JPRS ID: 9334 USSR REPORT METEORLOGY AND HYDROLOGY

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ME
6 OCTOBER 1980
NO. 7, JULY 1980
1 OF 2
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- FOR OFF[CIAL 'JSE ONLY _ JPRS L/9334
6 October 1980
_ USSR Report .
METEOROLOGY AND HYDROLOGY
- No. 7, July. 1980 _
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JPRS L/9334
6 October 1980
USSR REPORT
METEOROLOGY AND HYDROLOGY
No. 7, July 1980
Translation of the Russian-language monthly journal METEOROLOGIYA
- I GIDROLOGIYA published in Moscow by Gidrometeoizdat.
CONTENTS
Empirical. Models of Wind Velocity Distributton in the St'ratoaphere
and Mesosphere of the Northern HemispherP
(S. S. Gaygerov, et al.) 1
Nonlocal Parameterization of Turbulent Fluxes
(V. M. Voloshchuk and P. N. Svirkunov) 9
' Choice of Parameters for Formulation of Regressional Modpls
(M. S. Kogan and L. N. Romanov) 19
Optimization of a Method for Solving the Balance Equation in a
Spherical Coordinate System
(G. S. Rivin and Z. K. Urazalina) 28
~ Spatial Structure of Circumpolar Vortices of the Atmosphere and
Circulation in the Equatorial Zone
_ (Ts, A. Kanter) 38
Modeling of Transboundary Transport of Sulfur Dioxide With Allowance
for Vertical Movements
(N. S. Vel'tishcheva)......o 48
~ Effect of Change in Albedo of the Earth's Surface on the Earth's
_ Thermal Regime
_ (N. A. Yefimova) 58
Dependence of the Albedo of Polar Ice on Air Temperature
(L. A. Strokina) 67
Smoothing of Empirical Hydrometeorological Relationships by a Cubic
Spl ine
(A. R. Konstantinov and N. M. Khimin) 73
- a- [III - USSR - 33 S&T FOUO]
F(lu r)P'F`TOTar rTeP nT7r.V
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Determining Runoff During Winter and Transitional Periods
(V. S. Rl'azanov) 82
Method For Making Observations of the Water Surface Slope of River Flows
(V. V. Kovalenko)........................................ 94
Study of Kinematic Structure of Flow in River Mouth Reach Model
(N. A. Mikhaylova, et al.) ..........................o........ 102
Effect of Wintering on the Yield and Gross Harvest of Winter Rye
(V. k. Shavkunova) 109
Investigation of a Cloud Ensemble Model on the Rasis of GATE Data
(A. I. Fal'kovich) 118
Investigation of Spectra of Variability of Meteorolegical Elements and
Requirements on Meteoro'.ogical Measurements
(A. S. Krantsberg, et al.) 132
Evaluation of the Ynformation Content of Successive Radiosonde
Measurements of Meteorological Parameters
(A. F. Kuzenkov) 139
On the Problem of the Height of Installation of a Field Rain Gauge
(N. N. Podgayskiy)...v 146
Review of Monograph by I. D. Kopanev: SNEZHNYY POKROV NA TERRITORII SSSR
(Snow Cover Over the Territory of the USSR), Leningrad, Gidrometeoizdat,
1978, 180 pages
(A. I. Voskresenskiy and N. N. Bryazgin) 150
Review of Monograph by A. P. Fedoseyev: AGROTEKHNIKA I POGODA
(Agricultural Techniques and the Weather), Leningrad, Gidrometeoizdat,
1979, 240 pages
(V. N. Strashnyy and G. Z. Goloverdyuk) 153
Sixtieth Birthday of Samuil Moiseyevich Shul'man 156
At the USSR State Committee on Hydremeteorology and Environmental
Munitoring
- (V. N. Zakharov) 159
At the All-Union Exhibition of Achievements in the National Economy
(S. B. Iokhel'son, et al.) 160
Conferences, Meetings and Seminars
(I. A. Yankovskiy) 165
Notes from Abroad
(B. I. Silkin) 170
- b -
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UDC 553.557(215-17)
EMPIRICAL MODELS OF WIND VELOCITY DISTRIBUTION IN THE STRATOSPHERE AND
MESOSPHERE OF THE NORTHERN HE141SPHERE
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, J-s7. 80 pp 5-10
[Axticle by Profesaor S. S. Gaygerov, M. Ya. Kalikhman and V. V. Fedorov,
Cen*_ral Aerological Obaervatory, eubmitted for publication 15 ,7anuary 19801
[Text] Abstract: The article describea canstruction
of empirical models of the wind (including
zonal and meridional components) for alti-
tudes greater than 30 1m on the, basis of
joint use of data fram rocket and satellite
sounding.
The atmospheric layer in the range 30-80 lan remains poorly investigated due
to a lack of data. This layer is situated over the upper level of system-
atic ascents of radiosondes and considerably lower than the layex studied
by orbital artificial earth satellitea. Accor.ding3.y, the climatological de-
scrYption of the stratomesosphere for the tiiee being ia in the stage of
empirical modeling on the basis of data from infrequent rocket launchings
and thermal sounding from satellites.
, The term "empirical models of tte at~~oaphere" ususlly means the typica'1
(spatial and temporal) distrihutions of its parameters, obtained on the
basis of statistical FrGcessing and analysis of experimental data.
Great difficulties arise when developing empirical taodels of zonal and mer-
idional components of wind velocity in connection wtth the need for taking
into account the longitudinal differences which are eapecially significant
- during winter. It is found that for the levels of the upper atmosphere the
- greatest longitudinal d3fferences are characteristic of the meridional
wind components [5-7]. Due to the lack of data on the global distribution
of wind in the COSPAR International Reference Atmosphere (CIRA-1972) data
are given on the zonal components of wind velocity [3]. Even relativel3
recent studies are limited to a synoptic and atatistical analysis of ttie
zonal components of the aind, for the most part along the meridia:i 80�W
[1, 2].
l
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Due to practical requirements the need arises for ohtaining empirical
models of the wind haGed on global data, wi*_h the models extended to the
levels of the upper mesosphere. The posaibility of constructing such
models is becoming increasiugly realistic in connection with the appear-
ance durin& recent years of high-level charts based on ajoint analysis
of rocket and satellite data, and also with the development of wind ob-
servations in the high layers of the atmosphere by indirect methods (radar
tracking of 'Lhe drift of ineteor trails, observations of ionospheric inhomo-
geneities, etc.).
In this article we give an example of the development of empirical models
of the distribution of the zonal and meridional components of wind velo-
city in the altitude range 30-8J lan. These models are based on an analysis
- of the actual wind and geostrophic wind values, computed from pressure pat-
tern charts constructed on the basis of joint use of satellite and rocket
data.
- Data sources and methodological problems. The principal result of construc-
tion of wind models for the stratosphere and mesosphere of the northern
J ;iemisphere was maps of the mean zonal and meridional components of the
wind and their standard deviations for the levels 30, 35, 40, 45, 50, 55,
~ 50, 70 and 80 km.
_ In compiling these maps use was made of data from the international network
of rocket sounding stations and USSR scientific research shiFs for the
period from 1962 to 1977. The mentioned data were taken from the bulle-
tins of results of rocket sounding publiehed in the USSR and in the United
Ststes.
A
:'ig. 1. Maps of inean monthly zonal (a) and meridional (b) wind components
and their standard deviations. January, level 40 1m. 1) lines of equal
values of westerly and southerly components; 2) easterly and northerly
componenCs; 3) lines of equal values of standard deviations.
2
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On the maps for the levels indicated ahove we plotted tle monthly values
of the zonal and meridional components o.f wind velocity and their stan-
dard deviations, which were corrected hy means of construction and anal-
sis of high-level time sections.
Nnn IOJOSO 60ioJ0090 ,10 0 10 10 01~ pp ypsp 50 ,)p100 0 10 90 f010 0
BO m! W/ 90 so
~0 .
a ~ 0 c o 9
70. E lo .
~ 10
,50 10 o~ U o io.
t o � l o
-�/o
10
90 E ; c~a0 ~ `~~i.
'10, E -"'-10 I JO
' 0 10 70 10100 - l0 y20 0 10 I 0 0101010 fo 0-10
b DO 10 JO ylo 40 JO 10 d L)p JO 40 40 JO ?p
~ max min u~ ( max 0 mo~
70 ;nin \
40 ma,~ min
6Q 10 40
30 - ZO s~ma.~ Jp 10 &R
10
~ 10 / 20 ~ ~ mm
� JO 10 ZO TO min m~n 20 p 20
' '0 30 SU 70 90 70 SO JO 10 10 ,70 SO 70 90 10 SO 30 10
c' 1e0 � 9o�a.a E 9o'j.a W
I
Fig. 2. Time sections of inean values of the zonal wind along the meridians
0-180� (a) and 90�E - 90�W (c) and standard deviations 0-180� (b) and 90�
E - 90�W (d). January.
Taking into account that the observational data for some rocket stations
did not ensure the necessary spatial resolution far representation of the
planetary wind fields, the results of thermal sounding-from satellites
were also used in constructing the wind models. Weekly pressure pattern
charts for 5, 2 and 0.4 mb for each Wednesday in January and July for a
five-year period were compiled using rocket and sate'Llite data for com-
puting the values of the geostrophic wind. For the years 1972 and 1973
the charts were taken from [8]. Since 1975 such charts have been compiled
at the Central Aerological Observatory on the basis of data from satellite
sounding (VTPR radiometfr) received from the United States by way of ex-
change of scientific information. The charts gave rocket data and the geo-
potential heights on the basis of data from thernal sounding from a satel-
lite. The rocket and satellite data were in very satisfactory agreement.
The values of the geostrophic wind were computed using weekly pressure
pattern charts at 48 points in the hemisphere (each 20� of latitude and
30� of longitude). Then we computed the mean rlonthly values of components
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of the geostrophic wind, which together with the corresponding values
obtained on the hasis of rocket ohservations were plotted on charts fox
the levels 35, 40 and 55 km (which approximately correspond to the levels
5, 2 and 0.4 mb) and analyzed. Examples of construction of such maps are
' given in Fig. 1. Maps of wind at the remaining levels were analyzed pri- ~
marily on the basis of the results of rocket sounding.
The next stage in the development of wind models was the construction (on
the basis of the charts) of vertical sections of the mean monthly values
of the zonal and meridional wind components and their standard devia-
tions along four meridians (0, 90�E., 180, 90�W) from 10 to 80�N. The _
choice of the ir.dicated meridians was determined from the following con- '
siderations. The -tection 0-180� gives the latitudinal distribution af
the wind over the oceans of the northern hsmisphere, whereas the section
90�E - 90�W represents the wind distribution over the continents.
Description of models. As an example we will examine the distribution of
the zonal wind along the above-mentioned meridians in January. Fj.gure 2a,
c shows that westerly transfer predominates along both meridiane. Differ-
ences in winter circulation in the upper atmosphere in its western and
eastern parts are clearly expressed in the section 0-1 80� longitude. Over
the Atlantic Ocean there are two maxima of velocity of the westerly wind.
' One of these is situated at an altitude of 40 km near 50�N; the second is
present in the upper mesosphere at 40�N. Over the Pacific Qcean there are
three weaker maxima: the first is situated in the middle stratusphere at
- latitude 60�N, the second is at approxiuately this saxne latitude in the
region of the stratopause and the third, which is situated in the middle
mesosphere, is displaced into the tropics (Fig. 2a). I t should be noted
that the velocity of westerly transfer over the Pacific Ocean in the en-
tire thickness of the stratosphere and mesosphere is approximately half
the wind velocity over the Atlantic, which is attributable to the devel-
- opment of the Aleutian High. The easterly winds in the stratosphere and
mesosphere over the polar regions are asaociated with frequent movements of
the center of the circur.polar cyclone into the Canadian and European sec-
- tors of the Arctic.
Figure 2c shows the latitudinal distribution of the zonal wind along the -
meridian 90�E - 90�W. It is possible to discriminate two characteristic
peculiarities: stronger westerly transfer in the middle mesosphere and -
:he presence of only one maximum of velocity of the wasterly wind over
, I3orth America.
- Figure 2b,d, which shows the variability of the zonal wind along the men-
tioned meridians, makes clear that the highest standard deviations of the
- zonal wind component are situated in the neighborhood of the stratopause
and in the middle mesospfiere. This agrees with the gr eat variations of
temperature and geopotential of the isobaric surfaces transpiring during
the winter and having a qua.siperiodic nature.
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Results of Comparison of Represented Empirical Model of Wind Distribution
in the Northern Hemisphere Upper Atmosphere (EVM-1918) and International
Reference Atmoaphere COSPAR (CIRA-1972). Zonal Component
I 1 3BM- 1978 - C I RA� 1972
H ivi I 10 I 20 I 30 I 40 1 50 I 60 I 70 180' c. ui. 6
.
2 SI x e a p 6, 9A' a. A.
60
-16
-6
- I 2 5
42
8
50
45
55
-7
4
-10 I-21
43
-11
~ 45
65
50
-5
9
-8 -35
27
- I 2
25
72
45
-2
3
-6 -40
19
-6
0
66
40
-9
U
-1 -38
23
1
-20
52
35
-1 I
-1
1 -28
41
2
-27
35
30
-12
-7
1 -7
39
-5
-22
16
3
HlOdb, 90�
3. 2.
60
S
1
12 3
I 14
7
9
6
55
-9
-9
2 -3
7
-2
1
4
50
-9
-8
-5 -2
2
-2
4
4
45
-4
-4
-8 -3
-3
0
5
4
-40
-2
-2
-8 ' -2
-3
0
6
2
35
0
0
-8 -3
-1
2
5
-1
30
0
-1
-7 -4
2
3
~ 5
1
_
4 AHeapb> 90' s. .3.
.
