JPRS ID: 8653 USSR REPORT METEORLOGY AND HYDROLOGY

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L!
M~TEORQLaQY AND HYDROl4QY

ii SEPTEM6ER i9~9 N0. 6, JUNE i9T9 i OF 2
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1~(la UI~l~iC'IAt. US~ hNLY
JPRS L/8653 =
11 September 1979
l,1SSR R~e ort
. p
METEOROLOGY AND HYDROLOGY -
N,o. 6, June 1979 ~
:
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ro~ oF'~'IC~AL US~ UNLY
JPItS L/8653
1J. 5ep~~mber ].9'79
USSR R~PORT
METEOROLOGY AND HYDROLOGY
No. 6, Jtzne 1979
5e~.ected ar~ioles �rom ~he Russian-Language ~ournal Ni~TEOROX,OGZYA
I GIDROLOGTY.A, Mosoow.
CON7~NTS PAGE
Nonadiab~tic rtodel of Shorr-~tange Weather Forecasting
(V. P. Dymnikov, A. V. Ishimova) 1
~ Ccmputatiun of the Index of Forecasting Accuracy in an 'Ocean-
Atmosphere' System Model With a Grent Number of Degrees of
Freedom
(V. A. Ryasin) 15
Hydrodynamic Three-Level Model of General Circulat-ion of the Atmosphere
(V. P. Meleshko, et al.) 22
Energy Characteristics of the Winter Warming of 1976/1977
(I. V. Bugayeva, et al.) 36
~ Investigation of the Background Content ot Polvcyclic Aromatic
Hydrocarbons P~tesent in Air
(F. Ya. Rovinskiy, er al.) 47
_ Relationshin Between Vertical Movements in the Lower Troposphere and
[he Characteristics of Steady Precipitation
(V. S. Antonov) 54
Optical Density cf Cumulus Clouds in the Temperate Latitudes of ~he
European USSR 1nd the Tropical Zone of the Atlantic
(R. G. Ticnanovskaya) 63
`umerical Method for Solving the Problem of Free Oscillations of the
World Oc:ean in a Barotrapic Approximation
(A. V. Protasov) 70
~ - a - [III - USSR - 33 S& T FOUO]
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~
~ot~ ot~rrc:r.nt, crsc o~rt~Y
_ CON'1'L:NTS (Coneinuedl Pa~e
Wr~Crr I~xchan~;r~~ 13eCwcen Cl~e S~~ of Azov and the Blaclc Sea Wirh
(lprr~7ric~n o� ~ Rc~gul~Ci.ng 5truceure in Kerch SCrait
(.C. A. Shlygin) 82
memperaCure-SCr~eiFiE~d CurrettC in a Water Body Wieh Througtt Flow -
(V. I. Kvon) 92
Method for Computing WaCer Discharges
S. Khcrsonskiy) lU0
' Influencc ot Afr Temperature on Che Yield of Peppers
(L. Ye. Bor.hko) 1.07
5tatistical Srructure of the Field of Phenologicel Phenomena
, for Corn in Bulgaria
(Ye. Khershkovich, et al.) l14
Possibility of Resonance Excitation of Large-Scale Waves
, (E1. I. Ivanovskiy, A. A. Krivolutskiy) 123
Unusual Occurrenca of a Winter Thunderstorm in Alma-Ata
(R. 5. Golubov, A. A. Skakov) 128
Spectroscopic Method for Determining Atmospheric C~2 Content
(R. M. Akimenko, et al.) 131
Atmospheric InsCability
(N. P. Shakina) . 138
Operational System for Numerical Weather Analysis and Forecasting
at thc United States National Meteorological Center
(V. A. Antsypovict~, S. 0. Krick~ak) 15'1
Review of Monograph 'Atlas Okeanov. T. II. Atlanticheskiy I
Indiyskiy Okeany' (Atlns of the Oceans. Volume II. Atlantic
and Indian Oceans), Leningrad, Voyenno-Morskoy Flot SSSR,
1977 ,
(B. L. Yedskiy) 1G3
Review of Monograph by G. I. Shvets Entitled 'Mnogovekovaya
Izmenchivost' Stoka Dnepra' (Vnrilbility of Runoff of the
Dnepr Over the Centuries), Leningrad, Gidrometeoizdat,
1978, 84 Pages
(P. F. Vishnevskiy) 165
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~OR O~T~'ICTAL US~ ONLY
CONTCN'I'5 (ConCinued) pg~~
Confcrences, MeeCings and Seminars
(V. N. zAkharnv, eC al.) 168
News ~rom Abroad `
(B. T. 5ilkin) 180
Obiruary of Vas~~liy Vladimirovich Shuleykin (1895-1979) 182
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~on o~~zcr~., us~ orn.Y
.
PUBLICATION DATA
~nglish tiCle ~ MIsTEOROLOGY AND HYllROLOGY
No 6, Jun 79
Russiau title : METEOROLOGIYA I GIDROLOGIYA
Author (s) ; V. P. Dymnikov, A. V. Ishimova et al.
Editor (s) . Ye. I. Tolstikov
I
Publishing I~ouse : GIDROMETEOIZDAT
Place of Publication : Moscow
' Date of Publication : 1979 _
Signed to press ' : 25 May 79
~ , .
Copies : 3930
COPYRIGHT ~ "Meteorologiya i gidrologiya,"
1979
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UDC 551.509.313
NONADZABATIC MODEL OF SHORT-RANG~ WEA'i?;Elt FORECASTING
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 6, Jun 79 pp 5-14
(Article by Candidate of Physical and Mathematical Sciences V. P. Dymnikov
and P.. V. Ishimova, CompuCaCion Center Siberian Department USSR Academy of
Sciences and WesC Siberian Regional Hydrometeorological InstituCe, submitt- '
ed fnr publication 4 August 1978]
- AbstracC: The article gives a description of
a nonadiabatic weaCher forecasting model for
a broad territory on the basis of the full
equations of hydrothermodynamics for a per-
iod of 72 hours in advance. For solving the
transfer Aquations use is made o!: difference
schemcs of the fourth order of accuracy with -
a smoothing operator, also of the fourth or-
der. Phase influxes are taken into account
in the heat influx equation. The boundary ~
layer and orography are parameterized. The
fields ~f geopotential, temperature, wind~ _
dew point spread and sCeady precipitation
are precomputed. The results of numerical -
experiments for predicting Ghe �ields of
geopotential, dew point spread and steady
precipitation are given.
[Text] Introduction. The weather forecasting mode'1 examined in this study
is a natural development of the model described in [6J.
~ Before proceeding to a detailed exposition of the equations for the model
and the results of numerical ex-~eriments we will briefly discuss those
changes and additions which have been introduced in this version of the
r,~odel. We have introduced a description of the planetary boundary layer
and orography, computed the fields of humidity and steady precipitation,
taken into account the phase influxes of heat, and a Lso have chan~ed the
method for solving the transfer equation. The experience of work with a
nonadiabatic short-range weather forecasting model, used in the routine
practice of the West Siberian Regional Hydrometeorologfcal Insritute,
1
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1~Oit O~F'ICIAL U5E 4NLY
ind:Lc.~Ced Ch~~t Che use of schemes with ~ second order of ~ccuracy fnr
s~~acc, variables for ~~lving 11umi.diCy ~ransfer equations intiroduces large
errors (both phase and ~~xmplitude errors) as a result of the si~ntficane
clonmonotonictCy of tihese schemes and the greAt spatial gradients of humid�Lty
~te1d3. 'The u3e of a special sCructure of Che humidity transfer equat3ons
[3] only parCially elimi.natea Chis problem. Therefore, in this study we
huve changed to schemes with a fnurCh order of accuracy for space vari-
- abi.es in the Cran3fer equa~ions with a smooth:Lng operator a13o r~f Che ~
fnurC}i order [13]. These numerical experimentis with madel initial c~n-
dittons indlcuted that this echeme, alChough iC does not belong to a class
nf schemes with zn even exponen~ (7], is one of the be3C for describing
generalized disconCinuoua soluttons. Since a fourth-ord.er scheme in smoc,th
solutions in essence has a lesser phase error Chan a secund-order scheme;,
iC is also used in a mode]. for solution of Che equations f.or trans�er of
] hear and moment of momentum. '1'he above-mentioned operaCional model [5]
uses a special sCructure of the equations [3] for comp~iting the humidity
and precipitation fields; this requires direct compuCations of vereical
currents in the atmosphere far computing Che phase transitions of moisture.
It is known that the problem of computing vertical currents in the atmo-
sphere is very complex and as yet has not been completely solved. There-
fore, .tn this study we carried out para11e1 comparative computations of
tt~e humidiCy and precipitation fields using the equations proposed in [3]
and the generally accepted equations [11].
~ In conclusion we will discuss the pr.obLem of introducing of orographic non-
uniformities of the earth's surface into numerical weaCher forecasting moci-
els. If one speaks of t'ne ~oii~t description of the planetary boundary layer
and orography, this problem has not yet been solved. Moreover, we feel it
has not even been clearly formulated. Along these lines the source [2J is
rather interesting; we have used these results in our model.
Formulation of Problem
We will examine a baroclinic nonadiabatic model of the atmosphere in a ,
quasistatic approximation in the coordinate system x, y, p in a stereo-
graphic pro~ection. The equat;ons of the model, first reduced to a semi-
divergent form, read as follows
du 1 : du , 1 du 1 d u 1 dm~au
Ot + Y m u dx ' 1 m- oy r 2- dp + 2' dz t
1 dm=uu 1 du t dr (11
+ 2 oy 2 dv ~~'v--g dz'
, at, ~ z, a~, ~ a~ ~ am~~~t~ (2)
ar 2 m=u d.r m Z d~ t 1� dp T 2 dz +
1 dM2vv t dut dz
dy -I- 2 dP - 1, u=- g dy ,
2
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roR o~rrcr~. us~ ornY
BT 1 dT 1 dm~ uT +
~~i 1 11t`ll dY l/1~~v ~y 1" dp 2 dX
l a tl`'7~ ~ l an~ - mT ~~a am + v dy
Y
ad' ~ )
p~ ~in T) T= ~p ~ 3
~ r au aU 1 a o~
m l a.~ + tly dp 4
ds R T
~ dp pg ~ ~5)
Ph)
where u, v, 1: are the pro~ections of the velocity vector relative to the
axes x, y, p;
1 sln GO�
m - i + sin ~p ;
~ is the geographic latitude of the particular point of the grid; T, z
are the deviations of temperature and alritude of the isobaric surface
from their standard values; Y, T are the standard values of the tempera-
ture gradient (y =-a T/ ~ z) and temperature; ya is the dry adiabatic
temperature gradient; E ph are the heat influxes due to Che phase trans-
itions of moisture; cp is the specific heat capacity at a constant pres-
sure ' ~ ,
lt - 1+ m(u tlX ay '
,
~ where Q, is the Coriolis parameter.
We note that the origin of coordinates for our grid is situated in the upper
left corner.
In describing transfer and evolution of the humidity fields in the model
we will use two systems of equations, one of which is formulated in terms
of the combination of the deficiC of specific humidity and liquid-water '
content [3]; the second describes the evolution of specific humidity (for
example, see [11])
d~r 2 m:u m~v d~U + I; d~ 1 dm~u 4~ ( 5)
- dY 2 up ~ 2 dx +
3
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1 dm~~ ~A l d~b r dm dm 1 y r ~ d9m 1
-1- -d -I' i o - nt d? l u dX ~l dy ~ -;1 X
[UA = ma] XCL ~7a`7ua) p~ t_'$~, ~6)
dq~ I dqi , 1 dm~ uq
dd~ 1 nrtt aax i"r"b ~+-r-i T ap `2 dz 't-
a,~
+ 1 dm~ uq~ t 1 d ti qi _ m9i (u dz dy 1__,
wllere 'l dy 2 dP ` f
~ = 9~ 9m + (l c aar ) 9~~ ~8~
P
ql is specific humidity, q~ is maximum speci�ic hum3.dity, q2 is specific
water content, L:ts the specific heat of conden~ation, is the moist
adiabatic temperacure gradient, ~ is a function describing the proce~s
of falling of precipitation, M is the condensation rate. In computin~ the
M value it is assumed in equation (7) that the specific humidity in the
clouds is equal to Che saturating humidity and the condensation process
begins under the condition r= ql/q~ > l.
We will call the first model of computation of Che humidity field:~ model
A, and the second model B. The following boundary conditions are set on
the lateral boundaries : dT _ ds _ d~ _ dq, _ ~
vt - dr " dr - dc
In order to satisfy the integral laws of energy conservation far u, v,
~ we will use the con~iition u= v='G= 0 on the lateral boundaries of
tt~e integration region ~1]. At the upper boundary of the atmo3phere (in
our case at the level 200 mb) we set the condition ~ T/ a F= 0. As
the boundary condition at the lower boundar,y of the atmosphere we use w
- Wtr Woro> Where w is the vertical component of the velocity vector
in the coordinate sysrem x, y, z. For computing wtr we used a model oF
the boundary layer taken from [9~. The equation for the model has the
form t d:y 1 d:X
`iP1ip - i vx T dy ~ ~ 9~
Ty = u: sin (;%s - z),
where
~ ~c r= u= cos lB~ - zt,
u* is dynac;iic velocity, ~:~g is the�angle of the geostrophic wind at the
altitude of the atmospheric boundary layer, for which an altitude of 850
mb is used in the particular model,OL is the angle of wind rotation at
t':te earth's surface.
' The solution is obtained in the form of ~m iversal dependences on the par-
ameters Roa ~ , ~ , where
4
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rZ~) " f~, ~ $ (Yn/7 Y) ~
~ G",~~ ~ G- ustvg.
Here z0 is the roughness parameter, ~ is the convection parameCer, is ~
ehe temperature gradient at the altitude 850 mb; Q~ is the value of the
turbulent heat flux at the earth's surface. ~
The orographic componenC of vertical velocity at the upper boundary of
the boundary laye~ 3s represenCed in the forro of the sum of the two com-
ponents
Wor~ - Woro~ woro2~ (10) ~
where -
at a;~
. zc~ov~ = m' u~X" -F- m2 v dy , .
[op = oro]
` ~ is the elevation of the earth's surface above sea level. The expression
for worol is widely accepted and reflects the fact of nonpassage of air
through the earth's.surface. A more comple~c expression is for woro2~ Which
arises as. a result of nonlineariCy of the processes in the boundary layers
over an orographically inhomogeneous surface. Adhering to [2], for woro2
we use the expression ~
' woPr = a ~ uR ~ z~E~,
[op = oro] where a ^-104 sec.
In the function 7,p used in the model there is filtering out of waves whose
length is less than three grid intervals.
`
Solution Method
The problem (1)-(7) is solved by the splitting method. In the first stage
tliere is solution of a system of equations describing the transfer of the
~neCeorological fields u, v~ T, ql along the trajectories:
d I d 1 d Y 1~1~n= u u 1 dm= v�_ 0, (11)
ot + 2 m_ u dx + 2 m_ v dv + l dx + l d~,
Here
~ _ + u, v, T� qi ) �
The two-dimensional equation (11) is in turn split into two one-dimensional
equations which are approximated using finite-difference schemes with a
fourth orde~~ of accuracy for space variables and a Crank-Nicholson schem~
for time. The semidivergent form of the equations of motion (11) m2kes it
possible to construct finite-difference schemes retaining an obliquely synr
metric structure, which ensures an absolute stability of the schemes in
spectral norms. The difference scheme for the one-dimensional transfer equa-
tion has the f~rm:
S
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FOR 02~~zci~ us~ arnY
n~ t n 1
~k o ~r�k i Du (h) - ~ Dn h)} ~Pn+ 4 = E h'~ ~D+~-)~ Y"~ ~ (12)
where
Do ~h) ~ _ -~~`+'r ~R-t ~
2h
po h) 4 = ~R+~ - ~,r_s >
4h
~k-H1 -~fk
D+~ h ,
D_ ~ _ ~k - ~,r_~ ,
h '
~ t
~a-}- d = 2 ('Pa-}- 1 ~n,�
The term present on the right-hand side of (12) is necessary, as was noCed
in the introduciion, in order for the difference scheme to be close Co
monotonic. The ~ parameter is selected not greaCer than h so that the gen-
eral order of the scheme will be fourth. The system of finite-difference
equations with a five-diagonal matrix relative to ~he unknowns cp n+ 1/2~
obtained by solution of the equations (12), is inverCed using five-point
fitting.
The equations describing the problem in the adaptation stage are app:oximat-
ed by difference schemes with a second order of accuracy for the space and
time variables and have the following form:
un+~ - lln 1 n-~,1 n~f- 1 1 zk-i�j-1 zR'~'1
t 2 1~ ~v y 2 g C 2jh
(13)
n~- t n-}- 1
+ zM+l l -Zk_~ .
~ 'l h '
, Y /
v"+~-v~'+ l t
- 01 - 2 !t ~u"+~ u~`+ _ ~14~
R-11 n-~I tR+ ~ -:n` 1
~ zr-~1 -Zl ~~t i-i-1 !-1 :
- 2 g 2 h + 2 h ' ~15~
k~ TR-~.~ - kZ T"+ ~7~ 7) RT a_ E~b
PY T rp ,
6
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~dtt OI~~'~CfAt U5~ dNLY
zT
r 1/k,~1 " f1A . I ~~J+ t` t~t- I �r ~ t ~ i!
!n~ ~ - Y h_ ~ 1 h ~ ~p~ " ~~6~
. i~'r i I
~ `
t t~ i ~ 17 ) ~
_,pi~~ p'rlg~
wh~re ,
:R'~ ; ~ ~ : 2 ~
� ~ ~ t
ki r I 1- 1 m J t(u dx dY ~
l ,
kz ~ a r~ 1!?t ~ t(ll d~ dm 11,
1 !J
'I'he :~ystem of equntions (13)-(17), ~v in (10~, is r~duced tn u gystem of
finiee-di~ference equ~tions nf att elli.ptical Cype relaeive tn the g~dpot~n-
ti~71 trend ~
o Z"~'~ ~ 2"'~~ ~ ~
~nd is sdlved by the biorthvgonalizneion meehod.
F'or describing the evolution of the hLmidiCy fields in the ~sgimil~tion
seage, �or mod~l A we us~d th~ scheme
~ ~
fi~~ 1
1 ~ ~ ~ )
~ ~ - - 1 a `~~dT ) [ ~ ( 7a 7., ) + ~ X 18
3 ~
X RT -~~t ~l.
