JPRS ID: 8538 METEOROLOGY AND HYDROLOGY

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JPR5 L/8538
25 June 1979
~
METEOROLOGY AND HYDROLOGY
No, 4, ~PRIL 19~9
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JP ~tS L/ 8 5 3 g -
75 ~une 1979
METEOROLOGY AND NYDROLOGY
No, a, Anr~.i i979
Selected artiiclee from the Russian-language journal
METEOROLOGIYA I GIDROLOGiYA, Moscow.
CONTENTS PAGE
5emiempirical Mndel of the Thermal Regime of the ACmosphere and
~teal Climate
(M. I. Budyko) 1
_ Present Status of the MeChod for Seasonal Weather Forecaete and
Prospecte for Ita bevelopment
(N. A. Arigtov, D. A. Ped') lA
Numerical Model of Local Atmospheric Processes
(V. V. Penenko, et al.)...... 25
Spatial-Temporal Statistical Structure of Mean Monthly ,
Geopotential of the 500-mb Surface
(G. V. r,ruza, et gl.) 38
~Some Results of Computations of the Principal Energy Characteristics
~f the Zonel ~:irculation in the Upper Atmoaphere
(I. V. Bugayeva, et al.) 49
Dynamic Initialization of Initial Fields for a Baroclinic
Prognostic Model
(M. S. Fuks-Rabiz~ovich) 5~
Investigation of Depend~nce of Pallout oF Clob~l Radiouctive
Aerosols on MeCeorological Factors
(A. I. Osadchiy, S. G. Malakhov) 67
Dependence of Aerosol At~tenuation of (?ptical Radiation on
Air Numidity
(y. L. Filippov) 76
- a- (III - USSR - 33 S&T FOUO)
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~ok c~a�~~tcrnr, USL ()N1,Y
t;c~NTI;N'PS (Cnne tnuc~d) Pr~gc
Crieerion of Cdrr~~p~ndene~ B~ew~en ehe ntseributidn Curv~~ of
rrobabiliCiee oE Maximum WnCer Discharge
(n.. M. Mamatkanov, N. 5h. Kudaybergenov) A3
inCr~diurnnl Change in Strengrh of the Ic~ Cover oE Riverg and
- ~egervoirs During Sprfng
(V. M. Timchenko) 93
Itr.lentinr, nf 5now and Meltwater in ASriculCurnl ~'i~ldg
(V. N. Parehin, A. K. Alekseyeva) 100
Occurrence of ~rozen C:round in Che Chnnncl~ nnd F'loodpl.yins of
River~ nnd Their Influence on the Channel Procegs �
(A. A. Levaahov) 108
~ Generalixed Dependence for Hydraulic Cogrseneea oE Pnrticles of
bifferent Configuration
(V. I. Yefimov, V. A. Rusin) 11G
AgroclimaCic Basis for Distribution of Lentil Over the
Territory of the USSR
(C. C. Vasenina) 120
Ilydrolo~ical Peculiarities in the Deaigning of Canals in
Floodplains
(h. V. Plashchev) 126 .
Ttie Andreyev Formula for Taking Into Account the Accu~ulation
of Inflow in Calculating WaCer Discharge Pipes
(L. G. Rabukhin) 132
Some Results of Development of a Method for Measuring Density
and Temperature Using Palling Spheres .
(P. Dyubua, et al.) 136
Use of Pilot Balloon Measurements for Numerical Analysis and
Weather Forecasting
(P. K. Dushkin, et al.) 142 -
Sixtieth Birthday of Yevgeniy Mikhaylovich Dubryshman 153
Seventy-Fifth Birthday of Khoren Petrovich Pogosyan 155
Seventieth Birthday of Iosif Adamovich Yankovskiy 157
-b-
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CONTLN'T3 (Continued) PaBe
Conferences~ Meetinge and 5eminare -
(I. A. Yankovskiy~ eC al.) 159
Notes From Abroad
(B. I. Silkin)..~ 171
Obituary of Irakliy I1'ich Kherkheulidze (1908-1979)
(Z. I. Tskvitinidze, G. N. Khmaladze) 173 _
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PUBLICATION DATA
English Citle : METEOROLOCY ,AND KYDROLOGY No 4,
APR 79
Rusaian title : METEOROLOGIYA I GIDROLOGIYA
Aurhor (s) : :
EdiCor (s) : Ye. I. Toletokov `
Publiehing House : GIDROMETEOIZDAT
Place of Publication : Moacow
~
Date of Publication ; 1979
Signed to press : 22 Mar 1979 :
~
Copies ; 4030
,
COPYRIGHT ; "Meteorologiya i gidrologiya", 1979 '
.
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UAC 551.583
5EMIEMPIRICAL MODEL OF THE THERMAL REGIM~ 0~ TH~ ATMOSPHERE AND R~AL CLIMAT~
Moscow MET~OROLOGIY~~ I GIDROLOGIYA in Russinn No 4, Apr 79 pp 5-,17
(Article by M. I. Budyko, Corresponding Member U5SR A~ademy of Sciences,
State Hydrological, InaCitute, submitted for publicatiion 31 AugusC 1978]
Abatract: The article examinea the reaulta
of application of a simplified model of the
thermal regime of Che atmoaphere for clar-
ifying the laws of geneais of clia~ Ge and
atudy of the physical mechanism of climatic
changes.
; (Text) IntroducCion. Simple semiempirical models of climatic theory were
~ proposed about C_n years ago. They describe the mea~n laCitudinal diatribu-
tion of air temperature at tlie earth's sur~ace (Iiudyko, 1968; Sellera,
1965). Although the problem of the physical content of models of auch a
' type was later discussed in many atudies, up to the present time it cannot
be considered adequately clarifie3. In this connection we will preaent a
~ concise review of the principal resulrs of applicaCion of the first of the
above-mentioned semiempirical theoriea of the th~rmal regime and we will
discuss the problem of the correspondence between tliese results and condi-
tions of real climate. In this review we wi11 limit ourselves to an exam-
ination of the most important conclusiona.
1. A high aensitivity of the thermal regime Co relatively amall variations
of the heat influx, especially to variations over long time intervals, dur-
: iug which there is an intensification of the feedback effect between air
temperature at the earth's surface and the area of polar ice.
2. Indeterminacy of modern climate, that is, the possibility of Che exis-
tence, with existing external climaCe-forming factors, not only of the
observed meteoroiogical regime, but at least one regime differing consider-
lhly from the modern regime.
~ 3. The possibility of a total g,~~aciation of the earth with a relaCively
small decrease in thE heat ::~fi~~lx.
4. The development, during the Cenozoic, of a cooling cauaed by a decrease
. in the quantity of carbon dioxid~ gas in the aCmosphere.
' 1
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5. The appeurance in rtie I'leisCocene oF ~xCenaiva gl.ncinCione who~e cnu~e
wriH pc~r.i.oclte d~crrr~n~~~ in rr~diati~n auroe in Che hlgh 1f~tt~udGH during Ch~
warm periodg nf the yenr Erom v,irl.ntiona of' e].emeneH nf. ehe earth'~ urbit
nnd incllna~inn of th~ enreh'g axig.
6. Vnriat~ona of inean air temperature in ehe modern era caused by changes
in etmospheric Craneparency And incr~ase in the carbnn dioxide concentra-
tion.
~our of theae six concluaions (1 and 4-6) cgn be checked directly on the ~
baeis of empirical data. For evaluation of eha correctnesa of two conclu-
~iona (2-3) it is necessxry Go use indirecr meChods. Since Che mentioned
conclusinns follow from computations based ott a semiemp.irical model of
the thermal regime of the atmoaphere, whoae reaules ~re dependenC on the val-
ues of the empirical parnmeters enCering inCo the uaed model, we wi11 dis-
cuss the problem of deCermining Chese paraneters~
DeCermination of Model Parameters
Structure of model of thermal regime. The menCioned model oE thermal regime
of the atmoaphere (Budyko, 1968) is based on a soluCion of Che hent balunce
equation for the earth-atmoaphere system
Q~1-a) a/-}-C. (1)
Here Q is the radiation incident on the eueer boundary of the atmosphere, '
oC ia system albedo, I is outgoing long-wave radiatioc~, C is the receipts '
and losses of heat exchange when using rhe following empiricul expresaions
in this solution:
1= A-~-BT, ( 2 ) ~
~
where T is air temperature at the earth's surface, A and B are numerical !
coefficients dependent on cloud cover, ~
i
C~~(T-Tp), , (3) i
where Tp is the mean Cemperature for the earth as a whole, ~ ia a numerical .
coeffic3ent,
a=a(T), ~q~
(the dependence of albedo on air temperature, used for taking into account
the influence exerted on albedo by the formation of a snow-ice cover at ~
low temperatures).
To these equations we add expressions following from (1)-(4), .
Qn (1 - a~) = A �F ~sT~, ~5~
(6)
an ~ a~ ( T~ ) ;
2
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i
(
~ rox o~�ricr.nL us~ ort~Y
~
~ (rhe subscripr p denoCes vnlue~ rel~eing to Ct~e earth ne tt whole or one nf
~ the hemispheres).
~
In tihe computations on the basis o� ChesQ equa~ions of ~he digtir:l.bueion of
~ the mean latirudinal air tiemperaturea ehe dependence nf solnr rndieCion nn
, latieude w~s at~pulaeed using tabul~r data.
A solution of equaeions (1)-(6) can bQ obCained ueing different ~pproximare
methods which have been discussed in a number of inveatigationa, including
gtudies by North (1975, 19~5a).
The model presented above relates tio a ataCionary case and c~n be used in
determining the mean annual temperaCures. For computueions of the Chermnl
regime under nonstationary conditions Che equaCions (1) and (5) must in-
_ clude an additionnl term characterizing the change in heut content of tt~e
earth-atmnsphere system with time. Such a method was used in g study by
13udyko and Vasishcheva (1971) for determining ehe latiCudinal disCribution
of temperature in the warm and cold aeasons. Since the changes in heat
content of the earth-atmosphere system in ttie annunl variatlon are determined .
for the most part by fluctuati~~ZS of temperature of the upper layer of
ocean waCers, in the mentioned sCudy for taking this effecC into account
use was made of the equations for the heat balance of the ocenns. The prob-
lem of computing the changes in the thermal regime with time when using a
semiempirical model of the thertnal regime was later examined in studies by
Schneider and Gal-Chen (1913), Held and Suarez (1974), NorCh and Koukli
(1978) and oCher authors.
Albedo. The results of computations of the thermal regime of the atmosphere
are essentially dependent on the assumed values of albedo of the earth-aCmo-
; sphere system. In Che investigation mentioned above use wss made of two al-
bedo values: for the region free of ice caver, 0.32, for the region of arc-
tic polar ice 0.62 (Budyko, 1968). It was assumed that in the case of a
change in the area of the pol~r ice the albedo in the zone occupied b~ iC
remains consCant. In the discussion of Chis assumption it was noted that
the albedo of the earth-atmosphere sysCem is dependent on Che angle of in-
cidence of the sun's rays, decreasing with an increase in this angle. Such
a dependence, however, is relatively weak for cases of high albedo values,
characteristic for regions with an ice cover. At the same Cime, with an in-
crease in the area of the ice zone a tendency arises for an increase in al-
bedo due to a change in climatic conditions in the ice zone. it has been
postulated that these factors more or less compensate one another, as a re-
sult of which it is possible Co limit ourselves to a deterraination of the
mean albedo value for the zone of ehe ice cover regardless of its extent
';sudyko, 1969).
The actual albedo values tor different latitude zones, obtained by Ellis and
Vonder Naar (1976) on the basis of data from satellite observations, are rep-
resenLed in Fig. I., where the curves ~ N(1) and a g (2) characterize the �
alb edo values for the northern and southern hemispheres. The latitude
3 '
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i~,oK c~rrtc;rn~, usr nNt,Y ;
intervals, denoCed L1 ~N and Q~g in the figure, coxr~spottd to tihe regione
of tranaition from an ice-~ree zone ro a zone with a con~irwous ice cover
in each of the hemiepheres.
rc '
~
. ~
Q ' -B
dy,es '1
/~8 � ~
y ~ �
�
e ~ N _y
p 6o v~
~ N
D 4o y'c.w,
Fig. 1. Dependence of albpdo on Fig. 2. Air Cemperature at boundary
latitude. 1) Northern Hemisphere, of ice cover.
2) SouChern Hemisphere
The use of the data on albedo presented in Fig. 1 in computations of Che
present-day temperature distribution presents no difficulties. For estim-
ating the albedo values with a change in ice area it is possible to take
into account the relationship of the albedo values to the position of the
ice, which is clarified when using these data. In both hemispheres, aith
a considerable difference in the area of the polar ice and in the nature
of glaciations the albedo values in the zone of a permanent ice cover
differ rather little and are close to 0.6 (in Che southern hemisphere not
much greater than this value, in the northern hemisphere not much lesa). .
In the transition zones, where the ice cover occupies only part of the
space, the albedo decreases with increasing distance from the pole. These
zones occupy about 20� of latitude in each of the hemispheres.
It can be postulated that with a change in ice area the albedo of Che earth-
atmosphere system will be 0.6 in the zone of continuous ice, whose boundary
is situated aC a distance of 10� in a poleward direction from the mean boun-
dary of the ice cover, determined from its area.
In the transition zones, which exCend 20� in latitude, Che albedo can be de-
termined by interpolation beCween the values for the zone of c~ntinuous ice
and the value on the inner boundary of the transition zone under the assump-
tion that the albedo does not change in the ice-free zone.
~ 4
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~,or~ orrtr.inL usi. orti,u
~ In order eo valid~zC~ ehe pnrametierization of ~lbedo ln rlie case uf vari- !
aU1e ice ~rea it is necess~ry Cn examine Che dependence ox t:he meau lntii-
' eudinal albedn vn].ues ott cloud cover. A s~udy by Cess (~.)76) g~v~ dc~Ca on
~ subsCanCiA1 increase in c~.oud albedo with nn increase in 1~e:Ltude due Co
n decrease in solgr zen~Ch angle, na a resul~ of wliich rhe question nriaes:
to what degree is ehe increase in ~lbedo in tihe high 1ar:Ltudes dependent ~
on the presence ot the ice cover and Co whae degree on the conditions for
rhe reflecCion of solar rndiation on the upper surEace of elie clouds? Tn
discussing this pr~blem it must be remembered kh~t se~b].e regions oE high
pressure with a 1ow alr temperature und humidiey form over quite extens3ve
polar ice covers in Che high laCitudes and the cloud cove.r in Chese usually
is sm~ll. ~xamples of such a type of clicn~tic conditions ~re the cenCral
part of MCarct~.ca and the regions of occurrence nf QugCernary glaciations
in Che northern hemisphere. In this connecCion it can be surmised Chat
with Che movement o~ ice inCo the lower latiirudes a decrease in Ciae mean
_ albedo of Che 2one oF a continuous ice cover is improbable. It is possible
Ct~at for a"whiCe earCh" wiCh very low temperarures aC a11 laCitudes the
aemospher~ should be virtually transparenC for radiaCion, as a result of
~ which the earth's albedo woul.d approach Che albedo value for a pure snow
surf.ace (Budyko, 1974).
In computaCions of Che latiCudinal distribution of albedo it is necessary to
take into account Ctie position of Che mean boundary of the permanenC ice
cover, which is dependent on thermal condiCions. Since the temperature of.
Che earth's surface usually di.ffers little from Che temperature of Che
. lower air layer, iC can be postulated that in Che absence oE an anm P~ (1)
where /d ig dpngity.
~igure 2n ghowg ehe K~ field construcCed for Janunry on the bagi~ nf long-tercn
daCg. The sCrucCure nf the K~ fields is determined by the di~tribution of
rh~ fieldg of maxirnn end minima nf wind velocity and ttie verticnl P profile.
'rhe moximum K~ vglues (2�105 g/(m�sec2)) are related to th~ jet gtre~m re-
gion in Che troposphere: in laCitude the region ~f the maximum Vzon gnd KE
value~ coincide, wherena in altitude the ICE maximum ia approximately 2 km
below the Vzon mgximum. The regi~n of incregged KE vnlues in rhe laritucfe
zone 54-34�N is traced to 60 km, buC in contrast to the field of the zonal
wind without maxima 46 nnd 60 km. In the southarn hemiaphere in the luti-
. tude zone 10-20�S there is a K~ ma~cimum at nn altitude of 34-40 km, equal to
0.7�104 g/(m�sec2) (the focus of maximum velocities Vzon is siCuuted at al-
titudes 48-54 km).
NxM O!A?1~ !(~3+V~ Q Q
',a~+ ~ ,n b~ g:I b) i I I,..b : p~ � ~ .c.
:0~ : i~ ~ ~ ~pjp 1 I?
t I'
~ ~
j s:~ II( ~ I XO ; ~
, ~ ~ I �
~~'1~~' :1.~c' '
J; ~ ~ .A: I ~ ;
:I .
. ~
f , .
a~ . ~~j
~o ; A~?6' r J'.::: � : ~
' z~'~~
p � , . . . ::,i
N :
J JO f0 0�f0 �tG'b~s 06'c,r. SO JO fD 0�x7 46tW SO JO 1J 4�.~:1
S N g N S
Fig. 3. Spatial sections of field of generation of kinetic energy of zonal
motion CKE (m2/sec3). a) for January on basis of long-term data; b) devia-
tiona of GKE for January 1971 from GKE according to long-term data; c) de-
viations of CKE for January 1967 from CKE according to long-term data. Re-
gions of positive values shaded. Dots denote regions without data.
