JPRS ID: 9006 USSR REPORT MILITARY AFFAIRS

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I
~ AND MY ~ T
N0. 10, OCOTOBER 1979

26 DECEMBER 1979 CFOUO) 1 0 F 2
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- JPRS L/8830
26 December 1979
U SSR R~ ort
. p
METEOROLOGY AND HYDROLOGY -
No. 10, October 1979
Fg~s FOREIGN BROADCAST lNFORtOIIATlON ~Ei~ViCE ~
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JPRS L/8830 _
26 December 1979
,
USSR REPORT -
METEOROLO~Y AND HYDROLOGY
No. 10, Octcber 1.979
Selected articles from the Russian-l.anguage jourrLal. METEOROLOGIYA ~
I GIDROLOGIYA, MosCOw. -
" CONTENTS PAGE
Numarical Experiinent to ~onsider Orogr~,phy and Friction in -
Models of Atmospheric Dyriamics
(N. G. Godev, et al.) 1
Advanced Model of Atmospheric Plamsta.ry Boundary I,ayer
(A. G. Tarnopol'skiJ~ V, A. Shnaydman) ...............i'......... 12 ~
- A Twelve-Zevel Axisymmetric Numerical Model of a Tropical Cyclone ~
- (A. P. Khain~ 23
~i -
= Consideration of the Effect of Rotation and Motion of ':ortices on _
the Basic Flow of Ziquid
(A. S. Kabanov~ B. Ya. Shmerlin~ ~
Numerical Modeling of L�aep Convection Processes
(M. Alautdinov, ��~~��~~~�~~~~��~~~�~~~~o�~~�~~~�~~~�~~~~~�~~~� ,7V
Regularities in the Beha.vior of Radioactive Aerosols in the Near-
Ground Atmosphere -
, (K. P~> Makhon'ko, et al.~ 66
Ana.lysis of Motion of a Consta.nt-T.,evel Ballnon in Order to Determine
Certain T arb~:lent Atmospheric Gharacteristics
- (P. F. Demchenko, G. S. Golitsyn~ 73
Experimental Evalua~tion of the Qua.lity of Operatio:ial ~,erological _
Information -
(Yu. M. Ziberma.n, V. P. Tarakanova) 81
- -a- LIII -US5R- 33S&T FOUOJ
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CONTENT.S (continued~ P~3e
Numerical Modeling of W~nd-Driven Waves '
~ (V, K. Makin~ D. V. Chalikov) 86 ~
Electrical Conductivity Field of Seawater in North _
Pacific Ocean
(S. A. Oleynikov, D. M. rilippov) 96
Estimate of the Calculated Thickness of Stratified Ice
(V. P. Afanas'yev) 105
Certain Characteristics of Ice Cover Strength during Its
Break-Up on Rivers of the Baykal-Amur Trunk Zine Z~one
(Ye. F. Zabelina.) 112
~ Use of Meteorological Forec~.sts in ~ifferentiating NitrogAn
Supplements
(Ye. Ye. Zhukovskiy, A. P. Fedoseyev) 124 -
_ Certain Method Questions of Using Tensiometers in Studies of
Soi1 Water Pattern
(N. A. Muromtsev~ ...................................e 136
New Papers on the Water Ba.lance of the Danube R~ver '
(K. P. Voskresnenskiy, V. I. Babkin) 1~9
Review of Book by N.A. Zaytseva. and V. I. Shlyakhovo
Aerologiya. (Aerology), T.,gningr.ad, Gidrometeoizdat, 1978~
289 Pages
(N. F. Pavlov) ...........................o........... 153
Sixtieth Birthday of Mark Yevseyevich Beryla.nd -
(ed~itorial sta.ff~ 156
_ Seventieth Birthday of Oleg Alekseyevich Drozdov
` (N. I. B udyko, et al.) ...................o........... 158
_ Sixtieth Bi'rthday of I~arisa Rakipovna Rakipova.
(group of comrades~ 161
Sixtieth Birthday of Sergey Dmitriyevich Koshinskiy
(group Of C011.8~U8S, 163
A-~ the USSR State Committee for Science and Technology ~
(V. Zakha.rov) 165
_
b -
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CONTENTS (Continued) Page
~ Notes from Abroad
(B. I. Silkin~ 166
Obituary of Feofan F'arneyevich Davitaya
(staff) 17~
~
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i
r
PUBLICATION T1ATA
English title ; METEOROIAGY AND HYDROIAGY
' No lo~ oct ~9
Russian title . ?'~`?'EOROIAGIYA I GIDROIAGIYA
Author (s) ~
Edi~or (s) . Ye. I. Tolstikov ~
' Publishing House . GIDRO:+IETEOIZI)AT -
Place of Publication : Moscow
Date of Publication . 1979
,
Signed to press ~ : 20 Sep 79
Copies ~ 387~
COPYRIGHT : "Meteorologiya i gidrologiya,"
1979. ~
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trDC 551.511. 3( 215-1~)
NU1`~RICAL EXPERIMENT TO CONSIDER OROGRAPHY Q~ND r"~ICTION IN MODEIS OF AT~SOS-
PHERIC DYNAMICS
Moscow METEOROLOGIYA T GIDROT~OGIYA in Russian No 10, oct 1979 PP 5-13
[Article by Professor N. G. Gcdev, Doctor of Physical and Mathema,tical Sciences
- V. V. Penenko, and Candida�ce of Physical and Ma-thematical Sciences N. N.
Obrazts~v~ Bulgaxian Geophysical Institute~ Computer Center of the Siberian
vepar~ment of the USSR Academy of Sciences, submitted for publication 8 Januaxy
1979]
Abstract: The technique and results ase stated of a
numerical experiment to study the effect of o~ography
on atmospher~.c processes. The experiment was conducted -
based on the model of atmospheric dynamics for the Northern
Hemisphers.
LText] The orographic and thermal hetexoge~eities of the earth's surface
have a signif.icant effect on the structure of atmospheric proc~sses of dif-
ferent scales.
The purpose ~i this work is to analyze and experimez~tally study certain
methods for considering friction and orography in numerical models and their
effect on atmospheric processes. An examination of these questions is based
on the following hypothesis. It is assumed that -the effec~t of fric~ion and
orography on a-tmospheric dynamics are mutually de~pendent. By -this is mean-t
-that the turbu~en~ struc-ture of -the a~tmosphere depends on -the irregulari~ies
in -the eaxth's surface of different scales, while ~the effec~ of orography
in turn, depends on ~he ~turb ulence of the a~mosphere. Such an in~errela~ion- _
ship, in our opinion, genera-tes cer~ain eff~c~s tha~t have significan~t impor-
tance for a~tmospheric processes. The results of numerical experiments coni'irm
~ the correc~tness of such an assump~ion.
l. The initial poin~t i.n works ~ha,~t cover ths effect of oxography on a~mos-
~pheric dynamics is -the condi~ion -tha.-t air does no~ pass ~hrough the ear~h's
surface, as well as -the assignment of a link be~tween cer~tain pasameters of
the a-tmosphere and orography. Thess condi~tions are formula~ed differently
- depending on whether the a~tmosphere is viewed as an ideal or -turbulen~t liquid.
1
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If the atmosphere is viewed as an ideal liquid, then, as is known, ~the condi-
tion for non-passage through the eas~h's surface is provided by the expression
~7,~ ,~r ~ .
~oP It rl.r ~ 2~ dy k*'Ltil :,Z - =n ~xr ~'1~ (1~ -
- .
- wher.e z~(x,y)--function describing ~he relief of the eax~th~
, u, v,w--componen-cs of veloci-ty vec~tor ~ in direc~ion of axes x,y, z;
and .~r� --componen~s of gra.dient vec-tor p z~ . W i-th -the help of (1)
ox
adopted as -the, boundary condition for w with z=zp (x, y) , the effect of or.ography
on the atmospheric processes is taken into consideration in this case.
In the systems of coordinates x,y,p or x,y,~(p and vertical coordi-
nates, p--pressure, ps--prassure on eaxth's surface) which are ob~tained from
the system of coordinates x,y,z--identical transfortnations, the condition (T)
_ must preserve its physical sense, since in these transformations no new
- physical hypotheses axe involved.
If the earth's atmosphere is assumed to be turbulent, then in order to take
into consideration the effect of orography on the atmospheric processes, _
usua,lly the f~~llowing is done. It is assumed that the effect of friction and
= orography are independent of each other~ and they ase considered based on the ~
following two very widespread systems that ase equivalent among themselves.
a) with the help of (1) the orographic component of the vertical wind velocity
is defined. Then, considering that the earth's atmosphere is turbulent, while
- the earth's surface is smooth, the component of vertical velocity wt is
computed that is governed only by turbulence. The turbulent compone~i'~ of
vertical velocity wtyP is computed from the system of equations for a uniform
planetary boundaxy la er (PBI,) . Further it is considered tha.t -the sum of
these two components ~3]
_ ze~~? -F- ~^'n.p with z = h , ~2)
is s~.tfficien~t in order ~o -ta,ke in~to accoun~ ~he join-t effec-t of friction and
orography on ~he a~tmospheric processes. Here h--upper boundary of PBZ.
- b) the erography is ~aken into consideration by a special selection of the
coordinate sys~em, while on ~the lower boundaxy of ~he a~tmosphere_in some way
~ the friction force F'
~(z) is assigned which is already independen~t of oro-
graphy. In physical con~tent -this scheme is equivalent ~o condition (2).
Scheme (2) is based on the assump~tions -that -the friction force does not depend
on orography, while -the effec~ of orography on -the s-tate of the atmosphere
does no-t depend on turbuleizce. In -the real atmosphere ~hese hypo-theses, as
observa~ions demons~tra-te, axe not true~ Here one can add also tha~ the turbu-
lent structure of the a~tmosphere s~trongly depends not only on the horizental
2
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orographic hsterogeneities, but also on the thermal.
Now we will examine the qua.si-Ekman plane-taxy boundary layer (QEPBZ)
a~ a.bove tho horizontal noruniform surface. We will use such a definition for
the boundary layer in which the coefficien~ of vertical turt~ulent exchange _
v depends only on x and y; -this relationship is ta.ken in~o account through
- orography
- Y = Y (zo(x, (3)
Further wi~th the help of -this simple model we will examine ~he effect of
orography and fric~ion of ~he a~mospheric processes. We note tha,t all our
discussions refer to processe s of synop-tic scale. For such processes oro-
graphy must be perceived i.n a cer-tain averaged sense.
Assume that the linear model of PBZ is described by the system of equations
_ d '',v (Z, zo (x, Y)) dz -I- fv = fvg, (4) _
az " (z, zo (x~ Y)) dt - fu = - fuB, ~ (5)
au ao am _ 0. ~ ~ "
aX + dy + as 6
_ under the conditions
~ u= v= w= 0 with z= zu ~x, Y) and u-� ug,v v8with z--. h.
Here ug and v--components of geostrophic wind~ r(
f--Cor3.olis p~rameter. '
By comprising according to equa.tion (4~ and (5) the eddy equa,tion, excluding
( dx +~v 1 with the help of ( 6) , and by integrating for z from z~ to h, we
yl
~ obta.in for ~tr.e ver~ical veloci~y w(x, y, z) -the equation
fw (x, y, v(z, zo) ai ~
ax - ay 1I zo +
a Y a a:~ aZ~ h
a:~ v: aX ay ~ I =o ~7~
du ~v
In the boundary layer " dz and d: are reduced wi-th al-ti~ude, and -there=`~
fore it is possible, based on (7) ~o wri~e an approxima~e formula ~o define
w( h) on -the upper boundary of -~he FBI, -
a a~ au1 i a ~~z,
t`~> = f at ~
ax - dy 1 I t=zo+ f aZ X
X az ~v az - u oy
~I . ~8~ ~
z=zo
3
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T he horizontal components of the velocity vector axe found from equa.tions
, ( 4~) and ( 5) on the conditions
u- v- 0 with z- za (z, y) and u-� us, v-. vg with z-. h,
A ssuming M= u T i v, Mg = ug ivg, , where i= Y-1 we obfi,ain
d"~z, Zo ~x, Y)) dM - ifM iMg (x, Y)� ~9)
The solu~ion of ~his equation with -the adop-ted boundary conditions, as is
known, looks like
/1'~ = M8 ~po -F- lQo)~
where Fp and Q~--real functions ~ha,~c depend on z and zp(x,y), i.e.,
Po=~'o~z, Zo~x, y)) and Qo=Qo~~, zo~x, y))--
For u and v f`rom (10) the equa.lities follow -
ta=uBPo-vgQo,.
v= ug Qo vg Pp � (11)
After replacing u and v in (8) ~hrough (11) we obtain
~h) = a(G zo, vg) + b.~~ ro, vg] c~g, (t2)
where _
~ a= Q~ i a~, aQ~ _ i a aQ~
a-~ 1� az v:~ + j vs~ aZ ~z_Z - f~ at~ " a~ ~Y_t ~
a -o
- v d= P~ 1 8 v dPn 1 d dPo
b- C f az az~, + t az~ d: )Z== - f( d:~ v as,Z-z '
o u �
� dp~~ ~ _ dvg du~
~ _ ~ f az ~ ~ '"a - dX - ay ' _ -
:-:o ~
~
(c zo, vg) = ug az + v~ dt� ~[v v~l =~tig az- - u8 0?~~ l. (13)
l y~ yl
We will examine formula (12) for ~wo pas~ticular cases.
a) assume v=cons~ (Ekman boundary layer). In ~his case ~he solution to (9)
with the adopted boundary conditions is provided for by -~he expression
-(i+`)Y .:Y(z-so)
~Yfa - Mg C1 - e (14) -
~
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It is apparent that
i
f 1 z Z
II t-'~ = 1- e y~ o) ~OS 2 (z - za);
Q (2-to)
o- e ~ sin ~ l (z - zo).
Consequently, _
aP� f Qo _ f~ d=Po a" = a
~ dZ zo= l
v ~ ~dZ aZ� ~z_Z~ - ~ ~~=o a= ~===o = 0; d~
and ~
a~Zo) = 1; b~zo) = ~(Zo) 2
f�
- For the vertical velocity w(h~ from (12~ we obtain
rtz� ds v
''"~o (h) = us ~z vs dy ~ 'l f ~S - ?QIoP 4Q~rYP+ (1~)
i.e., the expression analogous to (2). Expressions (15) and (2) are equiva-
lent in their physical content, and this means that the models in which (2)
is adopted as the lower boundary condition describe the interaction of the
atmosphere with the earth's surface within the framework of the physical
~ontent of the lineas system (~Y-7) with the condition v=const. -
Expressi$n (15) differs from (12) by the fact tha,t it does not contain term
br0 z0 ~ Vg, 1, and the coefficients a and c in it are consta,nt. The f.irst means
that with 'linear flow-around of terrestria,l obstacles the dynamic effects are
not described (since in thi~ case ~0 z� v- v dz� _ ~dz~ and the
g~ - g dx a~ _
second--tha,t the effects of orography and friction are independent between
_ themselves, In normal practice it is acknowledged tha.t the comp~nent wty
depends on orography, and measures are takEn to correct it by means of in~ro-
ducing a coefficient tha~t depends on orography, ~ ~ '
r~T~- Cd ~zo~ 2,
The feedback, i.e., the dependence Wop on friction, is not -taken into
considera-tion.
b) we assume tha,t v= y~zo~x~ ~ The solu-tion in this case also will have
the form analogous to (1G~) ,
( +t)(z-so) ,
M~ = Mg \ 1 - e ' " =1Ng (Po ~Qo) = Mg ~o� ~ lsf
The difference in (16) from (1~) consists of the fac-t that in (16) through
- the coefficient v the dependence on. x and y is paxametrically considered.
5 -
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~ - - - -
For the ccefficients a, b, c we obtain
_ ~z = l dsa ; b = a ; ~ _ ~ 2r~ �
Thus for the vertic:al component of the velocity vector we have ~
~cb (ic) _ ~1-~' ~
01(~' z�' �a) ~ ~z za, v~] c ~r. (17)
Expression (17) describes -the effect of orography on dynamics in a turbulent
atmosphEre, as well as ~he effect of friction in -the presence of large-scale
- orography. It takes into consideration in an explicit form individual factors
of the studied process, tha.t are more pithy in their physical sense -than (2). _
We note that if ~ O~then with an increase in the altitude of orography its
~IZn
. effect rises (with other conditions equal~. But the relative increase in this
- effect dc is reduced with an increase in v, since
.'~V= dzo/ ~
,y= dc l t .
dzo 2 v dso
= A unique "smoothi~" of the orographic effect on the atmospheric dynamics is
obtained. Fric-Eion increases the weight of sma.ll obstacles and does not
"permit" the effect of -the lasge to grow excessively~ i.e., in this case a
natural procedure for the smoothing of orography is obtained that takes into
consideration the scales of heterogeneity in the earth's surface. -
3. We will now evaluate the role of orography within th~ framework of the
nonlineas model of the PBZ. Our goal will be to " isolate~~ and approximately
evaluate certain eff~cts of large-scale orographic effect. In this case
instea.d of ( 9~ we will have
d v(~o (X. y)) ~M - ifM ifMg f tt dM
dt dz
v d
ay +~e~ d'='t - F. (18)
We will compu~e the right side F of equa~;ion (18) approximately~ by using f'or "
this purpose the solu~ti.on to ~he lineax equation (9) which we will designate
through ~Y1=uo+ivo. As a resul~ we obtain
F=- if
M~ uo d~0 71~ ~'-y" wo ad ~ 1 g~ -
y
6
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By expressing u~~ v~, and w~ through 16 ,(17), and by considering for
~ simplicity that M~=const, we rewrite ~19~ in -~he form
F lfMs -1- A9~ ~Po (c v~) - Q ~v zo? vg~~ d=~ -F ~o a: _
'~'~81' 2 Ms ~ n y pc~~ ac2>) das ; ' ~ ig~~
where ~~~~=-if; a~~~=1;
_ - (z - za~ 2~a (Pe Qo); a~t1 ~ Zo+ vg)~
r~~~ = 21a (Po - Qo); x~'~ = fv xo, v81 �
In order to solve equation (18) with the assigned right side (19) and boun-
dary conditions M-+0 with z-?z0 and M-~Mg with z-~~ we obtain the following
expression
14�I = Mg [ 1 - e+ a ~ ~ `~~z - zo)~ -I- M~ Ia~l~ ( P~'~ -1-. lQ~~~) ac-~ ( pr~~ ;
+ iQ~2>)] = Mo Mi, ~20~ -
where �
vts~ iQ~s~ _ ` ~ 2 a ~ ~ f ~PZ ~~5~ ds - c~s ~ 4~ ~~s~ dx -
zo so
s ~
- [~1~ - ~P~ ~z j, f ~x P'S~ dz, (21) ~
Zo -
a (l+ilz. -a(l+t) z
~ (S = 1, 2)? = e ? ~z=e � -
Formula ( 20) has an itera-tive na~ure wi~h i-tera-tions with respect -to nonlinear - ~
ity. In prac~ice it is suf~icient ~o limi-t oneself -to the firs~ approxima,~tion.
The structure of (20) indica~es ~ha~ ~the firs~ ~erm o~ the right side yields
- a solution -tha-t corresponds -to the linear model of the PBL, while the second
is a correction for i-t as a consequence of ~the nonlinear terms. Consequent].y,
for the ver~ical componen~ o~' veloci-ty also we will have the presen~ation
w=w~+w1, where wl is a correc~tion �or w~ from (17) due to the nonlineax ~terms~
i.e,
-
~
_ ~h) = wo ~h1 J. ~ ~(~'a~s~, v~) ddz(S~ + a~s~~ yg~ d a=s~ ~z_so , (22)
s t
~
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where -
, � .
, aP,s~ aQ~s, 1
~ l 1 f~~~~ e ~(~+t)(i-s~) dt.
~z dz ~s=z~ v(zo) s
0
By ma.king the necassaxy transforma.tion we prasent the expression fox w(h) in _
the following form:
v (h) _ ~ (v zo, v8) -F h zo, vg] - A ~Z xo (ug + ~g~ -
-Blzi"s vX~+ya ay~~ ~~~~~-~'8~ xey -
a=:~ 3 ra2 r^ - a- s~~~ + R .
Dug v g f 10 ax dy o; = vx~ '
~
where
1 1 dv ~ -
_ 12u ~~f~~ -dzo' B_C- 1 A' D_A'
R--sum of small components which in the future we will ignore.
' The physical sense of the terms of this expression are examined in L4]. We :
note that if av~,_ ~ i.e., if we assume that the coefficient �~or turbulence -
dz~, - ~ _
' does not depend on orography, then a11 the coefficients A=B~C=D=O. And this
means that the numerical models in which ~ doeu not depend on orography
cannot take into consideration all the effects ths,t are linked with the forms of
the earth's surface.
Expression (23) describes certain new physical aspects of the effect of
orography and friction on the dynamics of atmospheric processes. These~ in
turn, are effects that are linked with the shape of the relief and the linear
flow-around of obstacles L1,4~~.
A convenience of the approach stated here is the possibility of "breakdown"
into individua.l componen~ts of the e~~ec~ of orography and friction on atmos-
pheric dynamics. T his makes i~ possible to understand better the essence of _
. the studied phenomenon~ and to deve].op a technique for its correct consider-
ation in numerical models. The analytical solu~ion to the equa.tions (9) and
(18~ is possible only a.n a particular case, when the coefficient of turbulence
does not depend on altit;id6. Otherwise ~the numerical method is u~'ed ~to ~trans-
form the operator in ~the ieft part of (19) and (18~ .
W ith the help of the described technique a series of numerical experi-
ments was made to predict the fields of ineteorological elemen-ts above ~he
Northern Hemisphere. For the numerical experiments a model of weather fore-
casting was used with respect to com~lete equations in the quasistatic approx-
imation on a spherical earth. The finite-difference approximation was
8
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c:onstructed on the basis of -the variation rinci e -
p pl and the method of split
~ting. A detailed description of this model is given in publication [3]. The
y algorithm for considering orography and fr.iction is included in the numerical
model of onc~ of the stages of splitting. T he computations were made on a
regular grid 3n a spherical system of coordina~es with spacing Q~10o~~e~5o
and with seven levels with respect to vertical (p=1000, 850, 700, p--
press~.Lre, 1~--longitude, A--supplement to lati~ude, ~`~?~2~, 0~0~~r~2) . The
calculations were made:
a without consideration for the effect o~' ~he eas~h's relief;
b with regard only for flow-around (i,e. ~ the terms (vz~, g~ and [pz~, ~tg]) ;
c with regard only for -the Zaplacian from orography; _
- d with regard for flow-asound and the I,aplacian fr om orography.