60
-22
-4
-5 -34
-8
-8
15
1'I
55
-12
0
3 -32
-18
-23
: 0
28
50
4
13
13 -48
-34
-25
-3
33
_ 45
-2
3
Il -57
-45
-22
-5
35
40
-8
-3
12 -59
-40
-20
-2
31
35
-10
-1
12 -52
-31
-24
-1
18
30
-8
0
8 -40
-30
-53
-1.0
-4
5H to n b, 90'
S. A.
KEY;
1. EVM-1978 - CIRA-1972
2. January, 90�W
3. July, 90�W
4. Jauuary, 90�F
5. July, -90�E
6. N
In summer, by virtue of the sym*etry of circulation in the stratosphere
_ and lower mesos.phere, the,latituciinal dtstribution of the zonal wind in
all the sections has an approxima.tely identical character. As iadicated
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60
-3
-13
13
11
22
13
12
4
55
-2
-�2
8
8
17
3 ~
4 I
3
SO
-3
ri
3
5
7
I ~
4
3
45
-3
~ 1
p
3
-1
2
i
4
40
-5
3
-2
4
-I
I
6
Z
35

7
p
4
4
5
6
0
30
o
q
4
5
8
7
8
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above, the principal form of representation of the developed models is
maps of the distribution of the zonal and meridional components of the
wind in the stratosphere and mesosphere in the northem hemisphere. Fig-
ure la shows that at an altitude of 40 km over the northein part of the
- Atlantic Ocean and adjacent regions of the continents there are maximum
velocities of westerly transfer, which is considerably reduced over the
- Pacific Ocean. The axis of the westerlv jzt stream with maximum winds
of more than 60 m/sec is oriented approximately along 50�N. Weak easterly
flows predominate over the western part of the Pacific Ocean, bounded by
the Arctic region, in coanection w.ith development of the Aleutian High.
The interpretation of ineridional circulation is most complex because of
poor study. In winter tlze distribution of the mer_idional components in
the polar and subpolar regions is most charar.teristic. Figure lb shows
that there is a prpdominance of air tranefer from Eurasia to North Amer-
ica in the stratosphere, which is attributable to development of tl.e
A1eu*_ian High and frequeut displacement of the center of the circumpolar
vortex ir,to the Canadian and European sectors of the A:ctic. Judging
from the maps constructed for the higher levels, in the mesosphere there
is a compensating flow in the opposite direction. The latter can be at-
tributed to the fact that the Aleutian High cannot be traced in the upper
mesosphere, whereas the center of the cyclon2 is displaced into the east-
ern sectoi of the Arctic.
Comparison with models developed earlier. Up to the present time different
authors have repeatedly wndertaken to construct global empirical models
- of c,iind distribution in the high layers of the ataasphere. The most modern
= of these is the International Reference Atmosphere COSPAR (CIRA) [3]. It
is therefore of interest to carrj out a comparison of the mean values of
the zonal wind on the basis of the data in the model described here with
the values in the CIRA-1972 model. The results of the comparison are pre-
- seiited in the table, in wY,lch we give the diff.erences in the mean values
of the zonal wind to an altitude 60 km along two meridians for winter and
- summer. The linitation of altitude is attributable to the fact that in
the CIRA-1972 model above EO km the longitudinal differences are not tak-
en into account.
It is easy to see a considerable discrepancy in the compared data in Jan-
uary. For example, at latitude 80�N over North America they attain 70 m/
sec, and in the middle latitudes approximatEly 40 m/sec. In the eastern
hemisphere these differences are also considerable and in the middle lat-
itudes approach 60 m/sec.
Such discrepancies can be attributed to the fact that, first of all, for
_ the development of the represented model we also made use of a consider-
able number of observations carried out in 1971-1977 using an improved
method. Second, in the considered model a more precise allowance has been
made for the J.ongitudinal differences in the characteristics of large-scale
cirGUlatory processes observed in wiuter in the northern hemisphere.
~
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As is well known, during sumner circulation in the upper atmosphere hae
an ordered stable character which varies extremely insignificantly from
year to year. From this point of view the small differences in the mean
valuea of the zonal wind in July which are diecovered in a comparison
of the two mentioned models are entirely explicable. At the same time
this can serve as additional confirmation of the reality of the model
descrihed here.
= Summary. Thus, on the basis of observations of the wind made using rocket
prohes and data on the geostrophic wind, computed with the additional
use of the results of thermal sounding from satellites, we obtained a
model distribution of the values of the zonal and meridional wind com-
ponents and their variability over the northern hemisphere in the layer
30-80 km. It appears that the characteristics described above really
reflect the wind distribution in the stratosphere and mesosphere in the
_ northern hemisphere.
It should he noted that the proposed models of latitudinal distribution
of the wind give some idea concerning the mean long-term conditions of
circulation in the stratosphere and mesoaphere in the northern hemi-
sphere. The models of zonal and meridional wind components for July com-
pletely reflect the characteristics of atmospheric circulation in summer
because the year-to-year varisbility at this time of the year ie inaig-
niiicant. This cannot be said of the wintQr wind diatribution (January)
due to the development of atratomesospheric warmings and the circulatory
restructurings associated with them. It is well known that mid-winter
- warmings in the upper atmoaphere in the polar regions of the northern
hemisphere are observed every year. Nevertheless, the circulatory re-
structurings associated with them are not observed every winter and ac-
cording to the dsta in some studies have a quaei-two-year periodicity [4].
- Accordingly, the routine use of long-term mean wind vaZues in the high
latitudes is not always juatified becauae in the process of averaging
~ over a series of years there is a conaiderable smoothing of the data.
Thus, the considerable year-to-year variability of wind distribution in
the polar regions of the northern hemisphere in winter is not reflected
in averaged models. As is well known, in some reference and standard at-
~ mospheres winter temperature models for the stratomesopause were develop-
ed separately for winters with and without warminga. In the future it is
evidently necessary to consider similar approaches in constructing wind
models; it is necessary to develop taodexs for winters without circulatory
restructurings (with a�predominance of wPSterly flow over the polar re-
_ gions) and winters with restructurings (with easterly winds over the Arc-
- tic).
BIBLIOGRAPHY
1. Gaygerov, S. S., Zaychikov, B. P., Kalikhman, M. Ya., Fedorov, V. V.,
VOZDUSHiVYYE TECIiENIYA V MEZOSFERE ANTARKTIKI (Air Currents in the
Antarctic Mesosphere), Leningrad, Gidrometeoizdat, 1975.
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rvn urriutcu. uOL u1vLt
2. Belmont, A. D., Dartt, D. G., Nastrom, G. D., Variations of Strato-
epheric Zonal Winds, 20-65 1an 1961-1971," J. APPL. METEOROL., Vol 14, -
y vo 4, 1976. _
3. COSPAR INTERNATIONAL REFERENCE ATMOSPHERE 1972-CIRA, 1972, Academic
Verlag, Berlin, 1972.
4. Gaigerov, S. S., "On Stratospheric Warmings in the Antarctic and Arc- `
tic," POLAR METEOROLOGY. WMO TEGHN. NOTE, No 87, 1967. .
5. Groves, G. V., "Atmospheric Structure and its Variation in the Region
from 25 to 120 km," AFCRL ENVIROH. RES. PAPER No 368, 1971.
6. Murgatroyd, R. .T., "Winds in the Mesosphere and Lower Thermosphere,"
PROC. ROY� SOC., Vo1 288, No 1415, 1965.
~ 7. Kantor, A. J., Cole, A. E., "Zonal and Meridional Wind to 120 km," JGR, Vol 69, No 24, 1964.
8. Staff, Upper Air Brancn NOAA. National Weather Service, National =
Meteorological Centre, "Synoptic Analyses, 5-, 2- and 0.4-Millibar
Surface for January 1972 Through June 1973, NASA SP-3091, Washington,
D. C., 1975.
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UDC 551.551.2
NCNLOCAL PARAMETERIZATION OF TURBULENT FLUXr S
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 11-19
[Article by Doctor of Physical and Mathematical Sciences V. M. Voloshchuk
and Candidate of Physical and Mathematical Sciences P. N. Svirkunov, In-
stitute of Experimental Meteorology, submitted for publication 20 Febru-
ary 1980]
[Text] Abstract: The authors examine a general scheme
- for nonlocal parameterization of turbulent
fluxes based on a formal aolution of the con-
tinuity equation. The kernal of the integral
expression,relating the turbulent flux to the
gradient of the mean concentration of an impur-
ity, is expressed in terms of the statistical
characteristics of the turbulent medium. The
article indicates the possibility of a nonlocal
relationship between the global meridional heat
flux and the gradient of the mean temperature
- profile, following from the well-known Budyko
climatic model.
_ The problem uf parameterization of turbulent fluxes is one of the most com-
plex aspects of the theory of turbulent diffusion which has not been com-
, pletely investigated. In most of the existing theories there is predonin-
ance of a semiempirical approach, the basis of which is a local parameter-
ization [ 5 ] : -
q = -Kq,
where I is the turbulent flux, < c> is the mean (determined from turbulence
records) concentration of the impurity, K is the so-called coefficient of
- i:urbulent exchange (in a general case a second-order tensor).
In order to ascertain K we make use of a variety of physical assumptions,
as well as empirical data. However, in a general case it is impossible to
make an imambiguous comparison of the exchange coefficient with the s tat-
istical characteristics of the turbulent medium. This is indicated, in
particular, by the circumstance that in the field of stationary turbulence
for some conditions, for example, with boundary conditions not dependent
~
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on time, the K coefficient can be represented conveniently by some func-
tion of coordinates, whereas for other conditions, such as diffusion
from an instaataneous point source, there are data indicating that K
is a function of time. A detailed analysis of this problem is given in
[9]. The main reason for such a circumstance is that the transport of an
impurity in a turbulent flow is determined by the entire spectrum of
velocity fluctuations, up to fluctuations of external scales. The exter-
nal scale of the turbulent flux as a rule is comparable with the charac-
teristic scale of change in the mean concentration profile [4, 5]. As a
result, the turbulent flux can be dependent not only on the gradient of
the mean concentration, but also on higher-order derivatives. The pres-
ence of this sort of "latent parameters" does not make it possible to re-
late the exchange coeff icient unambiguously to the statistical properties
of the turbulent medium.
It appears probable that such difficulties can be overcome by using a non-
local par2meterization in which the turbulent flux is related by a linear
integral expression with the mean concentration gradient. This hypotheses
was expressed for the first time in [2], in which, proceeding on the basis
of physical considerations, the author proposed some integral expression
relating the turbulent flux in the surface layer to the impurity concen-
tration gradient.
In this article we propose a general scheme of nonlocal parameterization
hased on a formal solution of the continuity equation.
Such an approach makes it possible, on the one hand, to confirm the hypo-
thesis of a nonlocal parameterization by formal reasonings, and on the
other hand, makes it possible to express the parameterization nucleus i^
terms of the statistical (generally speaking, Lagrangian) characteristics
of the turbulent flux. The lattzr can be useful in refining the different
approximate approaches in the theory of turbulent diffusion.
1. As the basis for the examination we will
a passive scalar substance
at ~ div cv = Q (r,
use the continuity equation for
t),
where c is the concentration, Q(i t) are the sources, v( , t) is the
velocity field.
(1)
In order to simplify the reasonings we will consider the medium to be in-
compressible: div v = 0.
Applying the usual averaging procedure, which we will represent by the sym-
bolization < . . . > , from (1) we obtain
a + div ( ) = Q (r, r), (2)
ar
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d1 div vc' = div Gv'c'> - div v' t~ > 110,
it is possible to shift the initial condition in the solution (5) to a later
moment in time, in particular, to the moment when the concentration is for
the first time stipulated arbitra;cilq, in a form not correlated with the
velocity field. This circumstance makes it possible to neglect the influ-
ence of the initial value of the fluctuation. Henceforth as a simplification
we will assume that T=00.
Multiplying expression (5) by v'( , t) and averaging, for the components of
the turbulent flux q=< v'c'> we obtain
- ~
- qj - f dt' f dr' ( V. Gc (r3, ts) > - (8)
- f dt, dr, < v; (r, t) G(r, t1 ti) v; (rt ti) > Vk < c (r,, tt)
Symlw lically, in shortened operator form, expression (8) can be written
in the form
q = ( (k, W Taking
this circumstance into account, after simple transforma'tione from (11) we
obtain
4 k, W) -i' i~') c w)� (15)
Inverting (15), for the flux we obtain the expression
y
q dr'' ~ dt' A(r t t') v _(2 tcoa (t-- t'))-3~2 eXp I - 2~0 (t r)r) (18)
( , I )
J where d'2(t - t') is the dispersion of the displacements of a particle of
- the impur~ty a,uring the time t- t'.
Accordingly G(k,cJ) will be determined by the integral:
._00
G dt exp ~i cu t - ; k= oa (t)). (19)
a
For a 2(t) we will use the Taylor formula and the asymptotic expansion fol-
t
lauzing from it:
31 (t)=2 v=t;dt'(1- t )R(t')-2x(t-tl~-O(t;)), (20)
~
where R(t) is the Lagrangian correlation function, nornualized to unity

f dtR (t)
t~
is the turbulent diffusion coefficient,.

dttR(t) ~'dtR(t)
~Q
U
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is a value clos in sense to the Lagrangian time scale. For the time t<
, tj~"2(t) = 2v2t~ + 0(t3).
Using these expansions in an evaluation of the integral (19), for q(k,cJ)
we obtain an asymptotic expansion:
- " . " _ - y
9(k, u)) lk (x - x= k= ti + i mu ti -F 6 (t,2)) c(k m), (21)
- and for the turbulent flux q(r, t) we accordingly will have
' d
q(r,t)=-y(~~c>-xtl~p-ti d T -1-0(ti) (22)
The first term in (22) correaponds to a local parameterization; the othez-s
correspond to corrections to it.