51
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~on~~ o� decrea~~d KE va1u~~ ~re iocniiz~d Lrt r~giong df chang~ in circulaCion
~ign, ther i~. in regiona wieh n zprn iantnr.h und in reKinn~ ad~nc~nG Cd ie
w1Ch 1ow wind velocitieg. In Ju1y, when ov~r th~ ndrthern h~ni~pherp in Che
etratn~phere ~nd me~osphere there ar~ ~a~t~rly winds Nl.th maximum v~locieie~
in th~ middie latitude~ gt an gleitudp of ~8-6~ km, in th~ kin~tic en~rgy
field at these e~me latitiudeg~ bue ~om~whae low~r, ~t nt~ ~leirud~ of 48-55
km, rh~re i~ a maximum equal tn 0.2~~04 g/(m~sec2). A sec~nd it~ maximum i~
situated in the tropoephere in thQ ~et etream xone'~nd is 2�104 g/(m'gec2)�
The zon~ o� minimum KE v~lue~ p~ee~~ at Ctie 1evp1 of gep~ration of the etraC-
oapheric eaaterly circul~tion and Che trapogphpriC we~t~rly c~reulation, th~t
is~ at the velopauge (3~, and aleo in the region of separaCion b~tween Che
~asterly summer ~irculation of the northern t~~misph~re ~nd ~h~ w~aterly win-
ter circulation of Che southern hemiephere.
For the remaining monthe Chere is aLso a coincid~nce in Che poeition og the
maximum V~on end KE values in latitude and a lowering of Che 1att~r in a1-
titude relaCive to the VZOn maxima in depCh to 2-4 krd in tt~e eropoaphere
~nd to 10-20 km in the sCraCOSphere. The maximum K~ Vultlpg f~ll in March
and the minimum values fall in the summer month~.
Now we will diacuss the available poe~ntial encr~y (AI'~) ot zonr~l mov~m~nt:
APE � J ~'~T - 7~~' 8rda~ ~2~ ~
� }
where R
't = ""_"~r k r ~
8P (
o
p -
R is the universal gas conetant of air, Tp iaige~het8mecificrheat capacityl
p, g is the acceleration of free falling, Cp P
of air at a constant pressure, d d is an element of volume.
Integration is carried out for the enCire considered region of the atinosphere.
It is known that the available potential energy is the diffcrcr~ce betw~fnthee
potential energy of a particular atate and rhe total potenti.yl energy
conditional state, obtained from the initial state as rs resulr of an adia-
batic process in which the isobaric surface~ an~heh=g~er~fcreciprocalltrnns-
tential temperature coincide, and accordingly,
ition from the total potential energy to kinetic energy and back is equal
to zero or is minimum. Together with the inCegral APE, it is interesting
to examine the spate ~~aitro~~ntial energyCat�a point which entersnintoCand-
ing thaC part of th P
the APE.
The principal characteristics of structure of the field of "speqific APE" in
all months remain similar: the maximum values in the region of the pole
and equator, the minimum values in the middle latitudea, a decrease in
"specific APE" with altitude (due to a decrease in The reserves of APE
52
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Fdlt OFFiGtAL U~ii ~NLY
in winCer ~r~ 3�i023 ~/(m~~@c~). in ~uunn@r eh~ AP~ r~~~rv~~ ~r~ i~~~ ehan
in win~~r, ~pproxim~teiy by ~ factar of 2-4 ~nd con~eitiue~ ~bout 1~i0~3 g/
m�~~c2~ wh3ch i~ ~sgo~i~e~d Wieh th~ aeeenuaeion ~f conCrA~C b~Cu~~n eha
pola gnd eh~ ~qu~e~r.
Now We will ~cnmin~ th~ p~culi~rities of th~ ~p~ti~i di~~ribueivn of th~ g~n-
~rgtion df k3n~tic enetrgy (a1t~) of zon~1 movemen~ per unit masst
Gtt~ ~ - P = ( ~ )
8 Y'
~ ~ ,
t3 mep ~ mer~ wh~re Rg i~ th~ ~arth'~ r~diu~~ p ig preeeure~ ~ ie let-
itude.
The reeults of eomputaeions of (i1tE for Janu~ry on the ba~is of iong-~erm
data are pre~ented in Fig. 3~. Since the tran~formation from potentiigi an-
~rgy to kin~tic enprgy ~s ~ re~ult af ineridional mdvem~nt ig g rev~rgibl~~
proceae, in the meridional a~cCion th~re gr~ boCh regiong of kinetie en~r~y
(positive regiona) and regione of transition from the kin~eic energy of
zonal movement to zonal potential energy (regions of negnrive valuee).
It follovs from Fig. 3a thAt the regions of negative valu~~ are 1oca11zed
. in the tropospher~ and str~atoeph~re of th~ high and temperate laCitud~g,
with a maximum of -0.24 m/sec~, at an altitude of 56-60 km, and in th~
equatorial latitudes aith a maximum at 48-52 km, uhich is -0.25�10'Z m2/sec3.
The region of generetion of kinetic energy is noted in the strato~phere in
the latitude zone 52-18�N with e maximum value 0.15 m2/gec3 ne an altieude
54-58 1~?. In July in the stratosphere and in the lor+er mesosphere, ae far
as the equetor, there ig ~ region of nega~ive CKE v~lues aith n roaximum in
ehe middle latitudea above 54 lan (-0.34 m/sec~).
M analysis of the GKP. field on the basie of long-term data in the course of
the year demonstrated that in the atratosphere and in the lower meaosphere
of the high and temp~rate latitudeg in autmner ~nd winter the GICE value$ are
negaCive, Whereas in the transitional seasons Chey are positive. According-
ly, in theee regions in the main aeasons of the yegr there is a transfonua-
tion from the kinetic energy of zonal movanent Co zonal potential energy.
In the tropical latitudes the negative GKE values are observed only in the
summer months; in ainrer, hoaever, gnd in the transition seasons there is a
tranaition from potential and kinetic energy. In the tropQaphere and lower
straCoaphere the GKE values are negative during th~ entire year. This indi-
cates that by limiting the frameworks of zonal circulation it is impossible
~ to explt~in the maintenance of stnble Zonal movements in this region of the
atmosphere. The gource of kinetic energy here is the kinetic energy of eddies.
In addition to computations of the energy characteriatics on the basis of
long-teren data, we carried out computations of KE, APE and CKE using mean
monthly sections for 1967-1974. We will consider how the influence of
winter etratoapheric Warmings is manifeated in the fields of energy
53
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~Olt OFF~CtAL U5~ ~NLY
ch~r~ee@ri~tie~. For ~n ~n~ly~i~ oE eh@ i~Elu~n~~ of wine~r wnrmings w~
~~~~ee~d J~nueri~~ a~ moa~h~ which ~r~ ~ufftei~nely reprp~pn~~Civ~ For
nn inv~~eigation o� Chi~ ph~nom~n~n. A11 Janu~ri~s ~~om 1567 Chrougll i9~4
~re broken dnwn inCo two group~s Che fir~~ include~ Januarie~ of thog~
ye$r~ ~h~n th~r~ w~r~ ~tr~ng warinings with a pr~~~ure rest~uctu~ing af the
f3~1d i.n th~ high i~titude~ (nn ehe m~gm m~nthly ~~~:eiun~ ehi~ wa~ ~nan3,-
f~~t~d ~.n the aeetin~-in of ~n eaaeerly eircul~tion~; to th~ ~pcnnd group
we aeeign~fl the Janu~ri~e o� thoge year~ ah~n th~ t~~rn~ing~ wer~ weak, with-
out re~~ructuring og circulation on the m~an ~nonthiy seceions ~4, 11, 19j.
Figur~ 2b,c represent~ th~ KE dev3~einn~ determin~d u~ing d~Ca for J~nu~ry
i971 (gtrong warming) and January 1967 (wenk aarming) from th~ KE computed
using iong-term data. In i971 there i~ a we11-express~d i8titudinal varia-
tion of KE d~viation~. In the high ~aritudea, to thp north of 72�N, there
ig a region of exceee of KE over the long-term v~lu~~ in virtually the en-
tire thickneae of the aemosph~r~, thet ig, th~r~ i~ an incre~s8 in KE. Thi~
i~ atCributable to the fect that in the high-latitude ~tr~toephere during
the aarmi.ng period there ie a high-altirud~ f~contgl znne ~ynd a con~iderable
intengification of the ~aind, especially the meridional cn~uponCnG~ which in-
creases by a factor of 2~3 in comparieon wiLh th~ lnng-t~cY.~ v~lu~g. To the
gouth of 72�N there is a zone of negative deviatinng and in the tropoephere
and in the lower gtrgtogphere~it is bounded by SO�N; wih~~ incr~aeing nlti-
Cude it expande and in the mesoephere attaina 25�N, thar tg~ in the temper-
nte latitudea during the period of varminge rhere is a decrense in the kin-
etic energy of zonal movement. ThuB, during n pariad of Wnrming th~re ig a
rediatribution of kinetic ~nergy aith altitude anci lati.Cu:ic~ an inCreage
iri KE is noted in the high latitudes and a decrease i~ obH~rved in the middle
latitudes.
in 1967 such a latitudinal variation of KL deviation~ is nbsent. We note
that such e atructure of the distribution of deviationa is also maintained
in other yeara with etrong and Weak warminge.
Now ae will show how Chg warming processes ~re reflected in ti~r ftelds of
GKE deviationa. Pigure 3b,c shows the deviations of GKE for ti~e Januariea
of 1971 and 1961 from the GKE for January, cnmputed on the basig of long-term
data. In 1571, in the atmospheric layer above 30 {am, in tt~e lgtitude zone
7$-50�N, and below 30 km virtually in the entire latitude range, tl~ere
is a CKE excess over the long-term values by a value of. about 0.1-0.2 m2/
sec3. Since in thi8 region t':e GKE, according to long-term daCa (Fig. 3a),
is negative and variea in the range from -0.1 to -0.01 m2/sec3, that is,
there is a*.ransition from kinetic energy to potential energy, the CKE for
.tanuary 1971 in the stratosphere and mesosphere for the high latitudes of
this zone becomes positive, whereas in the remaini.ng part of this zone, re-
maining negative, it decreases in absolute value. This means that for the
stratosphere and mesoaphere during the period of warming in the high lati-
tudes (80-70�N) there ia a tranaition from potential to kinetic energy;
however, in the region of the temperate latitudes (60-50�N) the rate of
transiCion from kinetic energy to potential energy de.creases in comparison
54
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F0~ tl~FtCCAt, UJ~ ONt~Y
wtth Ch~ rnC~ of tir~n~i~i~n ~n Ch~ b~~ig df ].~ng-e~rm d~en. SuCh ~ r~~rru~-
euring of eh~ Git~ fipld i~ d~r~rmined by Ch~ r~~tirueeuring o~ eh~ hr~~gurc
fi~lds in eh~ high laeieud~~ Ch~re i~ ~ ehang~ in eh~ ~i.gn nf eh~ pr~~dur~
gradi~n~ (an ~neicyclon~ i~ Aitu~t~d in eha poi~ r~gion)~ in ehc~ ldw~r lari-
tud~~ th~ pre~aur~ gradi~nt~ decrease. A~imilQr ~~ruaCur~ nf eh~ aK~ tieid
i~ ~h~r~~e~~i~e3~ for ~il J~nu~ri~g wh~n th~r~ w~r~ ~~rnng w~rming~ ~L96g,
1969, 1970~ 1971). In Jenu~ry wieh weak wgrming~ ~1967, 1972, 197~) ~here
were no such regular~.~i~~ in th~ att~ fi~1d.
Thu~, nur computations of the energy ch~raceerigtice (K~, GK~, AP~) demon-
~trat~d g~ubsCaneial differencp in their ~p~ei~l di~tribution in dep~ndene~
on aeaeon and the nature of circulation procea~es.
BIBLIOGRAPHY
1. Borieenkov, Ye. P., "Seagongl Transformatiion of ~nargy in ehe ACmo~ph~r~
in Che Northern and Southern Hemiaph~res," TItUDY AANII (Tr~nsectiong of
the AreCic and AnearcCic Scientific Reeearch In~Cituee), Vol 253, pp 109-
121, 1963.
2. Boriaenkov~ Ye. P., "~nergy TransformaCion in th~ Atmnsphere nE the Noreh-
~ ern and Southern Hemispheres and Interaction of Procesaes in Iloth Hemi-
spheree," METEOROLOGICHESKIYE ISSLEDOVANIYA (Mcteorological Research),
No 16, Moscow, "Nauka," pp 70-86~ 1968.
3. Bugayeva, I. V., "The Velopause and the Summer Stratoapheric Circulgtion
Regime," TRUUY GIDROMETTSENTRA 55SR (Trensactiona of the U5SR Hydrometeor-
ological Center), No 38, pp 1-96, 1969.
4. Bugayeva, I. V., Ryazanova, L. A., "Atmospheric Proceases in the Layer
30-60 km in 1971-1973," METEOROLOGIYA I GIbROLOGIYA (Meteorology and
Hydrology), No 8, pp 46-55, 1914.
5. Guterman, I. G., "Interlatitudinal Exchange of Momentum of Momentum,"
METEOROLOGIYA I GIDROLOCIYA, No 12, pp 21-27, 1977.
6. A NATIONAL PLAN FO[t ENERCY RESEARCN, DEVELOPMENT, DEMONSTRATION: CREAT-
ING ENBRGY CHOICES FOR THE FUTURE. VOL. 1: THE PLAN. ENERGY RESEARCli
DEMONSTRATION ADMINISTRATION, USA, 1976. ERDA-76-1, 122 pages.
7. DATA REPORT. HIGH ALTITUDE METEOROLOGICAL bATA. WORLD DATA CENTER A.
1967-1973, 236 pagec.
8. Dopplich, T. G., "The Energetics of the Lower 5CratospherA Including
Radiative Effects," QUART. J. ROY. METEOROL. SOC., Vol 97, pp 209-237,
1971.
9. Finger, F. G., et al., "Use of Meteorol~gical Rocketsonde and Satellite
Radiation Data for Constant-Pressure Analysis at Levels Between 5 and
0.4 mb," SPACE RESEARCH XII, Academic-Verlag, Berlin, pp 147-152, 1913.
55
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10. H~rrm~n, D. "Th~ bynamie~i C].imatol.~~y of ehQ Ser~td~ph~re in ehe
3outih~rn H~mieph~rg During Che Late Wine~r ].973," J. AT'M03. SCI., Vo1
33, No 9, ~789-1802, 1976.
11. John~on, K. W., "A Prelin~3~ary Study a[ Ch~ Seratc�phari~ Warming~ of
D~cember 1967-January 1968~" M~N. WEAZ'HER REV., Vn1 97, N~ 8, pp 553-
564, 1969. .
- 12. Kurbatkin, (i. P., "ACmo~pheric Sp~crral ~aroclinic Mod~l wiCh Heating
and Dis~ipation," GARp, PROGRAMM~ ~N NtJM~RiCAL 6XPERIMEN'rA~iON~ Rep.
No 7, pp 193-211, 1974.
13. Lorenz, E. N., "L~nergjr and Numerical W~~thgr Predietion," TELLUS~ Vo1
12, No 4, pp 364-373, 1960.
14. M111er, U. J., et ~1., "A Study of the En~rgetics of an Upper 3trato-
spheric Warming (1969-1970)," QU~+RT. J. ROY. METi;OROL. 50C., Vo1 98, pp
730-744, 1972. .
15. Muench, H. S., "On the Dynamicg of tihe Wincertim` Scr~tnflpheric Circul-
aCion," J. A'1'MOS. SC1., Vol 22, pp 349-360, 1565.
16. MONTHLY CLIMATIC DATA POR THE WORLD, U. S. Departro~n~. uf Cdromerce Weath-
er Bureau, 1967-1973, 730 pages.
17. Oort, A. H., "On Estimate of the Atmoepheric Energy Cycl~~" MON. WEATHER
REV., Vol 92, pp 483-493, 1964.
18. Oort, A. H., et al., "On the Variability of the Atmoapheric Energy Cycle
Within a Five-Year Period," JGR, Vol 81, No 21, pp 3643-3659, 1976.
19. Quiroz, R. S., "The 5tratospheric Evolution of Sudden Warming~ in 1969~
1974 Detenained from Measured Infrared Rs~diation Fields," J. ATMOS. SCI.,
Vol 32, No 1, pp 211-224, 1975.
56
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,
~
~ � FOR b~~'T.G2AL U9~ ONLY
~
~
UDC 551.509.313
UYNAMIC INITIALI~ATIdN 0~ INITIAL ~IELDS FOR A BAItOCLINIC P~tOGNOS~IC MOD~L
t~loscow t~TE0ROL0(3IYA I OIDROLOGIYA in Rugsian No 4, Apr 79 pp 50-57
~Art3cle by Candidat~ of Physic~l and Mathematical Sciancee M. S. Fuks-Rabin-
dvich, USSR Hydrometeorological Scientiific Reaearch Cenrer, ~ubm~.ttad fnr
pub 1ic~tion 30 May 1978) .
Ab~eract: '1'he ~uthor proposeA a method fnr eak-
ing inCo account information on eurface preaeure
trende during the formation of the fi~lds of in-
i[ial information for a baroclinic prngnoetic
model. For this purpoae the author uses ~ definite
~ modification of the procedure for dynamic initialixg-
tion of fields. A study was made of the propoaed
variant of the dynamic inirinliz~Cion procedure.
The article citee the resulte of numerical exper-
iments with a beroclinic regionel prognostic mod-
el indicating that the uge of thie approach exerte
a positive inf luence on the quality of the fore-
cast.