For illustration we presF~nt a bri~f description of the results of diurnal
forecasts of the geopotential field for the period 1-5 December 1964.
- -
,
The baric field above the Northern Hemisphere f`rom 1 through 5 December 1964- a~
was chaxacterized by thre6 main formations. The pole and the regions adjacent `
to it were occupied by a slowly changing depression. From it to the south
along the meridians 20�e.l. and 160�w.l. a region of low pressure was lowered
- which reached roughly the 30-th paxallel. Two well-formed anticyclones were
located on two sides of -this depression.
Figure la presents the actua.l geopotential field at the level 100 mbar for
2 December 19b4~. A forecast of the baric field from 1 through 2 Dgcember 1964
(Figure lb) without consideration for the effect of the relief unsatisfactorily
reflected the main chaxacteristics of -the processes that were occurring, The
region of low pressure was sepasated by three independent cyclones, whereby
their centers were not located in their places. The same can be noted also
for one of the anticyclones. Forecasting only with regard for flow-around
- did not result in a not'iceable improvement in the forecasting of the baric
field (Figure lc~. Figure ld shows the same forecast, with regard only for
the I,aplacian, It is apparent that the majority of the mentioned shortcomings
are eliminated, Figure le shows a forecast with regard for the influence of
the components in (23) that describe the process of flow-around and the I,a,pla- -
cian from orography. In this case one can also notice a certain improvement
as compared to forecast obtained without orography. A comparison of Figure
lb-e demonstratas that consideration of orography results in a more correct
description of the processes that are occurring,
Analysis of the results of numerical experiments makes it possible to draw
certain conclusions.
l. Inclusion of orography in ~he numerical plan leads ~o noticeable cha.nges
in their computation results. They can be divided into two groups. The first
group includes cha.nges associated with consideration of the Laplacian from
the func-tion z~. As was alrea.dy noted, ~he sign of ~hese changes above the -
given defini-te point depends only on the sign of -the ~S~aplacian and on ~he
wind velocity. In -the computations there was a clear tendency towards forma-
tion of baric centers of a cer-tain sign, Above the regions characterized
by negative values of the Iaplacian (for ~xample, Greenland, -the Himalayas
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and others~ an intensification of the anticyclonic formations is ~loticeabl8.
T his trend in our experimen~s was exa,ggerated. Above the c~ncave regions
(for example, the region of -the Mediterranean Sea), where L1 z>0~ a trend was
noted towards cyclogenesis, The second group of changes is associated with
- the effect of flow-around of he~terogeneities of the earth's surface, The
conducted experimen~s demonstra-~e ~ha-t -these changes axe sensitive io vari-
a-tions in wind direction.
_ a)~._; ~~~y ~ b~b1~
~ ,J e ~ s ~
~,e _ _ -
q ~ ~ ~~o ~ ~ y~ !~�/I ti 2~ / ,Y ~ i.~
~ ` 1'r `'`o~ ~,~J ~ ' .
~Y~~ az 1S , ~ ~
C a -
{~,rt ^ rs . i .
. y/ ~ A r-'
~ H
, ,F ~
=.T~;
cbJ-==~~~ p z1'~,,~ ~
G'~ ~ B c/~~ S U
fn'�~ :15 j' _ _
n c.p~, r :~f(, 4 ~B ~ ~
- � ~ ~rr l r:. `
~ ~ %
r ~t..~/~ ~r kP
(nlC~ ~ ~ [ . f ~ ~ =2
~ ~ ~y~^ \ "V1
�`16~ 8~ E~l
- ~ ~ ._.,.~~6
16 ~ 15 l~~s~ -F
a~
e~ J Figure 1, Geopotential Field at Level 1000
" ~s v ~.t': �
J,.... , ~ a . mbar
Key;
b~ 4,~~, ~ a. Actual geopotential field for 2 December
r- :.S ~s~y ~9~
32
- V b. Forecas-ting geopo~ential field with-
~ j c. ~ ou-t consideration for the effect of
e ~ the earth's relief
' ?6 ~ c. Forecasting geopotential field with
~I
1d; ~U regard only for flow-axound
d. Forecas~ting geopo~ential field with
regard only for Zaplacian
e. Forecas-ting geopoten~tial field with
regaxd for flow-around and Laplacian
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2. Consideration for the effect of the shape of the relisf (the term p 2z~ (u2g+
v2g) in (23~~ also leads to an improvement in the results. One of the reasons
_ consists of the fact -that the phenomenon described b~ this expr6ssion plays -
a considerable role in -the formation o~' atmospheric processes.
3. An improvement in the forecast to which consideration of expression p2z
( u2g+v2g) leads, is manifest mainly above -the moun-tain regions. This circu~m-
stance is important and in-~ensifies the effectiven~ss of the consideration in
_ the model of processes of flow-around.
4, The correctness of the consideration of the effect of moun-tain obstacles
on the atmospheric dynamics depends on the metnod of describing the real moun-
tains by the models. The model ~f mountain obstacles must be constructed ~uch
~ that it preserves those properties of the real mountains which are most closely
linked to the atmospheric dynamics. ~
BIBZIOGRAPHY
1. Godev, N. G. "Effect of Orograph;r and Neax-Ground Friction on Change in
Atmospheric Pressure," BOIGARSKC~CE GEOFIZICHESKOYE OPISANIYE~ Sofia, vol 1,
No 2, 1975�
2. Monin, A. A.; and Gavrilin, B. L. "Gidrodinamicheskiy prognoz pogody"
[Hydrodynamic Weather Forecast], Leningrad, Gidrometeoizdat, 1977.
3. Penenko, V. V.; and Obraztsov, N. N. "Numerical Model o~ Atmospheric Dyna- -
mics on Spherical Earth," METEOROI~OGIYA I G IDROI~UGIYA, No 1~ 1979�
Godev, N. "A Method of Determining Optimum Scales for Averaging the Earth's
Topography in Quantitative Study of Atmospheric Cyclo-and Anti-Cyclogenesis~"
BOUNDARY I~AYER MErEOROT~OGY, vol 12, 1.977�
11 -
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~ r~
~ ~ I(
_ ~ ~ -
uDC 551.(51a~522:551,2)
ADVANCED MODEZ OF ATMOSPHERIC PT~ANETARY BOUNDARY T~AYER
Moscow METEOROI~OGIYA I GIDRQI~OGIYA in Russian No 10, oc-t 1979 PP 1~-22
[Article by Candidates of Physical and Mathematical Science's A. G.
Taxnopol'skiy and V. A. Shnaydma.n, State Oceano~raphic Inst~itute~ Odessa
- Hydrometeorological Institute, submitted for publication 27~~~December 1978~
Abstract: Various methods axe discussed for closing the
system of equa.tions for ~he atmospheric planetary boun-
dary layer. An advanced model of the planetaxy boundary
layer is proposed in which closure is implemented with
the help of an equation for the rate of turbulent energy -
dissipation. Results of numerical. experiments conducted
in order to select the optimum set of numerical values
o~ the empirical constants ase presented. Examples axe ~
given of the computation of turbulence characteristics
according to the new model.
LText] Currently in the problem of numerical methods of weather forecasting
a lot of attention is focused on parametrization of the planetary boundaxy
layer (FBI,) of the atmosphere. In addition to methods based on compu-
tation of the neax-ground streams of impulsa, heat and moisture~ quanti-
tative chaxacteristics of the vertical PBI, structure are widely used for
- parametrization. The -transi~ion to nonadiabatic models of hydrodynamic _
forecasting required knowledge of differential chasac~eris~tics of ~the
boundary layer in -the horizon-~al plane~ ~or example, -~~e field vor~ticity
of the vec~tor of tangential friction s~ress, which governed an incrsase in
- the requirements o~' the compu~ation accuracy of ~the 1'BZ parameters. All
of this demanded a~'ur~ther per~ec~ion in -the models o~ the boundaxy layer,
and in particular, the use of physically more substan~tiated hypotheses for .
closure of ~he PBZ equation sys~em.
It is known -that ta close -the FBI, equa-tion sys-tem wi~thin the framework of _
so-called "K-theory" motion equa.tions are used~ the balance of kinetic _
-turbulen-t energy and a number of semi-empirical correlations. In the first
place, ~hey include hypotheses for the characteris-tic size of eddies which
can be conventionally separa-ted into ~wo groups:
- - 12
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1) the characteristic eddy size is expressed through the characteristics of _
vertical profiles of ineteorological elements;
~ 2) based on tha correlations for the second momsnts of hydrodynamic field a
differential equation is written for the cha,racteristic eddy size~
Analysis of the empirical expressians of the ~irst group is given in the mono-
graphs [3, 8, 23] and we will not dwell on them. We will only i,ldicate that .
- this approach was a necessasy stage for -the further development o~ the PBI,
- theory.
An imnortant step on the path of transition f`rom studies of the first group -
to the second was generalization of tize ~arman hypothesis for the characteristic
eddy size [3~ 6]. Based on the Karma.n and Kolmogorov hypothesis a differ-
ential equation of the first order was obtained for the characteristic eddy _
size, and from it--a differential equation for the turbulence coefficient
dk k db
dz b dz - a�~4 Y ~ 1~'
where z--vertical coordinate;
k--turbulence coefficient;
b--mean energy o~ turbulent pulsations relative to a unit of mass;
x~0.38- Karma.n constant;
a~ -constant.
The advantage of equation (1~ consists of the fact tha.t it makes it possible
to determine the turbulence coefficient with respect to external PBI, para-
meters (velocity of geostrophic wind C~ drop ir_ potential temperature S0,
Coriolis parameters 2c~ and irregulari~y z~). Introduction of this equation =
does not increase the number of empirical closure constants. However that
fact that _the turbulencs ,;oefficient is unambiguously expressed through turbu-
lence intensity is insufficiently substantiated and can be viewed only as the
first approximation in the problem on PBZ parametrization.
One can consider it more substantiated to construct a differential equation -
for the characteristic ed y size based on equa,tions of turbulent motion -
~ propo~ed by Kolmogorov [8~. A survey of the technique for construction and
a description of the actual equa,tions for the charac~eristic eddy size are
given in L17, 20, 22~. For clost~e of -the PBZ equa,tion system an equa.tion
- is used for the product of the characteristic eddy size for -turbulence
intensity in which the terms of advection, diffusion, production and dissi-
pation that are "standard" for ~the balance equations figure, The practical
use of this equation is significantly complica~ted due to the presence of
constants which, according to the data of different au~thors [17-19] can
significantly di~'fer. Therefore a decrease in the number of constants as
a consequence of selecting the corresponding equa~tions for closure of the
system is a reasonable perfection of the model.
= In addition to the use of an equa,tion ~or the cha.racteristic eddy size the
equation for the dissipation rate of kinetic turbulent energy into heat has
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become widespread in the works of hydrodynamic profile L2, 15, 25~. In
recent years alone this e ua.tion has begun to be used in problems of atmos-
pheric and ocean physics ~1, 4, 5, 7, z5~ 26~~ _
For the convenience of a comparative analysis we reduce the equa.tions used for
closure of the system to one view. We will examine the s~ationary barotropic
case where the unknown functions depend only on the vertical coordinate:
k~ du lz+( dv R~ ~e 1 a~ a dZ - ~ 2.
~ ~0
. l~ dz l \ dz a T J~-- y--
Z 2 d 9 d! ~kb d! 1~-
at t k1 dz )-F' C dz -�r'a i kl T dz ~ ds dz ~
a3 t dZ (kl dz a41 bs/s = (3}
~
' Q k e du + dv ae~ k h g dz E dz k tdz
- 1` 6 L\ dZ 1r ~ dz T
E= ~ (4~
b = Q ~ ,
. � - ~3 ' '
k = akl Y b, ~5~
k = a, b=/~. (g) .
Here u and v--hori.zontal components of wind velocities;
T--mean temperature in the PBZ limits;,.
0--potential temperature;
g--acceleration of free fall;
1--characteristic curve of turbulent pulsation;
8--dissipation rate of turbulent eddy energy;
aH~ ab+ a91 ~ a~ a'Z a3 a4 a8t ~ al ~2 a3 �Gk --empirical constants.
It is natural that e ither equations ( 2) 3) 5) and ( 6) or equa.tions
_ ( 2) ,(4) and (6) are used for closure. Tt seems ~o us more ex edien~ to
use equations (2)~ and (6) since in -this case the number o~ cons~an~s
is reduced. This selection is preferable also because in deriving the equa-
tion for the balance of kinetic turbulent ~nergy (2~ and the dissipation
- balance equations are used for pulsa-tions in the ~'low rate found by
means of subtrac-ting ~'rom the Navier-S~tokes equa.~cion the Reynolds equation~
and the identical-empirical correla~tions between the second and -third moments.
Therefore we used the equation sys~em (2), (4), (6)~ for quantitative es~timates _
of the PBZ parameters. Here ~he -task emerged of selecting the numerical
values of cons-tants ~rom a~airly broad range of quanti~ies ob~ained by
different authors 5, 14~, 16-19, 21, 24, 25~: _
ab =0,50=1,00; aA - aea =1,0=1,35; al~ =1,35=1,55; a.~~ =1,00 :-1,25;
a~ =1,80=2,OO;a., =0,04=0,10.'
- ~Equation (6) is used to compute dissipation.
~ 14
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This selection was made by comparing the observational data and results
obiained frcro solving the universal system of PBZ equations. '
In order to obtain a universal system of PBZ equations we write the qua.n-
tities that figure in the equations of balance and dissipation in a dimension-
- less form:
bn _ a,/` b~'~Z' ~In - k ds I y.' �rt - k ~dz I y;,
.
s
E-~' e Z_ 2~Z z k- 2~= k. -
" 2 u~ V2 ' � ;c v~, ~ rt- xl vY -
s ~ ~
~
Then equa,tions ( 2) ,(4~) and ( 6) can be rewritten as follows ( here for d9~dz
thA approximation is adopted proposed in [6~~:
Tin -I- Q~ ' p d dbn _
kn t r Qt~ kn dsR - eR =(I ~ ~7~ ~
~n + c~� kn d d ~R
kn - A~ .41 bn dzn kn dz~ - A2 e~ = Q, ~8~
� ka = bn~Em ~9~
v z~l
= Z~ (�o + Hn , .
x'gPo x' (7a-7y ) 1g
!~o = - 2 ~Z o cP T v2 ' ~ ae (2 ~Z)~ T '
.
x x- a3 ~ aP~
2 "az.
~=aa , At=Q Az= Q ~ As= �
Vas 1~ Y a~ 1�. �H al ~
Here
�p,v--inner and outer parameters of s-tratification;
P~--t~bulent stream of heat neax underlying surface;
Hn--dimensionless altitude of PBZ;
~--air density;
cp--heat capacity of air with constant pressure;
~U*--dynamic velocity; -
~a and ~--dry-adiabatic and actual (in upper part of PBZ) ver-tical
temp~rature gradients.
T he constant in the dimensionless equations (7~-(8~ are altered in the -
following limits: ~~0.23-0.72; A130,30-0.~3; A2=1~16-1.48; A330.48-1.00.
Before passin to a selection of the cons-tants we will study the asymptotics
of equations ~7)-(8) with small z for which in the equa.tion o~' balance and
dissipation one can ignore the eft~ect of the buoyancy force, and in the equa-
tion of balance--also the diffusion term. Since with small zn ~:.1, dn~ 0 and
kti"'Zn, then Eri~~-~Zn. After substituting -these values in the dissipation
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equation we obtain A 1+A1. If one assumes that in the equation for the dissi-
pation rate all the ~erms are one order, then the range of possible fluctu-
ation in constant values is narrowed: A1=0.29-0.48; A2~1.29-1.48; A-0.6~I--
, 0.74. The given range of Ag is correct only on the condition of qua~ity of
Oco and CC~~ for any stratification.
We made the numerical solu~ion to the system of dimensionless equations of the -
PBZ in which~ in addition to equation (7~-(9~ equations were used for turbu-
- lent tangential stresses
a~~" Qn -0 ~QR - ~n =0 ~1~~
dzn + kn ' dzn kR -
and boundary conditions: -
with zn=(xZy,lZo)-1 ~n=1, an=0, bn=1,
En=k~x R0, U~i=Un=~; -
with z~ oo ~I� p, o� 0, b� p. =R 0. ~ 11) -
The conditions for the dimensionless veiocity components (u ~~Vn) were used -
to determine the geostrophic friction coefficient,~,='~.(xC ~ and the angle for
= the comple�te rotation of wind in the planetary boundaxy la~ier (-a). Here Ro=
Cg~(2r~ZZ~~--Rossby number.
The numerical experiments to select the optima.l values for the constants were
made according to observational data on the high-altitude meteorological tower
of the Institute of Experimental Meteorology (Obninsk~, where regulax obser-
vations were made of the vertical distribution of ineteorological elements up
to altitude 300 m above the underlying surface. We had at our disposal statis-
tically substantiated data only for the stratification close to the neutral
in the lower part of the PBZ (�~=0-5) and fairly stable in its upper part
- (v=200-300) with different values for the flow rate at level 301 m. The
calculations were made for six gradations of wind velocity at level 301 m:
0-5.0; 5.1-10.0; 10.1-15.0; 15.1-20.0; 20.1-25.0; over 25 m~s. For each
gradation and fixed set of constants differences were found between the calcu- -
lated and the measured wi.nd velocity on nine levels of ineasurements in the
layer 8-301 m, and the root-mean-squaxe deviation in the entire layer
ds. ~
The calculation results demonstrated tha~ for ~he given range of oscillations
in the cons-tant values -the amounts ds are ~airly close to e~~,ch o~her. There
was also an insignifican-t difference between the parameters of the dynamic
and thermal in-~eraction o~' the underlying surface and the atmosphere~ the
ver-tical profiles o~' the wind velocity components, -temperature, coefficient =
and intensity o~' turbulence, and the components of -the vector of tangential
_ t'riction stress. For illustration t~able 1 presents the values of the al~i-
tude PBZ H~ the maximum turbulence coe~~icient km,v ~ a~ ~S for two sets of
~ constants: ~=0.~1; A1=0.31; A2-1.31; A=0.70 (upper line) and ~=0.36; A1= _
0.~8; A2=1.~8; A3=0.70. In the las~ t~ee lines for the mean values �~=2~
~ v=24~5, 1gRo=5.88, C-1~.0 m~s the average characteristics o~ the PBL ase
, placed for all six ~radations in velocity for the indica~ted two sets of
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~ constants, as well as the averaged data obtaint~d according to technique [9, 10]~
in which the generalized Karman hypothesis is used for closure.
TAB7~E 1- QUANTITATNE CHARACTERISTICS OF PBZ AND STANDARD DEVTATIONS FOR TWO
- SETS 0~' CONSTANTS
a 1
�o I v I Ig Ro I Cg a~~e'~ v~: as/cex I-a� I kmal~/Ce::l N~ M ck
4 175 5,80 7,6 0,30 24 4.4 473 0,45
0,30 24 . 4,8 996 0,48
2 225 5,26 I1,0. 0,49 29 11,6 728 0,49
0,49 28 ~12,7 768 0,66~
2 235 5,13 15,0 0,69 30 22,4 1029 1.06
0,69 29 . 24,3 1076 1,05
4 270 6,79 14,6 0,47 21 9,2 864 ~ 1,33
0,47 21 10,2 700 1,36
2 261 6,13 17,6 0,65 24 19,2 950 1,33' _
0,&5 23 20,7 ~ 968 1,3T
3 306 6,19 18,3 0,66 24 18,4 894 2.0~ ~ -
0,66 24 20,4 966 2,06
3 245 5,88 14,0 0,54 25 14,2 788 1,12 ,
0,54 25 15,5 829 1,15
0,59 23 26,0 98i 1,3fi
Key:
a. m~s ~
b. m2~s �
1!
i;! -
- As is appaxent from the results, calculations according to technique L9~ 10]
yield a greater value of ds. The differences in the amounts H, v.~ and a do =
not exceed 10/ of the actual values. The values of the turbulsnce coefficient
that are computed according to two different -techniques differ more signifi-
- can-tly from each other. One can assume that closure of the PBI, system of =
equations with the help of -the generalized Karman hypothesis re3ults in over-
- estima.tion of the magni-tude of -~he ~turbulence coefficien~.
Analysis o~' the findings makes i~ possible ~o draw a conclusion on the expe-
diency of using cons~ants S=0.~1; A1~0.31; A2=1.31; A-0.70 as optimal in the
dimensionless equation ~'or the balance o~' kinetic ene~gy and the rate of dissi- -
pation. -
The conclusions we obtained on the weak in~luence of numerical values of -the
constants (in the selec-ted range) on the PBI, characteristics refer to cases
of stra-tifica-tion close to neutral. The correctness of this conclusion for
stratification that significantly differs ~om ~the neutral was verified by
us by solving the equa,tion system (7)-(10) for the values �p from -30 to 30
_ and v from 300 to 1500 with variation in the sets of constants. It was found
tha;t for cases of stable and unstable stratifica-tion variation in the -
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numerical constant values, naturally~ with observance of the correlation A 2=1+
- A1 and the condition c( =~(.e results in differences batween the PBL parameters -
lying in the limits 10~--accuracy of their determination. This canclusion is
iJ.lustrated in t:able 2 where di.mensionless characteristics of -turbulence axe
- given tha.t are computed for those two sets of constan~s that are indicated in
the description of ~ able 1. It also follows from ~'able 2-that the turbulence
chaxacteristics significantly depend on the stra-ti~ication conditions. The -
maximum turbulence coe~ficient is especially significan-tly a~.~tered during the
transition of thn system from a~hermally s-table to an unstable condition. The
dependence of the geos~rophic fric-tion coefficien-t x and the angle of complete
rota-tion of the wind in the PBZ OC on 1gRo ~'or certain values and v(with
optimal values of ~he constan�ts) is given in f3gure 1.
TAB7~E 2- CHARACI'ERISTICS OF TURBUI~ENCE FOR DIFFEREI~ CONDITIONS OF SPRATI-
FICATION
IIapaa~erp ~
30 ~ 0 ~ -30
(g) IIapaMeTp v
300 ~ 900 ~ 1;:~00 I 300 ~ 9C0 ~ 1500 ~ 300 ~ 900 I 1500
Nn.103 287 24l 218 322 253 218 390 264 230
2~J 24l 218 333 253 230 379 264 230
(km),,�lQ3 20 16 15 3f 25 21 192 58 38
21 I8 16 38 25 21 169 55 37
~gRo�6 .
x.lps 86 83 3l 99 93 90 17l 116 105
' 88 35 83 1W 94 90 159 113 l03
-a� 28 31 3:i 2fi 31 34 28 32 35
28 31 33 26 31 33 28 32 34
~ ~BR~=8 �
x.1pa 63 b2 61 70 G7 66 101 79 ?4
64 63 G2 70 63 66 94 77 ?3
-o,� 20 22 24 18 22 24 16 21 24
I 2~) 22 24 13 ?2 23 l6 21 23
Key:
a. P arameter
x . . -a�
e,~s Q, so 6) b)~ .