If we denote by L and T the characteristic spatial and temporal scaYea of
the mean concentration field, it can be seen from S22) that the expansion
is carried out in powers of the parameters ~tL L-~ and tt `i'1. For prob-
lems wfth sufficiently slowly changiag external conditions the paremeter
tt T-1 can be amall. However, the vslue x tLL"2 for typical conditions of
turhulent currents in order of magnitude is equal to unity. This circumstance
is also the reason for the shortcominge in local parameterization. In order
to mr~ke them clearer, we will examine in greater detail the situation ~Ct~,
L-2>1. For the function < G( ; tj 1',t') > we will uae a self-similar rep-
resentation which follows from dimensioaality and isotropicity considera-
tions [5], r-A,) I
_ =-s (t - ti) g (z ' (23)
In this case the normalization condition must be satiefied
4- f dx x= z 1. (24)
8~
0
The function z is related to the dispersion 4Y by the expression
4 r dxx4 g (x) z' (t). (25)
0
Under the condition 7cttL-2>> 1, as is well ki:own.,[5], z(t),t.
We will examine the more general dependence
z (t) = 7 ta . . . (26)
We will limit uurselves to the stationary case a < c> /a r. = 0. In this
case the flux will be determined by the component G(k, 0), which can be
computed without putting g(x) into specific form:
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P'UK U:'r'1l:lAL USE UNLY
G (k, U) - (1+ z / (r k)ll� sIn l r
00 1
xdX x a g
0
c2i;
Substiituting (27) into (15) and inverting the Fourier transform, we obtain
the sought-for relationsh{p
(=r~l G, _ (28)
q - - f dr''A
~
where A(r) is determined by the expression
- ` _ 1 i
dx x �
( I b' (x) sin
A (r) = t - n d - ~ T~'' ' (29) -
(1 a~s 1 t a tin j ra - ll t+ t
~ ~ r z
In particular, in the inertial interval (z~t) we have an essentially non- _
local relationship
0. (7)
2 s p a a b a:'
As in [6], to both.sides of equation (50) we add the value I(L1yj)2, where
~ is some nonzero parameter, Chen
-
ri (~,!j) = -L f ~,L - F = 0. (8)
where
- - - - - -
Fe p-{- 2 J( u, V)- a
'r
a. ( i- ctg P a e 1(ury V2) - r~
L 1
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= Solving (S) as a quadratic equation relative to d~y we obtain
- 1 f F
2 r ~-J ~~J r r
4 F). (9)
~
For fi ndin g the stream function in the northern hemis phere we use the fol- �
lowing iteration process:
f-FVf2+4 7if'(l)).
,LU+U _ *(1+112) (X)
=p e)r(Pf), 0�. e) E D,
GO., E3) = P(~�, e),'(Pf), 0�.. e) E dD.
(10)
An inversion of the difference analogue of the Laplace operator was carried
out by a direct method [3]. This method uses a fast Fourier transform for
expansion of the sought-for solution and the known right-hand side along
' the parallel into series of - - -
- li +c li l .
{ cos 'N , sin N J
r
The equaCions then derived for the coefficients were solved by the elimin-
ation method along tfie meridian. The detetmined coefficients were used in -
determining the value of the sought-for function at the points of grid in-
' tersection once again using the fast Fourier transform [3, 51.
Numerical experiments. The regions of the opt3mwn a and q values were deter-
mined hy numerical experiments due to the nonlinearity of the iteration
- process.
In evalua.ting the rate of convergenre of the iteration process (10) it is
important to choose the norm for which this evaluation is made because we
are interested not so much in the convergence gr(J) as in the convergence
of the derivatives of this f unction. As in [7], we traced the behavior of _
the value
UI~-~ u` -F-v`;N,
- N
T,rhere1J =(u, v)' is the wind velocity vector, N is the number of internal
points in the D region.
The convergence o� the iteration process (10) was evaluated by a comparison
o f U(j) with the precise solution U(�p ).For each level as 11 U(`" ) 11 we
- selected the 11 U0031 value, which did not change even one of the first ten
signi�icant decimal piaces in the subsequent iteration. -
Henceforth we will say that U(j) has n true places, if for all i;~j we
have the inequality
. 32 ,
. P
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j~ Uli, II - II U(1) I~ 1 < Q,IU ni
where m is the decimal order II UQOp.
Table 1
Number of Iterations Required for Obtaining n True Places ef Solution
With M-Parameters, (I), With PT-Parameters (II) and With RU-Parameters (III)
_ . . _ _ - - - - ~
I 3 anpenR 2, A44e471 . 22 anrycra 99 e..,...,,t
- n=7
I 22 25 33 ~ 19 I 22 33
_ tI 13 I 12 21 9 ~ 13 20
III I 8 ~ 8 8 I 8 I 8 8
n-6
II 10 10 15 8 JO 20
'
111 I 6 I 16 I. 26 I 15 ' I 27
In [7] we carried out an adequate number of numerical experiments for clar-
~ ifying the opti.mum Yi values with A;= 0.5 with data in a rectangular region
- covering all seasons of the year. In this connection numerical experiments
- were carried out using data analyzed by Professor T. V. But' for 3 April
and 22 August 1965 at six levels. As the levels we used z= 0, 1400, 2900,
_ 5460, 9120, 11 870 m. These values correspond to the altitudes of the stan-
dard atmosphere with p= 1000, 850, 700, 500, 300, 200 mb. The finding of
_ the p values with the above-mentioned z values on the basis of data for
the isobaric surfaces was accomplished using the equation of statics, as
was described in [2].
Hereafter as a convenience we will use the following notations: we will
_ call the pair 0.5 and 0.5, used by Miyakoda, the M-parameters,
the pair OC = 0.75 and r~= 0.5 from [18] the PT-parameters, and the val-
ues aC = 1.0 and 0.15 the RU-parame'Lars.
The table gives the nimmber of iterations necessary for obtaining 8, 7 and
6 true placea of the solution with M-.parameters in case I, ;aith PT-para-
meters in case II, with RU-parametere in case III. This table shows that
the choice OG = 0.75 gives a gain in the numlier of iterations in comparison
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r
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AaE3
I 28 ~ 28 41 22 24 40
II 17 18 25 12 18 2~.
III I 8 ~ 9 I 9 I 9 10 10

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- with 06 = 0.5, as in the study hy Paegle and Tomlinson. At the same time,
with this value oG = 0.75 a choice Yj= 0.15 instead of Y? = 0.5 leads to a
_ further acceleration of the rate of convergence of the iteration process
~ (10), as can be seen clearly in Fig. 1. This figure shows curves of the
numher of iterations necessary for ofitaining n true places of the solu-
tion with z= 0, and z= 11 870 m respectively. We note that with n= 8
as a rule the nonclosure of the initial equation becoIDes a value of about
10-16 s2c'2.
~
Now we will examine these results in greater datail. In order to obtain
8 true places of the salution at the level 1000 mb for 22 August with use
of the M-parameters it is necessary to have 38 iterations; with the PT-
parameters it is necessary tc have 23 iterations; using the RU-psrameters
it is necessary to have only 9 iterations. With these same values of the
parameters for the data for 3 April at this same level it is necessary to
have 30, 18 and 8 iteratians respectively.
�7-~s
s
36
Z4
98
12
0
#B~
41
.36
30
24
~e.
i1
6
1
A
~�0,5
a�Q7s
n- j
~
~y"O'O`a�o,s
'7-q1s
a'=Q7S q�Q15
~ a�10
io:-- ~1'~15
~r-
R�0,5
a�0,75 q,0,5
.
~�~bis
~
d-Q1S
Q15
[t%1,Qi
V05

cr�0,5
S'S0 n-0,5
a
p%~
.~�~~7�015
a-Q7sq-q1s

t~" z�
�0,15
' ' 7
~
S

7 9 n
Fig. 1. Dependence of number of iterations s required for obtaining n true
places of solution on values of Ot and Yt parameters at the level z= 0(at
left) and z= 11 830 m(at right) for altitudes of isobaric surfaces 1000
mb (at left) and 200 mb (at righz) on 3 April (at top) and on 22 August
1965 (at bottom).
Similar curves were also constructed for other levels. The behavior of the
curves is very similar, which makes it poesible to speak of an optimum
value of the RU-parameters both in comparison with the M-parameters and in
comparison with the PT-parameters.
34
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In order to clarify the optimimm oC and rZ intervals, Fig. 2 shows curves of c
the number of iterations necessary for ohtaining 8 true places nf the
solution with z= 5460 m for different oC and )j values (as a convenience
- a nonuniform scale has been used along the x-axis).
- a�~r
s 5,55 ~a1,1s
J6
0
, 14 ir' -
~ Cr 0
~-~-~,~,.1r�~R�0,75
12
6~--�-----.~-
0
e'S a-Ris
J6 0
5'S i
JO P G�1,1
.
1B ~ ~ 1,0
11
6
0
0101 4013 QOJ 11 Q15 'QZS QJS 4f1f q =
Fig. 2. Curves of the number of iterations s required for obtaining 8 true
places of solution at level z= 5460 m for altitudes of isobaric surface
500 mb for 3 April (at top) and 22 August 1965 (at bottom).
With each fixed QC value the preferable interval for is the segment [0.05;
0.25]. The advantage of choice of the Yt values from this interval in com-
parison with n= 0.5 is obvious. We note that with a fixed QG value for
different rZ the number of required iterations from the mentioned interval
virtually does not change. Such a rather broad region of optimum r? values,
common for all lX , makes it possible to hope that the choice of one of the
'2 values from the indicated region will not give a marked change in the
hehavior of the rate of convergence of the iteration proceas even with
other factual data.
On the other hand, with stipulated YZ from the indicated interval it can be
seen that with oC = 0.5 the iteration process (10) converges considerably
more slowly than with all remaining OK values. For example, for 1"1 - 0.15
it is necessary to have 14 iterations with oc = 0.75; 10 iterations with W_
1.0; 9 iterations with ov- = 1.1; 11 iterations with aC= 1.15, but 25 iter-
ations with ot a 0.5 (for data for 22 August). For the data for 3 April
the behuvior of the relationship in the number of iterations with these -
same values of the o6 parameter is very similar. It should be noted that in -
bott-, cases with OL a 0.75 it is necessary to have more iterations than with
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OG = 1.0 andoC= 1.1. Thus, for oC the interval (0.75; 1.15) can be consid-
ered acceptable.
_ Summary. Similar curves were also constructed for the other levels. Ths be-
havior of these curves also leads us to the conclusior that the region of
optimum 2 values is tfie segment 10.05; 0.25], but with lZ values froin this
region ol from the"interval (0.75; 1.15) are optimum. The results of numer-
ical experiments show that the use of optimum o[ and rjvalues, without
chang-ing the total number of aritfimetical and logical eperations in one
iteratinn, decreases the numher of required iterations an the average by
a factcr of 3 in comparison with tfie M-parameters and by a factor of 2 in
_ comparison with tfie PT-parameters.
Although the region of optimum values for each level was found only for twi
dates, our experience [7] with computations for a Cartesian coordinate sy s- E-
tem with different values of ttie ri parameter with a fixed oe value shows
that the region of optimum rl values is virtually independent of the initial
information. Thus, the above-mentioned optimum values of the ot andrlpara-
meters can be recommended in practical computations for any factual data.
BIBLIOGRAPHY
1. Dzhahar-Zade, R. M., "One Al.gorithm for Solution of the Balance Equa- ~
tion," IZVESTIYA AN SSSR, FIZIKA ATMOSFERY I OKEAir'A (News of the USSR -
Academy of Sciences, Physics of the Atmosphere and Ocean), Vol 5, No 3,
1969. `
- 2. Kalenkovich, Ye. Ye., "Numerical Scheme for Predicting the Fieids of
Meteorological Elements for the Northern Hemisphere," Dissertation
for Award of the Academic Degree of Candidate of Physical and Mathe-
matical Sci.ences, Manuscript, Novosibirsk, 1970.
3. Marchuk, G. I., METOllY VYCHISLZTEL'NOY MATEMATIKI (Methods of Computa-
tional Mathematics), Moscow, Nauka, 1977.
4. Miyakoda, K., "Introduction to Numerical Weather Forecasting," CHIS-
LENNYYE METODY RESHENIYA ZADACH DINAMIKI ATMOSFLRY I OKEANA (Numer-
ical Methods for Solving Problems in the Dynamics of the Atmosphere
and Ocean), Leningrad, Gidrometeoiadat, 1968. -
5. Obraztsov, N. N., "Solution of the Helmholtz Equation on a Sphere," -
ALGORITMY I PROGRAMr4Y (Algorithms and Programs), No 2, 1975.
6. Rivin, G. S., Uraz3lina, Z. K., "Determination of the Initial Wind
Field for a Weather Forecasting Scheme," METEOROLOGIYA I GIDROLOGIYA
(Metearology and Hydrology), No 12, 1977.
7. Rivin, G. S., Urazalina, Z. K., "Optimization of a Method for Solving
the Balance Equation," METEOROLbGIYA I GIDROLOGIYA, No 9, 1978.
36
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8. Arnason, G. A., "A Convergent Method for Solving the Balance Equa-
tion," J. METEOROL., Yol 15, No 2, 1958.
9. Asselin, R. ,"Tfie Operati:onal Solution of tfie Balance Equation,"
TELLUS, Vo1 12, No 1, 1I67.
10. Bengtsson, L., "Four-Dimensional Assimilation of Meteorological Ob-
servations 4M0/ICSU," GARP PUBL. SER. , No 15, 1975.
11. Bolin, B., "Numerical Forecasting With the Barotropic Mo3e1," TELLUS,
Vol 7, No l, 1955.
12, Bolin, B., "An Improved Barotropic Model and Some Asgects of Using
the Balance Equation for Three-Dimensional Flow," TELLUS, Vol 8, No
1, 1956.
-A
13. Charney, J., "The Us.e of the Primitive Equations of Motion in Numer-
- ical Prediction," TELLUS, Vol 7, No 1, 1955.