[Text] Introduction. It is known Chat use of the dynamic iniCialization of
initial fields by use of the procedure of so-called paeudofor~casting [6, 9j
makea it possible to increase the succeag of numerical forecasting (6, 10]. -
The dynamic initialization of fields is also used in a four-dimengional
analysis of ineteorological informaCion (6], HoWever, until recently the dynam-
ic initializarion method on the basis of a paeudoforeease was rigorously
developed only for a barotropic model of the atmoaphere. It is evident
that with the mentioned conaiderations taken into account it is of interest
to generalize this method applicable to a baroclinic model of the atmoaphere.
Such a generalization, however, involves considerabl.e difficulties, examin-
ed in different studies [6, 8-10]. Below we propoae an approach making it
possible, as initial information, in a hydrodynamic forecast, to take into ~
account data on aurface pressure trends by meana of a simple modification
of the traditional procedure of dynamic initialization of fields by the
pseudoforecasting method.
57
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~'OR O1~FICIAt, U9~ tlNLY
It is w~1i known thaC ehe uee ~or fnr~c~a~in~ purpo~~~ dE daC~ nn ~urf~e~
preseure tir~nde, which i~ coromon in rouC~.n~ syn~pe~e rractiee, ieads tio
po~itive r~~u].te in a number of ~rognoet~,c models ~l, 3~ 4]. Nowever~ a~
not~ Chat in th~ manCioned stud~~e uee ig m~de of ~ynoprie, etaCigCical or
m~xed statiaticai-hydrodynamic dr ~ynoptiic-hydradyn~nic: ~pproar.he~. It e~~ms
d~sirable ~o examin~ the po~s~,b~lity of t~king add3t3onal infottnation inCo
~ccount on preseur~ tir~nd~ within the framework of n hydrndynamic mod~l on
th~ ba~~~ of an approach 3n which direcC u~~ is mad~ o~ the pro~noetic equA-
tiona of th~.e model. How~ver, a~ m~~t with ~ dif�iculty in th~t data on th~
~urfac~ preesure trend cgnnot be substituted dir~ctly ~.nto the syetem of
progno~tic equ~tione eince thie leads Co ~n overdeCermination of Che 18Ceer.
It will b~ demon~erated balow that by ueing th~ pseudofore~astiing procedure
in ~ definiCe modiEicaeion iti is poesible, uniformly within the fremework
nf a hydrodynamic model, to take into account data on ~urfgca prenaure
trende and form gn initial ataCe which would "abgorb" thin ugeful addieional
information 3n itaeif.
Invegtigation of Che Procedure of Initializgeion of F'leld~ i.n a Simple Mod~l
We will examine the idea of the method in a~imple Examti~le lur fl model of
tt~n~-dim~tt~~.oc~~l flow of an ideal heavy fluid in ~ linear approximeCion:
du d ~ _ 0,
de dx
d~0 du _ ~1)
~~N-~-O~
where K+~ conat is Che mean height of the fr~e surface, u is velocity, ~ is
geopoCential.
A knowledge at the initial moment of the valuea of the trends (in this case
the ~ trend) is equivalent to the fact Chat we know not only the initial
value cj p~~,S~t . p, but also, for example, the value ~1 ~ t� ~ t~ that
is, the future cj~ value in the first (or, generally epeaking, in Che n-th)
time integration inCerval. We note that under real conditiuns th~ future
~ val~~e is determined from the field of surface preas+ire treuds by meana
of linear tiime interpolation.
We will formulate the pseudoforecasting procedure in ~ucli a~,�ay that there
will be a forced adaptation of the ~ field to the ~p and ~ valuea, that
is, to data on geo~otential at the ends of some time interval.
In the "step ahead" procedures of pseudoforecasting, using the Euler model
with scaling, for system (1) (the values of the predicted parametera in the
first iteration are noted by the superscript ~
u~+~ = u� - (~o)X o t~
(2)
~n-~t = ~o - N ~ue~r 0 t~
u�+~ = u~ - )z a t,
58
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,
~
~ FOR ~F1~tC~At, U8~ ONf.,Y
I
i
i fQA,',~ ~ ~Ji
~ ~rd" wieh ehi~ e~m~ int~ rge~.on model v~ obt~in
, Performing Che ~e@p b~ckw 8 ~
; uh ~ un~t r~~~.e ~ f~ ~3~
i ~n y ~1 ~ ~t1n41~,r ~ t~
~ u~~~11 ~ u~+~ ~ (di~)x ~ t,
~ ~o+
,
where Che eubecrip~ x i~ th~ operaror for different~atian for x, e i~ Che
numb~r of th~ tim~ int~rval, L1t ia ehe time interv~i~ Ni,~ the number of
ehe iterae~on in th~ cyciic procadure of p~eudofor~ca8t~n~*~~~ a Aimp~if-
icat3on it i~ noeed oniy when obtaining th~ n~? v~1ua ufl , in dther
placae rhe v~ur~r~cripe h~~ b~~n omirred).
After a~e~p foraard (2) ae have
uA.~~ = u~ - t~o)~ ~ t-~ N~u~).~R t)~, (4)
and after a atep baclcatard t3) Ws obtain
u;,~+>> u~ _ - ~o)~ e t ~ t~ tu~)~~ t)' - (s)
- N (~o~.~x~r H~ ~un~~t.~a ~d t~~�
The firet term on the right-hand eid~ of (S) ie a dertvative of x from the
known field trend According~y, additionai information has obvioue~y
enCered into the result of integration and furthermore in the fotm of the
main term determining the change in the aind field in the particular mod-
ification of the paeudoforecasting procedure.
We note that this modification of the pseudoforecaeting procedure aith forc-
ed adaptation to ~he ~p and ~ 1 valuea is approximately tvice as economical
ae the traditional procedure, sinae for practical purpoeee it is neceeeary
to carry out integration only for the aecond and third equatione of eyeteme
(2) and (3), nnd not for all four. �
Inveatigation of the Initialization Procedure for a Barocliaic Malel
We will geaerelize the procedure coneidered above for the initialisation
of fields applicable to a baroclinic model. For this ve aill exemine a lin-
earized system of equationa ia a p-system of coordinatea for a two-layer
baroclinic model in full equationa (this linearized system of equations vas
derived in [7), but was used for other purpoees)s
59
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~R OFFICiAt~ tf98 ONLY
~~o, ~
a~ ~ ~ ~
~~-~=0~ ,
~~~a+,-0,
~'.+g~-o,
~Vf a+ r.. O~ .
t6)
m,~. atl
-ep_0~
i
ma ~ (Pr - P~~ =
fi'-ATa-BA~-O,
~ ~,-~,-ET,-FT,=O,
� pP~~
o,d o
mb
~ ~
Y,~,T ~----I
soe,~a ' " t
~
r,m,r :.`.....-J. -0
a~
mb ~oed i ~
P.
Pig. 1. Vertical struct~re of tao-layer model.
The verticel structure of the model ie represented in Fig. 1, from vhich the
annotations aYe understandable. The syetem of ten equations (6) coneiets of
prognoetic equations relative to the pareneteYa ul, u3~ T1, T3, p* (first
five equations) and five diagnostic equations relative Co the perameters
t~Z, GJ*~ ~1, ~i3, ~t~. Here ae use the folloaing notattong: ~ ia the
analogue of vertical velocity,
60
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~
~
I FOIt O~FICIAL US~ ONLY
S~Wr,~(~"Oi)~~P~~ ~�1P,/'
r
i
~
~ x~R/cp=~? oP-p,~500 a~6;
~ ~
j On Z'; S~ = r,~ (Oa -~)/2 P1?
i
A!' Cp (rc� -~es~~na? B= Cp7'sI ra~
i _
~ E=Cp(na-~i)/2ni~ p=:xn,~ipw~
~
~ F Cp ~na ~i )/2 sr~,
i
' In deriving the syetem of equatiions (6) we made the assumption
~
' ' R i ti_~ p~
~ n� p.-~=1 ~ r P~ 1 x p' ~
/ ~p+/ ~ CP~) p~'
We will formulate an initializaCion procedure, a8suming thaC we know addi-
Cional datg on gurface pressure trends, or, in other words, thAt we know
Che vglues p~ and pl of surfgce pressure at the enda of some Cime interval
(which in this examination ia eqaal to Che time interval e). As above,
uaing the Euler scheme for titne inCegration (with scaling), in the step
ahead we have (the field values in the firat iteration are designated by
the superacript
u' ~ u" ~ t
~ ~ te ~
T~ "+i ~ Ti - S~ u~~ ~ t; (1-~ 1, 3),
P~"-~'~=P�~'w"~t
. . . '
~'R+~ = - u',~+~ ~ ~ (7)
, s t x P,
. w' c mZ - u3 xT~ ~P+? - Ps)~
. ,
= AT' B r.'
3 . a .
= ~D~ E~ n-4~ ~ F?'1 n+~~
, r.�^+~ _ P'p�n+t
. . '
and then, for the aecond iteration in the step ahead
ui+~=u~ -~~~+~st
?
T~+' = T; -Sc~"z"+' ~l~ _ 3)~
P;+' ~ P;~
~oz+~ - - u~ J p,
61 ~ ~
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u~n~'~ c tu~+~ U~ x~ ~P� ns~+ ~
.
~a+~ ~ A Ta+i B n;+~~ ~
;
- ~,i.~~ _ ~,3+~ ETi+' T ~7s+'+
~8)
~tn+~ ~ P,p~.
~ ~ ' i
and then for the second iCeration in Che s~ep backward: ~
i
~
u(~~ut~1+~lX~Q~`~ ~
r n- T~ +t ~ w1+? ~ l~ (t ~ 1~ 3). , i
i
p�,, ~ p~ _~n+t ~ t~
. . .
tu'" - - !t'"~ p~
q lx
~ ' ~9) ;
u)"' n e~ tu~" - lla x~Pr ps~? ~
.
cp3 ^ = A T3 " B a~ ~ ,
,
~ _ ~3" ETi FT~
~i n~Pp'n
.
We will write similar expressions for the step backward:
~(11 111+~ ~ ~IX e t .
~
~T~~~~'~>> _ / ~'t'~ -~-Si Wz ~ ~ tj ~i ~ ~ ~ 3/)
~
(P;)~"+n =Po~ ~ _
- - (ui x)r~+u p p, ~ .
(10)
- ~w2)~y+~~ - ~ua ~P� -'P:)?
~~3)~"+u _ A ~Ta)~"+u ~'.B ~'`"~c�+~~ ~
~~~~(y+~) _ ~~a)~"+~) E(T~ )cr+U p (Ta~c*+~t , ,
(~.~J~~+~~ - Pp�. . ,
. .
We will now show how the considered fields change as a result of the full
cycle of the pseudAforecasting procedure (7)-(10) in a forced adaptation ,
regime. After rather unwieldy, but simple transformations we obtain the
62
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_ following ~xpre~ginn~ fnr ehe r~gul~anC fiald~s
~u~)t~+~1 cu~-}-BH(p~-p�~,~ ~t-I- (('Z Bt'-(A-I-F) S~-~,~ ui.~x ~P~,
+ 2 BP (P,? - P:) u3 x.~ I~~ t)' 4 I(~ t)'1~
(u~)t~+~? u~ BP (p; P�)x ~ t 0~8), whinh ~uarif-
ie~ th~ ~pCimi~m of Che authors oE (5, 6, 8], indicaGing thc poegibility nf
eCoChdBCiC predictinn of ehe optic~l chnranC~rieCire of an ~emn~ph~ric
~~ro~o1 on eh~ bn~is of dat~ on ~ir humidity.
T~ble 1 gl~o giveg ehe correlgtion coefEicienee e, deCermining the
cingeness of Che interrelaeionship, beCween Che changeg pa,, ~nd Q, e, L1~c,~ end
~ T respectively, which have extrpmely low values; llere gl~o for Che congid-
ered corrplation coefficienCa we havQ given the mgtrices of errore. Thu~,
the establiahment o� clearer cnrYelations between aerosol eurbid~.ty of the
natural atmoephere and absolute humidity, ndCed in a number of seudies, ns
righCfully observed by rhe nuChorg of (2J, evidenely ig of en indirecC na-
ture~ which contradicCs the conclusiona given in (3].
d xM�~
!0 � ~a.~
`R-~1
Q t '~~f~ `
b
0~ b\
~
.
. ~0.': ~ ~
e s ~ ~t
,1 ~r~
~ I ~
~ ~
1
~
~o= ~
a
W"
0,5 ~ 2 J 4 D,S f 2~t nKM
~'ig. 2. rtean dependences o~(~) (Table 4 illustrates weather conditiona).
~'or the purpose of determin{ng the type of dependence a T(f) for each of
the parts of the spectrum we determined the mean pro�iles a~(f), which -
is illustrated in Fip. 1. In ~rder to decrease the influence of the
error in measuring relative humidity, whic:i in our experiments on the
average was equal to f3q, it was deemed desirable to carry out averaging
of data for ~j, for ~ f intervals with a width of 6"/., and tlie mean value
79
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a~, (fi) nbe~ined in tihi~ wny i~ relnted en the middlp of rhe cnn~ider~d
intierval, which nn Che ~ta(~) pro�iles i~ d~noCed by dots. (The regr~~einn
c~yunCion ~ a(E) in euch a~orm h~nceforCh ig approxim~Ced by ~ Corre~pond-
inh nnnlyticul c~xpr.Q~~inn). The correspnnding error mnCrires d~~ Eor ~a~h
proEile nre given in T~ble 2.
Tab1~ 4
AA, TNn ~ SM rc~r no n~e
cneeTpe ontNyecKOA noroAd
~ C ANYifB 8lCH6t H OCCNH 3O-GO IF--QO ~,OO O~~ Z.O
Z d TO NtC b0-~b 20-b0 Q03 0,35 2,0
g ~ 60-7b 10-ZO A,09 0,41 l,,b
4 ~ 7b-90 10-20 0,10 Q~0 1.6
g s 90-95 6-tb 0,07 O~W 11~t~
6 e TYM8HH8q AdMKa 9~-~~ 6-~~ ~,ZZ ~1~~ Qg
~ d To ~te 90-100 I-5 Q,06 0,79 0,4
K~Y:
a) No of spectrum , ~
b) 'I'ype of optical weather
c) Spring and autumn haze �
d) 5ame ~
e) For haze
Taking into account that the dependence a a(f) has a nonlinear cr~aracter,
the analytical expression for the regression equaCion, from ou: point of
view, is conveniently determined in the form
f Kz
~a (~=Koa+K~aC ~w / ~ (1)
where Ko~, K1~ , K2 a are empirical coefficients dependent on wavelength.
The values of the latter, determined by the least squares method for a=
0.55-3.97� m, are given in Table 3. The resulCa of reconatruction of the
~ initial ~T(f) profiles by means of expression (1) are ahown by symbols
(circles, triangles, squares reapecCively) in Fig. 1. In turn, in (5], on
the basis of a complex analysis of data from optical and microphysical
measurements, the authors noted a tendency to a parallel shift of indi-
vidual records of the dependence a,1(f) (in the range f E 30-95x), which
indicates a possibility of using an expression of type (1) for predicting
the nature of transforraation of the optical state of aerosol formations
under specific weather condiCions.
It should be noted that the considered type of dependence ~j.(f) is moat
characteristic for conditions of quasistationary anticyclonic forrrations ~
in the temperate latitudes formed in continental temperate air.
Thus, the state of the aerosol, and accordingly, to a considerable degree
also the optical properties of the atmosphere, is regulated by a wh~le com-
plex of geophysical factors; under definite conditions the decisive link
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H~d~i oi~ r~c rnt, usi: c~N~,Y
in Chi~ praC~~~ i~ r~~.nCiv~ humidiey. T~ierefarc~, gny prer~qui~iee~ nn cdn-
gCrucCidn nf Ch~ cdrr~gpdnding mod~le mugC r~s~, in pnrrieul~r, on inform~-
Cinn dn g hnreiculnr m~CenroLogical param~ter. Tnking thig requirement
intd nccounC, it was deemed desirable ~d Crace in Cite dev~lnpmenC af ehc
id~nln~y (4] ehe change in Ch~ gp~eCrnl dependences with sripu~.aCed
].imit~ E c~nd rhe meC~ornlogiCal rnnge of visibiliCy SM. rnr t}lit~ purpnge
fdr differenC re~ions df change in Che i.ndic~ted chgracCerier~c~ (see T~ble
4) we C~mpuCed, etie me~n profiles of Che ct~ct'Eici~nrg ii~rn~n1 ctCeenu~Lion
o~a (~ig. 2); here glso fnr e~ch profile we h~ve ~raphically ehnwn the cnr-
regponding m~trix nf errnrs. An anglysis of ehe mean profileg aT , in par-
eicular, indic~tes (for exnmple, compa~e curves (1,2) and (3,4) (I~'ig. 2)
ehat for practical purpoeeg the generglizaeion of experimental daCn muse
be c~rried ouC in relat~.vely broad limirs of f and SM. Nevertheless, in
this gCudy in g description of Che mean sratistical curves o~~, on the
basis of an expreseion from [7]
a~ ~ ao, as ~?t~ -1- li~ ~ 2)
for compleCenegs of the primary informneion Che corresponding coefficienGa
np, n1, n2 were computed by the L5M for a11 f~nd 5M lir~itg (~ee Tnble
4). 'Their values are represented in this s~me Cable. The corresponding
resulCs of computations of a a,nf on the basis of ~ n} and (2) are repre-
sented 1~~; Che small circles in Fig. 2. '
Thus, special investigations of tlie interrelationship of the coefficiente
of aerosol attenuation and air humidity, cnrried out by the authars, again
confirmed the decisive role of relative humidity in the formation of the
optical state of the disperse phase. The resulting atatistical dependencea
unambiguously indicate the fundamental possibility of predicting the op-
tical state of an aerosol on the basis o� information on the meteorological
parameters.