. , � ` ,
D,10 ~ 30
' 1 ~
` ` _ ~ `~e
O,~Sy 6 B 104 ~ B lgRo
Figure l. Dependence of (a) and a(b~ on Ro, a.nd v
Key: -
- 1. �p=o, v=30o 2. �p=3~~ ~=3~~ 3. �p=o, v=900 4~. �~=0, v=15o0 ~
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Until now in studying the PBZ structure we operated with the inner parameter
of stratification which cannot be defined according to the data of standard
observations. Therefore in parametrization of the PBZ effects in problems of
dynamics of the atmosphere and ocean it is usua.lly excluded with the heip of
_ the correlation [10~
- � y ~ln (x'N�Roy) (12)
!Vl = 2
xn f
o x: '
where M=g b~ (2a~ZCRT) __in-tegral dimensionless paxame~er of stratification
- computed according to standard aerosynoptic informa.tion.
As an example Table 3 includes the results of computations according to formula
(12) .
TABI~E 3- INTEGRAZ PARAMETER OF STRATIFICATION M
~ ~ IlapaaterP
lg Ro ~ 3o i o~~
6 300 172 33 -207
90U 200 73 -107 r'
1500 224 102 -53
8 300 182 '23 -237 ~
900 205 53 -134 I
' 1500 223 ~5 -lUl ~
~I
KEy:
a. Parameter
Recently in the laws of resistance and heat exchange the ratio of dynamic -
velocity v.~ to the modulus of the wind velocity C that is the mean for the
boundary layer is used. A number of authors [11-13] have focused attention on
- the expediency of using the mean wind in the problems of PBZ parametrization.
We will show that -the amount C can be computed according to the paxameters Cg, -
a, x and Hn known in the model. Since
u=Cg cos a+Cgx d a�/dz,,,
v=Cgsina-C~xd~�/dz,,, (13)
then~ by integrating equations (13) with regard for (11) we find
~ g r +(H lZ+ 2~in a~~12. (14~
C; - C lt l R~ 7
n
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Now by analogy with i;he geostrophic friction coefficient we introduce the
concept of the integral friction coefficient xi=v~,~/(xC). The dependence of
X1 on Ro~ and v is illustrated in Table 4. _
TABI,E 4- INTEGRAZ COEFFICIENT OF FRICTION kl x 103
g IIapaMeTp �o ~ _
30 ~ ~ ~ -
- lg Ro ~3~ IlapaMerp v
3p0 ~ 900 ~ 1500 ~ 300 I 900 I 1500 I 3q0 I 900 ~ 1500 ~
6 96 95 95 109 1~2 I,10~ I lOJ I 184 I ~81 _
8 66 I 66 I 66 I 73 I
I
Key: -
a, P arameter
Relationship (14) can be used to solve the inverse problem: finding the
velocity of the geostrophic wind according to the modulus of the mean wind -
velocity in the boundary layer. Such a task arises, for example, in the use _
' of data on vertical profiles of temperature and wind obtained on high-altitude
meteorological towers~ to evalua.te the turbulence parameters in the PBL. Then
instead of the Rossb~number one should assign the number Ro~~(2~z~). The
link between Ro and Ro is found wi~th the help of correlation (14) for� dif-
ferent stratification conditions.
Thus, the inclusion of an equation for ~the dissipation rate in the closed
system makes it possible to develop a physically more substantiated PBL model.
One can hope that the use of this advanced model far parametrization of the
PBZ effects in hydrodynamic schem~s will result in an improvemont in the quality
of the forecasts. The results of the presented studies also will be useful
in solving other applied problems a,ssociated with consideration of the pecul-
iarities of the physical processes occurring in the atmospheric planetary
boundary layer.
-
BIBZIOGRA~HY
1. Vager, B. G.; and Nadezhina, Ye~ D. "Use o~ the Differential Equation for
Dissipation Rate in Simulating the Atmospheric Ground Zayer," IZVESTIYA
AN SSSR. FTZIKA ATMOSFERY I OKEANA, vol 12, No 1976.
2. Davydov~ B. I. "Sta-tistical Dynamics of Incompressible Turbulent I,iquid,"
DOKI~ADY AN SSSR~ vol 136, No l, 1961.
- 3. Zilitinkevich, S. S. "Dinamika pogranichnogo sloya atmosfery" ["Dyna-
mics of Atmospheric Boundaxy Layer"], Leningrad~ Gidrometeoizdat, 1970.
- ~DChergin~ V. P.-~'T~,oriya i metody rascheta okeanic~skikh techeniy"
"Theory and Me-~hods for Computing Oceanic Currents" , Moscow, Nauka,
1978.
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5, Kochergin, V. F.; Sukhorukov, V. A.; and Tsvetova, Ye. A. "Simulation of
the Processes of Vertical Turbulent Diffusion in the Oce~.n," "Chislennyye
metody rascheta okeanicheskikh techeniy" L"Numerical Methods for Compu-
ting Oceanic Currents"], Novosibirsk, Computer Center of the Siberian
Department of the USSR Academy of Sciences~ 197~�
6. Zaykhtma.n, D. Z. "Fizi.ka po anichnogo sloya a-tmosfery," ["Physics of
Atmospheric Boundary Zayer"~, Zeningrad~ Gidrometeoizdat~ 1970.
~ 7. Marchuk, G. I. ; Kochergin, V~ ~ F.; Klimok, V. I. ; Sukhorukov, V. A, "Mathe-
matical Simulation of Srsface Turbulence in Ocean," IZVESTIYA AN SSSR,
FI2 IKA ATMOSFERY I OKEANA, vo1 12, No 8, 1976.
8. Monin, A. S.; and Yaglom~ A. M. "Statisticheskaya gidromekhanika L"Statis-
tical Hydromechanics"]~ part 1, Moscow~ Nauka, 1965.
9. Tarnopol'skiy, A. G.; Shnaydman, V. A. "Farametrization of F lanetary Boun-
dary I,ayer in Foracasting Models," TRUDY GIDROME'i'TSE'NTRA SSSR, No 145~ 1974.
_ 10. Tarnopol'skiy, A. G.; Silnaydman, V. A. "Parametrization of Baroclinic
Atmospheric Planetary Boundary I~ayer," TRUDY GIDROMETTSENTRA SSSR, No 180,
1976.
11. Chalikov~ D. V, "Technique of P arametri~ation of Atmospheric Boundary I,ayer,"
- METEOROIAGIYA I GIDROLOGIYA, No 8, 1977. '
12. Arya, S. F. S. "Suggested Revisions to Certain Boundary I~ayer P arametriz-
ation Schemes Used in Atmospheric Circulation Models," MON. WEATHEH REV.,
~rol 105, 1977� ~ ~ -
13, Deardorff, J. W. "paxametrization of Planetary Boundary Zayer for Use in
General Circulation Models," MON. WEATHER REV., vol 100, 1972.
14~. Freeman, B. E., "Tensor Diffusivity of a Trace Constituent in a Strati- ~
- fied Boundary Layer~" J. ATMOS. SCI., vol 3~1~, 1.977.
15, Hanjalic, K.; T~aunder, B. E. "A Reynolds Stress Model of T urbulence and
its Application to Thin Sheax Flow," J. FLUID MECH., vol 52, past 4~, 1972�
16. Marchuk, G. I.; Kochergin, V. P.; Klimok, V. I.; Sukhorukov~ V. A. "pn
the Dyna.mics of the Ocean Surface Mixed Zayer," J, PHYS. OCEANOGR.,
vo1 7, 7-977�
1'~. Mellor~ G. I,. ; Herring, H. J. "A Survey of -the Mean Turbulen-t Field
Closure Models," AAJA J., vol 11, No 3~ 1973~
18. Ng, K. H. ; Sp~.lding, D, B, "Turbulence Model for Boundary 7~ayer Near
Walls," PHYS. FI~UIDS, vol 15, No 1, 1972�
19. Rodi, W. ; Spalding, D. B. "A Two-Fasame-ter Model of Turbulence and i~ts -
- Application to Free Jets," THERMO AND FI,UID DYNAMICS, vol 3, 1970.
21
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20. Rotta, J. C. "Statistische Theoric ~lichhomogener Turbulenz," ZEITR. PHYSIC.,
No 31, 1951.
21, Tsann-Wang, Ju. "A Compaxative Study on':~~axametrization of Ver~tical Turbu-
lent Exchange Process," MON. WEATHER REV.~ vel 105, 1977� ~
22. Volmers, S. ; Rotta~ J. C. "Equa-tions for Mean Velocity, Turbulent Energy
and its Scale," AAJA J., vol 15~ No 1977� -
23. Wipperr~ann~ F. "The Plane-taxy Boundary Za.yer of the Atmosphere," DEUTSCHER
WETTERDIENTS ANN. D. MET., No 7, 1973.
2~. Yamada, T.; Mellor~ G. "A Simulation of the Wangara Atmospheric Boundary
- Zayer Data," J. ATMOS. SCI., vol 32, No 12~ 1975~
_ 25. Zeman, 0. ; Tennekes, H. "A Selfcontained Model for Pressure Terms in
Turbulent Stress Equations of Neutral Atmospherlc Boundary I,ayer~" J. ATMOS.
ScI. , vol 32, No 9, 7-975.
26. Zeman, 0. ; Tennekes, H. "Parametrization of the Turbulent Energy Budget
At the Top of -the Daytime Atmospheric Boundary Zayer," J. ATMOS. SCI.,
vo1 34~, No 1, 1977�
~
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,
trDC 551,515.z
A TWEZUE-I~EVEL AXISYA~'IETRIC NUMERICAZ MODEL OF A TROP ICAI, CYCLONE
Moscow METEOROI~OGIYA I GIDROIAGIYA in Russian No 10, oct 1979 pp 23-37
~Article by Candidate of Physical and Mathematical Sciences A. P. Khain~ USSR
Hydrometeorological Scientific Research Center, submitted for publication 3
A pr 1979]
Abstract: A twelve-level axisymmetric model of a tropical
cyclone in z-coordinates is described. Parametrization of
- convective heating as a consequence of the reiease o:F latent
condensation heat is used, as well as a new technique for
parametrization of convective transfer of heat~ water vapor
and angulax momentum. F arametrization of the boundary layer
proposed by Deardorff is employed. In the initial moment -
a vortex is assigned in the gradient balance. The back-
ground temperature profile is considered to be identical
to the tropical temperature profile in the tropical zone
in the hurricane season. A compaxison is ma.de of the
findings with the obsorvational data.
LText] In recent years numerical modeling of tropical cyclones (TC) has
attained considerable advances. Besides the axisymmetric L13, 28, 30-32~
a number of 3-dimerisional models have appeared [~15~ 23]. A trend is
- observed towards modeling of the life cycle of specific TC. However the
potentialities of the axisymmetric models have fax from been exhausted.
They are used to verif~{ new ideas and me-thods in describing different phys-
ical processes E31, 33J� In addition, according to the dynamics and ener-
getics the axisymme-tric model T~ are close ~o ~the 3-dimensional [22].
Finally, the use of the axisymmetric m~,del makes it possible in reasonable
periods -to conduct a fairly large numbe:r of numerical experiments.
In our country work on simulating TC until recently was developed insufficiently
intensively, One should isolate the cycle of works of V. V. Shuleykin [10,]
based on the analytical presentations o~' meteorological parameters in the
TC. Tn [2~ 6] tasks axe se~ on numerical modeling of axisymmetric TC. A
more detailed survey of work linked to -theoretical s-tudies and numerical
modeling of TC is given in [~3, 6, 8, 12]. The given wrork presen~ts results
z3 ~
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on a model that is described in main details in L6]. The model differs f`rom
the majority of 13.sted works in the regard fox the hydrological cycle, presence
of parametrization of convective transfer of heat, moisture and angulax momen-
tum in clouds, and parametrization of the boundaxy layer.
On the assumption of the axisymme-try and hydrostatic equ~,librium the initial -
system of equations in -the cylindrical z-system of coordinates looks like
au _ r vl i a P
ru= _ a p~?~ _ a~~~u~ _ P kf, ( a= +
P ~t = P v I,f ~ 1 r dr dz dz "`di=
+ 1 a_ 1
1 u a k= o az p
cP 9(1 0,61 q) dr ,
r dr r-1 + dz ~ u .
~ t, ~ aPruv dpre~u dpw'v' ,
p a" p ra (f t' ~ or dz dz T
_ dt
+ a kv C
~r, + r d- + d (kv P az ~2~
dA l dpruA dpu,9 _ dps~'9' ~-Qk+Qhp+ -
P dt r or - dz d~ ~P -
+ P N v( ael i a r- - aAl ~~3~
r n k9 dr ly dr 1+- d= ~ f, kN oz 1~ r
aq 1 d p ruq a P~q a o~~
q'
~ d~ - - r dr - � dz us - ~ !pk + PMp) +
r kQ ~(r d~ ds (P ka d= J' ~4)
p=pRT(1-I-0,61q), (5)
_ ~ _ ~ ~ )R'cp = y , Po = 1000 ~s6, (6) -
Po
d a g ~7)
dz - (1+0,61 q)cp9'
dpw _ 1 d pru ~8~
dz - r dr '
where u--radial velocity component,
v--tangential velocity component,
w--vertical velocity,
_ T--tempera-ture,
A--potential temperature,
q--ratio of mixture of vapors--dry air,
p--pressure
~--density,
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Qk--heat source as a consequence of condensation in cumulus clouds,
QkP--heat so~m ce as a consequence of large-scale condensation,
Pk--precipitation f~ om cumulus clouds,
Pk --lar e-scale precipitation,
ku, k~,pke, k~--turbulence coefficiants with respect to the horizontal fox u,
v, 0 and q fields~
ku, lcV, k0, kZq--turbulence coefficients with respect to the vertical for u, v,
6 and q fields,
f--Coriolis parameter,
R--gas constant,
c--specific heat capacity with constant pressure,
gP=acceleration of free fall.
In (1) tha component with the pressure gradient is replaced according to (6)
by an expression that is more convenient for computations with pressure analog
(~r}; (5)--equation of state, (7)--equation of statics, (8)--continuity equa-
tion obtained in eval ating the order of magnitude of the components in the
complete equation [16~. The use of the continuity equation in the form (8)
jointly with the conditions of equality to zero of the vertical velocity on
the upper and lower boundasies of the counted region filters out the inner
gravity wave, and makes it possible to use laxge spacings in time iri the pro-
cess of integration [30]. The parametrization of the components d p~;'v' d p w~ H~
d a w' q' dz ' dz
and Uz ~ designating the transfer of the impulse of heat and moisture
by pulsations of the scale of cumulus clouds will be discussed below.
Boundary Conditions
The region of counting--rectangle with lateral boundasies r=0 and r=rm~, and
horizontal boundax ies z=0 (surface of ocean) and z=zmax~ The work used the
- following boundary conditions: on the upper boundary z=zmax
- kv az - ku dz - ke dz - kv a: - (9)
on the lower boundary w=0, the s-treams of heat, moisture and impulse ase found
with the help of parame-~rization of the boundary layer according to the Dear-
dorff [17] method. A detailed description of the employed technique for paxa-
metrization of -the boundary layer is given in L7] and is briefly described -
below.
The assumption of axisymmetry means that with r~0
u= 0; v= 0; ae - 0; aq = 0. (10)
Wi-th r=r~X the selection of boundary conditions, generally speaking~ depends
on -the amount rmax� In our case for -the field T and q r X~p km~ for the
_ field u and v rm~=570 km. With such r~,X for compensat~o'n of losses in the
angular momentum M with fricti.on on the earth's surface from outside the flow
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M must be directed ~12~. The question of the boundary layers with rm~^~600 km
is examined in [27, 32 . The setting of the boundary layers is facilitated by
the circums~tance that with an increase in -the radius the percentage of compo-
nents with second derivatives in the equa.tions rapidly drops. This permitted
the authors of publications.[27, 32~ to obtain fox the current function'~ the
following boundary condition:
a~ _ ~ ~il)
dr - L '
where ~--constant depending on selection r~X. W ith rm~ 600 km~ as in L27,
28, 32 L=1800 km is assumed.
The current function ~ in the z-system of coordinates is assigned by the corre-
lations
~ a~ , i a~
pu= r a: ~ Pw- r ar '
It is easy to show that (11) is equivalent to the followin~ conditions for
the radial velocity compon6nt:
dr~i ru
_ d~ _ - ~ (12~ ,
The remaining boundary conditions with r=rm~ in the case of flow within the
region (u(rmax~ are assumed to be the following;
drv d ( ~
_ a, = 0; 7' = T~ (z)~ 4= 9~ (z); ats = 13
where T~, and q~ --background profiles of temperature and ratio of mixture,
~ ps--pressure at surface with r=r~.
W ith outflow from the region (u(r >0) the values v, A and q were deter-
mined on the boundary with the he~ of the method o~ so-called finite differ-
ences directed against the stream (the boundary condi-tions axe not set).
P arametrization of Nonadiabatic Processes
T he heat source Q and the v~locity o~ condensation F were separated in (3)
and (4~ into two parts (Qkp, Qk and Pk , F' ~ govern6d by large-scale conden- -
sation and condensation in cumulus clo~ids ~convectivd). It is believed that
. the large-scale condensation occurs when q, computed in one or several of
_ the centers of the different grid increases the saturating valu6. It is
- assumed that the entire surplus moisture above the sa-turating value is momen-
_ tarily condensed and comprises -the large-scale precipitatiq~. During conden-
sation the temperature is increased (large-scale heating~ so that the final
saturating value, na-turally, differs from the initial. Computation of QkP
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and Pk was made by the iteration method (Newton). In cumulus clouds conden-
sationPand precipitation occur when q does not reacn the sa-t~rating value,
During condensation of water vapor in the cumulus clouds an enormous quan-
tity of latent h6a-t is released. In addition, the cloud transfers upwards
the heat~ moisture and angular momentum. As a result of transfer of angular
momentum the shift of the wind with altitude is lower than.follows from the
correlations of thermal wind [12]. In a number o~ moddls L1~, 28] the transfer
of the angulas momen-tum is considered by selecting a large value for the
turbulEnce coeffici6nt with respect to the vertical in ~he zone of developed
convection. However consideration of th6 transfEr o~' the momentum by clouds
is included more logically in the problem of convection parametrization.
For parametrization of atmospheric heating as a consequence of condensation
in cumulus clouds the hy othesis is used for the conditions of instab ility
of the second type (CISK~ ~16~, as well as the consideration of K uo L2~~ and
Estogue [18~ on the distribution of latent heat release with respect to the
vertical. We will is~late the atmospheric column of unit area and break it
down to horizontal planes on several layers. Assume in m lower layers the
conditions for convection resistance are fulfilled: there is convergencE
~ of moisture (convergence of mass~ and conditional instability (Y~i~, where
'y~ is the moist-adiabatic gradient~. (In typhoons in the zone of convergence
as a consequence of the high air humidity the conditional instability coin- -
cides'with the so-called convective instability LS~, The rising particl~s
have a largE supply of energy of instab ility. If the humidity is not great,
as on the periphery of TC, the condensation level is located fairly high, the
particles during 6levation to this 1~vel along the dry adiabatic curve can
become colder than the surroundings so much that above the conde~lsation 16ve1
= its temperatur6 becomes lower than the temperature of the surroundings. In
such a si-tuation deep convection, appaxently is impossible, despite y~
For parametrization of the source Qk in equa,tion (3~ we take into account the -
contribution of clouds that develop from each of the m lower layers~ Assume
Is--quantity of mois-ture converged in a unit of time in the layer under the
number ~m. As a result f'rom the levels lying in this layer~ in time L~t
clouds emerge that occupy in -the column above the base an area a'g. Then
_ ap ~ r where S$~ -quantity of moisture necessary for bringifig to satur- -
- q~ '
ation the isola-ted atmospheric column ~`rom level S to the upper boundary of
the clouds emerging f`rom this level. Thc~ con~ribution -to heating of the
a~mospheric column by clouds ~hat emerge from level S, according to ~21~, -
can be computed as follows;
- ce r~ ~ToS~ - l') ~ a 9 p (To~~ - T) with To6~ > ~ (1~) =
Q = ~
_ k~ ~ with To6~ , T,
wher~; T~ S--temperature of clouds emerging from level s(or according to the
employed pasametriza-tion, the -tempera-tLire of -~he moist adiabatic curve
restored ~`rom level .
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The summary heating velocity Qg is determined by the contribution of convec-
tive clouds that emerge f`rom all m layers (th~ action of these types of clouds
is considered to be independent from each other~:
m
Qk ~z) _ ~ Qk~,� ~15~
The velocity of convective condensation is determined from expression
Pk - Qk' `1~~..
where I,--specific heat condensation. Computation o~ Qk according to formula
(15) makes it possible -to a certain degree to consider the change in the point -
of cloud cover (or rate of cloud formation) according to altitude.
We will now turn to parametri.zation of the components w'6', w'q' and w'-v'.
We will use ths following expressions as definitions:
, -
~~06 - ~u~p~ ~ 4P1~ !(Qlbo = `1QJ6o - ~e',
eo6 = ~ob - d i ~jbo ~ e6o - B? ~ ~ / ~
?~l~ e~ - OC ~iC'o6 Ao6 "f' ~1 a~ w6o d6o~ . ' -
w = u?x?'o�'v ~l - C~ '~6oi d = OCeo6 'f' ~1 - z~'8~. ~1~~ -
The dashes above mark the amounts obtained by averaging with respect to area~
much greater than the scale of cumulus assemblies, but much smaller tha.n the
scale of TC. The strokes ma.rk deviations f`rom mean. The indices "oG" and
"60" refer to the amounts in clouds and the cloudless surroundings respect-
ively, a--percentage of space occupied by clouds.
- From (17) and (18) with regasd i'or ~he fact -tha~ a~0,
Q= ~--water density with ~ ~0 ~
F--complete pressure.
Equation (2) guarantess the nonpenetration of the advective mass~ impulse and
energy transfer through the interface; on the left s~.des of the first two
- equations (1) the group of terms tha.t can be differentiated with respect to .
with ~=0 turns to 0.