14. Hinkelmann, K., "Der Mecfianismus des Meteorologischen Larmes," TELLUS,
Vol 3, No 4, 1951.
15. Houghton, D. D., "Derivation of the Elliptic Condition for the Balance
Equatio n in Spherical Coordinates," J. ATMOS. SCI., Vol 25, No 1, 1968.
16. Houghton, D. D., Washington, W., "On Glotial Initialization of the Prim-
itive Equations.: Part I," J. APPL. METEOROL., Vol 8, No 5, 1969.
17. Miyakoda, K., "On a Metfiod of Solving the Balance Equation," J.
METEOROLe SOC. JAPAN, Vol 34, No 6,.1956.
18. Paegle, J., Tomlinson, E. M., "5olution of the Balance Equation by
Faurier Transform and Gauss Elimination," MON. WEATHFQ REV., Vol 103,
- No 6, 1975.
19. Paegle, J., Paegle, J. N., "1On Geopotential Data and Ellipticity of the -
Balance Equation," MON. WEATHER REV., Vol 104, No 3, 1976.
_ 20. Petterssen, S., "On the Relation Between Vorticity, Deformation and
Divergence and the Configuration of the Pressure Field," TELLUS, Vol
- 5, 1953.
21. Phillips, N. A., "Un the Problem of Initial Data for the Primitive
Equations," TELLTIS, Vol 12, No 2, 1960.
22. Shuman, F. G., "Numerical Methods in Weather Prediction: I. The Bal- ance Equa.tion," MON. WEATHER REV,, Vol 85, No 10, 1957.
23. Shuman, F. G., "Numerical Methods in Weather Predi.ction: II. Smooth-
ing and Filtering," MON. WEATEER REV., Vol 85, No 11, 1957.
37
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UDC 551.513
SPATIAL STRUCTURE OF CIRCUMPOLAR VORTICES OF THE ATMOSPHERE AND CIRCULATION
IN THE EQUATORIAL ZONE
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 35-41
[Article by Candidate of Geographical Sc,iences Ts. A. Kanter, Saratov State _
University, submitted for publication 11 November 19791
[Text] Abstract: In the 60-km layer of the atmosphere
there was found to be a three-level spatial
structure of circumpolar motion with strongly
expressed broadenings in the region of the
- tropopause and stratopause. It is shown that
- in the layer 20-40 km,.where the circumpolar
vortex of the winter hemisphere has a minimum
diameter, the aubtropical zone of high pressure
adj acent to it migratea along the meridian and
- causes a change in westerly and easterly cir-
culation in the equatorial stratosphere. It is
' postulated that a quasi-two-year cycle is the
cha.racteristic period of interaction of pro-
cesses in the northern and southern hemiapheres.
A difference in the structure of circumpolar
vortices in hoth hemiapheres was established.
A knowledge of the patterns of general circulation of the atmosphere is a
highly important link in creating a theory of climate and improvement in
' long-range weather forecasts. Accordingly, at the present time work has _ considerably broadened on the investigation and modeling of large-scale at-
mospheric proceases.
- However., the fact should be noted that the largest features of planetary
- circulation. caused by the temperature difference between the equator and
the poles, circumpolar vortices (CPV) of the northern and southern hemi-
; spheres,for the time being have been poorly investigated. However, the cir-
cumpolar motion is a grandiose unified three-dimensional formation. It -
takps in the extratropical latitudes, at least the troposphere, strato-
sphere and mesosphere; it is easily detected on pressure pattern charts for
all levels above 1000 mb. Now we wi11 turn to these materials.
38 -
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Mean long-term pressure pattern charts have now been published for each
month for the northern [2] and southern [39 4] hemispheres. They were pre-
pared for nine isotaaric surfaces: 1000, 850, 700, 500, 300, 200, 100, 50
and 30 mb, that is, to an altitude of 24 km. In addit{on to long-term
maps, daily charts are published for the northern hemisphere which char-
acterize the pressure field to an altitude of 30 lan (10 mb). Above 30 km
mean weekly pressure charts for six levels (35, 40, 45, 50, 55, 60 km) are
published f.or the northern hemisphere on the basis of data from rocket
sounding of the atmosphere [1].
We used the materials enumerated above, characterizing the 60-km lay2r of
the atmosphere in the northern hemisphere and a 24-km layer in the south-
ern hemisphere.
Figure 1 shows long-term mean monthly presaure pattern charts for the north-
ern hemisphere (January) for the isobaric surfaces 850 and 300 mb and Fig.
2 showe pressure charts for the levels 40 and 60 km (January 1977). An an-
alysis of this material, first of ally does not leave doubt that in the
winter (at least to an altitude of 60 km) there is a well-expressed cyclonic
circumpolar vortex; it is the largest feature of semiglobal circulation.
Second, in a comparison of the diameters of the CPV vertically there is
found to be a clear pattern first the vortex expands considerably (Fig.
1), then it is narrowed (Fig. 2a) and thereafter again expands (Fig. 2b).
This pattern is confirmed by all cartographic materials, both long-term
mean monthly and daily, to wit: topography of the isobaric surfaces 700,
500, 200, 100, 50, 30, 10 mb; pressure charts at the levels 35, 45, 50, 55
km. The CPV is very well expressed in the southern hemisphere, where its
contours are more concentric with the circles of latitude than in the
northern hemisphere and the pattern described above is manifested still
more clearly.
. \
% .501 P ~
32118
1SJ~ I
130
)
1 ~
I ~
~ I
i ~
1
1
~
~
t
B ~ high
H ~ low
1 `
\ 6`~
1 ~ 910
!
~
/ i
~
~
. ,
466
~7~1 Fig. 1. Mean long-term maps AT850 and AT300 (a, b). January, northern hemi-
sphere.
39
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~ r
,
~
\
.
~ Z'a ^ ze
H,rn M6 mb
sv e,~i ~
Q 6 Q)
i
1B
JO
m fOB ~
JOO
0 100
Fig. 2. P.ressure maps at the levels 40 and 60 km (a, b).,January 1977, north-
ern hemisphere.

B= Ilig,
H m low
_ _HKn pr+6
v,z
$0
Q9
40 ~T~
JO
90 BO DO 40 V'
700 � -
400 ' d
10 f00 - - L.
T-- - - - - - - -r
40 3,3 ~ ~
50 92
~ . ~
JO -
ZO 100 - - - - - - -
J00 1
0 700 _
0 40 80180 '+a (t.
0 700 ,
J00
20 100
i0 ~ i 1l
10
40 2 ~ ~
0,6
60 Q 1
Fig. 3. Models of planetary circumpolar movement of atmosphere. a) January;
b) July; I) northern hemisphere, II) southern hemisphere.
In order to compare the magnitude of the circumpolar vortices at different
altitudes in different hemispheres and seasons it is necessary somehow to
make a quantitative evaluation of the space occupied by them. The area
bounded by the last closed isohypse of the CPV can serve as such an evalu-
ation. In the proposed investigation the area was determined using a spec-
ial ovex.lay proposed in [5] and later improved.�
Figures 1-2 shour that the isohypaes of the circumpolar vortices do not dif-
fer too much fram the circles.of.latitude; therefore, for the purposes of
clarity the position of the last closed'isohypse should be expressed in
40
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degrees of latitude of the parallel which limits the area identical to it.
The described method was used in determining the boundaries of the CPV for
January and July at al.l isobaric surfaces in both hemispheres and on rocket
sounding maps for the northern hemisphere. This made it possible to con-
struct models of planetary circumpolar motion, repreaented in Fig. 3,
_ where for January and July we successively plotted (vertically) the dia-
meters of the circumpolar vortices at the isobaric surfaces 1000, 850, 700,
500, 300, 200, 100, 50, 30 mb, at the levels 40, 50, 60 lm, and envelopes
were drawn through their ends.
- Table 1
Boundaries of CPV (in Degrees of Latitude) in Troposphere and in Lower
Stratosphere in the Winter
- L {I306apttwecicue noeepxHOCrti, .u6
1000 I 850 I 700 I 500 I 300 i 200 100 I
I i 50 I 30
2 CesepHOe noayw apHe, AHdape
Her I 3-1 i 26 I 24 I 15 I 15 i 23 I 29 I 25
unB
4 3 IOacaoe non
ymapNe, xrona
42 I 38 1 27 ; 19 1 15 1 16 I 24 30
36
KEY :
1. Isobaric surfaces, mb
2. Northern hemisphere, January
3. Southern hemisphere, July
4. no CPV
Since the vertical structure of the CPV was specific, we will examine its
most important peculiarities in greater detail. ,
Table 1 gives the limits of the vortex at all isobaric surfaces according
to the mean monthly long-term pressure pattern charts in the layer from
1000 to 30 mb.
An analysis of this table and Fig. 3 clearly shows that in winter in each
of tiie hemispheres in the troposphere and lower stratosphere the circum-
- polar movement has a highly expanded part which is situated in the layer
300-200 mb. The area of the vortex in the region of the expansion on the
average is twice as great as outside it (850 and 30 mb). It mus` be noted
that the expansion of the CPV coincides with such atmospheric features as
_ the tropopause and jet streams. These three phenomena have a high probabil-
ity of an interrelationship and there is possibly an intercausality.
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A comparison of the data in Table 1 showe that the winter circumpolar
movement in the layer from 1000 to 30 mb in both hemispheres has virtually
identical limits at all levels. The difference between them is that the
southern hemisphere vortex has a greater depth than that in the northern
hemisphere (Table 2).
Table 2
_ Geopotential Height (dam) in the Central Part of the CPV in the Northern
and Southern Hemispheres at Standard Isobaric Surfaces According to Mean
Long-Term.Data
i n,,......~...,e I o L1inAampuPrs:uP nnnenxuocrif. .u6
KEY:
1000 1
850 I
I
700 I
500 I
I
3^0 200 1
100 I
50 l
30
Ceaepxoe 3
HQT 5
12S
270
I 504
836
1(18S
1516
1832
2240
s
n
u
fO~caa 4
-0,
12
112
252
484
824
1056
1452
1532
2112
1. Hemisphere
2. Isobaric surface, mb
3. Northern
4. Southern
5. No CPV
Table 3
Limits (in Degrees of Latitude) of Circumpolar VorCex in Troposphere and
Lower Stratosphere According to Data for 15 January for Five Yeara in the
Northern Hemisphere
H3�6ayxqecKaR ~ 1971
noaepzxocrb, M6 j~ I
1974 1975
I I
1976
I
1977
I
CpeltHee
2
850
38
46
41
30
37
40
700
29
31 I
34
27
29
30
Spp
24
25
27
25
25
25
300
22
22
20
20
20
21
200
23
23 I
21
23
19
21
IOU
24
26
25
26
21
24
50
40
47
I
35
39
43
40
30
54
53
41
I
45
47
48
10
59
47
~
52
~ 47
42
49
KEY:
1. Isobaric surface, mb
2. Mean
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Now we will examine to what degree the limits of cixcumpolar movement in
the troposphere and lower stratosphere are stable. In the first approxim-
ation this can be done by examining the vertical profile of the CPV on in-
dividual days. As an example we will take the 15 of January for different
years (1971, 1974, 1975, 1976, 1977). The boundaries of the vortex are
givo-n in Table 3.
Here we can note two facts. The first is a stable regularity involving a
broadening of the CPV from the lower levels to the isobaric surfaces 300
and 200 mb and subsequent narrowing of the vortex with altitude. This can
be seen from the data in each column. The second is the great stability
of the horiaontal dimensions of the CPV in the layer from 500 to 200 mb,
whereas above and below it the ].imijs'of the vortex vary substantially and
in individual cases the area of the expanded part is three times greater
than outside it.
Table 4
Limits of CPV in Atmosphere (in Degrees of Latitude) in Layer 40-60 km in
January in Two Years in the Northern Hemisphere
1976 - - ~ 1977
Ypoeexb, LIiicna
x 3-9 ~ I 0-16 17--23 24--30 31-7 8-1-F 15-21 ~ 22-28
l 1 ~ 2 I 3 I 4 I 5 6 7 I 8
44 57 50
40
60 I 50 I 32 I 0 I 29 I 53 I 54 I 35 I 22
KEY :
1. Level, lan
2. Dates
Thus, the circumpolar vortex has the most stable limits in the region of the
tropopausal expansion. The variation of its boundaries in the lower tropo-
- sphere is evidently associated with the distorting influence of macrotur-
bulent vortices, cyclones and anticyclonea, whereas the instability of the
boundaries in the sr_ratosphere is attributable to the fact that its temper-
ature regime in winter is unstable (the depth of the CPV and its diameter
are sharply reduced in the layer where stratospheric warming occurs).
Next we will turn to the vertical profile of the winter circumpolar vortex
in the layer 40-60 km on the basis of data from rocket sounding of the at-
mosphere [1]. Since these data for the time being are not being reduced to
long-term values but are being published, as mentioned above, in the form
of inean weekly pressure chares, we will cite the limits of the CPV in this
layer for four weeks in each of the Januaries of 1976 and 1977 (Table 4).
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Here in columns 2, 3, 4, 7 and 8 it is easy to trace the broadening of the
vertex from altitude to altitude. In column 1 this expansinn is expressed
- weakly, whereas in columns 5 and 6 it can be seen that the limits of the
vortex are even narrowed with altiCude.
An attentive study of all the matPrials for the mentioned time intervals
and also similar materials for other winter months in3icatecl that usually
from 40 km and above the CPV expands and it is narrowed only in the case
and in the layer where winter stratospheric warming occurs. This narrowing
is the greater the stronger the warming.
After summarizing the peculiarities of the vertical profile of the circum-
� polar vortex in winter it can be said that in the 60-km layer of the atmo-
sphere it is characterized by a three-level structure with two expanded
- parts in the regions of the tropopause and stratopause (we will call them
tropopausal and stratopausal expansions), and there is a third narrow part
between them (we will call it the "saddle" of the CPV).