The laCter conclusion sounds more convincingly taking into account that
, the first [6] and presenC stages in the inveseigation were carried ouC
in different regtons.
BIBLIOGRAPHY
l. Andreyev, S. D., Ivlev, L. S., Kabanov, M. V., Pkhalagov, Yu. A., "In-
fluence of Relative Humidity on Aerosol Attenuation of Optical Radia-
Cion in the Atmosphere," IZVE5TIYA W~OV S5SR, FIZIKA (News of Higher
EducaCional Institutes in the USSR, Physics), No 5, pp 54-57, 1974.
Z. Georgiyevskiy, Yu. S., Rozenberg, G. V., "Humidity as a Factor in Aero-
scl Variability," IZVESTIYA AN SSSR, FIZIKA ATMOSFERY I OKEANA (News
of the USSR Academy of Sciences, Physics of the Atmosphere and Ocean),
' No 9, *to 2, pp 126-137, 1973.
- 3. Malkevich, M. S., Georgiyevskiy, Yu. S., Chavro, A. I., Shukurov, A.
Kh., "Statistical Characteristi~cs ~f Attenuation of Radiation in the
ACmospheric Sur.face Layer," I2VESTIYA AN SSSR, FIZIKA ATMOSFERY I
OKEANA, No 13, No 12, pp ~257-1267, 1977.
81
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4. Cilippov, V. L., "Aemospt~eric Aerosnl FnrmuCiotts. Morphology nnd 5e~-
son~l Gradations," I~VESTtYA VUZOV SSSR, rIZIKA, No 5, 1976, 158 pgges.
Ueposited at th~ A11-Union InstituCe of Scientific and Technical. Infor-
mntinn No G34-76.
5. ~ilippov, V. L., Iv~nnv, V. P., Makarov, A. S., Ososkov, A. N., "Some
peculinriCies af Che bependence vf Aerosol AtCenuation on Air NumidiCy,"
I V5CSOYUZNOY[: SOV~SI{CHANIYE p0 A'1'MOSFEftNOY OPTIIt~ (~'irst AL1-Union Cnn-
~erence on Armospheric Optics), Tomsk, pp 254-258, 1976.
G. Filippov, V. L., Mirumyants, S. 0., "InvestigaCion of Che Dependence of
Aerosol AtCenuarion of Visible and Infrared Radiation on Air I{wnidity,"
I7.VE5TIYA AN SSSIt, I'IZIKA ATMOSFERY I OKEANA, No 7, No g, pp 988-993,
L9~2.
~
7. Cilippov, V. t,., Mirumyants, 5. 0., "Analysis of the Menn StaCistical
bependences of. tt~e Coefficienes of Aerosol AtCenuaCion in the Region
0.55-10 �.m," IZVESTIY~1 VUZOV SS5R, FIZIKA, No 10, pp 103-106, 1972.
8. Eianel, G., "The Ratio of the CxCinction CoefficienC to ttie Mass of At-
mospiieric Aerosol Parricles as a Funcrion of Clie RelaCive HumidiCy,"
.T: AEROSOL. 5CI., Vol 3, No 6, pp 455-~460, 1972.
~
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UDC 556.(51/.54+166)
CRIT~RION OF CORRESPONDENCE BETWEEN THE DI5TRIBUTION CURVES OF PROBABILITIES
OF MAXIMUM WATER DISCHARGE
Moscow MCTEOROLOGIYA I GIDROLOGIYA in Russian No 4, Apr 79 pp.70-76
[Article by Candidate of Technical Sciencea D. M. Mamatkanov and N. Sh.
Kudaybergenov, Kirgiz Scientific Research Power Section, submiCCed for
publication 5 June ~.978]
AbstracC: The auChors demonstrate the inad-
equaCe correctnesa of use of existing criteria -
for correspondence to the empirical distribu-
tion curve of maximum runoff in the presence
of observations of limited duraCion, which leada
to sysCematic errors in compuCations. Using as
. a point of departure the limited naCure of the
observations and Che peculiarities of construc-
tion of the empirical curves of the probabilit-
ies of maximum discharge of water, the authors
propose a correlation criterion which is a mod-
ification of the Cramer-Mises criterion.
[Text] On the ba:is of the computed maximum water discharge.ir is pos~ible ~
to calculate the spillways of dams, the handling capaciCies of bridges, can-
als and other hydraiilic structures. This same parameter to a great extent
cietermines both the construction and the makeup of the entire hydraulic
complex. Therefore, the computed maximum water discharge is E highly im-
portant parameter of the hydraulic complex, and Che correctness of its
determination governs the safety of the structures and their economic ef-
~ fectiveness. Accordingly, the ob~ective of hydrologi~sal computations of ~
the maximum discharges is a combination of the requirements of safety and
economic effect{.veness of the hydraulic structures.
The combination of these two requirements can be accomplished by means of
use of thE principlE of stochastic computaCions, based on determination of
the hydrologi.cal conditions for the formation of maximum runoff, on the
one hand, and on allowance for iCs stochastic excess, on Che other hand
[11].
33
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~OIt UI~~tCrAL USL' nNLY ~
Wieh use of Che eCochg~tiic merhod far cnmpuCatione o~ the mnximum warer
diecharge Che primary and most ~P~~'tignti p~rhetical)~probabiliCyndietirib-
beeween the empirical and ~hedreeical (hyp
uCion curvea, nn g~e~baoggg~rucCurea~in~c nnection withuthe uge of&diE-
of gunranCee of s y
ferent computed prnb~bilities oE exceas.
This problem has stillgndedevelopment~of new~,eaimplereandrmoreueffective
provement of ~acisCing
meehods from Che practical poine of view.
As is well known, the construction of an empirical curve tnr the probabil-
iCy of maximum Wgies ofgexceas of its elements,b representeddineehenEorm
of Che p robabilit
of the variation aeries . '
x~>xs>xa> ...>zn~ ~1~
according to tihe 5. N. Kritskiy and M. F. Menkel' formula
Pm� n+~~ ~2)
where m= 1, 2,..., n is the sequence number of the elements of the vari-
ation series (1) in the sequence of decrease.
Ttiis formula is :ecommended by the "Instructions on Determination of Com-
puted Nydrological ~ea~eadsrtotsome reserve7~.n theccomputations,hsatisfyC
ed volume of a sampl
ing practical requirements.
othetical) probability curve P(x), approximating
As the theoretical (hyp ,
the empiric~l funcCion Pn(x), it is possib:L_e to use a two- and three-
parameter gauma disCribution or a log-normal distribution, a Gumbel'dis-
tribution, a ~y3tem of Johnson distribution curves, etc.
For selecting the types of hypothetical distribuCion curves of probabilit- '
ies in the the.ory of probabilities and maChematical sCatistics specialists
have developed several criteria of the correspondence of empirical and
theo~etical distribution curves, such as the Kolmogorov and Cramer-Mises
(ncJ ) tesCs and the Pearson chi-square test. The application of these
tests to the probabiliCy dietribution curves for the observed daCa on
maximum water discharge for a limited duraCion is inadequately correcCi
and gives systematic errors including the following.
All existing correspondence criteria have been developed applicable to
the emp~rical function (sCepped curve) for the distribution of the ob-
- served data Pn(x)~dtusinr~theiformula forethe~classicalmtheoryfofhprobmple,
which is determine g
~ abilities,
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' m
Pm - ,
Aa is well known, tihis formula givea acceptable resu~Cs only with aufficiently
great n and is applicable Co ~he terms o~ a variation aeriea siCuated in a -
zone Ad~~cenr Co Che cene~:r Che disCr~.bueion. Indeed, rhe very center of
the disCribution, in the case of ].imited n, is displnced. For terms of a
ranked series, occupying ehe 1nsC place, wiCh nny finiCe n we will alw~ys
hnve Pm = 1, wherea~ for the firsC term o.C rhe aeries Pm = 1/n, which, Co be
~ure, i~ ~n extremely rougli evaluation. In addition, in all exisCing compur-
ution crieeria for all practical purposes one seeks an agreement betw~en
ehe theoreCicnl and empirical disCrihueion curves, the values of the prob-
abilities of excess of whose sample elements are deCermined using ~he exprea-
sion
P_ 2 m- l r m-0,~
m- 2n n ' ~4)
thaC is, tlie A. Khazen formula.
It is also known that this formula under conditions of a restricCed volume
of the sample always gives reduced values of the probabilities of 111gh
and exaggeraCed values of the probabiliCies of low runoff values in compar-
ison with formula (2), ChaC is, undersCates the ordinaCes of the runoff
distribuCion curves in the case of sma11 probabilities and exagg~rates
Che ordinates in the case of high probabilities. This can also be seen from
Tab le 1.
Accordingly, the use of the above-mentioned criteria applicable Co the dis-
tribuCion curves for maximum water discharges in the case of a resCricted
volume of the sample will always give sysCemaCic errors, since one seeks
an agreement between the theoretical curves and.the empirical curve, con-
striicted using formula (4), and not (2). The errors will go in the direc-
tion of an understatement of the maximum runo�f values, which is related to
a decrease in the safety guaranCee for hydraulic sCrucCures. Therefore, the
computation criterion for ehe correspondence of empirical and theoretical
distribuCion curves invariably must rake into account Che form of the for-
mula used in obtaining the em~irical distribuCion functions for the observed
data for the regimes of hydrological characteristics. Taking this into ac-
count, now wP will discuss Che problems i:zvolved in obtaining the corres-
pondence criteria for the empirical and theoretical distribution functions
for the maximum water discharge applicable to the formula for determining ~
probabilitj.es (2).
Table 1
Comparison of Empirical Probabilities (in Computed by Kritskiy-Menkel'
(2) and Khazen ~4) Formulas
Fo rmt~.a ~ l0 n= 30 n~ 4U ~ n= fi0
~
I '
z m-1 i r~:: ? im-n m=1 Im-_2 Im-.�n ~r~=l l ae_'l ~ni=n I n~=1 I m-3 l m: rr
(2) 9,09 I13,IS ~J0,~1 4,?f> ~,:;2 9:;,:~1 3,~14 4,53 ~J7,3G 1.G1 I",,^;> 9S.31i
(~1) 6,?3 Ilti.:S:~ ~3,2" 3,43 5,33 !~G.:ili I.i`l 4,:1 ^5,27 I,l~i i_',til :).8~1
85
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A~ the baeic derived criC~rlon we used Che criterion nc~1~, ~xpres~gd ueing
the formulg
" 2 m-1
Ii ~ua a 12 rt C p~x"'~ l n '
m-1 (5~
since it, being based on Che basis of rhe observed daC~, more fully uses ,
the ~nEormation ConCained in Chem and considerably more rapidly convergeg
to a 1.imiting 1aw, especially in rhe region of large W 2 valuea, which is
importanC in n stochasCic evaluation [2, 10]. AccordingLy, the proposed
criterion is a modification of the Cramer-Mises criterion.
Since these proUlems in tt~e eheory of probabilities and mathematical stat-
istics have been developed applicable to the distribution functions of
excess probabilieies, we will also use this approach, which exerts no in-
fluence on the results o� the problem Co be solved and only creates conveni-
ences in Che inCegraCion.
The considered Cramer-Mise~ criterion applicable to our problem is wriCCen
in general form:
~
w' ~ J~ (P (x~ - Pn (x)~" dP (x); (g)
and dP (x) = P' (x)dx, that is, it is assumed that the function P(x) has t}ie
der~=vative (probability density fu??ction) P'(x). Otherwise it is necessery
to unders~and integration in the SCielt~es sense. �Here Pn(x) is Che empir-
ical probability of nonexcess of the elemenCs x of an exiaCing sample of
the volume n. These values are determined using formula (2~ and are used as
their true values. P(x) is the hypothetical probability of the value Pn(x),
being a random function dependent noC only on the x value, buC also on the
type of Che tested hypothetical distribution curves and their statistical
paramerers.
Then, assume that there is a var.iation series of the maximum water disc~arge
with tfie duration n
x~ ~ x2 ~ z~ < . . < x~� (7)
In this case the x values are essentially positive, that is, x> 0.
If the integration limit for Che integral (5) is broken down into intervals
oo , xl), (xl, x2),..., (xn-1, Xn~y (Xn~ + oo), then expression (6) can
be written as follows:
x~ n-1 xml~ ~g)
~~,2 = [p (x) - P� (.r)~' dP (x) -f- ~ [P (x) - PR (x)~' dP (x)
J ~
_,p m= 1 X
m
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I
1~OEt l~ l'(;1'AL U~+1; qNLY
W ~ xi rtP x
I p (x) P~~ ( I' ~ ( ) ~
xn (8)
We wi].1 exAmine the ~oluCion (8) appllc~ble rn Che Cotmulns for determining
Che empirlcal probaUiliry o~ nonexcesa (2), which with stiipuYuC~d n dividea
~he inCerval (0.1) by (n~1) equnl parCg with the wideh 1/(n+l)~ In rhis
case ~t tihe discontinuity poine x= xm the ~unction Pn(x) passes 3n a~ump ~
from rhe value 2 m- 1./2 (n + 1) (in Che interval x~_l < x< xm) ro t:he value -
2 m+ 1/2(n + 1), maintaining the ].atCer value in the nexC :ineervAl. With Che
above Caken into above, Che empirical funceion (stepped curve) for the dis-
tribuCion o� hydrologicnl series nf maximum water discharge (7) ie determined
by the equaCions
_ pn ~x, _ ~ when x ` 0
pn ~x~ _ 1 when 0< x< x1 (9 )
r 2 (n+ ~ )
2 m-~- l when xm < x G xm.~l
P� (x) = 2 ~n+~~
where m = 1,2,...,(n - 1)
P� (x) 1
.
when x ~ xn
In this case, from (8), with (9) taken into account, we have:
~ P (x) -P� (x)l~ I ~`_xt
ft[P (x) - Pn ~x)~2 dP (x) _ ~ a X__ ~ ~
r a
= 3 Lp ~xi) 2 (n+1) ] '
m~-1 x=x
X ~ [P !x) - P~ ~x)~~ dP (x) = ~P (x) -Pn (X)ls m{~ _
3
-Xm x=Xrn
~ = 3 [P (xm-}.t ) - C n+~ -I- ~ (n.4-1) /J9~
~ x-+~
~ [P (x) - P~ ~x)~Z dP (x} _ ~P (.r) 3 ~ (x)1' _
xn X = Xn .
. 1 ~i3
. = 3 [p~x~~-~nfl + l~n+~;~f �
s~
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Substituting tihe derermined v~~.ues of rh~ inCegrglg into (8) and eolving
~hem, we obtnin rhe final compuration formu~.~
n m p
~ ) ~n~ ~ 11 ~~n~
~ -f- CP ~xm~ ` n+~ (~0)
M~1
The compuCed expression (10) can be called the criterion of correspondence be-
eween tihe empirical and theoretica~ (hypotheCical) diatribution curvea for
maximum runoff or simply (n + 1)cJ , which Cakes ~.nto account the maximum
possible information contained in a sample of limited volume, with formula
(2) raken into account, adopted for constructing the empirical function of
ehe ~ctually observed data.
It can be seen from (10) Chat with a full correanondence between the hypo-
thetical and empirical distribution curvea we have
~ n (11)
(~ti.~' ] ) w~ � (n ~ ~ .
Condition (11) can be satisfied only in the presence of a general seC or in
the presence of "ideal" samples o� a limited volume. In the remaining cases
n (12)
(tt-}- 1) w~> 11
In thts case with an increase in the volume of the sample, tending to infin-
ity, the value (n + 1)~ 2 tends to n/12(n + 1)2.
For the purpose of comparing the considered criteria we will assume that
there are "ideal" series with the duration n from the general seC. In this
case the hypothetical probabillties P(xm), considered as random values, will
coincide with the empirical values Pn(x) = Pm, determined from (2). There-
fore, substituting P(xm) = Pm from (2) into (5), we have
tt w= = I'l n-f- ~(n m
j r' 2 2 n l, - 6(n+l (13)
M-i
WiCh respecr to the proposed criterion (10), in this case it is expressed
"oy formula (11). In this case their difference
,
n�2 (14)
~1u,'- - JI w=' -(It 1) u~- � 12 (n t 1)=
characterizes the value of the systematic errors allowed by the criterion
ncJ2 with its application to the empirical distribution eurve for maximum
runoff, of Che stipulated duration n, constructed using the Kritskiy-Menkel'
f~rmula (2). .
88
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;
rOlt n1~T~'~CJAL U5~ nNLY
IC can ~h,erefote U~ seen ~t ae Che vulue~ of rhe systemciCic er~rors (14), ~1-
~.ow~d by Che cr~.eer~.on ntJ exceed rhe v~~.ue~ (n + 1)~ Z obtinined u~ing (1].),
nnd the vnlue (13) exc~eds tihe l~ttier Uy a Eactor o~ 2(n +~.)/n, thuC is,
- grenrer ehan by a factior of two~ Accordingly, tihe applicnCion ot the cri-
rerion ncJ2 Co the empirical disrribution curve for Che probaU~.liCy of mAx-
imum runof~ with ~ 13miCed duraCion of Che sample is in~dequaCely corr~ct.