Assiuning beforehand that the s~face can be of fairly complicated shape~ we
introduce a procedure for averaging equa.tions with respect to the assembly -
of surfaces close to each other (for more detail on this subject see [5~ and
[7]). By using further the standard idea of random amounts in the form of a
sum of random deviations from them that are averageii with respect to
87
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assembly, we will avdrage the equa,tion system (including the kinematic condi-
tion (2)). The avarage amounts u, w, P, obtained by such averaging reflect .
the effect of the average excited surface while the deviations f~om them--
u', w'~ P'--the pulsations governsd~ in the first place~ by the natural turbu- -
lonca of the volocity field `u w~ and secondly generated by.the high-frequency
compononts 7~'. In L5] and L7~ considerations are given on.the fact that the
two-point moments containing pulsa.tions-~', must rapidly attenuate the farther
from the surface. This makes it possible to omit from the equa.tions the terms
that contain such moments in the entire region, with tY:e exception of the thin
near-surface layers above and be~ow~ where it is necessary to consider their
effect in the pa.rametric form.
The selected method of averaging assumes that the ta.sk which it remains to
solve consists of a clear description of large-scale wave components in water
and in air. High-frequency (grid) components of waves and t urbulence must be
considered in the parametrical form. ~I~e note that here one cannot speak about
turbulence as a grid phenomenon since its scales reach dimerisions of the entire
boundary layer.
In sum, we approach the Reynold's equation ascribed in the c urviliriear system
- of coordinates (x,~), where altitude ~ is camputed f`rom the smoothed G--by
averaging of the surface (the averagi.ng sign for the moments of first order
is omitted):
u~ (uu -I- u~u~)x ~u~u w'u' -,qt u - ~X uu - ~ r u'u' - M~); _
_ - P'' -f- P'' ~i~ P: ~
'm~ -F- (rcru ~ u'~e~')X -'t- (,.~c'r�' ~e''w' - 71t w _ 7i.~. tt4Z' - r� n'w' - lb(m); -
~ _ - P-' r�: g? (3)
uX -f- - ~X u): _ (4)
~ir = ~'o - rx uo - '~x ua,
where Mu and MW designate the sums of the second and third moments which we
will not compute (see, however, [5~).
Single-point moments of the second order are presented in the form Af the
product of deformation tensor components (in the system of coordinates
(x,~)) and the isotropic turbulent viscosi~y coefficient K, expressed through'
thv turbulence scale 1, that linearily rises the farther from the surface~ -
and kinetic turbulence energy e(KTE)
1'-x~C~, K=l~e/c,)'l.~ (6) .
(x=0.4~- Karman constant, C1=~.6--constant). -
~i
-H
VV
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~
il ~ ~ ~
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This
Due to th~ first of formula.s (6) K forma.lly with ~~0 converts into zero.
~ standard difficulty is eliminated by parametrization of the near-surface
friction, which is discussed in detail in ~5, 7]. The final recommendations
are reduced to the fact that with ~�0 the terms PK u~ and PKwS are replaced
respectivAly by LS and y;XGs~ where 'Gs--local tangential to fric#,ion surface
cflmputed according to formula
~S = Pa ~ u~ ut ~ ~7)
where p u: -~u ~~-u-)-}-Yxl~'*-'~-1 ( u, w__velocity component directly above
interface~ u; w=-under it~,
c$--resistance coefficient. Under real conditions the approved cs is deter-
mined by the surface shape at high frequencies~ so that, based, for example
on the Phillips' spectrum for the inertia interval of+gravity waves, for es
the evalua.tion is obtained ~...y,2[~n(c2z+%bx)]-2 (z--altitude of para-
metrized boundary layer, bx--r~orizontal resolution of numerical model, c--
- constant on the order 103). Under laboxatory expeximents the surface of~en
- can be considered smooth so that ~ s... y.2 [ ln (c3z+v,,Jv) ]-2 ( v=molecular air
viscosity, c3--constant 10~. If the depth of the liquid is low, parametri-
zation is required of the near-battom boundary layer. Here a relationship
- of type (7) is used in which instead of the velocity drop the actual near-
bottom velocity will alrsa,~y fig??se.
T he con~iderations tha-t explain the possibility of ignoring the moments that
contain pulsation ti?' are inapplicable to the last term in equation (5~ since
it is computed on the actua,l surface. It is easy to understand that he term
describes the effect of grid components of ~aave action on the large-scale,
clearly des ribed portion of the spectrum. A discussion of this effect is
given in C7~.
The final system of equations in the two-dimensional variant looks as follows:
u: (uu 3 e- 2 KuX 2 K~x uc )z -I- (wu u- r~~ uu
2 _
-Ku~ -Kw~ -{-K~zw: - 3 ~ze-}'2lC~xux-2K~Xuc -
_ _ - P-'P.~ + P-''~xPc gt ~ix, ~8)
wt + (uw - Ku: -KwX K ~I,~ ~c )x + (ww - ~ - uw
3 e- 2 Kw; + K~Ix uc -1-1{'~Ix wx - fC~IX z~c )c P-1 P: ~ (9)
ux -4- (w - ~i.r u): (10)
"Ie = ~o -'Ix uo - f' ~ 1 t ~
e~+(ecc-KeX-K~.~e; )z+(ez~v-~~e-~Xue-Ke; -
- -K~xez+K~cec )c =K~~uc -;-ws-~Xwc )'+(2'~e )=~-a: (12)
_ i; ~
$9
. ;FOR OFFICIAL USE ONLY
~ '
,
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l,
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Here J designates the rate of change in the level as a consequence of the
waves falling down,
N~
- p: p- ~ r ~ ; nQ7~ ~ --deviation of pressure ~om hydrostatic,
- ~ gl--modified acceleration of freefall (g1~0 with
~ ~0 and gl"g (1-Fa~f'w) with ~r0) ,
e-(e/~ c,)~"1-~ -'-velocity of turbulent energy dissipation.
- The system of equations (8~-(12~ is solved in the rectangular ~-coordinate of
, the region of extent I, and altitude H+HW (Ha and Hw--orders of wavelength~.
T he periodicity of the function and t~ie neceasary derivatives are assumed
along the x axis. Thus if the adopted grid is counted along the horizonta.l
of m centers, the.surface can be presented by superposition m~2 of ha.rmonic
waves.
On the upper'boundary in the self-modeling region the turbulent impulse flow -
F v* is assigned, the turbulent energy determined by it, and damping of the
ver~ical velocity and pressure perturbations are assumed:
with ~-Ha u'w'=-v'-, e-c,pQv:, zw-0, p-0;
� 13
with p__N~, u-0, w-0, e=c,Tb.
~ Here ~b--near-bottom friction.
_ It follows from equations (8) and (9) that the vertical impulse flow F is
described by the exprassion
F = U'i1! -t ii~^u!' ~ - ~jX il~ll~ - /Nu - p-t Yj.C p~ ~1`~~
N
Here w=w-v~-t~u--vertica~ velocity counted f'rom moving surface; the upper
here and below designatesaverag ing with respect to the horizontal. A s is
apparent~ the impulse flow in the ~-coordinate is created by an individua.lly
described velocity field (first term~, turbulence (mixed three terms) and
pressure. Above the waves of small curvature the impulse transfer is imple- _
mented mainly by turbulent viscosity. With a'rise in the curvature the contri-
_ b ution of streams created by the wave components of velocity of pressure is
increased. This is illustrated in figure 1 wliere the~vertical distribution
of impulse. flow components in (l~) is present~d. The computations were ma.de
of two var;iants: with regard for the advective terms in the motion equa-
tions and without them. A s is appaxent, with''#'airly great curvature the
impulse transfer mecha,nism in the absence of nonlinear terms is strongly
distorted. In figure l,d for ak=0.~ (a--wave amplitude, k--its wave number)
results are given of ana.logous computations for the Stokes' wave for two
variants of spa.tial resolution.
- B y comparing figuxes ld and lc one can concludq that even for fairly steep
waves the differences in flow-around of the siriusoidal wave and the Stokes'
- 90 ~ ~
- , _ _
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~i,
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wave.aleresolutionsdoesfnotnresultgin alsignificanttchangebin therresults,~ the
spa.ti
; CH
'S Q~ 1 i
l~ ' Q~ , ~ ~
~ ~ ~
( 3 1 j ~ ,
5 ~ ~ 2 / I
3 ~ ~ 1
. ~ ~ ~
~ �
r
i
9 j 2 1 ~
2 � 2 ~
0, 5 � 1 ~ ~
i
~s d
~0 6) ~ b~ 2) /
. ~ .
' ~ .3 ~
S 3 ~ ~ .2
% 2 ~
? i ~
1 i2 i
> >r
~5 ~
' -2 0 2 ~ e e ~o -z ~ 0 2 y .s ~o�~;~
- Figure 1. Vertica.l Distribution of Impulse Flow Components
~
_ I( gy ~ ` - P~ u' m'-I-+I,~ u~ u~ �
a, ak=0.1 1~
b. ak=0.2 2� ~P
c, ak=0.4 3� ~
ak=0.4, above Stokes' wave
Dashed line gives results of computa.tions without advective terms
in equation. Dottad line shows results of computations with horizonta.l
- spacing, halven'.
We note that from (15) it follows as a kinematic condition that w=0, and also
, so that the impulse F~ is transmitted to the water
tlrrll~,~"Y~.1' 11~1~,'~mU ~ '~1
~ only by pressure and surface f`riction forces .
_ f-p = ts I) 71x'
(1~)
We also cit~ the formula. fox energy flow from one medium to anoth�~r:
� ~ A u t 2FJO~xTS#'Pre� ~1G~ -
o= o s-
91
, .
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I
~ RND T ~OGY
N0. 10, OCOTOBER 1979

26 DECEMBER 1979 CFOUO) 2 OF 2
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~
- A s the .first task we examined the use of the numerica,l model developed above -
for simul~.Lin~ the Stewart laboratory experiment [13] that measured velocity `
rLncl ~L~~rodynamic ca.nal abavo traveling mo ochromatic waves created by a wave-
producer. The results given in [1, 4, 7~ indicated that the mo~el quite
- satisfactorily reproduces ma.ny fine peculiarities of wind field above the -
waves and the spread of the wave itself. As a result such a diff icult to
measure characteristic was successfully obtained as the spectra of velocity _
field wave components at different altitudes above the waves. Calcula~ions
demonstrated that the monochromatic wave generates all possible modes in the -
numerical model already on a comparatively low altitude above the waves.
_ The model correctly reproduced the difference in the wind velocity profiles -
in different phases of the wave. -
P~zblication ~,2~ found interesti.ng peculiarities in the turbulent energy distri-
bution. The most spscific of them is the presence of four extremums: two
surface and two at the altitude on the order 1~10 of wavelength. The surface
ma.ximum is located to the left of the crest, and the minimum to the lef't of
the foot. The raised maximum is shifted roughly by i~?~J� from the crest. In
magnitude it somewhat exceeds the surface maximum. It is curious tha.t the
elevated extremum can easily be found by pulsation measurements with the use -
of phase averaging. This possibility, as far as we know, has not yet been
realized. It is curious that qua,litatively close results were obtained in
publication L8, 9~.
~
- The most unexpected result was obtained in studying the pressure field in
L3~ with different values c~v.~ (c--phase velocity of ~ave). With c~v~.=23.7
the distribution of surface pressure is described by a single-modal curve of
asymmetric form. The value p~ _(pmax -P~~~~~1;~~~'v: equals 30.9. With c~v.~=20
_ the pressure is described already by a two-modal curve. Up to c~v*=8 the
two modes are preserved, altering their shape. Sl is reduced f`rom 14.9 with -
c~v~=20 to 5.3 with c~v~~10. With c~v~=8 the pressure profi:~e again is
described by one mode, while Rl rises to 9.4~. The pressure be>comes symmetric
with c~v~~6. Thus, the energy transfer as a consequence of prassure is
implemented by the compiex interaction of the surface pressure field with the
- surface. This effect basically cannot be studied on the basis of the linear
- theory.
The results given below were obtair~ed in the next cycle of computations tha,t -
covers the study of the near-water atmospher~c layer with developed wave
action. In the same way as in publication [2, j, 8~ 9~, to simpl.ify the
computations here a single-la er task is solved consisting of integration
of the system of equations (8~-(12~ above the assigned surface. The differ-
' ence of the mentioned works consists of the fact that the surface was a
system of dispersing gravitation waves with the assigned spec~rum, each of
which is described by the theory of low amplitude waves.
As the initial the Pierson and Moskovits sp~sctrum [~12~ was selected that
corresponds, in the opinion of the authors, to the c~nditions of completely
developed waves
F=ag2c~-Se:cP~-R�~g/U W)'~~� ~ (17)
92
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Here W--frequency,
U--wind velocity at altitude of ineasurements H,
a-8.1 x 10'3~ ~=0.74~--empirical coefficients.
_ ~
By introducing the dimensionless f`requencyw=cJv~~g and spectral density F'~Fg3~v.~5~
and by presenting the velocity U in the forin
- �
.
v* ln H~ where z- 0,035 ( l~)
U- x o o-
a
~ we obtain
F=~uw-~5 exp Q ~_4), (19) - -
where Q--slightly altering dimensionless parameter.
_ � ~r ln Hg ! ~ (2U) -
Q ~ (?,035 v,,, ~
~
- where typical conditions of the component Q~10-6.
' By using the velocity scale v~ of length v2~g and time v~,~g we bring eq.ua.tions =
(3)-(5) to the dimensionless form. After this the entire task as a whcle "
depends only on one dimensionless parameter Q, which, taking into consideration
_ the approximateness of formulas (1.7), with completa subs~antiation can be
considered fixed.
~
We will presei~t dimensionless elevation Y~ in the form
A n A N AA nA
�r, (x, t) Ak cos (kx - u~ t). 1)
~
n
Here A-dimensionless harmonics ampl'tude with wave number k and frequency a~i,
linked~y the dispersion correlation a~. The amplitudes A ar9 selected
such that the successive set of realizations at each point h~s a f~equency
~ spectrum (20). Here one should immediately indicate the defect in the
proposed interpretation of the spectrum which becomes completely stripped only
in the case when the process is actually linear. .In the case of nonlinear
- waves for reproduction of the realization the informa.tion.about one spectrum
is insufficient,
As new boundary cQnditions on the surface ~=0 the components of surface
- velocity are assigned
- N
A /1 n A~ AA n~ �
rco (x, tj =~Akk cos (kx - w t),
~
n i~ N n'I: n nn .
~~c~o (x, t) =~,Ak k ~in (kx - ~ t). (22) -
~
- 93
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In the discussed computation N=16 is assumed. t~ith this value the iriitial
spectrum is described with fairly high accuracy: the discrepancy between the
integral characteristics y'- Wmaxn ~ , where Wmin and Wmax+
~ - ~ ~tu~
wm~n =
respectively,.the minimum and maximum wave frequency iricludec~ in the summary
elevation (22) an~ the theoretical amount is Integration of
`Fd w
u
system~(3~-(5) was carried out up to time ~=500 wi~th spac3ng with raspect to
~ime bt=l. ~he statistically equilibrium pa.ttern was achieved roughly with
t=50, The solution was traced according to the series of integral chasacter-
istics. An important cha,racteristic of the interac-tion--dimensionless velocity
of energy exchange between media Ao was obtained. This amount during the =
entire period of integration was s~,ably negative, which rorresponds to the
stream of energy from water to air. The mean amount A iaas roughly 1.5. The -
energy stream due to the normal forces was about 70J o~' the total. THe sign
for the energy.flow indicates that the P ierson-Moskovits spectrum is over-
~stimated in the region of low frequencies. This situation can be explained~ -
for example, by �tYie presence of swell components in the measuremerits placec~
at the basis of the approximation (17~ . The impulse flow throiagh the surface
is governed, mainly, by the turbulent viscosity that is no less tha,n 90f of
the tota.l. Currently analogous studies are being made of other types of
approxima.tion of a completely developed spectrutn. As an illustration of the
possibilities of the proposed method figure 2 presents momentary distribution
of turbulent energy and the current function above the surface. We will stress
that these distrib utions, of course~ cannot be obtained by simple superposition
~ of the results for individual harmonics, sirice flow-aroand of the complex
surface is a significaritly nonlinear process.
N
90J
Q) y 3 b~ O D .ji
S. ~
2 d I
_ ~ ~ 0
10 D ~ (
2 ~ 0
~ - 2 -0,5 '
~ ~ , ~
-1 0 i -1 ~ -0,5 ~
;0 -3 i ~ ~ OS i-2 ~ ~~5 , -0,5 ~I
I O r 1. .,1 1
O ~ ~ i ~ ;p~ ' ' ~
j i.J-
- I Z ?..z Z~.
Figure 2. Fields of Current Function (a) and Dinensionless Ener~~~,
of Turbulence (Deviation from ~.6~ (b~ above Surface A ssigned by
Formula (22~.
9~
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Thus, we have described the general approach and the main results of numerical
modeling of wind-driven waves. Now it is apparent that it is st~ll early to
speak of how suitable the proposed method is for solving the ma.in problem of
wind-wave interaction. At the same time it seems that th,e findings do not
r9pudiate the expediency of further steps in this direction.
BIBZIOGRAFHY _
1. Makin, V. K.; and Chalikov, D. V. "Numerical Modelin~ of Air Flow Above
Waves," IZV . AN SSSR. FIZIKA ATMOSFERY I OKEANA~ No 5~ 1979�
2. Makin, V. K. "W ind Field Above W~aves~" OKEANOIAGIYA, No 2, 1979� -
3. Makin, V, K. "Energy Transfer to W'aves," IZV, AN SSSR. F]~IKA ATMOSFERY I
IKEANA, 1979. _
4. Chalinkov, D. V. "Mathematical Model of Wind-Dr iven Waves," DOKZ. AN SSSR,
No 229, 19?h�
5. Cha.linkov~ D. V. "Matematicheskaya model' vetrovogo volneniya," [Mathe-
ma.tical Model of W ind-Driven Waves~, Isningrad, Gidrometeoizdat, 1979�
6. Barnett, T. P.; Kenyon, K. E. "Recent Advances in the Study of Wind Waves,"
REPORTS ON PROGRESS IN FHYSICS; vol 38~ 1975�
7. Chalikov, D. V. "The N umerical Simulation of W ind Wave Interaction," J.
_ FLUID MECH., vol 87, 1978.
8. Gent, P. R.; and Taylor, P. A. "A Numerical Model of the A ir Flow Above
Waves," J. FI,UID MECH., vol 77, 1976. ~
9. Gent, P. R. "A Numerical Model of the Air Flow Above Water Waves. Part II," -
J. FLUID MECH., vol 82~ 1977. _
~ 10. Miles, J. W. "On the Generation of Surface Waves by Shear Flows," J. FLUID
MEcx., vol 3, 1957�
11. Phillips, 0. M. "On the Generation of Waves by Turbulent 4~ind," J. FLUID
N1ECH,, vol 2, 1957� .
12. Pierson, W. S.; and Moskovits, Z. "A Proposed Spectral Form for Fully
Developed Wind Seas Based on the Simila.rity Theory of S. A. Kitaigorodskii,"
J. GEOPHYS. RES., vol 69, 196~1-.
13. Stewart, R. H. "Zaboratory Studies of the Velocity Field Over Deep- _
Water Waves," J. FLUID MECH., vol ~2~ 1970.
14~. Ursell, F. "Wave Generation by Wind~" "Surveys in Mecha.nics,"Zondon, 1956.
95
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r
tr~c 551.463.7:537.31(265/266)
ELECTRICAZ CONDUCTNITY FIELD OF SEAWATER IN NORTH PACIFIC OCEAN -
Moscow METEOROI~OGIYA I GIDROIAGIYA in R ussian No 10, oct 1979 pp 81-87
~Article by S. A. Oleynikov~ and Candidate of Geographical Sciences D. M.
Filippov, A 11-union Scientific Research Institute o#' Hydrometeorological Infor-
mation, World Data Center, submitted for publication 12 March 1979~
Abstract; F`rom materials of deep-sea observations made `
in the period ~om 1920 through 1970 a three-dimensional
field of specific electrical conductivity of seawater
in situ in the ocean is calculated on a computer. On the
example of the northern Pacific Ocean a general clima.to-
logical-stati:stical description of this field is given~
the main peculiarities of its structure and most cha.rac-
teristic elements of the vertical stratification are
noted (uniform layer of electrical conductivity, its
extremum layers, and so forth~.
_ ~Text] One of the most important physical and chemical properties of the ocean
~ and seawater as complex multiple-component solutions of strong electrolytes is
their electrical conductivity, in particular, the specific electrical conduc-
tivity of water in situ~ currently observed with the help of probes. It is
known that the electrical conductivity of seawater is determined by a number
- of factors, of which the main is the concentration of salts dissolved in
water, water temperature~ and hydrostatic pressure [7, 8, 12]. For the ranges -
existing in the World Ocean of changes in temperatuxe, salinity and pressure
- with theis increase a specific electrical conductivity arises. The functional
link of electrical conductivity with -the pa,rame-ters determining it ha.s been
_ fairly wi3ely studied under :laboratory conditions by ;nany autihors [5, 6, 10, 11~.
A large number of works have covered questions of perfecting instrumen-ts and
methods for determining salinity and density of seawater wi~h respect to its
electrical conductivity [9]. At the same time no published information is
found about the electrical conductivity in situ both of the oceanographic field~
the vertical structure~ stratifica.tion elements~ spatial-temporal variability
- in electrical conductivity and so forth.
The data of full-scale observation on alectrical conductivity in situ do not
make it possib le as yet to obtain a general pattern of the field of specific
96
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conductivity in the World Ocean, since they still bear a fragmer~tary, occa-
sional na.ture and are limi~Ced mainly to the surface and intermediate struc-
' tures of the ocean zones. However the Fairly accurately established depend-
enc~ or c~lc~ctric~.l cunductivity ontthTealmdistr butionlinitheaocean~spermithat
mtikos iL {~o~siblo to approxima.te i s
~his Fiold to bo obtained by computation on a computer. Such work was done
in the Center of Oceanolo~ical Data on technique of the Institute of Oceanolo~y
of the USSR Academy of Sciences for the Pacific and Atlantic Oceans based on
deep-water data file tha.t encompasses the period of observations t~ om 1920 _
_ through 1970, by the authors and L. A. Golovanova. The algoxithms, des~rip-
tions of the orograms and t6chnology of processii~g of deep-water information
on a computer are given in ~1, 3].
