ - ~B'~", ~ - Bz !'m; Pm - -
R 2 when m~`= 0.
'I~iis value is computed both for the entire considered wave spectrum and for
its different parts.
tJow we wi~.l proceed to the results of computations. First we will evaluate
those changes which occurred in the analyzed fields as a result of taking _
:~atellite information into account. As�demonstrated by computations, the
3
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= influence of saCellite data was manifested at approximately 40% of all the
poinCs in a regular grid (the average numbex of such points of inCersection
was 270, the minimum was 260, ehe maximum was 285).
Now we will discuss quantitative eatimates of the contribution of satel-
- lite data to analysis of OT~~~~ charts. For this purpose we will compar.e
the results of computations n varianCs A and AS. As a quanCitative char-
- acteristic we will cite the number of points of a regular grid wiCh dif-
- LerenC values of Che discrepancie. S. Yf this number of points is deter-
mined in percent of Che total number of poinCs aC which the influence of
satellite data was manifested, we obtain Clie following data:
Difference (,a) in analytical
results in varianCs A and -
AS, dam 2 2-4 4-6 6-8 8
Number of points, % 40 22 14 8 16
The results of comparisons show thaC at almost 40% of the points allowance
for satell~.te data led to changes of 4 dam or more, the mean change was
4.6 dam, the maximum change was 35.6 dam. Thus, their quantitative contrib-
ution is extremely significant. This same fact is indicated by the spectral
evaluation (dZ) of the differences between the A and AS analyses, computed
for tf~e hemisphere: .
Wave range, m 0 1-3 4-6 7-9 10-12 0-12 _
d2, dam2 1.4 2.8 1.1 0.4 0.2 S.S
The discrepancy for the entire considered part of the spectrum (max m= 12) -
was 5.9 dam2; Che maximum differences are observed in the zonal component
m= 0) an3 the longes~ waves (m ~ 4).
An interesting probler! i:~ the role of asynchronicity of observations. For
solvin~ this problem f:~i- vr~riant AS We carried out computations with and =
without allowance for tha differences in observation times, the results of ~
which demonstrated the fcllowing:
Difference (b) in results of
,~nalysis of OT1000 With and
~rithout allowance for asyn-
chronicity of observations,'
clam 0-1 1-2 2-4 4-6 6-8 8
Number of points, % 56 19 13 6 2 4
It can be seen that due to nonallowance for differences in observation times
in 25% of tlie casea discrepancies (S) arise which are more than 2 dam, in
12% of the cases :hese discrepancies exceed 4 dam, the mean discrepancy is
1.28 dam, the maximum discrepancy is 19.6 dam. Thus, even in a time inter-
val less than 12 hours one must not neglect the differences in observation
times.
4 _
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a b sae ss
aJ T sc4 b) L_ s~2 -
- ~ � s tz ssc T \
1~ ~ ~4 3e~
~V? ` ~ ~i ~ \
f''I ~ ~t se0 F~W X \
~~sca'~~ 1 . s,s~`sc~ r~~ ~ ~
, ~;s~c s!s sen ~ ~
- ~n , c x;; : Cseo ~ /~a. r
- S64 . ~ J
r " y '
1,i rf ~\i~ 1 aacP (,i72 '~.~�sya~~ `'~:r'/ l.J'/
~'~i4~,/~T T~ 60 ~ .6;~.5
~549~~/~
~ ~.,:c1; �
\ ~y'~ay \ ~ ~ {
\ � ..~Ofl' r ~ ~
l
` ~ (feJ sea ~ ~~Sff9Y~.
~ d
O~ , \ Z, r ti y
sea s~pt' \
. . \ ' -
sr~ ~ seo 1
~ r ` 1 ~ ~ -
,
~~~s. ~~~,.~~~a i - ~~~~~o ;
' ~ P~~sc,s'~~ u x,~~ ` ~ lo
`~1'10 ~"~-r;~-'1 SJ~Ii 6 ~ 4 ~J
~ 7 p i~ rt
f~ ~l~^4~;`~~~ ~ d~:'V r
~ S~~S4~,.~`~::Jj ~ V
_ J,-~~.~~,`': ~IJ,~~ ~ 590 1l'0 ~ ~
:r-~
\s~ CtJb~ _
~ t{1~~q, � 6 6 ' o
~ ` r ti ~ ,Z ~ " _
/
_
~~L~~~�
Fig. 1. ~xample of analysis of OT~~00 charts for 0000 hours on 28 April Z977.
:i) chart analyzed by weatherman; numerical analysis based on aerological
data (variant A); c) numerical analysis Lsing aerological and satellite
clata (variant AS); d) map of differences in numerical analyses with and wirh-
c~ut use of satellite data.
Table 1
Comparison of Numerical Analyses of OT1000 ~arts With Synoptic Analysis
I ~IICCO~T~jf~Q1t~(u%0~ ~
- = ll c npezenax 2 ~ 3
L u ~
a
n ~ ~~q I .}�.6 I )li ~O
A 31,GI2;;,OI1�I.SI3ll,61 4,i2
A~%,C :t7.3 '?:i.'~ l:~,U ?3.S 4.1~7
KEY: 1. Variant '
2. Vumber of points with b(dam) in range
3. Mean S, dam 5
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_ Table 2
Sp~cCra1 Cc~mpgri~on of Numerieal Analysee of OTi~~~ Chertg With n
5ynopCic Anglyais `
,
h
~ ~ 3naacuua d~ (dn:u') Ana Axtnaau�
- a1 ~IOH b0.'INOBWX 4NCl11 ffl ~ _
' a~ u i--;i 4-G! ;--b IU-12~ 0-12
_ ~C, I I;.a I 4,3 I 1,7 ~ 1,2 U,4 I 14,1?
:S,N ~ti.i 1.4 i.l U,b ltl,fi
K~! :
1. Vnriant
2. Valuea d2 (dam2) for rangeg of wave numbers m
Table 3
Kinetic Energy for Different Varignes of
Analysis (in Arbitrary Units)
,'luanaxonW nonna�
Ll dw~ ~nicc~ m 2
ca ~ ~ 1-t'l~ U-12
I
1 t,S '~c?1 359
AS (;i:~~ lti? :3lr ~20
K~Y:
1. Variant
2. Ranges of :~ave numbers
3. Syn
The presented data indicat~~~hat allowance for eatellite information eub-
stantially changes the OT10~~ charts. However, iC is imporeant to evaluate
_ whether in actuality in t~iis case there is an improvement in the quality
~ of the analysis.
It is difficult to give an answer to this question: there is no standard
which sh~uld be used in a comparison of the results of numerical analyeis.
I~or that reason it is necessary to ~eek indirect ways for evaluating the
~~ffectiveness of this information.
One of these ways is a computation of the a priori theoretical error in op-
timum interpolation. For such computations it is necessary to know the geo-
~;raphical distribution of sounding points, the levels of errors in measure-
cients by different observation sys[e~?s and the corresponding correlation
functions. Cotaputations of this type were cited in (6J. Without dwelling on
these results in deCail, We mention only that allowance fo r satellite data
reduces the relative square error in optimum interpolation from 0.34 to
6
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'
U.18 in Che noreh~rn h~miephere ~nd from 0.70 to 0.30 in th~ southern hemi-
- apherN.
Another approach ig bgshd on Che erbitr~ry choice of g standard for compar- '
~ igon. ~or exemple, as g gCgnderd we can elect that vgriant nf analysie which
ie c~g~umed ro be mnst religble. As such a standgrd we ueed a c~reful synop-
tic analysis of the dT10~p0 �harts ~or the norChern hemiaphere c~rried ouC aC
the U55R Nydrometeorological Cen~er. Tables 1-3 give the re~ultg of a com-
pnrigon of numerical analysea (variantg A and AS) with e synoptic analysis
(varianC Syn). Table 1 shows Che number of poinCe (Y.) for differenC grada-
tione of the discrepanciee (a ) beCween the analysea. The cnmp~rison wa~
mnde for th~ entire narthern hemisphere. It can be seen thaC as a reault of
u~e of egtellite data Che deviations from the eynopCic anglysi~ were somewhaC
Jecreased: the mean discrepancy was reduced from 4.72 r.o 4.07 dam, there
were approximately 77: fewer points with considerable discrepancies (greaCer
than 6 dam), and Chere was an increase in tt-.~ number of points with small
~leviationa. Table 2 gives spectral evaluationa d2. Here it can be seen
that nllowance for satellite daCa made it possible to brin~ the numerica~.
annlysie cluse to the eynoptic analyais in all parts of the spectrum, ex-
cept for the most short-vave part (m?~10). Still gnc~tlier characteri~tic
uhich can be used is the kineCic ene,rgy of the thermal wind (Table 3),
which in the variants AS and Syn was extremely close. ~
Ae nn illugtrution. F'ig. 1 showe a chart analyzed by a weatherman at the
IISSR llydrometeorological Center for 0000 hours on 28 April 1977 and numer- ~
ical analyeia charts correaponding to the variante A, A5 and the results
of a comparis~n of these variants.
A~lowance for satellite information led to substantial chang~s over ocean
:~reas and brought the analysis close to the synoptic analyais. In the re-
gion of the Atlantic Ocean to the west of Great Britain a region of cold
developed~ although lesa deep and eomewhat displaced in comparison vith `
the weatl~erman's chart. Northeast of the shores of South America the heat
rid~e became clearer. Over the Pacific Ocean, in the region of the north-
western xhores of North America, in variant AS in comparison With variant
A the nnalyais came close to the Weatherman's varisnt. The maximum differ-
ence between variants A and AS here attains 35 dam.
I~or evaluating the influence of satellite data on a forecast we computed
forec~sts for 48 hours in advance using the model in [1, 4]. AlloWance for
~atellite informa[ion reduced d2 from 16.4 to 14.7 dam2. However, this c~n-
~�lusion must F,e checked on the basis of a large number of cases.
Ne note in conclusion tiiat the cited results indicate the dFeirability of
~i~ing spatial-temporal optimum interpolation in the four-dia~ensional anal-
y~is of aerological an~ satellite measurements.
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BIBLIOG~tAP1iY
1. Anzhing, G. I., "I'ro}~nagtic M~del with U~~ of 5pecergl-Grid Traneform-
ntion," TRUDY GIDROMETTSENTRA SS5R (Traneactions of Che U5SR Hydro-
meteor~ologicgl Center), No 178, pp 40-51, ].976.
Z. Ilelov, P. N., Burtsev, A. I., "Num~rical Anglysie and Predicrion of Geo-
_ poCenCiel UBing Data from Remote Sensing of ehe Atmosphere from Satel-
liCes," TRUDY M~ZHDUNARODNOGO SIMPOZIUMA PO SPUTNIKOVOY i~TEOROLOGII
(Traneactions of Che InCernational Symposium on SatelliCe Meteorology)~
= Leningrad, Gidrometeoizdat. pp 3-20, 1977.
_ :l. Belousov, S. L., Ganditt, L. S., Mashltoviah, 5. A., OBRABOTKA OPERATIV-
NOY M~TEOR(?LOGICH~SKOY INFORMATSII S POMOSHCH'YU ELLKTItONNYKH VYCHIS-
LITEL'NYKH 1MASHZN (Processing of Routine Meteorological Information
Ueing ElecCronic Computera), Leningrad, GidrometeoizdaC, 1968, 282
pages.
4. Veyl', I. G., "Long-Range I~arecasting Using a Spectral Nonlinear garo-
clinic Model of the ACmoaphere," TRUDY GIDROMETTSENTRt1 SSSR~ N~ 71, pp
24-58, 1970. _
5. Candin, L. S., Kagan, R. L., "Constructing an Objective Malysis Syatem ~
for Various Data on the Basie uf the Optimum Interpolation and Optimum
Assimilation Method," METEOROLOGIYA I GIDROY.OGIYA (MeCeorology and Hy-
drolog;y~, No 5, pp 3-10, 1974. ,
6. Gubano~va, S. I., Mashkovich, S. A., "Evaluation of Che Information Con-
tent of a System qf Aerological and Satellite Measurements," 1~TEORO-
IAGIYA I GIDROLOGIYA, No 12, pp 9-14, 1977.
7. Kluge, I., "Allowance for Various Data in the Numerical Anal~sis of the
- Geopotential Field by Optimum Interpolation Method," TRUDY ME2HDU-
NARODNOGO SIt~OZIUMA PO SPUTNIKOVOY METEOROLOGII, Ler.in,grad, Gidr~-
meteoizdat, pp 43-49, 1977.
' 8. Mashko�vich, S. A., "Use for Four-Dimensional Analysis of Methods for
tfie As~;imilation of Meteorological Fields and Optimum Interpolation,"
TRUDY I;IDROMETTSENTRA SSSR~ No 1~3, pp 3-12, 1972.
'1. Meteliita, Ye. L., "Four-Dimensional Analyais of Data from Asynchronous
Observ,itions," TRUDY GIDROMETTSENTRA SSSR, No 197, pp 73-83, 1977.
- lA. 1':ir.tikanova, V. P., "On the Problem of the Accuracy of Temperature Sound- ~
ing c~f the Attnosphere and Artificial Earth Satellites," t~TE0Ri0LOGIYA
I CIDR~)LOGIYA, No 4, pp 76-78~ 1974.
11. liengts,son~ L., Morel, P., "The Performance of Space Obaerving Systems
for th~? Firet l..~RP Clobal Experiment," THE GARP GLOBAL EXPERIMENT. THE
- GARP P;ROGRAt~4iE ON NIJHERICAL E}~ERIMENTATION, Report No 6, 1974, 31 pages.
8
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~dR O~FI~~AL US~ UNLY
~ 12. PItOCE~DING5 0~ TiIE JOC 5TUDY GROUP CONFERENCE ON ~OUR-DIMENSIONAL
DATA ASSIMILATION~ p~rie 17-21 November 1915. :NE GARP PROCRAA4rt~ ON
NUMEYtICAL EXPERIMENTA'TION~ iteporC No il~ 1976, 437 pgg~s.
13. Trncton, M. 5., McI'hereon~ R. U., "On the ImpacC of Radiometric Sound-
ing Data Upon Operational Numerical Weather Prediction at NMC," BULL.
AI~R. MLTEOROL. SOC., Vo1 5$, No 11~ pp 1201-1209, 1977.
9
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rOtt Or~tCIAL ~15~ nNLY
UDC 551.509.313
NUM~RICAL MODEL OF ATMOSPH~RIC DYNAMICS ON A SPHERICAL LARTH
Mogcnw M~T~OItOLOGIYA I GIb1tOLOGIYA in Ftueeian No 1, Jan 1979 pp 11-23
[Article by Uoctor of Phygical and MathemaCical Scienceg V. V.~Penenko gnd
t;andidnte of Phyeicgl and Mnthemntic~l 5ciettces N. N. ObrazCsov~ USSR Hy-
drometeorologicnl 5cienCific Research Center, submitted for publication
- 'l8 April 1978j
Abstract: The auChors examine a numerical mod- _
el of atmospheric dynamics in isobaric coordin-
ates on a sphere. The discretization of the mod-
el is accomplished on the basis of the integral
identity approximation. The article ciCea examples ,
of use of the model for solving the problem of
weaCher forecasting in an ediabatic approxima-
tion for a tiine up to five days.
[TextJ This paper describes a numerical model for the modeling of the dy- -
namics of atmospheric processes on a spherical earth in an isobaric co-
ordinate syatem. The process of formulating finite-difference approxima-
tions is fotmulated on the basis of a determination of a generalized solu-
tion, dis~retization of the integral identity and the conditions of sta-
tionarity of the summator functional aris~ng in this case [2, 8J. As a
result, we obtain a family of energy-balanced finite-difference schemes
~~hose structure is determined by the grid region, elementary operators
for replacing the first derivatives of the space variables and Che quad-
rature formulas for approximating the integrals in the identity. For con-
:~tructing a sclieme for integration tn time we employ the splitting method
:ind the weak approximation method.
1. Now we will examine a system of equations in hydrothermodynamics used
for describing atmospheric processes on a spherical earth in an isobaric
coorJinate syatem [3J:
drt , ctg 4 1_ d H_ (l.la)
ar r Q ~v + l.J ~ a sin ~ d'.
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du riq rt' -!tt I df~ ` (1. lb)
dt ~ ~u ~ d Q
~f~' ~ Y~ RT : = s (l.la)
~lt gp ' ?
" ~ ~p ~
T ~ d H (l. ld) _
.
~i~ u = n, (i. i~> _
wh~re t ig~time, ~ ig longitude, e is the complement Co latiCude, p ig
pregsure, u=(u, v,t) ie the wind velocity vecCOr, T, H are the devia-
tions of Cemperature and geopotential from the standard values T(p) and
~~~P), ~'a ar.e the gradient of standard temperature and the adiabatic
temperature gradient re~pectively, ~,e 2 SL cos 8 ie the Coriolis parameCer,
~ ie the nngulnr velocity of the earth's rotation, a is the earCh's ra- -
clius, g is el~e nccelergtion of free falling, E ie a function of space co-
ardinates and time describing the nonadiabatic heat influxes to a unit vol-
ume,
- d a~ a~ t~ a~ a.
~ or c:"
tn` d~ u ~4 +
div m ri ~ t a y u + a~ c~:in G~ + d=: .
a sln U d~ , ~P
In the derivation of equations (1.1) we uaed the assumptions of the free
c:onvection method, and also assumntiona concerning quasistaticity of atmo-
spheric processes.
A solution of equation (1.1) will be souQht in the region
~
Dr=10~t~t~~.,D, U=Us`!D~,
(1.2)
Dj-jU~Ys2r.. 4�s6~6~1~ D;~=1P�~P~P'I� ~
~~I~cre p~ and pl is the pressure at the upper and lower boundaries of the
:itmnt~phere respectively, 6 0 3 0 nnd A 0. All
the resulCs will remain in force, but in place of the first two formu?~'e -
(11) we obtain .
. 2 a k ~r a 1~c ~r ~ -
~ /'1 . I.
a= S~
~j S~ t' 'l ks, .
It therefore follows that formula (14) and the formula (18) which follows
from it rem$in unchanged, that ie, Che exCernal acouatic wavea have the
same frequency as in the fu11 equations. At the same Cime, in the case ~)a~c,
1 with S-+ 0~-?~, thaC is, there are no auch oacillations, whereas in
the case a~ S, 1 with $ ~ 0~ Z-? J~2; expression (10) in Chis case showe
Chat p-r0.
We will apply the results to a study of the problem of a change in the fre-
quency spectrum under the influence of turbulence. We will take into account
. vertical turbulent mixing occurring primarily in the lower atmosphere
in the planetary boundary layer, and horizontal turbulent mixing. We will
begin with the firat. There are differenC ways to takQ into accounr. the
CricCion of air ugainst the earth. As in (3~, we will do thia by the
method indicated in [5]. In accordance with this method, all the equations
in the model remnin the same as without friction, and are assumed to de-
:~cribe the procesaes adequately everywhere. But at the lower boundary of
the atmoaphere we stipulate a non-zero vertical velocity, taken from the
upper boundary of the Ekman boundary layer, which is assumed to be drawn
o ut into a film. The magnitude of this velocity is given by the known
Dyubyuk formula [5]
aa ~ K ~PX~ + Pyyl,
nnd K a 1.4�102 m. Uaing expreseions (8), we obtain hence in place of the
boundary value condition (2) the following condition for amplitudes:
. � 32 ~
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,
. w = - ~~k~ P~ ~ 2 ~ ~
'Thus, ou~ model now consista of the syseem of equations (1) with the boun-
- dnry value conditions (2'), (5) and condition (7) for the initial daCa.
It eherefore followa that Che solution, as before, is given by formula
- (lU), but from (2') we now obtain, for determining ~ as a function of k,
the equation / 2 ~ ~
cb 3~ G, al ~ .b- c.~ 2 1, b.}. l, a~, (13' )
\ i r~ rh k ya
=
i= ~
Hence it follows direcCly Chat not one of the frequenciea ~(other than the
values a~ 0, as before, being a solution), aince ~l2 >~.2, can now be
real, beceuae in accordar~ce with {ll) this would mean that a and ~8 , and
eherefore, in accordance with (12), the Kummer function at the left and
the function associated wiCh it on the righe, are also real; therefore,
at Che left in (13') there would be a real expression, and at the right
a complex expresaion. Then, on the basis of (2') and (3) in place of
(6) we have -
r
ur ~f f E~xdydz ~0,
nb
becguse, for example,
! ~ '/~x.r [f.C K f I~PJ'.r~x' ~p.r~~ [iX ~ l~
wiCh periodic condiCiona. This means that all the solutions are now atten-
uaCing. Now we will convince ourselves that Che mechanism of this atCenu-
ation is such Chat long acoustic waves attenuate rapidly in conCrast to
quasigeostrophic and some acoustic waves attenuating slowly.
For our purposes, obviously, it is sufficient to examine how the asymptotic
' formulas (18)-(20) change if equation (13) is replaced by (13'). OmiCting
' rhe computations, we will cite the results.
' In tl~e case a) ~ a I~ ~~1 in place of equation (14 ) we have _
i 9(.
b+-~
j a- 1 1 �~~k ~~i' - l=.
~ Iience, for determining i1 we obtain a cubic equation accurately coinciding
~ w i t i~ t h e e q u a t i o n f o r t he similar problem in a quasistatic case [3]. Its
~ :ipproximate solutions are
i
~ _ 21 _
` i. - - iK k~ ~l ~ < >
gN ' - ~ k= + 1-
~ and
' k, g y ~1 k- (18' )
i i.~.a-i,o-iK 21i.o '~'Hr� ~
-f
~
33
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- whcre ~ p iq Riven by form~la (1g). The ~olution (Z1) carre~pond~ td qua~i-
E;en~trnptiic wnve~ nnd (18') cnrre~pnndg to external gCdUHt~C Wnveg. In
~rder tn chnrneteri~e the inten~ity nf attettugCidn we wi11 t~ke, f~r ex-
nmpl~, ~ wave with a l~ngth of 4,5U0 km. Then the lifeeime ~G ~ 6.3 d~y~
for n qungigeogtrnphiG di~turbenCe ~nd 0.4 dey for exeernr~l gCbUHti~C
wav~g. We nnte that fdrmula (21), in cnntrggC to (18) and (lg'), ig glgo
cdrrecC ~or ehort Wgvee.
In the cgge b)I~I ~I~I~ 1 we nbtein
7
i, ^ i,~ IK -s- ~ ~
2/
wt~erc ~n ie given by formul~ (19). For ~ wave wieh the length 4,500 km
'G = 0.9 day, thgC is~ long internal aco~~stic waves aCrenuate gomewhat
irar~ ~lowly than externa~ acoustic wavea, but far more rapidly thgn qu.~gi-
f;eoetrophic waves.