P8 ~
'Che vertical currents necessary for computing ~ in equation (18) are com-
puted from the heat influx equation (15). The accur~cy in predicting the
humidity ficlds is determined to a substantial degree by the accuracy in
computing the systema Cic vertical currents L, which constitute one of
the principal dynamic factors determining cloud formation processes in
the ~tmosphere. A r.omparison of the vertical movements, compuCed from
(15), with t}~e currents determined using Che continuity equation, indicated
tt~at the regions of ascending and descending movemer~ts ~grce rather Well
with one another; Chere is a difference only in v~icie. For predicting pr~-
cipitation, as in [5j, we used Che following scheme for computing the
moisture accumulating in the layer, wliir,ii, rezchin;, .i tl~resliold valuc q2,
falls into the lower-lying layer. In tlie second scheme (B) the computaCions
of precipitation were made under.the condition r a ql/q~ > 1. The computa-
tion scheme has the form ~ ~
T"+~ - T~+ 1 ~ ~ (9~t~ ` 9i+ ~ (19)
co ~
9;'~ = 9?~ ( T~+~
7
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~Ott d~~IC~AL US~ ONLY ~
~
The gystem df ~qu~tinn~ (lg) ig ~olved by ~h~ iterarinn m~eh~d.
Num~riC~1 Cxp~rim~neg
`Cht numeri~~l ~xperiments w~re c~rried due for n fiv~-1~ve1 mod~l in ~ r~~-
tr~ngul~r grid m~~yuring 3~ x~3 wieh gn i.n~~rv~l nf 37S km wi~h ie~ c~neer
~t Novo~ibirgk. Ag tlte initi~l d~C~ we endk th~ g~~pnti~neigl ~nd d~w pnine
~pr~nd v~1u~g dbr~in~d ~s g regulti nf nb~eeeive ~n~1y~i.~ of m~t~droidgiG~l
fields under the progrsm d~velop~d by eh~ US5it Hydrnm~t~nroldgic~l C~ne~r
C1]. The valuea nf the funceions u, v, x~r~ der~rmin~ed ~t ~h~ ~C~nd~rd levels
1000, gSO, 700, 5d0, 300 mb; the q~ v~iu~g ~re determin~d ~e in-
eermedi~tc 1~v~1g 92~, 775, 60~, 400 mb. Sin~~ no ~y~t~m~~ic m~~~Ure- -
mpn~~ are made far the liquid w~e~r c~ne~n~ in cl~udg, in compuCing th~ in-
iei~l v~1ue~ df ~h~ functinn it ig pn~Cul~t~d eh~r ttt~ ~p~ci.fi~ liquid
w~ter content q~ ~e the initial mament in time ig pqunl en xero. The qu~lity
di the forec~~t w~~g ~v~lu~ted using eh~ r~gult~ of ob~ective ~naly~ig. In
drder tc~ evglu~t~ the qu~liey oE the geopoCgntial f~r~cave use was m~de o~
tlie ugu~l synoptic~st~eisti~gl eh~racterigricg: E ig rhp mean rel~Civ~
error, k is the cnrr~laeian cneffi~i~nt, P i~ th~ probnbl~e guccegg of fore-
cast ~f tr~nd signs:
~
!r ~ ~ ~Tw " tul ( tnp � l~~) !
S a 1 s 1
n ~
~~t~~~=^~
Izl ~
R
~ G( t~R -=o) L. ( top'~' tn~
. , ~ ~
Is 1 (ty.~~ " sei'-' n (~np " fo) R
k- ~ : ~ ~ ~
~
~ (s~R tul ~ ' ~tnp'~ =n)
~_i (:,;.~-:�1-~~t n ~_t (tn~--:~~ ~_i n
1 ~
Nt' N~`
P= R ~
(~K = act(u~l); fip ~ predicted] where N'+'(N') is the number of points ~t
which tt~ere is g correct (incorrect) prediction of the trend sign; the
poin~s at wh ich one of the trends is equal to zero, Whereas the other is
nnt equal to zero, are not included in eitlier N{' or in N'; z~Ct is the ac-
� tu~l height of the isobaric surface at the time for which the forecagt i~
m~de; zpr~d is the predict~d value; zp is the geopotential value at the
initial moment in time; n is the number of points of intergection used in
evaluating the forecast.
In order co evaluate the dew point gpread values we computed the frequency
of recurrence df forec~gting errorg by gradatioas. The evaluation was made
for the territory of the West Siberian region (at 110 points of grid
8
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~d~ ~r~~~~~, u~~ ~cn~r
interseccidn) in ~~t~~nrd~n~~ with the progr~m develdped in [l~j. '~h~ re-
gu1e~ of ehe ~valu~tinn~ ~re gi.ven in Tab1~g 1-5. N denoeeg the numb~r
df !~ieu~einn~ used in computfn~ the evaiu~tidn~~
T~b1~ 1
Me~n ~v~lu~eidn~ df pr~~l tCt~i~t~ df G~npeCpnei~l (~nr F'iv~ L~ve1~ j U~ing eh~
_ ~niei.~l U~~g fnr 1~ Sepeember 1g7S fdr ehe ~ime d0(03)
- - _ Cpn?c nporHOa~, u
~
(:~eWn 48 ~s 17
1 e I k r I ~ I k I o~ e k ~
~ I I
~i 1 0,95 0,~;~ u,~#G ~ t,i8 Q,~#J 0,30` 1,23 tl,~#I d,37
~ , O,Sti 0,~2 0.48 1,07 ~ 0,6(1 tl,~6 I I~[l8 0,~0 0,48
~ U~~~ 1).i0 0,52 I,d2 0.51 ~,34 ~ 1,2U ~,~3 0.37
~ ~ 0,; t 0,72 rl.;i 0,95 I 0,S5 I U,36 I 1,01 U.51 0,45
K~Y :
1. 5Cheme
Z. ~nrec~~t time, hnur~
Table ~
~requen~y nf Itecurren~e af ~rrnrs in predict3on af new pdint Spr~~d Ug-
� ing Initi~l b~t~ fnr 19 S~pt~mber 1975 for ehe Tir~e 00(03) for 24, 48, 72 hrg
~ 3 CpnK npo~NO~a, M
~ 2 24 48 I M
al = -
~ i J ~--3' ( ~--6� I >7' 0-3' ~ ~--G I ~9- ~ 0-3� ~ ~-6' I >7^
~
d ~ E ,3 ? , I ~3 I ~ s~ ~s z
s~ ~a ! o.;; ~ s~ 2 so ~ ~
d~ ~~a ~;~a ~ t':~s i as ~ s s~ ~ to
r! 7b ! 2a I u;; J ~ 2s t 79 ~ 2o t
a~ 5 f j 3 t; { l l 36 ~ tb 41 31 4A
~ ~ ir ~ KO I IH ! 2: 4i ai 6 61 34 5
~ a i tiFi 1 2i ! ~J ~~1~ 31 ~ 2~ 52 30 = 18
i 6~ i a ~ 74 ~ 1~ 3~s :i6 ` 6 i 2 2 4 4
Kf:Y :
1. 5~~rf~7cc, mb
2. 5cheme
3. Time of forecast, hours
`Cuble 1 illustrates the prnb~ble success of rhe forecast of geopotenti~l
on thc b.~~is of initial data for 19 5eptember for the time 00(03) for 24,
4~ and 72 hours in advance u~ing fdur scfienes:
~n adiabatic forecasting scher~e. in Which the tran~fer ~qu~tions are ap-
proxim.tited by finite-difference ~cheme~ vith a second ord~r of accuracy;
9
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b) ~in ndinb~Cic ~ch~me in which ~lie er~nsfer ehu~einn~ ~r~ npprdxim~C~d
by differenGe ~Chem~g with u fdureli drder d~ geGUr~cy;
e) a~on~ldiabatic scheme, the basis ~or wtiich is gcheme (b) with the intrn-
~fucti~n df ~ bdund~ry lgyer and phage h~~t influx~~;
d) ~ch~m~ (C) i~ ~upp~emene~d by e~kin~ intin ~~~oune drdgr~phiC nonuniform-
itieg d~ ehe p~rth'~ gurf~ce.
`~~ble ~~~VpS the frequencies of r~~urr~nc~ df ~rrnrs in prediceing the d~w
pdint ~pr~~d uging twd gChemes:
~ forecrasting gcheme in which eti~ equgtidng fnr ehe eransfer of humidity
fi~ldg ~re ~pprbxim.~ted by finiCe-diff~r~n~~ snh~me~ wiCh n~~~ond order
nf ~ccur~cy;
b) the equ~~eiong fnr Che tr~ngf~r di tiumidiCy fi~lds gr~ gpproxin~Ced by
~Chemeg with ~ fourth ord~r nf gC~ur~cy with ehe gddition nf ~ digsipgtive
e~rm; the gch~me shnws th~C Che frequency of recurrenc~ nf l~rge errorg in
predi~eing eh~ d~w pdint ~pread in ~esence is legs if one usey a schemc
with n fnurCh order nf accuracy.
- 'Table 3
Me~n I:valuxtions of prediction of Ceopotentiul With Allowance for Orogr~phy
(a) ~nd Without Allowance for Orography (b)
i ~ 2 Cporc nporHO3a, w
4 1~~ 24 48 ~
~
Ci t~ N I ~ I k I P N i ` I k I? N( ~ I k P
I
a ~ 0,80 O,G9 0,:~1 4 O,S12 0,62 0,44 3 1~05 0,60 0.33
6 7 U,86 O,til 0,46 ~ I,QO O,~i4 U.40 3 1,18 O,.il 0,28
g~ a 7 0,~0 0,64 U,49 d u,88 0,+?8 0,4~1 3 O,~J U~:~4 0,42
rf 7 0,91 U,faS 0,46 4 I,1~0 0,50 0,34 3 I,1' 0,4ti U.~S
c 7 0.74 0,68 ~1,54 a o,~5 O,a'? 0,~1!? ,3 0,90 0,56 0,4~
6 7 0,82 O,ti3 0.52 4 I,W U,60 n~4:1 3 1,11 0,49 0,45
0 7 0,7U 0,78 0,63 4 O,i4 O,i3 0,;~('i ;3 0,81 U,6,'~ 0,5fi
6 7 11,i5 0,7ti 0.6U ~ 0,8.i 0,7a U.57 ;3 1,0$ 0,6U 0.47
~ a 7 U,67 0.8U 0,53 4 0,76 O,i9 0,61 3 0,80 0,69 0,60
6 i O.iO 0,79 O,SN ~f 0,36 O,i9 U.61 3 U,97 O,ti6 0,5ri
K~1t :
1. 5urf~~ce, tnb
2. prediction time, hours
3. 5cheme
As indicated by Table 3, the inclusion of orography in the ~aodel improves
the qualiryo uf the forecast at the lower l~vels by approximately S-lOX.
Tnble 4 illustrates the quality of predictions of the dew point spread using
tWO gchemes for computing the humidity fields, described in the model of
prediction of rt~teorological elements cited above. The frequency of recurr-
ence of errors ig approximately identical for both schemes. The same can
10
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~
I~'0[t 0~'I'ICIAL USF: ONLY
~
be ~~~Ld nbdue Ch~ zdneg o~ sCe~dy preCipiC~Ciott (I~'ig.
_ 7'ubte 5 givc~ thc m~~n ev~7~.U~C~.dtty nf pr~di.C~~.nn df dew pdinr yt~r~dd fnr
z4, Gg, 7Z hourg in g~cnrd~n~e wi~h ~ch~m~ A. -
Tnb1e 4
Mec~tt ~'requency of ttecurr~nce n~ Crrdrs in ~rediaeidtta of bew pnint Spregd
fer Z4 hnurs U~ing Snhemes A~nd n
a
~i z
c. 4 N -3� �~G
d ~
m
0o K
V
945 A 3 ~ 8'l I 14 ~ 4
77b A a( 7~ I 2U ~ 1
B 3' 78 i'?$ ; I
bpp A ~1 ~ Hi ' 2J ; 4
B I 3 67 ~ 32 ~ I
400 'd ~ ' 6~ ~ :9 ~ ti
tt I 3 ev i~1 ~;i
K~Y :
. 1. 5urface, mb
2. Scheme
Table 5
Mean Frequency of R~currence of Errors in Prediction of Dew Point Spread
for 24, 48, 72 tiours Using Scheme A
~ ~ Cpo~: uporNO~a, K
F
" 24 48 72
y ~ ~
a~ N 0�--~� ~ d--ti' >7� N 0�-3' ~1- 6� ~7' N 0-�3� 4-6� ?i�C
0
i �
'.12:~ ~i 69 2 4 I 5~ GO 2Y 12 I fi ;~0 32 13
i7~ ~ i 0 21 ti 6~ '?~J 6 5 i 0 21 3
Ii0~1 5 R1 :{I ~i ! ~ h0 31 7 5 57 :37 6
d00 :r ~ fi~J 2; ~ ~ ~ 63 2S 'J 5 giJ 32 8
~
KEY:
- 1. 5urface, mb
2. Prediction time, hours
11
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~Ott 0~'F'ICIAL US~ nNLY
~ ~
v
~ ~ ~
,
OMC!f ' ~
~ ~ r
; ~ ~~,~I i'%,'~.1!/~ i~~
, +ceo ~c
/ , ~ , ,
, ~
~i,~.
~
~ , ~
A �A~1A'~ ~ i ~ ~
- I
�
Z
~ a ~
~ \
~ ~
` ,
. r/, ,
, ~ r ` ~ ~ /~/i , 4\ /
~ t ~ :1
~ / ~ ~ t, r�~~ ~ .
~ ~ AAMA�AT ~ 8
- ?ilaal
~ig. 1. predicrinn of zonss of st~ady precipitation for 24 hourg on the basis `
of initial data for 22 January 1978 for the Cime 00(03) hours using schemes
A and B. 1) zone of predicted precipitation, 2) zone of actual precipitation
Summary
Our numerical experiments make it possible to draw only a preliminary con- _
clusion concerning the quality of the prognostic scheme since the numbez
af experiments is inadequate for a st~tistically reliable evaluation of the
result. Nevertheless, some conclusions can be drawn. It can be said with ~
assur~nce that the u3e of special difference schemes with a high order of
accur~cy and close to monotonic ~n essence reduces the number of l~rge
error~ in tl~e predicCion of the dew point spread. A comparison of two mod-
els of prediction of the hua?idity fields did not indicnte significant ad-
vanCages of either one. The factis that in the present version of the
model no opCimizaCion of comput~tion of vertical currents was carried out.
As was elready mentioned above, the zones of vertical currents, computed
from the heat influx equation and from the con~inuity equation, gnd also
from the quasigeostrophic t.S-equation (4], coincide quite well, but their
values differ extremely substanCially. Since it is impossible to say what
vertical currents are closer to the true currents, it is necessary to ad-
,~ust their amplitude relative to a particular prognostic model. If it is
taken into account thae the liquid water content of clouds is .~lso pr~e-
dicted in model A(necessary, for example, for. computing cloud albedo),
preference must be given to this model. xhe r.pproach zo allowance for oro-
graphic nonuniformities of the earth's surfa~~e used in the model requires
12
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~Ott dt~F'ZCIAL U5~ dNLY
~ more c~r.~ful ~n~lysls, p~rticularly from ehe poine of view o~ evnlunting
th~ ~ucce~~ of ~ prcdiCCion of a~~noypheric cyclonic aCtivity. A gep~r~te
p~her wi11 be devoCcd cd ehi~ prnbl~m.
B.[DLIOGtZAPHY
l. Art~nnv~, A. t.., "New V~rigne nf ~ progr~m fdr ttduCine dr3~cei.v~ An~l-~
ysig o~ Ob~eCCive An~ly~ig nf GeopntenCi~~ df Is~b~ric Surf~aes,"
M~~'~;dAOLOCIYA I GIUItOLi~GIYA (Metenrology xnd Hydrology), N~~ g, 1974.
2. Cddev, N., "Influence of Ordgr~phy ~nd Surf~ce ~'ri~eidn on Ch~ngeg in
AtmnsptteriC pr~s~ure," gULGAttiAN G~OPHYSICAL J., Vnl 1, No 2, 5~fia,
1g75.
3. Uymnikdv, V. p., "One ~ormulr~tion of ehe prnblem nf predicting Humid-
ity ~'ipl.ds in *.hp Atmo~phere," IZV. AN 555It, ~IZIKA A'PMOS~~RY (News of
the U55t~ Ac~demy nf Sciencey, physics of the Atmosphere ~nd Ocean),
Vol 7, Nn 12, 1971.
4. bymnikov, V. P., Gusev~, N. V., "Some Methnds fnr Computing Vertic~l
Movements in the ~ree Atmosphere~" TRUbY ZAY.-SIB. RNIGMI (Trunsac-
tion~ of the WesC 5iberi~n Itegiongl Scientific Research NydromeCeor-
alogic~nl Institute), No 14, 1975.
5. byronikov, V. p., et al., "prediceinn of MeCeorologic~l Elem~nCs in n
_ t~estricCed Territory Using ~ull ~quaCions," M~T~OROLOGIYA I GIbROLOG-
IYA~ No 9, 1975.
6. Uymnikov, V. P., Isliimova, A. V., "Adiabatic Model of WeaCher Forecast-
ing Using Full Equations for a Grid in a Stereographic Projection Over
an Extensive Territory," TRUDY zAP.-SIB. RNIGMI, No 25, 1976.
7. 'l,hukov, A. I., "Limiting Th~~orem for bifference Operators," USPEKHI .
MA~'E2IATICtt~SKIKH NAUK (Advances in the Mathematical Sciences), 14, No
3, 1959.
8. ishimnva, A. V., "Adiabntic Madel for Pr~diction of Meteorological Ele-
ments Using ~ull ~quations Over an Extensive Territnry," SBORNIK nOKLAWV
VTOROY V5ESOYUZNOY KON~~RENTSII MOLObYKH UCHENYKH GIbROMETSLUZHBY 5S5R ~
(Collection of Reports of the Second All-Union Conference of Young Sci- ~
entists uf rhe U55R Hydrometeorological Service), Moscow, Gidrometeoiz-
dat, 1977.
9. Lykosov, V. N., Shemetova, G. V., " Allomance for the A:mospheric Bound-
ary Layer in the Short-Range Weather Forecasting Problem," TRUDY ZAP.-
SIB. RNICMI, vo 25, 1976.
10. Marchuk, C. I., Kontarev, G. R., Rivin, C. 5., "Short-Range Weather Fore-
casting Uaing Full ~quations for a Limited Territory," IZV. AN SSSR,
PIZIKA ATMOSFERY I OKEANA, Vol 3, No 11, 1967.