A s a computation formula the semi-empir_ical expression was used that was _
compiled according to the data of the works of E. Aceerboni and F. Mosetti
[6~ and A. Bradshow and K. Schleicher ~7~
/ i /1 � 10-`:. ~ ~ 1 p-~ Cn~/M) , -
D~ - D~ ~1 l \u7iw2'{' 3W4~ l -~"`~5~8~ ~ ~ -
where Di--specific electrical conductivity of seawater on observed level i;
B'i--electrical conductivity of seawater on observed level ~rith atmos-
heric pressure (6) as a function of temperature (t�C) and salinity
~S�~oo) ;
/ i oa~,
D~ = I 2,1923 0, t 2842 ~+~~~~,ua2 eo,oo2n r; , 1+~'l'!43 e-o.ooo~~e sl X
\ ~ i
~ e-o,ooaoiss csi-:~s~ ~rr-2o> ~
lV, W2+ 1r~:swa) 1usWs) 1� l ---correction multiplier that takes into
consideration the effect of hydrostatic pressure on electrical conductivity -
depending on salinity S and temperature t of seawatar C7~ on the observed
level;
lG', = 1,5192-4,5302 � 10-2 l,+ 8,3089 � 10-4 t j-7,9 � 10-6 tj ;
1~'~ =1.042 0-3 B~-3,3913 � I 0-8 B'j 3,3 � 10-13 Bi ;
- Cv 3=~} � I O-4 -f- 2,577 � 10-5 Bi -2,492 � 10-9 B~ ; -
W4= 1-1,535� 10-' tl -f-8,276 �]0-3 t? -1,657 � 10-'t~ ; ,
lVs = 6,95 0-3-7,6 � 10-5 t _
W6 =35-S~;
fi; = P ,-10,1325.
The hydrostatic pressure P i(in decibars~ was defined by the method of three-
space approximation employed in the U.S. National Center of Oceanic Data.
The computations of electrical conductivity and it;: vertical gradient were =
made for each hydrological station according to the temperature and salinity
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data (riith regard for pressure) on the standard levels up to depth 4000 m with
further averaging of the data of all stations with respect to five-degree trape-
zia fbr the mean multiple-year, as well as for the therma.l and cold half-years.
Besides the mean values of slectrical conductivity and its gradient in each
five-degree trapezium on the same levels their extremeum values were deter-
. mined, standard deviation, dispersion, coefficients of variation, asymmetry,
excess, error in computation of all the calculated amoun~s, frequency and
rate of occurrence with respect to gradations. F`rom the analysis of the main
errors in computation governed by the heterogeneity in the spatial distrib- _
bution of observational data it follows that on the dominant portion of the
water area errors in computation of the mean are several times lower than the
natur~,l variability in electrical conductivity (standaxd deviation~ in the -
corresponding five-degree squaras. In the least studied central and near-
equatorial regions the water area in the upper 200-meter layer of the ocean
they do not exceed (1-2) x 10-1 C m~m~ dropping to (0.1-0.5) x 10"1 C:m~m at -
its shores. The computation errors linked to the inaccurate determination of
temperature, salinity and pressure on the given level~ in terms of the clima.-
tological-statistical study with lasge spatial-temporal scales of averaging
are insignificant~ and in our estimates, do not exceed 0.05 x 10-1 om~m.
A nalysis of the findings of the computation make it possible to reveal the
basic laws governing tha formation and reconstruction of the field of specific
conductivity in the ocean~ and to study its vertical structure in the spatial-
temporal variability on the characteristic surfaces ~standard levels). ~
W ith the help of the electrical conductivity vertical distribution curves the
following basic elements of its stratification were successfully isolated:
surface uniform (homogeneous) layer of electrical conductivity~ layer of
extremum gradients located in the seasonal thermocline~ and finally, the layer
~ of deep maximum of slectrical c:onductivity lying under the main thermocline
of the ocean L4~.
A s a surface uniform layer of electrical conductivity the layer is adopted in
which its vertical gradient with respect to the absolute amount does not
exceed 1 x 10-3 C;m~m2. The given criterion was selected by us in accordance
with the conditions for isolation in the ocean of surface isothermic and
isohaline layers within which the vertical gradients usually do not exceed
1 x 10-2o C~m and 1 x 10-3 �~oo~m respectively, The thickness of the
surface homogeneous layer of electrical conductivity in the northern Pacific
. Ocean is not constant. Depending on -the physical and geographical conditions
tha,t detarmine the intensity of the wind and density processes of mixing it
is altsred both with respect to the water area and from season to season. From
the most avera.ge annual values in the central region of the near-equatorial
area (75 m~ the uniform layer of electrical conductivity gradua,lly is reduced
to the north to 10-15 m above the middle latitudes, and up to 0 at the coasts
of the ocean (figure la) . In the cold half year (figure lb~ it is the ma.x- ~
imum and the most developed (up to 1.00-200 m) at the subarctic front a,nd in
the region of the southeast branching of the North pacific Current. In the
summer period (figure lc~ the characteristics of the homogeneous layer are -
close to the mean annua,l values (the dimensions of the coastal region where
it is lacking are somewhat increased~. _
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1 1 1 1 1 1
17 ~ -
_ ~ ~
0~ b 150 , 100
~
0 ~ -
, o ~ f00 ~ ~
I ZS ~ r.7 ~ SD 7S ~ i ~
50 rps` Q 0.- 75' r i
15 v 0 . -75 ' 15
0 120 160 160 120 80~
8)
~ U, ~ ~
_ 40 ~ /y , y
0
o /0
ZS
e
a 5D ~
' 7 7
~120 160 160 120 ~90~
Figure l. Thickness (in Meters) of Surface Homogeneous Layer of Electrical
Gonductivity in Northern Pacific Ocean
Key: -
a. A verage for year b. In cold half year c. In warm half yeax
(hatched sections of
water axea where homo- -
geneous layer is missing)
. The subsurface layer of extremum vertical gradients of electrical conductivity
is of certain interest since it is the layer of the jump in electrical conduc-
- tivity. It is governed by those hyclrophysical processes in the ocean which
result, in paxticular in the formation in its scarface str uctural zone of a
layer of seasonal jump in water temperature that determines the main laws
governing the formation of the electrical cond~activity field up to the axis
of its deep minimum. The mean annua.l thickness of the layer of electrical
conductivity extremeum gradients, i.e., the layer where its v~rtical gradi-
ents with respect to the absolute amount excee3 5 x 10'3 .m,m (which corres-
ponds to the criterion of isolation of the layer of temperature jump with
respect to its gradient 5 x 10-2oC~m~ is altered in the northern Pacific
Ocean from the north to the south~ increasing from 20-30 m in the Bering Sea
to 150-200 m in the region of the equator. The average annual depth o~ occur- -
rence of the nucleus of this la.yer is greater (150-200 m) in the center of
tha water area (in region 20�n.l.) and is reduced on the average up to 75-100
m at the equa.tor and up to 20-30 m in the high latitudes (figure 2,a~.
The average annual amounts of the gradients in the nucleus of the extremum
layer (figure 2b~ are (-6- -10 ~ 10'3 Cm~m2 in the northern to middle lati-
tudes, and in the equatorial-tropical belt reach (-1~- -22~x 10-3 Cm~m2.
99 _
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j 12 1 ~ ~ 1
f ~ Q~
, 2550 '
( Q � ~
- 0 _
~ SO
Q 100 - ~SO 200
= 150
0 0
' 6) ~
~ b P. ~o~ -r
40 , 4
o -6 '6
~ -f0 _6 -6
� -14 -1
~ . ;
a -~y _ -z _
~12D 1 ~
Figure 2. Core of I,ayer of Maximum Electrical Conductivity Gradients
Key;
a. Topography of core (in meters~ _
b. A mounts of electrical cot;3uctivity gradients (10'3 Cm~m2) in core of
maximum layer (northern part of Pacific Ocean, mean values for year)
It is characteristic that in the cold hali' year above the middle latitudes, due -
to the fall-winter cooling of the surface waters th�3 layer with gradients over
- 5 x 10-3 Cm~m2 is completsly washed away, and the deepening of its core an the
section of the water area is increased (as compared to the average annua,l (by
50-100 m).
The most characteristic element in the stratification of the examined field
is the layer of deep minimum of electrical conductivity whose formation is -
linked to the peculiarities in the vertical distribution in the ocean of temper-
ature, salinity and hydrostatic pressure. Under the influence of the first ~
two factors, with respect to the con~ribution to conductivity of those domi-
nating over pressure within the limits of the surface and intermediate struc-
tural zones, electrical conductivity rapidly is reduced wi-th depth, ma.inly
following the course of water temperature in the main thermocline. The pa~tial
reduction in electrical conductivity as a consequence of the decrease in
salinity with depth is fairly insignificant and accordir~ to ~ur data is not
more than 10-~2~ (according to the con~tribution to electrical conductivity the
cha.nge i:~ water temperature by 1�C is roughly equivalent to the change in
salinity by , however the range of change in the latter in the ocean is
almost by an order lower tha.n the temperature).
With a transition to the deep structural zone, under conditions close to the
isotherm, and with the practically uncha.nged salinity, the leading factor that
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determines the nature of va.~iability in electrical conductivity with respect
to the vertical becomes the hydrostatic pressure that compensates for the
effect of temperature and salinity on the axis of minim electrical conduc- _
tivity and ~overns i-ts further growth with dapth. In [7~ it is demonstrated
that the increase in the electrica.l conductivity as a con~oqdenth ro ahl
in~ro~.^c~ 1n ~~ressure fxom 0 to 10 000 decibars,(i~e., up p ~ Y
].~,OU~ m) rc~achos 12~.
In the northern Pacific Ocean the nucleus for the minimum layer occurs at
depths 1500-1800 m in the high latitudes~ and on the average, at a depth 2500 m
in the equa.torial-tropical zone. The topography of the minimum layer in the
southwest section of the examined water area has a more complicated relief
due to the variation with depth in the lower boundary of the thermocline in
this region. The values of electricaJ_ conductivit~r in the minimum layer also
~ are altered fro~r~ north to south increasing f`rom (29.0-31.0~ x 10-1 Cm~m in
the Bering Sea up to 31.5 x 10'~- Cm~m on the equ,ator and in the tropical
latitudes. The greatest variability in electrical conductivity in the minimum
layer (standard deviation over 0.14 x 10'1 Cm~m and the variation coefficient
0.4~~ is noted along the western shore of the ocean. This layer is prac-
tically not subject to seasonal changes.
In accordance with the thermal pattern of water the maximum average annual
values of electrical conductivity ar9 observed on the surface of the ocean
(r'n places at depth 10-20 m)*, where the are zqnally altered from 30-31 x
10'1 Cm~m at the Beri.ng Strait to (55-57~ x 10- Cm~m in the southwest water
area (figure 3a). The farther from the surface the field of electrical co~nduc-
tivity in the ocean is subject to multiple reconstructions, linked to the
thermocline factors and water circulation. At depth 200 m(figure 3b) the
regions of its extremum values are shifted: #~he least (30 x 10'1 Cm~m~ to
- the Arctic front, the greatest ((45-4'~~ x 10' Cm~m~ to the regions of
intensive lowering of warm and highly-saline waters of the subtropicJ.
In the southeast water area the values of electrical conductivity at these
depths become reduced ((37-38) x 10'1 Cm~m) as a consequence of the advective
effect of the subarctic water and the rise of the deep water along the axis
of tropical divergence. With secondary reconstruction of the electrical
conductivity field that is traced in the intermediate structural zone of the
ocean~ roughly from depth 500 m~ the fea-~ures of its zonality begin to be
restored (figure 3c), however the reduction in the electrical conductivity
at depth 1000 m in the direction of high latitudes is already insignificant
(only 1.5-2.0) x 10-1 Cm~m). In the deep structural zone the electrical
cond uctivity field is strongly smoothed, being reconstructed in a meridiona.l
direction. The mean multiple-year values of electrical conductivity at
depth 4000 m are alt~red ~`rom region to region only ~y a tenthof a unit (f`rom
31.65 to 31.75 x 10- Cm~m), increasing from the central section of water _
- area to the shores of the ocean (figure 3d).
The absolute and relative variability of electrical conductivity in the
northern Pacific Ocean is the maxi~num in the surface structural zone. The
~~~creased average annual values of standard deviation and the variation
~-In the winter period the maximum values of electrical conductivity in the
high latitudes are noted at depths on the order of 300-500 m and more.
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_ coefficient are confined to regions of dynamic instability of water and are
observed in regions of A rctic and subarctic fronts, as well as in California
_ (on the ocean surface) and the region of the tropical cyclonic circulation
in the layer 50-100 m(over 3 x 10-1 Cm~m and 8/ respectively). The extremum
values are reached by the standard deviations and the variation coefficients
at the shores of Japan~ in the region of encoun~ter of warm and cold waters
in the K uroshio and Oyashio curxents ~respectively over 5 x 10-1 Cm~m and
10-14~ on the ocean surface with de h the vasiability in electrical conduc- -
tivity~ especially in the in ermedia~e structural zona rapidl drops and at
depths 4000 m on the average is 0.05 x 10-1 Cm~m and 0.1-0.2I~.
The intra-annual (seasonal~ variability i.n e lectrical conductivity governed -
ma.inly by thermal factors is most pronounced in the surface str uctural zone
of the ocean. The maximum excess in the summer values of electrical conduc-
tivity over the winter are traced on the surface of the Pacific Ocean in the
moderate and middle latitudes (positive differences are 6-8 x 10-1 CM~m~, i.e., ~
there where the seasonal course in the water temperature is most noticeable. -
In the direction towards the equator the differences are reduced to 0,3-0.7 x
10'1 Cm~m. With depth the seasonal differe nces in electrical conductivity
are attenua.ted and change their nature. The region of the greatest positive
differences of electrical conductivity at depth 100 m are shifted to the
equa,tor ((1-3) x 10-1 Cm~m) . The remaining part of the water area at this
depth is chara.cterized by an alternation of regions of positive and negative
differences in electrical conductivity not exceeding~ by the way~ the amount
1 x 10-1 Cm~m. On the lower boundary of the surface structural ocean zone
the seasonal differ ences are smoothed: the summer values of electrical conduc-
tivity noticeably s urpass winter only in the southwest section of the water
area ((1-2) x 10-1 C m~m).
1 1 1
Q) bl �
. . '
Q: 35 b D;
40 ,iS y
o ys o 40
5o y5
o e
0 -
~ ' .fs
SS 0 ~ -
0 '
~ I C~~I~ d P J1,7.
0~30 ' 31,65
0 -
35,0 I I u 3l,~
I ;
Jf,75 Jf, 65 ~~a -
_ IJ~ ~J7,5 'p 718 I
�...__Jh~ 16C~ 120 BO ii) 1 0
- Figure 3, Dist~ibution of Electrical Conductivity of Seawater (10-1 Cm~m) on
Ocean Surface (a), at Depth 200 m(b), at Depth 500 m(c~ and at
Dep-th 4000 m(d) (Northern part of pacific Ocean, Mean Values for
Year)
10?
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The average annual field of vertical gradients of specific conductivity on the
stu~iied water area differ in considerable heterogeneity, especially wi~hin
the surface structural ocean zone. The greatest variability in electrical
_ conductivity along the vertical is cY~aracteristic of the la.yer of water temper-
- ature jump. On the aver~e the electrical conductivity gradients f`rom (-1--2)
x 10-3 Cm~m2 in the surface 1-~9ete la er of th~ ocean increase in absolute
a.mount in the layer 50-75 to ~-6--7~ X~Q-3 Cm~m in the western section of
the subtropics, and reach the extremum values for the entire water area ((-14-
-16) x 10-j Cm~m2) in the region of the tropical cyclonic circulation as a
consequence of the sharp thermal contrast produced here by the elevation in
cold deep water. The farther f`rom the ocean surface the field of vertical
electrical conductivity gradients is smooth, acquiring the features of zonal _
distr ibution. In the layer between depths 100 and 500 m in the high latitudes
a region is tracdd of positive gradients with extremum at depth 100-200 m(over
1 x 10-3 Cm~m2) linked to an increase in electrical conductivity below the
nucleus of the cold surface layer, characteristic for Arctic type water ~2].
The most noticeable attenua.tion in the vertical gradients with depth is traced
rou~hly up to the axis of intermediate water where it averages (-0.15--0.20~ x
10-j Cm~m2~. Below the axis of the dedp electrical conductivity minimum the
vertic~.l gradients adopt positive values that are constant for the entire
ocean (0.03-0.04~ x 10-3 Cm~m, govsrned by a rise with depth in the hydrostatic
pressure with practically unchanged temperature and water salinity at great _
depths.
In conclusion one can note that the electrical conductivity of seawater in
situ, whose general ideas of spatial-temporal distribution and variability
in the example of the norther n Pacific Ocean we have attemptad to give here,
as an integral character istic of the state of seawater can be employed in
solving research problems linked to classification of water masses, isolation
of frontal zones, regions of convergence and divergence~ zonss of upwellings~
and so forth~ and ~or applied purposes (electrometry, fishing, marine electric
geophysical exploration, underwater communications and so farth). In partic=
ular, the knowledge by the developers of probes-electrical ;salinometers of
the basic peculiarities of such an oceanographic field as e'Lectrical cond uc-
tivity of seawater in situ will make it possible to increa~,e quality, effect-
_ iveness and accuracy of the created instruments, and this means also the _
reliability of the observational findings.
_ ~
B IBI,IOGRAPHY -
1. Golovanova, Z. A, "Description of Set of Programs of Climatological and
S-tatistical Processing of Deep-Water Data on.a Computer~ as Well as Their
Stora.ge in Archives," TRUDY VNIIGMI-MTSD, No 33, 1976.
2. Stepanov, V. N. "Mirovoy okean. Dinamika i svoystva vod" [World Qcean,
_ Dynamics and Properties of Water~, Moscow~ Z naniye, 197~4,
3. Filippov~ D. M. "A lgorithms of Climatological and Statistical Processing
_ of Deep-Water Data on a Computer," TRUDY VNIIGMI-MTSD, No 33, ~-976�
4. Fili,ppov, D. M.; and Oleynikov, S. A. "Layer of Minimum Values of Elec-
trical Conductivity in the World Ocean," DOKIA DY AN SSSR, vol 2~2, No 2,
1978.
l03
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Khnrn~ R. "Morskaya khimiya.(struktura vody i khimiya gidrosfery~" ~Marine
- ~:h~~m1 t~ I.r�,y r ruci.~irA ~ I' W~.te.r and Chem~stry of' HydxosF~here~ 1, Moscow, Mir ~
7'J'1?..
6. Aceerboni~ E.; and Mosetti~ F. "A Physical Relationship Among Salinit.y,
Tamperat~e and Electrical Conductivity of Seawater~" BOLL. GEOFIS. TEOR.
- AppL. , vol 9, No 3~-4, 1967.
7. Bradshow, A. I,. ; and Schleicher, K. E. "The Effect of Presstzre on the Elec-
trical Conductance of Seawater," DEEP-SEA RES.~ vol 12, No 2, 1965.
3. Connor s, D. N.; and Kester, D. R. "Effect of Major Ion Variations in the
Marine Environment on the Specific Gravity-Conductivity, Chlorinity-
Salinity Relationship~" MARINE CHEMISTRY, vol 2, No 4, 1974.
9. Cox, R. A.; Culkin, F.; and Riley, J. P. "The Electrical Conductivity~
Chlorinity Relationship in Natural Seawater~" DEEP-SEA RES., vol 14, No 2,
~967, .
10. Ribe, R. L.; and Howe, J. G. "An Emp9xical Equa.tion Relating Seawater
_ Salinity, Temperature, Pressure and Electrical Conductivity~" MAR. TECHNOL.
soc. J., vol 9, No 9, 1975�
11. Thomas, B. D.; Thompson, T. G.; and Utterback, C. I,. "The Electrical
Conductivity of Seawater~" JOURNAI, DU CONSEII. PERMAN. 1NTERNAT. EiCPLOR.
_ MER. , IX, No l~ 1934~.
12. Wsyl, P. "On the Change in Electxical Conductance of Seawater with Temper-
ature," LIMI~IOL. OCEANOGR., vol 9, Na l, 1964.
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vnc 551.326.7:626.01 _
ESTI~NIATE OF THE CAI,CUZATED THICKNE5S OF STRATIFIED ICE
Moscow METEOROIAGIYA I GIDROIAGIYA in Russian No 10 ~ oct 1.979 PP $~'92
[Candidate of Technical Sciences V. P. Afanas'yev, Leningrad Institute of -
Railroad Transportation Engineers~ submitted for publication 1z Feb 1979]
Abstract: It is noted that for structures on.open sea
aseas of temperate latitudes in determining the ma.gni-
tude of ice pressure one should adopt as the calculated
the ice thickness with regard for stratifications. A
brief description is given of the process of rafted sea
ice fo~mation. A technique is presented for approximate
evaluation of the calculated thickness of rafted ice. -
The technique is designed for use in determining ice
- pressure on marine hydraulic enginsering structures in
the absence of systema.tic observational data. -
~Text] In the active norms for determination of ice loads on -the hydraulic _
engineering struct~es, SNiP II-57-75 [Construction Norms and Regulations] it
is recommended that the initial data on the ice situation be adopted on the
basis of full-scale observations. However often it is necessary to m~ke compu- _
tations, especially at the fixst stage of planning, without having a suffic- _
ient volume of materials of these observations. Such cases can occur not only
- in a short period of observations as compared tn the required, b ut also with
planning of str uctures on water axeas where determination of the ice charac-
- teristics presents considerable difficulties~ for example~ on wa-~er axeas
where no ice-navigating ships pass and where the ice drift '_s the main
sign of the dynamic state of the ice cover.
Iri the absence of full-scale observations to select certain ice chaxacteristics
(rate of ice dr ift, for example) the norms proposed that the recommendations -
given in them be used. For selection of the ice cover thickness such recom-
mendations are usua.lly missing in the nor ms. The data given in the hydro- ~
lagical references on the thickness of ice refer to ice thickness of natural
(thermal) accumulation. Analogous information is presented by different
organizations of the Hydrometeorological Service. Such informa.tion, however~
in tha majority of cases cannot be used for computing the mas ine hydraulic -
engineering str uctures. This is explained by the fact that the ice thickness -
105
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+ of natural accumulation can be adopted as the calculated in planning hydraulic ~
- engine~rinJ st.ructures only on comparatively closed, limited water areas where
~th~ ~~.r.acc~:~.:~ of ice for:r~ation occurs under calm conditions, For structures
1_ocatc~ci on open sections of the sea coast or far t`rom the shores, ice flelcls
must be used as the calc ulated form of ice forma.tions which consist of strati-
fied ice and hummocked piles. At the same time the thickness of the strati-
fied ice can exceed the thickness of the ice of natural accumulation in the
calculated period (as a rule by the end of winter~ by almost double.