Now we will examine the relationship between the vertical profile of the
winter CPV and the peculiarities of circulation in the tropical and equa-
_ torial zones. Figures 1-2 clearly show that the circimmpolar vortex borders
on the subtropical region of high pressure. Naturally, circulation in the
tropical and equatorial zones is determined by the position of the axial
line of this region. 0
The vertical profile of the subtropical zone of high pressure, like the
circumpol:ar vortex, has a three-level structure. At the levels of the tro-
popause and stratopauae, where the CPV is considerably expanded, the sub-
tropical anticyclonic zone is narrow and is "pressed" toward the equator.
Its axial line reaches latitude 10� (Fig. lb). In the region of the saddle
- of the CPV the high pressure zone is "floating." For example, in the north-
ern hemisphere in January 1976 its axial line at the isobaric surface 30
mh ran approximately along the parallel 28� and in January 1977 7-90 to
the south.
Migration of subtropical anticyclones along the meridian has a very impor- tant series of consequences. tt leads to a change in the direction and in-
tensity of transfer in the tropics and- in the equatorial zone. In the equa-
torial stratosphere-the change in circulation has.a quasi-two-year cyclic-
ity. This phenomenon, discovered about 20-years ago, is now being extensive-
ly studied [6-9]. It is exceedingly noteworthy that the layer in which aa
alternation of westerly and easterly circulations is observed completely
caincides with the region of narrowi,ng of the circumpolar vortex, that is,
with the region in which the anticyclonic zone can first come close to the
equator and cause an easterl;; flaw in its aone, then withdraw from it, giw
ing place to a small-cellular circulation with westerly, less stable winds.
We recall that this peculiarity of the pressure field is characteristic of
the winter hemisphere. However, on the planet one of the hemispheres is
always a winter fiemispfiere. It can be assumed that in the course of one year
44
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they alternately ensure easterly transfer in the equatorial atratosphere,
and in the course of the next westerly,-manifesting itself as an indi-
cator of a unified circulation mechanism. In this case the quasi-two-year
cycle is the characteristic period of interaction of processes in the two
hemispheres. This assumption requirea further checking. It becomes possible
wiCh an increase in the quantity and quality of aerological and rocket ob-
= servations in the equatorial and tropical zones.
Now we will proceed to an examination of summer circumpolar movament of the
atmosphere in both.hemispheres (Table S).
Table S
Limits of CPV (in Degrees of Latitude) in Troposphere and Lower Stratosphere
in Supnner
1000 I 850 700 I 500 I 390 I 200 100 I 50 I 30
2 CeBegeoe nonymapHe, monb
_ HeT ~ 38 I 37 I 39 I 40 ~ 41 I 53 IatiTnuuh.~ox laur~iuexnoi
3 uns I i 4 4
5 tOmHOe nonymapNe, Axsapb
4
47 ~ 41 ~ 36 I 26 1 24 1 24 1 34 1 55 JBHTNllHKJ10H
KEY:
1. Isoharic surfaces
2. Northern hemisphere, July
3. No CPV
4. Anticyclone
5. Southern hemisphere, January
As indicated in the cited tables, and also in Fig. 3, in summer, as in win-
ter, the circumpolar vortex has a three-level structure. The lower part is
the cycl.onic vortex, the upper part is the anticyc?otd-^_ vortex, at each of
rhe considered levels taking in all the hemispheres, whereos the tliird is
a thin layer between them in which the circinnpolar movement is disorganiz-
ed (in the northern hemisphere this is the layer between 100 and 50 mb,
_ and in the southern hemisphere 50-30 mb).
The difference in the vertical profiles of summer CPV in both hemispheres
is suhstantial and involves the following. First, its lcwer part the cy-
clonic vortex differs witF.respect to vertical exte7it by approximately
4-5 km (in the northern hemisphere it is shorter). Sec.ond, in the southern
hemisphere there is a clearly expressed tropopausal expansion of the CPV
(Fig. 30, whereas 1n the northern hemisphere it doera not exist (Fig. 3b).
Third, in summer the cyclonic circumpolar vortices of the southern hemi-
sphere have a greater depth than in tiie northera hemisphere.
45
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Thus, the difference in the underlying surfaces in both hemispheres finds -
total expression in t he difference in spatial structure of the largest
features of planetary circulation.
Summary
In a study of circumpolar vortices in the 60-1m layer of the atmosphere it `
was discovered that they have not only a strongly expressed three-level
structure, hut in ac cordance with this, the subtropical high-pressure
field has a similar s tructure, that is, in essence, the entire planet3ry _
pressure field. A direct result of this is a multilevel st.ructure of the
wind over the equator.
It was found that in the expanded parts of the CPV there are such atmospher-
ic phenomena as the t ropopause, stratopause and 3et streams, whereas in the
layer of narrowing of the vortex subtropical anticyclones migrate along the
meridian, causing a cfiange in the westerly and eaeterly circulations over
the equator.
A specific structure of tfie pressure field probably could also be detected
- in a study of layers of tfie earth's atmospfiere ahove 60 1m, as well as in
the atmospheres of o tfier planets. This would make it possible to clarify
specifically how pfiysicochemical and astronomical factors exert an infltr-
ence on planetary circulation.
The fact that the dif ference in the underlying surfaces of the northern and
southern hemispheres is manifested toCally in the difference of the ver-
tical structure of tfieir circumpolar vortices can become a key to con-
struction of models of the "underlying surface - three-dimensional planet-
ary circulation" system. Such models are necessary both for reconstructing
the pattern of general circulation of the atmosphers in climates of the
past and for predicting the nature of future circulation as a result of nat-
ural or inadvertent change of the underlying surface.
BIBLIOGRAPHY
1. "Atlas of High-A1 titude Charts for the Layer 35-60 km," PRZLOZHEttIYE
SYULLETENYU "REZUI,'TATY RAKETNOGO ZONDIROVANIYA ATMOSFFRY" (Appendix
to the Bulletin " Results of Rocket Sounding of the Atmosphere"), No 9,
lI, TsAO, GUGMS, 1978.
2. ATLAS KLIMATICHE SKIKH #LHARAKTERISTIK TEMPERATURY, PLOTNOSTI I DAVLENIYA
VOZDUKHA, VETRA I. GEOPOTEPITSIALA V. TROPOSFERE I PdIZHNEY STRATOSFERE
SEVERNOGO POLUSHA1tIYA, VYP IV (Atlas of Climatic Characteristics of -
Temperature, Dens ity and Air Presaure, Wind and Geopotential in the
Troposphere and Lower Stratosphere of the Northern Hemisphere) No IV, -
edited hy D. I. S tekhnovsk3.y and B. S. Chuchkalov, Moscow, Gidrometeo-
izdat, 1174.
46.
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- 3. Zas tavenko, L. i. , ATLAS TCLIMATICHESKIKH KART BARICHESKOY TOPOGRAFII ^
NIZHNEY STRATOSFERY YUZHNOGO POLUSHARIXA (At1as of Clj.matic Pressure
- Pattern Charts of the Lower Stratosphere in the Southram Hemisphere),
Moscow, Gidrometeoizdat, 1475.
4. Zaetavenko, L. G.s Zakharova, I. B., Olintseva--Nebrat, G. G., ATLA9
KLIMATICHESKIKH KART BARICHESKOY TOPOGP.AFII YL'ZHNOGO POLUSHARIYA
- (1000-10 mb)(Atias of Climatic Pressure Charts of the So uthern Hemi- -
sphere (1000-10 mb)), P4oscow, 1972. _
5. Kanter, Te. A., ISSLEDOVANIYE NEKOTORYKH SVOYSTV Bp.RICIiESKO(;0 POLYA
SVOBODNOY ATMOSFERY METODOM PLOSHCHADEY I TSIRRUMPqLYARNOC-0 MODEL-
IROVAIIYA (Investigation of Some Properties of the Preas ure Field
- in the Free Atmosphere by the Areas Method and by Circumpolar Model-
ing), Saratov, Izd-vo Saratovakogo Un-ta, 1975.
6. Kats, A. L., TSIRKULYATSIYA V STRATOSFERE I MEZOSFERE (Circulation in ~
the Stratosphere and Mesosphere), Leningrad, Gidx.�ometeoi zdat, 1968.
7. Nemirovskaya, L. G., "Wind Structure i.n the Stratosphere of the Equa-
torial Zone," TRUDY GiUROMETTSENTRA S`3SR (Transslctions of the USSR
- Hydrometeorological Center), No 128, 1974. �
8. Pavlovskaya, A. t\. ,"Structure of Global Geopotential Fields in Rela-
- tion to Quasi-Ttvo--Year Cyclicity in the Equatorial Stratosphere,"
METEOROLOGIYA I GIDftOLOGIYA (Hetaorology and Hydrology), No 7, 1973.
' 9. Pogosyan, Kh. P., "Some Characteristics of Wind Cyclicity in the Equa-
torial Stratosphere,1� METEOROLOGIYA I GIDROL0GIYA, No 9, 1973.
10. SINOPZICHESKIY BYULLETEN'. SEVERNOYE POLUSHARIYE (Synoptic Bulletin. -
Northern Hemisphere), Mascow, Gidromettsentr SSSR, 1971-1975.
:
1
s
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UBC 551.510.42
MODELING OF TRAtdSBOUNDARY TRANSPORT OF SULFUR DIOXIDE WITH ALLOWANCE FOR
VERTICAL M'JVIIMENTS
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 42-49
[Article by Candidate of Physical and Mathematical Sciences N. S. Vel'ti-
shcheva, USSR Iiydrometeorological Scientific Research Center, submitted
for puhlication 25 January 1980]
[Text] Ab.stract: This paper presents the results of work
_ on improvement of the model for evaluating the
- long-range transport of sulfur dioxide by means
of improvement in the approximation of boundary
conditions at the earth's surface, introduction
of a nonuniform vertical interval, and also al-
lowance for vertical movements. The author gives
the results of computation of the flux of sulfur
dioxide through elements of the boundary and its
precipitation onto the underlying surface.
A study of the transport of contaminating substances for distances of 1,5U0-
2,000 km is important for determining the contribution of different coun-
tries to contamination of the air.basin. Experimental methods for determin-
ing the fluxes of impurity through boundaries are costly. Accordingly, dur-
ing recent years there has been development of a combined approach matching -
the use of different models and observation systems [8].
The development of models for evalua.ting the transport of impurity pursues
two objectives. First, using them, compute the quantity of matter transport-
ed acroas the boundaries of different countries. The second objective is a
determination of the quantity of substance precipitated onto the underlying
surface. The collection of this information is necessary for evaluating the
degree of the effect of contaminating substances on the environment. ~
_ A three-dimensional model for computing the concentration of sulfur dioxide
- during its propagation over a distance of 1,500-2,000 km has been formulat-
ed at the USSR Hydrometeorological Center (1976) [2]. The choice of a dif-
. ference acheme and an investigation of its stability for solution of the
three-dimenaional equation for the tranaport of mass of impurity were
48
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deacrihed in [3]. In this investigation emphasis is on improvement of the _
model [2] by an improvement in the approximation of houndary conditions at
the earth's surface, introduction of a nonunifo rm vertical interval, and
also development of a variant of a model with vertical movements taken in-
to account. In addition, we give an algorithm for computing the flux of
contaminating substances across the elements of a boundary and their precip-
itation onto the underlying surface.
The propagation of an impurity in the atmosphere will be described by the
three-dimensional equation
.
aq aa dQ 24 6:~Q 64
or v ay waz = KS dX: ~ 77l (1)
1
+ a: (K= dz ~-'R-s+ F,
where q is the volumetric concentration of 502; u, v, w are the components
of wind velocity; KS, KZ are the coefficients of horizontal and vertical
diffusion; R and S are the S02 losses as a result of chemical reactions
and washing out by precipitation, F is the source.
In o rder to solve equation (1) we selected the following boundary and ini-
tial conditions:
K=az-~q-0 atz=0,
(2) _
q = 0 atz=H,
where p is a parameter determining the interaction between the impurity and
_ the underlying sur�ace; H is the height of the mixing layer, which was as-
sumed to be constant for the entire region and equal to 2 km for the com- -
puted cases. A zero concentration was stipulated at the lateral boundar- - ies.
9(Y, y, z, 0) =0 (3)
for model computations and
q(Y, y, z. 0) = qo (Y, J, z) (4)
for comparison of the results of computations and observational data, where
q0(x, y, z) is the mean daily SO2 concentration during the preceding 24-hour
period.
Befo re proceeding to an exposition of the res ults of numerical experiments ~
we will discuss two matters related to representation of equation (1) and
checking of the conservative character of the scheme.
- The equation for the transport of a mass of impurity was reduced to dimen-
sionless form using the following expressions for its coefficients:
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~ V
x- x,5 L: z= z~; r7t % lt = 116 V: v= Z'4 V: i11 ='(1'6 m~
t=fb - L, h=Ks.b~.V; K,=flz.6 L; S= K;,blf ~5~
v ~ s m= m
j 6= dimensionlessJ where L is the horizontal scale, which was stipulated
at 106 m; V is the ctiaracteristic velocity (10 m/sec); m is a scale factor
determining the relationship between the horizontal and vertical scales
(S x 102); the sufiscript "6" indicai:es dimensiorLless values.
In making the numerical experiments the diffErence scheme was checked for
the conservation of mass. The balance of mass was computed in the entire
volume in each time interval on the asaumption that the impurity is intro-
duced by a single source situated at an adequate distance from the lateral ~
houndaries in order to exclude their influence and also with 0.
v v .
q l~ t~-
~ t't,t=~ ql) + ~\Rl+'Si~'~t- (K, dZ~ f!
(b)
+ 1: a (w9 )t ~ t+
^v
where N is the ntunber of points in the considered redgion; the last two
tQrms on the right-hand side of expression (6) designate the loss of mass
tfirough the upper hoimdary (G) as a result of diffusion and vertical move-
ments. For a more precise evaluation of the loss of impurity through the ~
boundary the.derivatives were approximated with a second order of accuracy.