13
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11. Mnrctiuk~ G. r. , et a1. , GTnitdUINAMICH~SKAYA MOU~L' l7gSNCHCY 'CSIItKUL- ~
YAT5II A~'MnSr~RY (Hydrodyn~mi.c Mndel o~ G~nernl. Circul~C~.on o� th~
, ACmo~ph~r~), ~r~prinf~ VTs SO AN S5SIt, Nd 66, 1.977. _
lZ. dkinsh~vich, R. I. , Itivin, G. S. , iJraznlina, z. K. ,"~:vglu~~:ion of R~-
~u1rs of Numeric~l ~xper~.ments," TItUUY zAl'.-SIg. RNIGMI, No 29, 1978.
13. Krei~, llc~inz-OeLo, 01~.ger, Jos~ph, "Comparig~n o� Accu~ate ME~thods for
the Integr~Cion nf Hyperbolic ~quations," T~LLUS, Vol 24, No 3, 1.972.
14
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.
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COR OFt~ TC7Ai., US~ ONLY
~
UDC 551.(509.313:465.7)
COMpUTATSON 0~' 'TH~ INb~X 0~ ~ORI:CASTING ACCUItACY TN AN "OC~AN-A1'MOSPH~RC"
SYSTCM MbDCL WITH A G1t~AT NUMI3~R OF' D~GItE~5 OF FR~~nOM
Moscow MCT~OROLbGIYA I GIUROLOCIYA in Rusgian Nd 6, Jun 79 pp 15-20
CArticle by CnndiduCe of Physic~l and Mathematical Sciences V. A. Ityasin,
USSR Hydromer_EOrological Scientific Resenrch CenCer, submitted for public-
ation 11 Octnber 1978J
Abstract: In order Co ascertain ehe 13mieing
possibilieies of a model in predicCing real-
ity ie is necessary to be able to cnmpute
the in~ex of forecasCing accuracy within
Che framework of the model. This paper pre-
sents a mettiod for computing this index
and the dependence of the accuracy index on
the measuritig system is considered.
[TexCJ The results in this study are a logical continuation of the results
in [3, 4J. The authors of [4J presented a straCegy for uscertaining the
limiting accuracy of a iorecast of the state of the real "atmosphere-ocean"
system in a class of deCermined models of this system. An imporCant compon-
ent of the strategy is computation of the forecas:ing accuracy index within
the limits of the selected model. In (3] the author presenCed a method for
computing the accuracy index of a forecast which is applicable compleCely
to tlie "atmosphere-ocean" system models wiCh few parameters having the num-
ber of degrees of freedom n~ lOZ-103. For finite-difference models with the
number of degrees of freedom 104-106 the method [3] cannot be realized us-
ing existing electronic computers. Therefore, for models with a great num- -
ber of degrees of freedom Che need arises for developing another method for
computing the index of forecasting accuracy. 5uch a method is set forth in
this study.
Ass wne that a determined model of the "atmosphere-ocean" system with a great
number of degrees of freedom is stipulated. "Determinism" of the model means
Chat its initial state ~ 0 unambiguously determines the state of the model
~ t at future moments in time t> 0. Assume that it is necessary to campute
the index of forecasting accuracy within the framework of the model in the
presence of a definite observation network and a stipulated time regime
15
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~ox o~rzcr~, us~ ox~,Y ~
uE op~r~etnn nf i~s sti~rinn~. I3y rhe menaur~m~nes ~N) wiehin
~ eh~ fr~mcwnrk df ehis mnd~1 w~ wi11 und~r~ennd tih~ eet n� valu~s ~harace~r-
izing Che model pttxttmeeers~ far ~x~mple, tempernrure, heighti of rhe ~.sob~r-
ic ~urE~ce, surf.~ce pre~sure, flaw velociCies, eCc., on ~ Cr~~ecenry un-
kn~w?i eo th~ nbserver [4] beginning frnm ehe po~.nti ~ ~:~ch m~nsur~mene -
li~~ ~7 eempnr~l ~nd sp~ei~l eie-in~ The ~ssumpti~.on nf a dee~rmitt~d n~tiure of
the mddel m~keg it posgible Co reluCe ehe ~ measuremenCs to ,9 0 by ehe ex-
pression
Ei ' ai (~o) ~4-
where ~ i( is ehe parameter tu be me~s~red, !J ~ is the measurement error.
In ttie model it is postul~ted that ~ 0 and d i, i b 1, N represent a random
ver.tor and rnndom value~ stipulated in snme sCochastiic space.
n
_ On ehe b~sis of ehe evaluaCion ~ p, being a funcCion of the obs~rver
makes a decision nbout the initial state, from which, in his opinion, emerged
~ tt~e tra~ectory of the model, giving the seC of ineasurements 5^',. This tra3ec-
Cory is prognostic and differs frocr the actual Cra~ectory
Assume Ch~t � is a norm characCerizing the energy of the ytate of ehe
model, p is a confidence coefficient close to uniCy. The accuracy of the
forecast within the limiCs of Che model, on the basis of ~ information, is
ralled t}ie value Y~, satisfying Che equaCion
� 1'IIIar-~rIItic:;~ o~ genera~ c'~.rcul.~tioh a:1d th~ fhpr~
m~l. r.egime csf th~ ~etnosphere, but Iess succ~s~fully rept`adu~e su~tt ~~i~r-
act~ris�i~~ WhdSe fottn~~tidt~ ig greatly ittfluettced by p~o~esgeq a~gdci~E~d
with ba~~cli~i~ ingt~nbil.tty, ~nd a1~o mesosc~ie p~oCes3e~. As ~~u1~, in -
e}~e model~ tliere ig an e~t~ggeration of the intensity of m~an zonal fluw
ln th~ niidd.te latitude ero~o~phere, ~rherea~ the eddy cdmpen~ne df kinetir
an~ ~~vailable pntetttial energy i~ underegtim~ted.
In tliig article ue wi11 de~~ribe a three-~level ftydrddynamic mad~el df gen-
er~1 Ci~cul~tion oE ti~e atfnosiihet`e fnr a hemigphere, devel~p~d ~e th~
M~~in ~edphygiC~1 Observatn~y imeni A. Voyeykov~ 'Thi~ rood~1 ig a edm-
promi~e v~riant bet~teett the terhttical possibilities of e:tisting eleCtran-
ic rnmput~ers~ gttd the aspiration to con~tru~t a model more me~ningful frdre
the ~hysi~al p+~ine of view. U~ing this model we ~ariried out ttum~rical ~x-
p~rtmentg fnr the reodeling of ge,~eral circulation and the thermal regime
~E ~he atmosphere far J~nuary conditions. Some di the regults o~ these
ex~erimentg are digcu~ged beluw.
Uescri~tion of Model
1.1. ~und~ment~l ~qu~tion~ ~~nd ~dundary Gondicion~
tn the tt~~lel we used the full ec~uations of atmospheric d~+namics, written
in c~ t~-~y~tem vf r.oordin~tes ~pplicable tn the pl.ane of a qtereographir
pro3eCtidn.
~qu~tton~ oE horizontal mdtion
~u ~ nly d ~rr ~ d~ ~ 1 ddo (1''1 ~'~t~11~
r--~ (1)
p d~ 1- R 7' ~ ~ n ps A d c~ ~i.~
j( dx dx ) y rn d
e
.
dV dUr dV_v'j y dsV U~~~~ ~ f~j~~_
vr _ax + dy_~ d. ~z~
(d~t~ d in p, ' ~ d:r
p.~ t d
v R~ O r m d Q ~~a~ ~
b) Ne7t ittflux equ~tion
~ ~ir m~aur avr alr Ak r ~
vr dx- dy ] 1 d: " cp nr o- ~3)
d N ~ , L ps 1 -
- rn nr d: ~ n~ ` tn m r~ Flr
c) 11eat transfer equaCion -
23
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~r,~ o~~~cint, us~ oc~Y
~9 r r1 U_q_ d V q 1 d. a q_~~l p~r
dt nt ~ dx ~ ay J`+` ~ a i m o a m'f' so ~ 4)
d) Cnneinuity ~qu~tian
.
~~i' ~ mr C n~ ~-t� ay, � pa do ~
e) ~qu~~idn nf hydrd~t~tieg
_ _ k' (6)
ao o '
- In ~ddieidn, we u~e ~~rpr~,~~iun for v~reic~l v~ldcity in ~ v'-t~y~rem of
~nordiaate~, nbt~in~d frdm the c~ntictui.ey pquation
' ~ 1 du + dV ~E ~ aU + ~V dE
h,a �llt a~Cdx dy, J(tlx dy, '
0
H~re u~nd v~re the hdriznne~l Gdmponeneg of velnrity in the dir~crion of
the x- and y- ~xes respectively~ ~ is temp~r~Cure, q is sperific humidity,
pg ig presgur~ ~t rh~ e~rth'g gurface, ~ ig g~opotentigl, ~ is vertic~l
- veld~ity in ~n igobari~ cnordinaCe sy~Cem, ~ i~ v rtiCal velocity in n
cr -~~drd~Z~t~ gy~tem, v'~ P/p~, p ig pr~agur~, f~l~ ~s the C~riol t p~=e
~mcrpr, f is the m~tric t~rm of the equaCiong of motion, 'CX and y
th~ Compunent~ c~f Curbulent frictional str~sg in pro~ection onto th~ x-~
y-~xeg, ~ ig the r~diative heat influx, r ig eh~ qua~ntiey of condeng~d
naisture, ~t ~nd ~~r~ ehe vertical turbulpnt fluxes of heat and mai~ture -
respectively, ~g~, Fgv, ~st and ~g are ter~ describing the horizontal
dif fusinn ~f momer?t~mi. h~at and mo~sture,
( uP. ~Pi TP1 4Pa ~
I U. T? 4 I = ( , M ~ , ~ , .
m ig the scale fector for a m~p in a~tereographic pro~~ction, L is the
gpecific h~nt of condens~tion, c ig the ~pecific heat capacity of dry
atr aC a consCanr pressure, Et ispthe apecific gas constant for dry air,
g is the ~cc~ler~tion of fre~ falling, A is the thermal equivalent of a
work ut~it.
The following boundary conditiong are used in the model: at the upper and
lower boundaries of th~ atmosphere ar! 0. The vertical turbulent fluxes
of momentum, he~t and moisture at the lower boundary of the atmosphere
~re determined from the equations for the atmospheric boundary layer. At
the lateral boundaries, which approximately coincide with the equator,
we have the condition that the normal component of horizonta]. velocity
and also the derivatives (along the no nual) of temperature, humidity and
, the tangential component of wind velocity are equal to zero.
24
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~~ok d~~~~tr.~nt, vst, orti,Y
1.~2. 5patiul Seructurc~ ~~f riodei
In th~ mnde~ we u~~ a Nquare grid for a~tereographic p~o~ecr.ion with Ch~
prinCip~~l ~~~1~ at l~titude 60d. Th~ tneal number of pointig nf inCerg~c~
tidn c~t e~ch level in ~ hemiqph~rc ig 1481; the menn grtd ineerv~l is 425
km.
'fh~ v~r~i~~1 ~eru~eure di th~ model inaludes Chree l~tyerg with a uni�dtm
tY ine~rv~l. 'Th~ princip~l varic~ble~ u~ v, T, q and tJ ~r~ dpehrmin~d ~C
ehe 1eve1~ u"~ 0.167, 0.5~ 0.8~3.
1~~. Numeri~~l 5nlutinn of 5yq~em nf ~qu~tidng
F'nr solueintt nf the ~ygtem of equatidnq (1)-(7) we use the finite-dif�er-
enre scheme prbpoqed by Lil,ly [8j, h~7ving ~~econd order of apprnximatinn
with r~~pece ea ~pace v~riables. ~dr the adopCed bound~ry condiCidn~ und
in the ~bsen~e af energy lc~sgeg t~nd g~~ins Chig gchemc~ ensurey congerv~Cion
df m~sg ~nd toe~l energy. In cr~?puting the forCe of the presgure gr~dient
in the equ~eian~ of moeion (1)-(2) we will use the difference ~pprnximnCion
propnged in ~12j. ~ demonserated in (6], Chis approximation ensures an ac-
- curncy ~f CnmpuC~tiong in g U'-syst~m which is ehe same ns in ~n isob~ric
cnordinae~e gy~tem.
~qu~ttions (1)-(5) ar~ integrated in time by the central differences method
with an inCerval of 10 minutes. In order to exclude rhe ficCiCious s~lution
whicb ariges, ufter each 48 intervnls in three successive intervals we em-
ploy the three-point filCer
.4' = A' + 0,~ (;1'-~ -i- A'+~ 2 A' 1� (8)
`Ctien Che equ~tions are integrated again in one interval by the Matsuno
scheme (4j, after which the calculation~ are continued using the central
differences scheme. For the equatians of motion Che adopted scheme is par-
~ tially implicit, since Che force of turbulent friction is taken in the suc-
ceeding time interval.
In order to consCruct matched initial fields of the principal meteorolog-
ical elemenrs for a hemisphere a complex of compuCer programs was developed
and applied. The initial fields are ~onstrucCed in two sCages. In the firsC
sCage, in an isobaric coordinate system, for seven uniforaily aituated lev-
els we constructed the relative humidity fields, and also the temperuture
fields, matched verCically using the equation of statics and the fields of
horizontal components of velocity, matched horizontally in a quasisolenoid-
al approximation, by solution of the balancc equation. In the second stage
there is transfotmation from an isobaric coordinate system to a U= system
taking into account the relief of the continents and tt~e vertical structure
of the particular model of the atmosphere.
25
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~OR O~~tCIA~, US~ ONLY _
1.4~ ~arc~m~e~ri~ntian nf N~ngdi.~b~eia prnC~gg~g
'Thc rnc~d~l takpg inen ttc~oune etie prinGi.pg1 ~n~rgy g~ing c~nd 1n~a~~ aper~-
eiv~ in eh~ r~g1 ermdgph~r~.
It~di~Cinn. In compuring Chd ~~di~tidn he~t influx~~ ~nd eh~ r~di~tion
bc~lnn~~ ~C Ch~ underlying gurf~c~ ~n ~11ow~n~~ i~ m~dp for eh~ ab~orption
nf r~di~Cinn by w~rer v~pnr ~nd ~~rbon dinxide, gagCC~ring nn mal~~ule~ nf
~ir ~nd n~ru~nl, nnd alsd ~bgnrpeion ~nd ~eaeti~ring of r~di~tion by cloud~.
In anmputbeidng nf 1~,ng-w~vp r~di~Cion uge ig m~tde of Ch~ int~grnl Lr~ns- -
migginn funnG3dn propnsed by F. N. Sh~khCer [ld], by m~~n~ of which al-
Low~nce i~ made fc~r ehe ~bgdrpeion nf r~di~t~.on by waeer vapor nnd C02~
In Cnmputing ehorC-wnv~ rgd`i~Cion we uae ehe gub-nzon~ solur congC~nt, in-
C~gr~l erungmi~sion funcCion �or ehe apecera]. eection U.7-5 ~ m(3) and th~
gcnCeertng function propo~ed by V. V. Sobal~v (9].
'~t~e model eakes inCo ttncount two-layer cloud cover w3th fix~d boundaries:
ehe lower 1eve1 ig situgt~d in Ch~ layer (0.667-0.833), ehe upper 1eve1
in the lay~r (0.333-0.667). It i~ assumed that ehe cloud eroit~ as an
ideally black body at ehe temper~ture nf its upper and lower boundnrieg.
Th~ nlb~dd nf clouda of the uppeY ~nd lower levels was assumed equgl eo
0.25 ~nd 0.50 respectively. The radiation fluxea under condiCions of v~r-
iable cloud cover are computed on the assumption thaC the fraction~ of the
celestial sphere simult~neougly covered by clouds at the two levels is equa].
to the product of the tenths of cloud cover ae theae levels.
b) Larg~-scale condensatinn and convecrion. Allowance for the heaC influxcs
asaociated with phase transirions of water in the atmosphere is made by the
parameterization of two processes: water vapor condensation~ caused for _
Che most part by large-acale movements and the release of laeenC heat dur-
ing convection, arising in the moist-unstable layers of Che atmosphere.
Large-scale condensation takes place if the moist air reaches the critical
relative humidity hk = 0.8.
In order to compute the heat influxes caused by mesoacale convective pro-
cesses, we will use the so-called "convective adaptation scheme" [Sj, in
which the equilfbrium gradienC is assumed to be dependent on rel~Cive
humidity and the moist-adiabatic ~rradient ~11].
The total quantity of precipitation, both large scale and convective, is
determined as the sum of precipitation forming at the individual computa-
tion levels.
c) Turbulent influxes of momentum, heat and moisture. The model makes use
of a relatively simple and tested scheme for camputing the turbulent flua-
es and influxes of momentum, heat and moisture, based on the empirical. ex-
pressions derived by Deardorf [13].
According to [13], the coefficient of vertical exchange in the atmospheric
boundary layer is dependent on temperature stratification in the lower lay~- i
er with a thickness of 1.5 km and the Richardson number.
26
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~Ott dl~'t'ICIAL 115t~: I~NLY
~n the model ie i~ pdy~ible to dix'fer~ntiate four typeq of underlying ~ur-
~t~~eg :
gurfc~ce nf Che cnntinentg, free of ic:e nnd ~ndw. The ai.r CempergCure Tg
~~t the ~urfaC~ ig ~nmput~d frdm the he~t btxl~nce equ~ti~n
~
ort 7~~ FI L E (~i '.~K ~g , ( 9 )
wt~er~ rl i~ the he~t flux into the goi1; 5 is ehe b~l~ttce ~f gharC-wgv~
r~tdiatiidn ehe underly~ng gurface, It~' iggCtte de~cending ~1ux df lnng-w~v~
r~diatiinn nC eh~ e~rth, c)"* is the SCe~~n-I3nl~zm~nn cnnse~nt.