It should be recalled ~hat the value of ice thickness plays an especial role
- in computing the magnitude of ice load. This is apparent from the~ calculated
_ formula of SNiP II-57-75
P=mRp bh, . (1)
where .P--load from moving ice Field on structure taith vertical anterior edge;
m--coefficient of sup ort shape;
R=kR , where k=f(b~h~ is altered from 0.5 to 2.5;
= b,hp-wi~th of structure and thickness of ice.
, In fact, h affects the value of ice load not only directly, but also through
the amount R. Thus, for example, with an increase in h 1.7-fold the value of
= P can rise (pfor the real width of single supports~ already more than 2.0-fold.
T his is a lso s hown l
~y tlie graph in figure 1. It is evident that the magnitude
oi' ice load on the structure depends to a considerable degree on the correct
selection of the calculated value of ice thickness. A nd since the ice load is,
as a rule, the greatest horizontal~, and consequently, determines the relia- -
bility and efficiency of the structure, an estimate of the calculated ice
- thickness is one of the most important questioris of engirieering ice technology.
h/ho : PIPo K _
K
S ~i Z~~ -
P%fo�,
i
_ 3 hlho 10
~
~
1 -
0 / 0,2 Q4 0,6 !;3'1�.
Figure l. Dependence of Ice I,oad on Support on Change in Ice Thickness
Key:
P~--pressure with h~b=0.2, h~--thicknsss of ice equal to 0.2b
~A s compared to others. _
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- As is known~ to estimate ice thickness of therma.l origin a number of formulas
have been proposed in which the ice thickness is defined mainly depending on
- the sum of cold with a more or ZA55 complete consideration for the hydrometeoro-
logical cha.racteristics of the ice foxmation conditions, for certain regions
' correlatiobeen Vro os di~A scantsx mplesweiwillhcite the knowniempiri alaforeS
have a.lso p p
_ mula of N. N. Z ubov
h2+50 h=8~m,
where E6--sum of degree-days of frost.
In order to determine the thickness of the stratified ice, initially formed
mechanically ~om the shape of young ice, until recently there were no calcu-
lated relationships. This a.rticle examines a technique of approximate estimate
- of the thickness of this form of ice cover. `
The observational data demonstrate that in the open sea one can rarely encounter
an ice cover of natural accumulation in a pure form. Usually ice fields domi-
nate that to a certain measure are subject to raftings and pilings [1, 3, 6~.
The processes of stratifications during compression of ice prove from the very
beginning of ice forma.tion, and are especially pronounced for fields of young
ice of thickness up to 10 cm, sometimes with considerable salinity and high -
temperature~ also for ice with great thickness. W ith thickness over 15-20 cm
the solid ice during compression begins to break up, f`ractionate and form piles.
A general idea about the rafted ice formed during compression (shift) of ice
in the open sea is given in table 1, compiled from data of full-scale obser-
vations taken from different sources and i.ncluding from the author, It is
apparent from table 1 that the number of layers in the stratified ice can reach -
10 and with a thickness of the young ice 7-20 cm (thermal accumulation) sections
can be formed of ice fields with general ice thickness of the order 70-80 cm, -
- and even about 1 meter. After stratification the ice rapidly ~eezes together.
A lthough interstratifications between the la.yers are less strong than the
ice of the actua,l layers, nevertheless such a stratified ice is destroyed as
the observations show as ono integral without stratification.
= One should evidently view the overall thickness of stratified ice as the thick- -
ness of ice that has been stratified in the beginning of the summer season
plus the increase in ice as a result of further freez ing. Based on this
conclusion and using for the computation of thermal accumulation of ice the
formula of N. N. Z ubov given above in crder to estimate the thickness of _
stratified ice in the calcula�ted period one can suggest the following rela-
tionship [,4~:
~ h ~ +50h,~=8(~6o+~6n), (3)
where hH--thickness of stratified ice cover at the end of the calculated period,
cm;
_ l07
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EA~--sum of degree-days of frost for the rema.ining time after stratification;
- EA�--sum of degree-days of f~ost corresponding to the acc wnulatioci of ice
of thickness equal to the thickness of the initially stratified ice
(it is a conditional amount~
TA ' -
"Year ari3~ - FF--fiF~iickness hN--Thickness Qua.n- -
Sea, region Month of of Ice of Nat- of Ice of Strati tity
Observations ural Accumu- fication~ cm of Author
, lation~ cm ?~a. ers
Thick-
ness cm
Gulf of Finland 189~r N ~~-5~ 90 Several S. 0.
_ 2~-27�8�1� layers Makarov
[6]
Gulf of F.inland 1923-1932 ~
II-N
I region 30 82 The same V~ I.
Arnol'd-
_ Clyab'yev
II region 50 90 J
III- N regions 10 60 �
_ II region 1927, II 55-6z 6-8 �
~b -
II region 1923~ II 2~ 60 "
Gulf of Finland~
middle and western
sections 70-100 up to 10 V. I.
7-15 Arnol'd-
~ Clyab'yev
1
The same, fair- 1962, III- 15-20 50-60 " V,]'J .
way N Betin
Cas ian Sea, 1960, II 26 62 Several ~,3~V.
nor~hern section layers Z~~yanova
G ulf of Finland 1965 ~ N 30 75 ~ VS~P .
15-~7 Cf]nas'yev
2
III region -
- " 1966, III 15-20 6p ~_5 _
12-15
Note: I region 29-23�e.l.; II region 23-26�e.l.; III-N regions to the west
of 26�e.l.
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Figure 2 presents a graph that clearly demonstrates the proposed technique
_ for determining the calculated thickness of stratif~ed ice depending on t~e
sum of degree-days of f`ro~t and the initial thicknF~ss of the rafted ice h~.
The moment of formation hH is assumed here at th~.ckness of monolayer ~1 to
h=15-20 cm, which corresponds to the period witr sum of frost E01, eq
Z25-175 degree-days. Curves 1 and 2 are constructed according to formula (3~
respectivel for h=70 cm corresponds to EON~ approximately e ual to 1110
degree-days~ and h~=90 cm ~~i9K corresponds to 1500 degree-days~.~ For compar-
ison of the processes of growth in two different types of ice cover the graph
gives curve 3 that is constructed according to formula (1~ for thickness of an
- ice cover of natural accumulation (without consideration oi thA factor of an ~
' increase in ice 'tYl~.CI{I1055 as a consequence of rafting~ . On the graph ice
thickness values are plotted that are taken f`rom table l. The placement of
- the data on the graph was made s~rith regard for the sum of degree-days of frost
that meet the corresponding ice periods and the region of the sea. The values
of ice thickness and natural formation are placed on curve 3, the maximum
- values of thickness of the stratified ice corresponding to them are placed
more or less precisely on curve 1. With respect to the probable period of
rafted ice forma.tion we find on the continua.tion of curve 1 the initial thick-
ness of the stratified ice cover. This amount equals 0.67-0.'77 m. The
remaining tabular values of stratified ice thickness lie on curve 4. They,
in all probability, are not extremum for the given region of the sea and cannot
serve as calculated amounts.
dhMY.
AcM �
100 2 dh~
JO
BO I~ 1
60 j v 3 10
_ n ~ 5
.
_ . ,
40 ~~1~-
~ ~ ~o
- 20 jl 06 09
� oy ~10
_ al i f Bo n B
0 -
J00 300 500 700 900 fB
_ Figure 2. Graph of Growth in Sea Ice Thickness
Ke1,2,4 Stratified ice Observational data:
3. Ice of thermal accumulation 6. S. 0. Makarov
'bi ( according to N. N. Z ubov 7. V. I. Arnol' d A lyab' yev
_ and V. V. Betin~ 8. V. P. Afanas'yev
5. Curve of reduction in h 9. V. V. Betin
10. Z. V. Zuk'yanova
FA --sum of degree-days of frost from moment of ice formation
_ ~On the x.-axis only the actual sum of degree-days is plotted F,A=EA1+F9~. -
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B y examining the graph one can ascertain a satisfactory coincidence of the
experimental points with theoretical curves. This indicates the applicability
of tho ~roposed method for estima.ting the thickness of stratified ice. Further,
1 t is ~.~~pa:r.ont f.rom the graph that with an incr.ease in tha winter period the
difference ah~ between curves 1 and 2 is gradually reduced. In the percentage
expression (right y axis~ this is demonstrated by curve 5. Thus, whereas in
the initial period the difference reaches 25/, alxeady within FA =900-1000
dogrea-days it is reduced to 10~ (such a period of accumulation ~n the ice
cover thickness corresponds �~o the hydrometeorological conclitions of a number
of seas in the Soviet Union). Consequently, the possible error obtained in
~.ssigning the initial thicknes:.~ of the stratified layer h~ in the beginning
- of the winter season gradually ~uring w~nter towards the calculated period is
_ also reduced. Tn order to increase the reliability of the planned structure,
in our opinion~ one should however, adopt for the computation the value hH on
curve 2. A s is apparent on curve 5, such an increase in the calculated thick-
ness of ice corresponds to a degree of accuracy of detsrmining other ice magni-
tudes and the requirements of SNip Iz-57-75�
_ Onc~ should add that close results to those obtained in formula (3~ can be
obtained if instead of formula (2~ for compilation of the calculated relation-
. ship in evaluating the st,ratified ice thickness one uses other empirical
formulas, for example tlie Stefan formula
h ~ 3~~,A. (4) �
In this case the calculated formula will look as follows:
h~~ = 31~~Ho -t- L'H~~, (5}
wher.e FA~ and EAN designate the same as in formula (3)~ however the numerical
_ value E~N is assumed to be equal to 700 degree-days. Here the difference in
the value of the stratified ice thickness in the calculated period as
compared to tha.t computed accordi.ng to formula (3) is obtained in the limits
of one-tenth of a centimeter.
One should also note that the use for the examined calculated formulas of -
more complex rslationships to determine the thickness of the accumulated ice
with regard far additional hydrometeorological factors is hardly expedient,
- since the initial data for them have fairly approxima.te values.
Thus, the thickness of stratified ice is one of the most important calculated
characteristics in determining ice pressure on structures for regions of
the open sea~ for the formation of the ice cover is closely linked to
dynamic process6s. An estimate of the thickness of such ice ca~n be made
according to one of the empirical formulas for d~fining the thickness of
accumulating ice depending on the sum of degree-days of frost with an -
increase in this sum by a number corresponding to the thickness of the
initially stratified ice cover, approximately equa,l to 80-90 cm. _
In order to pinpoint the values of the stratified ice thickness adopted in
the computation in planning hydraulic engineering structures it is desirable
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a ~
to continue obsexvations by the organizations of the Hydrometeorological
;ervi cc~ c~ I' ~~o.rma.tion and d~evelopment of stratified ice with measurement of its
i;tiickr~c~ss ori a broader scale on 3ifferent seas, not limited to regions of
traditional observations. -
BIBZIOGRAPHY
. 1. Arnol'd-Alyab'yev, V. I. "Z'dy finskogo zaliva po dannym issledovaniy s
sovetskikh ledokolov za period 1922-1932 gg" [Ice of ths Gulf of Finland
~ According to Research Data from Soviet Ice Breakers for the Feriod 1922-
1932], Leningrad, 1933�
- 2. Afanas'yev~ V._ F. "Zedovyye nagruzki na vert5.kal'nyye opory morskikh
sooruzheniy" [~Ice T.,oads on Vertical Supports c~f Marine Structures], author's
abstract of dissertation for defense of scieni:ific degree candidate of
technical sciences, Moscow, 1973�
- 3. Betin, V. V. "Computation of Main Components of Ice Cover of Baltic Sea,"
"I,eningradskoy GMO" [Zeningrad Hydrometeorological Observatory], No 2,
Leningrad, 1963.
4, Z ubov~ N. N. "Morskiye vody i 1'dy" [~Seawater and Ice~~ Moscow-I,eningrad,
Gidrometeoizdat, 1938.
5~ Luk'yanova Z. V. "L'dy Kaspiyskogo mory i ikh fiziko-mekhanicheskiye L
- svoystva" ~Ice of Caspian Sea and its P hysical and Mecha.nical Froperties~,
author's abstract of dissertation for defense of scientific degree of
candidate of geographical sciences, Baku~ 1964~.
6. Makarov, S. 0. "'Yermak' vo 1'dakh" ["Yermak" in Ice], St. Petersburg~
_ 1901.
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vnc ~56.535.6(571.6)
CERTA IN CHARACTERISTICS OF ICE COVER STRENGTH DURING ITS BREAK-UP ON RNERS
OF THE BAYKAL-AMUR TRUNK LINE ZONE
Moscow METEOROI~()GIYA I GIDR07AGIYA in Russian No 10, oct 1979 pp 93-l01 -
LArticle by Ye. F. Zabelina~ USSR Hydrometeorological Scientific Research
, Center, submitted for publication 26 February 1979~
Abstract: Using S. N. Bulatov's calculation me~hod
probability characteristics are ob~ained for the
, thickness and strength of the ice cover by the~time
of break-up on rivers.
An analysis is made of calculated characteristics
recommended by ths Construction Norms and Regulations
to estimate the dynamic loads on structures during
~ the ice drift period. '
The �~~ssibility is shown of simplified computation
of strength characteristics of the ice cover~ inclu-
ding for sections of the Baykal-A mur tr unk line river
zones not co~vered by hydrometeorological observations. _
- ~Text] The active development of natural resources in ths zone of construction
of the Baykal-Amur railroad trunk line (BAM)~ refinement of the projects for
BAM construction~ pla.nning of ths industrial~ general and other structures
associated with it~ organization of construction work~ transporta-tion oper-
ations, operation of the hydraulic en~ineering structures and so forth advance
a number of problems in studying the ice cover of rivers, one of which is -
determination of the thickness and strength of ice.
In all the ice engineering computations, including in the computation of ice
loads on hydraulic engineering structures~ the most complex~ to a consider-
able measure conventional~is the selection of the magnitude of ice strength
limits, especially in relation to the rapid cha,nge in mechanical properties
of the ice cover in the melting period. Of greatest importance are the
strength cha,racteristics of the spring ice in the period of shif~ and ice
drift, i.e., in that period when dynamic eff'ect of the ice on the structures
occurs. '
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By now fairly extensive material ha.s been accumulated on the st.rength of spring
~ ice under full-scale conditions. However there are no published data of exper-
imental determinations of ice strength on rivers in the BAM zone, with the
exception of results o tests on the A mur River at Komsomol'ska-Na-Amur made
by V. M. Timchenko [,10~.
It is necessary to note tha.t field tests of ice cover strength in the majority _
of cases end several days before they start to shift, which results in an
exaggeration of the strength values for the ice drift periods, and consequently~
a surplus increase in the supplies of strength of the structures and construc-
tion outlays.
The SN1F II-57-75 [Construction Norms and Regulations~ that ha.s been active
since 1 January 1976 recommends the use of the tensile strength of ice for
compression depending on the mean air temperature during the previous ice drift
of 3-6 days and ice salinity (see table 27 SNIP).
N. K. Korzhavin [6~, considering that the data of table 27 of SNIP do not take
~ into consideration in a proper manner the entire set of factors, and primarily,
the length of the preparatory period before break-up, proposes for rivers in _
the zone of BAM development to adopt for the initial stages of ice drift (first
shifts) an increased tensile strength of ice for compression~ equal to 75 T~m2~
which corresponds to the mean air temperature (a.^c~ording to table 27 of SNIP)
equal to -3�C, and for the highest levels of ice drift--45 T~m2. The tensile
strength for bending R N is assumed to be equal to 3~4 of the magnitude of
tensile strength for compression R~.
The current state of research makes it possible to ma.ke an indirect estimate
of the strength characteristics of the ice cover according to the factors that
determine them in the period of inelting . Th met~od developed in the USSR
Hydrometeorological Center by S. N. Bulatov ~l, 2 makes it possible to compute
the thickness and strength of inelting ice for eac day~ starting from the date -
of removal of snow from it to the moment of complete loss of strength. The
calculated formula here looks like
_ ~ ~ - Y JI J~~l? ~ 1 ~
where ~--relative breaking poin~ of inelting ice for bending;
S--qua.ntity of solar radiation absorbed by ice, determining the content
in ice of its liquid phase;
S~--qua.ntity of solas radiation dtz~ing whose absorption the ice completely
loses strength. The qtaantity Sp depends on the ice structure. In
the calculations S~ is assumed to be cons~tant, equal to ~4 cal~cm3. Deter-
mination of the S values is made by computing according to meteorological
elements for the period of inelting the fractions of solar radiation absorbed
by the ice covar layers and the averaging of these f`ractions with respect to
ice thickness. The ice thickness is computed in parallel with_co putation of
- ~ the amount S. The accuracy of the computation is fairly high L11~]. In
particulas~ this was confirmed for the examined reg'on by 78 tests made on _
the A mur River of ice overhangs for bending [10~ 11~.
Since the S. N. B ulatov method in ma.ss calcula.tion becomes very awkward, a
program was developed and checked-out on the Fortran langua.ge for t~he
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computer BESM-6. The i.nitial information here is the data on temperature and
air humidity, wind velocity and the relative cloud cover according to obser-
vations on the closest meteorological station to the assigned section of the
_ river, the thickness of the ice cover and the heibht of the snow cover on the -
" ice before the start of inelting, as well as the latitude of the locality. The
stren th cha.r.acteristics'~~ and thickness of ice h were computed for the period -
from 9 0 to 1 75 for certain sections of the river located both in the eastern
and in ~he wes~ern part of the BAM route. The selection of these sections ~ -
was defined, first, by the presence of a meteorological station near the water-
measur ing post second we strived so that these stations would reflect the
conditions of differen~ rivers in the zone. Thus, for exa.mple, the aroas nf -
the basins of the examined rivers changes from 2410 km~ (Byssa River~ to 1.720
million km2 (A mur River). The ma,ximum ice thickness for winter fluctuates in
limits f~ om 0.87 m~Byssa-River- Byssa point~ to 1.82 m(Olekma River--Ust'-
Nyukzha. point) .
Figure 1 presents the course of change in the mean values o.f ice strength and
its thickness (in relative units~ for the period of inelting. It is apparent
on the figure that after the rem~val of snow the ice thickness is reduced
slowly, while its strength under the influence of the absorbed solar radiation
drops quickly. Thus, in the first 10-12 days after removal of snow the ice -
cover above and below almost did not melt, but in its mass intensive formation
of liquid phase occurs, which governs a decrease in the relative ice strength ~
to 0.3-0.5 of tha initial amount. -
n,~
~o
0,8
h ~
. 3
J6
2
0,4
0,2 ~
y
3 2
0 8 16 24 30 n
Figure 1. Course of Reduction in Averaged Computed Values of Thickness h
and Strength of Ice Cover ~ for Period of Melting in Relative Units;
Key; (n--days of ice melting after romoval of snow~,
1. Olekma River--Ust'-Nyukzha point _
2. Selemdzha River--Stoyba station
3. B yssa River- Byssa point
F ublications [6~ 9~ examine -the strength characteristics of spring ice depen-
ding on the duration of the preparatory period by which is understood the
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difference in the dates of break-up of the river and transition of the mean .
air teml~erature through 0�C in the given point. Such an appro~.ch to an esti-
mate of ico cover s~trength is someqha-t conditional and for the examined region
- is not indicative. The main decisive reason for reducing ths ice strength
_ during melting is absorption by the ice of solar radiation. On the examined
rivers the intensity of solar radiation influx in the summer period is great,
while the low snow cover is destroy'ed long before the transition of the mean
diurnal air temperature through 0�C. The melting period of the ice cover is
1.5-2-fold grea-ter than the duration of the preparatory period, determined
according to the transition of temperature through 0�C, consequently, the
degree of reduction in spring ice strength is considerably greater.
In the formula (1) given above ~R~RO, then
R = Ro ( i - S/So)',
where R--ultimate strength of inelting ice during bending, i.e., one of the
parameters recommended by SNIP for computations of the load of the ice effect
on hydraulic engineering structures; -
R--ultimate strength for bending for ice not subject to the effect of
solar ~adiation and having temperature of 0�C.
V. A. K oren'kov [5~ from data of his own observations~ as well as the obser-
vations of I. P. B utyagin, V. M. Sokol'nikov et al. gives the value of u1~i-
mate strength of ice for bending in the pre-ice drift period as Rp=55 T~m .
S. N. B ulatov Ll~, considering that these data are exaggerated by 5-10~ as a
consequence of the lack of consideration .for the scale effect suggests that _
the mean value of ice ultimate~strength be adopted as 50 T~m2. V. M. Timchenko
L10] as a result of the experimental studies of physical and mechanical prop-
orties of inelting ice cover on the A mur River at Komsomol'ska-na.-Maur obtained
R~=70 T~m2.
To analyze the calculated characteristics recommended by SNIP in estimating
the dynamic load on structures i.n the ice drift period a computation was made
of the ultimate strength of ice for bending and the thickness of the ice cover
by the moment of drift of rivers intercepted by the BAM route. The strength
during shif~ was viewed as the greatest in break-up. The computation was
made in each case for nine points. A total of 220 cases were computed.
Guarantee of the currant level of planning requires information of the proba-
bility characteristics of the ice cover strength. SNIP does not contain any
information about the frequency of the proposed calculated values of ice
strength.
In order -to obtain the probability characteristics for ice ultimate strength
for bending the moment of shift curves of frequency were constr ucted whose
coordina-tes are given in table l. In the numerator values axe shown of the
ice ultimate strength determined with R~=50 T~m2~ and in the denominator--
with R~=70 T~m2. The data of table 1 indicate that the computed values of
ice strength not only are average, b ut also with probability of excess 7./,
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in other words, with frequency one in 100 years are considerably lower tha.n
thoso thai; a.ro recommonded by the ac ~ive SN1P to estima.te the loads and
- ~~:(`f~r.i, c~ f' .f c~ ~n ;;tructure ~ at tho momc~nt of break-up. Ttws, :~or examplc~,
l.ho >>1 I,1.n~.ti L~~ .ti~t,rongttl o.C ic~ for bond.i.ng R~, accordin~ tc~ SNI~' must be ~�~sumc~ci
to bo c~qua.l to 33 T/m2. K. N. Korzhavin L6~ :for rivers intersected by tho 2
BAM route suggests for the starting s~~ates of ice drift the value Rh=56 T~m .