In tl~e case c)~a I~ 1 we obtain ~ h k~ a~y ~ .
l. ~ t t --1.~
~s ' (20 ~ )
1 ~KR ~
wi~erc ~ is given by formuln (20). The presc~nce of the factor e'2kN for
the fict tious part ahowe that ehort internal acoustic waves attenuate very
weakly. If, for ex~mple, L~ 30 km~ then 'C > 100 dayg. ~
A sim{lar problem in a quasisCaCic case (3j has six sclutions: 0, the
_ values (21) and (18'), and also Q. As we now see, a quasistatic ap-
proximatinn, virtually not distorting stationary, quasigeoatrophic and
external acoustic waves, filtera out the internal acouetic waves, adding
in place of them standing waves with the frequencies Q.
Now we will proceed to an analysis of the role of horizontal turbulent mix-
ing in the considered model of the atmosphere and we will show that under
its influence, first, the disturbances attenuate with a velocity dependpnt
little on their type, and second, the long-wave disturbances attenuate far
more slowly than long acouatic waves under the influence of vertical turbu-
lent mixing. This is a very important circumstance and shows that under the
lnfluence of vertical turbulence a quasigeostrophic and hydrostatic balance
(H e~t~nblished at long waves. If it appeared that the little-selective in-
Eluence of horizontal turbulence is appreciably stronger than [he selective
Influence of vertical turbulence, the fact of a iaore rapid attenuation of
xome types of oscillations in comparison with others under the influence of
this latter doea not have any importance.
In (6J the assumptinn was made ttiat allowance for the forces of horizontal
_ turbulent viscosity, that is, the addition of Laplacians of the correspond-
Ing components of the velocity vector to the three equations of motion,
leads to the attenuation of free oscillations with a logarithmic decrecoent
v k2 is [he coefficient before the Laplacian). It is clear that such a
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- ~o~ o~~icrni. us~ oxLY
~ ra~u1C would be nbtgin~d rigorouaLy oniy in g cg~e if rh~ Laplg~ign nf Che
cnrr~gponding function~ wae added to egch of the five equaCidns. Allowance
dnly fnr vi~ro~ity or ~nint gLlowanc~ fnr vi~co~ity nnd h~nt cdnducCivity,
with thp re~ult Chat the gygCpm of ~qugrion~ (1) ig replnced by the ~qu~-
tion~
u,~-r~~-t~,-?~~~u,
y~ py - lu + r~ v,
'iC~=--Pt~1;P-hr~tv,
y~ ~ - u,~ - vy --'t~u~,
p~ r w_.. ~ua. z~Y +~~:1 + c' P)
(the vigcogiCy and thermal cnnductivity coefficienCs ~re congidered equal)
~hould, in gen~ral, lead to a different regult. And in actuality, again
_ nasuming thgt r~ 0 and making computationa, eimilar to the preceding
ones~ it can be demonstrated that the amplitude, as before, is determined
by formula (10). but the firet two formulag (11) have the form
2kO~1-lrk=1 ~ 1r(r.*!�.k~?=-l=
a - S ' - (11'
` s~Y.+t~--l~ ' ~ 2As~ )
nnd Che dependence 7?(k) ig determined by the transcendental equation -
b
~1'+ b~l
~c~-~~ b~ a)~~+tKkti ~~.-+,,,k:~~_t1X .
(13") -
X ~ f - ~ i , b -r 1, a
Now we will note the following. Por long waves the difference between
these formulas and (11) and (13) is emall. Therefore~ it is possible to
investigate the role of the'parameters K and ti separately, assuming rheir
total contribution to be additive. We will noC do this for ahort waves~
I~ut in this case the problem is easily solved even without such an assump- _
tion.
We will begin With long wavea. The influence of K has already been inves-
tigated. We aill clarify the role of horizontal turbulence, solving equa-
tion (13) with the notations (11').
In the case a)~dl~~~~l ae have equation (14), rrom which folloWS the cubic
c:qiintion ~
a((a-~-IYk~~=--l=~-().-}-frk=igN "x ~ k'=~~
the approximate solutiona of which are
A~ ~ -tvks
(22)
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,
~Oit d~~ICIAL US~ nNLY
I
nnd
%.g, ~ L, )p-- t y~~ ~ ~la~~~
wh~re ~lp i~ given by fr,rmula (lg). If it ig aseumed, n~ i~ ugu~lly done,
thgt w~ 106 mz/~ec and we ggain exgmine g wave with the lengeh 4,500 krn,
th~ inten~iCy of gttenuntion of qugeigeoetrnphic disturbgnceg 1) is d~-
tern?ined by the velue ~G ~ 3.0 daye~ and external e~oustic waves t a
5.9 dny~. -
In eh~ cae~ b)~~ 1 we have equation (16)~ frnm which followe the quad-
raCic pquation �~r.~ , A ly --11
i. i. 1 Y k=) 4 H ~ 0'
the approxi~a~ate solution of which is (18"), buC ~ p is given by formuln
(20).
The case c)~~~~~~~, 1 ig not poasible at long waves.
Now we will proceed to an anglyais of ehort wa~es. On the other hand, we
liave only tihe case c). From (11') and (13"), uaing the correaponding asymp-
totic form (7)~ we obtain
b 1+!Kk F 1 ~ k~ )
r_. ~ -}-lt-: ~~lKkji~+lvk~j '
and the emall e parameter is given by formula (17), and o~ a 2kH. If E_
U, then
b ~ k~ t
i.o ~ t ''Z' t ~2 kg (x -1) ( ~ tt) - ( Z , ~ (23)
and with � taken into account~ we obtain
l=-(Kk)~ 2k~q (r.-1) (~+n,
~ -F 2 !q'k/
~2 kg (:-1) C 1 -4~ n~ -1 r 2/
~.aa%.~- tag~~ - 1 \ ~
r~+21~kJ + (Kk)~ 2 kg (:-1) I~+n1
\
where ~ i;s given by formula (23). With 'V a 0 we have formula (20'). In
particular, we see that attenuation under the influence of vertical turbu- _
lent mixing~ due to the simultaneous presence of horizontal turbulence, be-
c~me still less (in the denominator of the last formula the second te*~m is
proportional to ti). Thus, the principal effect on short waves is exert~,ed
by turbulent mixing. It is unimportant whether reference is to formula
(23) or fonmula (22); it is easy to check that the corresponding frequency
for any k i.s also a solution.
With reapect to long-vave disturbances, as we see, vertical turbulent mia-
ing, exertiing virtually no influence on quasigeoatrophic waves (with L=
4,500 km th~~ lifetime 'G e 6.3 days and due to horizontal turbulence
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�~.b days), raptdly exCin~ui~hpe ~~~u~tic di~turb~nc~~ (~C� 0.4 ~nd
0.9 day re~pectiv~ly for ext~rnal ~nd internel vev~e~ aher~~g due to hor-
iznnC~l turbul~n~~ 5,9 deye). -
~'hug, eurbulenc~ ~n~ur~s hydrogCgticiCy and qu~gigeo~trophicity of long-
wgv~ di~turbanceg in ~ n~utrally ~tr~tiEi~d ~tmogphere. Ie cgn b~ d~nan-
gtrgt~d thaC th~ eituatinn i~ gl~o the game in a~tgbly etratifipd ~em~-
- ~phere.'
$IBLIOGltApNY
1. Gandin~ L. 5., Laykhtman, n. L., Matveyev~ L, T., Yudin, M. I.~ USNOVY
UINAMICN~SKOY MBTBOEtbLOGiI (Principlee of Uynamic Meteorology), L~nin-
grad~ Gidrometeoisd~C, 1955~ 647 pagea.
2. Dikiy, L. A.~ "A~oustic and Gr~vitational Oscillations in Che Atmo-
ephere," IZVESTIYA AN SSSR, SER. GEOFIZ. (Newa of the USSR Academy uf
� Sciences, G~ophygical Serieg), No 8, pp 118G-1194, 1959.
3. Kadyehnikov, V. M., "Influence of Surface Friction an Mean and Shear
Neutrally Stratified Air Flowe," M~TEOROLOGIYA I GIDROLOGIYA (Meteor-
ology and Hydrology), No 2, pp 19-28, 1976.
4. Kamke. E., SPRAVOCHNIK PO OBY1~10VENNYM DIFPERENTSIAL'NYM URAVNENIYAM
(Handbook on Ordinary Differential Equations)~ Translated from German,
Moscow, "Nauka," 1971, 576 pages. _
5. Kibel', I. A., WEDENIYE V GIDRODINAMICHESKIY~ METqDY KRATKOSROCHri0G0
PROGNOZA POGODY (Introduction to Hydrodynamic Methods of Short-Range
Weather Forecasting), Moscow, Gostekhizdat, 1957, 375 pages.
- 6. Monin, A. S., Obukhov, A. M., "Small Oscillations of the Atmosphere
and Adaptation of Meteorological Fields," IZVESTIYA AN SSSR, SER. GEO- ~
FIZ., No 11~ pp 1360-1373, 1958.
7. Yanke, Ye.~ Emde~ F., Lesh, F., SPETSIAL~NYYE FUNKTSII (Special Func-
tione), Translated from German, Moscow, "Nauka," 1968, 344 pages.
37
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~o~ o~~iciaL us~ ox~,Y
~ _
UDC 551.(501.45+507.362)
AUTOMA~IC OONTROL OF DATA FROM rF~4'L1tA2'UR~ SOU'NDING OF TNE ATMOSPHERE
N'ROM MET~OROLOGICAL SAT~LLITL5
Moacow M~T~OROLOGIYA I GIDRpLOGIYA in Russian No 1, Jan 1979 pp 34-41
(Article by Profesaor L. S. Gandin and V. P. Tarakenovg, Main Geophyeical
Ubaervatory, eubmiCCed for publicatton 26 April 197$]
Abatract: The authors have evaluated the pos-
aibilities of different methods for automatic
control (checking) of data from temperature
sounding of the aCmoaphere from meteorological
satellites. It is ahown Chat on the average not
leas than 7-8r of the telegrams with data from _
indirect sounding contain serious errors. For
detecting and eliminating these errors it is
feasible to uae atatistical horizontal and
vertical control methods, somewhat modified
~ by taking into account the correlation of ran-
dom errors. As a result of this correlation
the sensitivity of the considered methods
proves to be quite high, despite the great dis-
persions of the random errors.
(Textj For many years data from temperature sounding of the atmosphere from
meteorological satellites have been disseminated on a routine basis. How-
~ver, attempts at ti~e use of this information together with ordinary radio-
:;onde data in constructing initial fields for numerical forecasting for the
_ most part have led to disappointing results: forecasts with the use of data
from indirect sounding have, on the average, been no better than without
::uch use. As a result, up to the present time data from indirect sounding
have not yet been included in the operational lines for Che routine pro-
cessing of aerological information at the world prognostic centers, in-
cluding at the USSR Hydrometeorological Center.
One of tl~e reasons for such a situation, in all probabiliCy, is as follows.
In the process of collecting, processing and moving any information through
communication channels there will inevitably be individual serious errors
which must be detected and corrected, or as a minimum, the erroneous data
38
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~Oit O~~ICIAL US~ dNLY
. .
_ mus~ be dieearded. ~'hi~ i~ Che ob~ective of inethodg fdr ~utnm~eiC eontrdl
(ch~cking) wiCh use nf gn ~leerronic comput~r, eo which, in p~rtl~ular~
r~dio~ond~ d~t~ ~r~ ~ub~~CC~d rdutin~ly (1, 5]. Nowever, gpplic~ble td
d~ta from 3ndir~eC gnunding nne only are gutomaeic conerol method~ not em-
" ployed, buC there hae bp~n v3rCu~11y nn digcus~inn of ehe problem of CreaC-
~ ing guch methnde.
In gn parly ~tage in th~ d~velnpmene of indirecC snunding the rouCinely dig-
~emingt~d informaCion on the vertical profiles of Cemper~Cur~ and geopoCen-
tial more or legs uniformly covered tih~ earth's surfac~ and nn appreciable
part of Chie information was for th~ region of lgnd cover~d by dgCa from
ordingry r~dioeonde observationg. Nowev~r, during recent years there has
been routine transmiegion of eatelliCe sounding daCg nnly over the oceans
and seas, where Ghere were few radiosonde data. Under such conditions the
principal meana for checking data from indirect gounding is not their com-
pnrison with data from direct sounding, buC a checking of their inCernal
~onsieCency.
t?ne of the methods for such checking could be statiatical checking (control),
which is used eatengively applicable Co radiosonde daCa. It involves, as is
well known (for example, see [4]), a checking of satisfaction of the equa-
tions of sCatics (barometric formula for relative geopotenCial) in each
- laye.r beeween two ad3acent main isobaric surfaces, and specifically,
compuCation of the nonclosures ~ i of Che equation of statics using the
formulag
= Hr+~ - Hi - A~ - H~ (t, tr+~)~ (1)
where i is the number of the isobaric surface, ~I is geopotential gp dam, t -
- is temperaCure, �C, Ai and Bi are constants:
A~ - 18~2 Ib r? SP dam; B~ _~i,3i2 ~g p~+i (2)
~ r+ ~ C -
ln .~ddltion to individual serious errors, the ~ i nonclosures are caused
I,y always existing small random measurement errors and also by the devia-
tion of the vertical temperature profile in the layer from a linear pro-
file relative to the pressure logarithm. Therefore, the hypothesie of the
presence of serious error arises only when ~B i in absolute value exceeds
some admissible nonclosure L1i whose value has been estimated in advance.
Analyzing in such cases the distribution of nonclosures ~ i in adjacent
layers, most cotmnonly it is possible to as~ertain the cause and magnitude
uf tt~e serious error and introduce the corresponding correction.
T:ible 1 describes the results of static checking of 912 telegrams with in-
ctirect sounding data for 20 July 1974 reaching the USSR Hydrometeorolog-
Ical Center. [These data were put at our disposal through the kindness
of Ya. M. Kheyfets.J Each telegram conCained data on temperature at 15 sur-
f.:ices from 1000 to 10 mb and on the relative geopotential of all surfaces
:~bove 1000 mb.
39
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Tnble 1 showg thar nbout S~ of ~11 eh~ relegrnrag conC~in ~pridu~ ~rrorg
deteceed by eegtie che~king (etgCi.c checking (contYOl) is noC cgpgbl~ of
- d~e~~ting ~11 g~ridu~ ~rr~r~). Thi~ p~rc~nC ig ~ppr~ci~bly low~r th~n for
rgdio~onde datg, but it gnes wiehout saying that it ia impossible Co
~iegl~ct such a nunb~r df errora. We algo se~ Chat more eh~n 709: of the d~-
C~CCpd serioue ~rror~ ~an bp corr~ceed wiehnur nmbiguiCy using etatic cnn-
Crul, ~nd an~ther l0y by me~n~ of a simple combingeion nf ~egeic conerol wieh
~ome other merhod.
UnforCunately, beginning in ,1~1y 1977 the dgCg from indirecC gouttding, Cra?~s-
~ n~itC~d on ~ roueine bagis, dn noC contain informati.on on eemper~ture, buC
only include relaeive g~opoC~nCia1. 7.'hia deprive~ tihp userg nf Che possibi;t-
ity of extremely convenient detection and elimingtion nf serious ~rrora in
this informaCion by means of static control. _
Another widely used method ia horizontal static control. This involves op-
timum interpolation hnriznntally to the.point to be checked on the basis of
data for surrounding points and comparison of the interpolated and mbserved
values. In this case the admissible nonclosure is assumed to be proportional
to the mean square error in Che menCioned comparison, which is computed
in the proceas of deCermining the interpolation weights [1, 3].
In evaluating the poasibilities of horizontal statisCical conCrol of data
from indirect sounding it must be Caken into account Chat Che random errors
~f these data, first of all~ subatanCially exceed ehe average errors of
radiosonde data, and second, in contrast to the latter, are horizontally
correlated.
The problem of the magnitude of random error in indirect sounding is now
quite clear: data from many authors ([7, 11] and others) indicate an agree-
ment with one another that the mean square errors in data from indirect
sounding are approximately twice greater than ir? the case of direct sound-
ing. For example, for Che temperature in the troposphere the estimates are
2-3� in comparison with 1-1.5�C for radiosonde observations.
It is understandable that this fact reduces the'possibilities of horizon-
tal checking of indirect sounding data.
The situation is different with the correlation of satellite sounding errors
l~orizontally, or to be more precise, along the satellite flight trajectory.
'1'he ideas of different authors with respect to the reason for this correla-
tion and information on the correlation functions of errors are contradic-
tury. At the same time, the fact of the presence of correlation of indirect
sounding data, which was not given due attention over a series of years,
now is generally recognized. This can be judged from a series of studies
by Soviet and foreign authors, such as [7, 9, 10]; the correlation of errors
is traced to distances comparable to the correlation radius of temperature
itself.
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~
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Table 1
lteaulte of Static Checking of Indirect
Sounding U~ta
I~uau~iecTeo renerpaai~~
g npoucttt~x K ~utcay ~
nces CONiitITl.1~�
TC11C1'(18M~ ~IW!f Tf.iC� 4
r~a~~
Bccro reaerpa~iM . , . 917 100
COMIINT@Ab11W~ ~(~HIIWC . G9 7,6 ~p0
7 OAIt0~118~I~lOC ItCfip1R1C11I1C . a0 5~,5 92
8 ABY~~~a4~~oe ncnpaanenNC 7 0,8 10
y 6onen c~o;~;u~e owiiGKii 12 1,~ I8
KEY~
- 1. Numb~r of telegrams
2. In percent of number of...
3. all telegrams
4. questionable telegrams
'i. All telegrams
G. Doubtful data
7. Unambiguoue correction
8. Ambiguous correction
9. More conplex errora
The correlation of random errors does not decrease, but on the contrary, in-
creases the possibilities of the detection of serious errors against their _
Uackground, that is, the poasibilities of horizontal checking. In thie de-.
tection procese it is desirable to use not optimum interpolation, but op-
timum comparison, that is, determine the interpolaCed weights ai from the
requiremenC of a minimum of the disperaion of error in comparison of the
lnterpolated value and the obaerved value, and not with the true value.
tJith correlated observation errors these two requirements lead, generally
speaking, to different values of the weighta. (In such detection it is de-
~irable to use not Che optimum interpolation procedure, but optimum (in
statistical sense) comparison).
41
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1~nlt n'~CZCrAL USC ONLX
A~aume thnt ig Gh~ ob~~rv~d deviaCion nf Che metQarolo~ic~~. elem~nC _
Erom th~ mean value at the i-th pnint:
I~ =f~ a,, c 3>
wher~ f~ i~ ehe erue vglue and d i i~ ehe ob~~rvgtinn ~rror attd aesume
that the errors correlgee with one anoeher but do ttoe correl~te with the
tru~ value~. Then the covari~tions
~
,n~;-f,fi~ m,~rl,f? n~r=a,a~ (4)
(the line de,~ignatea statietical averaging) ~re relaCed by the expre~sion
_ ~
m~~ ~ n:~~ + n~~� (5)
The diapergion -
r,
_ ~fo --f)' ~g~ -
_ ~ of the interpolation error at the p~int 0 in accordance with the formula
Io = ~ r~~ j, (7)
is then expreaeed by the formula
a n n
E' = moo - 2 E ai mo i-~- ~ E ai ~tJ "~U~ ( 8)
ra~ r_ i ~_i -
and the diapersion
~
E~ _ (fr f~.l ~9)
of the error in comparieon of the interpolated value with the observed
value by the �ormula
~ ~
n n
~ _ /!!00 - Z ~ Qf 1/to ! ~ ~ J~ Q~ 11l~~. ~ ~
!a1 f-t~=1
Therefore, with stipulated weights ai the E and E values are related by
the eacpression N �
E' = E~ ~t,~ - 2~ a~ 1to r�
i=~ (11)
Khowing, in particular, that a positive correlation between obaervation
errora (npi > 0) leads, all other conditions being equal, to a decrease in
dispersion of the comparison error.
The req~i~ement of an E minimum leads to a system of equations for deter-
mining the weights
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h~~
~ ~ A
~ fI~ JJI~~ ~ H1~
, ~ (12)
and Ch~ r~ryuir~m~nti df ~n ~ minimum 1ead~ ed eh~ ~y,~tem
~ . M r w
~ct~m,~~ ~to~, (13)
1=1
which in thp pre~enc~ of correl~tion ~rror~ differ~ fram (12). In the cnn-
erol, in cantrngC to ob~~ctivQ analy~ig, it i~ desirable to use gy~e~m
(13), which makes it poseible to decreae~ ~ gdditionally, Chae ie, in-
creaec the aensitivity of the method.
I~'igure 1 pre~~ntg gom~ r~~u1Cg of numericgl experimenCg carried out wieh
the p~reicipaeion of m. V. Knrosteleva fnr evaluaCing Ch~ pogsibilitieg
c~f horizontal control of egtellite eounding data itt dependence on the dis-
rance r between ~1d~8~EriC observ~tion points. This possibil3ty ie character-
ized by n value of the relaCive ~nmparison error
. ~
~ ~lq~ -
e~ .
Y~?w~
~1 '
~ qe
/
/
4~ /
~
4� ~
/
:
/
^
~ ~
t
. V ~ ~ ~
r u ~oo ~ r.;~~ ~ ~.,M
~i~;. t. Dependence of inean square relative error ~ in comparison of inter-
rol.ztton value of temperature with obaerved value on distance r betWeen ob-
~ervntion points. 1) nii ~ 2.25 (�C)2, noncorrelated errora; 2) nii ' 9
(�C)2, noncorrelated errora; 3) nii ~ 9(�C)2, correleted errora; optimum
interpolntion; 4) nii = 9(�C)2, correlated errors, optimum comparison
Curve 1 in Fig. 1 describes the possibility of checking of radiosonde data
_ ~ 1.5�C), and cuxves 2-4 data from indirect sounding
3�C) in cases of absence oE correlation of errors (curve 2) and its presence:
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.
rnn o~~~~~nt~ u~~ ortt~Y
wlrt~ eh~ u~~ in ei~~ cnmpuC~tiong nf the w~ightg d~ ~yge~m (12) Ccurv~ (3)
_ .~nd ~y~t~m (13) (~urv~ 4). A~ompnrigon e~f ehe lae~~r wieh eurve 1~how~
eh~t th~ ~~tt~ieiviey ~f horizon~al contrtil df ~~e~1~it~ daea is ~dm~what
high~r ( E i~ 1eg~) thnn for rgdic~~nnd~ d~t~ in Ch~ c~~~ af ~m~11 di~-
t~nc~g r~nd ~pproxim~C~1y Ch~ g~m~ in Ch~ ca~~ of ~~rg~ r. ~'h~ po~~ib-
iliti~e of thi~ c~nerol wnuld b~ decre~~~d ~om~wh~e in Ch~ Ga~~ of uge
c~f ~y~e~m (12) end would b~ ~r~atly d~cr~~g~d if eh~ r~ndom ~rrnrg ~f in-
dir~ct gounding are unCOrrel~t~d with one another. -
Table 2
Corr~laCion (Abov~ Diagonal) and Cov~ri~Cion (~e1ow ~iagon~l, d~mZ) Matrice~
of the Relgeive ~~opor~ntial for WinC~r Spggdn -
1 Caoir, .w6 1000/~.~i~) ~ 85017U0 I 70b~b00 I 500l400 I~t001300 I 300/7u0 I 400/I00
I
I U(N1/850 8,94 0.88 0,~~ 0,60 O,b 1 --0,18 -0,41
RSII/700 H,i 1 10,9T O,gl 0.7~ 0,5J -~U,13 --0,57
700/500 10.4b 14,67 ~ 2~.84 0.91 0.71i ~0,7i ~.GI
fiW/~00 ~i.~l~i 7,1 t 1;1,0~ 8,8~ 0,89 --0.1 U -0,70
ao0/;l00 4,G7 G,00 ' Il,ar, ~,le y,50 n,l-? -O,Go
3WI200 -1.6d -2,~3 I--3,57 --1,137 I,~N 12,=IG 0,87
.00/100 -10.?~) -laly ! ~--27.12 -17,~J -IG.II Ip~h 75.~1
K~Y :
1. Layers, mb
Table 3
Parameters of Vertical Control of Relative Geopotential for Winter Season
~ C~ou. uG
flapa�
Merp 1 ~ap ZuT IO~M,'830I b.iU/1~0 ( 700l5G0 800/~400 i~00/300 I 3001100 I 200/I0~
a) , - O.:,t O.t9 0.32 0.91 0.80 I,11
ur~-t. r a) ~ 0.~{SI U,~9 0.32 0.83 0,51 1,1~
el c - 0.3~: 0.81 0.33 0.9a 0.81 1,~0
0.78 0,:ly 0.91 O.A~1 0,'!2 0,~ 1 -
'ir~t. r 6) 0.73 0,~6 0.1~1 0.38 0.17 0,60 -
O,1S O.:i7 ' 0,81 O,a~ 0,26 0.~0 -
al 4,U ?.8 3.9 2.8 4.0 5,3 17,9
~t Q) ~.9 4,U 6,~ 4;1 5.4 5,~ 20.d
4 n~w�) 4l 2.8 ~.0 2.9 ~.7 ~.a 18.6
lC~Y :
1. Parameter
'2. Variant
3. Layers, mb
4. dam2
44
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~dR U~~~CtAL US~ dNLY .