H~re uge i~ m~d~ nf Che rel~tidn~hip between ehe hettt flux inCo the goil
~nd tih~ r~di~eion Ualgnce fnr ehe underlying surf~ce [7);
gurf~Ce nf th~ enntinentg, covered with snow ~r ice. The eemperature is
~~lsn rdmpue~d frdm the h~~ti bal~nce equ~tion; ehe fluxes of h~~e inCo tihe
gnil and ~v~pnr~eidn are negleceed;
_ ice-cdvered ncenn gurf~ce. The ~urface temperature is cnmputed f~rom the
he~e b~lance equ~tion. 'The l~egt ~lux through the ic~ with a stipulatied
, wgC~r tempernture bene~th the ice is C~ken into accnunt, wheretts evapor~-
Cidn ig neglected;
gurft~ce nf the ocenus ~nd se~s free of ice. The temperature at Che sur-
f~ce is cnnsidered known and the air is cnnsidered saeurated.
d) Horizont~l diffusion. Tlie mod~l uses ~ nonline~r scheme �or computing
diffusion wl~ich is based on the ide~s of three-dimensional isoCropic tur-
bulence [8]. In Chis schem~ the eddy viscosity co~fficient is proportional
to the total defnrmation of large-acale hnrizontal flow
k- 2('
m' 1(UT ps~~~~~ (10) .
l J
where D~ is relative shear and DT is the relative change in linear dimen-
sions with conservation of area. The value cY = 0.25 was selected for the
horizontal resolution ~ s used in the model. This diffusion scheme is used
widely in a number of models of general circulation of Che atmosphere, al-
though, as indicated by recenC investigatinns, it is inadequately selective
in suppressing perturbations with a small wavelength.
e) Computation of cloud-cover tenths. As is well known, a number of empir-
ical forn?ul~s have been proposed for computing cloud cover tenttis in which
this characteristic is expressed through relative humidity. A preliminary
checking of a number of such formulas has indicated that not one of them
makes it possible to obtain satisfactory zonal distributions of cloud cover
simulCaneously in the low and high laritudes.
In tl:e model the cloud coverage at each level (n2 and n3) was computed using
the expressions
nz = -0,27 -}-1,07 /i: 0,05 Qzr
J13=-0,4'~'~lg'~'0,~~ Q3r ~11~
2~
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~OR OFFICIAL USE ONLY `
in whl.ch ewd p~r~m~eerg wer~ uged: relneive humidiry h gnd sp~Ci�ic humid-
iey q in g/kg.
2. Mndeling df Armnsphcric Circulurion for Jttnunt-~? Cond~Cions
Fnr ehe purpo~e of gCudying Chn ~rop~re~.eg uf the mod~l ~nd ~v~luet~.ng iCs
po~~ibiliei~g 3n de~cribing ~ r~~~ c~im~t~ w~ carried ouC a numericgl ex-
perim~nC wieh modeling of circul~einn~ eh~ tihermal regime gnd mnisCure
cyCl~ in th~ ~tmnsphere for Jnnunry.
Ag ehe g prinri gtiipulated fi~~ds we uaed d~ta taken from different climatic
gources on tempergeure af ehe oc~nn surface ~znd boundarieg of the ice and
snnw coverg, albedo o~ the continents nnd oc~ans. Sol~r angle wns asaumed
Co be equ~L Co ieg value for mid-J~nuary. As wng indicue~d ~bnve, in n
numbcr nf inveaeigations ie hns been demonstrated that in the integration
of ehe equ~tinns of atmospheric dynamics with a fixed solar angle and a
gtipulated tempergture nf the ocean surface the ~Cmosph~re aCCains a quasi-
sCec~dy regime after approximaCely 40 days~ if ae the initial momenC Che aC-
mosphere was in n staCe o� reat. When using re~l iniCial daCa Chis point
sets in after 10-16 days.
~or the particulttr model the system of equations was integrated for 60 days
- from the real initial state, for which we used Che specific synoptic situa-
tion for 5 January 1971. The character.istics of the mean state of the atmo-
sphere were obtained by averaging of the values computed in Che model for
31 days (from the 25th through the 55th days of the forecast).
As a resule of our numerical experiment we obCained a great number of char-
acteristics of general circulation and heat exchange in the atmosphere.
Due to the limited lengCh of the article we will give only some of them.
Figure 1 gives the altitudinal-latitudinal distribution of inean temperature.
It can be seen that in the troposphere the computed temperature values co-
incide well with the actual values. The temperature in the upper layers of
the atmosphere is close to the actual Cemperature in the tropical zone, but
to the north it decreases considerably more rapidly than is observed under
real condiCions. Evidently, the reason is that the upper computation level
in the northern :latitudes is situated in the stratosphere, which is churac-
terized by proce;ases not taken into account in this model.
With respect Co Che altitudinal-latitudinal distribution of specific humid-
ity, also represented in Fig. 1, as in the real atmosphere, the specific
humidity maximum is observed in the lower layer of the atmosphere at the
equator and averages about 14 g/~cg. The computed vertical gradient of
specific humidity in the lower half of the troposphere in the zone from the _
equaCor to 50�N approximately coincides with the actual value. In the polar
regions the computed moisture content was less than the actual value.
28
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t~dit nCI~'LCIAL U5~ dNI~Y
_ p Nd ~
1S0 _ ,b,y
~
;
:
, ~:56~ f~,_.. Q1 rsG. ,rg...- a~
. ?----�4a 9~~.~-g ~~~=~~~,r ;,s~
,
SDO ,.J
' ~ a"-�
~ ~ ..~'1' ~ .r1s ~ fB~
lSO~ -24 ~'~f6."~l4 f / ~ / 74~
l000 ' i i. l ~~~:~'`:,r ~
~sa - _ _ ~ ~ r.. W ~ W
~1) ~~rr,,... (f) f,~,r---r'-r0
~
sot b ,~~as~? b '~,....-a? r
~oco ~
l,fG t'JP~-'
\~~2eJ~ s ~1 ~ ~
~ / 2, \ p / / ,
~ ~ 4 ~ p ,
?
~~c,�~ 2, 0 2 9 12 ~6 g~.,~-
, / ~4 . ~p 4 - ~ /
~ ii~.�~~/ ~ ~ % .;7, , ,-7.~~~~/-4/
.Jc.w.~J 70 SO JC tC 90 r10 60 40 PG 0
F'ig. 1. N.titudin~l-latitudin~l temperature distribuCion T�C (a), specific
humidity q g/kg (b) ~nd zonal velocity v m/sec (c). A1 left computed,
at right acCual for January [21].
This same figure shows the compuCed and actual alCitudinal-latitudinal
distributinn of thQ zonal component of wind velocity. As in the real at-
mosphere, there are two regions of easterly flows (in the Cro~ical xone
and ~n Che polar latiCudes) and an exCensive region with west-easC Crans-
fer, occupying tl~e greater parC of the northern hemisphere. The poaitians
of the high-altitude 3et stream and its mean velocity ar~ correctly comput-
ed. However, in the middle troposphere the velocity of the zonal flow in
the model is greater than in the real atmosphere as a result of the exag-
gerated meridional temperature gradient, computed in the model.
It should be noted thae the model correctly reflects the principal charac-
teristics of circulation, and specifically, its tricellular structure. As
in the real atmosphere, for January it is the so-called direct Hadley cell,
situ~~ted in the tropical zone, which is strongest. In January the ICZ is
usually situated in the southern hemisphere, but since in the model the
boundary is a"wall" at the equator, the Hadley cell, naturally, is dis-
placed somewhat Co Che north. Nevertheless, its position in the latitude
zone to 30�N corresponds Co L�he actual data [14]. The same can also be
said with respect to the second circulation cell (Ferrel cell), which,
as ir_ the real atmosphere, is situated in the zone from 30 to 70�N. Final-
ly, there is a very weak direct cell in the polar latitudes, as is also ob-
served in actuality.
Now we will cite a number of characteristics of heat and moisture exchange
in the atmosphere obtained as a result of the numerical expeY~;~ent. Figures
2a,b show the latitudinal distributions of the radiation balan.:e at the
29
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~Oit OI~~ICIAL US~ ONLY
und~rlying gu~fn~e ~nd ~t Chn upp~r bnundttry nf thn atmn~phere ~eg[~~CC-
ively, whicli cgn b~ Cnnsid~red quiC~ c1n~~ en tih~ ~nCug]. di~~r~.buCion df
ehe~~ pnrnroee~r~ (1, 15J. Tha Compue~d m~ttn plnn~t~ry ~lb~do of th~ "~grCh-
atmosphere" ~ystem ie about 35%. The ~.at3tudinal v~rintion of Che Curbu-
lent flux of h~ae Cn ehe ~Cmneph~re ig r~pr~~ented in ~ig. 2C. The c~mpuC- ~
ed c.urv~, in g~ner.gl, r~fl~ceg eh~ diseribue~.nn of thi.~ ch~r~Geeri~ein
obCnin~d nn th~ b~gis nf uctu~l dnCg. A d~Cniled anglysig nf Che ~xpari-
m~nt~~.l resuleg ~t~nw~ th~r pog~~.b1y a r~gulti of Ch~ ~chpme for compu~ing
ehe bdund~ry l~yer gdnpted in ehe model eh~ fluxe~ over Che ne~~ns in eh~
high lgeirudes arp som~wh~C ~xt~gg~raC~d, wh~r~g~ in th~ low 1~Cieud~e th~y
~re undersented in comp~rieon wieh rhe actual daCn.
xon/(cr+~~ MuN)
a,2 A A .
G) ~ nanAcM~~ MuN) 6) b
O,f p~t
0 ' p ~
-0,~ .p~~
-0,2
-0,3
D) ~ a~ d
~ ~o~:/ceK=
~ ~
2 , ~ + g/~ec2 ~
~ ~
~
t o ' 1 , ~ ' `
~ ~ .
a~ -y ,
B nM/cym e ~
s ~ HM/tym g e~ ~D rRC~IM~MYM~ A
y y ~ . ~ 20
i
--~-2 ~
~ ~ ~ 2 i
~ f0
..~~_-i
~soc.~. ~o so Ja ~o o ~ eo 60 4n 2o n~
Fig. 2. Latitudinal distribution of characCeristics ~~f heat and moisture
exchange. 1) actual for January, 2) computed.
KEY:
A) cal/(cm2�min)
B) mm/day i
I
,
30
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t~ot: or~~~~rCtAT, USt~. ONLY
I~L~ure 2d shnwg Cltc 1;~rit :d.i.~la:f , . r.i'�.ution nf thc nc~ment ui= ;aurf~Ce f~ia-
tinn fc~rCe~. 'The ~~ett~al d?Ca weru ~:.~lcen tr.~m a z~Cuc'y by li~. ~ l~rm~n ~i4~. In
ttir lnw 1nCiCude3~ in ~cc;oxdance wie}i these d~~ea, ~li~ru C~; uri infl.ux nf eh~
r~l~eiv~ momene of mnmettCum tn the ~tmogpher~. In the mtddl.e 1~C~.Cttd~~ th~
l~~g nf momen~um wag under.:~t~ired by ,lpproxim~tely ~0%. However, ~s indi-
C~7eed in ~ number o~ yru~lie:~, Ncll.arm~~n's d2~ta 11lUyC bC con~ider~ d cxu~ger-
~t~d by appruxim~tely ~ne-third, 3ince ehe mnment of friceion~l ::rc:eg wng
~ompu~ecl in [ 14 ] nnly f
dr thc ~cc~ns (without elte land being t~lcen into aC-
cdunC). 'T~king ehis inro ~cr.ount, l.r. can be concluded th,~r th~ v~lu~s nf
Chc momene dC �ricCionnl E~rcey c~mpuC~d in the model agr~~ we11 wieh Gh~
.7CtU~71 dat~.
'The lcte:ttudinal disCributton c~f precipit~tiion ~b~~nined in Ch~ model is i1-
lusCr~hted in I~'ig. 2e. ttos~ uf the computed preclpie~~tion is ~cc:nunted for
by .tnrge-~c:~le prec~.ritntion, whcre~;~ convective precipie~tion for th~ mosC
p.nr.t nccur~ in Che tropic.~1 and equatnrial zones. Thc gr~ph clearly shows
twd m~:cim~, one of which is caused by the intensive falling af precipit~~
tion in ~ zene of b~roclinic in~tability, whereas the other is ~SJOC~.~C~d
with convection in ehe rropics. ~'igure 2f shdws the laCitudin~~l distribu-
tion nf evapornCian. The figure ahows th~C aC ~lmost ~~l.l lattCudes Che
quantity of moisture entering ineo Che aCmnsphere ~~is a resulC of ~v~pors- ,
Cion is undersCated in coroparison with empirical data. We note thaC other
existing models o~ atmdepheric circu].ation giv~ lesser values for evr~pora-
tiott in cnmpurison with (1], at least for the temperate latitudes. ~'or Ct~e
ernpical zone our model gtves ev~~poration values closest to the datr~ rub-
lishcd by M. I. Budyko [1] it~ compariKOn with oCher existing modelg.
f0'~na~lcym
I e d) A
~ i~~r 10~~t1(tMi�cym) ~
� O ~ :t : i ~ Q Bl
90'C.tu. 70 SO JO `~70 C ~b i!~~ ~~~:�a
� 61 ~ oo
� o o ~
~ J ~
O ~ .
~ 7
�e ~ Q ~r.~~.1..f..1~.. .L.~.�
/ ~
I ~ ~
.fe / "B ' ~
~ ~ 2 ` /
.py �16
~ig. Meridional transfer of heat and mc~i.sture to the north. 1) actual
for January [21], 2) computed
KEY:
A) cal/day
_ B) g(cm2�day)
~
31
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ro~ oF~zcinL us~ ornY
s
n ~
~ ; s fe
n
~s p % ; ,
r ~
~
7 ` S
f0 ~ ~ps
~ \ U
p _ ` pl
I~ ~ 1
1
s ` � f~ '
,
h o , .
6 P~: N t ~ ~
s �o~ ~ 2 ~S ~O,J
s~ ,
0 f p st
- 2 f s 2
, U,
~
o ~
s
:
s
s
~
r
r
as 1 p
s ~
f ~o
r Cst
i o
S ~ �
~ ~20
t:7_ .f QS?
S / q~,.~
s ~oas '
~ o ~ a 4s ~j
0
o,~
Fig. 4. Precipitation field (mm/day). a) computed; b) actual. January
32
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I
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Fl.gurc 3 shnwe Ch~ mertdiott~l Cransfer, of hcaC and moi:~ture. The computed
tr~nns~er of heat Co tihe north by large-sca~.e eddies (~1.~;� 3a) agrees saC-
isfacCorily wirh Che ~tcCual d~t~ published by Oor~ [17]. The computed heaC
tirunyfer v~lues, ~saoci.ated with mean meridional circulaCion (I~'ig. 3b),
were l~ss than the actual values, which is atiCributable in part to ab-
sence in tlie model of heaL exch~nge wl~ti the snuCtiern hemisphc:re, 7'he mer-
idion~il tr~nsfer of mo:isCure (Fig. 3c, d) has simtlar char~cteri~+:ics.
FigurE~ 4 shows the computed and acCual precipiCation f:Lelds. Comparison of
thes~ maps shows Chat both moisr ~~nd dry regions are modeled ra~her we11.
We give TaUle 1, characterizing the balance of heat influxes to the atmo-
sphere in ~he norChern heintsphere for Janu~~ry. Tn cc~mputing the actual he~t
influxes we used data from differenr authors [1, 17-19].
In the 1~st column of the men~ioned Cable Che t?eat flow across the equ~3tor
is equal to zero, since in the model this flow i~ not eaken into AccounC
as a result of the presence of a"wall" at the equator.
In general, the integral t~eat influxes agree we11 with ehe actual data. The
positive balance of heat influxes, obtained using data from independent in-
vestigations, is evidently a result of errors in computations of individual
- components of the balance. With respect to the balance computed in the mod- -
el, its small value indicates that from the 25th through the SSth days on
Che average there was a b~~lanced influx of heat with a very weak tendency -
to cooling.
Table 1
Heat Influx Balance in the Atmosphere for a Hemisphere in January, �C/day
Types of influxes Actual data Computed values
Radiation influx -0.91 -0.88
Turbulent influx 0.22 0.16
Influx as a result of water vapor condensation 0.64 0.73
Influx as a result of heat transfer across
equator 0.16 0
Influx as a result of transformation of poten-
tial energy into kinetic energy -0.03 -0.02
iialance of heat influxes 0.08 -0.01
In conclusion we note that S. V. Bogachenko, I. P. Guseva, L. N. Magazen-
kov, G. V. Parshina, V. I. Ponomarev, D. A. Sheynin and Ye. P. Yushina
participated in the numerical experiments and analysis of the results.
33
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IIIBLTOGRAPHY
ATLA5 T~PLOVOGO BALANSA Z~MNOGO SHAR.A, (Atlas o� tihe Earth~s HeaC Bal-
~nce), ediCed by M. I. Budyko, Moscow, Gidrometeoizdat~ 1963.
2. Berlyand, T. G., Strokina, L. A., "Cloud Caver ~tegime on the Earth,"
TRUDY GGO (Transactions of the Main Geophyaical Observatory), No 338,
1975.
3. Yevseyeva, M. G., Podol'sknya, E. L., "Integral Tran~misaion FuncCior.
in the Near-IR Spectral Region," TRUDY LGMI (Trnnsactions of the Lect-
ingrad Hydrometeorological Institute), No 49, 1974.
4. Lilly, D. K., "ComputaCion Stabilixy o� Numerica] 5olution~ of Non~ta-
tic~nary Nonlinear Geophysical Problems of Fl.uid Dynamics," CHISLENNYYE
METODY RESHENIYA ZADACH DINAMLKI ATMOSFERY I OKEANA (Numerical Methods
for Solving Prob]:ems in Dynamics of the Atmosphere and Ocean), edited
by L. R. Ihnitriyeva-Arrago~ L. V. Rukhovets and B. Ye. Shneyerov, Len-
ingrad, Gidrometeoizdat, 1968.
5. Manabe, S., Smago.rinsky, ,1., Stricicler, R. F., "Numerical Modeling of
the Mean Pattern of General CirculaCion With Allowance for MoisCure
. Exchange Processes," TEORIYA KLIMATA (Climatic Theory), edited by L.
S. Gandin, A. S. Dubovand M. Ye. Shvets, Leningrad, Gidrometeoizdat,
1967.
6. Meleshko, V. P., Sheynin, D: A., "ApproximaCion Errors in Compu~ing the
Pressure Gradient in a 0= Coordinate System," TRUDY GGO, No 394;' 1967.
7. Ogneva, T. A., "The Necessary Density of a Network of Heat Balance
Stations," TRUDY GGO, No 230, i968.
8. Smagorinsky, J., Manabe, S., Holloway, J., "Results of Numerical E~c-
periments With a Nine-Level Model of General Circulation of the Atmo-
sphere," TEORIYA KLIMATA, edited by L. S. Gandin, A. S. Dubov and M. Ye.
Shvets, Leningrad, Gidrometeoizdat, 1967.
9. Sobolev, V. V., RASSEYANIYE SVETA V A't'MOSFERAKH PLANET (Light Scatter-
ing in Planetary Atmospheres), Moscow, Nauka, 1972.