d, q 1
ds= z_ ~2 9n -5 Qn_t 4[JR-2 - Qn-3)1
d (wq) z ( 2 ('~Q)n�-t L (4E'4)n--)� (7)
\
The results of the following numerica.l experiments relate to solution of
equation (1) without allowance far vertical movements.
Model computations, using equation (1) and its dimensionless analogue, ob-
tained using expressions (5), indicated that the mass deficit the dif-
f erence between the left and right'aides of formula (6), is reduced by a
factor of 3 when using the dimensionleas form of equation (1). These re-
sults can be attributed to the faet that with a changeover to a dimension-
less analogue of equation (1) there is a decrease in. the relationship be-
tween the horizontal and vertical intervals, and aleso between the terms
of the difference equation.
Now we will examine the problem of the approximatian of boundary conditions
at the ground surface. In a preceding study [2] aq/a z in equation (2) was
approximated with the first order of accuracy by means of introduction of
a ficr.itious level, in accordance with [4]. In this case the value of the
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first elimination coefficient
- Kzf ~ z - 3i2
a.- ~=,~s=, ~,2
to a high degree wasdependent on the relationship between KZ and With
a0-f 1 the solution became little stahle. In order Co improve the approx-
imation use was made of a principle proposed by A. A. Samarskiy [7] and
based oa expansion of a q/ a z into a Taylor seriea at a boundary point
and its determination througFL tfie solved equation. Then the first elim:Ln-
ation coefficients assume the following form:
k j
n� K:+01 zT26 z2/9t' (8)
(K:9i-Kz4n-qo3 4 zTqo2a t=;~t)
60 k: +Piz+ 2.1z=111t ,
where L1 z and At are time and height intervals and the subscripts on q
indicate the level at which this value was selected. In such an approxim-
ation method the question ~;rises: what is the value of the sought-for func-
tion at the level adjacent to the boundaYy which should be used in comp~~3
..ing ap and bp? We teated two variants: I) at z= 1-- use the value qn~'
with a correction for scattering by diffusion; 2) at z a 1-- take the val-
ue qn. Model computations indicated that the uae of qn at z= 1 gives a
bent~~3 value of the deficit of mass of impurity (3x) in comparison with `
q+ , at which the mass deficit is 11%.
LuE to the f act that most of the sources are situated in the Iower part of
the boundary layer, a more detailed allowance for the structure of this
layer is desirable. A solution ef this problEm was carried out in two di-
rections:
the initial algorithm, using a uniform vertical interval, was modified
by the introduction of an additional level (150 m) in the lower 300 m;
the change in the coefficient of vertical diffusion with altitude was -
taken into account.
The introduction of an additional level considerably reduces the deficit
uf impurity mass: whereas the use of a large interval in the lower part
of the atmosphere gave an excess of the renaining mass by 17% in compar-
ison with that introduced, when the grid was made finer in a downward
direction the mass deficit was reduced to 2-3%. The sharp decrease in mass -
imbalance of the impurity observed with the introduction of the addition-
al level is attributable to the fact that this ].evel is introduced in a
- layer of a considerable concentration gradient (the source in our case
_ was stipulatsd at a height of 300 m) . As was demonstrated in [3], the -
closer the initial dispersion ls to the selected grid interval, tiie lesser
is the value of the residual term with the replacement of the differential
equation by a difference equation. The concentration Zevels in the entire
layer in the case of a nonuniform interval were aomewhat lower and above
the source its sharper decrease was observed.
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6
The inclusion in the model of a variable with height KZ (in our case Kz in-
. creases to 300 m and 3ecreasea uputard) leada to a ayatesnatic exceas (up to
's 9%) in the mass of matter rematning in the conaidered volumP comparison
with the mass introduced. The reason for tfiis becomes und.!�._standable xf we
represent the term descrihing vertical diffusion as

a /Kz ay ) axz aq , _ K= _a'_q
_
oz - as~ '
d l a v
When KZ changes with height, the vertical transport va7.ue is determined by
both terms, and in the last analysia is dependent on the Kz and q profiles.
It hae been estahlished theoretically and exper imentally [6, 8] that both
functions decrease with height, except for the lower 200-300 m, and there-
fore thP contribution <
will almost always he positive. In other words, the introduction of the var-
iahle KZ into the equation for the transport of masn will lead to a nonsta-
tionary solution. With respect to Che concentration profile, we note that
with a constant Kz there will be slower mixing in the layer where the source
is situated and therefore a smoother change in q with height than with var-
iable KZ.
Now we will proceed to the formulation of a difference scheme which takes
vertical movements into account. The inclusion of w in the model for the
transport of contaminating substancea involves two difficu].ties. One of
these is determined by the complexity of computation of the vertical velo-
city components. The second is associated with the introduction of the term
a Q/az into the model. The considerable anisotropicity of the process in
horizontal and vertical directions requires the creation of a stable numer-
ical scheme which would be econorlical.
We computed the transport of impurity for a distance of 1,500-2,000 km on
the basis of the real wind field at the standard isobaric levels. Accord-
ingly, as a first approximation it was decided that vertical movements
_ would be computed from the continuity equation, using the same information.
In order to increase accuracy and obtain a greater amoothness the deriva-
tives were approximated with a second order of accuracy using a six-point
- scheme within the region
d 1 1
dx 2 h ~ (?i. t+t - 4 (4/-1. W - T1-i. r_ i ) -
(9)
- t
~ (.?i-I-i. !-Ft 'FI+1, I-t)b
and using a three-point scheme at the boundary. For example, for i= 0(the
~ x coordinate) the derivativp was computed using the formula -
'd h ~2 o : (10,)
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Vertical movements were determined using layers with a thickness of 500 m.
A qualitative evaluation demonstrated a satisfactory agi^Iment of the
computed fields of vertical movements with the nature of the pressure
field.
A nimmerical scheme for the solution of equation (1) with the conditions
(2)-(3) or (4) belongs to the splitting method. The principle for its con-
struction is that the operators for each direction of coordinates are re-
_ duced to the upper time level and are represented in the form of a product.
At the lower time level we select an expreasion satisfying the approxitna-
tions of the differential equation and stability. An important difference
in our scheme is in the metfiod for obtaining the products af the operators.
Adhering to thE idea expressed by Ye. G. D'yakonov in [5], the product of
- the operators present on the right aide of the difference scheme is
~ (E - z 2-1k +
n
- S=1
3
~-t~,,, .1,�;n+t(F-~'-S),
s=1
where 6q . - d? 9 .
- s s dxs s~ K.~ OX., ,
s
s= 1, 2, 3; E is a unit operator, realized in the Xirs` time interval.
However, taking into account�the great difference in the order of the ad-
- vective transport terms and the scattering by diffusion [2], the operators
describing advection were solved alternately in all the intermediate inter- vals, and diffusion, the gains and losses were included only in unit time
intervals. Taking what has been said into account, the acheme for realiz-
ing (11) can be written in the form
3 3
~ r
(E + A,) /
c~"-`~13 = g. I E - , -iS) t ~ _1se't t (F-R-$), ~
S =I ~ S=I (12)
2 ~
~E rt t
E -E-
~
A solution of system (12) was obtained by the elimination method. On the
basis of the results descrihed above, we introduced an additional level in
the lower layer and w a q/ a z was approximated using the expression
d9 2 ~ wi-Iwtl x1+i-zi -
d " z;_ 1- z;_ 1 1 2 zl - s;_ 1 ~9~- i- 9i) (13)
+ wr+lw"
2 z,+,-z; (9i-q;_1)l.
J
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_ The same as the scheme without vert.ical movements, conservancy was deter-
mined by expression (6).
Numerical experiments cqrried out with a different number of levels select-
ed at different heights indicated that the use of seven levels in compar-
ison with five considerably improves the mass deficit (1%), whereas with
Eive computation levels the deficit is 12%.
It is interesting to evaluate the influence of vertical movements on the
vertical distribution of the concentration. It was found that with the
introduction of vertical movements there is a more uniform distribution of
the impurity than without them. In addition, the introduction of vertical
velocities reduces the time for stabilizing the solution, that is, with
the introduction of w the solution becomes stationary 36 hours after the
initial moment, whereas when they are absent a complete stabilization of
the solution does not occur even after 48 hours.
aI
b) .
~
M ~
~z ~ � ~ i
.o nJ
; _ ,
~J3 1 ^1,0~ ~
~fZ.. v . I
,
O ~�SI~~}�
I . ~
Fig. 1. Computed mean daily concentration of sulfur dioxide ( g/m3) at
ground surface (1) with allowance for vertical movements (a) ~and without
allowance for vertical movements (b) and precipitation of sulfur dioxide
onto surface (g/(m2�day)) (2) on 15 Septemher 1974. The observed concentra-
. tion values are indicated in circles.
Figure 1 gives the computed concentration fields with and without allowance
for vertical movements. As can be seen from a comparison with the measured
values, a model with.w hetter tiescribes the concentration field than with-
out w. Appreciable difference: are observed in southern Scandinavia, in
northern France and in southern England.
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In solution of the prohlem of propagation of an impurity an important ques-
_ tion is the form of representation of S02 effluent. In further developing
- the model we used data on S02 effluent ob.tained as a result of implementa-
tion of the "Joint Program for Evaluating the Diatant Transport Qf Air Con-
taminants in Europe" [8] and representing the S02 flux (tons/(km~�year))
from an area of 127 x 127 km2. In the case of one-dimensional models the
conversion'from the flux to the influx of S02 (ftg/(0�teour) is accomplish-
ed hy normalization to the height of the considered layer. This assumption
is not correct from the point of view of experimental reliability [8]. The
entry of S02 into the atmosphere occurs for the most part through stacks
whose height is from 40 to 150 m and the effective height of the effluent
[1] is in the range 100-600 m.
lde made the assumption that the ejection of S02 from a definite area corres-
ponds to the total influx to the layer into which the contaminating sub-
stances enter. For conversion from the flux of impurity to the influx we
introduced the function F= - d Q/ a z, which was computed by layers. Such
a representation can be used in a more realistic deacription of the vex-
tical nonuniformity of effluent.
The influence of different stipulation of the S02 discharge on the distrib-
ution and degree of the surface concentration was evaluated using a vari-
ant of the model with the introduction of real effluent and with stipula-
tion of the initial concentration at the earth in the territory of Eurasia.
The concentration fields were computed using the real wind for a 48-hour
period and were compared with the measured S02 levels in the European net-
work of stations. Three experiments were computed: 1) the S02 mass was in-
troduced into a 1,000-m layer and uniformly distributed vertically; 2) the
S02 influx to a layer with a thickness of 400 m was stipulated in the form
a Qia z and was introduced at the level 500 m; 3) an experiment similar to
the second, but the S02 mass was nonuniformly distributed in the 625-m lay-
er (in 250 m-- 20%, in 500 m-- 80%). An analysis of the results indicated
that the distribution of centers of high concentration, like its value, co-
incide more witti the real data when the sources are described by the third
method (Fig. 1).
= The precipitation of S02 onto the underlying surface was determined by time
integration of the flux at the ground, determined from condition (2). The
quantity of S02 in mg/m2 in 48 hours is shown in Fig. lb. We note the fact
- that although the concentration levels in regions remote from large indus-
trial centers (for example, Scandinavia) are small, the precipitation of
S07 here is close to the quantities observed over central Europe.
Finally, the SOZ flux across elements of the boundary was computed using the
formula
Q= qn. : Vn, z COS (1), /l.~i`
~ ~
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where qn and Vn~Z are the concentration and velocity at the center of
an area d~th sides equal to Che length of an element of the houndary and
the vertical interval, ohtained b.y means of interpolation from the near-
est points of grid intersection; pC is the angle between the direction of
the normal to an element of the Uoundary and the extension of the vector
determining the wind direction.
-zoo 0 0 -100 - 0~7
1 3 W U za
-oo
3
so
3r0
~ E
B 1000
0 2 f ~ . 10 12 14 16 16 10 Ii Tv
Fig. 2. Vertical time section of fluxes (W westerly, E-- easterly) of
sulfur dioxide Chrough segment of weatern houndary of USSR observed on 13-
14 Septemher 1974.
Figure 2 shows a vertical time section of impurity fluxes (in kg/hour)
across a segment of the western boundary of the USSR (from Kaliningrad to
the Gulf of Riga) as observed on 13-14 September 1974. We should note the
considerable variability of the fluxes both vertically and with time. The
latter circumstance is particularly important in computing Che quantity of
matter transported across the boundaries of individual countries.
BIBLIOGRAPHY
1. Berlyand, M. Ye., SOVREMENNYYE PROBLEMY ATMOSFERNOY DIFFUZII I
ZAGRYAZNENIYA ATMOSFERY (Modern Problems in Atmospheric Diffusion and
_ Atmospheric Contamination), Leningrad, Gidrometeoizdat, 1975.
2. Vel'tishcheva, N. S., "Numerical Model of Distant Transport of Sulfur
Dioxide," METEOROLOGIYA I GIDROLOGIYA (Meteorology and Hydrology), No
Q, 1977.
3. Vel'tishcheva, N. S., "Numerical Solution of the Turbulent Diffusion
Equation in the Field of a Variable Wind," TRUDY GIDROMETTSENTRA SSSR
(xransactions of the USSR Hydrometeorological Center), No 139, 1974.
4. Godunov, S. K., Ryahen'kiy, V. S., WEDENIYE V TEORIYU RAZNOSTNYKH
SKHEM (Introduction to rhe Theory of Difference Schemes), Moscow, Fiz-
matgiz, 1962.
5. D'yakonov, Ye. G., "Difference Schemes With a Splitting Operator for
General Second-Degree Paraholic Equations With Variable Coefficients,"
ZHURNAL yYCHISLITEL'NOY MATEMATIKI I MATEMATICHESKOY FIZIKI (Journal
of Computational=Mathematica and Mathematical Physics), Vol 4, No 2,
1464.