According to the data of our computation on the s-tudied rivers the ice of' such
strength cannot be encountered once in 100 years.
~ ~
TABLE 1- PROBABILITY CHARACTERISTIC OF ULTIMATE STRENGTH OF ICE (T~m2~ AT
MOMII~IT OF SHIFT
IIPCAen nj10YHOCTH JIbJjB B hlOMeHT 110A'BN?t(3CH
~ 1 ~ ~ 2 ~ ~ ~ O~E'.CIIe42NHOCTblO ( �,6 )
Pexa IIy~~xT
I 1 I 2 I lU ~ 25 I 50 I 75 I 90 I 9:i I 98 I 99 -
- KxpeHra ~1 aaavHHCKOe 3,0 4.4 2,8 1,6 0,3 0,2 _ _ _
Il,U 1U,0 5,G :3,6 2,4 1,2 U,4
~ Onet;e~a (13 crb-H~oxxca 14,8 14,0 12,0 10,2 8,0 ~i,6 3,6 2,2 1,0 ~,8
20,4 19,6 16,8 14,4 I1,(i 3,4 :~,'l l,8 1.2 ~~y
3CA ~1.~ MF{dK 1n,J I 7,3 4~f) 2,~ ~,4~ ~,~i n,~ 0,6 n,~)
k 14,7 12,fi IU,2 Fi,G 3,G 2,0 l,l 1,U ~~b U,7
~7~ Hopa ~15 crve :y;ti~r;i 12,8 11,2 7,4 4,S ;i,2 1,0 Q,S _~,3 0,3
17,1i 1G,U 11,'l 7,1i 4,8 l,5 1.~+ ~i1,4 O.4 U,4
~ g~ 18,fi 16.4 12.0 8.0 4,4 2.3 0~) i1,4 ~,3 0,3
CeneM.u?xa CTOHG3 1( ~ - " ~
~ '13,6 11,6 15,ti 1I,U 6,U 3,'l I,li i.U 0,4
~9~ 5~cca 6~oca ~17~ 12�2 10.5 6,8 4,0 1,3 0,4 O,t _
15,4 l4,U lU,v %,0 2,4 U,7 l),'l -
~10~ AMryt+b I~IpymKa~l$~ 12,0 ll.? R,7 6,6 4,4 2,2 1.0 0,4 ~.2 0~2
_ 16,3 1:,,4 12,U ~1,2 6,U 3,U 1,4 (i,S u,5 0,4
~ 11~ A?~ry~b JjyacH' ~ 19~ `~.5 S,2 5,G 3,6 1,$ ~,S 0,3 0,1 _ _
12,G 1I,5 7,8 5,U 2,5 I,1 O,9 U,2
Key;
l. River 1Q. Amgun'
2. Point 11. Amgun' `
3. Ul-tima.te strength of ice at 12. Kazachinskoye
moment of shift with frequency (J) 13. Ust'-Nyukzha
Kirenga 14~. Bomnak
5. Olekma, 15. Ust'ye E1'gi
6. Zeya 16. Stoyba
7. Nora 17. Byssa
8. S e le mdz ha 18 . Ir umka
9. Byssa 19. Duki
~'I'he values of ultimate strength of ice bending were determined according to
the data of computation of relative ice cover strength given in publication
L9~.
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The reason for the exaggeration in the calculated strength of ice is the fact -
that table 27 of SNIP does not take into consideration change in the ultima-te
strength of ice under the influence of positive ai.r temperatures and the radi-
ation influx of heat. As was shown above, on the examined sections of the
.r.ivors br.e~,k-up was praceded by a period with air temperature abave 0�C and
a l~ngthy neriod of decrease in ice strength under the influence of solar radi-
ation.
In order to estimate the dynamic loads from the effect of ice on structures it
is necessary to have information not only about the strength of the ice cover,
but also its thickness by the moment of break-up. SNIP recommends assuming
the calculated ice thickness to be equal t~ 0.8 of the maximum ice thickness
for the winter period, with frequency of 7J. In order to verify the correct-
ness of these recommendations in the examined region curve5 of frequency were
constructed for ice thickness at the moment of shift. The data of table 2
indicate that the obtained amounts~ with probability of excess ].�fo, correspond
to the calculated values of ice thickness determined according to SNIP.
TABLE 2- PROBABILITY CHARACTERISTICS OF ICE COVER THICKNESS (m) AT MOMENT
OF SHIFT
. ('Z, 3~ C \ TOQI ABN]KKH ~ OG2Cile eHHOCTbIO ~ T
( z A,~~ I
Pexa IIyxxr ~ ~ ~ ~ A .
o~ 1 'l i U 2�.`i 5U 7:~ 90 J5 9~i J9
. ~s~ I I
- 7~i~~~ '
Itxpexra 1 Ycrb H~oK~sca 2Ei 3,2~? 2.60~,4~'1,~12I~,S0 l�?'~ ~2.2.} j:OS O:S1 ~~,~;~i ~~,"~li
~ Onexsta
~8 Hopa 1 Ycrbe 3nb 25 1,64 1,3G l,~iU 1,t150,~)SO,SUU.G2U.:,UU'-140',snu.:i'l
9~Cenee~uxca Czon6a 1~ 'lfi 2,,~.~ 2,US1,)21,~21.12O.SSO,GGU,44U'ill)'~4U,2U
10 Bx~cca 6brcca 16 26 1,60 1,241,12U,J0~).720,~i60,420.291),2;5~,~`.?I0,15
~ 11~ An+ryxb NpyMxa 17 25 1,88 1,4G 1,40 !,?3 1,10 0,92 U.GSI~~,4;, O,;i2 ~1, Iti -
Key:
l. River 8. Nora
2. Point
3 N umber of years of observations 9~ Selemdzha
4. Maximum thickness of ice with 10. Byssa
frequency 1/ 11. Angun'
5. Thickness of ice cover at moment 12. Kazachinskoye
of shift with f~equency (J~ 13. Ust' Nyukzha
6. Kisenga 14, Ust'ye E1'gi
7. Olekma 15. Stoyba
16. Byssa
17. Irumka
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It is necessary to note that currently probability characteristics have been
obtained for the maximum ice thickness for rivers in the development zona of
the BAM route L4~, consequently, determination of the calculated character- -
istics of ice cover thicicness by the moment of break-up do not produce any
difficulties in solving a different type of planning task.
The calculated relationships recommended by SNIF for estima.ting the load and =
effect of ice on structures includes complex characteristics of strength that
are a product of the ultimate strength of ice and its thickness to certain
degrees. Tn order to obtain the probability characteristics for the date of
shift for each year the amounts of the complexes of strength of the type Ry~h2~
R 1~?h, R h were computed. To guasantee the necessary ma.rgin of safety we
s~arted from the greatest measured value for the initial ice strength~ assuming
RD=70T~r~2. According to these data curves of frequency ware constructed whose
coordinates are given in table 3. A nalysis of the findings demonstrates that
the amounts for the complexes of strength determined according to the SNIP
recommendations are two times and more greater than the computed values of the
complexes, with probability of excess ]J.
The approximate extrapolation of curves for freque~ncy 0.33J ( t~equency of once
in 300 yeax s~ demonstrates that in the g5.ven case the obtained amounts for
_ the complexes of strength are 1.5-fold and more lower than the complexes deter- -
- mined according to SNIP. Therefore it is expedient in planning tci take into
consideration the amounts of the ultimate strc~ngth computed with r"egard for
its spring reduction for f`requency once in 100 years (~equency 7.~). The
adoption here for all rivers in the BAM zone ~f any one constant amount is
not rational, since R~ with fre uency lJ changes from point to point to
considerab le limits (see table 1~.
At the same time fulfillment of such computations for ice strength with the
help af a computer under r:eal conditions of planning is difficult due to the
excessive labor intensity of collecting such meteorologica 1 data for a fairly
long series of years. In addition often the need arises for computing the
ice cover strength of sections of river that are generally not covered by
hydrometeorological observations. In such circumstances another approach can .
be recommended: direct computation of the parameters for the curves of
frequency of ice strength by the moment of break-up, and precisely--the mean
a~:ount of strength of ice R~, its mean quadratic deviation from the norm
and coefficient of asymmetry CS.
We will begin with computation of the ice strength norm.
The main factors that determine ice cover strength by the moment of break-up
are the maximum ice thickness and intensity of the influx of solar radiation
in the spr ing period. Since the BAM route is extended along a latitude in
limits 51-57�n.l. one can consider that the diff.erence in the average multiple-
year influx of solar radiation is not great, and the effect of this factor
over the territory is squivalent.
Analysis of the maximum ice thickness on the rivers of the BAM zone demon-
strated tha.t on a majority of rivers it is in the average multiple-year
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TABLF 3- PROBABILITY CHARACTERISTICS OF COMPI.EXES OF STRENGTH AT MOMENT OF
SHIFT
_ 5 a 6 KoMnnexc~ rtpo~~ocrx
~U C
(1~ ~2~ v= �Hv
PeKa :flytm:r o Q c~x ~ K~ aZ
so ~~oo.V 1 2 10
0
xG CAYCOC
1
( 7~ K~+pej~ra Kaaa~~tt cKO 18 Roh 34,6 9,8 8,9 b,6
Rah~ 19,9 4,0 3,4 2,0
i
R~ h 5,2 1,0 0,9 0,6
(14~)
- ~~j~ OneK~a Ycrb-Hrox~xa 2G Roh 115,2 65,3 57,8 42,0
- R,h2 220,8 120,0 ] 0$,0 68,0
~
R~ h 17,2 4,5 9,1 3,0 '
(15)
~9~ Hopa Yc~'be 3nbrx 2~i Roh 58,9 . 26,1 23,1 14,9
R~h~ 57,8 21,0 18,2 11,2 ;
i ~
- R~ h 8,8 1,9 1.T 1,2
~10~ (;cie~+~xca CTOi~6a ~i6~ 26 Roh 91,8 59,7 50,9 28,9
RAh~ 140,2 80,0 68,0 34,0
~
R~ h 13,5 2,6 2,4 1,8
r1 l
- ~ 1~~ B~cca 5~cca `~l 26 Roh 57,6 21,5 18,7 9,7
I Rah~ 55,2 16,0 ] 3,0 6,4 _
R~ h 8,6 1,8 1,6 I,0
AMryt~b NpyMxa~ lg~ 25 R~h 67,5 28,0 24,6 17,1
R�h2 75,8 29,0 25,0 15,0
. t
' I R~ !t 10,0 2,U 1,8 l,4 _
_ Key:
1. River 10. Selemdzha
2. Point 11. Byssa
3. Number of years of observat;ions 12. Amgun'
4~. Complexes of strength 13. Kazachinskoye
5. Amounts of complexes of strength 14~. Ust' -Nyukzha
determined according to SNlp 15. Ust'ye E1'gi
6. Complexes of strength at moment 16. Stoyba
of shi.ft with f`requency (f ~ 17. Byssa
7. Kirenga 18. Irumka
8. Olekma.
9. Nora
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~Con~,inua.tion of t~,ble 3]
e ~oMenr noAsu~cKU o(ecne~ieuHOCrbto ~6--continuation) -
i l I
25 50 75 I 90 95 ;98 I 99 _
3,3 I,1 0,4 0,09 0,05 � - -
1,2 0,3 0,05 0,04 I 0,03 - -
~ - ; :i
0,3 0,1 0,04 0,02 O,O l� - ~ _
32,6 23,3 14,9 7,6 3,2 i 0,7 0;4 �
96,C 28,0 15,0 7,0 2,5 I O,b 0;4
2,4 1,8 1,2 0,7 0,4 I 0,2 0,08
- 8,9 4,8 2,2 l,l 0,7 0,3 0,2
- , 7,2 3,6 1,2 0,5 0,4 0,3 . 0,2
0,9 0,6 0,4 0,2 0, I 0,08 0,44 '
16,E 7,5 2,8 0,9 0,7 0,6 0,5
14,U 5,0 2,0 0,8 0,6 0,~ 0,4
1,2 0,8 0,4 0,2 0,1 0,08 0,0T ~
6,8 'l,0 0,4 0, t - -
3,0 l,0 0,4 0,1 - � -
0,6 0,2 0,06 0,02 - -
14,0 8,6 2,9 0,9 0,6 0,5 0,4
11,0 6,5 2,0 0,8 0,4 0,3 U,2
1,2 0,8 0,4 0,2 0,08 0,0~4 0,03
_ ~eriod 1.2-1.4 m, and on certain sections of the rivers in th~ basins Olekma _
and Aldan 1.6-1.9 m. A greater ice thickness occurs only on the sma.ll f`reezing
rivers at area of the basin up to 600 km2, however on such rivers~ as a rule,
with start of water run-off the ice travels upwards, gradually washing the
channal, and the ice effects on the structures are insignificant.
The dependence of the ice cover strength norm at the moment of start of shifts
_ ( Rri~ on the norm of maximum ice thickness (1-: is expressed by the equa,tion ~
R
~ =6 . 57h-3. 9~
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' Two other parameters of distribution of ice strength as ths calculations showed
are altered on the rivers of the BAM zone in comparatively small limits. There-
- fore one ~an adopt the amount of the m6an qua.dratic deviation from the norm
~2.8 T~m , and the coefficients of asymmetry CS 1.20.
The obtained parameters make it possible to compute the amount of ice ulti-
mate strength of bending by the moment of break-up of any frequency, by using
the tables of normed amounts of ordinates for the assigned frequency (Foster-
Rybkin tables). The ordinates taken from the tables for the adopted CS and
- frequency P are multiplied by the assumed amount The obtained deviation
from the norm is added to the mean strength of ice R~ computed according +.o
equation (3).
The errors in constructing the frequency curve of i.ce cover strength are deter-
mined for the amounts that exceed the norm (table 4~~.
~ TABLE 4- PROBAB SLITY ERRORS DETERMINED FOR R~ WITH DIFFERENT FRDQUENCY
a 06ecrteYexxocrb, %
_ 1 I 3 I 5 I 1U I 25
L T~ar^I l,fi I 1.3 I 1,2 I 1.2 I Q,7
- EoTU (~,115 1~.04 O.U4 U,04 O,U2
Key:
a. Frequency, f
The ovorall accuracy of the computations is characterized by a probable error
l.l T~m2. -
Table 4~ traces the increase in error with a reduction in frequency. Therefore
an analysis was ~.+stempted which revealed the link between the deviations in
ice strength from the calculated amount with the norm of the maximum height -
of snow. This is explained by the following reasons. The first~ the greater _
the amount of snaw-supplies in the basin~ the higher the rise in the level
- in the pEriod of break-up and the more considerable the mechanical strength
~ of the effect of the flow on the ice cover. From hers~ with a high snow cover
one can expect a higher strength of the broken ice. Second, the greater
height of snow on the ice corresponds to the greater height of snow on the
basin. Therefore with a great height of snow the period of effect on ice of -
, solax radiation will ba lower~ and consequently, the strength of the spring
~ ice by the moment of break-up is greater. -
The effec+, of snow on the strength of the ice cover, naturally, is more signif-
icant in the extremum years, and therefore is traced for cases of 1.~ frequency. -
For consideration o~ this eff6~t, the empirical formula is suggested
- ~R�=25h~- 10, (4)'
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where nR~,--erro:r for effect of snow,
h~--norm of ma.ximum snow height.
With regard for the correction the accuracy of computation R N7 ~o is increased
and is characterized by the probable error 1.1 T~m2. The for~ula is construc-
- t~ad with such regard that a possible underestimation of the ice cover strength
~s the minimum.
For the most simplified evalua.tion of ice strength by the moment of break-up
�the empirical formula can be used
R� ~o,o =1 Z h, -r 35 h~ -16,4, (5)
- where RN~--ultimate strength of ice for bending with t`requency 1,/,
h~ --norm of maximum ice~ thickness,
h~ --norm of maximum snow height.
The accuracy of computations according to the given formula is characterized
_ by probable error 1.5 T~m2. If one even assumes an error with frequency 1,I
_ and computes the ice cover strength by ~ne moment of break-up for the greatest
norm of maximum ice thickness in the BAM zone 1.9 m, we obtain RH o=23 T~m2.
As is apparent, even this amount is significantly lower than that~ecommended
by SNIT'.
In fulfilling computation in the case of the absence of observations the norm
of maximum ice thickness h~ and the norin of maximum snow height h~ can be
determined according to charts ~4, 7~.
The aforementioned makes it possible to draw the following conclusions:
1. A roduction in the strength of the ice cover before break-up on the examined
- rivers is very significant. T his is characteristic for rivers of the given
region and is linked to the insignificant height of the snow cover on the ice
and the intensive influx of solar radiation in the spring period.
2. The computation of complexes characterizing the ice strength during break-
up demonstrates that in all cases, even with f`requency of once in 100 years
and once in 300 years adopted in the calculations as the limit~ these comp-
' lexes are 1.5-2-fold lower than those adop-ted in the active SNI.P.
3. The calculations made permit obtaining of probability characteristics for
the ice cover strength by the moment of break-up, including for sections of
rivers not covered by hydrometeorological observations.
B IBZIOGRAPHY
l. B ulatov, S. N. "Computation of strength of Melting Ice Cover and Start of
Wind Drift of Ice," TRUDY GIDROMETSENTRA SSSR, No 7~4, 1970.
2. B ulatov~ S. N. "Metodyka rascheta tolshchiny i prochnosti tayushchego
ledyanogo pokrova dlya tseley rascheta i prognoza srokov vsl~ypiya rek
- i vokhranilishch: Metodicheskiye ukazaniya" [~Technique for ComFuting
- 122 ~ -
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Thickness and Str.en~th of Melting Ice Cover for P urposes of Calculating
and Predicting the Periods of Break-up of Rivers and Reservoirs: Method
Instrtzctions~, Moscow, Gidromettsentr, USSR, 197~�
3. B utyagin~ I. F. "Prochnost' 1'da i ledyanogo pokrova" LStrength of Ice and
Ice Cover], Novosibirsk~ Nauka, 1966.
4. G inzburg, B. M. et al. "Osnovnyye kharakteristiki ledovogo rezhima rek
rayona Baykalo-Amurskoy magistrali" ~F3asic Characteristics of Ice Pattern
_ of Rivers in the Baykal-Amur Trunk Line Region]~ Moscow, Gidromettsentr
_ USSR, 1976.
5. Koren'kov~ V. A. "Reduction in Ice Strength in Spring Period," "Sbornik
dokladov po gidrotekhnike" [Collection of Reports on Hydrau'lic Engineering],
No 8, 1.967~ S~eningrad, Enexgiya.
6. Korzhavin, K. N. "Effect of Ice on Bridge Supports on BAM Route," TRUDY
NIIZHT, No 181, 1977�
7. P upkov, V. N. "Formation, Distribu-tion and Variabilii;y in Snow Cover on
Asian Territory of USSR," METEOROI,OGIYA I GIDROIAGIYA~ No 8, 196~.
8. sN~e zz-57-75� "Nagruzki i vozdeyst~viya na gidrotekhnicheskiye sooruzheniya
(volnovyye, ledovyye i ot sudov~" CConstruction Norms and Regulations II-
57-75� Zoads and Effects on Hydraulic Engineering Structures (Wave, Tce
and From Ships)], Moscow, Stroyizdat, 1976.
9. Samochicin~ V. M. "Zoning of Major Siberian Rivers A ccording to Nature of
Spring Ice Ilrift~" TRUDY NIIZHT, No 94~ 196g. ~
10. Timchenko, V. M.; a.nd Shilina,, Z. I. "Properties of Ice Cover on Rivers of
. Eastern BAM Z one in Spring Feriod," TRUDY DVN IGMI~ No 69, 1977. -
11. Timchenko~ V. M. "Experimenta,l Studies of Melting of Ice Cover of Amur
River," TRUDY DVN IGMI, No 52, 1975�
123
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- ttnc 551.509:631.81~.1
USE OF METEOROIAGIGAZ FORECASTS 1N DI ++RENTIATING NITROGEN SUpPI~I~iENTS
Moscow METEOROTAGIYA I GIDROIAGIYA in Russian No 10, Oct 19?9 pp 102-110
- LArticle by Candidate of Technical Sciences Ye. Ye. Z hukovskiy~ and Professor -
A..P. Fedoseyev, Agrophysical Institute, A 11-union Scientific Research Insti-
tute of Agricultural Meteorology, submitted for publication 3 A pr 1979]
Abstract: The question is examined of agrometeorological
substa.ntiation for economically ontimal periods of conduc-
ting nitrogen supplementary feedings. A technique is
described that makes it possible to formulate require-
ments for the justifiability of the seasonal forecast
of precipitation used for the annua,l differentiation
of a,gricultural engineering decisions in accordance
with the expected agrometeorologica]. conditions. W ith
the help of the proposed technique for a number of
regions of the Nonchernozem zone the effectiveness of
_ different economic strategies is avaluated.
LText] The accumulated experimental data and available production experience
indicate that in the general complex of agricultural-engineering measures
directed towards obtaining high yields of grain crops, an important place is
occupied by a scientifically substantiated system of fertiliz ing that takes
into consideration both the soil-climate conditions of the examined region
- of farming, and the specific agrometeorological peculiarities of each specific
year ~6, 9-12~. In this sense not only the main fertilizings, but also the
nitrogen supplementary feedings made in different periods have serious impor-
- tance.
~ , _ -
From an organiza.tional viewpoint the fall supplementary�feedings of winter
- crops with nitrogen have indisputable advantages, since they facilitate mech-
anization, permit significant reduction in the intensity of the spring field
work, and so forth. In addition, in conducting supplementary feedings in
fall their action is manifest from the very early spring, immediately after
the beginning of vegetation, as a consequence of which the danger of lodging
of the plantings is reduced. However the nitrogen fertilizers, in fa7;ling
in late fall on the surface of the soil or on the snow cover, under c~irtain "
12~
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conditions of weather can bo removed by tho me`lting-snow wator or blown away
- by the wind together with the loose snow. Therefore in individual unfavorable
years effectiveness of fall supplementary feeding is significantly lower than
the effectiveness of spring introduction of fertili.zers. A s shown by analysis
here a decisive role is played by precipitation that falls in the win~er period.
With a relativoly sma.ll quantity of it the effectiveness of the fall supple-
montary feeding,is increased, and with a large quantity--on the contrary, is
reduced. Thus, one should attempt to switch to the use of differentiated agri-
cultural engineering and guarantee a change in the periods of conducting
~up~lementary feedings depending on the peculiarities of each specific year
lz .