,
Uu~ Cn Ch~ impog~ibtllty nf ytr~ttr. c~hecking, iC iH c~CCOrdingly d~~ir~ble
ta u~~ eh~ ~Ceei~ticgl m~Chod fdr eh~eking indir~et aounding d~e~ by m~~n~
u~ v~rCiC~l ine~rpolgeion. Applie~bl~ to radi~~dnd~ d~ta, gueh ~ m~th~d w~g
hropd~~d by M. Yudin [8] (~l~a [16j).
Ie i~ md~t de~ir~blp ~n u~~ ehig appro~Gh in ~heCkin~ eh~e vnlu~g of eh~ r~l-
~tiv~ g~~pot~ntial (rhi~kn~~~) di th~ 1~y~r~ beewe~n ehe ~d~~CpnC m~in i~o-
bgrie ~urface~
ti, ~ x~~.~ ~ H~~ cia~ )
'I'he inforroation on th~ ~tatigeicgl ~~1~rion~hip b~Cue~n the va1u~~ di th~ -
rpl~tiv~ g~opot~nei~i h of different layer~ n~~~~~~ry in ~~rrytng nue ~uch
_ rh~eking can b~ obt~in~d ~~~i1y c~n th~ b~gig nf ~v~il~ble dgtg dtt th~ ine~r-
l~v~l temper~ture cnrrelatinn. Prp~ig~ly frntn the b~romeCric formul~ fnr
relntivp g~opotenti~l (~ompgr~ (1) gnd (2? We d~rive Che expreg~inn
m~R~ B~ g~ (mSR m~~~~+~~ ,~'f' mi+~, ~.~i (15)
ah~re m;R~ ~ ~h~ � f~~~hk
gnd ~ m~R~ = ~~r " ~i~~t~ t,?~
- ~rp ehe ~ovgrigtidn~ of relgtive g~opotential of "slementary" layerg and
Clte t~taper~Cur~ di the i~ob~~ic eurfaceg reepectively end Bi gre coeffic-
ientg determined uging formula (2).
As nn example, in Table 2 ae have given the values m~k, computed uging data
from V. I~. Boltenkov on the interlevel correlatinn of temperature for the
ainCer season ((2), see algo (Sj). Since the relative geopotential is pro-
portional to the mean temperature of the l~yer, it is characterized by n
qreater vertical sratigtical cohesivehpsg than the temperat~re of the iso-
bdric gurfaces. This can be 3 udged by ~amparing the valueg of the correla-
tion c~efficients; ~R~
~llt) `t~~~;) fiAR~, ~IA~
cited in Table 2 above the main diagonal With the data published by Bo1Cen-
kov nn �jk~ [2, Sj. -
It ig desirable.that the vertical control of relative geopotential be ac-
' complished by caeang of interpolation using data from two adjacent layers
abnve and beloW that being checked, and for the extreme layers by -
m~nns nf extxapolation using date for one ad~acent layer. As in the case
uf horizontal checkin~. it is desirable to uae an optimum comparison.
Ar~ an example, Table 3 givee the resultg of computntion of the interpolation
weighcs ni-i,i gnd ai+l,i gnd the admiagible noncloaures
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~
~ e, - kE~ (i7)
nf ~ucl~ control on the basis of data on Che covariations h�rom Tab1e 2.
In th~g~ compuCation~ th~ di~p~reione of errore in determining hi wer~ com-
rut~d u~ing eh~ formul~e _
iif;~ = Bi ~Kii~ ~ ~~i~~, (18)
The regultg nf Che computaCiong are given for the following varignta: -
_ fo~ r~dio~onde data; in this caee for the 1000 mb au f~Ce iC ie aseum-
~d that n~~) � S(�C)Z, ~nd for Che rem~ining eurf~cea ~~~1.5(�C)2 (i
1); th~ errore werQ coneidered uncorr lnted, that ia n~
b) fnr date from indireCt gn nding; n~i~ ~ 16(�C)2 n~~ ~ 6.25(�C)2 (i ~ 1)
with uncorrelated errors nih~ = 0; _
c) for datg from indirect e~unding with correlaeed errors, such that
n~~i,~ ~ ni~`i+~ = U,60 and n~n?~, r~+~ = 0,20.
In the computations it was aeaumed that k n 2.5 (comp~re [5J).
't'he data in Table 3 lead to the conclusinn thae in the absence of correla-
tion between the errora the poesibilities of vertical control of data from
t~atellite eounding on relative geopotential would be far lower than for
radiosonde daCa, but as a result of the correlation of errora of indirect
~ounding Che posaibilities of vertical checking of both types of informa-
~ tion approximately coincide and are considerable.
Specifically, the admissible nonclosurea of vertical checking of data from
satellite sounding on relative geopotential decrease due to the correlation
of random errors by a factor of more than 2, as can be seen from a compar=
ison of the G1i values in lines b) and c). An exception is the extreme lay-
ers (in our case 1000/850 and 200/100 mb), the possibilities of whose check- ~
ing, naturally, are not great. With respect to a comparison of the d i val-
uee in linea a) and c), it showa that the admiesible nonclosures of vertical -
checking of data from i.ndirect saundin~ are even aomewhat less than in the -
casc of direct sounding.
The weights and admisaible nonclosures cited in Table 3 can also find di-
rect use in developing a routine method fo: the checking of data fzom in-
direct sounding of the atmosphere.
BIBLIOGRAPHY
l. Belousov, S. L., Gandin, L. S., Mashkovich, S. A., OBRABOTKA OPERATIV-
. NOY METEOROLOGICHESKOY INFORMATSII S POMOSHCH~YU ELEKTRONNYKH VYCHIS-
LITL~L'NYKH MASHIN (Proceasing of Routine Meteorological Information Us- -
ing Electronic Computers), Leningrad, Gidrometeoizdat, 1968, 282 pages.
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2. Boltenknv, V. P~, "Some CharacCerisCics of Three-Dimenaional Macro-
~tructure of Air TemperaCure," TRUDY GGO (Transactiona o� the Main Geo-
p~y,`sical Observatory), No 191, pp 47-57, 1966.
3. Gahi~~n, L. S., OB"YEKTTVNYY ANALIZ METEOROLOGICHESKIKH POLEY (Ob~ective
Analysis of Meteorological Fields), ~,eriingrad, Gidrometeoizdat, 1963,
287 pagea.
- 4. Gahdih, L. S., "On Automatic Checking of Current Meteorological Inform-
ation," METEOROLOGIYA Z GIDROLOGIYA (Meteorology and Hqdrology), No 3,
pp 3-13, 1969.
_ 5. Gandin, L. S., Kagan, R. L., STATISTICHESKTYE METODY INTERPRETATSII
METEOROLOGTCHESKTKH DANNYKH (Statiatical Methode for the Interpreta-
Cion of MeCeorological Data), Leningrad, Gidrometeoizdat, 1976, 359
pages. -
6. Gandin, L. S., Prigodich, A. Ye., "Statistical Checking of the Vertical
Profiles of Geopotential," TRUDY GGO, No 348, pp 123-131, 1975.
1. Tarakanova, V. P., "RegulariCies of Errors in Determining Temperature
_ and Geopotential Using Data from Indirect Sounding of the Atmosphere,"
TRUDY GGO, No 348, pp 46-52, 1975.
8. Yudin, M. I., I1'3.n, B. M., Rukhovets, L. V., "One Method for Checking
_ and Correcting Aerological Telegrams," N~TEOROLOGIYA I GIDROLOGIYA,
No 5, pp 35-39, 1964. -
9. Annex, F., REPORT OF THE TLJELFTH SESSION OF THE JOINT ORGANIZING COM- -
MITTEE, WMO, Geneva, pp 5-7, 1976.
- 10. Phillips, N. A., "The Impact r~f Synoptic Observing and Analysis Systems
on Flow Pattern Forecasts," BULL. AMER. METEOROL. SOC., Vol 57, PJo 10,
pp 1225-1240, 1976.
1.1. Smith, W., Personal communication, 1975.
47 -
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~
- UUC 551.515.2(261)(263)
ACTIVITY OF T}iE HURRICAN~ SEA50N IN THC NOI~TH ATLANTIC
Moecow MC'T~OItOLQGIYA I GIDROLAGIYA in Itugeinn No 1, Jan 1979 pp 42-49
[ArCicle by V. A. VeCroumnv~ Odee~a HydrometeorologiCal IngCiCute~ submitC--
ed for publication 1 t~rch 1978J
AbetracC: It ig proposed ChgC the nctiv-
- ity of the twrricane aeason in an ocean-
ic region be characterized by a complex of
quantitative valuea: intenaity coefficienC
K~ mean seasonal velociCy of movemenC of
Cropical cyclones V, and also their total
_ internal energy U. These characteristics
were computed,for the period 1886-1974 for
the tropical and temperate zonea of the -
North Atlantic. The mean values und var-
iability of K~ V, U agree well with uni-
directional climatic vc~riations ~ver the -
northern hemisphere.
(Text~ A great many sCudies (1-6~ 9-11J have been devoted to all possible
~npects of development of tropical cyclonea (TC): frequency of recurrence,
movement, cloud and inCernal structure, energetics and theoretical invest-
t~ation~. Howev~r, the activity of individual TC and the hurricane season
In Kenerul have not been adequately discugsed. The qualitative characCer-
iKci~g "intensive," "active" (llj, etc. used earlier in different descrip-
tion~ were ambiguous.
'I'I?erefore, our ob~ective was at least a partial discussion of the problem
~f activity of the hurricane aeseon, to find quanCitative values of Chis
:ictivity, and also to ascertain the possibility of using information from
'I'C for describing tl~e peculiarities of the tropical zone and the thermody-
namic processea transpiring in it over a long series of years.
It is known that the exiatencP of TC is associated witri an entire complex
of necessary and for the time b~ing still not thoroughly studied adequate
conditions in the ocean and atmosphere ~5, 6]. On the basis of regular ob-
rcervations for each oceanic region we regiatered information, in the form
48
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' ~ ~UEt O~~YCIAL US~ dNLY
nt ehe number of 'CC, rheir Cr~3ecenrieg ~nd oCher nhttr~ceerigeics, nn eh~
r~nltzntinn nf Cl~e neceg~~ry and nd~qunt~ ~ondition~ for Cheir exigCenCe
[n tlie oc~nn-~tmosphere syeCem.
r\++ tli~~ metrc~rolo~ic;~t-~~~~nnn~rapl~ir. c~nditian~ ~~cnmpnnyin~ rhe fnrmatinn
uf 'CC, tl~c authnrg uf [2J ug~d the eurbul~nt C~nn~f~r nf 1nCertt hegt nf cdn-
- d~ngntion C~C, Ch~ eurbulent heat Elux inCo Che nenx~gph~re frnm the oce~n '
gur�dc~ tjti, t~ttd gl~o Che realizgtion of Che lnt~nt h~at of condensgtion A.
- All Che~e p~rgm~Cere are eoneid~red to be the resule of inCergctinn betweect
the ncenn gnd th~ ~tmo~pher~ gnd g TC ig reggrded gg Che reaulC of. thi~
prdcegg. Taking into nccount Che conclusion in [2~ thet Che valueg of the -
r:~neinn~d parametera before and in the period of formntion nf TC differ con-
sid~rably (by an order nf magniCude or more) from the "quiet" etnte of thn
~tmosphere, it ig pa~gibl~ Co speak of the ~xiaCenc~ of TC ae same optimum
in rh~ thermodynamiC atate of the ocegn-genw sph~r~ gygCern.
'Ct~e grent variability tn the number of TC from yeur to y~gr (1, 3, 6, 10, 11J
mnkeg it pnsgible only in genergl fe~tures to formul~te a hypothesis concern-
ing tlie value to be aeaigned to this opCimum, realized in powerful atmospher- -
tc eddies, nnd on the inCensiCy of such a realization.
T{~e intengity of an individual 'TC at the present time is evaluated on the
I?asi~ of Clie pressure nt itg center, maximum wind velocity, duration of per-
rstr~tence of these extremal conditions, and finally, on the basis of the
economic and human lossea caused by Chem. The intensity of the entire hur-
ricnne season fs judged~ for example~ on the basis of tt~e total number of
7'C and their number reaching Che hurricane stage. However, it is not dif-
Eicult to compare the~e characterisrica and they are not exhaustive for
analy~is of either an individual TC or for the enCire hurricane season.
The application of a sirople method to already exiating information on TC
nakes it possible Co obtain an index of hurricane intensity which can be
used in characterizing individual TC and hurricane sensons in different
~~cennic regions. We propose that thia index be expressed by the ocean area -
5.~~ over which existed e TC determined from tl~e length L of the trajectory
and the zone affected (diameter D) by the TC:
ST~ � LD.
'I'liis .~re~~ durin~ the season rQlated to the ocean area So, such as the North
~ltlnntic, will y,ive the dimensionless coefficient
K = ST~/So,
~l~owin~; ~ver what part of the ocean region the necessary and adequate condi-
cions were realized during tl~e course of the season.
'I1~r 1rnFth L of tt~e trajectories for all TC in the North Atlantic during the -
~~eriod 188Er1977 in the stages of a tropical storm (TS) and hurricane (Hr)
wns determined using the materials contained in (10, 11J) and differing
49
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Tgble 1
_ Cl~rirric~t~rt~iei~H af Ine~nKity oE tiurricnnh 5en~on in North AC1~nCic (1886-1974)
Mi1Nl'lIM)~M ,~IminN~~a Cpeaiiec
u+ Muoro� rt V,
r cpe~unz 1 cpc.uu~~ 2 .~rTi~rr 3
4 ~(031a~U1~11QH! UHifH~UANOffll ~~1~
10 8ecb pert~oH . . , 0,92 0.03 0,3J 0,19 0,~8
11 K)~cuee 30� c. w. . ; I 1;24 I 0,01 I 0,3y , 0.21 I 0,5:~
12 Ccecpuee 30� c, w.~ . 0,90 I 0,00 O,;fB 0,21 O,b6
5 Cped?~~x cKOpoere Beuxcxua TL( (V xx/~)
9ecb perxoN . . , 3r 4 14,~ 22,9 3,7 O,IG
IC1~cuee 30' c. w. . ; I 30,t1 I 12,U ~ 19,1 ( 3,3 0,17
G~eepi~ee 30� c. w. , b4,2 IO,I ( 30,8 7,4 0,24
6 CjIA1MQ(1MG1t eHyrpexHAa 3NPp2UR Tu JG CC30H ~U~/~ 3p1~
B~ecb perooH . , . 670,0 24,4 258,6 125,0 0,48
Kl�tHee 30� c. w. . . :I 538,4 I 12,2 I 173,0 92,6 0,54
- CeeepHa 30' c. m. , 192,5 0,O(~ AS,G 47,8 0,56
~ C;IJMMOpNCII ANyfPlHMJflI !Hlptpll TL( 3Q It~OH MQ dl~ CBAtpHOl7 AfdQMTUKLL ~U~lO~~ apr/MS)
1 n Becb pen+on . . . 20,2 Q.7 ( 7,8 3,8 0,~8
K)~cece 30� c. w. . . 29,4 I 0,7 9,5 I 5,1 ( 0,54
Ceeep~+ee 30� c. ~u. . 12,9 0.0 ~ 5,8 3,2 0,56
` 8 CyM,N~pM(1R BNJ/TpL'MHRlt JNCp.UA Ja fC34lf HU ll~ f1.1011(Cf~ll,
rrod KoropoA c~wcctaoee.~u TL( (U�10~~ 3p.;~.~~)
10 Bec~ pcr?+on . . . 3.2 1,4 2.0 0,3 0.16
IU�cHCe 30� c. w. . . 3.8 I 1.5 I 2,5 0.4 I 0.l7
12 Geeepi~ee 30� c. ui. . 4,~ i 0.0 l.~i 0,8 0,;l3
9 CIJX.NO~lHQR k~iHPi{IYPCKCR 3Mt'PtGR, zcNCpupyr~wc+ TU ~a fC30M ~U�/~ 3/f:~
Bec~ pernoN . . . :I 16.1 0,6 6.2 3,0 I 0,48
K)~;uee 30� c. w. . 12,9 I 0.3 I 4~ I 2,2 0,54 -
Cexepree 30~ c. w.~ 4.~ 0.0 ~ 2.1 1,2 0,56
KEY:
1. Max:tmum of ineans
. Min:tmum o f inegns
'S. Lon~;-term mean
~i. Inti~naity coefficient (K)
5. Mea~i velocity of movement of TC (V km/hour)
6. Tot~il internal energy of TC during season (U�1026 erg)
7. Totf~l internal energy of TC during season per m2 in North Atlantic
(U � ]1014 erg/m2 )
.3. TotFil internal energy during season per m2 of area over which TC -
exiected (U�1015 erg/m2)
9. Tot~~l kinetic energy generated by TC during season (U�1026 erg)
10. Enti.re region
- 11. To acouth of 30�N
12. To n~orth of 30�N 50
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with respecC to reli~bility and eyetematization itt accordance wieh a
~~nified method. A~oint nllowance for ehe extent of the era~ectories
in the eCorm and hurricane stages was made by ua Caking into eccount
th~t the Q~, Q,~ and A valuee during the pre-hurricane period corresponded
to their valuea in ~ m~Cure hurric~ne (2].
The c~ho~.ce of Che mean diameter of a TC was complicaCed due Co the differ-
ent mel~nd for evaluaCing ite boundaries (on the bgsie of the diameter of
~ontinuous cloud cover, on the basie of the laat closed isobnr, on rhe
basis of the determined minimum wind speed, on the basis of Che diameter
c~f the rAin zone [3, 4, 6] etc.). However, theoretical inveatigationa of
Atlantic hurricanes, agreeing with the reaults of ineasurements in nature~ _
make it posaible to validaCe thia choice (5, 9].
Cor nn "average tropical cyclone" the radius, equal Co 2� of ineridian, ia
~letermined as rhe distance Co which cyclonic circulation ia propagated
[5].
V. V. Shuleykin [9] eatimates the radiua of a"standard" hurricane at 225
km. It serves as the outer boundary of a sort of "hurricane nucleus,"
playinb a decisive role in all the energetics of the system. The region
over the overheated ocean surface with such a radius is a real heater of
~ heat engine of the fifth kind, the cooler for which is all the space
surrounding the hurricane system [9].
Con~id~ring the reaults of the investigations reported in [5, 9], we de-
cided that the diameter of an "average tropical cyclone" would be equal
to 4� of ineridian.
If the area of the North Atlantic So is assumed to be bounded by the lati-
tudes 10 and 50�N, and in longitude by 20 and 100�W, it measures 3.32�1013
m2 and will reflect the real boundaries of existence of a TC in this re-
- f;ion. The tropical part of this region from 10 to 30�N and the zone from
~0 to SO�N will be equal to 1.83�1013 m2 and 1.49�1013 m2 respectively. -
in the computations of these areas.we took into account the changes of
map scale with latitude.
As ~1 result we obtained the coefficients of intensity of hurricane sea-
~ons K Cor the North Atlantic as a whole and separately for the zones to
cl~e south and north of 30�N (Table 1).
- I.t Eollows from Table 1 that in the secular variation K varies in the range
I'rom 0.03 to 0.92. For the tropical part it varies from 0.02 to 1.24, and
In tl~e temperate latitudes from 0.0 to 0.84. In a single year (1933) of
ehe 89 years whi.ch we consi.3ered the area of the ocean over which TC ex-
isted exceeded the area of the tropical part (to the south of 30�N). Dur-
[n~ this year the intensity coefficient was 1.24 and the number of TC
was the maximum (21) for zhe entire observation period. Despite this, K
Lor the temperate zone (30-50�N) in 1933 (0.53) only somewhat exceeded
Che mean long-term value (0.38).
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The variability of K(wiCh reepect to Che standard deviation d and the rel-
ative vnriability Vc~ conaiderable in magniCude, is approximately iden-
- Cical far the tropical and temperare zones of the region and is somewhat
- leas for th~ ent3re North Atl~neic.
'i'he great activiey of the hurricane s~asona in 1887, 1893, 1933, 1953 and
1958, noted in [10, 11]~ found ies refleceion also in the quantitative K _
vglues: 0.82, 0.85~ 0.92, 0.72 and 0.64 respectiively.
A weakening of aativity of the hurricane season in 1970 and 1972'(11] was
accompanied by a decrease in the number of TC and their intensity coef-
f3ciente; the latter were more Chan three timea less Chan their mean long-
term value: 0.11 and 0.12.
The general direct dependence of K on the number of TC is natural, but it
cloes not have a regular nature. For example, for a number of TC equal to
7(and during the conaidered period there were 8 such years) the.intensity
coefficienCs varied from 0.56 to 0.11. Therefore, iC is clear that the cli-
matological characterization of the hurricane season solely on the basis
- af the number of TC incompletely reflects its peculiarities.
The coefficient K, quantitatively describing the intensity of the hurricane
~eason quite well, ia dependent on the total length of the TC tra~ectories.
However, it only indirectly gives some idea concerning Che time during
which the conditions in the ocean and atmosphere opCimum for the life of
'CC prevail. Determination of this time will undoubtedly refine Che charac-
Cerization of intensiCy of the hurricane season.