10. Shekhter, F. N., "On Radiation Diagrams," TRUDY GGO (Transactions of ~
the Main Geophysical Observatory), No 150, 1964. ;
11. Benwell, G. R. R., et al., "The Bushby-Timpson 10-Level Model 0~1 a �
Fine Mesh," SCIENTIFIC PAPER, No 32, London, 1971.
12. Corby, G. A., Gilschrist, A., Newson, R. L., "General Circulation Model
of the Atmosphere Suitable for Long-Period In~egrations," QUART. J.
ROY. METEOROL. SOC., Vol 93, 1972.
34
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~'O~t OH'~ICf~i, U~~ ON~.Y
t~. Ue~rddrf, T~ tJ., "~mpiri~al nep~nd~n~e df eh~ ~ddy CaeffiCi~nC tc~r
IIe~C Upnn St~l~ility Abov~ ~he Lawa~g Sd ~n," J. AI~PL~ M~T~OROL~, Vd1
6(4), 196~.
14. H~ll~rmttn, S., "An Upd~ted ~g~im~C~ of th~ Wind 5tr~~~ on th~ Wor1d
n~~e~n," MON. W~A~HEI2 ItCV. , t?n1 95, i967 .
15. "Mod~lling for the ~irgC GA1t~' Glnbni ~xp~rimenC," GAItp PUBLICATIONS
s~xi~s, rtn i4~ 1974.
lb. New~11, it. , Kidgon, T. W. , Vincene, b. G. , Bc~er, G. T. , TN~: G~N~ItAL
CIItCULATtON 0~' 'THE TnOPICAL ATMOSPliEttL AN~ IN'~~ItACTIdN5 tJLTIt ~XTFtA'~ROP-
tCAL LA'~ITUUCS, MI~, DepC. Meeeorol., Vc,l 1, 1972.
17. Newe11, R. Vincene, b. G., Udpplick, T. G., ~'erruzgd gnd Kidgon,
T. W. , TH~ ~N~~tGY ~ALANC~ OF' Tlt~ GLdBAI. ATMOSpH~It~, Americnn Metear-
nlogical Sdci~ey, BosCon, M~ss., 1969.
lg. Oort~ A. H., "The Obs~rv~d Annugl CyC1e in the M~ridional Transport nf
Atmoapt~eric ~nergy," J. ATMO5. 5CI., Vol 2$, 1971. .
19. Oart, A. 11., PeixoCo, T. P., "7'he Annua] Cycle nf the ~nergeCics of
the Atmosphere dn a Planetary Scale," JGR, Vol 79, Na 18, 1914.
20. Oort, A. N., ltassmusson, E. M., ATMOSF'1t~RIC CIttCULATIOI~ STAT25TIC5,
Professional Paper No 5, NOAA, 1971.
35
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FOit O~~IC~AI, U3~ bNLY _
UDC 551.511
~NCRGY CHARACmCRISTICS n~ TH~ WZN'r~R WA1tMLNG OF 1976/1977
M~~Cdw M~T~UItOLOGIYA I GIDRdLOGIYA in Itu~si~n No 6, J~n 79 pp 33-40
(Arricle by Candidates of Geogrgphical Scienc~s I. V. Bugayeva, L. A. Rya-
zannva~ end U. A. T~rgsenko, ~nd Cand3daCe of Physical gnd Mgthematical
Sciences G. tt. zakharov, Central Aerological Obeervatory, submitted for
publicaCinn 13 July 19~8~
Abatract: On the basis of rockQt and satel-
lire data obCained during recent years Che
authors examine the characteristica of syn- _
optic proceases during the winCer period in
the stxatosphere and mesoaphere. Th~a comput-
ations af the energy characteristics indicat-
� ed that during a period of wgrmings Chere is
a restructuring of the vertical profiles of
kinetic and available potential energy.
(Text] The month February 1977 marked the 25th anniversary of Scherhag's
discovery of the so-called "Berlin phenomenon" [4]. This phenomenon was
the marked increase in temperature in the winter stratosphere by more
thnn 40�C. During recent years satellite data, making it possible to de-
termine the temperature and geopotential values on a global scale at dif-
ferent levels in the stratosphere and mesosphere, make possible a detailed
study of stratospheric warminge.
In this study, for an analysis of synopCic processes and computation of the
energy characteristics, we have used pressure pattern charts for the 10-rob
surface, high-altitude charts of constant levels up to 60 km published
by the Central Aerological Observatory [1], pressure pattern charts for
5, 2 and 0.4 mb, constructed using satellite and rocket data, and also
time sections for the atmosphere based on data from rocket stations in
the western and eastern he^~ispheres.
- All the enumerated materials, and also some associated computations, made
it possible to ascertain several large waves of a sharp temperature in-
crease in the stratosphere and mesosphere in the winters of 1976/1977 and
1977/1978 in the high and middle latitudes of the northern hemi.sphere. The
36
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~'Ott nt~it~'tCtAL U5~ tlNLY
diytlrt~uigl~ing citargcteri~tics oE the mentinned wltte~rg were: firgt~ ehe
preyen~~ n~ ehr~~e e~mper~itur~ ~t1CYCF1y8 W~iV~S with g fin~l w~~ming in
Mnrcl~, se~~nd, J~~nu~ry ~nd March w~rmingg chn~~cteriz~d by ~ gr~~e it~-
t~nyity, c~ccurring wirh pressure re~CruGturing in the p~1n~ r~~gidn~
~nd clde~gified ag "~trdn~," third, the ~ranapiring proc~~gpg wer~ gr~gt~
1y influ~ne~d by bd~h ehc I'acific Oc~~n ~nd Ael~neic ~nti~yclnnes, which
fr~qu~ntly extended ~rom trdpugpheriC lev~lg ineo eh~ me~d~ph~re. 'The db-
yerv~d char~~teri~eicg nf winter 1~rd~~ggeg pl~yed ~ d~finiC~ rn1~ in Ch~
bringin~ ,~bnur nf e~r1y gpring gtr~tnspheriC rpgeru~euringg.
~he firgt ta~ve of grr~eospheric warming fdr ehe winr~er of 19~6/1977 wng
nbyerv~d ici the yecond httlf df Novemb~r 1g76. S~Celliee daC~ ~nr thig
periad shdw ~ broad reginn of he~e frem th~ C~gpien Sen tc~ Ch~ I3erin~ S~~
wtth tempercttureg ~e the C~n~~r equ~1 to -2U�C gt the isnbaric gurf~~e
S mb. At th~ same time, ~t the cold focus, displ~ced tnw~rd Greenl~nd,
the temperc~tt~re w~s reduCed to ~-70�C. The m~ximum temperatures were ob-
~erved in the region of the str~topause and over Kheys Island ~ttnined
12nC, wh~reas over Volgogr~d it ateained 9�C. This wnrming was noC~d only
over the eastern hemisphere. Uuring ehis p~ridd there w~s an intensific~-
tion of the Pacific Oce~n gnd Indochin~s~ ~ttticyclones, which ~oined into
a single zone of high pr~ssur~ ~xtending frem the Arnbian Sea to Chukotka
:.nd Alnska. A gimilar enrly wineer warming was nlso obaerv~d in November
1968.
n gecdnd warming wave began aboue 15 becember. buring this period there
was an intensification of the pacific Ocean anticyclone. The anticyclone
~ttained maximum cdevelopment during the period 21-25 December; by this
time its center was situated nt 65�N near Alaska. Such a marked displace- _
ment of the anticyclone to the norCh caused Che development of a high-
altitude frontal zone over the pole: over Kheys Island the easterly and
southeasterly winds in the layer 45-50 km attained velocities of 130 m/sec
and the temperaCure at an altitude o� 45 km was 0�C. The cyclone shifted
tn th~~ north~rn tiector of Che European U5SR; Che region of cold associated
with it was situated r~ver Greenland and then moved Co 45�N and was situat-
ed over Norttl America.
Tl~e Atlantic anticyclone began to develop almost simultaneously with the
Pacific Ocean anticyclone and beginning on 27 December there was a marked
intensification of the Indochinese anticyc~.One, which began to move no~th-
ward rapidly: thus, on 27 December its center was situated at 37�N, where- ~
as by 1 January it had atCained 52�C. The regions of heat associated with =
it at the 10-mb level had a temperature of -15�ti. By the end of December
there was a joining of the Atlantic and Indochinese anticyclones; the
high-level charts show that this combined anticyclone penetrated into
the mesosphere. During the period 25-31 December it could be seen well
not only at ATS and AT2, bu~ also at AT0.4�
At the end of December the temperature field in the stratosphere over the
entire northern hemisphere was characterized by relatively high values
both over Eurasia and over th~ western hemisphere. Even in regions of
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~dld, ~gsd~i~~e~d wiCh ehe cycldnic G~ntier, did tih~ e~mp~r~tur~ ittG~'eg~e
by xU�C ~nd ~etnin -SS�C ingtead of eh~ u~u~~. -70 75�C (~t Ch~ 10-mb
l~vcl).
tn J~nunry th~ m~ximum e~mp~raeur~ chang~ dver Khey~ Iglgnd wgs nnt ob-
~~rved in the neighbnrhnod nf ehe gCr~tiopgu~~, as w~~ th~ c~~e durtng
th~ fir~t wnrmi.ng, bue ~t an ~l~ieude nf 35 km. Ther~ waa g gr~dugl low~r-
ing nf the r~ginn nf heat 3.nto the middle ~trraCogph~r~.
Ae ~ numb~r nf Am~ricgn ~C~tidng loc~ted in the northern region~ th~re was
~lgo n merked temp~r8ture incregse. ~or example, ae ForC Churchill on 3
January iCe valu~ ~e kh~ 1~v~1 42-46 km was more than 20�C.
Ar ehe beginning nf January Che seructur~ of the presgure field diff~red
by layerg: in the gtrgtnsphcre there was g triaellular structure with a
cyclone, diapl~c~d onro the ~uropean USSR, and two anticycl.onea in the di-
rectinn of the Pgcific nnd AtlanCic Oceana. In the lower meaosphere (50-
55 km) a fnur-celled field was formed: two cyclonic centers and ewo anti-
cyclon~s, where~s abnve 60 km there was a strucCure wiCh two cells: cyclone
and unticyclone. Deapite Chese differences in atructure, a pressure re-
structuring over the pole was observed in gll layers.
In mid-January the warming process in the stratosphere continued, but pass-
_ ed into the middle and lower layers. At an altitude of 50 km over Kheys
Island Che temperature had decreased to -48�C by 19 January. In the meso-
sphere an ordinary winter circulaCion began to be restored with a cyclonic
eddy in the region of the pole and relatively low temperaturea near the
mesopause. During the period from 10 through 21 January an anticyclone in
- the form of a large unified center was established over the pole in the
, layer 30-40 km, whereas a cyclonic field, represented by several individ-
ual regions, surrounded it along 50�N. Such a structure of the pressure
field is characteristic for spring resCructurings. By the time of forming
of anticyclones in the region of the pole at the 10-mb level the tempera-
ture had increased Co -45�C. The main region of heat was situaCed in the
lower layers of the stratosphere.
After 21 January there was restoration of normal winter circulation.
FQr the warming, which was accompanied by a restructuring of circulation,
we compuCed the mean geopotenCial values along different circles of lati-
tude and as a whole for the hemisphere. These values were compared with
the mean geopotential values before and after the warming. Interesting
results were obtained.
Satellite data were used for computing geopotential. The caean geopotential
was computed for 75, 55 and 35�N with an interval of 30� in longitude at
the three isobaric surfaces: ATS, AT2 and AT~~4. In order to evaluate the
geopotential values before the warming period we used data for 9 December
1977. As the time of warming we selected the geopoCential values for 6
38
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~OIt O~~ICIAL US~ ONLX
J~nu~ry 1977 and fnr ehe end of w~rming for 14 Jc~nu~ry 1977.
TI� re~ultg nf eh~ CnmpUt~~idng (T~b1e 1) indicgt~d that the h~ightg o~ ehe
gpnpdC~nrial gurf~ceg incre~sed during tihe perind of wnrming ~ who~.~
~nr rh~ hemigph~re (ehe heighC of th~ ATp~4 qurf~ce incr~nped by 168 dntn).
l~dw~vrr, in th~ l~w ].~titude~ they d~cre~~~ somewht~t (AT~~4 by 16 d~m),
' but Cnnsidernbly 1~gs ehan th~y increge~ in ehe higlt laCiCude~ (AT0~4
by ~21 dgm). ~hu~, nnly ~ redistribu~inn of energy by 1.atitude cuttnot ex-
plgin ehe w~rming process. ~'he energy evidene~.y nlsa arrives from the
lnwer- and nbove-lying layere o� ehe aCmosph~re.
Table 1 ~
Mean GeopotenCigl Valueg (Ii dam) ObCained Using Rudiometer llaea from the
Isobaric 5urfaces
2 CenepHU~ wtitpota, zpad
~ ~ ~
p .u6 - 3 _ "
75 J5 3.'1 ~J y+, ~
JJ ~ J " ~ ~.7 5J ~~J
1 ~s os oz
` a ~ - -
4~~ACK~G~A 1976 r. 5 G aueapa 1917 r. ~ 14 �Hnapx 1977 r,
5 3322 3~6G J;i~S 3aa~ti :3:i11 1:,3Q 3541 3:i2i a~~3 3515 3;i34 3:i31
2 3890 4044 d20,i ~l~�!i �11~:i �IliS 41!)5 ~#Ii~J ~312K 4135 419U a1~2
U,4 5019 5149 5~304 +~I~JO 33~~4 5349 ri397 ;~359 5249 5306 a'i90 ,i315
KEY :
1. mb
2. North latitude, degrees
3. hemisphere
4. December
S. January
The third, final warming wave began in the third ten-day period in February.
The waLmi.ng process aCtained its maximum development on 6-9 March, when a
temperature of 22�C was noCed over Kheys Island at 45 km and the southerly
wind had a velocity greater than 60 m/aec.
In the lower mesosphere the anticyc'one, extending from the direction of
the Pacific Ocean, occupied the pole, changing the circulation over the
western hemisphere. The rocket stations Thule, Poker Flat and Primrose
Lake during this period noted stable easCerly winds. In the mesosphere '
an anticyclone was observed over the pole about two weeks. In the strato-
sphere there was no pressure restructuring in the high latitudes. By 20
March the warming process had ended.
In order to characterize the intensity of circulation in the first two warm-
ing waves we computed the index of ineridional circulation IM by the Kats
method [2] using the daily values of geopotential height at the 10-mb
39
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~OI~ O~FICTAL US~ ONLY
-
level ulong the circles of ~.atiCude 7d� and 40�N for Nc~v~mb~r ~n~l Deeember
1976 ~nd J~nunry 1977.
Table 2
Temper~Cure ~t SernCop~us~ (e�C) gnd Index of Meridional CirculgCion (IM
d~m/d~gree meridian) ~e 10-mb Level buring ~irst and Secnnd Warming Waveg
1976/1977
!lo no� g nepi~on ilocne B nepnoA flocne
re~t.1~Ili1N I norenne� norenne� ii noren� notenne�
~ IIIIA Z HIIA 3 11CHItN NNA 5
~o. xeac. 6 -I~ 12 -24 *2 -46 � `
~w ~o^ c. w. 1,66 1,20 2,60 1,0
t ~ -15 +9 -30 -8 --23
eorrorpaa
!M ,~pe c. 1,08 2,2 1,32 3,26 1,88
K~,Y :
1) Before warming 6) Kheys Island
2) During period of first warming 7) 70�N
3) Afrer warming 8) Volgograd
4) During period of second warming 9) 40�N
5) After warming
The index of ineridional circulation during this period in the high and
middle latitudes has two clearly expressed main maxima corresponding to
the moment of onset of warmings. The maximum value IM in the high lati-
tudes in the first warming was observed on 17-19 November and exceeded
by a factor of 2.5 the IM value before the warming, whereas in the middle
latitudes iC was by a factor of two.
The second IM maximum is noted in the third ten-day period of December; it
is greater than the November maximum and in the middle latitudes the IM
' value attains 3.26 dam/degree meridian, whereas in the high laCitudes it
has a value which is somewhat less and equal to 2.6 dam/degree meridian.
A comparison of the index of ineridional circulation with the temperature
values in the neighborhood of the stratopause according to data for the
stations at Kheys Island and Volgograd indicated that near the moments of
the IM maximum it is possible to observe the maximum temperature values
(Table 2) .
A distinguishing characteristic of the winter of 1977/1978 was an intensive
development of the subtropical zone of high pressure in the Atlantic Ocean
region. The anticyclones developing in the troposphere were frequently high
and attained the 50-mb surface, and sometimes also the 10- and 5-mb su~
faces. The warm regions associated with the Atlantic anticyclones moved
40
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~dtt dCT~'I~~AL U5~ ONLY
intn Ch~ pnlur laeiCudes r~nd c~used gtra~ospher~.C warmi.n~g.
- .
~ O,N6
0,46 .y~~ ~ ~
10,0436 1~,.~ ~p-ts ~
~ '0~454�n~ '
~ y~ ~
/ ~ O~J9~! : tl 35 ,
' N '
. ~ ' .
. -24� ~ .
. ~
O~JS 0~40 � ~ ~ .
. 0,45 ~ .
. ~
. g � ~
~ ' � ~ . . :~9 ~~J~7 ~ ~ ~ � � � ,
. ~
l{461 0,4
~ '�p,40 N '6~~ g
0,45 ~ . � f0~ ~ � . ~ ~ O,JS
~ . . ~ .
�
. . ~
.
. ~ p, 40
. ~
. ~
0,45
.
s
Fig. 1. Pressure map at an nltitude of 55 km on 14 March 1978. The dots rep-
resent satellite orbits.
The first warming was observed in mid-December-early January; it was local
and was noted only in the neighborhood of the stratopause. The temperature
in this case increased by 30-40�C. Temperature maps for the levels 35 and
40 km for 3 January 1978, constructed using data from an American satel-
lite, show a displacement of the warm region into the polar region. The tem-
perature at the center of the region became higher than those values which
are observed in the subtropical zon~. This gives basis for assuming that
in addition to advection, other factors also participate in the warming
process. During the time of this warming there was no pressure restructur-
ing ar the 10-mb level.