As is we11 known [2, 10], Che limiting distribue~.o~n of nu12 9rti~~9r~.C9 i~
very complex nnd with n-rao is clnse to the ~uncCion
' n, (x) = lim n i rc .r~
(15)
i r ~j + ~ ) _ t~ ?+tt'~ J + 11? -
_ ~ ~ 2 - ~ j 1 E~ ~r { ~ C lti x ~
1
x ~;o ~ r`~ l r( j.}. a
~ ~
_ ~ ~ C 16 x ~
4 '
where Jk(Z) is a modified Bessel funcCion (Bessel func~ion of a�ictitious
argumenC). IC was demonstraCed in [10] that when n> 40 Che distribution, in-
dependently of Che Cype of iniCial hypothetical distribution, is close to
Che limiting distribution (15), for whicY? the values of the critical points,
corresponding Co some (frequently used in practical computations) ~~ignif-
icance levels [2, 10], are presented in Tab1e 2.
Tab le 2
Value of Upper Limit of n W 2 in Dependence on Significance Level. q%
1 J'ponim 3ua~m~.iocT;i q= p In ZQJ ~ 1C0�6
50 I 40 I 30 I 20 I 10 I 5 I 3 I 2 I 1~ U,1
I~p~ireveci;ct~ I �
~ T04hi1 Z,1 . ? . IO.11Sd IU,1 {G7I~),1~5~13I0,2~11~`9,3173`0,4G1410,54S~JI0,G193I0,7~13511,1679
KEY . .
1. Significance levels q= P[n~~2> ZqJ�100%
2. Critical points Zq
This table in equal degree is also applicable fcr the critprion (n + 1)W Z,
since it was obtained from the limtting function (15) with n-~oo and is not
dependent on the type of initial hypothetical disCribution curve. Indeed,
formulas (2) and (4) with large n~ oo give identical results. This also
leads to legitimacy ~f use of Table 2 for (n + 1)~ 2. 1'he method for prac-
Cical application oi the proposed criterion is precisely the same as the use
of the criterion n~ 2, jointly with the values of the critical points cor-
responding to the stipulaced significance level, obtained from its limiting _
d~stribution function (15),and applicable to river runoff is set forth in [8].
8S
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As a prac~ical exemple we will examine series of maximum water dischargea
oP the Tissa ?~.ver at Delovoy village during 1933-1963 (n m 31, Q~ 307'm3/
sec) taken from [13]. The sCat~stical parameters Cv and CS of ehis seriea
were obtnined by ~n evaluation by the method of the moments of probabillt-
ies of excess of the :tnieial values, on Che basis of Che criterion of the
minimum of the sum ot the absolute error.s for the evaluaCed parameters [8],
Caking :in~o acco~int the weights o� the parameters to be summed. They were
equal to: C~ = 0.51, Cg/C~ n 5 and coincided with the valuea obCa~.ned by
the mr.ximum similarity method [13].
'rhen, using Che Kritskiy-Menkel' curve wiCti the deCermined values of the
parameters C~ and Cs/C~ we determined the value of the criter~vti (n + 1)c~ 2,
which was equal Co 0.0542.
Assuming a significnnce level q= 5% and employing Che values of Che criG-
ical poinCs Zq from Table 2, we obCain Zq = 0.4614.
Now we will construct the critical region for checking Che correspondence be-
tween the sample data to the hypoChetical (theoretical) distributions of a -
three-parameCer gamma distribution with C~ = 0.51 Pnd Cg/Cy = 5 in the form
(n + 1)~ 2 > 0.4616.
The determined value of the criterion (n + 1)~ 2= 0.0542 fa11s in the re-
gion of admissible values and substan.tially to the left of the criCical
limit Zq = 0.4616. Accordingly, a three-parameter gamma distribution with
the parameters C~, = 0.51 and CS = SC~ = 2.55 with the significance level
q= 5% does not contradicC Che observational data.
It should be noted that the proposed criterion can a1.se be employed for
evaluating the statistical parameters of a hydrological series of maximum
water discharge if it is represented in the form
n m y
- (~t 1) wz = ~l ~nn} 1~_ ~ I p~ (X~n~ X~ C~~ Cs) - n t 1, _?nin. (16)
m=~ I.
Thus, using data from Che above-mentioned series we obCained the same val-
ues of the parameters as above. This shows the possibilities of its use
in problems of evaluation of parameCers. However, for the final derivation
it is necessary to carry out large-scale computaCions and compare the re-
sults with other widely employed methods. We plan to devate a separate ,
sCudy Co this.
In conclusion it can be noted that the use of the proposed correspondence
(conformity) criterion (n + 1)~2 in application to curves of disiribution
of the probabilities of maximum water discharge, with a restricted sample
volume n, is the most correct and ensures the maximum possible use of in-
formation available in actual observation series and also the adopted meth-
od for constructing empirical functions.
90 ~
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Zs ~ ~ : I ~ , L 1~ ~ Z OF Z

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i'OIt UF r IC [ AI, t15ti ONI.Y
~JHLior,t~APftY
L ~llekgeyev, C. A., "U~e of tlt~ Gutnbel' Ui~jCClbutlutt Curve fur l:v~l.ur~~ing
tt~e Prob,,E~i ~ tey of M~ximuro Wnter Uiychnry,r.s," M1;Tl:UftU1,OGIYA I GIDRt)-
1.OGIYA (Mete~rold~y ~nd Nydroloky), No 1, pp ]G-25, 19Fi1.
2. i3o1= shev, L. ;1, , Smirnov, I. V. ,'TAIlLI7'SY M/1'Ci~LiT'ICH~SKOY 51'A'CIS'fIKI
('I'~bles of M7thera~~ticc~l Statir~tic~), V'I'~ AN 5551~, Moscow~ 196$, 474 pagra.
3. Gumbel', F., 5'CA'i'I5TIKA HK5'I'RFTtA1.'NYKII '1.NACHENIY (5t.7ei~ticH of f:xtrcm~l
V71ue:s), t4o~cow~ "Mir," 1965, 450 pnqe~.
4. K.ilinin, C. F'. ~ I'ROfiI.F?4Y C;LOHAL':~OY CInKOLUGII (Problemg in Gl.c~bnl Hy- �
drolo~;y), i.enin~rad, Gidromereoizdnt, 1965, 378 pageg.
5. K~rtvelishvili, N. A., '~EORIYA VFROYA'fNOSTNYK}I PROT5~550V V GIbKU1.UGII
I R~GULIROVA.WII RTs'C}f:~OGO STOKt1 (7'heory nf Stochc~~tic ProccgheH nnd Ny-
drology ~7nd Rcv,ulntion of River Runoff), I.entn~rad, c;idrom~tedizcl.~t~ 1967,
291 png_g.
h. Kritskiy, 5. ;1.~ Menkel', M. F., "E3asic Points in the Method for Cnmput-
ind MaxiAUSn Runoff," TRUUY GGI (Trr~n~actions o.f ttie 5tetc llydrological
- Institute), ;~o ~62, pp 3-17, 1969.
7. Y.ritgkiy, 5. N., "Probability Distributinn ~unctions ilsed in bescribing
E'luctuation~ of Ftiver F{unoff~" VOb"JYY~ RESUR5Y (Nater Resources), MoHCnw,
- ":+yuY.a," :"ro 5, PP $6-88, 1975.
fi. tl;lraatic.~nov, A. 1d., :dObF.LIROVA:tIY~ L Yft~USKA7JIKIY~ KOLEBANIY ftECNNOCO -
STO}~.A (Mc~d~lin~; and Prediction of Eluctuations of ftiver Runoff), ~runze.
' "Kyrgyzstan," 1973, 240 pages.
9. ;~Sc~rorov, A. A., "Cotaputation of t1~~ximua Water Discharges of fcivers in
tf~~ Yl.~nniny, of Hydraulic 5tructures," 1%V~STIYA AtJ 5SSR~ 4TbELENIY~
TF.KfiNIC}{F;SY.1Y.t{ h'AUK (Neas of the U55R Academy of Sciences~ Division uf
Techntc:?1 5ctences), No 7, pp 1104=1116. iy52.
l0. S:~irnov, I. V. , Uunin-iiarkovskiy, ~i. 5. ~ Kl;p.5 T~ORI I V~ROYATNOSTEY
I;U1'^f'~ll~Tl.C1i~5Y.0Y 5TATISTIY.I DLYA T~Y.}iNICH~5KIKH F'RILOZHF.tiIY (C.~urse
in the Theory of Probabilities and M.zther~~tical Stati~tice for Practical
~1ppl ications), S4oscow~ "2Jauka," 1969, Sl2 pages.
11. S~~knlo~skiv, A. i..~ R~CN~I(lY STOY. (River Runoff), Leningrad, Cidrometeo- ~
ir.dnt, 1968, 639 pages.
12. Sokalovskiy, D. L., Shelutko, V. A., "Use of the Cur~bel' Dietribution
Curve for Evaluating the Probability vf Occurrc~n~e rrf ltaximura W:~C~r
pischarges," TRUDY LGMi (Transar.tions of the Leninp,r.~d }iydroraeteorolog-
" ic.al InRtitute)~ No 35, pp 32-36, 1969.
91
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FOft U~~tCtAL U5F: nN1,Y
,
13. [tozhdegtv~ngkiy, A. V., Chabotaxev, A. I. ~ STATI5~'If;H~SKIYL 1~TOnY V
ClbitOLOCit (Statieticai Methddg in Hydrdingy), Lpningr~d, Cidromet~o-
ixd~t~ 1974~ 424 pageg.
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~ak ~~F tr, rni, usi: c~Nt.Y
UbC 556.535.5
INri2AUIUitNAL CNANG~ IN 5`TRENGTH OP TN~ tCE CbV~ft 0~ RIV~RS AND R~5~RVOIK5
OURINC SI'RINC
:~Ioscow MLT~OItOLOCIYA I CIb~~LOCIYA in t~usgian No 4, Apr 79 pp 77-81
(Articlh by V. M. Timchenko, Ukrainian Weather Bureau~ subrritted for public-
nCion 21 June 1978J
Abetract: Using field mengurements, the author
has mude a quan~:tutive egCiroate of the inCra-
diurnnl variation in the atrength of a thauin~;
ice cov~r. On rivers nnd water bodie~ aitunted
in regions aith a solar type of gpr~ngs and r~nrk-
ed varintions of ineteorological conditions the
cuaplitude of the intrndlurnnl changes in gtrengtl~
~ttains 60-70% bf its tntal decrease durin~ the
entire period of the spring tt~awing. M empir-
ical dependence of ttie intensity of the intra-
diurnal changes in the liaiting breaking point
of the ice cover on the air temperature sums
was obtained.
[TcxCJ A quantittttive evuluation of the strength of the melting ice cover
has come into ext~~nsive use in hydrologicnl forecasts and ice engincering
computations. There are definite recnmmendations and also methods for com-
putinq the strength vf ice on rivers and s+ater bodies during gpring. In par-
~ ticular, acc~rding to the TECNNICAL INSTRUCTIOIV5 (SN 76-66), the computed
- strength of ice for any type of load on hydraulic structures in spring is
ast~umed to be constant. A ma,jor step fo nrard in Caking into account the
m~ch~nical qualities of spring ice was the developr~ent (by S. N. $ulatov (lj)
of a methnd Eor computing the diurna~ values of strength of the melting ice
cover, �+hich opened up broad prospects for developing methods for computing
and predicting the tines of openin~ up of rivers and reservoirs~ prediction
of ice jam-induced rises in water level, etc.
The practice of using the mean daily strength valuee show~ that they rather
precisely reflect the change in this characteristic witf~ time. tlevertheleKS,
sometimes against the general background of such a change there is a super-
positioning of intradiurnal variations comr~ensurable with the degree of
93
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gencral decrease in ice n~ren~th during the entire Cime nf iC~ thuwing.
71~e I'Lr~t quantitritiv~~ dutn on the m~gnitudr n� Chp intrddiurnnl changep
!n strength ~f the melttng ice cover wcre nbtnin~d in field inv~~tigatinn~
on the Amur at Khab~rovbk (6J. buring *he mnrning hnure, n regult of the
nighttiroe freezinp, di the upper l~yer, the stceng~h of �he ice covex on
thiy rlver increaned by 10-3b:. Later, in n ~aCudy o!' the m~chnniCal nnd
radi~tion propcrties of the rt~nwing ic~ ~over on the Amur itiver ~C K~m-
9biqOL~Sk on the Rar.dol'nay~ ~tiver ~r Terekhovkn (primorskiy Krny)
~nd on Kiyevskoye Iteservoir (Sj ~rr_cial experimenCg were devoted to an
investigntion of the intradiurnht vnriationg ~f iC~ str~r~gth.
e~c
. s ~ ~ ,r
o ~
�s
-1D
.'s GKt/cnt ~i 1 �
G kg/c 2 ~ ; - -2 1
~ ;
4 ~ r ~
-
. ~
_ .
.
0 ~ ._t____._L ~ ~ ~ ~
?O ~J ?S ?9 SrZ~ 10 15 20 ?S J 1 S1p'
Fip;. 1. Ai.r temperature 8 and strengtn of ice cover d. 1) Razdol'nayu River,
1976; 2) Kiyevskoye Reservoir, 1977.
s~
~ \
.~,J
�st
y .
-s~~f .c
o .
�s r1
~ �o
'f .s['v'- sa
~
ts: "~f r~ r~ : ~
Fig. 2. Complex graph of the variation of air [emperature (9 ) and ice cover
� ice~ ~n Razdol'naya ~tiver at diff.erent depths. The figures on tt~e curves
represent the depth of ineasurement of ice cover temperat~sre.
94
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~oK n~~icrnL usr oNC.a~
'I'he chnice of ob~ects for invegeigntion~ w~g de~ermined ~o a coneidereble .
degree by the difference in nnturnl condiCianp nf. thc reg~nns. Ar rhe
~ame time the principle of comparabiliey of resulCg i~ ndhered ea. In
particular, i~ is of definite interest to compare the regime af intr~diur~
_ nal chnnge in thc atrength aE ice of idenCical Chicknese un l�he Razdo].'n,7yn
Riv~r and on Kiyev~koye ~eservoir~ where Ch~ meteorologica]. concliti.oc~g dur-
ing spring nre very differenk. IC le aufficient Cn recall tl~ae the maximu?n
poseible inCensity of receip~g of aolar radintiott on the ice during Ctie
period of iCe thawing on Chia river and reservoir differe by approximnte.ly
150-170 cal/(cm2�day). At Terekhovkn village there are great ine:rudiurnal
changes in Che meCeorologicnl elementa. The amplitude of Che veriaCion~
for air Cemperature, for exa~nFle, here attaine 15-20�C.
The additional invesCigaCiona for egch of the mentioned w~ter bodies includ-
ed a determination of the atrength of the ice cover during a 24-hour period,
measurement of Che thickneas and Cempergture of Che ice cover, meteorolog-
ical and nctinometric obaervations. As a strength index we used the limit-
ing breaking stress (1] obtained duriag testing (downwgrd imparting of
force) of cantilevers prepared in the natural ice cover. For the purpose
of excludi~tg the scale effect on the results of comparieon of etrength of
the ice cover, we tested samplea of an epproximately identicul size wiCh
a crnas-secCional area of 3,000-4,000 cm~. In Chose cases when for r~ny -
renson a sample of a different aize was teated, the result of the testing
wna corrected taking into account the difference between Che eample aec-
tion and the adnpted size. We ueed the recommendations and forroulae of
1. P. Sutyagin ~2].
The frequency of ineasuremenCs was established in dep~ndence on the ampli-
tude o~ the i.ntradiurnal variations of ice strength. In individual casea
the experiments were carried out at nighttime.
We carried out a total of more than 630 teats of ice cankilevera for break-
ing stress. This made it possible to obtain some qunntitative indices of
the intrudiurnal change in strength of the thawing ice cover.
The intradiurnal variations in strength of the ice cover are a result of
change in the meteorological conditions of t}iawin~ in the course of the
d~iy. As an illustration of this, Fig. 1 shows time-colluted curvea of the
change in strength of the ice cover on the Razdol'naya River and Kiyevskoye
Reservoir and the variation of the ~.:incipal element uf the heat bnlance
at the ice surface air Cemperature. In addition to the great total am-
plitude of the variations in air temperature in the Razdol'naya River
~egion we aote a very frequent (almost daily) transition of. sir temperature
through zero degrees in both directiona: to positive and to negative velues.
Taking into account that during the daytime an average of up to 240 cal/cm2
of solar radiation heat anter~ the ice cover thickness on the Ra~dol'naya
River during the period of iCS melting, it becomes completely understandable
that there is a rsarked change in ice strength during the cours~ of the day
on this river. Qn individual dag�s the amplitude of variation of limiting
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I~OIt ~~l~i~ tt:lAl. lty1: 11NL1'
brenking ~rreHy ~ttfiin:3 3-4 kg/cm2, which ig 60-70% n~ the Cdenl decreng~
in ~CrengCh nf Ch~: ice C~yv~r ducing ~1~~ entire thawing period.
A.~ indicfited by me~suremen~.i o~ ice tempQruCure which wer~ curried out u~-
in~ exten~ible qoit thermomet_ers �rnz~n ii~ nC diff~rent depthg (10~ 20~ 40~
50 ~m), the variutions in ~ir tempernture, intensi~ic~d l,y the heut irflux
during thc dnyeime due to ~o1sr energy, leud~ Co a significnnt temppr~ture
vari~ti~n oC the ic~ l~~yer iCSelf. It goes wiChout saying ChaC in ehe upper -
layerg rhese variri~lo~i~ ar~. ~re~ter anct in Chc lower l~yrers are lees (~ig.