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6. Zilitinkevich, S. S., DINAMIKA POGRANZCHNOGO SLOYA ATMOSFERY (Dynam-
ics of the Atmospheric Boundary Layer), Leningrad, Gidrometeoizdat,
1974.
7. Samarskiy, A. A., WEDENIYE V TEORIYU RAZNOSTNYKH SKHEM (Introduction
into the Theory of Difference Schemes), Moacow, Fizmatgiz, 1971.
8. THE OECD PROGRAMME ON LONG-RANGE TRANSPORT OF AIR POLLUTANTS, OECD,,
Paris, 1977.
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UDC 551.(583+-521.14+524.34)
EFFECT OF CHANGE IN ALBEDO UF THE EARTH'S SURFACE ON THE EARTH'S
THERMAL REGIME
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 50-56
[Article by Doctor of Geographical Sciences N. A. Yefimova, State Hydro-
logical Inatitute, submitted for publication 15 January 19801
[Text] Abstract: The author evaluates the influence
of the feedback between changes in mean glo-
bal air temperature and albedo of the earth's
surface (including changes in albedo with a
change in vegetation cover) for conditions of
warming of climate ir. the example of the epoch
of the Early Pliocene and for conditions of
cooling during the last glaciation.
Introduction. In a study of climatic changes with the use of semi-empir-
ical models it is necessary to take into account the feedbacks between
the thermal regime of the atmosphere and outgoing radiation, air humidity
and albedo of the earth's surface. It must be remembered that the influ-
ence of the first two factors on the therma.l regime is manifeated in all
casea, whereas the third is manifested when there are more or lesa pro-
longed climatic changes.
- Changes in the albedo of the earth's surface when there are variations
in the thermal regime occur as a result of an increase or a decrease in
- the area of the pnlar ice, snow covert and also due to changes in the
types of vegetatian on the continente.
An allocaance for feedback between the thermal regime and the snow-ice
cover was introduced in the studies of M. I. Budyko (1968) and Sellers
(1969).
In the studies of Manabe and Wetherald (1975, 1979) the feedback between the
the thermal regime and changes in snow cover on the continents and sea ice
was taken into account separately.
Cess (1978) brought attention to the need for allowance for the feedback
between the thermal regime and the change in the albedo of the vegetation
cover on the continents. An evaltiation of Che change in albedo of the
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vegetation cover and its influence on air temperature was made by Cess
in the example of the epoch of the last glaciation on the basis of data
from CLIMAP (1976) and Gates (1916).
In this study an attempt is made to evaluate the overall effect of aTl the
components of the feedback betwzen change in the mean globai air tempera-
ture and albedo of the earth's surface. These evaluations were made for
conditions of cZimatic warming in the example of the epoch of the'Early
Pliocene (about 6 million years ago) and for the conditions of cooling
during the last glaciation (about 18,000-20,000 years ago). The results
are compared with paleoclimatic data and the results of computations
using a climatic model.
Warm climate, Early Pliocene. As the initial data for determining albedo
of the surface of the continents under the conditione of the warm climate
of the Early Pliocene we used the maps prepared by V. M. Sinitayn (1965,
1967) showing the distribution of the vegetation cover, air temperatures
of the warmest and coldes` months, and the annual sums of precipitation
- over the territory of Eurasia. On the basis of these data, with modern
climatic analogues and types of vagetation into account, it was possible
to reconstruct the annual variation of temperature and the characteristics
of the snow cover in the high latitudes. Then, using a known method (Budy-
ko, 1971; Yefimova, 1977), we determined the mean monthly and annual al-
bedo values for the territory of Eurasia and the northern half of Africa.
The mean annual albedo val.ues obtain$d in this way for the latitudinal
zones of the mentioned continents were deemed characteristic for the lat-
itudinal zones of the continents in the aorthern hemisphere as a whole
by analogy with the circumstance that in the modern epoch the mean albedo
values for the latitudinal zones of Eurasia are extremely close to those
for the northern hemisphere.
The mean annual albedo values for the continents in the present epoch were
obtained on the basis of materials used in constructing maps of the heat
- balance components (Budyko, et al., 1978; Mukhenberg, 190). When determin-
ing the albedo of the continents for the modern epoch an allowance was made
for the real areas of forested expanses, meadows and agricultural fields.
According to paleoclimatic data, the climate of the Early Pliocene was
warmer and moister in comparison with the modern epoch. In the middle and
high latitudes of Eurasia and North America the vegetation cover was char-
acterized by a richer species compoaition and the forests occupied exten-
sive terrizories extending to the northern shores of the continents and
to the south of the boundary of the present-day forested zone.
The snow cover was situated coneiderably to the north and was briefer than
at the present time. As is well known, the albedo of the forests both dur-
ing the growing season and in the presence of a anow cover is less than the
' albedo of tundra, grassy vegetation and thin forests. Accordingly, over a
great part of the surface of the continenta,the aYbedo was less than ia
the case at the present time.
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The mean albedo of the land surface in the northern hemiaphere in the Plio-
cene was 0.060 less than the gresent-day value (the difference in albedo
of the land in the northern hemisphere between the present:-day epoch and
the Pliocene was oUtained as the mean weighted value of ttie differences in
the albedos of the latitudinal zones, taking into account the solar radia-
tion levels incident on the earth's surface).
Taking into account the relationship of the areas of the land and ocean,
the mean difference in albedos between the present epoch and the Pliacene
for the en[ire surface of the northern hemisphere was 0.024.
In order to evaluate the influence of change in albedo of the surface of
the continents on the thermal _egime we determined the difference in al-
bedo of the earth - atmosphere system in the considered egochs ('601-s).
It was obtained by summing the differences in albedo of the earth's surface
- of the latitudinal zones (QoC~,..., da n), taking into account the influence _
exerted on planetary a'ibedo by Rayleigh scattering and cloud cover (td) in
the form proposed by Cess (1978):
Aa'S - Aa' (0,69 - 0,52 N),
where Qoc's is the difference in zonal albedo of the earth - atmosphere
system.
The mean zonal differences in a].bedo are given in the table. The mean dif-
ference in albedos of the earth - atmosphere system for the entire north-
ern hemisphere between the present epoch and the Early Pliocene was 0.0104
(in the averaging allowance was made for the dependence of receipts of
solar radiation at the upper boundary of the atmosphere on latitude). This
value was governed by the change in albedo of the continents as a result
of change in the types of vegetation and snow cover. Some of the differ-
ence in albedo caused by differences in the vegetation cover was obtained
from a comparison of present-day data on albedo of the surface of the con-
tinents during the summer months wich the albedo in the Pliocene under
conditions of absence of a snow cover over the entire considered terri-
tory. This part of the difference in albedos was equal to 0.0040; the re-
ma3.ning part 0.0064 was related to differences in the distribution
and duration of presence of snow cover 3uring these epochs.
It is known from paleogeographic inveatigations that at the end of the
Tertiary the area of the sea ice in the arctic basin was considerably less
than today. In accordance with the data of V. M. Sinitsyn on the thermal
regime of the cold season in the northern part of Eurasia it can be assum-
ed that in the Early PLiocene the boundary of the sea polar ice ran approx-
imately 15� of latitude to the nortli in comparison with the present time.
An evaluation of chaage in albedo of the earth - atmosphere system due to
this contraction of the area of sea ice indicated that it decreased by
0.0035. Thus, the total- decrease in albedo of the earth - atmosphere sys-
tem during the Pliocene was 0.0139, includlng 0.0104 as a result of the
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change in the albedo of the continents 3nd 0.0035 due to a decrease in the
area of the sea ice. The contribution to the total. change in albedo from
- the c.hange in albedo of the vegetation cover was substanCial, constituting
about 30% of the total change in albedo of the earth - atmosphere syatem.
tiie note that this evaluation applies to the northern hemisphere. For the
earth as a whole tiie general change in the albedo of the earth - atmoapheYe
increased somewhat due to the great chang6 in area of the polar ice and de--
creased due to the lesser ar2a of the conCinents in the southern hemi-
sphere; the corresponding albedo change was O.Oi02 (0.0050 due to the de-
I ,:rease in the area of sea ice, 0.0052 as a result of decrease in the snow
cuver and change in vegetation). The contribution of the difference in the
state of the vegetation cover to the changE in albedo for the earth as a
whoie was less than the evaluation ci*_ed above, constituting about 20%.
Cold climate. Epoch of the last glaciation uf the Pleiatocene. In deter-
- mining the alhedo of the continents in the epoch of the last glaciation
of the I'leistocene (ahout 18,000-20,000 yaars ago) we used CLIMAP data
(1476), the paleogeographic generalizations of A. A. Velichko (1973),
I. T.Avenarius, M. V. Muratova, et al. (1978) and others. In these inves-
tigations it was established that under conditions of a cold and in many
regions of more arid climate of the glacial period the forest vegetation
on the continents was replaced in the high latitudes by tundras, in the
temperate latitudes by tundra steppes and thin forest, in the lower lati-
� tudes hy savannas and steppes. There was a conaiderable broadening of
zones of dry steppes, semideserts and deserts. In accordance with this
change in the vegetation cover, and also in connection with the occurrence
- of continental glaciation in the high and temperate latitudes there was an
increase in the albedo of the surface of the continents. _
~ Taking these changes into account, we determined the mean annual albedo
values and the difference in albedo of the surface of the continents in
I the glacial period and the modern epoch for the earth's latitudinal zones.
~ The mean difference in the albedo of the land surface during the period
, of glaciation and the present epoch (obtained by averaging the differences
in the albedos of the land by 10� latitudinal zones, with allowance for
ttieir areas and the distribution of solar radiation) was 0.083.
Taking into account the ratio of the areas of the land and ocean, we com-
puted the mean zonal differences and then the total difference in albedo
of the earth's surface caused by the change in albedo of the continents
during the glacial period in comparison with the present epoch, which was
0.024.
Taking into account ttie already considered dependence of planetary albedo
on cloud cover and the receipts of solar radiation we computed the mean
zonal (see table) and total mean difference in the albedos of the earth -
atmosphere system during the glacial period, caused by an increase in the
albedo of the continents as a result of change in the vegetation cover and
the presence of continental glaciation. This value was found to be equal
61
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Mean Zonal Albedo Differences
1 w
90-80 1 80-70 1 70-60 1 60-50
2 CoapeMeHxaa 3noxa -
- CeeepHOe
4 tiunywapHe I 0,0575 0,1416 0,0799 0,0288
3 CospeMexHaa 9noxa -
CeeepHOe
4 nonywap;ie
0
-0,0958
-0,1343
-0,0794
5 IOH:HOe
nonyuiapNe
0
0
-0.1416
-0.1469
to 0.0105. It was found that the contribution of the increase in continen-
tal glaciation to the change in albedo of the earth - atmoephere system is
0.0041, whereas the r emaining part - 0.0064 - is attributable to the
change in albedo due to a change in snow cover and vegetation (0.0030 and
0.0034 respectively).
An evaluation of the influence of an increase in the area of polar sea ice
on change in albedo during the glaciation period indicated that because
of this the albedo of the earth - atmnsphere syetem increased by 0.0110 in
comparison with the present epoch. Moat of this albedo difference (0.0090)
is attributable to the extenaive occurrence of a zonz of sea ice in the
southern hemisphere. Thus, the total increase in albedo vf the earth - at-
mosphere system in the glacial period in comparison with the present epoch
was 0.0215; the contribution of change in the albedo of vegetation (0.0034)
to the total change in the planetary albedo was about 15%.
In astudy by Cess (1978) the change in the albedo of the vegetation cover
in the glacial period is about 0.01 or 40% of the total change in the
planetary albedo, which also was somewhat greater (0.025) than that ob-
tained in our study. These differences are probably partially attributable
to the fact that Cess determined the differences in albedo for July, where-
as here we have made computations of the mean annual values. Another rea-
son for the indicated difference is the noncoincidence of the data used on
the albedo of the surface of the continents. We feel that the data of Posey
and Clapp (1964) on the albedo of the continents in July for the present
epoch, which Gates and Sess used in the computations, are considerably too
low. For example, in large territories occupied by different types of vege-
tation - from forests and thin �orests to steppea, praries and savannas,
they adopted an albedo of 0.07-0.15, whereas using the observational data
which we employed in constructing the maps the albedo of these types of
vegetation is from 0.12 to 0.22.
EffPCt of f eedback of albedo changea on thermal regime. The changes in al-
bedo of the earth - atmosphere syetem in the Early Pliccene and during the
last glaciation make it possible to evaluate the changes in mcan global air
62
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EartYi - Atmosphere System (AoC'g)
30HW, epaO
50�-40
40-30 I
30-20 I
20-10
10-0
6 N.7H. .1CT H238A
I 0,0155 I 0,0068 I 0,0036 I
0.0021 I
O,pppg
18-20 Tuc. oer ttaaa,q
-0,0451 -0,0033 -0,0008
-0,0021 I
-0,0044
-0,0047 -0,0058 -0,0030
-0,0030 I
-0,0026
KEY :
l. Latitudinal zones, degrees
2. Modern epoch 6 million years ago
3. Modern epoch 18,000-20,000
years ago
4. Northern hemisphere
5. Southern hemisphere
temperature at the earth's surface caused by this factor. Assuming that
with a change in planetary albedo hy 0.01 the global temperature changed
by 2.10C (Budykfl, 1974, 1979) we find that in the Pliocene the change in
the mean annual air temperature at the earth's surface as a result of
change in the alhedo of the earth - atmosphere system was about 2.1�C,
including 0.4�C due to a change in the albedo of the vegetation cover,
0.7�C due to changes in the snow cover and 1� due to change in the
area of sea ice. Taking into account that the approximately doubled con-
tent of carbon dioxide in the atmosphere in this epoch leads to a temper-
ature increase by approximately 2.5�C (Budyko, 1972, 1977), we find that
the total increase in air temperature in the Early Pliocene in comparison
with the modern epoch is about 4.6�C.