The second warming wave began on 25 January. At the end of January, at all
levels from 30 to 60 km, a pressure restructuring of the field was ob-
served. The temperature maps, compiled on the basis of satellite data
41
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for 31 J,inuary 1978, ne 35 ttnd 40 km show suttnner tempcr~ture d~.stribu-,
Cton Ln C}t~ pnlnr reginn~ AC ~n altieude nf 40 km over the pole there i~
ttn isothc:rm far 0�C. In contr~sC to Che prec~ding warming, ehig wa~ mora
extensive, chnracterized by a presaura restruceuring of the fieLd and ehe
lowering nf ehe he~t reginn ~.ntn the lower straeospti~re (to 20 km). Ac- '
cording to dat~z for Kheys Igland, the greatest amplitude nf temperarure
chAnge, equ~1 to 65�C, was noted in tr~e region of altitudes 28-30 km.
Simuleuneously wiCh wgrming in the stratosphere, n~ mesospheric altitudes
there w~s formntion of 1 region of cold. Over Kheys Island at an a1CiCude
nf 70 km the ~emper~tiure decreased by ~pproximately 40�C. The warming wgs
brief, nnd by 6 F'ebruary the process for the most part had ended. Accord-
in~ to the high-~1Cieude maps, constructed for 8 February 1978, in the lay-
er 35-60 km in Che extr~tropic~l lat3tudes of the northern hemisphere
a cyclonic circulaCion had been restored. In the first half nf March there
is u third warming wave which is acr.ompanied by the advance of the high-
nre55ure rr.~:t.cm ~tnd the heat zone :Ln pol.eward direction.
It can be seen from the high-altitude maps for constant levels for 14 March
that the anticyclone occupies the polar region at alCitudes 35-55 km
from the direction of Che Pucific Ocean and Canada (Fig. 1).
In the third ten-day period of March the process of final warming ends;
the anticyclone was dieplaced from the pole into Che Chukotka region and
iCs altitude decreased to 42 km.
IC is of definite interest to examine the change in some energy character-
isti~s dur.ing the warming period. As nn e:cample we give computations of
the following energy characteristics for the second warming wave in the
winte~~ of 1976/1977: kinetic energy (KE) per unit volume, meridional ad-
vection of kinetic energy (MAKE), generation of kinetic energy of zonal
moCion (GKEZM), zonal available potential energy (ZAPE), meridional advec-
tion of heat and mass [3].
In the computations we used meridional sections of the zonal meridional
wind and Cemperature for two meridians: 65�E and 75�W from the equator to
the pole for the layer 20-60 km.
The energy characteristics were computed for 8 December 1976 before the on-
set of the warming and 22 December 1976 during the ~oarming.
Figure 2 represents meridional sections of kinetic energy for S and 22
December. The KE distribution on 8 December is characterized by three
clearly expressed maxima associated with the maxima of zonal velocity: in
the eastern hemisphere in the middle latitudes at an altitude of 35-38 km
(101 J/m3) and in the equatorial region at an altitude 25-27 km (101 J/m3);
in the wes ern hemisphere in the high latitudes at s~n altitude 25-28 km
(2�101 J/m~) (Fig. 2a). The KE reserves in the layer 20-60 km in the east-
ern and western hemispheres are close and are 0.?.3�1020 J(these and
42
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~ rnK oHyr~cr.~ ns~ orrL~r
gimilur evnlunrions were mude an ~he a~gumpCion of tt xdnnl diser~.buCion of
temper~ture ~nd velocities in ehe en~tern nnd west~rn hemiapheres). Most
n� the K~ is deCermined by ehe xdn~~ veLoc~.Cy. Zes contribuCinn is 0.12�
lOZ~ J in boCh ~he easrern und weseern hemispheres.
~ Q J ~o'' ~o'' ~o' ~o�' >o" ~1
so N \ u 1 ~o, yq'',io'
N i v ~ " J�1o� v
f0~ H ,10,'~ 1d�
so H ~I
10'
4d ~0 ~ f0 ? FI -f0 ~ ~0 ~
~o� ~ ~ fo� N e�~o' ~~~o'
30 ~~~o U 8 H
B ~ ~o�
20 ~o' ~ B
~o so qo so >o ~o so 9o so y~ c.w. N
A BocmovNOe $ 3ano8HOe A Boc~rrovNOe ~ 3onelNOe
~ noayurapun C no.oywopu~
Fig. 2. Meridional section of distribution of kinetic energy. B) regions of
maximum values, H) regions of minimum lcinetic energy values, J/m3. a) 8
December 1976; c) 22 December 1976.
KEY:
A. Eastern
B. idestern
C. Hemisphere
By 22 December the KE reserves in the eastern hemisphere had increased to
0.26�1020 J and in the western hemisphere to 0.22�1020 J. The KE maximum
in the eastern hemisphere attained values 2�101 J/m3. The KE maximum attain-
ed still greater values in the western hemisphere 3�101 J/m3 (Fig. 2b).
The greatest KE increase in the eastern hemisphere is observed in the lat-
itude zone 70-90�N from 0.29�1018 J to 0.20�1019 J.
In the western hemisphere in this same latitude zone there is also the max-
imum KE increase: from 0.19�1019 to 0.52�1019 J.
The developmene of the Pacific Ocean anticyclon~~ and its northward displace-
ment led to a marked intensification of ineridionality in the high lati-
tudes. For example, in the latitude zone 70-90�N in the eastern hemisphere
the contribution of zonal velocity to KE was Q.65�1018 J, whereas the con- _
tribution of ineridional velocity was 0.13�lOly J. In the western hemisphere
43
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~Oi~ O~~ICIAL US~ ONLX
the prcdominun a o� the contribution of ineridionnl veloCity is sti1.1 gretit-
cr 0.55�10~~ nnd 0.47�.1.p1~ J respccCiv~~.y.
~o~" a~ ~'~"6 mb
a~
O,k
60 ~ a6
1 _ .
?
SO ~ ~ \ 1 2
~ ~
1 ~ ~
40 ~ ~ ~ s \2
. ~
10
~
� ~
JO ~
1-
?~0 QA~ Q04 0,06 0,09 Q10 Q1? O,1ti Qf6 Q18 K3,f0"d
~~0 Q2 Q9 Q6 Q113, f0"d~ln Jl~
Fig. 3. Vertical profile of kinetic energy (a) and available potential en-
ergy of local moeion (b). 1) 8 December; 2) 22 December
During the period from 8 through 22 Dec~mber there was a aubstantial re-
atructuring and vertical redistribution of l~. Figure 3a shows the ver-
' ticnl profiles of KE for 8 December (curve 1) and 22 December (curve 2),
constructed for the northern hemisphere. Whereas for 8 December (before
the onset of warming) there was characterisCically a monotonic decrease
in KE with altitude, the vertical KE profile for 22 December reveals a
well.-expreased maximum in the region 30 km. In the lower part of the atmo-
spheric region which we considered (approximately to 23 km) there is a de-
crease in KE during the period fram 8 to 22 December; aloft up to 60
km there is a considerable KE increase. A similar picture is observed
in both the western and eastern hemispheres.
The mean rate of KE change from 8 through 22 December (during a period of
considerable KE grawth) as an average for the hemisphere was 0.20�10� J/
(day�m3). The maximum KE increase was observed in the zone 70-90�: 0.44�
10� J/(day�m3) in the hemisphere, 0.32�10� J/(day�m3) in the eastern hemi-
sphere and 0.55�10� J/(day�m3) in the western hemisphere. It is interest-
ing to compare these values with the estimates for the generation of kin-
etic energy of zonal motion (GKEZM). On 8 December the mean absolute GKEZM
values were 0.20�102 J/(day�m3)~ on 22 December 0.23�102 J/(day�m3).
r-
These estimates show that exchange between zonal potential and kinetic en-
ergies can introduce a substantial local contribution to the evolution of
KE in the atmospheric region which we considered.
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rok n~~zci~~ us~ drnY
mhe regerves o~ ~v~ilnble po~ettCi,tl energy nf. zon71 moei~n (7,AY~) in th,c
entirc l~yer from 20 eo km du:ing the congider~d p~~idd eh~nged in~ig-
nlt'Lr.,nnely: from n.1.~�10 ~ J an 8 ne~ember to 0.1~~10 J nn 22 Dea~mb~r.
13u~ w~~ nrite ri Nt~bse+�it[nl redi~eriburian oE 7.AI'1, wirh n1CiCude. ~igur~ ~b
HI~~wH v~reic:~~l pro~il~g nE 7.AI'~ c~ngtru~ted �or th~ nnrthern h~mi~ph~re
for g Uec~mber (CUrve 1) and z2 UeCember (curve 2). Approxim~t~ly ~bave
the 16 mb gur~~ce Chere is ~~?n ~ppreci~~ble decre~se itt zAt~~ nn 22 ll~c~mb~r
in comparisnn with 8 necember; belnw ehig surf~ce, on Clte nther h~nd, th~re
is ~n incre~ge in zArL (~t the lower bnund~ry o� ~he region to 0.6�1U~5 J/
m). Thu~a, thc ch~ngc in KI: and zAPC with aleitiude i~ in nntiph~~e.
Tgb1~ 3
Me~n Absolute Values of KC Influxes, Influx of He~C (J/dgy�m3)) ~nd Influx
of M~sy (~/(day�m3)) as Result of Meridion~l Circul~tion, 1976
$ becr_mber 22 becember
KC influx b.12~101 0.92�101
Heat influx 0.35�103 0.72'103
M~s~ influx 0.23�101 0.45�101
In conclusion we will digcuss the estimates of ttie influx of KE, henC and
mas~ as ~ resule of ineridional circul~tion. Tab1e 3 gives estimatea nf
ehese parameters for the t~orthern hemigpherP for 8 and 22 Uecember.
'Che contribution of the m~ridional circulation to change itt KE (in compar-
ison with Che mean rate of K~ change) is extremely significant and can ex-
ert an influcnce on the KL change. During a period of warming the KE in-
flux as a result of ineridional circulation increases by almost an order of
magnitude. 'The influxes of heat and mass as a result of ineridional circul-
ation also increased during a period of warming (by a factor of gpprox-
imately two).
Our computations make it possible eo draw the following conclusions:
'I'he period before the onset of a warming (8 becember) was charncterized
by a monoConic decrease in KE with ~l.titude; during a warming period Chere
is a well-expressed KF: maximum in the region 30 km.
2. During the period of the warming process there is a KE decrease in the
lower stratosphere (below 23 km) and an increase in Che above-lying layer;
in general, in the layer 20-60 km the KE almost doubled.
3. The ZAPE vertical profile (bot}~ before the onset of warming and during
the warming period) is characterized by t}~e presence of a maximum aC ap-
proximately the level of the 16-mb surEace; above this maximum, during
the period of warming there was a decrease, and below an increase in
ZAPE; on the whole the ?.APE reserves in the entire layer 20-60 km changed
insignificantly.
45
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~Olt d~~ICIAI, US~ ONLY _
`~h~e r~~~lt~ ~~r~ ~vid~ntiy Gh~r~cr~rieti.e for moge w~rm~.ng~ nccurring wieh
~ pr~~~ura r~~truCtu~ing.
BIi~Lt()(~ItAt'HY
1. A'TLAS VYSOTNYKH KAIt'~ SLOYA 35-60 km/TgAd (ACIa~ nf High-Level CharCe
fnr th~ L~y~r 35-60 km/Ceneral A~rdlogi~~~. Oba~rvatory), Moscow, Nos
1U, il, 1~7g.
2. Kae$, A. L., T5iitlttJLYATSIYA V 5TItATOSF'E1tE I MESOSFERE (Circulatinn in
the Ser~Cn~pher~ ~nd Megoepher~)~ Leningrad, Gidrometeoizd~t, 1968.
3. LnrettCS N. ~~'ItIRdbA I T~O1tIYA OBSHCH~Y ~SIRKULYATSII ATMOS~RY
(Naeure gnd Th~nry df Gen~rgl Circu].geion of the Atansphere), Lenin-
grad, GidrnmeCenizdat, 197n.
4. Scherhag, R., "Die explosionsartigen Stratospharen eiwarmungen dea
Spatwinters 1951-1952," BER. D~UTSCH. WETTERUIENST, Bd 6, No 38~ 1952. -
J
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UDC 543.426;547.6:614.11
INVBSTIGATION 0~ TH~ BACKGItOUND CONTCNT OF POLYCYCLIC AROMATIC HYDROCARBONS
I'I~S~NT IN Alit
Mnscow METEOItOLOGIYA I GID1tOLOGIYA in ~uss3an No 6, Jun 79 pp 41-45
~ [Article by Dnceor of Chemicnl Sciences F. Ya. Rov3nskiy, T. A. Alekseyeva,
CandidnCe of Physical and MaChematical Sciences T. A. Teplitskaya, Insti-
tute of Applied Genphysics, Moscow State University, submitted for public-
~Cion 23 October 1978]
Abstract: The article describea an investiga-
tion of Che background content of polycyclic -
aromaCic hydrocarbons (PAH) in atmospheric
air by means of extraction at room tempera-
ture and narrow-band lumine3cenC spectroscopy
(Shpol'skiy effect), including the spectra of
fluorescence, phosphorescence and excited
luminescence. In the organic matCer of aero-
sols, without use of chromatography, it was
~ossible Co deCermine 11 PAH, a number of pyrene
alkyl derivatives, homologues of naph~halene,
phenanthrene and chrysene. The quantitative
contenC is given for the seven prevailing com-
pounds. The ~ontent of 3,4-benzopyrene varies
from 0.001 to 0.04 �.g/100 m3.
[Text~ Polycyclic arvmatic hydrocarbons ~PAH), frequently having toxic and
carcinogenic properties, are substances occurring quite widely in the en-
vironmenC.
For the purpose of effective monitoring of the level of concentration of PAH
in the environment, especially in atmospheric air, it is necessary to have
rapid and reliable methods for the precise identification and quantitative
determination of PAH.
In many studies for the determination of carcinogenic polycyclic hydrocar-
bons in atmospheric air researchers have limited themselves to the search
for only the one strong carcinogen 3,4-benzopyrene, regarding it as an in-
dicator of the entire PAH group [10~. But Che organic matter of air samples
contains tens of aromatic hydrocarbons, some of which have a weak or ques-
tionable carcinogenic activity, whereas others are relatively highly ac-
tive (2]. A significant contribution to the total carcinogenic effect
47
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of PAH is from substitutied aromatic sCructures, since in contrast to Che
holonuclear structures related to them, in the substituted homologues o�
PAH Chere is ~requently an intensif~.cation of the carcinogenic propertiies
and the biological effecC can vnry greaCly in dependence on insignificanC
structural variationF.
The hydrocarbons accompanying 3,4-benzopyrene most frequently are carcino-
gens or cocarcinogens, enhancing the overall carcinogenic effect. In some
cases some of Chem can play tne role of inhibitors of the carcinogenic
e�fect, and then they lead to a decrease in the degree of the carcinagenic
effect. Accordingly, the spePdy deCermination not only of 3,4-benzopyrene,
as an indicator of the carcinogenic effect, bu~ also the entire range of
PAH, including substituted aromatic structures, is of great importance.
There are a number of physicochemical methods for deCermining PAH in en-
vironmental ob3ects: ulCraviolet absorption and molecular mass apectro-
metry, gas-fluid chromatography, and sametimes use is made of the lumin-
escence spectra obtained under ordinary conditions at room temperature
[5]. In the USSR, since the time of discovery of Che Shpol'skiy effect
in 1952, the development of inethods for determining PAH in environmental
ob~ects has rested on narrow-band luminescent spectroscopy. Up to the
present time this method has been used in various media for determining
up to 15 different holonuclear PAH; the particular ones detected has dif-
fered greatly among different researchers. The methods of hot extraction
of PAH and subsequent chromatographic separation have been generally em-
ployed j3, 9
Modern data on the occurrence of PAH in different natural ob~ects make it
possible Co postulate that the most usual way in which these molecules
arise ir~ nature may be either a thermal effect on organic matter or syn-
thesis, most frequently at high temperatures. The possibilities of chem-
ical transformations in the temperature effect process are also indicated
- by some prin,ciples and experiments in classical chemistry and biochemistry
[4, 8]. Therefore, when there is reference to determining the background
concentrations of PAH, the methods for preparing the samples for analysis
and the techniques for the analysis itself must exclude all types of tem-
perature or any other hard effect, and determination of only some holo-
nuclear structures is inadequate for determining the degree of the over-
all carcinogenic danger.
In this connection it was important to develop a method for the speedy de-
termination of PAH, including substituted aromatic structures, withouC
using hot extraction and chemical chromatography.
Such a method was developed on the basis of application of the Shpol'skiy
effect and has been described in [1, 6, 7]. In order to broaden the range
of determined PAH it was necessary to use all types of emission spectra,
' including not only the fluorescence and phosphorescence spectra, but also
the spectra of excitation of luminescence in a wide range of wavelengths
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r~x nr~~'i,CiAL U5~ nNLY
_ from the ultr~vinler ~o et~e red. ;,,~cli an app~o~ch m~d~ it po~sibl~ Cd de-
vel~p and uye ~ ~omplex nf lumine..aent-~p~CCr~l me~hndg ~mploying mnd~rn
typr:? of Hpectroflu~rimet~r~, whicti m~keg i~ poss~bl~e nr~C only Cd det~r-
mine hydrnr.~rbnn~ hnving ~e~nd~rd ~7n~lo~ueg, bue ~1gn ed diggnn~~ eh~ typp
oC molecul~r gtruCtiurc wl.th pns~it~l~ ~ide ~ub~eitueion~ of any lwnin~~c~nt
ttr~.lecule, giving structur~nl spec~ra und~r th~ cdndiCion~ of Ch~ Shpo1'-
gkiy effec~ [1]. Identifiratinn usi.ng ~tiand~rd an~ingu~s is ~~~ried nue
on Che b~s:ts o~ uge o E et~c uC1 -s --s h `
Zi = ~'1 + 1?'~, 2_~ _ .Y1 -F l)!:, .C~, a'_, y_~ E ~ .
The eigenvalues of the matrix A" are purely fictitious and the eigenvectors
of rhe problem (9) with corresponding normali?ation satisfy the orthogonal-
ity condition
_ I~ ,
~~Q~~;n - �na~
where b P is the Kronecker symbol, p and q are the numbers of the eigen-
vectors. 1~his follows from the property of antisymmetry for the matrix Ah
.