2). With nn increusc in depeh there is ~ len~Chenin~ of''the tiroe inrervul
b~tw~e~i the onyet of rhe air ecmperuture and icc Cemperaeurp extremn. Thc
te?n~~cr:stur~ wave:~ re~tr.h 1.16 is associated with a change in Che behavior of tlie re-
sistance coefficient for particles whose form differs c~nsiderubly from
' ~i sPhere. In order to obtain the dependence (9) to f N 2.0 it is possible
Co limit ourselves to use of experimental datu.
Ttie sequence of determination of ~tur and f is as follows. First far one di-
~~meter of a particle of a particular maCerial we experimenCal].y determine
the rate of its seCtling a1. Then, stipulaCing a ser3es of fi values, us-
ing (9) we determine ~ tur and from (7) we compute the rate of its settl.3ng
W for a stipulated fi value.
Constructing the computation dependence tJ =~(f) and plotting the experi-
menCal value ~ on it, we det~rmine the form factor for a parCicular material ~
of the particles f and from (9), ~ tur~ Which make it possible to determine
the value of hydraulic coarseness from (7) For particles of any size.
Comparison of computed data using (7) with t'~e experl~ental dat~3 indicated a
sufficiently good agreement.
We note thac iC is noC necessary tl~at our parameter and the similar V. N.
Goncharov parameCer [2] be considered similar, since they l~~ve a radical
diff erence. The soluCion of this prob"lem, proposed by Goncharov, seems to
us virtually infeasible because even for particles with an identical form
factor it is necessary Co have experimental data for So in dependence on
the temperaCure of the fluid and its kind.
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N'Ok OH'~tt:tAt, Ily~ nNt,Y
UltitIUGW,PI~Y
I. Arwuv, M. C., 'I'c~dc~K, c). M. ~ CIt)INVI~ICIIt:SKtY1: i Tt:l'I.OVYYL U."?NC)VY IZAISCI'1'Y
AI'I'AtU~'t'~?V S~) y'PA`I'S111NARNYM I K11'YA~3HCIIIM !I?kN)S'1'YM ;ii.tlYl~f (Ilyclr~iul l~
~nd ~t~~rmnl Principie~ of np~rarinn df Apparatug W~th 5tatinnnry nnd
~luiciixed Granular L~yerg~, L~ningr~d, "Khimiyn," pp ~1-34, 1~168.
2, Gnn~chbrnv, V. N~, DINMiIKA RU5LOYYKI~ i~OTOKOV (byn~tniC~ dE chanhei ~idWg),
L~ningr~d, Gidrom~tcoixdat, pp 2UU-208, 1962.
Gorbiu, ti., `C~PiLd0i3M~N i GLU~tdM~KlIANIKA DISY~Et5NYKt1 SKVl7ZNYK11 pO~OKOV
(ti~at Cxch~np,~ dnd llydrom~chqnic,~ nf Ui~per~p 'Chrnu~h ~1nug)~ MoHCUtJ~
"~nergiya," pp 45-57, 1970.
4. K~rdugh~v, A. V. , PROtiL~MY UINA.MIKt Y~5'T~S'i'V~N1tYKli VdUNYKt{ pU'CUKdV (Prob-
lem~ itt the Uyn~ni~e of Nnturbl Wneer ~lows), t~ningrdd, Gidrom~tp~i~-
dnt, pp 26g-27U~ 1960.
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FOtt 0~[~iGiAL t1~~ ~NLY
UDC 551.SOs635.b58(47)
ACRbCLtMA'~IC BASIS ~OR UISTitIHUTION 0~ L~NTIL dV~tt TNE T~ttRITORY OP TN~ US3R
t~bg~oW I~'P~OROIAGIYA I GLUROLI~GIYA in Rugeign Nn 4~ Apr 75 pp 98-102
(Arti~l~ by C. C. V~~enina, NnrtN~rn Cau~A~ug Admini~er~tidn nf th~ Nydrn-
metenrdidgi~al S~rvicc, gubmirt~d f~r pubii~ntion 3 Octhb~r 1978]
Ab~tr~~e: 'The guthor ~xamine~ rhe prc~bl~m~ rElnt-
ing to ~limeric ~v~luatinn nf th~ re~nurcee of
the ~urapenn t~rritory nf the U55R ~pplir_bbl~~ t~
the cultivgtion df l~ntil. Ie w~g poesibl~ to dp-
tarmine the ~limatic rgngeg nf pos~ible and d~~ir-
nble (wiCh re~pe~t td agrom~~eoralAgical condition$) ~
rulCivation of the crnp fnr grein.
('~~xt~ A decigive role in en~uring g fully ~c~und nutritiun of rer.ple ie
plgyed by protein. Howev~r, nt the preg~nt time protein ig produced at
les~ than hnlf the n~cpseary nurm~ 21-22 kg per man per ycar (3~. In this
connectinn th~ problem of increasing prnduction of plant protein ie on~
uf the most timely.
Among thc legumes it is of interest to examine the high-protein crop~len-
tils I,~ng culinaris. This crnp has great posgibilitiQe and ig of univera~l
importnnce (food, fodder, industrial, egxonomic). On tt~e bueiu ot the con-
tent of protein in eeeds (up to 36%)~ rate of digegtibitity, hfgh tnste
qualities nnd nutrition it ~ur{~.ygaes other legumes. In addition, lentilg
ure an edv~ntageoug export crop. The cost of its gr~in on che wnrld ~arket
ig c~nsiderably greater than the cast of peag, and other legwnc~g, 3-4 times
greater than ehe coat of the grain crops: wheat, rye and b~rley (8j.
In the U5SR the area of lentil cultivation befnre thn_ Secand N~rtd Wnr
attained almost 1 million hectares (1937), Wnich wa~ 667: di thc antir~:
Warld area under this crop. With respect to the prUduction of lentil and -
itg exporC the USSR occupied firet place in the Warld. Among the legwaeg
lentil s+i[h respect to sown area aas smnller befor~ 194]. only re]~+tive
to peas. After the 5econd Norld War the area in lentil vnx sl~c~rply r~duced,
in 1961-1963 attaiaing its minimum. In 1963 the area undcr lentil wea reduced
by a fnctor of e Lnoat 30 in comFarison aith 2941.
In all the main tegions of lentil praducCion this crop is inferior in yi~ld
to peas, but With a high level of agricultural engineering itn yields con-
stitute 15-25 centners/ hectare. Ttie record yields of lentil in the USSR
120
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.
~ok d~~tctni, us~ hNi.v
~x~~~d~d 30 c~n~nerg/h~~egr~.
ncH?,?,roaa -
I
,~M1~~
I'A t Ne~oeo e ~
~r .,ti 'S A
M ~K9A 1f
~.~~r - _
.t i
~
~
: ~
, a6 , ~ r,,.
NEtl
~
� r
� wM0A0 ~
JAfiI~ t...,
e ~
.
_ ; - = .
. - -
~
. - ~ ~ ~ ,,o
r,,,,i ~ -J = -
Pig. 1. Regione of cultivnCion of lentil in the ~urnp~nn U551t. Limit~ of
ripening of lgntil far grain aith the folla+ing prob~bility: 1-- 509:, 2--
80~; 3-- menn yield of lentil~ centnere/hectnr~.
7'he intere~ts of th~ national economy require a coneiderable ~xpan~ion in
the caming yeare of plantings of lentil nnd an incren~~ in its yield.
One nf th~ ways for eolving the formulated problemg ie a rational digtrib-
ution of l~ntil over thp territory of Che USSEt.
'I'he reault~ nf our investigatione made it pos~ible to determine the degree
of correspondence betWeen the climatic conditiong of the P.urnpean U55R and
[he biologic~l pp~uliarities of lentil. It Was possible to establish cli-
matically sound oreas of the crops for grnin which are possible nnd desir-
nble aith respect to egrnmeteorological conditions.
The m~thnd fnr formulating experiment~l investigntiong ~nd d~veloping agra-
mete~orologicgl indices far the development ~nd productivity nf lentil have
been exasoined in our studies [1~ 2J. The agromet~orolo~ical indices vf th~
rat~ nf development of lentil, the dependencc of its yield on nir teropera-
ture nnd precipitation totals, and the resulte nf gtudy of inetcnroingical
conditions in the Lurnpean territory of th~ US5R were used Eor agrnclitmtic
validation of the zone of cultivntion of Ientil and evaluation of the agro-
~limatic conditiona of th~ territory, determinir.~ the rate of development
and yield of the studi~d crnp.
The informatinn nn the influence of weather conditions on the yield of len-
til in large part gives the qualitative characteristics of this phenomenon
(4~ 6, 7j. O~~r developments of the quantitative characteristics (indices)
121
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~d~ nr~ict~. us~ oNLY ~
nf eorr~l~tion b~ew~~n c~i.r e~npe~r~Cure, pr~~ipiegtint? gnd yi~id of l~neil
m~d~ it poa~ibi~ un th~ b~~i~ of ~ir r~cnp~r~~ur~ gnd thp precipitation ~wo ~
~n d~tenain~ eh~ paggibl~ v~lu~ of the grgin yi~1d. Thig etudy wae pr~-
~~d~d by an analy~ig nf w~dther conditi~n~ under which eech yield vae form-
~d (from evaiigbi~ cn~~~ of d~tprminatinn of yteld in ee~d Bei~ctinn ~ec-
tdrt~). ~
'I'h~ r~gulte nf th~ inv~geig~tinn~ indic~e~d th~r i~neil is mo9t productive ,
~mean yi~id nf 1G-20 CQnCn~r~/h~cC~re) whpn it i~ culCiv~ted under condi- ;
~idng of mnd~r~rely a~rm weaCh~r~ vieh a m~~n air Cemperetur~ of 15-18�C
during the growing ~ega~n ~nd g pr~Cipitgtion gwn during eh~ period frnm
gpr~uting to maturity gt h~rv~~ein~ ~qual Co 100-180 mm.
'Ch~ h~rvesting matutiity of l~ntil ~et~ in wi~h the accumulation n� a tem-
p~r~ture eum df 1,500�C. 'i'hg i~nthermg nf eh~ge gur~~ h8v~ n prob~bility df
50~, th~e ig, thp maturity of 1QnCi1 will t~ke plnce in S y~arg out of 10.
Cor ev~lugring th~ gen~rnl trendg in th~rmal resource~ in the practic~ of ,
liydrumet~nroingic~l gupporC of agriculeure u~e ig made nf the eum of active
tempec'utuCeg above 10�C, gince at a temperatura nf 10�C end gbove moet
plantg have an active groaing geason. HoW~v~r~ Che auCumn transition of
temperature through 10�C coincides with the period of on~et of gutumn
freezes during which there cnn be damag~ and ev~n total loss of the harvest.
'Cherefore, We took into gccount the condition~ of the groving g~eeon from
the date of transition of temperature through 10�C in epring to the dnte
of transition through 15�C in autumn. In thi~ conneceicm a need aroae for ~
conv~rsion from some sums to others. Such a conversion (reduction) vas
cnrried out by introducing a sa-called climatic correction obtained for
the period from the date of tranaition of inean daily air temperature in
autumn thrnugh 15�C to the dgte of transition to 10�C. ~'he climatic correc-
tion Was about 300�C. ~
Ues~ite the fact that lentil is an early sown crop~ in agricultural practice
it~ sowing is carried out at timee of CrAn4iri~n of the mean daily air tem-
perature through 10�C. 'I'herefore~ there aae no need to introduce an ~ddition-
gl climatic correction for the onset of the period of calculation of the gum
of active temperaturea. The aum of active temperatures during the period be-
tWeen the transition of air temperature through 10�C in spring and 15' in
autumn, equal to 1.800�C, dete~ines the northern boundary of growth of this
crop. Por accumulation of thia sum of temperAturea vith a probability of
80~ and 90X it ig necessary that their mean long-term eum be higher. Uaing
the A. N. Lebedev grapha (SJ, for computing the aums of inean daily air tem-
peratures above 10�C With a different probability ae find the final sum oE
active temperatures ensuring reliable cultivation of the investigated crop.
It Was found that the sum of temperatures, equal to 1~800�C, is ensured 80X
vith a mean climatic sum of teaperatures of 2,000�C, by 90X With a ewo oE
temperatures 2.?00�C. Therefore, the isotherra of the sum of temperatures
2,000�C is the northern boundary of stable cultivation of lentil.
122
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t~'dl~ Ut~'~ICIAL USL ONLY
ir ha~ been e~e~bli~hed eliut tl~~ ndrehern Uound~ry dt ~tab1~ ~ultivdeinn
of lentil ~or ~r~in in the ~urd~~~n U5:~It run~ ~idng Ch~ 1in~ ltigd-M~~c~w-
tv~nnvn-Izhev~k (~ig. 1).
tn rhe ~urnp~nn U55tt ehe cultiv~tidn d~ the ~rnp ig f~~~ibl~ in r~giong
wh~re durin~ C11e perind from gprauein~ tb hnrv~gCing maeuriey 1e~g ehnn
ldd mm nf pr~Cipitatinn fdllg wieh n mp~n dir r~rnper~eur~ durin~ ehi~ pee-
idd nf mnr~ eh~n 19~C and in region~ of heavy r~ing, when i.n the Gdur~e
ot thig ~ntne periodrwr.e th~in ~lU mm of pr~~ipientiinn fcill. Und~r ~u~h ann-
ditiong th~ yieldg ~f l~neil ~re ldw, n~ gCc~ee ge~d-~~1~etidn g~aCinng
l~s~ rh~n 10 Cen~nerg/hectare~ in prnduction fi~1d~ ~bnue 5 c~nenprg/
hect~re. Agguming thig yield vnlume en b~ ehe minimum ~d~.~i~gibl~, we wi11
n~gume Cht1C the isnline nf 10-~~nener yi~ldg gC geed-gel~cCinn gC~tidng,
~;ov~rn~d by the ~bove-mentinned m~tedrnlugiC~1 nondiCion~, ig ChN b~und~ry
for eh~ ~ultivntinn af 1cnCi1 ~dr gr~in fp~gibl~ with r~gp~CC td r~grnm~t~nr-
ologienl ~dndi;tong. 'rhp nnreh~rn boundnry oE cultivtttinn of lenCil (iga-
line aE yieldg ld G~nen~rg/h~ce~re) p~g~e~ thrnugh Khme~'niegkiy, tn eh~
n~rth nf Gom~1', to gryangk ~nd tihen Gnincideg with the boundary af m~tur-
ing of tiic ~rop. A cdn~id~rnble d~ere~se in ehe yield nf lentil in ~he
mdist zdne c~f the ~urdpe~n US5[t, where Ch~ nnnunl qunntity df precipit~-
tidn excpedg possible evapor~tinn, is obgerved ne a result nf nn ~x~egs
of rooistur~, ~ gre~t number of rainy d~ys nnd ~ decregse in ~oil EertiliCy.
'The sum of precipit~tion in th~e~ reginng during Che pertod frdm gprouting
to maturity exceeds 200 tnm ~nd th~ ~ne~n t~mperatur~ is not nbov~ 16-17�C.
'rhe gnuehern boundnry of f~~gible cultiv~eion of lentil for gruin p~egeg
someah~t to Che sourt~ of Kherson, Uonetsk, Vnroshil.dvgr~d, to 5ar~tov ~nd
then through the snuthern part of Kuybyghevgkay~ Oblast.
In tl~e very arid zone, c~rresponding to the zone of dry geeppeq, plnnCin~K
~~f lcneil can exist only to a limited extenr, prim~rily in regions bounding
an the moderately arid zone. In che southeasCern part of the European U5SR
the lentil yields are reduced due to inadequate supply oE aown arens With
t~oisture With high s~ean air ter,~peratures during Che growing scason (more
th~n 20-21�C). Dc~ptte the fnct thut the crop is drought-resist~nt, its
cultivation wicl~ou~ irri~;ation is irrationtil in a vcry ~rid zone. WiCti ir-
rig~tion, houever, in early plantingx, it is poesible to nchieve a consid-
eruble increase in its yields. _
buring the last decade Cl~e area~ ~own in lentil h~7ve been cnncentrated pri-
m.~rily in the R5~SR (9$9; of ~11 the areas sown in lentil in the U55R). 'Che
Volga region accounts for 54,800 hectnres (93x of the entire sown in lentil
in ti~e Soviet Union), the Central Chernozem regi~n uccounts for 2,800 hec-
tares (slightly less th~~n Sx), ~nd nther regions less than 17.. The gre~test
sown areas in lentil are in 5aratov~k.7ya Obla~st (76R), in the Ta[~rs{cnya
A5SiZ about 10;;, in Voronezhskaya Oblast ~9;, in Kuyhy~hevs~k.7y.~, I'enzen-
skaya, U1'yanovskay:~, Tat~hov~kaya Oblasts approximatcly 27 in ench c~bl.a~t.
123
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t~Uk c)1�'i~'tC; I 111~ 1?5L UNLY
Lentil i~ mngt prnductive in ti?e f~ll~wing a:~.la~~d' ~c,r'~ _~vt3ka;.'a (~outh-
~rn hnlf), Ur~1'~knya, K~yby~hevgk~y~ (nnctl~~rn hal~), Pen~~n~k~yn, Ry~-
~~ngkny~, Orldv~kny~ (~nutheng~~rn hnlf), Kur~kr~y~, ll~igurndgkny~, Sumgk-
nya, Ch~rni~uvdkny~, Kievgkny~, t,ipee~k~yd, 'ff~mbnv~k~~yn, V~rnn~zh~kny~
(northw~~t~rn h~lf), poltnvgkaye, '~ul'gk~yn (gdu~h~c~~Cern ~~rt), Ch~rkegH-
kay~, Kirdvu~rnd~k~~y~, Un~prop~trdv~k~ya (nnrChwwq~~rn pnrt), in thh ~ut-
nnmm~u~ r~publicg: T~tn~gk~~?yn, t~lnrdovskaya, Chuvaf,h~ke~~a, M~~riy~k~Y~. ~i~
me~n yi~1d~ nt rhe ~~~d-gel~~tidn ~C~ti~n~ in th~ 1n~ntidned ~b1n~C~ and
:~utenamnug republi~$ ~tenin 15-x0 a~ntner~/}i~Cenrr_ (13-14 G~ntn~re/hecr~re
~long th~ Un~pr ttiv~r vgll~yg). In ehp remninin~ ~.~rrttory of 1~nei1 ~ultiv~
netc~n wiChin thp linitg nE ehe ~ur~phan US51t eh~ menn grnin yi~1ds st th~
~~ed~s~l~Geiott gt~rinng ~re ebauC 1U-14 ~~ntnern/hectare.