Lf the length L of the tra~ectories is related to the time of their existence,
it is possible to obtain the mean velocity of movement of TC during the season
- in the storm and hurricane stages for different parts of the region (Table 1).
The maximum mean velocity of TC during the season in the tropics was 30.8
l:m/hour; the minimum was 12.0 km/hour. Our computations confirm the known
fact of presence of a great velocity of TC in the temperate latitudes (the
maximum of the mean V Chere is 54.2 km/hour; the minimum is 10 km/hour).
'Che amplitude of the mean velocity in the temperate latitudes, and also
its variability, during the considered period is approximately twice as
~reat as in the tropics. The long-term values in the tropical (19.1 km/
hour) and the t~mperate (30.8 km/hour) latitudes reflect the mean velocitLes
nE the zone of Trades and westerly transfer.
- It is obvious that this characteristic in itself is important and can become
separate theme for investigation.
A deeper understanding of dffferent physical processes arises in an under- ~
:~tandinq of the energy characteristics associated with them. Therefore, we
~ r.klde an .zttemnt to determine them for the TC for the hurricane season in
tl~e considered region. An individual TC could be characterized most com-
pletely by the energy balance for the entire volume and during the entire
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period nf ite life, and for a aeaeon by the total indicea of tihe bal- -
nnce components. However, auch computations involved enormous difficulties
r.nused~+Bo,tli by Che ingdequacy of ineCeordlogical information from ocean
;ireg~ ~nd~'by elie conetantly changing parametera of each TC in ehe differ-
c~nt sta~~s of iCa exisCence. At the presenC-day aGage calculations of the
energy~balance ~nd it~ individugl componenCs for a re~1 TC (2, 4, 5] with
~ number a,f boundary condiCions is a difficulr problem, bue it is soluble.
Such studihs of TC on the basis of daCa for TC which are 30-40 years old
are still�more difficult due�to ehe deficiency of ineeporological data.
- Theoretical inveatigations oF an "average tropical cyclone" and Che con-
clusiona from them which agree with the characteriaCics of real TC observed -
in nature [5, 9] make it poasible to determine the mean value of the energy
parameters of a TC for a long aeriea of years. Such an assumption involves
' some percentage of error, but on the other hand it gives some idea concerning
_ the energy level of the TC during the aeason and its contribuCion to Che
total energy of the northern hemisphere. As a result, it wi11 be possible
Co trace tihe long-term course of this characteristic in relationship to _
climatic variaCions.
The total internal heat source of an "average" TC [5], equal to Che outflow
of the energy produced in it, is 56.4�1010 kJ/aec or 5.64�1021 erg/sec.
The total power of a"standard" hurricane as a function of the underlying
~urface of the ocean is assumed to be equal to 2�10$ MV or 2�1021 erg/sec
(9]. 'Phe close, but lesser than in [SJ energy level is probably associated
with its computatton for a fixed water temperature (2$~C) and air tempera- -
ture (27�C).
In a determination of the "order of magnitude" of the latent heaC set free
in a TC, a value 2-4�1025 erg/day was obtained in [6] or 0.23-0.46�1021 -
erg/sec, that is, an order of magnitude less than in [5] and [9]. In [6]
there was no indication of the dimensions of the TC for which the liberated
energy was estimated. �
Computations for the real typhoon "Nancy" give a total internal energy for
c~ne of the days of 826�1025 erg/day [4] or 9.56�1022 erg/sec, that i.s, th3s
value exceeds by more than an order of magniCude the levels obtained in
5, 9]. The latter was caused by the radius of the typhoon, greater than 2�
of ineridian. Near 20�N (where "Nancy" was siCuated) the mean radius of the
'I'C must be 185 miles [3]. Recalculations of the total internal energy of
clie typl~~on Eor an area with a radius of 2� in meridian gives a value 10.05 _
�L021 erg/sec, which only exceeds by a factor of 2 the similar energy for
:~n "average" hurricane according to Palmen and Newton [5].
- In our calculations for an "average" hurricane with a radius of 2� in merid-
ian we used a total internal energy equal to 5.64�1021 erg/sec. In the opin- -
ion of the authors of [5] themselves, this quantity is somewhat (by lOX) too
low, but rather fully characterizes an "average" TC. Multiplying this quan-
tity by the total seasonal lifetime of TC in the storm and hurricane stages,
53
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~
we obCgin~d the mean v~1ue of Che toCal internal ener~y nf the TC (U) dur-
ing each yegr. The mean and extr~mal U are given in Table 1.
Table 2
Vulueg of Chargceerigtice of Tropical Cyclones in the North AtLantic Uuring .
Di~ferenr Climgtic Perioda (1886-1974)
, Cpeauna rho~ocTb g CywMnpuwil nuyTrP~~ 4
Ko~~~nui.eut iwreucug~ ~oii~:einia TU ~a HuA IICTO~~IIIIK Tert~a
Fiocri~ ce~oiia yp~raiiou K ceao~i V, ~/k TL( aa ceaot~ na
flepuolt U~ 10~~ 3pe/,w=
. C zA�
1 i1CC 'I ~ I~,~ ( = CI~ICC� I'(~~ I t IICC ~ l( VQ t
6 Beee peauoK
1890-191A 0,37 U,?0 O.~i;~ 0,05 22,0 I.~1 0,20 I,S ~ 7,i7 4.411 0,52 l,fid
1915-1939 0,~14 (1,1'J (?,;~Fi (~,Q~i ::i,0 U,I+, I,~i 1i,8~9 ~4.17 O,til l,il
1940-19Ei4 1~,4~4 I),lr; U.~):3 11,Oti 2d,~{ ~l.I U.1? 1,~3 V,;1Q 2,53 U.;;4 I,lii
19G5--197~4 U.33 O, i:i~ O,~IIi U, l l 21. ~i 2,~' 0,11 I, i i, l3 1, 30~ (l,qfi 1,3G
_ 197U--1y74 U,Z7 l),1~1* l),:~3 U,17 21,0 ?,4' U,11 3,0 ~i,94 i,7$+ 1?,53 ~1,(17
~ lOarHee 30� c. u~.
1890-1914 0,3~ 0,22 0,.'~i 0,09 18,4 ~,0 ~1,Iti !,2 I!),7Ci !'i,?~i (1.fi4 2,Iti
191,ri-19;i~J 0,39 0,4~? '?.~4 (1,10 2U.'2 1,~1 0,22 1,`~ 1 0,17 ti,lt? ~t,liG ~,47
1940-19ti~1 U,40 0,1:? U,3`l A,U(i 1!I,i, U.IY q.'~ 0,44 :;,til 11,3,9 1,45
1965-1974 U,18 Il, l;!' 0,48 U,0!) 17,0 Y,:~' 0,1;~ 1,~ l 7,,'35 1.51' O,d,4+ 2,51 -
197Q-1J71 I 0,2.~ U,14� U,~,3 0,17 17,7 '>.S' 0,16 3,3 ~ 6,34 3,34+ 0,5,3I 4,1:~ _
8 CeeepHee 30� c. w.
I890-1914 O.S~~ 0,?3 U,fi.i O,OJ .30,1 ;.6 0,'2:r :3,1 ;?,?4 ;i.3'l (l,fi2 1.31i
_ 1915-1939 0,27 (1,IG O,GO O,U7 31,5 R,~ 11,27 3,d 4,03 2,1i9 O.f>1i 1,11)
1940-19G4 0,4~ n,t3 o,3.g 0,07 3?,S h,? u,l~l ~~,5 6,a:+ 1,4~ O.:;G I,o�~
19G5-1974 0,41 U,Y1' 0,52 0,15 2i .4 f,,0+ p,7~ 4,3 ~;,93 3.84" 0,:'~5 2,7:~
19T0-1974 (i,29 0,21* 0.72 0.20 2G,4 7,i� 0,2~J 9,6 5,~1~) 4,45 ~0,83 5.5fi
g � HecMeuie~~naa oueNKn (a�_i)
K~Y:
1. Period
2. Coefficient of intensity of hurricane aeason K
, 3. Mean velocity of TC movem~nt V during season, km/hour
4. Total internal TC heat source during season per m2 U�1014 erg/m2
- 5. mean
b. Cntire region -
- 7. To south of 3U�N .
8. To north of 30�N
9. Unbiased evaluation (~n-1~
if it i:~ taken .fnto .~r.~ounr tliat TC, in canrrast to extr.atropical cyclones,
~enerate .~nd maintain tt~eir c}iaracteristic availaUle pot~ntial energy due
to the setting free of latent heat in the moist air rising from the lower
layers, increasable by the ~low of latent and perceptible heat from the sea,
and also that the liberation of latent heat expended on heating of the upper
54
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erorn~~here CnnsCiCutes un irrever~ible procegg (5], ie bec~meg clegr hnw
importunt iC ig en examin~ Che problem n� TC an en~rgy redietribuCion
mech~nism.
If it ie ~~sumed thaC the ~fficiency nf ~ h~~C engine (which a TC is) is
2.4X ~SJ, it is possible to determine Che kinetic energy generaeed (Tab1~
1). -
~able 1 showa that the levels of the toCal internel energy of g TC are sub-
~ect to greae varigbiliey (V~ ~ 0.48-0.56). The yield of en~rgy from TC in
the eropical zone is twice as gr~at ~s in Ch~ xone 30-50�N. 7'he maximum en-
ergy release during a aeason wag observ~d in 1933 and the minimum wag ob-
served in 1914. The total energy yield from TC during the hurrican~ season
from n aquare meCer of area nver which TC exiaCed on the ~verage wag almost
tl~ree tim~s greater than the energy which could be ~asigned to the entire
North AClantic. The varigbility of this TC index has ~ raeher etable nature:
ite relaeive variabillty for the zone 10-30�N ia 0.17; for Che Cemperate
laCitudes it ia 0.33 and 0.16 for the entire region.
Now we will make some comparisona for estimating energy proceasea in TC.
't'he mean kinetic energy of the norChern hemisphere in aummer is approximate-
ly 19.1�1026 erg [3J. However, the mean kinetic energy of TC for the North
Atlantic for the 89 years which we invesCigated was 6.21�1Q26 erg, that is,
a third of thia energy. We emphasize that it was generated during 53 days
the average lifetime of TC in~ the TS and Hr stages. The maximum level
of kinetic energy of TC (16.1�1026 erg) was only somewhat less than ita _
mean value during thQ northern hemisphere sumner. The generation of the
kinetic energy of inean meridional circulation in summer in the northern
hemisphere is estimated at 1�1010 KW [Sj and during the hurricane season -
(53 days) is approximately equal to (4.6�1026 erg) iCs generation in TC
(Table 1).
The heat transport by ocean currents in Che northern hemisphere, directed
~~oleward, attains a maximum at 20�N: 2.4�1022 c~~/year or 2.8�1026 erg/day
[8]. During the hurricane season it is 145.8�10 erg, Chat is, approxi-
mately one-half the mean total yield of energy produced in a TC (258.6�
1026 erg) and ia comparable to the heat of TC released in the troposphere
- hetween 30 and 50�N (85.6�1026 erg).
The problem of the methods for atmospheric use of the energy released by
the atmosphere is important and remains inadequately studied, although
:some aspects of this problem were touched upon in a series of studies
[5,6]. Directly in the zone 30-50�N the energy of TC is expended on heat-
I.ng of ttie troposphere and the transformation of atmospheric circulation.
'fhe energy of TC in the tropical zone (to the south of 30�N) is transport-
~~d northward by the mean Hadley circulation and participates in maintain- -
Lng the intensity of the frontal zone and ~et streams over the hemisphere
[sl-
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~OR O~~IGIAL US~ dNLY
Wc hirvn i~1r~~dy ~xnmin~d Che pr~~~nc~ df ~ gnod corr~spondence df TC in-
~iC~~ for Che Ndreh AC1anCi~ ~nd clim~eic vnxiari~n~ on e glnb~l ~c~1~ ~
in pnrC in (1~. Th~ qualiCativ~ly new in~drmntion on Ch~ CropicaL zone
in Chie region obtained ~bove an th~ b~gie of Che chargce~risCic~ of TC
for n leng eeri~g uf ye~r~ ~leo makes it poeeibl~ ed c~mp~r~ th~m wieh
, c1~n~Ci~ v~rigCi~ng fdr rh~ lg~e ceneury. T~king into gccoune the conclu-
gion~ in (8~ ehgC regional Climaee 3~ p~rC of iC~ gen~r~l changes gnd
el~! w Ix ~ EneCnr df gr~~C imp~~r~~nc~ Cn be cnngider~d, ~nd tl~~e rhp Nnrttt
AC1anCic ie a eeneiCiv~ indicaCor of th~e~ climaCic changeg, we wi11 com-
rare thp distriburion o� th~ p~ram~eer~ which w~ obCained the intengity
Copfficient K, ehe mean velociCy nf TC V and iCs CoC~l ineerngl energy U
during dif�erenC periode of unidirecCional climgtiic variations and in
upneral we will attempt to evaluate its modern trende.
Table 2 giveg th~ mean vgluea and vnriability of K, V and U during clear- -
ly expregaed periodg of warming (1915-1939) und cnoling (1940-1964). As g
~ comp~rigon we hgve algo examined a 25-year peridd of an ingignificgnt in-
r.rease in air temperature over rhe northern hemisphere in the modern per-
tod (1965-1974).
~or the entire water aren of Che North At~gnCic during the period of cool-
ing there are a maximum intensity of the hurricane season, a maximum mean
velocity of movement of TC for all the perioda and a maximum value of the
released energy. The atandard deviation and Che relaCive variability of
these characterisCice are not only less than their values for the entire
series, but also less than in the two preceding 25-year periods. This is =
evidence of the stability of atmospheric procesaea �orming and determining
the existence of TC in an epoch of global cooling.
lJarming over the hemisphere was accompanied by K, V, U values close to the
mean long-term values, but appreciably smaller than during a cooling. The
- standard deviation was approximately equal to its value for the entire ser-
ies, but greater than during cooling. The relative variability of K and U
liad a maximum value for all the considered periods. In contrast to a cool-
ing, the atmospheric processes determining Che existence of TC have an un-
titable character.
- The distribution of the considered TC parameters for the modern period
- (1965-1974) and especially during the last five-year period (1910-1974)
Cor the entire region of the North Atlantic and its parts has tendencies
similar to the warming period (1915-1939). The intensity coefficient for
the entire region during the last decade was equal to K for the warming
epoch. During the last five-year period, in comparison with the period of
cooling, it decreased by approximately 40X. The relative variability of
K in the modern period ~exceeded its value for the cooling epoch by a fac-
tar of 1.6 and corresponded to the warming period.
A peculiarity of the distribution of the mean velocity of movement of TC
V is an increase in its amplitude between the tropics and the temperate
latitudes during cooling and a decrease during warn?ing. A minimum value
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di the gmplitud~ wng nnt~d dUring 1~70-1974. 'Th~ v~ri~bility f~r th~ pn-
tir~ rc~ginn durinq di~f~rene climgtia periodg dd~~ n~e hnve clegriy ~xpr~g~-
~d Gend~nairg. HAWpV@~~ fnr znn~~ to thp gouth gnd egp~cinlly to Che nnrth
nf 30�N it i~ e~sy to Crgc~ Ch~ corr~gpdnd~nce o~ ~h~ mttximum d~nd Vd vg1-
ue~ to th~ warming period and the minimum va1u~~ during ehe cdoling p~riod.
Uuring the modQrn period o' and VQ aYe cln~er in v~1u~ Cn Ch~ warming p~r-
iad. .
A decr~gae in Che total inCernal energy of TC, char~ct~ri~tic nf th~ wgrm-
ing epoch, i~ clegrly rr~ced during ehe mndern p~ridd and ig ~c~omp~ni~d
by a coneidereble incrpage in Ch~ rel~Civ~ vgriability di this ind~x.
In checking the hypotheaig of a statistical ~i~nific~nce of the d3fferettC~~
in the anmple meane (Table 2) u~ing the Stud~nC t~se (7j, on the nggumption
th~t Che K, V~nd U geCs glmogt conform ro a normnl lnw, ~ignifiean~ differ-
~nce~ w~r~ nbt~ined in ~ comparieon nf Che meang fdr rhe Gnaling~warming
epoch, cooling-l~gt 10 yearg ~ponh. Thig is mgniEegted ta a high degree
with reepece tn K and U in Che eemperate l~tieude~. 'rhe reli~biliey of the
KubsCanCial difference in mean valueg was gs~igned a con�idence coefficient
0.95.
T1~e sigttificance nf the difference in sample meane w~s also checked by a
r.omparison of their difference with the confidence limit expressing the
limits of random variations. The confidence limiCe of the means (6 ) with
an evgluatien reliability 0.95 are given in Table 2.
5wnnwry
1. Aq a result of our investigation of TC on the basis of dgta for many yeara
it was found to be poasible Co characterize quantitatively the ponrly atud-
ied activity of the hurricane season by some new parameters: intensity coef-
ficient K, mean velocity of movement of TC V and their mean total internal
c~nergy U.
2. Qu:~ntitative values of qualitatively new informaCion on the tropical zone
of t}~e North Atlantic with respect tn the TC characteristics K, V, U, togeth-
er witl~ the generally accepted parametera, can be used as predictors in the
prepnr~~?tian of long-runy;e and background forecasts.
3. Atmospheric processes, fHVOr.ing the development and existence of TC, dux-
in~; a period of general cooling have a relaCively stable charac[er. During
period of warming the relative variability of these processes approximate-
ly daubles. ,
BIBLIOGRAPHY'
- 1. Vetroumov, V. A., "Variations in Climate and the Frequency of Recurrence -
of Tropical G~?clones in ~Iorth America," METEOROLOGIYA I GIDROLOGIYA
(Meteoroloqy and Nydrology), No 12, pp 28-33, 1977.
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2. Giin~k3y, N. T., KnLe~nikov~, L. A., "Tde~l t{~gt Tr~ng~nre i~? the Aenx~~
~~h~r~ frnm th~ Oc~~n Surface in th~ R~~ian df ~orm~eion of Hurrie~ne
~Nilda~ (1964)~" M~T~OROLnGIYA I GInROLO(3IYA, No 9, pp 75-87, 1974.
M~meddv, 1:. 3., P'~?vlav, N. I., TAY~UNY (Typhoong), L~ning~Ad, Gidro-
m~tedi~dat, 1974, 139 p~g~~.
4. p~vlnv, N. I., Gor~h~knv~, V. V., "~n~rgy Ui~tributidn in ~ 7'yphodn in
UiFfprent 3tage~ c~f itg D~v~lopr.ent," T~UDY ~VNIGMI (Trgn~~ct~.on~ df
Che ~ar ~aatern ScienCific tte~e~rch Hydrom~t~~roi~gic~1 Institut~),
No 32, pp 149-1S9, 1971.
Palmen, N~wton, C.~ TSIRKULYA'TSI~NNYY~ SI3TEMY ATI~D3~EltY (Circul~-
tion Systema in rhe Atmosphere), Len3ngr~d, Gidrom~teoizdat, ~9~3,
615 peges.
6. Ftil', G., TROPICH~SKAYA METEOROLOGIYA (Trnpicel Met~orology), Mngcnw,
~L, 1963, 366 page~.
7. Rumshiskiy, L. z. , MA'1'EMATICHESKAYA OB1tABOTKA 1tEZUL' TATOV ~KSP~ttIMLNTA
(Mathematical Proce~Bing of ~xperimentnl lteeult~), Moscow, "N~ukg,"
1971, 192 pages.
FIZICH~SKIYE OSNOVY TEORII KLIMATA V YEGO MOU~LIROVANIYA (Phygic~l prin-
ciples of Che Theory of Climate and iCs Modeling), TRUDY M~2HDUNAROUNOY
NAUCIINOY KONP~RENTSII, ORGANIZOVANNOY VMO I MSN5 Pitl POU~ERZHKE PROGRAMMY
OON PO OKRUZNAYUStiCHEY SREDE (STOKGOL'M, 29'IYULYA-10 AVGtJSTA 1974))
(Transactiona of the International Scientific Cnnfer~n~e Or~anized by
the WMO and the IASA in 5upport of the UN Envirotunental Program (5tock-
holm, 29 July-10 Auguat 1974)), I.~ningrad, Gidroraeteoizdat, pp 5-83,
1977.
9. Shuleykin, V. V., "Development of a Tropical Hurricane With Uifferent
Water Surface Temperatur~s in the Ocean," TROPICHESKAYA ZONA MIROVOGO
OK~ANA I SVYAZANNYYE S NEY GLOBAL'b'YYE P1tOTSE5SY (Trnpical Zone of Che
World Ocean and Associated Global Proceeses), Moscoa, "Nauka," pp 16-24,
1973.
t0. Cry, G. W., "Tropical Cyclones of the North Atlantic Ocean," U. S.
WEIITHBR BUREAU TT~CHNICAL PAPER, No 55, Washington, D. C., 1965, 148
pages.
11. MONTHLY WEATHER REVIEW, Vol 93-103, No 3-4, 1965-1975.
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~ ~dtt OI~~~GIAL U5~ dNLY
UnC 551.~465.53:515)(571.6)(265)
GUttf~LA~ION H~T'W~~N CI1tCULATION P~CULIARI'C~~S b~ TH~ NORTHW~ST~ItN I'AttT 0~
'1'~E PACI~IC OCgAN AND W~A'rl~t~it CONUI'CIONS IN Tli~ SdUTf1~1tN ~Alt ~AST
rtogcd~r METEA~tdtbG~YA i GtDR~LOGIYA in Itu~gi~n Nd 1, Jgn 197~ pp SO-55
[Ar~ic1~ by V. V~rdnina, ~~r ~g~tern Hydrnmetedrdln~i~~l S~i~ntific R~-
~car~h In~titutp, ~ubmittpd fnr publicgeinn 10 April 19~Sj _
Abgtr~cr: An ~?CCetnpC W~~ mad~ to explain the
v~ri~bility of we~th~r conditiong in ehe souCh-
. ern part of Che ~ar ~ag~ on th~ b~gig n~ dynem-
icg of the Kuroehio Curr~nt th~ m~gndering
and eddy farmation proc~gs~s. prognostic r~la-
tion~hipg ~re obtained. ~h~ c~nclu~ion is drawn
that there i~ a need for uging satellite inform-
~tinn d~tg in dev~loping methodg for the long-
r~nge for~ca~ting of hydromet~orologicgl ph~nn-
mena.
(Texc] According to modern eoncepts, for successful prediction of weather
it is necessary to take into account circulation in the ocean, processes
~~f interaction between the ocean and the atmnsphere. As is Well known, in
che redistribution of heaC on the earth an importent role ig played by sea
c~rrent~. They tranaport enormous masses of hegt from one p~rt of the earth
te another. The influence which sea currentg exert on the climate attd
we.htl~er of the continents has been degcribed in many invegCig~tions.
1)urin~ recenc years gerious changes have occurred in our ideas concerning
ti~e nntur~ of currents in the ocean. The old concept of "smooth" large-
r~cale curr~nts has been replaced by ideas ~up,g~sting a system of eddies.