Assume that we must determine several eigenvectors and the corresponding
eigenvalues of the problem (9), close in absolute value to some prestipul-
ated number ?'j, that is, find several eigenvalues less in absolute value
and the corresponding eigenvectors of the problem
(A''-i~,E) L=i�~y (11)
N
in the space ~h, where E is ttie identity operator.r Taking into account the
representation (10) of the vectors from the space ~ h, the problem (11) is
written in the form
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, A~ ~ " �E
- y, E A" `~a ~ W � E 0 ~
~~r (~2)
Multiplying equr~Cion (12) by the operator -
A~' r E (13)
B ~ ( - y~ F. A"
we arrive At Che problem
-
Agz=vz, (14)
where
AA _ ` B, z _ ~ = (15)
Thus, if the dimensionaliCy of the unitary space ~ h is equal to n, instead
of the problem (9) in this space we have the equivalent apecCral problem
(14) in the real space R of the dimensionaliCy 2 with the real symmetric
maCrix Ag in the scalar vroduct
~
~ ~ D _ Dti 0 , (16)
w)R =(DR~ x~ 2+ w E R~ R- ~
0 Dh
By solving the partial spectral problem (1~?), we thereby find the orChogon-
al base of the invariant subspace of the B matrix. Since the B matrix has
the structure (13), and the eigenvecCors of the Ah matrix have ~he form
(15), it is easy to see that the vecCor components 4/i and i~ 2 zk of the
AB matrix corresponding to different eigenvalues will also be the orthogon-
al base of the invariant subspaces of the dimensionality two of the Ah
matrix in the space ~ h, and the ~igenvectors of the A matrix will have
the form (10).
A modification of the iteration process, known as the simultaneous itera-
tions meChod [9], has been developed for solving the partial spectral
problem (14). The essence of the proposed method is as follows.
Assume that in the space R we have some linear subspace Rm, generaCed by
the base, orthogonal in the sense of the scalar product (16), such that
the pro3ections of the first m eigenvectors Ag onto this subspace are dif-
ferent from zero. For convenience in further reasoni~gs we will exatnine
the base vectors as vector-co lumns of the matrix ~ 0 of the dimensional-
ity 2n x m, where 3 is the number of the iteration interval. An iterAtion _
with the number 3 consists of five main stages.
1. From the base ~ ~ we form the matrix of the dimensionality 2n x 2m
~i = ~~o, F (AAl] . ~17~
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whr.rr. ~(A~) i.s 9~mr �unctinn of the marrix A~, 1r~uvl.n~; lnvarianC th~ char-
nr.CeriqCic liner~r 9Uti9paces of Che m~trix A~.
2. Wr. Hep~iriiC~ t.hr. linr;irly tnd~~pendent v~~cCor-column~ by nrthogonfil.izr~tion
of ~h~ col.umn c~f the mu~rix. As a result we urrive ar ~ m~rrix of
thc dimen~ionallCy 2n x~(m 1) we retain in the base the vectors obtained
in the preceding iteration, it follows from forming of the matrix B3 in the
spectral problem (19) that it has the form
~
,
~ ~C T
v
where Q and F are some real matrices and .~.~-1 = diag ~v~ " 1, VZ`1,...,
y m-1~ is a diagonal matrix formed from the first m eigenvalues, obtained
in the iteration with the number j- 1 and arranged in an increasing order.
We have the following inequalities
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v( ~ v~~~, ~ vl-i, . . . , vm ` v~', (20)
that is, iterations of eigenvalues with idenCical numbers form nonincreas-
ing sequences, and Che limiting elementa of these sequences wi11 be the
eigenvalues of Che initial problem (14). The proof of this assertion is
based on the division theorem for symmetric maCrices [6] and the minimax
principle j8].
It still remains to examine the problem of choice of the function F(Ag) frow
(17) in the iteration process. Taking into account that we must determine
the lawer eigenvalues of the Ag matrix, the F(Ag) function must be selected
in such a way that firsC of a11 iC will suppress the components correspond-
ing Co the higher eigenvalues of the Ag matrix. '1'herefore, a simple method
for forming the F(A~) vectors in (17) is the application of one or more
intervals of known iteration methods employed for determining the minimum
eigenvalue of the Ag m~trix [6]. In this respect the most preferable method
is the inverse itexations method [6]. In the problem which we considered
the special form of the ~perator A, and in the last analysis, the Ah matrix,
makes it possible to invert the matrix operator B, determined by the equa-
tion (13). In actuality, the organizaCion of one interval of the inverse
iterations from the A~, maCrix requires solutions of a system of equations
of the type . ~
A ~ E Y F,
y y -
- r~ E A'' , Y, Fz
or, which is the very same, the system,of equations
L-i~E, H ~z.}.iy)=F,-I'tFa~
( W -I~Ea) (21)
where E1 or E2 are unit matrices of the corresponding dimensionality, and
F1 and F2 are,real vectors from the space ~ h, determined by the base vec-
tors from C~ 0, and the matrices L, H and W were determined in (8).
We introduce the new notations: _ _
x+ ly _ xu F~.+ iF~ _ Fu
~ X. F.
, �
and making similar transformations, the system of equations (21) is written
in the form ~
( L- i Y~ E, ) x� + Hx~ = F,,,
~ y
_~,,~E_.f~I(~~~~~E~~-?y) z~-F~- 1~(L-i~lE?)-' F�� ~22~ -
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With lu~own xS ehe ~olueion xu ~f Che fi.rs~ of the equatinn~ (22) is de-
termined directly, :3~I1CC the opr.r~tor L- i~ Isl i~ bl.ock-di~gonal, with
ordinury secbnd-order ~qu~re binclc~. zn ehe golut~.on o� ehe second equa-
eian from (22) we c~re de~ling wieh ~ binclc - three-diagona:l cnmpl.ex matrix
A~---(i~~~-~lY/(L--ir~~i)�'N), ~z~~
Chne is
~r?
Ax` =q, (24)
where
q~F - W(L--~riEi)~~ F~n
Ai B~ U
C~ A~ B3 ~25~
~ A= . . ,
- 0 CN_~ AN_~ B~~_t .
Cn? A,v
Here A~ are square and Bi and Ci are rectangular complex matrices, thp
specific form of which is determined by the rule of ordering of points in
the grid region and a finiCe-difference approximation of the problem (1)-
(2). The number of square blocks in the A matrix is equal to the number of
sections 8= 6i (or ~J) of the grid region and the dimensionality
Ni of each square block Ai is equal to the number of points in the grid
region in the corresponding section.
For solving the system of equations (24) we prepare a direct algoritt~m
for the i.nversion of the matrix (25) using its expansion into Che product
of the unitary matrix and the upper triangular matrix. Use is made of a
block variant of the tiausholder merhod with a partial sampling of the
"leading" column [7J.
We use the method of realizing one interval of the inverse iterations di-
rectly for solution of the system of equations (7) with stipulated values
of the tide-generating force, and in particular, this makes possible the
quite effective detettnination of periodic solutions of the problem (7)
witti a periodic (in time) rig;lt part fh with an arbitrary period JL of
oscillations, that is, numerically solve the problem of tidal waves in the
world ocean [3]. In actuality, assume that the right-hand side of the sys-
tem of equations (7) is stipulated in the form
77
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rox o~~zcit~, us~ oxLY
1,, y e 1~ ~ .
(Z6)
wher~ fh is ~ grid vector-funCtiion noti d~p~ndent nn ~he v~riable e, and
~ 2 J~ ~ti . We will se~k iiolueion of the prob].em (8) in ehe form
r.
Y.h ~ ~-1rof
5ub~tieueing expres~inns (26) and (27) into (7), we obtiain Che equgtion
- f w~,~n + An ~;o ` fo , . (28)
whoae form, with an accur~cy eo ehe notationa, coincides with (21).
~
:r----
_ ~
~r /
~ ~ ~1 \
?
, ~ S
- ~ ~ ~ i
1 ~ . ~y� ~
.
~ 1 ~4~ ~ 1` 1 13 ~P
1! ii \ ~j-~~
I' JO r' \ Cf ~ ~ ( ~ ) 15
~ 1 / ~ C14 l ..._i
LJ
\ � -r~---= 9 =J ~f=~ f0 /
Fig. 1. Region of solution of problem of free oacillationa and isolines of
smoothed depths of the world ocean.
~
_I ~ r 1 - ~4
. ~ ~
~~~9 r
_ ~ 4'!~
n '~~r
~ 9 ~ ~ ~~~~w ~
~ ~ ~ ` . ~f~'.' : \ ~,�7.i
~ - - , ~ , . : ' ~ , ~i~~
, : ~ ~ ~ ; ~ , ~ ~ .
'=;~~1,M,~ . . ,
~ ~ ~ f! ~ ~ ~ ~ 1 ~ ~
f0'n~~; ::t ~ ~~4 i ~ . 1 i i ` ~ `l~
. / ~ ~p ; ~ ~ r
%'i~~ ~ i 1 ;i ~ ~ f ~ J~
~ ` f~ ' ~ ~i~i ~~...'i4 B~
~ ~ .100~ 7_~ �
j~~~ , ~ 80 1, s ~ ~ ~ ~ ~
~ ' 1 ~ r~ ~-4 " ' , S ,
~ _ _ f ~ , ~ ~ .=r''r ' ,
'r . J'- t ~ ~1 4. - _0 ,
_ Fig. 2. Main semidiurnal wave M2. 1) cotidal lines each 30�, 2) isoampliCudes
Numerical Experiments
In order to carry out numerical computations using the model descrihed above
the region G was selected in the form represented in Fig. 1. In this same
figure we show isolines of smoothed depths ot Che world ocean. The n~bers
78
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of ~he ignliney correypond to u uriifnrm breakdown ineo 18 pnre~ Ue~ween
~hc m~ximum (max(U) ~ 5.2 !cm) ~~nd minimutn (min(n) ~ 1 km) depCh value~.
The grid re~tdnw were c~0il9lxUCl:pC~ wi.th use af uniform intervals 4e m n'~ ~
5�. With ~his r~~ol.ution Che m::~trix A in �ormul~ (25) h~s the order 1427.
r"~ ,
J ~ + ~
J,�; ' p z . --a ' - t
`~~~.8~~,,i ~ .
~
~ ~ ~ . J ~a " i i i i ~ ~~}j?
i Y ~S � ~ ~ 1 I j 6
' ' ' ~ ~ '
~i:~'.` ~ ` ~ I~ ~�~J~~ 2~ ~~J ~ ~
Z' 1 ~ y~~~~ 1\ ~..~i ill
..el ~ 'l ll 1~~"~ 11~ i ' ~ " � f ~ ~ I / 1 ~
~~li ~N ~ i ~ 1~ `1~~ l~`~.i ~
r~;r� 1~~ i~ A 6 1~ f1~
ii~ 1I ~1,'J` `d"`~ i ~ 1 ~
~ ~~~6 ~
~_r.~',~~ ~ ~ 4 ~ ro- ~ 1,~~. ~ .
r" ~ ~ ~ 1~ 't+ `i ~ ~ =f~i i ~ ~ j.
r R~i-"~ 1 i ? ' i ~ ~i ~ ~ ~ ~ �,J~,�
I'~~ ~ , ~ It r Cr ' 1 ~ ~0~ J. ~ ~ 1
I,/ 1`~J.~,;,g 11-'1Y J 9~ ~Q ~i `Y ~j i i
/ , - S:3'-L:�% 'i: \.'.F s=r ='4- -.1- 'T"f~-! ~ ~
~ ~ . . ,
' Fig. 3. Cotid~l linas (1) and isoampliCudes (2) of computed eigen�unctiori ~
with period of oscillation~ ''G = 12.3562 tiours.
The computarions indicaCed an adequaCe effectiveness of Che proposed meChod
and ttie pattern of Che fields of isophasal and coCidal lines of the'cnmputed
rtZ wave qu~~litnCively coincides wiCh known ex*:~r~:^~nrs~l and numerical ideas
concerning its structure [3), [11]. We note t'iaC since in the considered
model friction is absen~, tlie values o� Clie isoamplitudes were exaggerated.
Table 1
CIep?~onW Ko.ie� ClerHOAN ttone�
~~0~~'~~~ Gain~ii coGcrerii� r~O~Yn~~ 6aNxt~ co6creeu�
coGcree~r� uar c~yi~hunii ~o6c~rnett� it~tx ~yuKUt~i1
ttNX 4HCC11 ,~1 ~ HWX 4}ICClI K
1 2 1 2
1,517703 11,5000 1,446935 12,0622
1,SU5195 1 I,5954 1,412512 12,3562
1,490266 11,i I15 1,38~716 12,5951
t,472138 I I,8557 I,374438 12,G985
KH;Y : 1,453413 I 2,0085
1. Moduli of eigenvalues
2. Periods of oscillations of eigenf~~ictions 'G, hours
In computing the eigenfunctions of the difference operator Ah in the iter-
ation process m was selected equal to 14. In different variants of the.
computations the cor.vergence was attained on the average after 10 iteraL -
tions. The criterion for ending of the computations was not only a coincid-
ence of the eigenvalues obtained in two successive iterations, but also
the condition of invariance of the corresponding subspace with the base
vectors from in formula (17). It was assumed that the invariance is
observed if the corresponding Gram matrix of the normalized vectors from
deterniined in (17), has the rank m, ;:hat is, if with an adequate de-
gree of accuracy of in eigenvalues the Gram matrices are equal to two and
the others are equal to zero. T.n addition, it follows from formula (15)
- 79
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eh~~e ehe sp~nCrum of etie Ag m~Crix mugt b~ mulCiple. This is algo one of ~
the crit~ria f:nr ~nding the iCeruCiong.
'~he use of inverse iteraCionq in cnmbingtion with tihe simuleaneous itera-
tinng methocl fnr ~ group of vector~ noC only ensures a r~pid convergence,
bue ~lso to gome degree giveg definiCe guarantee that in Che computed
intervnl ehere nre no other eigenvglues other Chan tihose which have been
found.
As.~n example we will ciCe tiwo variants of compuC~tiona of eigenvalues
of ehe operaeor Ah with m n 14 for 1.405143905�10'4 nnd 1.454444�
10'4, thae is~ for frequencies in ehe neighborhood of the M2 and S2 waves
respectiveJ,y. Among the 28 eigenfunctions found in these two variants,
only 18 were dif~erene, thaC is, Che interva~.s of the computed eigen-
values were superposed on one another. Table 1 gives tt~e moduli of the
computed eigenvalues and Che corresponding periods of oscillations of
the eigenfuncCions of the Ah operator. Figure 3 illustrates one of the
eigenfunctions wiCh a period of oscillations 'G ~ 12.3562 hours.
r
In this article we tiave for the most parC examined the camputakion sepects
of solution of the partial spectral problem for discr~:~e analoguey of the
linearized tidal operators. The application of this method for studying
the dynamics of Cidal oscillations on the basis of a geophysical interpreC-
ation of the resulea of numerical experiments will be discussed in special
publications.
~ The author expresses appreciaCion to G. I. Marchuk and B. A. Kagan for for-
mulating the problem and constan~ attention to the work and to V. V. Pen-
enko for assistance in developing the method.
BIBLIOGRAPHY
1. Gantmakher, F. R., TEORIYA MATRITS (Matrix Theory), Nauka, 1967.
2. Ladyzhenskaya, 0. A., KRAYEVYYE ZADACHI MATEMATICHESKOY FIZIKI (Boun-
dary Value Problems in MathemaCical Physics), Nauka, 1973.
3. Marchuk, G. I., Kagan, B. A., OKEANSKIYE PRILIVY. MATEMATICHESKIYE
MOllELY I CHISLENNYYE EKSPERIMENTY (Ocean Tides. Mathematical Models and
Numerical Experiments), Lenillgrad, Gidrom~teoizdat, 1~77.
4. Mikhlin, S. G., VARIATSIONNYYE METODY V MATEMATi~:iESKOY FIZII:E (Vari-
ation Methods in Mathematical Fhysics), Nauka, 1970. _
S. Penenko, V. V., "Computation Aspects of Modeling of the Dynamics of At-
m~spheric Processes and Evaluation of the Influence of Different Factors
on Atmospheric Dynamics," NEKOTORYYE PROBLEMY VYCHISLITEL'NOY I PRIKLAD-
NOY MATEMATIKI (So~.e Problems in Computation and Applied Mathematics),
Novosibirsk, Nauka, 1975.
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rnn nr~icznL us~ ornY
6. Wilkinq~n, ,f . 1~. , ALGI~I3RAICHL,SKAYA PIt013T~~MA 50135'TV~NNYKH 'LNACHCNYY (A1-
~ebrutc ~'robl~m o� Cigenv~lues), Nnuk~t, ~570.
7. Wilkitt~nn ~tnd Reinsch, Sp~AVOCI-INIK ALGORI7.'MOV NA YAZYIt~ ALGOL (H~ndbook
of Algori~hms in ALGOL L~xngu~ge), LINEYNAYA ALGEAItA (Linettr Algebr~?), _
Moscnw, Mashinostroyeniye, ~.976.
8. i~ ~7ddeyev, ll. K. , I~'addeyev~t, V. N. , VYCHr5I~~T~i.' NYYI: MLTOllY LINI:YNOY AL-
_ GCBRY (CnmputaCion rieChods of Linear Algebr~), Moscow-Leningrnd, ~'iz-
m~egiz, 1963.
9. i~'addeyev, D. K., raddeyeva, V. N.,~VYCHISLI'r~L~NYY~ M~TObY LIN~XNOY AL-.
GT:BRY: zAI'I5KI NAUC~INYKII SI:MINAROV LOMI (Compue~tiion MeChods in Linear
Algebra: NoCes of Sci~n~ific 5em~.nars of Che Leningrad Division of the
MaChematics Institiu~e), edited by V. V. Voyevodin, Leningrad, Nauka,
Vol 54, 1.975.
10. Platzman, G. W., "Normal Modes of the Atilantic and Indian Oceans," J.
PHYS. OCEEINOGR., Vo1 5, No 2, 1975.
11. 7.ahe1, W., "MaChematical and Physical Characteristics and ReCent Results
of Ocean Models," ?.ECTURE NOT~S IN PHYSICS, COMPUTING METtiODS IN APPLIED
SCI~NCES. SECOND INTERNATIONAL SYMPOSIUM, December 15-19, 1975, Springer-
Verlag, Iierlin-Heidelburg-New York, 1976.
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UDC 551.46.062.5(262.54)
WAT~R EXCHANGE B~~WEEN THE SEA OF AZOV AND THE BLACK SEA WITH OPERATION
OT~' A 1t~GULATING STRUCTUI~ IN IC~1tCH STRAIT
Mogcow M~T~OROLOGIYA I GIDROLOGIYA in Russian No 6, Jun 79 pp 67-73
[Article by Cgnd�tdate of Geographical Sciences I. A. Shlygin, State Ocean-
ogrnphic Institute, submitted for publicaCion 5 January 1979]
AbstracC: By ehe method af mathemaCical model-
ing of the water and salt balances in Che Sea
of Azov the author has computed the parameters
of water exchange Chrough the Kerch hydraulic
complex. It was possible to determine the stat-
istical characteristics, variability and guar-
anteed probability of the magnitudes of Sea of
Azov and Black Sea flows in different stages
in the process of regulaCing sea salinity. The
article gives the guaranteed probabilities of ~
the total time during which discharge openings
are opened for Che passage of migratory fish
with an accompanying wind flow during the spring
and autumn.