It is evident that to solve the set task, in the first place, long-terr~i
(seasonal~ forecast of precipitation is requixed. However, as has been indi-
cated in a more general term many times, this one condition is insufficient:
it is necessa,ry in addition, for the success of forecasts to exceed a certain
minimum permissible level [2, 4, 8~. Otherwise instead of differentiation of
the economic solutions according to �~~he expected (predictable) weather condi-
tions it is more advantageous to adhere to the so-called clima.tologically
optimal strategy [3, The latter in the given case will consist of conduc-
ting supplementary feedings either always in spring, or always in fall (depending
on the specific condition of a certain region of farming~.
Taking the aforementioned into account, we will describe a certain technique
that makes it possible to formu~_ate requirements for the success of the corres-
ponding seasonal predictions, and by using it we will ma.Ice a number of numor-
ical estimates tha.t indicate where and in what cases the transition to differ-
entiation of supplementary feeding is actua,lly expedient, and where it is not.
The calculated scheme stated in the work of Ye. Ye. Zhukovskiy [5~ was placed
as the basis of this technique. -
Model for Making Optimal Solutions With the Use of A lternative Forecasts
We will designate by Oi~ expressed in monetary or natural units of ineasurement
the profit t'rom supplementary feeding d�( j=1, 2~ under nonditions where winter
refers to type Fi(i=1,2~. For definiteY~ess we will stipulate further tha.t
F~.be considered winter with normal or insufficient qua.ntity of precipitation
(according to the terminology adopted below "dry" winter~, while F2--wintex
with excess quantity of precipitation ("moist" winter)~ dl fall supplementary
_ feeding, and d2--spr ing supplementary feeding. In accordance with such desig-
' nation the amounts B11 and A12 will characterize the profit from fa11 and
spring supplementary feeding in ~the year with dry winter~ while A~~ and 022--
the profit t~ om the same supplementary feedings in moist years. e matrix
of utility that responds to the examined alternative model for decision
making can be descr ibed in the form of a square (2 x 2~ in table 1. _
It is evident tha,t the amounts Ai~ will depend on increases in the harvest
which are obtained as a consequence of in~roducz_ng fertilizers, the outlay
for cotiducting supplementary feeding and the c~st of one centner of finished
product. In the first approximation they can be computed according to the
formulas -
0ii=gy~t-a+b, @iz=gJ~2-a, ~ (l) . -
Os~=gys?-a+b, 0~2=g~ss-a
iz5
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Here yl~ (i,j=1~2)--increase in ha.rvest from introduction of supplamentary
feedin~; d� under conditions of winter Fi; -
g--cost oi~ one centner of increase in grain with subtraction of additional out-
lays for its harvesting, transport and drying;
a--outlays for spring supplementary feeding;
b--"organizational"economic effect obtained as a result of transition ~`rom _
spring supplementary feeding to fall. -
i
TABLE 1- OVERAT,T, VIEW OF MATRIX OF UTII,ITY 2 x 2 -
F d
I di ~ dx
F~ e~~ etz
Fs 9si ess
TABLE 2- MATRIX OF CONT7NGEDICY FOR AT,TERNATNE FORECASTS
n i
F I ~
n? ~ nz
F~ Ptt Pis P~o
Fs Psi P~ P~o
E Poi Pas 1
Further we will examine only the case where between elements Ai~ the following
correlations occur
> e,~, ~s= > az~, (zl
~ i.e., in the years with dry winter fall supplementary feedings economic-
ally more advantageous, and in the years with moist winter--spring,
We will further assume that the consumer has at his disposal a categoric alter-
native forecast of precipitation which is characterized by a matrix of contin-
gency Ilpi~i~~ assigned in the form of table 2. The elements, included in it
pi~(i,j=1,2~ are combined probabilities of the forecasted (nJ�~ and the actua.lly
realized (Fi~ weather conditions; pl~ and p2~--clima.tological probabilities of
dry and moist winters; p01 and p02--probabilities of corresponding formu-
lations of forecast. It is natural to consider that the examined forecast in
a mathod relationship is substantiatEd, and consequently, thA inequalities
occur -
P~~~ =P>>iPo~ > P~o, ' ~3D
- P2~2 = ~~~//~oz > Pto ~ ~
126
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Here pl/1 and p2 2--probabilities of realization of those weather condi- _
tions which were/expected from the meteorological forecast (probabilities of
correct predictions).~
Further adhering to the Bayes' approach we will consider that ths optimum
are such economic solutions which result in the obtaining of the ma.ximum
average gain [l, From this viewpoint, with assumptions (3) three strate-
- gies are important:
F1--constant (regardless of the forecasting recomtrtendations~ conducting of
' nitragen supplementary feedings in the fall;
S2--constant conducting of supplementary feedings in the spring;
Sf--differentiated agricultural engineering that provides for the estab-
- lishment of different periods for introducing fertilizers depending on tha
predictable winter conditions, and precisely: with expected dry winter fall
supplementary feeding is conducted~ and with moist--spring. There is no
sense in examining the strategy of action that goes against the forecast con-
sisting of conducting spring supplementary feeding with an expected dru
winter and fa11 supplementary feeding with a moist winter, since in the
fulfillment of conditions (3) this strategy will be inevitably worse than
Sl or S2.
T he following amounts of the mean gain G meet the listed variants for making
economic decisions: .
- G~ =6>>P~o-~-~s~Pso, ~4~
G2=0,sp~o+~sspso, ~5~
s s
o,= ~ ~i,Pi,� . ~sr
~~l -
By comparing these expressions with each other it is easy to show that the
differentiated strategy Sf pr.ovides better (from the viewpoint of the mean
gain) economic results than the nondifferentiated (clima.tological) s~rate-
gies S1 and S2 if the two-sided inequality is fulfilled
,c, > Piji"+ ~
(14)
P=1z ~ P2jz~
occurs ma.ndatorily. In fact, according to the correlations (12)-(13) the
nonfulfillment of both inequalities (1~4) ~rill designa.te that the sum �=p1~l+
, p2~2 is less than a unit. However according to condition (3) for any
successful forecast the amount � must be bigger tha.n a unit. Therefore the
assumption on the simultaneous nonobservance of both inequalities (14~)
contradicts the previously made assumption on the method of substantiation
- of the employed forecasting technique. Consequently, only one of the
probabilities must satisfy certain requirements that ma.ke a successful ~
forecast also economically useful--depending on the conditions either pl~l~
or p2~2.
In particulax, if
V~ > P,o/Pzo ~ 15i
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then the requirements are made for ths amount pl/l~ and vice versa~ with
fi 200 41,1 33,6
Key:
l. Region 6. Volga-Vya.tskiy
2. Soil 7. Medium and heavy loams
3. Central 8. I,ight loams and sandy loam
4. Nonchernozem 9. I,oamy soils
- 5. Baltic and Belorussia
As for the regions of the Baltic and Belorussia, as well as the Volga-
Vyatskiy region, then these cases can immediately be excluded from further
examination since regardless of the conditions formed in the first of them
the economic adva.ntage always rsmains for the spring supplementary feeding
~e11~12~ e21~22~ ~ and in the second case--for the fall (911~12~ 021~22~ �
Thus only the variants axe important for the central region for which a
different effectiveness of various periods of spring fertilizings is cha.r-
acteristic--in dry years here late-fall supplementary feedings are economic- ~
ally more advantageous, and in moist years--spring. Conseq uently, for
these two cases it makes sense to solve the question of differentiation of
agricultural engineering depending on the expected conditions of the fall-
winter period.
According to table 4~for the mean-and heavy-loamy soils of the central ~
Nonchernozem region the parameter
_ , 58,1-66,0
~ _ ~ ~ , = U,83.
~J~J-4.l~U
_ 13z
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Ths frequency of winter conditions that foster in an economic sense fall~om -
supplementary feeding for this zone can be assumed to be equal to 57~.
here
. n,,, _ 0,57 = ~,33.
P:~~
Comparison of the computed va.lues of parameter ~ and the ratio p~~p20 shows
that in the given case in absence of forecasts it is more advantageous to _
conduct fall supplementaxy feedings (Sk: _
S~rgey Dmitriyevich began his scientific-production activity in the Baku
weather bureau after graduating in 19~9 f`rom Azerbaijan University. The -
results of the initial stage in scientific activity were dsvelopment of a
_ 163
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regional method for short-term forecast of strong and storm winds, and
const.r.uction of a series of maps of the typical wind fields of the Caspian
Sea. Their introduction at the end of the 1950's into the operational prac-
tice of the mercha.nt marine in the Caspiar~ Sea had great national economic
_ importance.
All the subsequent work of Sergey Dmitriyevich was linked with Novosibirisk,
where he moved in 1961. Working in the Novosibirisk branch of NIIAK [Scien-
tific Research Institute of Aeroclimatology~, the Novosibirisk branch of the
USSR Hydrometeorological Center,;and since 1971 in the West Siberian RNIGMI~
- whero he has been actively engaged in the theme of studies on Siberian
- hydrometeorology. The extent of his scientific interests and knowledge permit
~ S. D. Koshinskiy to be engaged in very broad circle of questions of synoptic
and marine meteorology, aerology, climatology, and methods of processing
patt~rn information. His direct participation in the creation and introduction
of a system of inechanized processing of climate characteristics on punched
card computers and electronic computers promoted the preparation and publica- -
tion in 1962-1969 of the multiple volL~me "Spravochnika po klimatu SSSR" ~
~Reference on USSR C lima.te~. A considerable contribution to the study of
the continental shelf of the USSR seas has been his research tfiat has been
generalizsd in several volumes of the monograph "Rezhimnyye kharakteristiki
_ sil'mykh vetrov na moryakh Sovetskogo So uza" [~pattern Characteristics of
Strong Winds on Seas of the Soviet Union~. Other works published by him
have great practical directivity; there are over 90 of them.
Sergey Dmitriyevich focuses a lot of attention on the scientific-organi-
zational, publishing, pedagogical and social work. For many years he has
been chairman of the meteorological seminar~ editor of TRUDY ZAp.-SIB. RPIIGMI~
and the scientific leader of post-graduate students and competitors. Commu-
nist S. D. Koshinskiy is a propagandist, and a continuous leader of a philo- -
sophical seminar. -
- For his services to the motherland during the years of the wax and for bril-
: liant work Sergey Dmitriyevich has been awarded the Order of Great Patriotic -
War and many medals, and has been given the badge "outstanding worker of the
USSR hydrometeorological service".
In congratulating hiM we wish him strong health~ long years of life and
= further creative successes.
- 164~
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AT THE USSR STATE COMMITTEE FOR SCIENCE AND TECHNOLOGY
Mosccw METEOROLOGIYA I GIDROLOGIYA in Russian PTo 10~ Oct 1979 pp 125-126 -
LArticle by V. Zakharov~
~,Text~ A new staff ha.s been approved for the section of service and under-
ground water resources and water balance of the scientific council "Complex
Use and Protection of Water Resources" of the USSR State Committee of Science
and Technology.
The director of the GGI LState Hydrological Institute~, Doctor of Geograph-
ical Sciences A. A. Sokolov has beEin approved as cha.irman, cochairman--
Doctor of Geological-Mineral Scienc:es G. V. Kulikov, deputy chairma.n--
deputy director of the GGI, Doctor ~f Geographical Sciences A. I. Shiklomanov
and head of the department of the Institute of Water Problems of the USSR
Academy of Sciences, Doctor of Geological-Mineral Sciences I. S. Zektser,
and scientific sacretary--candidate of technical sciences V, S. Vuglinskiy
(GGI) and candidate of geological-mineral sciences N. P. Akhnet'yeva (Insti-
tute of W ater Problems of the USSR A cademy of Sciences).
G. A. A lekseyev (GGI~, L. V. Brazhnikova (GKhI~ [State Scientific and Tech-
nical P ublishing House of Chamical Li.terature~, E. V. B uryak (State Committee
_ for Hydrometeorology and Environmenta'1 Control~~ B. M. Dobroumov (GGI~, A.
S. Dubov (GGO~ LA. I. Voyeykov Main Geophysical Observatory~, I. A. Zheleznyak
(tJkrNIGMI) [Ukrainian Scientific Research Hydrometeorological Institute~~
Yu. N. Ivanov (SARNIGNI) [,Saratov Scientific Research Hydrometeorological
Institute~, I. F. Karasev (GGI), V. D. Komarov (USSR Hydrometeorological ,
Center), V, V. K upriyanov (GGI), R. A. Nizhekhovski (GGI~, Ye, G. Popov .
USSR Hydrometeorological Center~ 0. V. Popov (GGI~, V. A. Rumyantsev
~GGI~, G. G. Svanidze (Z.akNIGMI~ ~Transcaucasian Scientific Research Hydro-
meteorological Institute~, V. G. Fedorey (DVNIGMI~ ~Far East Scientific
Research Hydrometeorological Institute~, and S. I. K harchenko (GGI) entered
the staff of the section from the State Committee for Hydrometeorology and
Environmeiita]_ Control.
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NOTES FROM ABROAD _
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 10, Oct 1979 pp 126-127 ~
LArticle by B. I. Silkin~
LText] As reported in SCIENCE NEWS, vol 114~ No 12, 1978~ p 200, among the
specialists there is no unity on the question of how great is the mass of -
solid products entering the earth's atmosphere as a result of volcanic activ-
ity. Estimates of different scientists aro in extremely broad limits between
4~ and 150 trillion grams per yeas.
For the purposes of pinpointing this amount a group of colleagues of the
University of Washington (Sea.ttle, Washington~ headed by Dzh. L. Stit flew
over six active volcanoes on a laboratory airplane in the states of Alaska
and Washington (extreme northwest of the United States).
During the flights volumes of clouds of volcanic origin were measured and
the qua.ntity of gases S02 and H2S, water vapox and solid particles, contained
in them was determined~ as well as the dimensions of particles of discharge
during different phases of eruption.
As should be expected the more active stages of eruption, especially those
referring to the explosive type yield a greater quantity of solid particles
than those occurring "calmly." Thus the St. A ugustine volcano in A laska
during active eruption discharges into the atmosphere about 4 x 105 kg~s of
solid particles, and during less intensive activity--only 3 x 102 kg~s.
Then during a decrease in intensity of volcanic activity this amount dropped
to 4 x 101 kg~s.
However an unexpected observation was made, that is especially important
to meteorology and clima.tology. It was found that the discha,rges which -
follow directly after the active eruption, as well as the smission of gases
that is uniformally emerging that is inherent to more moderate~ stable
phases of eruption axe the most importan-t sources of smaller solid particles
and gases, which essentially~ ma,inly effect the weather-forming factors.
166
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Based on their measurements the researchers drew the conclusion tha.t the
St, Augustine volcano during eruption between 1976 and 1977 dischaxged into
the atmosphere about 2.5 x 1011 g of particles that remained for a long time _
in th~ ai.r space.
The le~a.der of the expedition Dzh. L. Stit comp~.red the St. Augustine volcano
in volume of sulfur products discharged by it with the "average dimensions
of a metallurgical plant." In addition, the volcanoes were an important
source for the influx of hydrogen sulfide into the atmosphere. A 11 the active
volcanoes of the earth, taken together, evidently erupt into the air shell
roughly 1 billion grams of this gas per year.
As reported in EOS, vol 59, No 9~ 1978~ P 8~9 the A merican artificial earth
satellite "Geos-3" was equipped with on-board equipment tha.t permitted it in
any weather to record important meteorological and oceanographic information
in relation to the central and northern regions of the Atlantic. In partic-
ular, it records data on the state of the sea surface (altitude, wave direction)~
wind velocity~ site of location of the Gulf Stream Channel and rate of move-
ment of water masses in it.
It was established that tha eastern "edge" of the G ulf Stxeam lies 1 m higher
than the western which is located 100 km from it. This gradient~ that is
distinguished by the precise apparatus of the satellite (radax altimeter~
permits determination of the current boundaries.
All of these data are being transmitted to earth and enter the space center
on Wollops Island that belongs to National Aeronautics and Space Adminis-
- tration of the United States. This is served by the system of information
on ocean dynamics set up by NASA which records in computer memory the time
that the observation was made~ and the geographical coordinates of the points _
to which it refers.
As reported in NEW SCIENTIST, vol 80, No 1131, 1978~ p 670 the environmental
protection administration of Great Britain has published official report on
- the state of the environment and its cha.nge in the last 5 years. This docu-
ment contains statistical data according to which the discharge of sulfur -
dioxide by industrial enterprises and residential facilities of the country -
has been reduced by 20~ as compared to 1970. It is especially stressed that
at the same time the complaints of the Scandinavian countries are being
satisfied to a certain measure that sulfur dioxida transported by the pre-
vailing winds from the British Isles, falling with the precipitation~ increases
the acidity of the lakes of Sweden and Norway to a degree tha.t is harmful
for commercial fishing.
A reduction in the quantity of sulfur dioxide entering the atmosphere of
the British Isles was started 8 years ago and is directly linked to two
factors. First~ from this moment oil and gas extracted on the shelf in the
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North Sea and replacing the coal that in combustion produces sulfur dioxide
. began to play an ever greater role in power engi.neering of England. Second,
in the same period new rules were introduced that significantly reduce the
limits of permissible discharges.
The report also states that between 1973 and 1976 ths qua.ntity of lead -
entering in the form of pasticles into the air space of the British Isles
f~ om the metallurgical enterprises of England and Wales was roughly halved.
However the degree of total atmospheric pollution with lead was not reduced,
since the discha.rge of this element by automobile engines sha,rply increased.
In the period between 1970 and 1976 automobile transport operating on gasoline
increased the discharge of carbon monoxide, lead, hydrocarbons and nitric
oxides almost by 20~~ and diesel automobiles--roughly by 10/,
The official document also contains data about the degree of pollution of
river water, pollution with oil of seacoasts, lead c~ntent in drinking water,
radioactivity of milk and "noise pollution" among the aviation on the entire
territory of Great Britain.
~-x-~ -
As reported in SCIENCE NEWS, vol 114, No 16, 1978, p 264 a lengthy series
of observations.made on the territory of St. Louis (United States) indicated
_ that "a warm island", section of atmosphere above a major industrial center
has a significant effect on the weather and clima.te of the surrounding space.
It is cleax ly felt even at a dista.nce of 40 km, on the opposite shore of the
Mississippi River~ in the adjacent section of the state of Illinois. Among
the most noticeable results of such an effect is the increase in the qua,ntity
of precipitation, frequency and duration of thunder storms.
In order to verify the applicability of such conclusions to conditions of
other cities the same group of specialists tha,t studied the weather of St.
Louis headed by Stanley M. Sha.nnon (hydrological administration of the sta.te
of Illinois) set up analogous experiments in the environs of Chicago. A t
the same time the study was ma.de of the effect on meteorological conditions
of a large fresh water basin such as Zake Michigan on whose shores Chicago
stands.
T he observations (including radar) demonstrated that the avera.ge qua.ntity of
precipitation falling during thunder storms emerging to the northwest of
Chicago i:!creases as they advance over the city of Chicago and further~ over ~
the territory of the nor thern section of the neighboring state of Indiana.
~ The effect of such an increase in precipitation was traced up to the city of
I~a Port (Indiana) that is located roughly 80 km from Chicago. It is
assumed tha.t the factor that promotes this phenomenon is the existence of
- a large region a~lmost deprived of vegetation.
A t the same time it was established that the effect of Lake Michigan on the
clima.te and weather of Chicago is not so great. Although it results in a
168
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_ certain decrease in the mean temperatures~ the lake cannot significantly
alter the effect of the urban "waxm island."
The observations in the region of Chicago for further accumulation of data
will be conducted for another 2 years.
, ~
~ 169
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OBITUARY OF FEOFAN FARNEYEVICH DAVITAYA (1911-1979)
Moscow METEOROI,OGIYA I GIDROIAGIYA in R ussian No 10, oct 1979 pp 127-128 -
[Article by staff of USSR State Committee for Hydrometeorology and Environ-
mental Control~
LText] Soviet science has borne a heavy loss. In the bloom of his creative
forces at 68 years old on 29 June 1979 the most prominent scientist in the
area of agroclimatology, the honored scientist of the Georgian SSR, academician
of the Georgian SSR Academy of Sciences, director of the Institute of Geo-
graphy of the Georgian SSR~ and president of the geographical society of
Georgia Feofan Farneyevich Davita.ya died.
- Davitaya gave about 50 years to fruitful service of science. After gradu-
ating in 1932 from the All-union Institute of Subtropical Cultures he
entered post-graduate studies at the Main Geophysical Observatory. In those
years Feofan Farneyevich gave a scientific substantiation to the climate zones
of grapes in the USSR, and in 1936 successfully defended his candidate disser-
tation. In 1938 his monograph "Klimaticheskiye zony vinograda v SSSR~"
~Climate Zones of Grapes in the USSR] was published which became a reference
_ book for agrometeorologists~ viticulturists~ and viniculturists. In this
work for the first time a number of important method questions were solved
on an agricultural evalua,tion of clima,te, agroclima,te zoning and speciali-
- zation of prodt~ction, which had a significant effect on the forma,tian of
scientific thinking of many a.grometeorologists and climatologists. In 1.950
Feofan Farneyevich became a doctor of agricu.ltural sciences. His disser-
tation was based ~n the theory and technique of agroclimate zoning of agri-
culture in the example of develop:nent of a more specific problem, arrange-
ment of viniculture and specialization of wine making, as well as their
advance into the more northern regions. Possessing great erudition and a -
broad range of scientific interests he took up the solution of both general-
theoretical problems and applied tasks. Under his leadership and editing
in the first years of development of virgin land in 195j a monograph was
published "Agroklimaticheskiye i vodnyye resursy raynov osvoyeniya tselinnykh
i zalezhnykh zemel [Agroclima.t and Water Resources of Regions of Devel-
opment of Virgin and Unused Iand~. The method that he created for predicting
170
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the provision of heat in the vegetation period made it possible to give -
forecasts with high frequency ( 80-9(Y~) .
, ~
~q ~ s . s
~k . k . .
< Y
. < f~
3 ' W/+' ','`~/~.S'i ,Mj.
r.~ ~Z~::;~~~..:, .
.
~
' ~2~'.C:;:':
a~ v:~~..~~ . :
~ f~' ...~..r.~`.:t ~ .
f~~~~
. x . ~ } ^ ~ `E~ ~YF ; i
=t� ~ }~~.~,r,IC
~~kx, n:..~::: .
rKR.'/:>.:`';' -
p~ 7;%
~ e.
~ ~ . . d k% " ~ � '
F:o'~ ~
.
~ .;.,.x~i~:. ^~"f' ;
X"F .;~Y�� .
- ~:;iiiv ~i': .
:;:;x;k.?�
..yj:i:t:f`::f;s;%;::y;::