A polygon eac~eriment cgrried out in 1970 by Soviet scientists in the trop-
tcnl zone of the Atlnntic and subs~quent investigations [1] indieated that
the principal carriers of kinetic energy in the ocean are eddies With motion
~~f w,~ter in clockwise (Warm nnticyc~onic) and counterclockwise (cold cyclon-
Ic) directions. At each particular moment it is possible to diacover an en-
- tire geries o� such eddies in the ocean, different in extent and With dif-
ferent rea~ons Eor their appearance.
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'I'ha eeudy nf the physicai ngrure nf 8mnii- and megogcale eddy formatione
in Che ocegn and ~their inCeraction with Che surrounding medium is Che ob-
)ecCive nf Ch~ ~ninC Soviet-Americnn POLIMOD~ program. The experiments
h~~un by "Porignn-70" ~r~ cdntinuing, but even now our investigationa
- dhow tliat the atntisr.ical pic:Cure of eh~ d~.seribuCinn of eddie5 in the ~
ncean (in epgc~ and 3n Cim~) varies. Mogt fr~quently they gre diacovered
in th~ r~gion of the main oceanic currents (1, 9, 10~. Here, in addition
Cc~ smg11-ecele nnd memogCale eddies, there are large-scale eddiea formed
Erom meander~. The diameter nf these large dynamic fnrmations varies from
geveral tens Co severgl hundrede of milea. Warm anticyclonic eddies have
a Cendency to move norChward; cold cyclonic eddies have a tendency to move
~outl~werd. In the atmoaphere guch eddies are usually displaced in opposite
directions; anticyclonic to the souCh, cyclonic to the north. Giant
eddiee circulations, formed from meandera, determine tihe oceanic condi-
tiong over extensive wgeer areas [2, 10].
In order to clarify the role of ineandering processes and large-scale ocean-
ic pddies in formation of weather in ad~acent regions we carried out a com- -
parigon of data on oceanic circulation conditions in the northwestern part
of the Pacific Ocean wiCh data on the monthly quantity of precipitation
- in Pritnor~ye during the period 1954-197b. F'eculinrities of atmospheric pro- -
_ cesaes were noC Caken into account. It was assumed that Che quantity of
falling precipitation during the month for the selected territory is ren
index of varioua peculiaritiea of atmoepheric processes, in the develop-
ment nf which a aignificant role is played by thermal conditions in the
conside~ed region of the ocean (3, 4, 8]. _
ng ia well knawn (2, 7, 9], the northwestern part of the Pacific Ocean, be-
ing a region of interaction between the warm Kuroshio Current and the cold
Uyashio Current, differg from Che surrounding waters by intensive heat
transfer procesaes and eddy formation on f ronts. Here it is common to ob-
~serve cases of the forn?ation of large-acale eddies from the meanders of =
the Kuroahio [2~ 10, 11]. Several quasistationary regions of current mean-
clering are traced: a curvakure of the current in a southerly direction
(cyclonic meander) most frequently is observed between 137-140�E, 145-148�E
and 152-155�E. The curvature of the cuxrent in a northerly direcCion (anti-
cyclonic meander) moat frequently is obaerved between 141-145�E and 148-152�
1:.
According to data in (2, 9, lOj, the cyclonic eddies formed from the mean-
clers of the Kuroshio have a tendency to be displaced toward the south and
southwest, whereas anticyclonic eddies have a tendency to be displaced to
the north and northeast. With displacement, under the influence of process-
es of horizontal and vertical mixing with the surrounding water, the eddies -
r~re destroyed. The rate of movement of the eddies, in connection with the
xpecific conditions, varies from 0.5 to 2 miles/day. The lifetime of these
circulations ia a~alf-year to a year. '
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Aema y ~J~9r._i~~~ ~?,cHa y ~l'=
4
~974a ~Z;~J / J,7~ i971L '~'~~~~,f
A ~ B ; 2
S
t 1. ~?,,1
_ ~p � ; , I .
---~�~-�~9 ' ~
~;1 , c y,o ~
~ ~~c ~ r~ f
- , I .~,~4 ~ 2 ti
42 ';;~~~r f ,
(c, t ! ~
\ r ~ ~
, \ 4,2 ~
j ~ ~ ~ 61 y'~ S ; -
~ y~ ~ 75 ..~I 59 ` ~l ` .
~ JS :
g y~e 20 �
, ~
Aemo �'t~: J,Q 3,7 BecNa r -
187St ti:'~ 1972t ~ ~
C ~ D ~f b .
y'~ ~ -'r 4
0
I n ~
~ ~ a ~
o .
~ .G:~ -~~~y~~ ~ . 15 ~
,:i:.~'1~"~y
~ 4 ~ ~ '
i ~ ~ ~ 9 y7 ~S s~ ,
3 6~ ~o
~ 4~9 9,i 4~B ~
y~e f0~
~5 - i � -
Fig. 1. Dynamic maps of thE ocean surface relative to 1000 mb (according
to V. P. Pavlychev) (at left) and diagrams of transport of water (numerator,
106 m3/sec) and heat (denominator, 101~ Cal/sec) by the Kuroshio Current
(reports of the Far Eastern Scientific Research Hydrometeorological Insti-
tute) (at right) during period of development (1971, 1974) and destruction
of ineander and formation of anticyclonic eddies (1972, 1975).
I:EY :
A) Suiuner 1974 C) Summer 1975
f3) S~ring 1971 D) Spring 1972
G~clonic eddies exist considerably less time .*.han anticyclonic formations.
- Anticyclonic eddies are characterized by the greatest frequency of recurrence,
Lntensity and lifetime. These are formed from meanders of the Kuroshio, whose
Eormation occurs in the region 141-145�E. At the beginning the axis of the -
r.urrent in this region forms a slightly expressed anticyclonic curvature
to the north. This curvature (meander) gradually increases. _
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x R~.~
1J0
1 f0 -
90
~ ~
_ ~9 ~ .�_?_L
Qo.,~
700 200~
~
~ ~
t,~cc E:~~ ~;~s
- ' ~
:~cc~ ; ; ~ ~ ~ I �
1.~~ ~,:~I;~
L ~ ~ ~Y
l:0: h%~ ~li ~ , -
1~f4 19.�B 1962 1966 19~0 1914 1978
~'ig. 2. Long-term course of averaged quantity of precipitation R over Pri-
mor'ye ttrea (X of norm) during May-August and mean water discharges Q
(June-September) on rivers of Amur region. 1) on Ussuri River (Kirovskiy ~
post), 2) on Bureya River (Kamenka post). '
AC Che bage of the meander Che disCance between Che oppoaite sectors of
the Kuroshio is narrowed; an ac~ticyclonic eddy is formed which is later
detached from the main Kuroshio Current. The lifetime o� the meander from
the moment of its appearance to separation of the warm (anticyclonic) edd-
ies, according to the data in [2~, is from one to five years.
' Tiie degree of development of ineandering processes in the considered region
is different in different years. Thus, according to the investigations of
i~. P. Bulgakov [2J, V. P. Pavlychev [9] and V. V. Pokudov [11], during
the last 20-25 years, according to data which are far from complete (due
to the absence of continuous observations), the development of anticyclonic
meunders (surges of warm waters) in the region 141-145�E was observed in
1955, 1956, 1959, 1960, 1968, 1971 and 1974. On the other hand, in 1954,
1958, 1966, 1969, 1970, 1972, 1973, 1975-1977 the Kuroshio Current did not
i~ave great curvatures. During Chese years to the north of it there were
r~nticyclonic eddies formed from meanders. The Kuroshio occupied a more
Houtiierly position.
An example of a diagram of water transport (m3/sec) and heat transport (Cal/
sec) by ttie Kuroshio Current in sections in the layer 0-1000 m during the
period of development and destruction of an anCicyclonic meander and the
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Corm.~tion nE unCicycloniC eddies is ehown in Fig. 1. The computation~
wer~ made in the Division for Study of Nydrologicgl prncegges in the
Wnrld Ocean in the ~~r ~a~tern Scientific Etesearch Hydrometeorological
In~titute on the bnyi~ of the resulCs of expeditionnry invesCignCions.
The dynamic mapa were tnk~n from a study by V. p. pnvlychev (9j. Uging
tt~ese m~pa, constructed on the bngis of observation~ of Che denaity field~
it is pogsible to obtain aome ide~ concerning the streamlines and the
velocity of geosCrophic currente at any horizon above the zero (reference)
:3urface. In thia cnse as the reference aurface the lower observation hori-
r,on 1,000 m-- wns taken.
As we gee, the datn in the figure graphicnlly show different degrees of
nenndering of the Kuroshio during different years. In Che spring of 1971
the uni�ied Kuroshio flow was observed only to the south of Japan (Fig. 1,
at ri~;ht). To the e~nat of 142�E Che currenC divided into individual branch-
, es, forming meanders. The northern branch of Che currene attained 40�N and
~?t n meridir~n upproximately 145�E turned southward. In tihe spring of I972
lhe Kuroshio did not meander. The Summer of 1974 differed from the summer
~~f 1975 by having a surge of warm watera to the north. In 1975 the Kuro- -
sliio axis was displaced southward; an anticyclonic eddy was observt:d to
tt~e north of it. During these years a graphic idea concerning Che vari~-
l~ility of the current position is given by dynamic mapa, where the Kuro- -
shio flow is clearly traced from the close spacing of the conCours (Fig. -
1, at left).
What weather conditions were observed in Primor'ye during the period of
development of anticyclonic meanders in the region i41-145�E and during _
the period of their destruction and the formation of anticyclonic eddies? _
'I'aking into account that for processes of interaction between the ocean
- and the atm~sphere the considered region is characterized by asynchron-
ous rel.stionships [3-5, 8] and that the formation of eddies here most fre-
_ quently occurs at the beginning of spring and at the end of winter (10],
for the purpose of obtaining prognostic dependences we used data on the
mont}~ly quantity of precipitation durinR May-August 1954-1976 f.or 10 sta-
tions in Primor'ye. Precipitation was averaged in area.
~'i~ure 2 shows that during periods of development of anticyclonic meander- -
ing in the region 141-145�E (see the mentioned years) iC was most common
to observe an excess of precipitation, whereas during the years of their
destruction and the formation of anticyclonic eddies there was a shortage
uf precipitation and drought. The existence of the detected relationships
_ is also indicated by data on the long-term variation of summer discharges
~RV1-IX~ of water in the rivers of the Amur basin: Ussuri River (Kirovskiy
post) and the Bureya River (Kamenka post). During the period of development
~~f a meander the water discharges on the Ussuri River increase by a facCor
~~f 2-3 or more, whereas during the period of destruction they drop off.
Ttie reverse picture is observed on the left-hand trfbutaries of the Amur:
the ~reatest water discharges are observed most frequently during the
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destruction (absence) of ineanders in the Kuroahin and Che formation af
nnticycloni~c eddie~; the minimum disch~rges are observed during Che dev~l-
opmenC of a meander (Sj.
The physical s~nse of the deCermined relationehips can be explained in the -
following way. During a period o� dev~lopmenC of large-scale attCicyclonic
meandera (surgea of warm waters) in the region 141-145�E the high-alCitude '
- frantal zone over the conaidered region [3] is diaplaced toward the norCh.
'Che extent of the Far Eastern high-altiCude ridge decreases from south to
~iorth during the epring-summer period. The zone of convergence of flow -
rilofC i~ eituated over Che Kurile Islands or thE Sea of Okhotsk, and there-
fore the frequency of recurrence of anticyclonea of the Okhotak group in-
creais~s (4]. In the absence of aneicyclonic meanders the fronCal zone in
Che atmosphere over Che considered region occupiea a more southerly posi-
eion. In this ebse the greatesC frequency of recurrence of anticyclonea
ia not obaerved over the Sea of Okhotsk, but over rhe norChwestern part of
the Pacific Ocean.
The role of Okhotsk anticyclones in Che formation of summer weather over
the Far East is well known (6]. With their intensive development, in Pri-
mnr'ye [here is a predominance of moist weather; with weak development
- there is a predominance of relaCively dry weather. In the first case
- the wesCerly and southwesterly cyclones, encountering a pressure barrier,
become stationary over Primor'ye or regions cloae to it; in the second
case they pass along the Amur basin and m~re southward of Primor'ye and
Chis causea the noted peculiarities in variation in the quantity of pre- ;
cipitation.
The determined relationships indicaCe Chat the pec~:liarities nf ~levelopment
of atmospheric processes over the northwestern part of the Pacific Ocean
and the regions adjacent to it are influenced to a consi.derable dPgrez not
only by the "ocean-continent" temperature gradients [12], but also by the
~ temperature contrasts between warm and cold water masses and the loc~~Ii~a--
tion of this zone of contrasts in space. The sign of Che temperature anom-
:~ly of surface waters during the period of development (destruction) of a
roeander and the formation (destruction) of the anCicyclonic eddies can be
very different. An analysis of the maps of ciistribution of waCer tempera-
ture anomaliea at the ocean surface in the considered region during the
~ummer period 1966-1976 indicated tliat 1969 and 1971 were extremely cold.
Ln ti~e first case to the east of the Japanese islands there were anticy-
clonic eddies'and the Kuroshio Current occupied a southerly position. In
the second case, an anticyclonic meander was observed in the considered
re~ion. The subtropical waters, as was noted above (Fig. 1, at right)
were propagated to 40�N. The summer of 1968 was extreme].y warm. The season
was characterized by the development of an anticyclonic meander, by the
propagation of warm waters to 40�N and norChward.
'1'he noncorrespondence between the actual temperature field of the ocean
and the distribution of water temperature anomalies is evidenCly attrib-
utable to the fact that the norms ava~lable to the researcher in fact
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= ctre no~ entirely indicaCive for evaluating the thermal state of the water
masses in Chis season (month). Thie problem requirea addiCionnl inves~i-
;,ntione.
- Our investigaCions indicare that daCa on the dynnmics of the Kuroahio Cur-
_ rent in the region 14~.-145�E (meandering and eddy formaCion) give import-
:int information for evaluating weaCher conditions in the future. This re-
quires regular expeditionary obaervationa of the Kuroshio regime.
Recently Chere has been rapid development of inethods for satelliCe oceano-
~raphy.. Photographs taken from satellitea make it possible to see the boun-
daries'o'f currenta (temperature contrasts), cyclonic and anticyclonic mean-
ders and eddies. This meana that daCa from satelliCes and the deCermined
relaCionships even now can be used in developing methods for and preparing
long-range forecasts of hydrometeorological phenomena.
BIBLIOGRAPHY
1. I3rekhovskikh, L. M., ISSLEDOVANIYA MIROVOGO OIC~ANA (Investigations of
the World Ocean), P1tIItODA (Nature), I~o 11, pp 4-15, 1976.
' 2. Qulgukov, N. P., "Principal Characteristica of Structure and Position -
of the Subarctic Front in the Northwestern Part of the Pacific Ocean,"
- SIJtiAlu'fICHI:SKI.Y I~'RONT S~VEROZAPADt~JOY CH~ISTI TIKHOGO OKEANA (Subarctic
Front of the Northwestern Part of the Pacific Ocean), Vladxvostok, pp -
10-25, 1972. _
3. Voron~na, V. F., "On the Problem of the Interrelationship Between the
Subtropical High-Altitude Frontal Zone and the Southern Subarctic Front
in the Northwestern Part of the Pacific Ocean," TRUDY DVNIGMI (Transac- _
tions of the Far Eastern Scientific Research Hydrometeorological Tn-
, stitute), No 30, pp 81-88, 1970.
4. Voronina, V. F., "Role of the Subarctic Frontal Zone in the Northwestern
Part of the Pacific Ocea~ in the Formation of the Anticyclonic Field
Over tlie Sea of Okhotsk," TRUllY DVNIGMI, No 63, pp 164-172, 1977.
5. Voronina, V. F., "Role of the Subarctic Frontal Zone in the Formation ~
- of the Sumcner Water Content of Rivers in the Amur Basin," SBORNIK RABOT
� PO GIDROLOGII (Collection of Papers on Hydrology), Leningrad, pp 3-9,
1977.
- b. I1'inskiy, 0. K., "Okhotsk Anticyclone," TRUDY DVNIGMI, No 7, pp 10-32,
- 1959.
7. Kaganskiy, A. S., KisliCsina, L. N., "Experience in Investigating the
Variability of Turbulent Heat Exchange in the Northwestern Part of the
Pacific Ocean," TRUDY DVNIGMI, No 63, pp 3-13, 1970.
65 -
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8. Kryndin. A. N., "Ito1e o[ tiie Temperature Field of the Ocean in the For-
mnrto~i of Anom~zli~H uf Armo~pl?eric Circulntinn nnd AridiCy Momnlies
- for WinterH iit Sen (ln the Lxample oF the NorChwesCern i'nrt of Che
Pacific Ocean)," TRUUY NIIAK (Transactions of the Scientific lteaearch _
~ Institute of Aeroclimntology), No 36, pp 21-48, 1966.
9. Pavlychev, V. P., "On Che Interannual Variabili~y of Oceannlogical Con-
- ditions in Che Kuroshio Region," OKEANOLOGIYA (Oceanology), Vol XVII,
No 2, pp 200-205, ].9~7.
10. Pavlychev, V. P., "Water Regime and Position of the SubarcCic Front in
the Northwestern Part of Che Pacific Ocean," IZVESTIYA TINRO (News
of the Pacific Ocean Instirute of Fishing and Oceanography), Vol 96, pp -
3-18, 1975.
11. Pokudov, V. V., Vel'yaoCs, K. 0., "Principal Peculiarities of the Hy-
drological Regime and the Position of Boundaries of the Subarctic FronC
from the Northwestern Part of the Pacific Ocean in Winter," TRUDY
DVNIGMI, No 62, pp 3-21, 1976.
12. Ugryumov, A. I., Kupyanskaya, A. P., "Seasonal Aspects of Influence of the
Ocean on Atmospheric Circulation Within the Limits of Che North At-
_ lantic," TRUDY GIDROMETTSENTRA SSSR (Transactions of the USSR Hydro-
meCeorological Center)~, No 167, pp 3-14, 1975.
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.
UDC 551.510.534
NUMERICAL MODELING OF SYSTEMS FOR OBSERVING AND ANALYZING 020NE FIELD
Moscow METEOROLOGIYA I GIDRpLOGIYA in Russian No 1, Jan 1979 pp 56-65
[Article by Candidate of Phyaical and Mathematical Sciences 0. M. Pokrov-
skiy, Ye. Ye. Ivanykin and A. Ye. Kaygorodtsev, Leningrad State University,
~ubmitCed for publication 1~June 1978]
Abstract: The authors have formulated Che prob-
lem of numerical analysis of the ozone field
on the basis of the totaliCy of daCa from -
ground and satellite observations. The ar- -
_ ticle proposes an algorithm for the recursive
assimilaCion of information supplying optimum
statisCical evaluations at the points of inter-
section in a regular grid. Also examined are
' spatial interpolation schemes, as well as
schemes for the smoothing and assimilaxion
of different types of ozone data. A study is
made of the spatial structure of evaluation
errors. The effectiveness of assimilation of
the temperature and ozone fields in the strato-
sphere on the basis of a combined observation
system is demonstrated. The characeeristics
of accuracy in estimating ozone when using
different analytical schemes are presented.
~Text) There are two approaches for attaining a satisfactory accuracy in
determining the ozone field. The first involves an increased complica-
tton of u satellite experiment program (carrying out combined measurements
~~f the limb, transparency and at the nadir [2]). In this paper we discuss
the possibilities afforded by another approach. A refinement of estimates
of the three-dimensional ozone field at the points of grid intersection
c�an be accomplished on the basis of realization of recursive procedures of
optimum spatial smoothing and assimilation of data from satellite and ground
measurements and also the use of additional information from observations
of the temperature field. In this case use is obviously made of factual in-
Eormation on the statistical structure of the considered random fields.
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Table i
Examples of Numeri.cal Analyeie of Ozone Field
_ l 13xo;~uaa iui~pnpWUUi+~ � 2 Pe~va~Tarw o~~reKtne!ioro ananFi3a
~ M . ' -
~ h o � oGuiee co.~cp>tia~iu~ ~ BepruKa~buoe
~ � Q ~ � _ 10 11pacnpeAeneHNe
~ ~ o ~ d
6 .g.
~
- 10 I ~ S ~ a ~ O ~ /1 !
~ ~ .G, o e ~ A o ~ ~ �W oQ H6 ~019 ~ aplap,
~ I ~ ` ~ ^ ~ � ~ 10-~ c~
v31 ~ 0. r- n ~ao ci gF ~ 12 ~ ~ -
~ ~
c( 1 ~ ;1 cz U 3 8,4 2,3 ~ 8,5 i 9,2 15 76 -
13 1 ~ 8~ c 1~ 4 10,2 2,7 6,4 � 12,~J 20 71
- 'S l�1 I c U I 6,0 2,1 4,7 I t~,4 16 5R
I 4 1/ 1 c U 2 6,2 2,5 7,0 ~ 5,1 13 6~ `
9 4 c 0 4 6,9 2,8 I 2,0 6, $ 23 i U
- b N L c l) 5,1 ?,0 5,1 ~ 5,6 18 7G
? N 6 c 0 ti o,3 ?,I 12 ~ 4,1 13 75
,'t 3 c 0 3 ~ 7,~5 :t.0 IG ; G,3 25 74
.0 1 jf 2 H 150 6 12 4,6 G4 I 4,8 16 83 -
_ � '1 !f 2 ?tZ 781 5 19 7,0 75 ' i, 6 2~ 85 -
14 3 E 4 x 19U 3 23 7A G6 , 11 17 CO
4 4 c 69U 1 27 9,5 70 ~ 8,1 20 Si
Ir 1 I~ 2 N 1TIU
H 6 H'li2U 4 II 4,'l I 29 ~ 6,3 20 5:
15 2 If 2 x 1710
I (i x 1720
l N 5 N 13f,U 4 8,9 3, ~S :0 5, 4 17 37
3 I N 'l k 1710
N fi x 17~0
~ Et Fi K 136~1 -
H 1 x G!)0 4 i,0 2,6 13 3, J 14 2:
I 4 E 1 x 192~1
E 2 x ~10 ~1 24 7,0 46 IS 2~J i i
~ f~ F. I H 1~211
I E 2 x 910
E 3 x 190 4 19 5,~ 28 10 21 54
~i N 2 c 171U
/1 6 . 1720
~f J � ~~1~ ~4 5,J ,7~ 7,8 ~J l~
% N 2 ?r ~I~O ~ -
I H G � ~%~n
N . I;3Gn ~
L/ 1 li9(? 4 ll 4.5 i 32 G,G 22 G3
r�~ ~ 1 N 1 . 1120
1~ !1 4 . 1i10 I I
~i . ~~o ;
s . ~ r~ '
2 . ll 2 4,1 1.6 ~ 3.4 3,ti 9 38
r~v 1 2 H 1120
_ 17 1/ 1 t U 1 5,5 l,y , 3,4 a,4 l2 40
2 !1 'l x 112n +
ti N 1(KJO -
_ I c U I 3,8 I.'! ' 1,S 3. ~i 9 28
:t t 1 H 19'?~) I
F 4 c 1~ 4 8,6 '_>.2 3,8 I1 20 51
4 !i I rt 1!)2U �
F' 't rr I ~N)
I G 4 ~ U 4 G.9 I.!; i 2.2 S,S 16 32
~ + i I
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i
K Ir~Y :
L. TnpuC inf~rmntion 11. Verticgl di~CriUuti.on
2. Reaults nE ob~ective ana~yais 12. nb
3. Malytical scheme 13. Satellite data
4. Number of variant 14. ExCrapolation _
5. itegion 15. Interpolarion
6. Observation points 16. Smoothing of satellite daCa
7. Type of information 17. SaCellite and ground measurementa
8. Diatance to point of inter- 18. Europe
aection, km 19. India
9. Evaluation point 20. 8~teii~.c~
, 10. Total content 21. ground
Note: Numbers of ozone sounding aCaCions: 1-- Varanasi, 2-- Akhmedabad,
3-- Kodaikanal, 4-- Dum-Duma, 5-- New Delhi, 6-- Mont Abu (India); 1--
Lisbon, 2)-- Mont Louis, 3-- Arosa~ 4-- Hohenpeiaenberg, 5-- Berlin,
(~urope)
~
qe ~
Q4
~
p f79J ?000 J000 ,p nM
Fig. 1. Latitude component of horizontal correlation function of total ozone
content.