Judging ~rnm ~gromut~ordtogical conditian~, ~n inc~�~ase iti sdwn areng nf
l~neil ig fe~~ib1~ in the C~nergl Chernoz~m r~gion (in Liri~e~keya, Tambov-
gk~y~, Kur~k~y~, gelgnrndgkayg, parei~lly in Vornnez)~~k~y.~, Ob1n~Cg~ in elte
Vo1g~ regidn (in penxengk~y~, U1'y~n~v~k~y~, ndreherc~ ha1`. of Kuybyshcvsk~-
~y~ Ob1~gC, Snr~tnvgk~yn (in the irrignted ~egtern r~~~i~ns of. rh~ obl~~t)
~nd in the Tnt~rskayg A55It. In the pnumer~ted r~~ione che weaCher Condi-
tion~ ~ngurp m~gn yi~ld~ af lenCil nf 15-20 centncr~/hc, ~_,~r~ ?t thr 1r.vc~1
df d~riculkur~l techniques emplc,yed uC staee secd ~;c~l~Cll irl :~tnttan~ dur-
ing the last deCnd~g, buC ehe record yields in prc~~ucti:~:~ exc~ed ~(1-3f+ Certt
ners/hect:~r~. 'l~~ese regien~ are favorable in ctim~tir. r~_:pe~~ts Ebr th~~ cu'.-
tivation of lentil for se~d. In ~ddiCion, it ?s r.~t i~~n~t ~rn~~cien thc
soWn ~rens of lentil in the northeagtern part of r'�~ Uk~�-~~c (Cl~:i�nlr;~v-
sk~y~, 5umgk~y~~ Khar'kovgkay~, Poleavykuya nbinsts), !n the Vc~l.p,o--Vy~t~:kiy �
Etnyon (in thc s~uthern half of Car'knvgknya Obin:~t, Morduvskny~ ~nd C.hu-
veshsk~7y~ A55Rs), nnd glsn in Ryazanskaya Oblsut. 'The ~oil�~~ti~aciC condi-
einns in Che indicgted zone~ nf lentil cultiv~tion mdke tt pos:~ible td
achieve high indices in lentil culCivation and to nbtain ti~i6h income frdm
tC.
Thus, our agrometeorological studies make it posaible to dr:iw ~he foll~~win~
conclusions: _
1. 7he norChern boundary of lentil rr~turing (60ti prot~.~bi.i ! ty j~uc resputids ~o
the isotherm df sums of r~ean daily (above 10�C) temperarur~s 2000�C�
2. 'fhe boundary of rational cultivntinn of lentil (y1e1J :~t 3eed selectidn
stations greater than 10 centners/hectare, in production fiel~l~ more
than 5 centners/hectare) passes throu~h ehe nortliwe::t~~zu ,~~r~ uC th~~ zone
through Khmel'nitskiy village, to the nort}~ ~f Gunr.l', to nry:~nsk, t4n~cow,
Ivanovo, Izhevsk. 'The southern boundary runa slony, the line K}ic:rson-Dvnctsk-
Voroshilovgrad-Saratov and then through rhe southcrn ~art uf ituybysh~vst:~y.~
Oblast. tJith irrigat~on and rigorous adherencr ta :~~�sinF ttmes the south~rn
boundary can be someort~at displ~ced to the ~auth.
3. The air t~operature during the period from ~pr.~uting tn fiar~esting ttwcur-
ity, equal to 15-1$�C, and a precipitation sum o� 100-1Sn mm wttii a leve?
of agricultural techniques equal to that at state seed s~lectlon src~tions
124
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t~'dlt hC~~CtAL U~F~ UN1~Y -
~n~ur~ ~be~ining yi@ld~ df ~,~eneil ~~~d~ af 15-2~ ~~nCn~r~/h~ce~ir~. 9ueh
cnndieinng gr~ cr~n~~d in eh~ ~u~rnp~an USqit in ehp C~nernl ~tiexnnx~m nnd
Vn1~~ ~conomi~ re~inn~ ~nd in T~tarak~yn ASStt. In Ch~ mentinn~d regidn~
~ rh~ nrgnnixneinn n~ lpneil ~~~d eul~ivaei~n ia mn~e r~Cinn~1. In nddielan,
nn eh~ b~~ip d� ~grom~eeorological condition~ il i~ deeirnbl~ tn ~xpnnd
the ~re~s gnwn in l~ntil in the nor~he~~te~n p~rt d� th~ Ukr~ine, dnu~h~rn
h~if nf Gnr'kovgic~ya Obin~~, Mordovgk~ya ~nd Chuv~~h~k~y~ ASSRn.
~IgL20GI2ApHY
1. V~g~c~in~, G. G., "Influ~n~~ df Soil Temperatur~ and UepCh of S~pd P1~~~-
m~nC nn RgC~ dL App~~r~ne~ of L~ntiil Sproutg," S1~OItNiK RAi~nT GOtt'KOVSKdY,
VOLZHSKOY I EtYgINSKOY GMO (C~112CCidn df P~p~r~ nf th~ Gnr'kiy, Vn1g~
~nd Itybinsk Kydromee~orologiegl ObeervnCories), Cidrom~t~oizdnt, No 9,
pp 60-62, i972.
2. V~~~nin~, C. "b~v~lopmenC di t,~nCil P1gnt~ in Uep~nd~nC~ dn Agro-
m~t~orologtcal Condttion~," BYULL~TBN' VSLSOYUZNdGtl O~DCNA tLNINA IN-
STITUTA ~tAST~NIY~VOUSTVA IM. N. I. VAVILOVA (~u1leCin of Ch~ A1~-Union
Urder of L~nin IneCiCute of Pl~nt CulCivneion imeni N. Vnvil~v), Na
28, pp 41-45, 1972.
3. Gorlanav, I., Shaykin, V., "An Important prdbl~n in SCienc~ ~nd Practicgl
Life," S~L'SKAYA ZHIZN' (Rural Life), No 3(16070), 4 Janu~ry 1974, p 2.
4. 2iganshin, A. A., "ComparaCive Evalu~Cion of Leguminoug Crnpg," TRUDY 2-oy
NAUCIINOY KON~~RENTSII PO ZERNOBJBOV~'M KUL' 7'URAM NA VO5T0lC~ LESOST~PNOY
POLOSY (TransacCions of the 5econd Scientific Conf.erence on Leguminous
Crope in the Eastern Part of the t~ooded Steppe 2one), pp 76-81, 1961.
S. Lebedev, A. N., GRAFIKI I KAR1'Y DLYA RASCHETA KLIMATIC?1~SKIKH KHARAKTER-
ISTIK RA2LICHNOY OBESPECHENNOSTI NA YEVROPEYSKOY TERRITORII SS5R (Graphs
and Maps for Computing the Climatic Characteristice of Di.fferent Prob-
abilities in *he European U5SR), Leningrad, Gidrometeoizd~t, 1960, 116
p~ges.
6. LeonC'yev, V. M., C1IECHEVIT5A (Lentils), second reviaed editian, "Kolos,"
1966, 178 pages.
1. Luzina, Z. A., "Geographical Variability of Biological nnd Economic Char-
acteristica of Lentil," TRUDY PO PRIKLADNOY BOTANIKE, CENETIKE I SEL~KT5II
(Papers on Applied BoCany, Genetics and Selection), Vol 34, No 1, pp 164-
175, 1962.
8. Tntarintsev, A. I., "Present Status and Prospects of Lentil Cultivation,"
NAUCHNYYE TRUDY ~iNII ZERNOBOBOVYKH KUL'TUR (Scientific Transactions of
the All-Union Scientific Research Institute of Leguminous Crope), Vol 1,
PP 19-26, 1966.
125
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~OR O~FICIAL US~ ON1,Y
UUC 556.(S3S.5*536.5+537)
ItYDROLOGICAL PLCULIAItITI~5 IN TH~ DLSIGN~NG 0~ CANALS IN ~'LOODPLAINS
Fbacow t~TEOItOLOCIYA I GIDROLOGIYA in Rusaiun No 4, Apr 79 pp 103-105
~Article by Candidate of Ceographical 3ciences A. V. Pinghchev, A11-Union
Sci~nrific Reg~arch Ingtieute fdr WaCer Pre~erv~tinn, submitt~d for public-
ntion 7 June 1978]
Abetract: Dangerous hydro].ogical ph~nomena Fire ~
examined (plane deformations in a chennel and
floodpl~in, wind wavee, iCe phenomen~) which
muse be taken into account in Ch~ d~signin~ of
canalg in river floodplaing.
(TexCJ In the Ukrainian Divi~ion of Gidroproyekt appcinlietg have developed
a downatream variant of a route for the Dnepr-Donb~e~ Canal, in accordance
with which the canal is not run along the Warer divide~ but glong the flood-
plgin of the tributaries of the Dnepr and Severskiy Doneta. In accordance
with a similar variant, apecialiats at this institute have also planned
a Don-Oskol canal. The route of this canal pasaes along the floodplain of
the bon and Oskol tribuCaries the Potudan' and Kotel Rivers. The water '
level in auch a canal is cloge to the ground water level of the ad~acent
territory. 'fhe downstream variant, in comparison with rhe water divide var--
iant, has a number of advantages, of Which the most important are a decrense
in the loaeeg of water in filtration without apecial antif iltration measnres
and the enery of ground Water into the canal [4).
In the designing of canals on river floodplains it is necessary to take 'Snto
~ccount a number of dangeroua hydrological phenomenn, n~ung which we musr
first include plane deformati~ns in the river et~annel nnd floodplain~ wind
waves and ice phenomena in the flooded floodplnin.
When laying out the route a factor of considerable impartance is the close-
ness of a meandering river channel to the canal plannpd in the floodplain.
As a result of plane deformationa of the channel there can be destruction
of the dikea eafeguarding the canal from inundation by high aaters, pumping
etations, pipelines, electric transmiasion lines and other structure~.
126
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rc~ri ~i~r~etnt. u~i, oNt,v
itt ~~leceing thc rnurc ~or ~t canal it i~ n~ceg~nry tn vi~u~ilize cl.e~rly
tli~ ~~genne nf ehe ch~nnel prnce~r~~g Cr~ngpiri.ng in ttie river ~nd ~o kndw
ehe r~gulnririe~ in eheir d~velnpmene. A p~rCicularly in~pnre~ne problem i~
the prepnraeintt n~ ~ prdgndgei~ ~vnlunei~n df hnriznne~l ct~form~Clnng df
~h~ riv~r Ghnnnel nnd floodplnin. Ie Cnn b~ m~dc~ on ehe bn~i~ af ~h~ merhr~d
for hydrdingieal~?norpliold~ic~l nnnlygi~ eh~ ch~nn~1 proc~~~ d~v~lnp~d ~e
th~ SCnte ~lydrald~i~a1 ~ngtitute (N. Ye. KnndrnC'y~v, I. V. Pnpnv, B. Sni-
~hchenkn) [2j. 'Miig methnd muk~s iC pogsibl~ tn ~gG~blish the ~ype of chnn-
n~l prnceg~, wieh un udequ~t~ ~cGUrr�y Cd deee~mine th~ ru~c df hnrixdnt~l
d~fnrm~ti.ong nnd n~Cdrdingly mdkp ~ v~lid Ch~i~~ nf a rouCc for Ch~ cnnnl
nr cn1],gpsing whiCti m~y n~nur along s~gmene~ df gr~aC ~xtent. Ae th~ pr~genC
eim~ rhi~ method ig being u~ed exC~nyiv~ly in plucining rivet crn~singg for
high-t~nginn pow~r 1in~s (3], pip~lineg ~nd wnter inegk~ ~Cru~Cur~s. Hnw~v~r,
the hydrningical-morphnldgic~l ~tt~lysis meChnd has sri11 noe b~en developed
npplicubl~ eo th~ choiG~ nf n c~nnl rnuee ~n fldndplning.
At ehe pregenr time thi~ work ig being done ~e ~he 5CMC~ HydroingicaL Inge-
ituCe. Ie h~g formul~Ced Che b~giC poinC~ in Che In~truCCions ~or ~vgluttCing
Ch~nnel ~~nd F'ldodplnin procegges in Che plnnning of C$n~l~ in ~lnodplaing.
Amdng Che Cyp~s of floodpl~ins defined by Clie 5Cate liydrold~ic~l Institut~
the mdst conveni~nt and divergified cnnditinny for thc luying oue af canelg
hre on the floodpl~in~ of freely megndering rivers. Such flnodplnins, hgving
a great widCh, nre chnr~cterized by the fnct th~e the current ~dne df inean-
dering frequently does noe occupy the eneire expgnse from one v~11ey slnpe
to Che other. $eyc~nd the limits of the exCengive floodpluin ureay et~er~ are
secCorg of floodplain which ~re not sub~ectad Co refnrmation and which ur~
guitnble for the lnyin~ out of cannlq. Under theac cnnditinn~ iC i~ pnssible
to get by witti n minimum number of intersectiong of river chnnnels by the
can~l route ~nd there i~ a minimum volume of e~rth work; this cnn be done
by laying out the canal nn the lowest Cerraced part of the floodplain. In
the laying out of a canal there is ~ possibility for makittg use of ox-bow
lakes and floodplain distributaries when laying out routes. However, the
complex relief of the floodplain surface favors the appearance of currents
on Che floodplain durin~ its itiundation and Chese currenCs c~n elien cnuse
erosion of the slup~s of proCective dikes.
Maps of Che distribution of types oE ctiannel process contained in the hgnd-
books R~5UR5Y POVERKHNO5TNYKH VOU S5SR (5urfnce Wat~r Resources of thp USSR)
can be used for a preliminary ~udgment concerning Che principnl typeg of
floodplai~ns. At Che same Cime using the classificaCion of floodplains for-
mul~ted by the State Hydrological InstiCute and tticse maps it is possible
eo draw prcliminnry conclusion:~ concerning the types of floodplnins en-
countered in diff.rent segments alvng the canal ro~te. On the busis of n
prelimin~ry ~nalysis of the cartographic mater;al it i~ passible Co estab-
lish the type of ch~nnel process. Then it is possible to define tnorphologic-
aily uniform segments and ttie general tendencies itt channel reforawCions,
as well as the peculiarities of development of individu~l channel (me~nder)
macroforms. Parti~ular attention is devoted to reacheg within which tt~e de-
velopment of the meanders can constituCe a danger for a canal and its
' 127
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i~n[2 Ul~t~'LCtr~L Uyt3 (~Nt~Y
~rrunCur~g. IC i~ po~~ible Cd d~Cermin~ Che ~~rlncl.~~al. lcidtc;~g r~~ tl~e ct~c~ztp
no1 prnce~~, en ~sr~bli~h the mdrphom~eric ~nd hydrhmorphnl~gi~n1 d~p~n-
deucns nnd rd ~grimae~ ehe raGea of horizdne~l ~nd verCicHl d~fot7nati~ng.
'I'h~ m~~ttd~ri.ng xnne i~ ~~aegbl.i~hQd for ~nch re~7ct~; tih~ i~~nu1. r~uCc i~ lpic~~
duC ~ak3ng rhe devploptn~nt nf theg~ prac~~ge~ ineo ttacount~
Wh~n cn?1~truGtin~ ~ Cunnl nn n riv~ti f landp~.~in 1.ts dik~s c~?n uplit tihe f lnod-
~~luin fldw ~nd 1~ad tn ~n incr~~a~ in ehc digChgrges in ~ny of eli~ cue-off
p~rt~ di th~ ~ldedpl~in. 'Tl1ig C~n ~~ugp an incr~~g~ in ~h~ wnter 1~v~L and
th~ c:urr~nC ~�~lncity in Che flc~ndpl~in s~cCor. 2n such ge~m~nCg n~ th~
c~n:~1 bord~r~d by dik~s with ~n inar~a~~ in eh~ w~e~r l~vel. the dikeg t1i~m-�
gelve~ nnd thQ floodplain cun b~ gub~ecCed eo erosidn gnd nther unfavor~bl~
con~equ~nces. Inf.orm~Cinn dn th~ mngniCudp nE i.ncrease in WHC~t' leVNl in Che
dik~d ~~gmenC, the appe~r.nnne df Curreneg wirh Congider~blt. velociti~g .~ncl
th~ ~ning-QUe di the ice is n~cessgry for l~ying out the rc~ute nf a cc~n~l, _
~~cerraining hdw high ehe dik~~ shnuld be gnd making a deciginn nn the rein-
fnrcpm~nC o~ Chetr aueer glopeg.
Wind w~ves ~r~ ~lso nmong eh~ dangernu~ hydrological phenomen~ which mugt b~
~nk~n inCo F1CCOllriti in the plnnning of cannl~.