[Text] Water and salt exchange through Kerch Strait is of fundamental im-
portance in forming the hydrological regime of the Sea of Azov. It not
only exerCs a direct influence on sea salinity (the fraction of salt Px-
change with the Black Sea is 97% of Che salt balance of the Sea of Azov),
but also exerts a decisive effect on the chemical and biological bases
- of productivity, and also on the extent of areas of different salinity,
which in turn limit the habitats and development of different species of
fish.
Modern negative changes in the hydrological regime of the Sea of Azov have
occurred as a result of Che totality of natural and anthropogenic factors,
expressed in a reduction in the inflow of fresh water (the nonreturned with-
drawals alone amount to 9-12 km3/year) and changes, in this connection, in
the characteristics of water exchange through Kerch Strait. The ratio of
the quantity of inflow of Black Sea waters Co runoff from the Sea of Azov
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,
~otz oH~t'LCZAL USL ONLY
in naturul period w~~ 0.68; duritig the 1~ge eight yearg ie was 0.85 [5].
Chattge~ in nc~ r~ea regime were G:cpressed in a disruption nE ehe b~l~nce
of biogenous substances, ~ deCer:Lc~raeion 3.n Che oxygen regime, and mosC
impnrrunt.Ly, an incre~~c in Cha mean salini~y of yea waCer from 10.5�/00
uttder nntur~~l condiCiona Co 12.4�/0o during the last eight yenrs. Thus, ~
study of l�he characCeriytil.cg nf w~ter exchunge is neceseary for ~n inv~st-
ig~tiou of thc ettrl.re complex oE hydrolog:tca~., hydrochemical ~nd biological
changes in Clie seA reg3me.
'Ihe modern p~irnmeters of watier exchange, as well as its changes by periods,
are ret'rospecCive; the statistical characteristics are given in [1, 5].
At the same time, in order to opL�imize the hydrological regime of the Sea !
oE Azov, tl~ere are pl~ns for carrying ouC a whole complex of waCer manage-
men~ mcasures, postulatin~ u change in Che water balance components of the
sea. Among l�liese measures the most ~.m~orCant are ttte s}ii�ting of runoff
from other basins and regulation of ~oater exchange through Kerch Strait. In
both cases tliere is a change in the condiCions for water exchange between
. the Sea o~ Azov and the B1ack Sea. Hawever, with a certa~n degree oF prob-
~ibility it can be postulated that whaCever may be the influence exerted on
river runoff (increase in withdrawal, shifCing of direct:ion of stream flow,
etc.) on a scale not exceeding the present-day changes in river runoff,
the general patterns in variation of water exchange through Kerch Strait
will remain unchanged. IC would be a different matter with the construc-
tion of a regulating structure, when the artificial restriction of entry
of saline Black Sea water and the controllable discharge of waCer and salts
from rhe Sea of Azov will first make i~ possible to reduce the salinity of
the Sea of. Azov and subsequently maintain it at the opCimum level. .
~
The probl.ems involved ir, a change in sea salinity in a case of regulated
water exchange were fir~,t examined in [6, 7, 9]. Computations of regulation
of the salinity and level of the Sea of Azov have been made by the method
af mathematical modeling of the water and salt balances of the sea [9].
in the computations use was made of river runoff and apparent evaporat:ion
series obtained by Ye. A. Asarin and A. M. Naumov at the Gidroproy~lct by
the statist:Lca1 tests method; the statistical parameters of the natural
series adopted in the modeling are given in Tab1e 1.
The annual quantities of natural runoff were modeled using ttie D. Ya. Rat-
kovich scheme [8J. Tt;e intra-annual 3istribution Qf runoff was ascertained
by analogy with the distribution of equal annual volumes of the observed
untransformed runoff. The total prospective ~zithdraw~l, determined taking
into accaunt the dispatcher graphs of reservoir operation, was superposed
on the series obtained in this way. The water consumption in the basin was
taken in the basin in accordance with the "Sea of Azov Scheme" (residual
inflow 28 km3), and also artificially increased by 2 and 4 km3. As a result, -
we obta�ined three inflow variants, each with 25 30-year records in nach.
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Table 1
Staristical i'arameters of Naeurul Itunoff and App~renC EvaporaCion Uaed in
Modeling (Accord.Lng tn Ye. A. Asarin and A. M. Naumov)
CpeAFiee M~toro�
PeKn (croop, y48CTOK~ ,ner~iee ~~saqeftHe2 C~ Ca
~
g p. Aoti, L~x~ana 21,6 0,34 2 C~
4 p. ,Q01~, Y4tl~TOK uNM718 -
A~+oncxoe Mope 6,3 0,62 2 Co
g r KyGaNb, KPBCHOJ(8P 13,4 0,1? 2 Ca
6 Btt4nMOe HenapeHtte 20,03 0,18 0,0
K~Y:
1. River (station, reach)
2. Mean long-term value, km3
3. Don River, Tsimla
4. Don River, reach Tsimla-Sea of Azov
5. Kuban' River, Krasnodar
6. ApparenC evaporation
The monthly values of apparent evaporation were obtiained by multiplying the
total annual value of the element by a coefficient constant for each month.
The latter was determined from long-term data on the intra-annual distrib-
ution o� precipitation and evaporation.
The discharges through the hydraulic complex were determined using hydraulic
dependences for a bottom spillway with a broad apron (a total of 34 water-
discharge spans). The level drop in the pools of the hydraulic complex was '
determined by the algebraic summation of the balance level, formed by river
_ runoFf, precipitation and evaporation for the Sea of Azov po~l, and the
mean monthly level for the Black Sea pool, and a special level-differ-
ences correction. The latter was obtained by V. P. Belov and Yu. G. Fi'lippov
[4j by Che hydrodynamic method using star.dard wind fields [3J.
The camputations were made using 30-year runof� and apparent evaporation
series with time intervals corresponding to the "lifetime" of standard wind
fields (from 6 to ~+8 hours). The time for computing one 30-year series on
a"Minsk-22" electronic computer is 12 m~nutes.
The process of regulating salinity of the Sea of Azov is accomplished in
three stages.
1. The mean sea salinity for each computation ~nterval is greater than
10.5�/00. The water accumulates in the Sea of Azov to the upper reading .
(+10 cm abs.). When this reading is exceeded t~ere is a discharge of the
excess Sea of Azov waters. However, if the quantity of water entering the
sea is less than. the quantity evaporating and the sea level drops, upon :
reaching the reading -60 cm abs. the Black Sea water is admitted. Since ~
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~ox or~xci~ crs~ ornY
y under nverage condiCions Che fresh Ual~nce of the sea is positive, w~.th
prednminantly d~.ychnrge of Sea of Azov wnter there ~.s a decrease in the
s~alr reserve and u decrease in sea salinity.
2. Upon aet~ining a s~l3nity of 10.5�/0o tihe additional withdr~~wal of fresh
wuCer is po~siUle. Therefore, in Che nexC cnmpuCa~~.on interval a correction
is subtracred from the pro~ected river runoff; this correcrion :is equal to
ehe volume of the ~dditiional withdrnwals for er~ch computatiion ~.nterval
(the volume of these wi~hdrawals is up eo 6 km annual~.y).
3. However, if with addiCional withdrawal of river water Che salinity con-
tinues to drop, with its decrease to 9.50/0o there is a discharge of the
overflow sea prism. In thc next compuCAtion intervals, when the level in
the 5ea of Azov ponl exceeds the 1eve1 of the B1ack Sea poo1, there is a
furrlier disch~nrge of Sea o� Azov water; wiCh the opposite situation there
is entry of Black Sea water. Such mutu~lly opposite inflows of water occur
up to Che Cime of an incrcase in Sea of Azov salinity Co 9.5�/00.
From Che poinC of view of an investigation of water exchange, stages 1 and
2 are equa'l1y imPortant and hencefarL-h will be considered ~ointly.
In roodeling the regulating process, regardless of the stage of decrease in
sea salinity, there was modeling of spring and autumn passage of fish .
through the hydraulic complexes. It was assumed Chat the passage of the
migratory fish through the dam occurs in April-May from the Black Sea into _
the Sea of Azov and in Ocrober-November in the opposite direction with an
accompanying wind flow. For this purpose the level drops near Che dam _
created by the wind were used [4]. In Che ~vent of formation of level dif-
ferences associated with "accompanying" winds, seven openings in the dam
are opened (length of the spillway front 100 m) and. the fish are able to
pass through with the accompanying wind current, ti3t is, the same as un-
der natural conditions. The volume of fish passing through was taken in-
to account in the further analys~s as a component part of the water ex-
change. At the same time, we ascertained the total time during which the
s~~i:L:lway openings were open for the passage of fish.
The computed volumes of flows of Sea of Azov and Black Sea waters through
the hydraulic complex durir~g each computation interval were summed for
obtaining the monthly and annual water exchange values (VA and Vgs respec-
tively). The analysis was made using the total annual water exchange val-
ues for all series (a total of 75 records). -
. It was postulated that the ~vork of the hydraulic complex will begin in
1990. Therefore, Table 2 gives the mean values and dispersions of water
exchange through the hydraulic complex with the realization of a mean
projected inflow of river waters in a volume of 28 km3/year during the
last 17 years of the investigated 30-year periods. This table also gives ~
the mean values of these characteristics with an inflow of 26 and 24 km3/
year. According to the data in [lJ, the present quanti.ties of water
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exct~ange ~re VBS a 33. 5 kin3, O' 2= 24.0, VA e 48.8 km3, 4~2 = 49.0.
V~ xM'
90 �
q)
S 95
90
7S
SD
2S
V, xn' 6)
PO
S
90 10
25
SO
~ ~S
p 90
1991 1994 1996 19Sl9 ?Oq7 7001 ~aaaroa~~
� Years
Fig. l. Chronological graph of equally guaranteed volumes of Black Sea (a)
and Sea of Azov (b) flows.
Accordingly, with regulation there will be a considerable decrease in the
volume of water exchange (especially the inflow of Black Sea waters). The
ratio of the volumes of inflow of Black Sea waters to outflow from the
Sea of Azov decreases from 0.7 to 0.2. Such a radical transformation of
water exchange unquesCionably will change the overall picture of forma-
~ tion of hydrological elements in the sea.
Figure 1 shows graphs of the chronological variation of water exchange vol-
umes of different guaranteed probability, constructed on the assumption of
moderate asymmetry (CS = 2 C) of the series of water exchange volumes. In
computing the guaranteed probability we took into account the nature of the
dependenc~: of water exchange components on river runoff; with the minimum
values of river runoff there are minimum VA a.nd maximum Vgg values. By :
analogy with runoff they are assigned a high guaranteed probability.
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roti Ci~rICIAL US~ ONLX
Tab1e 2
Menn Values (kmJ) and Dl.sper~ion ~f a Series nf V~1ues for WaCer F~xchange
Through ~he Kerch H,ydr~ultc Complex .Eor a Me~n R~.ver Runoff 28 km . Onset
of Regu1 at:ton 1990
TIp{ITOK N3 QTTOX A `
f'o,n ~n~o~p~ 2 ~epHOe Mope 3
~ v`{ I ~A I o' -
~sso o,a o, i2 s,s 2s,~
1991 O,~J U,45 8,3 47,1
199~ i?,8 U,13 8,3 30,7
I993 U,~ U,45 9,4 45,4
199~1 I,U U,4~~ G,7 15,2
1995 1,1 0,33 6,4 2t,2
1996 1,2 2,y3 6,6 IJ,~3
1997 1,;; 1,80 7,0 16,7
199H 1,J 6,2:5 6.7 33,1
1999 1,l 0.57 7.9 27,5
2000 1.3 1,5.5 6,5 2p,3
2001 2.1 4,11 4,8 17,1 ,
`1002 I.i 2,15 6,1 23,U
2003 ?,2 7,17 8,2 71,4
:2004 :3. ( 22,42 S,6 87,0
:.'005 2.0 4,31 4,9 15,4
200G 1,4) 5,38 6,2 30,1
Cpen~iee 4 1,5 4,26 7,2 32,G
Cpcanee npti
crohe 26 xM~ 1,6 2,82 6,3 24,9
CpeAFiee npH
cTOKe 29 n~~ 2,2 5,43 5,3 20,6
K~Y:
1. Year 4. Mean
2. Inflow from Black Sea 5. Mean for runoff 26 km3
3. Outflow into Black Sea 6. Mean for runoff 24 km3
With a general insignificant increase in the mean VBg -aalues and a decrease
in V~ zn the course of the investigated series, associated with a general
decrease in salinity, it is possible to discriminate two variability max-
- ima falling in 1997 and 2003. The second maximum is greater than the first.
The appearance of these maxima is attributable to the fact that in 1997
active releases will begin in one case(third regulation stage). In 2003
there will be four such cases. In the remaining 21 cases of the investigated
variant the stability is stabilized in the r.ange 9.5-10.5�/0o by means of
an increase in the water intakes.
Figure 2 sliows the guaranteed probability of the annual volumes of water
exchange and river runoff.
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T N,~ 7
40 ~
tl00
~ 6
70 � J 5
40 �
700
2
0 q
~ 1 S 2~ 90 60 80 90 9S 99 9S~l9
Fig. 2. Guaranteed probability of river runoff (1), runoff of Sea of Azov
(3) and inflow of Black Sea (2) waters, and also Tgg and TA values in the
firsC and second stages of regulation (4, 5) and during time of active water
y releases (6, 7).
In the analysis an attempt was made to determine the dependence of the
VA and VBS values on river runoff and apparent evaporation (by analogy
with [1, 5]). However, it was not possible to detect stable correlations
for the annual values of the mentioned parameters. The reason for this
is that Che construction of a hydraulic complex in Kerch SCrait wiJ.l lead
- to the transformation of the Sea of Azov into a reservoir of the long-term
regulating type with a useful regulating volume 18.5 lan3 (between the
readings +10 and -60 cm abs.). The annual runoff of the rivers is 25-30 km3,
less 17-23 km3 of apparent evaporation, giving an excess of the fresh bal-
ance S- 10 km3. This volume can be completeXy accwnulated by the sea.
Therefore, an analysis was made of the mean Vr~~, VBS and VA values for each
record in the first and second stages in regulation and in the third.stage
~ separately. There was found to be a rather stable relationship between ~
the mean values of the water exchange components and mean river runoff;
the nature of the dependence for the,^,e two cases is substantially different.
In the stage of a decrease in salinity and with its stabilization by means
of the withdrawal of river water the dependences of water exchange on river
runoff are nonlinear and are described by the exponential equations
?A = 0,04TH . VP1."d�~ X
X e(1~h5&S VP ~ 1 ~
t
V,~ - 1~023' 1~~~ V~8~194u
X e0,149b Vp ~ ~ Z ~
(A = Sea of Azov; Black Sea; p= river]
which are valid in the range of Vriver variations from 20 to 3~F km3.
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'Ph~: multtple cnrrelat:ton coefficienC for expression (1) is equal to 0.98;
for expression (2) it i.s equal ta 0.70, which is unquesCianaUly significanC, -
since w~rh a 5% signiPicance leve]. under these conditions the coefficient
becnmes slgnl.fic~nC i� it exceeds 0.32, whereas with a 1% significlnce
level ie ls equal to 0,38.
'Phe nonline arity of the cor~elations is manifested most clearly in the
range of Vriver values close to 20 km3. In this case the fresh sea balance
approaches zero and in order to stabil�ize the level the need arises for
changing the operatl.ng regime of the hydraullc complex to increase
the admissions of I31ack Sea waters.
- In the sC~ge of active enL�ry of water the dependences of Che water exchange
coinponents on river runoff have rz linear f.orm:
V!~ = 0.74 Vriver - ~2.42 (3) ~
~I3S = 7.2~? - 0.22 Vriver� (4)
Ttie linear correlatton coc~fficient for equation (3) is equal to 0.96; for
equation (4) 0.85.
The linear dependences of VA and Vgg on runoff and their nature (direct
for Sea of Azov flow and inverse for Black Sea flow) show that in the case
of .free water entries through the hydraulic complex under the conditions
for regulation of salinity the water exchange regime approaches a natural
regime.
One of rhe important problems involved in the influence of the regulation of
water exchange on the hydrobiological conditions of the sea is the problem
of the poss ibility of the passage of migrating fish through the dam. The
conditions for the modelitig of the passage of fish were indicated above.
The objective possibilities of the passage of migrating fish are determined
pr.imarily by the time during which the spillway openings were open for
thetr passage with an accompanying wind flow. The duration of tt-~e individ-
ual situations favoring the passage of fish is determined by the duration of
favorable types of wind fields [3] and varies, as indicated, from 6 to 48
hours. The total time for the season is essentially dependent on the stage
of the sea freshening process. In the first and second stages of salinity
decrease t~-:is time is a function of the mean river runoff and sea salinity
(Fig. 3)~ In the case of high salinity values the time for opening of
the floodgates to a high degree is dependent on the river runoff (that is,
the balance level of the Sea of Azov). Ttie parameters of c?~seness of the
graphic dep endences are 0.73-0.91. In the third stage of the regulation
process it was not possible t~ detect correl.ations between the time of
opening of the openings in the dam for the passage of fish and the para-
meters of the water and salt balances. This is attributable to the fact
tha~t in this stage the balance level varies abcut its mean long-term value
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(-30 cm abs.). llowever, in the process of decrease in salinity the level
~tands near. the upper readings (+10 cm) nnd iCs variability is conside r-
ab.l.y less. I~'igure 2 showa curves of the guaranteed probability of the
TgS ai~d 'PA values :Ln the stage of a decrease in salinity (4 and 5) and -
in tt~e process o~ its stabilization. For the Tgg and TA values in the
third stag~ of regulation the theoretical and empirical guaranteed prob-
ability curves (5 and 7 in Fig. 2) virtually coincide. For TBS and TA,
obtained in the first and second stages of the process of decrease in sal-
- inity (curves 4 and 5), due to the strong asymmetry of the series, emp ir-
ical guaranteed probabillty curves were construcCed. The mean Tgg value in
the First and second stages of regulation was 95 hours (or = 68), TA 880 -
hours ( V' = 61 hours), in the third sCage of regulation these values a re
equal to TBS = 360 hours ( a��t 204) , TA = 504 hours (0'= 130) .
V, nn, _
900 /
J1 ~
~
l,~900 B00
10 T