Such an approach was recently used successfully in a numerical analysis of
= main meteorological fields for the purpose of increasing the effectiveness
ul' remote sansing d.�a [1, 5, 6].
- Ob~ective Analysis Algorithm
'1`tie problem of numerical analysis of the characteristics X of some three-
climensional meteorological field X in a statistical formulation essential-
ly involves a refinement of the a priori evaluation X, characterized by the
empirical covariation matrix,~ , on the basis of use of a set of linearized
equations in the form
. k)~ ~1~
~Y~=A,�ex,+~, (i=t,. . ,
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.
Nkr~ l'? a! h ~1 C Z)d ~ ~
40 k n / ~ Y
* J1 ? ~
l~ ~ 2 ~ % , 3
x~ -
x x ~
x
~0 4 x\ x x /
x ~ ~
l 31 x~
~ .
x x x
_ . ~
~ ~S f O,E QE 1 0 0,5 1 0 O,S(6q/Sq)'~
Fig. 2. Vertical distributions of relative reaidual dispersions. a) analysis
of ground observations; b) analysis of satellite observations: 1) extrapola-
- tion, 2-4) interpolaCion using 7.-4 points; c) assimilation of satellite ob- -
- servations: 1, 2-4 and 5 point (India), 3-4 point (Europe); d) assimilaGion
nf satellite and ground observations: 1, 2-- ground data at 1 and 2 points
- (India), 3-- ground data at 1 point (Europe).
4kM
1
f
20
`%=x ~x
)
o.~ o, 4 o,e R
Fig. 3. Profiles of correlation coefficients of spatial relationships of _
temperature (1), statistical relationahips of temperature and ozone concen-
_ tration (2) and spatial relationships of ozone (3).
describing the system of observations. liere ~ xi = xi - xi is the vector of
cleviations of the vertical distribution of the meteorological elemenC from
its mean valuea xi at the i-th geographical point where an observation was
~ r.~ade. The matrix operator Ai relates small variations of the vector of the
jaf ineasured characteristics ~ Yi = Yi - A[xi] with the corresponding fluctua-
tions of the parameters to be evaluated L1 xi. Therefore, if A[x] is nonlin-
ear, then JA
A, _ ;~r~ (x,l�
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~ Table 2
~xampleg of Agaimilgtion of Temp~raeure nnd Ozon~ ~ielde
Bxonnan ~uu o?~auun' 9 neaynbTarw o6behTUUUOro auanuaa
~~4 5 ~'i 7 ro8 ~9` ~6utee coAepxcaNUe 1~ BepTNKBlIbH08 _
, � o ~ acn eAeneuue
~ ~ n m
a d
~ m z Q ~ ii
x a ~ ~ '
p m~~ m ~ ~ o ~ ~ ~Q ~ ~
y x~~ ~ ~j~ 03l ~b~ i ~ti O
~ rT. tZ C~ C. ~ f+ DS ni b~ \..i ~ la I b~ ~
12 ~ I 1 eo 18 0 1 8,5 2,6 3,9 I~J 2~ 66
'1 2 cu . 2 9,8 1,~J ~1,1 21 27 63
r 1 1 cr . l 8,3 2,4 '3,G 1(i 2;3 50
, 13 2 1 kr 19 . I T,8 '?,2 3,~ 14 ?0 40
14 11Qr l 2 Hr 20 ~~GU 1 25 7,3 34 17 :G 58
~ 2 I Nr 5GU
~ 2 Hr 0 2 21 ti,6 �1 14 2U 36
, 3 2 ?t: ~iliU _
1 rc~ 0 1 13 ~4,1 1 I 9 15 23
15 utt 1 2 cr 21 5fi0 1 27 7,8 38 18 27 60
~ 1 cr, co ,~ti~
i cr 0 1 21 6,3 24 16 23 48 -
3 2 cr, ~ ;iGtl
1 cr 0 1 IS 4,G 12 1'_' 18 30
16 ~ I cr, co ~iu0
2 cr, co ~ p 2 7,; 2,2 3,l 13 13 31
2 2 cr, co ~it~0
~ cr, co U 1 6,6 ':,4 ?;1 12 13 30
n r, co ~~,1)
17 car ~ 2 Hr, co U 2 7,1 2, l 2,3 l: 16 26
2 2 Hr. co 5t~)
_ ~ vr, co U 1 6,0 I,8 2,2 11 17 27
KEY :
1. Input information 13. information on temperature
2. Results of ob~ective analysis 14. aerological temperature sounding
3. Analytical scheme 15. ozone measurements + satellite
- 4. Number of variant data on temperature
S. Observation points 16. spatial assimilation of satellite
G. Type of information data on ozone and temperature
7. Distance to point of inter- 17. assimilation with use of aerolog-
section, km ical temperature measurements
8. ~valuation point 18. satellite data on ozone
- 9. Total content 19. satellite data on temperature
10. Vertical distribution 20. ground data on temperature
11. nb 21. ground data on ozone
l2. sr~tellite ozone sensing
Note: Numbers of stations; 1) Hohenpeisenberg, 2) Berlin ~
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NK a~ \ f b) DJ
a ~ b o c d
3 p Q
PO ~ J 1 ! 1 p J
x ~
~ Y~ ,
x~ ~
` x~
x J
n o,s ~ o,s ~ o v,s z o as~ ~i64~:
~'ig. 4. Ageimilation with data on temperature. a) interpolation of gerolog- -
ical data; b) interpnlation of saCelliCe data; 1, 2) from one point, 3)
from two pointe; c) aesimilation with Chermal gounding daCg at current _
point: 1, 2) abaence and presence of data; d) aegimilation with ~erological
data: 1) abaence of data. 2~ 3) aseimilgtion at 1 and 2 points
Having empirical atatistics, it is possible to define apati~l regions lying
within the limits of the correlation radius of the rgndom field.'We will
take one such region G. The ob~ective of this obj ective analyeis is
taining evaluationa of Che meteorological elementa at the poinCa of inter-
aection of a regular grid. If p is Che number of the points of intersection
situated in the region G and n ia Che number of standard vertical tevelg,
then the number of parametera to be evaluated at the grid pointa of inter-
section is pn and the total number of components of the combined vector X
is equal to r s(k+p)n, which corresponds to data at the grid points of in-
tersection and observation points. The combined vector of the initial data
L1 Y= (d Yi, L~ Yk) * has the dimenaionality s= mk (m is the number of
parameters measured at each of k observation points). Having a priori stat-
istics for Xi it is possible to compuCe the corresponding vector of the
mean values X and the covariation matrix ,E . We rewrite (1) in the form of
the matrix equation
c1 Y=A �~.l' a (2)
relative to the combined vector Q X= X- X. We will examine the structure
of (2). The matrix A has the block form A~(A ~0); the submatrix A has a
block-diagonal structure
A,O.....0
0 A:.. U
- A- -
0 0 . . . . . .4R
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~o~ d~~tcin~. us~ ~rn~r
'11~~ dim~n~inns~l ity ciC A 1~ km x kn. Thp zpr~ maC~rix block 0 in A i~ r~lnt~d
tl~r. r.nmron~ntH nC th~ vc!Ctc~r X~ Cnrrc~pc?nding t~ thc dr~tn thp pointg
~+f lnt~rpeeCidn uE ri ~rgulnr grtd, ~nd hn~a the dimensinnallty km x pn.
- W~ wi11 d~not~ th~ Q-eh row of eh~ A mgerix by gi. 'I~~en ~y~e~m (Z) ~~n be
r~writt~n in th~ form of a eeC of gc~,1~r equgEinns
~ ~r~ ~ y (t ~ 1, . . . , kml,
- W~ will ~e~ume thgt the m~~~ur~ment prror~ 6l are independene rgndom vg1-
ueg With z~ro meane ~nd th~ digper~i~n The principnl advanengp df (3)~
dietinguishing it from (1), is that (3) contains th~ c~mbined v~ctnr of n11
rhe param~Cer~ tu b~ ev~luated A X. Ugu~lly in a numeric~l ~olu~inn of the
c~b~ective an~l~gi~ problem difficulties arig~ which ~r~ re1~C~d tn rh~ n~ed
for inver~ion of poorly atipulated matric~g wiCh ~ gre~t dim~ngionality (3j.
In (4j, in order tn overcome these difficultieg, g binck-by-block invereion
method ig rropoaed. ilelnw w~ diecus~ the po~~ibiliti~~ of a recurgive ~valu-
ntion algorithm. ilaving a sygtem of ~qunCinng in tl~e form (3), the evalua-
tion algoriChm can be writt~n in the form of ehp following recureive pro-
~edura: Xo g~ ~ a'n ~ 0;
2) ~ X~ = ~ .1~~' ~ r t g~ ~ . - ar ' ~ X~
br +a~~B~_~�n~
31 Bi = B~ - B1. ~ ~ n~ ~ (Bi- i ' ~i~"If ~i Q~ ' gt- ~ ' a7
= i ~ . . . ~ km).
After s= km recursive algorithm intervals the procedure for evaluating
a meteorological field within the limits of the G region is completed. The
covariation matrix E a Bs characterizea the accuracy af the evaluations ob-
tained X~ X+ ~ Xs. Thus, a realization of the described algorithm in gen-
~ral does not require an inversion of the matrices. The a*gorithm stability
is dependent on to what extent the sum ~~+1 + gl+l~gl. 'a~+l exceeds 0. In
:~ny case
b~+~ . Bi . ni+~ >~.~+t > U.
'M~rreEore, the corrections obtained in each algorithm interval have a"smooth-
~~d" cl~.lrncter. The rntios of the diagonal elements of the covariation matric-
c~ ~ and E ure the values of the relative residual dispersions (RRD); (cr~i/
~ii~2 are graphic atatistical parameters charactertzing the effectiveness
aE numerical analysis at the points of grid intersection.
Modeling of Ozone Observation Systems
On the basis of the reaulta of ineasurements from surface ozone sounding sta-
l�inns [9), which we regard as the pointa of 3ntersection in a horizontal
grid, we computed the first and second moments of the random three-dimension-
al ozone field. In thia case it is necessary to have information not only on
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Che toCa1 ennt~ne, bue ~lgo on th~ vertical ozone prnfile. There,fore, rhere
wae a pogaibi~i,ty of ugin~ dxta for only two groupg of aCat:[ons (India
b gtation~, ~urop~ 5 etnti,ons). We ue~d sampleg conaisting of 60 realiz-
tlCinn~ (recnrds) (for each of rhe considered eCationa) and relating to the
~pring p~riod of 19~i9-1972 (9].
7'he gtrucCurp of ehe v~cCors Co be evnluated X is characterized by the dimen-
gionality n a 10. Th~ firet Gomponent is the toCa1 content u1(m atm-cm), the
nine follnwing c~mponents corre~rond to the vertical distribution q(nb) at
particular obaerv~tion poinC.
Now we wi11 di~cuas method~ for atipulating Che spectfi~ form of the opera-
torg Ai. Tn Che cage of ground measurements rhe role of the indicated opera-
tor is played by the unit matrix I. We wi11 assume that satellite measure-
ments are tngde at Che n~dir,using a three-channel IR spectrometer (ozone ab-
:~orption band 9.6 � ra, centers oP intervals: ZQ45, 1055, 1065 cm'1, spectral
r.esolution ~ 5 cm 1). Tlie elemenCs of the matrix operaCor Ai ~re compuCed
in accordance with the acheme presented in (2], on the basis of the corres-
ponding mean profiles q. The random observation errors E were modeled, pro-
ceeding nn the ~eaumption thaC Che levels of errors in ground observations
sre S�19'3 cm for 4!, 3 nb for q, and the errors in satellite spectrometer
measurementa ure 1 erg/(cm2�sec�sr.cm'1).
In the course of an analysis of the computation resulCs we discovered a
simil~rity of two statistical characteristics: the correlation coefficient
Uetween w and q, and also the relative residual dispersion for the remote
sounding method. It can Cherefore be concluded that data from satellite
nadir measurements for the most part contain information on the total ozone
content. A more precise determination of the vertical distribution of q
is accomplished by meana of a q- ~ regression.
Figure 1 shows the smoothed dependence of the horizontal correlation function
of the total ozone content obtained on the basis of processing of data for
46 stations in the northern hemisphere [9].
: Numerical Models for Spatial Analysis
Informution on tt~e spatial statistical structure of the ozone field make it -
poHSible to uae more complex analytical models for the interpolation, smooth-
in~ and assimilation of elements not only for the vertical, but also for the
l~orizontal components. The results of these computations are presented in
Table 1 in a uniform form. The table gives the absolute and relative errors
and also the RRD of tlie ~ and q estimates. The characteristics relating to
c~ were averaged for h.
First we will discu~s optimum interpolation, the need for which arises
when there is a noncoincidence of the points of intersection in the regular
~;rid and the observation points. We will discuss the accuracy in determining
ozone on the basis of the remote method directly at the observation point
(analytical scheme c). In this case the error in evaluating cJ is equal to _
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(5-10)�10'3 cm, wh:tch ia a relative error of 2-3%. The RRD of the evalua-
tions are 5-15%. For the q profile ehe similar characteristics fall in
tl~e range 5-20 nb, or 10-25%, and the RRD of the evaluations are 60-80%.
Thus, the relative errors in determining the q profile exceed by an order
of magniCude the errors in evaluations of the total content. The simplest
1nCerpolation method is extrapolation from the observation point to the
closest po3.nt of intersection in the grid (scheme 3). The data for var-
ianta 3- 1, 2, 3 make it possible to note the 1ow accuracy in estimates of
rhe total content, even when using data from ground measuremenCs. The de-
t~rmination errors increase lesa appreciably. However, the RRD of Che esti-
mates ~exceed the 80% level. In Che case of extrapolation of data from sat-
ellite,~neasurements the errors in the estimates are still greater (3 - 4).
'1'he RRD values for q are,85-90%. Comparison of the ~ variants 1, 2 makes
_ it possible to note a dependence of the extrapolation error on distance.
_ Optimum interpolation (scheme u) ensures a significant increase in anal-
ytical accuracy (Fig. 2a,b). With an increase in the number of points at
_ which.ground observations were made (u - 1-5), it is possible Co increase
the analytical accuracy by a factor of 1.5-2. The absolute values of the
errors for the Curopean region are somewhat greater than for the Indian
region. Nevertheless, the RRD values are approximately identical for both
regions. The data for variants u- 6, 7 indicate a smoothing of the e~::�ozs
in satellite observations when using an optimum interpolation algorith~n.
In this case the errors in determining ~ are equal to (10-1.5)�10'3 cm, -
~ahich is 3-5%. The errors in evaluating the q profile are 5-10 nb, or 10- .
25% respectively. A comparison of variants c- 5, u- 6,7 indicates that
~he interpolation procedure more effectively refines the q profile than
aS . A comparison of data for u- 2, 3, 6, 7 leads to the conclusion that
the accuracy of analysis on the basis of the results of satellite measure-
ments is 1.5-2 times lower than according to ground observations. We note
that the vertical structure of analytical errors va~ies little with an in-
crease in Che number of ground observation points (Fig. 2a) and is smoothed
with an increase in the number of satellitie measurements (Fig. 2b).
- In a case when the system of satellite observations is sufficiently "dense"
in horizontal coordinates (relative to a re~ular grid) an important role
must be played by tlie procedures of sp~~tial smoothin; and assimilation.
'l9ie spatial smoothing of satellite information ~g ~eandcc)~en25r3s~/an ~e
crease in evaluation accuracy (c - 3, cc - 1) of q y
ItRD values in this case are reduced by a factor of 1.5. The limited ef-
fectiveness of smoothing of errors is evidently attributable to the rela-
tively greater distances between observation points. The vertical structure
o� errors in this case (Fig. 2c) remains extremely inhomogeneous. For re-
~;ions liaving a network of ozone sounding stations the procedures of assim-
Llation of data from satellite and ground measurements (scheme.cyc) are of
practical importance. An examination of the variants c- 3, cyc - 1,2 indi-
cates that the use of information from ground stations situated at a dis-
tance of 1,000 km makes it possible to increase the accuracy of sounding
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from a~aCCllite by n L~cCor of approximately 1.5-2. The vertical ~truc-
ture uf nn~lyticxl errorK fe c~onetderably amoothed (Fi~. 2d). 5omewhet
~>oorer resulte were obC~ined f:or elie Curopean region (~yc - 3, ~i),~ -
'C}~e ~iCed reaearc}~ resultg indi.cnte that in�ormnCion on the ~CE?Ci~CiCal
etructure of the three-dimensional ozone field creaCe~ tt b~sig fnr the
effective use of ob~ective an~lyais procedures for the purpoge of reducing
- nbaervarion errors, increasing Che value of data from remote ~ensing, and
:~lso for repreeenting Che c~l.lected informaCion at the poinC~ of intersec-
Cion of a regular grid.
Asyimilation of Uzone and Teropernture Pields
T}ie low nccuraCy in determining ozone from saCellite measurements dictatea
tiie usc of. ndditional information. Data from ground observations supply
- clnta Eor only nn inaignificanC part of the eartti's surface. On the other
li~nd, already over a period of years a saCelliCe system has been in develop-
i~ent for tiiermal sounding of Che atmosphere. Researchers [11] also note -
. the presence of a significanC statistical correlation between the distrib- -
ution oE ozone und temperature in the stratosphere. Guided by these pre-
requisites, we cnrriPd out modeling of a combined syatem of satellite and
ground observntions of ozone and temperature simultaneously. In this case
ehe componente of the cector of parameters to be evaluaCed were obtained
from data on the total content u~, r.oncentration q and temperature T. Only
two stationa in F.urope Berlin and Hohenpeiaenberg had synchronous
serological data of ttiis type.
In the computations we used samples consisting of 60 ozone profiles and 60
temperature profiles for each of the mentioned stations for the spring per-
iod 1970-1971 [9]. In an analysis of the system for remote temperature
sounding of the stratosphere we used the matrix operator Ai, corresponding
to the "weight functions" of the 4-channel SCR satellite IR spectrometer
(lOJ. In the computations it was assumed thaC the error in spectrometric
measurements made for thermal sounding purposes is 1 erg/(cm2�sec�sr�cm 1);
tf~e error in aerological sounding is 1�C. The errors in measuring ozone
were the same as above. -
Now wc~ will exnmine briefly the principal correlation characterisCics of
the ozone and temperature fields. T'_ can be seen from the data in Fig. 3
Chat Che s~atiaL correlations of t}~e temperature field are the strongest.
'I'he cross-correlation of temperature and ozone on the average is 40-50%
:ind is close in structure and value to the spatial correlation for ozone, -
but is considerably poorer than the temperature corr~lations. -
tieveral typical situations can arise in the assimilation of ozone and tem-
- ~~erature informatton. We will examine them. The results of numerical model-
In~; rire presented in Table 2. The simplest case is when we have information
un temperature (scheme T) at a point of intersection in the horizontal
;;rid. It i.R f~~ind that the presence of satellite (T - 1) or aerological
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('C - 2) informution on Che tl~ermal atructure of the sCr~toaphere ensures
obCrilning nnt lexy preciee (on Che average) ozone estimntes ehan on the
bneis ~o~ remote ozone sounding (c - 1). A comparison o� ct~rves 2 in Fig.
_ 4tt~b'wiCh the graphs in ~ig. 2c mak~s it poasible Co noCc~ Ch~C the arruc-
- ture of the informntion obtain~d on q from the result~ of eemperature
younding differe considerably from ChgC which is char~cteristic for the
_ ozone r~roote sensing method. This cirr.umstance serves as an additional
bnsi~ fnr the assimilaCion of bor.h types of ineasurements.
Now we will examine a case when as the initial informarion for obtaining
nn ozone estimate nt a grid point of inCersection iC is possible Co use
data from aerological sounding of temperature obCained at ad~acenC meteor-
c~logicnl atations (scheme Uat). A comparison of the variants T- 2, uat -
1 leads to the conclusion that wieh a noncoincidence of tlie temperature
- observation point with a grid point of inCersection the accuracy in es-
timatinq ozone decreuses considerably. The use of two independent temper-
.nture measurementa (uaT - 2) and uae of ozone measuremenCs (uaT - 3) makes .
" ~~osaible a considerable increase in the accuracy of esCimating ~ and q.
- In this cr~se the errors are 15�10'3 cm and 10 nb reapectively. Tt?e vertical
structure of analytical errors is quite homogeneous (Fig. 4a).
Now we will discuss the possibilities of use of data from remote temperature .
sounding for estimating ~1and q(scheme ucT). A comparison of Che variants
uaT -2, ucT - 1 indicates that tt~e replacement of aerological temperature
clata by satellite data leads to an insignificant loss in the accuracy of
_ the estimates made. The addition of satellite information on temperature
r~nd ozone at an ad~acent observation point (ucT - 2) leads to an increase
- in ttie accuracy of cJ estimates by 20% and q by 10%. The inclusion of data
from surface measurements of ozone in combination with satellite information
un temperature (ucT - 3) has a more appreciable effect. The homogeneity of
the vertical structure of errors in this case is illustrated in Fig. 4b. Thus,
in the interpolation of temperature data the accuracy in estimating ozone
is (15-30)�10'3 cm for ~ and 10-20 nb for q.
Now we will examine an analytical scheme based on the spatial assimilation
c~f satcllite data on ozone and temperature (scheme ccT). In actuality, our
~:~?m~r,irt~un of the variants ccT - 1, 2 and c- 1,2 leads to the conclusion
t}i.zt the use of data from remote temperature sounding makes it possible to
increase the accuracy in estimating ozone by 20-50%. The corresponding RRD
va].ues are reduced by a factor of 1.5-2. However, in this case the vertical -
nonuniformity of satellite ozone information (Fig. 4c) begins to have an
~ effect to a greater degree than in the situations considered earlier.