R~tt~er i~igh w~v~s c~n be formed on Ch~ inundZCed broad f l~~odpl.nins nf rivpr~
~nd the englneerii~g structures situttred thcre can b~ subjpcted to destruc~
tinn. The greatesC d~ngcr nrises when a pnrCicular~v stron~ wind coincides
with p~rticul~rly ~trnng fldoding, ~1Chnugh ehp pr~bahility nf cninc:tdenr.p ~?i
these twn phennmen~ c~n be beyond the limit~ ~~C the norm~~l ir.ed ~~nd tuk~n-intu
,7ccount probabilitie~.
Inform.~tion on the heigtit af the wind waves, egpecially nn brnad ~nd deeply
inundated floodplains, is necessary when enlcu]aCing Che height ~f the dikes
protecting the canal.
'I~~e I~ydrological investigations carried out by the Hydrometeornlogicnl Ser-
vic~ in lakes and reservotrs ~s a rul~ include observation~ c~f. waves. 5ucf~
ob~erv~~ttons nre not being made on f~nodplaina inund~t~d ~C t~Lgh water.
As ~ result of l~ck of field daCa r~nd experimental data until now there ar.e
i~o retiable procedures ~nd methods for compuCing the tieight ~f wind waves ~n
an inundaled floodplain. Most frequently for this purpoHe ypF~rtalists use
methods developed for takes and reservoirs, especially~the A. P. f3rasl~~vykty
method [5].
In order to determine the computed height of wind wavex on an inundated
ftoodplain it is most acceptable to use the merliods develrned at the St~+t~
Hydrological Institute [3, Appendix VI~. In selectin~ the c~mputed wave
heiAht an expression is derived directly t~~T� the probal~ilt~v nf w:?vc' I~e~F~~~.
tn computations by this meti~od it is necessnry to have reFime st~ct~a:~tic cl~nr-
ncteristics of the factors determining ~rind waves curv~s of tiic probat~iltty
or Erequency oE recurrence of wind velocity F?t~d etie same rl~nract~ristics f~r
the water level.
128
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t~c~K nt~rlc;rnt, tts~. c~tvt,v
~1~~ ElydrdingiCn]. In~CiCuC~ h~~ ~rdpo~pd n~imp~ifi~d nnd b de~~1.].e~l m~Chnd
~or ~onsCrucCing Cha wnv~ hei~he prob~Uilltiy nurv~. Th~ ~impl~fi~d compuen-
tiott method dn~~ nne ~n~ure nbtiaining pr~ai~~ regultg in tih~ ragidn nf 1nw
probab~.l3ti~~. Tn order e~ p1oC ~ prob~bili~y curv~ i~ i.~ nece~ggry Cn hnve
cpnside~~ble mnteri~l dv~r a ldng ~b~~rvnridn p~riad. Th~ d~e~il~d m~~hod
f~ ba~~d on u~p ~f rrdUf~btl3ty den~iCy curve~ for wind v~lnnieia~ and 1ev~1
po~itinn~.
Hnw~v~r, the meehods for CompuCing wind wav~g in nn inunda~ed znn~, prnpogQd
by the SC~Ce HydrnlogiCnl IngCieuti~, ~hnuld b~ imprnved for ehe purpo~~ of
eheir g3mplific~Cion.
In ehe liydroingical validntion of the plgn for g~can~l on a flnndplain ir
i~ neceggary to have det~il~d ch~racteristica of the river ice reg~me, ehe
i~e rp$im~ nn the floodplain and ar th~ ~ource feeding Ch~ cannl. ~or g
river ~inwing ne~r the C~n~l and g source from which Che wAter ig fed inro
ehe can~1 th~ description can be prepared on rhe bggig of n~tiual observ~-
rinns and datg obenined by cnmput~eiong. Wieh resp~ct to river floodpl~ins,
information on their winter regime is ueually lacking. How~ver, on a flood-
plgin, g considerable part nf which ie nccupied by n c~na1 gnd iCS dikes,
dangerous hydrological phenomena can occur which must noe be overlooked
- when planning canals here.
In invegtigating the ice-thermal regime o� a pro~ecCed can~l use is made of
nbaervaeional daea from the Hydrometeorological Service network and the re-
sults nf an analysis of data on the winter op~ration of exieting canalg.
Use is also made o� ~ theoretical comput~tion methnd for determining dif-
Eerent elpments of ehe winter regime (derermination of the getCing-in of
ice, thickness uf the ice cover, slush formation, eCC.). As a result it ig
possible to clarify the thermal and ice regimes of the canal and poesible
ice difficuities and measures are laid out for eliminating them and en~uring
normal operation of Che structure under winter conditiona.
Z'he going-ouC of Che ice in spring on n floodplain occupied by n canal gnd
protective dikes can be classified as a dangerous hydrological phenomenon.
However, for our lowl.nnd rivers the going-out of Che ice in spring occurs
in the channel. It ig Cherefore usually assumed that it can inflict damage
only to structure~ situated i.n the main channel of the river, where when
Chere are high levels, and accordingly, n great current velocity, the cur-
rents have a maximum desCructive force. However, provieion must be made
for the possibility of damage to atr~Ctures by ice forming directly on
tt~e floodplain itaelf, on which high waCers can be formed during winter.
This is characteristic for rivers in the southern regions of the country.
AC ordi~ary high warer the floodplain is flooded for a relatively short per-
iod. liowever, cases have been noted when in winter, as a result of thaws and
rains, the flood~lain will be inundated for a long time. Wc obaerved such a
high winter water on the Severtskiy Donets River at Mayaki village in Donets-
kuya Oblast [1). As a regult of thawa and rains the river flaodplain was in-
undated for u period of two months. Then th~re was a drop in air temperature
129 _
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I~'OC~ U~'~'ICTAL I15~ C1Nl~Y
~ind nn ice anv~r with ~ eliickn~~~ up t~ ?U c?u w3s [orm~�J tt~~ ~.l~~dplai~?.
nuring mov~m~nrg rha i~~ :Ln~1.i~r~d ~nnbid~r~bl~ dam~~u on tlie supportg ~E
~1~~eric ernn~mi~~ion ~nd Crnnmunic~e~.on lines ~ieuaCf~d here.
In th~ h~~nning nf c:~nalg ie ig n~cpg~nry rn C~ke inr~ ~r.c:oun~ ~he ir~
Lc~f~d~~ ~:~n sCxucf:ures an the fid~anin~.~, (b j. tn c:nmputing ~h~~n it ia n~ce~-
$~ry Cn kt~nw rh~ ic~ ehinkneg~. The fnlldwing two ~a~~~ ~an be con~id~r~d:
1. Itiv~rg wieh ~rn~rgpn~~ of ~h~ iC~ nnro rh~ flnudpl~in. 'The gning-out ~f
eh~ ice in ~pring cninCides wi_th fldndp]~in ic~und~Ci.on. Ia thig c~ge eh~
ice is curried frdm eh~ riv~r onCn th~ floodplnin und ehe iCe Chickn~s~ ig
determined by Che Cnndirinn~ of itg acc:retion in Ch~: rivers; cc~mput+~ei~n~ ,
of ice ~hicknega gr~ mnd~ usin~ ehe formuing ~cnployPd for rivers.
2. Th~ ic~ go~g nue on eh~ floodplgin ie~elf. ~'or computin~ the fl~e thick-
negg it is poggibl~ tn use formul~s d~rived fnr r~gervdirs bec~u~~ fl~ndplnins
Can be reggrded gs water bndi~s with a w~ak flowehrou~h.
Wh~n lakeg are presenr it ig necesgnry tio e~ke int~ xanounC the png~ibility
of formarion of drifting ice fields.
The dimen~ions ~f ehe floeg and their tt~ickness :.r~ Jatcc,i,t.~1~d F~y clirect
nbgerv~tion~ in the field, by analogy or by compueations.
On lc~w ~~ndy flnodplnins the ice cnn be carr.F~.i ~~t~~.~ ~he.:: th+~ ciu~~~ ~hcn
the t~:~ i~ going nut nnd it is piled up again:;t che L,.lofic oti ~hc prntec-
tivc dikes. A d~gtructivic effect an the slop~~ uC chu ~lkc~ is al~o ~:xcrCtd
bv ehe ice cover fr.eeztng to eh~m.
In this article we have only discussed a sma11 fracGion aE Lt?e l~ydrologi~ai
_ phetiiomena which musC be taken into account wi~an ~~lecting the rour.e f or c~
c~nal on a floodplain. In the future, taking into f1CCOUtIL th~ requirements
of proEessional planners, it is necessary ta de:velop r~etl~o~s f.ar comput Lng
the ho?�izontal deformationa uf river chnnnel:~ For. cl1 EC~~fr?:t cvp~~ ~E meunJer-
ing. It is ~lso necessary Co develop a mettwd Cur cumput:ng tiie depth of in-�
undation oE the floodplain duri.ng high water:? uncl L1~~uJ w~t~rt~ uf dif f~r~nt
probgbility. The dimensinn~ df protective dikes cannot L~ ~omputed wi~}~o~t
having such data.
BIBLIOGRAPNY -
1. Plashchev, A. V., "Damap,e of Structure~ b~ rc~: nn a}tiver ~loodplnin,"
M~TEOROLOGIYA t GIUROLOGIYA (Meteorology an~i Eiydrol~~gy), No 2, 1958.
2. popov, I. V., DEFORMATSII RECHNYKH RUS~L I GIDRUTEKHt~ICHESKOYE STROI-
'ftiL'5TV0 (Deformation~ of River Channels and Hydtau'.!c Construction),
i.eningrad, Cidrometeoizdat, 1969, 328 pages.
3. ~iT:KOMENDAT5II PO UCE1~'TU RUSLOVOGO PROTSi~SSA I~Ri PROYCKTIROVANII L~P
(Recommendationa ~n Allowance for the (,1i~~une1 N~~r~~.s !:i E'l~n:iin~;
Transmission Lines), Leningrad, Gidrometeoizdat, 1913, 180 pages.
130
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i~dk O1~[~lf:fAl., l~tii~; ONLY
4. ~Cd~.~berg, V., "Wnyg Cd b~er.ec~ge tihQ Cd~e nf Cngin~~ring Compl~x~~
for ~nCerb~gin 5hi~ting nr ItunnfE," pltdBL~MY OKHI2ANY T ISPbL'ZOVANIYA
VOn (Prnbl~m~ in Pr~~~rving and U~ing 1d7~~zs), No 3, rp 195-199, 1973.
5. `~~KHNICH~SKIY~ USLOVIYf1 b1'R~i)CLCN~YA VOLNOVYKII V(1~DCYSTVIY NA MORSK~YC I
~CHNYY~ SOOttUZHCNIYA ~ ~CRCGA (`T~chniC~1 Sp~cifi~aCionB fnr Detierm~n-
ing Wav~ ~ff~crg dn S~n gnd Riv~r SCruceur~e ~nd Sh~re~), SN-92-60,
Mn~cnw, Gng~rr~yizd~e, 1960, 1'32 pgges.
6. UKAZANIYA p0 dpIt~U~L~NIYU L~UOVYKH NAGItUZOK NA ItCCHNYY~ SOOItUZHENIYA
(In~Cructions nn Uetermining Ice Louds on Itiv~r Structur~~), SN ~6-
66, Gos~Croy SS5R, Mogaow, SCroyizdnt, 1967.
131
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I~OIt 0~'I~'ICYAL USL ONLY.
UDC 556.166:627.81
THE ANDREYEV FORMUL~\ FOR TAKING INTO ACCOUNT TH~ ACCUMULATION OF INFLOW
IN CALCULAT?NG WATER DISCHAltGE PIPES
M~oscow METEOROLOGIYA I GIDROLOGIYA in Ftussian No 4, Apr 79 pp 105-107
[Article by Candidate of Technical Sniences L. G. Rabukhin, Volgograd Civi].
Engineering InstituCe, submiCted for public~tlon 5 June ].978j
AbstracC: On the basis of the res~tlts of co~n-
putations made using the war.er balance equr~~
Cion the author gives an analysis of accuracy
and Che field oF applicabiliCy of the 0. V.
Andreyev formula, uaed for taking intn ac-
count the influence of accumulnr.ion of. inf.]_ow
in the cASe o� curvilinear hydrograpi~s. It was
possible to determine the values of Che c~ef-
ficienes making it possible ~o use this formula
for computations of regulation of r~~noff in the
case of hydrographs constructed in accordance
with the INSTRUG"TIONS ON DETERMINING COMPUTL~D
~IYDROLOGICAL CHARACTERISTICS SN 435-72.
[Text] 0. V. Andreyev (1], using data from r.c~mputations for r.onstrucCing hy-
drographs and determining the openings in sCructures, with accumul~Cion tak-
en inCu accounC, work done by A. A. Kurganovich at thc Kiev ili~h~~*ay Insti-
Cute, obtained the dependence ~ ~
9m = Q,n - U,7 1~/,~
(1)
where qm is the maximum water discharge pass.iiig thraugh the structure, Qm
is the maximum water d~scharge f lowing in fr.c~m the basin., Vm is the maximum
water volume accumulated in the pond-reservoi.r, W is the runoff volume.
The ordinates of the inflow hydrographs for six time intervals were computed
by A. A. Kurganovich on an electranic computer usin~ the Equation for Che
balance of runoff volumes.
In Che derivation of formula (1) 0. V. Andreyev, on the basis of daCa from
A. A. Kurganovich, established ([1], p 27) ChaC with the relationship qm/Qm >
1/3 the triangular hydrograph of water inflow to the structure, introduced
132
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~'Ok Uf~~tCtA(, tJSf. ONLY
into ehe computariong, doe~ noe correspond to ch~ entire runnff vdl~m~, but
unly tcs 0.7 W.
Tdble 1
Vnlu~~ of thc k C~~fEi~ient
npN tpyf,e AttaMetpb~ d; ,M ~~p~~C
_ _ SNl4~I~H
~,n I t,7;, I k
0,3 o,;u o.~n o,~s o,~3 o,7a
0,6 0,8~ U,BG O,h~ 0,88 O,g7
1,5 O,~:f O.H9 O,ib O,9t 0,~0
K~Yi 7,G U,J1 O,S)2 O,~J~ O,y3 0,97
1. With pip~� hevin~ diameter d, m
2. N~nn vnlueH
k
2
`t
O,d
C,6
p r,, ! J,G t,ti
Fi~. 1. Uependencc of the k coefficient on ehe inflow hydrogrnph fnrro coef-
fici~nt ~l. 1) wieh curv~ of dependence of volume of pend~rQServoir on depth
of type V1; 2) with curve of depend~nc:e of volume of pond-reg~rvoir on depth
oE type V2,
The process of accumulaCion of a high water is influenced to a cons~derable
extent by the fnrm of the inflow hydrograph. Hccording to the IN51'RUCTION5
ON UETCIZMLt~ING CO;~'UTED HYDROLOGICAL CfiARACT2Ri5TIC5, Clie form of the inflow
hydro~rr~ph is takun fror~toodels of ob~erved ltigh and flood waters (roost di~-
advant~7geo~s for operatior~ nf pl~nned atrucCurer~) or from a gtnndard equation
((5j, ~ection 4.41). Ti~e configura~ion nf tli~ hydrngraph is char~cterized by
the hydrogr.~ph forra coefficie:~t ~ or the asymroetry coefficient kgn. The 71
and kga values are gi.ven in editions o: t}~e mnnograph RESURSY F'OVERK1iNOSTtVYKH
- VQD S5SR (5urface Water Reyources of the US5R}.
T'he 0. V. Mdreyev foraula (1) is frequently cited in the lit~rature ~2, 4 and
elsewhereJ and is used in planning. (In (1, 2 atid 4J different leCter nota-
ei,,ns are used: for exar~ple, in ~1J ~h~ qm value is denoted Qg and the W
parameter is designgted Wst.J It is therefore icaportant to know which ef the
types nf hydrographs crnatructed in accordance with Lhe INSTRJCTIONS (5]
corre~po~.~s to this formula. For clnrification of thi~ problem we uaed the
results of compuCations of round pipes, taking accumulation into nr.count,
whtch we made usin~ :he water balance equ~tiQn 7t Che Valogograd Civil En-
F;ineering Institute on an "Odra-1204" electronic ca,nputer. The camputations
133
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, ~
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t~'Cltt UN~'IC;[AL Uyl. (1NLY
wer~ m~dp uging diff~r~ne vglueg of the m~ximum inflduing di~~harg~g Q~,
dur~einn nf infldw T, pipp diam~eer~ d, r~gitn~~ ~f uae~r mov~m~nt in pip~e
uiehd~e ~ h~~d, w:th p~rti~1 ~nd fu11 h~~d~, ~nd thre~ ~y~~~ af cutv~~ ~E
the dep~nd~nce c~f ~nd vdlum~ V dn d~peh tfis V~ ~~~3a N~, VZ ~ 4600 Hy~2,
V~ ~ 500n N~ aith indi~~g nf ~urvntur~ nf elt~ vnium~ eurv~ ~qu~1 tn
U.3~5, b.3x5 ~r~d b.25 rp~peceively. 'Che ~2 v~iu~ r~pr~~~ntg th~ raein of
the gren~e~t d~gr~e nf c:urv~ture of eh~ v~lume curve V~ ~(t1) in th~ in~~er-
vgl b~twe~n th~ initi~i and m~ximum W~tpr hdrixnn~ in th~ pnnd-r~~hrvoir ed
ehe Jiff~ren~e in th~ rendin~s n~ the~e h~rixdn~.
`Ct~e Coraputntidn~ ~?ere made fdr hydr~graph~ With furm ~~~ffi~i~ntg ~1 from
0.~ to 2.6, which t