Ilow we will discuss an assimilation scheme with the ~�ec ~f data from aero-
lo~;Ical me~zsurements of temperature (scheme caT). On the basis of a com-
ps~rison of caT - 1, 2 and c- 1, 2 we conclude that the use of data from -
SurE.zce tempernture observations in a numerical analysis ensures an in-
crease in the accuracy of estimating cJ by 20-40% and q by 30-50~. In
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this cnge the It1tU decrense by a factor of approximately 2, aeCaining values
10-30%. IC ahould be noCed thut in mulCipoint assimilaCion the replacement
~f gerological information on temperaCure by satellite information does
ndC lead tn a significanC loss in accuracy in estimating ozone (ccT - 1, 2,
caT - 1, 2). There is some smooChing of the vertical atructure of errors
(Fig. 4d) in comparison wiCh the ccT scheme. _
'Thus, temperature dara are an imporCant predictor of the ~ctual ozone disCrib-
ution in Che etratosphere. The use of Cemperature information (remote or aer-
ological) makes it possible to increase rhe accuracy in numerical analysis -
of the ozone field by a factor of 1.5-2.
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~ ~ ~OIt OF~ICIAL US~ ONLY
D I13LIOGRAPHY
1. t3oriaenkov, Ye. P., Denisov, S. G., Pokrovakiy, 0. M., Smit, V. L.,
- "SpnCial Analysis of the Temperature Fie1d Us~ng Measurements from
n MeCeorological Sntellite," METEOROLOGIYA I GIDROLOGIYA (Meteorology
= and Hydrology), No 9, pp 24-34, 1976.
2. Boriaenkov, Ye. P., Kaygorodtsev, A. Ye., Pokrovskiy, 0. M., "DeCer-
- mination of Che Ozone Profile from Outgoing Thermal ItadiaCion," ME^�.'EOR-
OLOGIYA I GIDROLOGIYA, No 5, pp 11-22, 1977.
3. Gandin, L. S., OB"YEKTIVNYY ANALIZ METEOROLOGICNESKIKI3 POLEY (Ob~ective
Analyais of Meteorological Fields), Leningrad, GidrometeoizdaC, 1963,
287 pAges.
- 4. Pokrovskiy, 0. M., "Assimilation of Data from DirecC and Indirect Meas-
urements in the Statistical Analysis of Meteorological Fields," METEOR-
OLOGIYA I GTDROLOGIYA, No 6, pp 33-39, 1974.
5. Pokrovskiy, 0. M., Ivariykin, Ye. Ye., "Numerical Modeling of Schemes
_ for tt~e Spatial Analysis of the Geopotential Field Using Data from
Remote Sensing of the Atmosphere," METEOROLOGIYA I GIDROLOGIYA, No 7,
pp 45-55, 1976.
6. Pokrovskiy, 0. M., Ivanykin, Ye. Ye., "Ob~ective AnaJ~:sis of the Hwnid-
ity Field on the Basis of Data from Remota Sensing," M~TEOROLOGIYA I
GIDROLOGIYA, No 2, pp 39-48, 1977. -
7. Rao, S. R., LINEYNYYE STATISTICHESKIYE METO~Y I IKH PRIkiENENIYA (Linear .
, Statistical Methods and Their Application), Moscow, "Nauka," 1968, 548
pages. -
- 8. Albert, A. E., Gardner, L. A., STOCHASTIC APPROXIMATION AND NONLINEAR
, REGRESSION, MIT Press, Cambridge, Mass., 1967, 204 pages.
- 9. OZONE DATA FOR THE WORLD, Published by Met. Branch ~ept. of Transporta-
tion of Canada and WMO, 1965-1975.
10. Smith, W. L., Woolf, H. M., Abel, P. G., Hayden, C. M.., "Nimbus-S -
Sounder Data Processing System," NOAA TECHN. MEM. NESS-57, Washington
D. C., June 1974, 99 pages.
L.L. Spankucli, D., Dohler, W., "Statistische Charakteristika der Vertikalpro-
file von Temperatur und Ozone und ihre Kreuzkorrelation uber Berlin,"
GEODATISCHE UND GEOPHYS. VEROFFENTLICHUNGEN, R II, H 19, 1975, 132 -
pages .
~
~
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~ UDC 551.584.5(514.51)
~VALUATION OF THE FACTORS FORMING THE MICROCLIMATE OF ALMA-ATA CITY
Moscow METEOItOLOGIYA I GIDROLOGIYA in Rusaian No 1, Jan 1979 pp 66-71
[Article by Candidate of Technical Sciences Kh. A. Akhmedzhanov and V. I.
Degtyarev, Kazakh Scientific Research Hydrometeorological Institute, sub- -
mitted for publication 5 May 1978]
AbeCracC: On the basis of microclimatic inves-
tigations in built-up areas, in streeCs, at in-
tersections, in open areas and squares and using
aircraft sounding of the underlying surface and
computations it has been established that one of
the principal factors favoring an increase in air
temperature on clear days in summer by 8�C and in
winter by 10�C in Alma-Ata city in comparison wirh
_ its outskirts is the fact that the area is built
up. Urban microclimate can be regulated to a con-
� siderable degree by the rational distribution of
green areas, fountains and water surfaces, in com- -
bination with the built-up area.
- [TextJ As a reault of the intensive growth of population and the size of
cities the changes occurring in their climate are becoming more imgressive
,1nd appreciable. Large cities, regardless of their latitude and landscape- -
~limatic zones, with respecC to their macroclimatic conditions are heat
islands [9, 14, 16, 17, 19]; amidst the small cities of the steppe, semi-
~esert and desert zones there are also oasis cities [5]. However, the pres-
ence of one heat island over a city is more clearly expreased in cities -
in plains areas, provided that at the same time they are characterized by -
uniformiry of built-up areas, a uniformity of green areas, etc.
The microclimate of Alma-Ata is formed under parti.cularly complex orograph-
ic conditions [2]. The steppe begins along the northern margin of the city
and this steppe undergoes transition into desert; its southern margins
" come right up to the northern slope of the Zailiyskiy Alatau. On the south, -
southeast and east the city is framed by hills which rise 400-700 m above
the city. In addition, the relief of the city, although uniformly, drops ~
off from south to north with a change in elevation by 200-250 m. Such a
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combin~Cion of relief and the city ereate a complex 3rru~Cure of ineer-
~ction oF the fgctors forming microclimate.
'Che urban built-up nren is one of the factora introducing aubsCanCial
c:hangea in almoaC ar1 ehe microclimatic characteriatica of this particular
city.
, � TaUle 1
1)istribution of Radiation TemperaCure (tequiv �C) of Walls of Buildings of
_ Different Orientation by Obaervation Times �or Alma-Ata
1 ~
2 Opuefirouua cren :,.taiiml
= BpeH~ 3 I ~g4 I g 5 I In66 I 107 I to381 39 I C310
1
fl?roape 12 -
11 ~ N 30 MuK ;3 3 8 11 10 ~1 3 3 -
12 30 ti fi 13 1:~ II 5~ ;i ~
15 30 2 I 2 I 2 I 2 I 2 I Fi I' 3 I ~i
An~e.~e 13 .
6 3t; 4 i G 3 I I 1 I
- 9 30 4 li 12 13 41 ~1 4 4
I2 .'~U :1 .i / I2. ,I2 9 J
15 ,?0 3 3 3 3 G 9 10 6 _
_ . . Nro.re 14 . -
6 30 ti I1 1(1 4 2 2 2 2
9 30 r~ ~ ,R i;i lti i . 5. .5 '
12 30 ~ 13 1~ l0 5 5
15 30 4 4 ~ ~ 9 14 13 7
is so u o 0 0 0 2 2 2
CeHraGpe 15 , '
fi 30 3 7 7 ~3 I l t 1
9 3Q ~1 1~# 17 12 ~ 4
12 30 ? 7 l~t Ifi 11 ~i �
15 30 3 3 3 3 6 13 13 8
KEY:
1. Time g~ W
2. Orientation of building walls 10. NW
_ 3. N 11. hours...minutes
4 � ~ 1'l . January
5� ~ 13. April
6. SE 14. July
S 15. September
8. SW
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In order to mc~ke n quanCitaCive eseimare of the degree of influence of =
the Fac~ors ~avoring both an increase and decrease in Cemperuture in the -
~ r.ity we cArricd out computr~tions of the rndiation temperatures of wall
s~rfacea, measurements of Che temperature of the underlying surface of a
city from ~ sounding aircraft and experimental invesCi~ations aC founCains,
wulls of bulldings, in aquares and streeCs, ~t intersections, in green -
_ ~~reas xnd in open sp~ces in ~ city. These essentially involved measurement -
_ of temperature and air humidity, deCermination of wind direction an~d velo-
city at a height of 1.5 m uaing MV-4 aspiration psychrometers and MS-13
anemometers.
CompuCations of the radiation tem~erature of th~ wall eurface (t quiv~ were
carried out using actual regime data for scheduled observation t~fines at the
.11ma-Ata Hydrometeorological Observatory. The computation formulas used
were the formulas derived by A. M. Shklover [13]; Caking into account that
Eor the conditions prevailing in Alma-Ata according to the SNiP (Construc-
l�.ion Norms and Specifications) P-A-7-62 the heat transfer coefficienC at
the surface of a barrier is aob8 = 20 Cal/(m2��C) and the coefficient of ab-
:~orption of solar radiatior. by the outer surface of a barrier is P= 0.6.
With the exposure of a barrier construction to solar radiation the surface
temperature of the w~ ~.s sub~ected to the insolation during the day~ime
- during the course of the enCire year increases by 13-17�C and the tempera-
ture of the shaded walls increases up to 6�C as a result of secondary scat-
rering in comparison with the surrounding air (Table 1). K. A. Birskaya and
'L. L. Lomtatidze [1], on the basis of field observations and computations
for the Tbilisi urban area,drew the conclusion that for surfaces with dif-
- ferent orientations the solar irrad:iation is equivalent to a considerable
temperature increase: for the eastern and western walls by 22.4�C, for the
southeastern and southwestern walls by 20.2�C, for the northern walls
by 6.2�C, for southern walls by 15.4�C, with a maximum (by 27.4�C) ~
for the horizontal surface.
lleating of the wall surfaces and the underlying surface naturally also in-
creases the temperature of the surrounding sir. This is confirmed by mater-
tals from flight experimental observations made in July and August 1973 and
~~veraKed for 3-5 days during periods of clear and semiclear weather. These
. same tables give data for equivalent and equivalent-effective temperatures
computed using the P. A. Kondrat'yev formulas [7]. -
- 'Che southern wall of a four-story building situated in a group of houses
- heats the ad~acent air layers. As a result, at a distance of 1.5 m the air
temperature on the average is 1.7�C higher in comparison with the tempera-
ture at a distance of 1.5 m from the norttiern wall of a building standing
' parallel to it. From rhe moment of incidence of the rays on the north side
(about 1530 hours) the air at the wall begins to heat rapidly and after
1.0-1.5 hour the temperature is evened out. The influence of the southern
- wall is also clearly traced at a distance of 20 m.
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- ~ .
t
'1'he win'd velociCy in the gap between the long sides of the buildings in
the coneidered case attaina maximum valuea in the middle of Che passageway
and mic~imtttn values at Chc south wall. 'i'he conaiderable weakening of wind "
velocit~+,at the sourh wall must be attributed to an increase in Curbulent
exchange.
AaphalCed surfaces also favor an increase in air temperaCure. The air tem-
perature maximum in Lenin Square (the central part of Alma-Ata) was greater
by 2.3�C at 1430 houra than in an ad~acenC public garden and the relative
_ ~~umidity was lower by 14~ (Table 2).
The temperature differential between the square and the public garden favors
the developmenC of convective exchange and an increase in wind velociCy over
Ltie square by 70y in comparison wiCh the wind velocity at the Alma-Ata
Hydrometeorolo~ical Observatory and in comparison with Che public garden
by a factor oF four.
On the bnsis of similar investigations carried out at Samarkand, Volgograd,
rlslikliabad, Tashkent, Ii~ku and abroad, it was established that during anti-
cyclonic weather in parks and wooded areas the air temperature can be re-
_ diiced by 8�C, wind velocity Uy 80~, and relative humidity is increased by
~ 10-20% [3, 6, 8, 10, 18]. Trees, especially broadleaf trees, forming a
~:ontinuous wall, are good absorbers of noise, reliably protect living _
~~uarters against dust and improve air exchange in the city [15].
Green plantings improve the microclimate of an urban area, create good con-
ditions for rest in the open air, and sa~eguard the soil and walls of build- -
ings againsC excessive heating. The distribution of temperature and air
~~umidity in a city can, to a considerable degree, be regulated by rational dis-
- tribution of green areas.
Taking into account the high effectiveness of green plantings, Z. N. Chebo-
tareva [11] recommends for the conditions of Central Asia a normalization
not of the area free from built-up sectors and pavements, but the mass of
green with intensive irrigation. A similar opinion was given by Yu. L. Rauner
;ind M. M. Chernavskaya [9J on the basis of the radiation and heat balances
of the city. They note Chat~in order to ensure the maximum possible micro-
climatic effect, in the southern regions of the USSR about 70-80% of the
l~uilt-up area ahoald be occupied by plantings. In the middle zone this ef-
Cect is attained with the ~reening of 50-60% of the built-up area.
In the opinion of ma~y hyqienists, tt+,e total area of green plantings in a
city should occupy approximately half of ttie entire area [12]. As a result
of different peculiarities of cities relief, climate and distribution
of industrial enterprises ~he distribution of green plantings in the
.irea must be different. _
- I.n southern cities, in semidesert and desert zones of our cuuntr~?, du~ to
- the ~reat dryneas of the air and inadequate soil moistening, especia~ly
~lurinq the hot period, a need arises for irrigating the territory for the .
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Tab1e 2
DistribuCion of Air Temperature t, RelaCive HumidiCy r, Wind Velocity u,
LquivnlenC Temperature (ET) and Equ3va7.ent-Effective Tempernture (EET) in
_ Section Square-Lawn Area-Public Garden and in Meteorological Area of the
Hydrometeorological Observatory
a ~ J U a v U V
_ ~ 1 ~ ae ~ 2 ~ 3. m q v 1 v a~ 3 m 4
~ , . ~ m , m ~ n m m
5 n~ousaae ~ 6 Crceep
13 97, I 31 2,0 3U,G ?!1, I 13 2;'i,:~ ~12 Q,6 28,$ 28,3
14 I 23,2 I 2fi I 2,1 I 31, ~i I 30,? 14 I 46,1 I' 3i I 0,(i I 2~J,6 I 29,1
15 2~,7 2b l,!I 31,!1 ,3U,7 ! 15 ~6,~ ~;i 0,3 30,1 29,A
i
~ fasoK 8 MereonnaqaaKa 1'MO
I;i 27,1 ,'i7 I,;3 10,3 29,;i I 13 ~ 25,G I~i2 1,0 28,9 28,1
la I 1i,3 I 3;i I I,I I ~30,~i I 2.1,h 14 I 21i,G 38 I I,4 ( 29,9 I 28,8
Ib 27,4 32 1.? ~31.1 30,3 ~ 15 27.7 I;ii 1.7 30.7 29,5
t:EY :
1. Time
2. m/sec _
3. EffecCive temperature
4. Effective-equivalent temperature
~ 5. Square
6. Public garden
7. Lawn area
8. MeCeorological area Hydrometeorological Observatory
rurpose of maintaining the green areas and ameliorating.overheating condi-
tions in the city. In our opinion, the most promising means for supplying
water to cities is fountains.
As is well known, fountains are surfaces of active evaporation, and accord- -
ingly, heat absorption. Therefore, e~;perimental investigations were carried
c~ut at fountains of all types in the city of Alma-Ata. It was establ~shed
~hat the fountains reduce the temperature of the ad~acent air layer by 1.0-
3.0�C and increase the relative humidity by 10-20%. With respect to micro-
_ climate, the most effective means was found to be lawn sprayers and these -
.~re also recommended for broader use in making a city green and supplying -
lt wirh water [4J. In combination with green plantings, fountains (in their -
di.ffe::ent variantsl are an extremely effectiVe means for reducing the over-
iieating of the environment in the built-up spaces of a southern city.
84
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~ . ~-~P
~ 6) ~ xo~oD ~
_ ; ~ ~ -lt
~ ~ / � ~ % -IO
y ~ -IE ~ -9
i
~ itnno A 'f � r %
.6 el i l : i
4.� /
+6 ' ~ ~ '~t
j ~ ,l ! ~
? e ~ � i ~ ; .y
' �7 i i -JJ/e
�Q a ~ ~9 t i~ .y , -1
' ' I
7 I -f4 iw en o �f0
-9 XWOS~E enr,c 1 -JS ~
~i a a ~ .f6 i o
~ ~i~ ~ 17y s 1
a ~ ~ .s Xao3 ' ~ ~
~ 1 0
6'''~
9.e e` itn~^~`, j .~6 `'�ii
- -9 ~e~ \ -t7 ~
' ~ . .e - X0~08 li ~
~ B
X0."�CJ i~ .~p9 - �I4 ~ ~ !
. ` \r?~~
I.- -
Fig. 1. Field of radiation temperature (�C) of underlying surface at Alma-
Ata on the basis of the results of ineasurements with an airborne radio-
- meter on 12 December at 1550-1800 hours (a) and 13 December 1975 at 0715-
0910 hours (b). The dashed line gives the conventional boundary of the
city. A) Warm; B) Cold -
As mentioned above, on sunny summer days asphalt and concrete pavements -
are ~reatly heated and tliis favors heating of the soil iaith ~lepth; in
i.iddition, an increase in the heating of the underlying surface and the
soil in the city is also favored by a considerable increase in wind velo-
city. And this, in combination with the above-mentioned factors, favors the
- Eormation of an increased temperature background in the city.
- lor example, observations of soil temperature in the cities Novyy Uzen'
(1969-1970) and Bal?chash (1971-1972) indicated that in the summer months
tn tlie upper 50-cm layer there is an increase by 3.0-5.0�C in comparison
wirh sectors outside the city. As is well known, during winter the radia- _
l�ion 1?eating of the underlying surface is considerably weaker as a result
uf ~ decrease in the influx of solar radiation and a more intensive thaw-
ing oF the snow in the city, but in general a substantial increase in the
temperature of the underlying surface persists, which is also favored by r
rhe internal heat release of an industrial and communal nature.
The ci:cumstances c~i~tl.~iited above indicate, first of all, a complex natu~Le
, c~f formation of urban microclimate, second, that local circulations caused
by temperature contrasts, seem to be a result of a combining of all the
factors enumeLated above.
The synchronous instrumental measurement of air and soil te~nperature with-
~in a large city requires enormous efforts. Therefore, *.~e attempted to ob-
tain some idea concerning the field of distribution of temperature con-
trasts in the city by means of ineasurements of the radiation temperature
of the underlying surface. 85 -
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rigure 1 ahowa mapa o~ the rndia~ion remperar?~:e f�ield (temperaCure~ tak-
ing into accounr hea~~,ng by direct solar xays) o~ the winter underlying
aurface of l~.1.mn-ACa city, plotted on the basia o~ data �rom eounding w3Ch
nn IL-18 sounding aircraft of Che Main Geophysical ObaervAtory imeni A. I.
Voyeykov during perioda o� maximum and minimum daily hea~in~ of ~he city,
thnt is, for the early evening (1600-1$00 hours) and morning (0700-0900
l~ours) periods on 12-13 Uecember 1975.
In the city.in tlie ear.ly even3.ng Chere ~re three clearly ~xpresspd heat
foci. 'Cheye ctgree we11 with areuy which are built up with buildings with '
~our or more storiea with a great density (Fig. la). The most intense of
- thes e foci ia aituated at the center of the ciCy, with a maximum increase
Ln the radiation temper~ture oF the undexlying surface up to +0.2�C in
the neighborhood of the thermoeleceric power station. A second focus with -
n temperature of -4�C occupies the indusrrial area of the city. In the
wes tern part of the city (microregions) there is the weakest heat focus
_ with a temperaCure of-6�C, whereas beyond Che limits of the city there
are sectors with a radiation temperaCure of -10�C. Along the floodplains
of the Malaya and Bol'shaya Almatinka wiehin thz city area there is a
decrease in the radiation Cemperature of Che underlying surface caused -
by the runof� of cold air from the mountains. This is manifesCed partic- -
ula rly clearly in the vicinity of the Bol'shaya Almatinka River. In the
northwestern and southweatern parts of the city there are sectors with a
- stagnating air mass and its cooling. _
In the morning the nature of the field of radiation temperatures of the '
~inderlying surface of the city somewhat changes. It is possible Co trace
a temperature decrease over the entire area of the city, but its con-
tras ts with a maximum differential to 10�C at the center 3.n comparison
~~ith its margins persist (Fig. lb).
- In conclusion, for improving the microclimate of the city it is possible
to recommend the following: [T
1. For Alma-Ata it is desirable to weaken the "heat islands" by means of
cre ating green zones (parks, public gardens, boulevards) of a meridional
direction through the entire city; there must be a further increase in
tiie greening of the built-up urban area. I*s distribution should corres-
- pond rigorously to the conditions for protecting the city against con-
taminations, noise and other unfavorable agents.
'L. Aircraft soundings with the use of radiometers or heat sensors constit-
ute the optimum method for the regionalization of cities with respect
to their temperature regime.
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13IBLIOGRAPIIY
1. B~.~gkay~, K. A., LomCatidze, Z., "Landecape-Climatic Characterizatiion
of,~'bilisi and Recommendationa on the SCrucrural Makeup of Built-up
_ Arene," VLIYANIY~ I~SZ'NYKH PRTRODNO-KLIMATICH~SKIKN USLOVIY NA PRO-
- Y~KTIROVANTY~ GORODOV (Tnfluence of Local Naeural Climatic CondiCions
on Che Planning of CiCiee), Moscow, Gidrometeoizdnt, pp 166-169, 1974.
2. Gel'~'i~gol'Ca, N. F., GORNO-DOLTNAYA T5IRKULYATSIYA SEVERNYKH SKLONOV
TYAN'-SHANYA (Mountain-Valley Circulation of ehe Northern Slopea of the
Tien Shan)~ Leningr~d, Gidrometeoizdat, 1963, 329 pagea.
- 3. Clazacheva, S. N., "PeculiariCiea of Formation of the Climate of Urban- _
ized Areas," VOPROSY GEOGRAFTI NIZHNEGO POVOLZH'YA (Problems in the Geo-
uraphy of ~he Lower Volga Region), Volgograd, pp 85-98, 1973.
4. laegtygrev, V. I., Karamyahev, V. A., "Evaluation of Che Influence of
Fountains on the Micrnclimate of a CiCy," TRUDY KazNIGMI (Transactions
the Kazakh Scientific Research Hydrometeorological Institute), No
4y, pp 153-159, 1972.
.i. Isherskaya, Ye. V., Fetisov, L. M., "Peculiarities of the Temperature
_ Regime of Cities in Different Landscape-Climatic Zones," KLIMAT I
GOROD (Climate and the City), Moscow, pp 41-43, 1974. -
6. Krasnoshchekova, R. S.,."Microclimatic Effectiveness of Green Plantings
~ in Cities," PRIKLADNAYA KLIMATOLOGIYA (Applied Climatology), Moscow,
pp 51-54, 1974.
7. Mamontov, N. V., "Statistical and Stochastic Characteristics of the
Equivalent-Effective Temperature in Weatern~Siberia," TRUDY ZSRGMTs
(Transactions of the West Siberian Regional Hydrometeorological Cen-
ter), No 5, pp 3-17, 1972.
8. Pardayev, G. R., "Microclimatic Regime of Parks and Squares in Samar-
kand," UCHENYYE ZAPISKI TASHKENTSKOGO GOS. PED. IN-TA (Scientific Notes
of Tashkent State Pedagogic Institute), No 80, pp 126-133, 1972.
9. Rauner, Yu. L., Chernavskaya, M. M., "Heat Balance of a City and the
- Influence of Urban Greening on the Temperature Regime," IZVESTIYA AN
SS5R, SER. GEOGRAF. (News of the USSR Academy of Sciences, Geograph-
ica7. Series), No 5, pp 46-53, 1972.
10. Semnnov, Ye. S., "Effectiveness of Greening of Plantings and Eiements
- of External Urban Structure in Improving the Microclimate of Residen-
ti~l Areas in Cities of Central Asia," OZIaOROVLENIYE OKRUZHAYUSHCHEY
SREDY GOROJOV (Making the Urban Environment Healthy), Moscow, pp 71-81,
1973.
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11. (;Ii~+bc~L~ir.uvr~, 1'., "1)r.nKLCy oG Clu~ llul.lt-up Ax'~aa ~?nd Microclimnee
o~ th~ ArQa o~ Rhel.denCiul Microregiana in the Oases o� Central Asia,"
KLIMAT I GOROU, Mascow, pp 131-133, 1974.
12. Cherkinskiy, S. N., Bery~uahev, K. G., GIGIYENA GORODA (Urban Hygiene), .
Moacow, "Znaniye," 1970, 78 pages.
13. Shklover, A. M., "Heat Engineering Computations of Outer Barriers in
Sou~hern Itegions," STROITEL'NAYA PROP41tS1iLENNOST' (Construction In-
dusCry), No 3, pp 81-86, 1951.
14. Angell, J. K., Hoecker, W. H., Dickson, C. R., Pack, D. H., "Urban In-
f].uence on a Strong Daytime Airflow as betermined from Tetroon Flights," -
J. APPL. METEOROL., No 6, pp 924-936, 1973.
15. Bernatzky, Aloys, "Grosstndtklima und Schutzpflanzunger," NAT[1R. UND
MUS. (BRD), Vol 102, No lr, pp 425-431, 1972.
~ t6. Lowry, W. P., "The Climate of CiCies," SCTENT. AMER., Vo1 21, pp 15-
_ 23, 1967. -
_ 17. Miess, Michael, "Planungselevante und kausanalytische Aspecte der Stadt-
klimatologie," LANDSCHAFT UND STADT, B 6, No 1, pp 9-16, 1974.
18. Quitt, Evzen, "Z~;ten a teploCni pomery mest," ZEVET. PROSTR., No 2,
- pp 87-94, 1973.
19. Vukovich, Fred M., "A Study of the ACmospheric Response Due to a Diur-
nal Heating Function CharacCeristic of an Urban Complex," MON. WEATHER
REV., Vol 101, No 6, pp 467-474, 1973.
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, , ~
UDC 551.465.552 -
NONSTATiU1VARY TWO-pARAMETCR MODEL OF THE MAIN OCEANIC THERMOCLINE
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 1, Jan 1979 pp 72-85
, [Artic;le by Professor P. S. Lineykin and A. V. Frolov, USSR Hydrometeor-
ological Scientific Research CenCer, subm3.tted for publication 12 July
1978]
Abstract: The authors propose a precise solu-
tion of the nonstationary probl~m of sCruc-
ture of the main thermocline. This makes it
possible to trace the evolution of disCurb-
ances in the temperature field caused by the
interaction of currents and the distribution
_ of density in the ocean. At the same time it -
is.possible to obtain a more realisCic de-
- scription of the vertical structure of the
temperature field in the ocean than is pos-
sible when using "single-parameter" models
~ and to give a quantitati~:~ description of
the velocity and direction of displacements
of characteristic points on the temperature ~
profile (inflection point and point of maxi- _
- mum curvature).
a [TextJ At the present time a great; number of studies have been published
~~n the theory of the main oceanic thermocline, based on geostrophic rela- _
tionships and the equations of turbulent "diffusion" of density, includ-
ing all the convective te� hs (see reviews [6, 7, 16, 17]). Despite th e
fact tiiat a total solutio ~~f this problem, with the influence of shores
- and Uottom relief of the ocean taken into account, has not been obtained -
even for the simplest boundary conditions, it has been possible to explain -
tl~eoretically a number of peculiarities of thP vertical structure of the
cicean and the thermohaline circulation associated with it.
The successes attained are associated to a considerable degree with. the use
of stipul~ted models of the distribution of the density anomaly S(relative-
ly constant value at the bottom) along the vertical. For computing the den-
ti�tty prof:~t.l.e in these mc~dels it is necessary to know only one parameter,
wtiicli is found from solution of the problem; therefore they are called single-
parameter models.
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I. ~ ~1 v ~
6 MARCN i979 FOUO 2 OF 2

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AC th~ yume time, ir~ the internal r~gidne of lErg~-~~~1~ ~ubtrnpiral cir~
c~ulatinng, occupyinY ext~nsive ~reag di th~ world ore~n, ehere ig ~ mor~
comrlex structure of the d~neity field. ~rom the eurface ~o depths of sev- -
ernl hundred meterg :hp density ig vircu~lly conatunt ~nd only b~low Chi~
_ be~;in~ te increage ~~.~rrly (vertical profile d with an inflection point).
Single-parameter model~ ~re inconvpnient for degcribing such typeg nf ver-
_ tic~l density distribution and thie greatly narrowg thp sphere nf their
.~pplication.
In order to eliminare the metttioned ehortcoming of single-p~rameter modelg~ =
in [8, 15J n homogc~neous ln~+er is "spredd" nver the thermocline. Hdwever,
for closing the problem wiCh guch an gppro~ch it is impo~;sible to get by
without additiona~. aseumpCions, for exaunple, the requirem~nC that verCic~l
velocity nt the diacontinuity of two layers be equal Co z~ro (8j.
The purpc~se of ~hi~ stuoy is formul~tion nf a two-parame*er model, which
will make it pogsi~le t~~ deacribe more complex density disCributions than
:~n exponentf~il or any other single-p~rnmeCer model. In particular, ~ two-
p~remeter model can repreaenC different b prufiles having an inflection
n~inc or some other characteristic points and the d~forr~ations of such pro- .
- �iles with time can be traced (reference is to long-period changes with a
cr~aracteristic time scale of about several months). In addition, it is of
tt~r~oretical, and practical interest to tnvestigate the transporC and ~t~for- ~
r~tion of a deneity (temp~rat~~re) di~turbance ut the free surface of ~he
~~cF~an, stipulated at some ~nitial moment in time.
The proposed modc:l is simple and the most natural generalization of an ex- -
ponential ~ distrtbution. At the same time, the fundamental equations af
_ the dynamics of a barocl.inic ocean can be here completely satisfactory _
under some additional conditions which wil~ be mentioned below. `
- 1. F'ormulation of Problem
We will examine a nonatationary circulat~.on in a baroclinic ocean outside
- the boundary layers. The ocean is situated on a~-plane, hes a fini[e
= depth and is bounded only by an eastern shore, which is arbitrarily modeled ~
by a vertical wall extending along a meridian. The c!.ynamics of circulation
is govcrned by the vertical Ekman velocity wd and the density anomaly S d
::eipulated at the lower boundary of r~~e friction layer. Going on the basis
- c?f esrimates of the orders of magnitude in the fundamental equations of
hydrothermodynamics for a baroclinic ocean ~1, 5], we take the initial sys-
tem of equations in the form
~ 2 ~~v= -~p-g?k; (1.1)
(1.2)
C (P'~) = 0,
(1.3)
- P=Po11-a"T);
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I
r
POR 0~'~ICIAL U5E QNLX
dr � d~T
~ dr + y ~ ~ T ` x o~~ , (1.4> .
where ~ is th~ ~r~effi~i~nC of verttcal eurbi~lent heat df.ffugion; .S~i ie the
vector dP Che earrh~e rotation; v ia Che velncity v~ctor; p is the pre~sure
~nnmaly P(p ~ P- PHgz); p is dPnsiCy; P p is standnrd mean density; k is _
n unitvectdr of Che aormal to the ~-plane; T ie temperature� is the
coefflci~nt of rhermal expaneion of water (oc* = 2�I~"4(�C)"i); g~" the
accelera~ion of free falling.
'Che system of Cartesian coordinatee is left-handed~ the OX-axis ia direcCed
eo the ease~ the OY-axia ie directed to the north, the OZ-axis is direcCad
~ownwgrd. The origin of coordinatea ia ~ituated on the eastern shore in the -
cemperete latitudes. The lower boundary of Che ~kman layer ~t Che ocean eur-
face is selected as the origin for reading of the vertical coordinate (z ~ .
t)). ~
, 'The approximations made in the derivation of equations (1.1)-(1.4) filter
the rapid wave movements in the ocean, but maintain the slow process of
mutual adaptation of the density and curr.ent fielde with a characterietic
time scale of about several months.
Uaing the "potential" function
~
~ Q~x, y, ci - g j r cx, v, z? r) d= Q~ Ix, v, t) ci. s)
_ . ~
the system (1.1)-(1.4) can be reduced to a single equation for Q[SJ:
Q" P$ ~ (Q~~ Q") P Q,~ Qru = x ~ir , (1.6)
The derivatives of x, y are denoted by indices, of z-- by primes, of t--
l~y a dot over the variable; J ie the Jacobi operator, f is the Coriolis
parameter (f = f0 y)~ ~ s df/dy is the Rossby parameter.
i~le aill atipulate [he vertical boundary conditions:
z- 0: w s wQ (x, y, t), Ea (x, y~ t); (1.7)
s=H(x, y): zr=u dX +v dH, ~=0.
r (1.8)
Ilerc vd is vertical velocity at the friction level
,a - - ~ rot (1.9) -
Q P~ t ' `
F is vind shearing atrese at the free surface; d~ is the density anomaly
~~t tl~e friction le~el. E and Sd are considered to be known from observa-
tions.
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The firet of the expreasions (1.8) ie rhe condition ~or bottom streamline
flow E~ H(x,y) of a barotropic current; th~ second expreseeg abeence of
_ dengiCy flow an the bottom of the baein.
On gn eastern shore ie is naCural to require that Che normal componenC o~
~~elocity Vn and Che normal derivaCive of the density anomaly d~/a n be
equal to zero. However, the selected method for solving the problem does
not make it poesible to ~atisfy~these boundary conditions and therefore _
we replace them by less rigoroua conditions:
~ N N
= r> ~ v~ d= = o, vR dZ = o. c~. ~o>
a o
Now we wilt proceed eo the dimensionless variables, related Co the main
- variablea by the following expreaeions:
z-LX, ~ety,- z=ZoZ,- r~eor~ a~a~a, f=iof,- ~i.ii~
where L is the horizontal scale, Zp ie the characteristic depth of the
thermocline, 9 p is the time seale, a ~ is Che characterisCic a value. -
Using them we tranaform equation (1.6) to the form
Q'~ + f. Q:Qiii.{.. Q~ !(~1'~ Q"1-7aQ~~'=0. (1.12)
In place of (1.8) we obtain =
z = 0: (1~ _ f= i (x, y, ~t), Q" = a (x, t), (1.13a,b)
i= h: Q~ = a'~ ~~Q~ h'), ~liit = 0. (1.14a,b) -
~ Here the following dimensionless coefficients appear
Y _ ~Ra,~Z,~e,, a _ ~L ~ _ Xn~Io~ i.~ J"E0 (1.15) -
~ r~1vL ~ Iu ~ `~BaoZo ~ ~B~oZo
and the dimensionless functions
(1.16)
S (x~ y, t) _ - rt~tr ~ o = ~ h _ ~
bu Z~
the physital sense of which is obvious. In particular, ~ reflects the
wind effect,$ is turbulent heat diffusion, h is dimensionless ocean
Jepth.
The principal unknowns of the p~coblem are expressed throuah the potential
- function in the following way (the lines over the notations of the dimen-
:;ionless values have been omitted):
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_'I
. ~ox o~~rcr~. us~ orrr.x
q~a~ z~~ ~y g L~ z~~ QX , .
u- f~~ I' v- Pu~
~ K s~~ Z~ U.r ,
= w W o~~la ~ r ~ ~ ~ h = K ~n ?u ~,i Q"~ a
(i.i7>
C = ~~o~'o , ~ i=A -I- Dn -
?o Po~'~
where u, v, w are Che velocitv components along x, y, z, ~ ia the level of
- el~e free surfnce.
For evaluating Che numerical v~.lues of tlie external parameters of the prob-
- tem we assume
f p= 10-4sec'1, 1. 5� 10'13cm-1 � aec'1, L= 5� lO8cm, -
Zp = 105 cm, = 1.5�10-3 g/cm3, ED = 1 g/(cm�sec2),
x= 1 cm2i~ec, 6= 2�10~ sec, 103 em/sec2. (1.18)
. Tt~en we will i~ave
yg0,1, ~c=0,i,i, i:s4,4~ 10-~, $=2,2� 10-~. (1.19)
In [5J it was demonstrated that tlie representation of Q in the form `
Q~X~ yi Zi � U~C~ y~ t~+2tv ~x~ y~ t/'~'l~l ~C~ f,~ Z~ ~~..20~
makes it possible to study separately the dynamics of the thermocline and
tiie barotropic layer situated beneath it, taking their interaction into
account. The barotropic components of current velocity determined by the
first two terms are not dependent on depth. However, baroclinic motion at-
cenuates with depth and for all practical purposes is concentrated within
the limits of the thercnocline. The functions U and N are selected in such
:i way that M(x, y, h, t) = M'(x, y, h, t) a 0.
Substituting (1.20) into (1.12)-(1.14) and using the boundary condition -
(1.14a) for excluding Ux, we obtain
M" -r ( r J (N~ r~) + z.~,~ -E- :1-I,~~ /t1~� =
f ! M', M") ;a A~1"' = U, (1.2I)
~
z - p: Mr ~ i. ft : - ~ J (I~'~, .tl' _ 1; {1.22a,b)
~ z-h: Nf=M'.-M".=~. (1.23)
where h/f is "reduced" ocean depth.
- ':'hus, it is necessary to solve equation (1.21) for the unknown functions `
M(x, y, z, t) and N(x, y, t), satisfying the five boundary conditions (1.22
- :i,b), (1.23) vertically ((1.22a) in this case will serve for determining N)
93
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und rhe Cwo ~'so�tened" boundary conditiona (1.10) on the lateral wall, and
nl~o the initia] conditiong, which will be formulated later. '
2. Shcution Mett~od
'~Jp will use a representaCion of the baro~linic componenC of the potenCial
function in Che form [7j
M(x, Y~ a, t)=- (m (x, y~ t) n Ix, y~ t) �s~ e-+? ~x, y, (2.1) -
wl~ere m, n, k are unknown funct.ions, which must be found. Since one of these
is expressed using Che boundary condition Chrough the oCher two, there are
two independent paramet~r~ in (2.1) and the model can be called a two-para- -
meter model.
It is ea3y Co confirm, using expressions (1.17), thaC with n= 0 Che funcCion
k'1 corresponds to the concept "depth of Che baroclinic layer of the sea,"
defined as the level at which the density anomaly is aCtenuated by a factor
uf e relati~c to its value at the surface and m is Che sCream function of
- b~~roclinic total flows, multiplied by the Coriolis parameter f.
in any density models there must be satisfaction of Che physical require-
inents of attenuation of the density ana,~aly with depth and stability of
stratificatiotil of waters, which for our two-parameCer model have the form
k> 0;
~ = A'1" _ (mk' - 2 nk + ~tlr~a) e-": ~ (2.2)
da nr _
oZ = M (3 ~ck~ - ml~~ - ~tk'z) e-'~= > 0,
and if the regions or the world ocean situated in the subtropical latitudes
are considered, also the requirement of the existe:~ce of an inflection
point on the density profile:
when 1� > 0 M~~' = p, that is Zn = 4 n~krnk, O~ (2.3)
or Miv(x, y, 0, t) ~k~(mk-4n)>0, (
2.3a) ~
~~here z~ is the depth of the inflection point.
- After elementary transformations of the system of inequalities (2.2), (2.3a)
we obtain
~ k>0;
rnk< (2-kz) n; ~2 � 4~
ntk G (3-kt) n;
mk>4n.
Conditions (2.4) impose sone restrictions on choice of the functions m, n, k.
'11~ey must be saiisfied, a[ least, within the limits of the barocli~nic layer.,
tiince in the abyssal layer the density anomaly a becomes negligible and the
restrictions on m, n, k lose sense.
94
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~
Th~ dtCference in the ~,-.?.ues enclosed in parentheses in the Chermocline is
~wHtttve. Tl~~~~fore, 1� n> 0, it followa from Che ~ir.st ehree expressione -
('L.4) tt~nt mk 0.4 m, b= 0.2 m, a< 0.06.
'I'aking the cited error into account, the increment in wave height for one
:~ound signal must nor be lees than 3 cm. For practical purp~seg it is more -
convenient that thia increment be a multiple of S cm (5~ 10, 15 cm). =
F'or cx.hmple, with ql = 5, qZ ~ 5~ b= Q,2 m and �i: s 1 aec
~
_ hmean = O.OSK1 (m), Tmean ! ~�~SK2 (sec). ~
_ It stiould be noted Chat the repet3.tion rate of the sound signals, as demon- ~
5krztec;l~y experience in aperating the GZ-2 under field conditions, must
= not excaed 1 iiz. Such sound signals are e~sily discriminated and counted ~
I~y e~r from the loudspeaker of th~ radio receiver when ther~ is a high in-
eerference level. The chopper and generator of counting pul.ses are connect-
ed by n programming mechanism upon ending of the period of averaging of
the measured aaves.
' 141
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�
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~t~It tl~~~~IAI. US~ ONLY
Th~ high noi~e itamunity of the gdopted coding gy~t~m wh~n eh~r~ ig ~~~n-
~ieiv~ rec~iving gntenn~ ~naur~~ a congid~r~bl~ ~ff~~~iv~ rgng~ for th~ -
reli~b 1e r~dio rec~ption of ~~go~m~eion from th~ G2~2. Far ~x~mp1~, wh~n
ueing ~ radio ~ti~~idn of Che "Kargt-M" typ~a g~ rh~ rgdin tr~ngariCe~r, ehe
rang~ r~f t~i~m~trin comnunic~~ion ~teain~d 50 km.
�
In ord~r eo prpp~r~ th~ u~~r Eor th~ r~~~pCinn of wgv~ d~t~, pridr to ~~ch
contact with the GZ-2, th~ int~rval~ b~tw~~n which w~r~ g~21~Cted ~e Qither
one or thrae houre, ~ prelimin~ry ~ound ~ignal with a dur~tion up to 16 eec
ia fed through the radio ch~nnel.
When p lacing the C7.-2 apparatu~ ~t deprhg ~r~gCer than 20 m th~ guppnre u~ed
i~ a Froud~ buoy (6]. Such a buoy is a long hollow tub~ (~ig. 2) fgbric~ted
of AMG-~6 light ~luminum alloys. The tube ia aeeembled of ~ eet of hollow
~~elpd cylindrical gection~ with connecting pieceg. A damping di~k ig
mounted on the lower end af the buoy in order to decregae Che period of
naturt~l oecillatione. The ueef~l lift of Chia buoy in th~ caee of a metg-
centric heighC of 2 m and with wave heighCs up Co 6 m ig 10-15 kg. The
total ma~s of Che buoy doee not exceed 100 kg.
At dep Che up to 10 m the ~elf-contained part of the GZ-Z is placed in a con- ~
Cainer mounted on the top of a column of caging pipea drilled inCo the bot-
- tom. Ag demonatrated by aea testg, such supports have withetood aave ~oads
for a period of 2 or 3 years. In seas with a variable mean level the radio
wave meter, mounted on a fixed support, is supplemented by a unit for auto-
- matic determination of conCact with mean eea level. The unit c~ntain~ a
- number of counter-"and" logic paira corresponding to the number of buoy
contacte present in the zone of change in tide height or height change in-
duced by the wind. The counter of each pair counts the closings from a def-
inite buoy contact, whereas the laet trigger of the counter controla the
pair "and" logic, being a shutter for the Cransmiasion of pulses regiater-
_ ing the closing of contact into the wave counter.
When measuring real waves, due to their irrpgularity, it ig more likely
that there will be opening of that "and" logic which is controlled by the
counte r counting the water closing of the contact situated near the mean
gea level.
The unit for determining the mean level contact, together with the time re-
lay, can be used as a device for cutting off the self-contained unit during
n calm in order to save current. Thus, if any of the counters is not com-
pletely filled during the time mTm~ (ahere m is counter capacity~ T~X is
the maximum wave period), the current is automatically cut off.
tn order to determine the optimum capacity of the counter m We carried out
:~nalytical computationa and field tests. It is obvi~us that the greater
the m value, the more precise is the determination of the zero contact
nnd the greater is the increase in the required pos~er for the self-contain-
ed unit. Accordingly, it was necessary to determine the minimum capacity
c~f the counter which would eneure the admissible n~easurement accuracy.
142
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F~tt C1~~ICtAL US~ tlNLY
In rcgnrding t1~p ~ln~ing~ c~f d~finiee cantn~t~ a~ ind~pend~n~ mengurement~
w~ r~~~ll eh~~ ~~C~rdin~ r~ eh~ eh~ory a~ irre~ular w~ve~ eh~r~ #.g m m~th-
~mdti~~l ~~ppeentinn of individual rig~~ in eh~ W~ve-e~v~r~d g~~ ~urfa~e.
`i'hi~ ~1~~ ~n~~n~ ~haC Ch~r~ i~ ~ c~nfidet?~e cnef~iCient ~uch r1~at the posi-
tinn n~~~eh*~ wav~-~hv~r~d gurf~~~e uiii f~i1 in th~ rgng~ x~g (Wh~re ~ i~ th~
eonfid~ne~ ~v~lu~ti~n). ~f th~ po~i~inn ~f ~a~~:n i~ve1 i~ ug~d th~
dr~gin uf th~ r~~dit~~, eh~n x~ b.
+
The ~uChqrg of (~j ~x~min~d eh~ e~rdr in determi~ling eh~ meat~ heighe df Ch~ -
w~veg, gov~rned by a noncorr~~pond~nce b~ta~en r1~e po~ition c~f ehe zerd
~onra~t and eh~ ~egumpd m~~n 1~v~1. Th~ gccur.