The increase in air temperature in the northern hemisphere (4.6�C) obtained
for the Early Pliocene is very close to the similar value determined from
the paleoclimatic maps prepared by V. M. Sinitsyn (4.8�C).
During the period of the last glaciation the decrease in air temperature
as a result of the increase in planetary albedo, in accordance with the
data cited above, was 4.5�C, including by 0.7�C due to the change in the
albedo of vegetation, by 0.6�C due to change in the snow cover, by
0.9�C due to an increase in continental glaciation and by 2.3�C
due to an increase in the area of polar sea ice, especially in the 5outh-
ern hemisphere. The difference in the mean global annual temperatures dur-
ing the glacial perio d and in the modern epoch (4.5�C) found here is close
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to the values obtaiaed for July by Gates (1976) 4.90C and by Cess
_ (1978) - about 5�C.
It is obvious from the materials cited here that in the study of climatic
changes transpiring over long time intervals there is a need to take into
account all the principal factors exerting an influence on the albedo
of the earth's surface, including the state of the vegetation cover.
Fig. 1. Dependence of change in albedo of the earth - atmosphere system
Qa(s on change in glohal temperature AT. 1) Pliocene - modern epoch, 2)
last glaciatiori - modern epoch.
Infl-uence of changes in air temperature on planetary albedo. Figure 1 il-
lustrates the dependence of planetary albedo on changes in mean global
- air temperature at the earth's surface. In this figure ao4s denotes the
change in albedo of the earth - atmosphere system in comparison with the
modern value, A T is the difference in mean air temperature relative to
the modern epoch, determined independently on the basis of paleoclimatic
data and computations using climatic models.
We note that the accuracy of the data used in constructing this graph is
limited, in particular, due to the fallure to take into account the in-
fluence exerted on planetary albedo by changes in the cloud cover.
It is evident that the feedback between air tempera ture and albedo of the
earth's surface considerably intensifies the sensitivity of the thermal
- regime to variations in the heat influx. Takiag into account the depen-
dence of temperature of the lower air layer on albedo of the earth - atmo-
' sphere system cited above, it can be concluded that the relationship rep-
- resented in Fig. 1 doubles the sensitivity of the thermal regime to vari-
ations of the heat influx with an increase in the concentration of carbon
dioxide in the atmosphere in the Pliocene.
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A still greater role is played by the change in albedo in development of
cooling during the last glaciation. Assuming that this glaciation was
caused by the redistribution of the solar energy arriving during the warm
and cold seasons of the year at different latitudes, we can conclude
that change in the albedo of the earth's surface was of decisive impor-
tance for the mentioned cooling.
Although the influence of changes in the albedo of the earth's surface
is fully manifested for prolonged climatic variations occurring during
time intervals during which continental ice covers are formed or are de- -
_ stroyed, i t is also of importance for relatively short cl imatic changes
transpiring over the course of decades and centuries which lead to a
change in the area of sea ice, snow cover and vegetation on the contin-
ents.
BIBLIOGRAPHY
l. Avenarius, I. G., Muratova, M. V., Spasskaya, I. I., PALEOGEOGRAFIYA
SEVERNOY YEVRAZII V POZDNEM PLEYSTOTSENE, GOLOTSENE I GEOGRAFICHESKIY
_ PROGNOZ (Paleogeography uf Northern Eurasia and the Late Fleistocene,
Holocene and Geographic Prediction), Moscow, Nauka, 1978.
2. Budyko, M. I. ,"Or igin of the Glacial Epochs," METEOROLOGIYA I GIDRU-
, LOGIYA (Meteorolody and Hydrology), No 11, 1968.
3. Budyko, M. I., KLIMAT I ZHIZN' (Climate and Life), Leningrad, Gidro-
meteoizdat, 1971.
4. Budyko, M. I., VLIYANIYF. CHE-LOVEKA NA KLIMAT (Man's Influence on Cli-
mate), Leningrad, Gidrometeoiadat, 1972.
5. Budyko, M. I., IZMENF.NIYE KLIMATA (Climatic Change), Leningrad, Gidro-
meteoizdat, 1974.
6. Budyko, M. I. SOVREPiF.N110YE IZMCNENIYE KLI14ATA (Modern Change in Cli-
mate Leningrad, Gidrometeoizdat, 1977.
7. Budyko, 14. I., PROBLEMA UGLEKISLOGO GAZA (The Carbon Dioxide Problem),
Leningrad, Gl.drometeoizdat, 1979.
8. Budyko, M. I., et al., TEPLOVOY BAI,ANS ZEMLI (The Earth's Heat Bal-
ance), Leningra d, Gidrometeoizdat, 1978.
9. Velichko, A. A., PRIRODAiYY PROTSESS V FLEYSTOTSENE (Natural Process in
the Pleistocene), Moscow, Nauka, 1973.
10. Yef imova, N. A., RADIATSTONNYYE FAKTORY PRODUKTIVNOSTI RASTITEL'NOGO
POKROVA (Ra diation Factors in Productivity of the Vegetation Cover),
Leningrad, Gidrometeoizdat, 1977.
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11. Mukhenberg, V. V., "Albedo of the Earth's Solid Surface," TRUDY GGO
(Transactions of the Mairi Geophysical Observatory), No 193, 1967.
12. Sinitsyn, V. M., DREVNIYE KLIMATY YEVRAZII, CH. l. PALEOGEN I NEOGEN
(Ancient Climates of Eurasia,.Part 1. Paleogene and Neogene), Lenin-
grgd, Izd-vo LGU, 1965.
13. Sinitsyn, V. M., WEDENIYE V PALEOKLIMATOLOGIYU (Introduction to _
Paleoclimatology), Leningrad, Nauka, 1967.
14. "CLIMAP Proj ect Members. The Surface of the Ice-Age Earth," SCIENCE,
Vol 191, 1976.
15. Cess, R. D., "Biosphere-Albedo Feedback and Climate Modelling," J.
ATMOS. SCI., Vol 35, 1976.
16. Gaees, W. L., "A Numerical Simulation of Ice-Age Climate With a Global
General Circulation Model," J. ATMOS. SCI., Vol 33, 1976.
17. Manahe, S., Wetherald, W. T., "The Effect of Doubling the C02 Concen-
tration on the Climaee of a General Circulation Model," J. AZ'MOS. SCI.,
- Vol 32, No 2, 1975.
18. Manabe, S., Wetherald, W. T., "On the Horizontal Distribution of Cli-
mate Change Resulting from an Increase in C02 Content of the Atmo-
spfiere," Preprint, 1979.
19a Posey, J. W., Clapp, P. F., "Global Distribution of Normal Surface A1-
bedo," GE(','HYS. INTERN., Vol 4, 1964.
20. Sellers, W. D. A., "A Global Climatic Model Based on the Energy Bal-
ance of the Earth-Atmosphere System," J. APPL. METEOROL., Vol 8, No _
3, 1969.
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UDC 551.(583+521.14+524)(268/269)
DEPENDENCE OF THE ALBIDO OF POLAR ICE ON AIR TEMPERATURE
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 57-60
[Article by Candidate of GeograpMical Sciences L. A. 5trokina, State Hydro-
- log;cal Institute, submitted for publieation 15 January 1980]
(Text] Abstract: A study was made of the dependence of
the albedo of the snow-ice surface on air tem-
perature and the angle of incidence of solar
rays in regions of Arctie and Antarctic ice
cover for more precise determination of the
feedback between the thermal regime and the
area of polar ice in models of the theory of
climate.
Beginn ing with the studies of M. I. Budyko [1] and W. Sellers [12], in
most modern models of the theory of cl-imate an allowance is made for the
feedhack between air temperature and the area of the polar ice. Since with
an increase in the ice area the albedo of the earth's surface increases,
this leads to a decrease of absorbed radiation and a decrease in air tem-
perature. The inverse process occurs with a deerease in the ice area.
Since the considered feedback intensifies the fluctuations of the thermal
regime, in accordance with the adopted terminology it is considered posi-
tive.
For a correct allowance for the dependence between the thermal regime and
the area of the polar ice in models of the theory of climate it is neces-
sary to study the influence of air temperature and the angle of incidence
of the solar rays on albedo of the ice cover.
In one of the first studies devoted to this problem it was postulated that
with an increase in the area occupied by the ice cover the mean albedo of
the earth-atmosphere system in the ice cover zone changes little since a
decrease in albedo due to an increase in mean solar al�titude in the first
approximation is compensated by a change in climatic conditions in the
ice zone, iicreasing the mean albedo [2]. Later Lian and Cess [13] made
quantitative computations of the dependence of albedo of the earth-
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atmosphere system on latitude; with allowance for the influence exerted
on albedo by changes in solar altitude. However, they did not take into ac-
count the effect exerted on reflectivity of ice by thanges in the complex
of climatic conditions in connection with spreading of the ice cover. From
these computations it follows that there is a decrease in the mean albedo
of the ice zone with an increase in its extent.
Ax � _ f
3
~ ^ Bo
o ~
-5~
't'r
.
A.
90
,i
~
10 -6J
~ I. . ^
K = siupw-ice
: �
� ~ ~
.
.ov
� ow
r ~
~

M
. x.X
� 2
-4C '?0 0 Ml'C
Fig. 1. Latitudinal variation of the Fig. 2. Dependence of albedo of the
albeda of sea ice (1) and air tempera- snow-ice surface in the Arctic (1)
ture (2) in the Arctic during the Ap- and Antarctica (2) on air temper-
ril-September period. ature in the course of the polar
day.
;o
;r
JJ' _ y0 -10 0 T'C
a K r.
r,G K = snow- et
ea sJ
es
-ZO 82 87
-yO 60 BO z'
Fig. 3. Dependence of albedo of snow- Fig. 4. Change in albedo of snow-
ice surface in Aretic and Antarctica ice surface in Arctic and Antarc-
on air temperature for solar zenith tica in dependence on air tempera-
angles from 55 to 65�. ture and solar zenith angle.
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This conclusion evidently does not correspond to the conditions of a real
climate. It can be noted that with the existing differences in the ex-
tent of the Arctic and Antarctic ice covers the mean albedo of the earth-
atmosphere system, according to satellite data, is greater over Antarctic
ice, which in area exceeds the zone of arctic ice. This fact is probably
attributable to a considerable degree to the above-mentioned effect of a
change in climatic conditions, which are associated, in particular, with
the appearance of stable regions of high pressure over extensive ice
_ covers. Under such conditions cloud cover is usually limited and the al-
bedo of the earth-atmosphere system is closer to the albedo of the under-
_ lying snow surface than in the case of an overcast state of the sky [3].
In order to understand the dependence between the temperature regime and
the area of the polar ice it is first of all interesting to clarify the
relationship between the albedo of the ice surface and air temperature
on the basis of empirical materials. For this purpose we used climatic
handbooks and uanographs on the meteorological and radiation regimes of
the polar region in which most of the data are presented in the form of
charts of the mean long-term monthly ai.r temperature and the albedo of
sea ice [4, 5, 7-9, 111. From the mentioned maps of the Arctic Ocean we
read the air temperatures and albedo of the sea ice during the period of
the polar day (April-September) in the polar region and at the circles of
latitude correspondi.ng to 65, 70, 75, 80 and 85�N with a longitude in-
- terval of 5�. The mean latitudinal temperature and albedo values deter-
mined in this way for the Arctic are presented in Fig. 1 as a function of
latitude.
It can be seen that the albedo of the surface of arctic ice changes cQnsid-
erably with latitude, decreasing from the pole to the southern edge of the
floating ice by 23% (curve 1). This change in albedo corresponds to an in-
crease in the mean air temperature during the period of the polar day by
1].�C (curve 2). It ig necessary to clarify to what degree the discovered
albedo change is dependent on the thermal regime and to what extent on
the angle of incidence of the solar rays.
The presence of a dependence between air temperature and ice reflectivity
can be postulated from data presented on the graph (Fig. 2). This graph
shows the mean monthly data for albedo of the ice cover surface in the
Arctic and also data on the albedo of the snow surface in Antarctica, ob-
- tained from long-term observations at the stations Mirnyy (66�33'S, 93�O1'
E) and Vostok (78�28'S, 106�48'E), in dependence on air temperature.
In an examination of the data in Fig. 2 it must be taken into account that
the mean monthly albedo of the ice changea not oniy due to the differences
- In air temperature, but al.so as a result of changes in solar altitude, de-
creasing with an increase in these altitudes.
For a separate analysis of both dependences we found the empirical relation-
ship between the mc:an monthly albedo values for the polar ice and air tem-
perature for several 10� intervals of the values of the minimum monthly
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sular zenith angle (z), falling in tha range of zenith angles 40-90� dur-
ing the period of the polar day. Figure 3 shows one such graph, which cor-
responds to the minimum monthly values of solar zenith angle from 55 to
65�.
In this figure, as in Fig. 2, one can clearly see the correlation between
the albedo of the ice surface and the air temperature, which intensifies
considerably when the temperatures are above -10�C.
The materials in Fig. 3 and graphs similar to it for other zenith angle
intervals made it possible to evaluate the dependence between the mean
monthly albedo values and the minimum zenith angle for air temperatures
below -10�C (Fig. 4). As might be expected, it was found that with one
and the same air temper.ature with an incre8se in the soiar zenith angle
- the ice albedo values increase. However, this change in albedo is not
great. It does not exceed 4-5�L at air temperatures -20�C and below. In
the temperature region above -20�C this dependence is still weaker. For
higher air temperatures, close to 0�C, it is diff icult to establish the
dependence of ice albedo on zenith angle on the basis of empirical data
because in this case small temperature changes result in considerable
variations in the albedo values, which greatly exceed its changes caused
by differences in solar altitude.
The slight dependence of the albedo of a snow-ice surface on solar alti-
tude was also pointed out by A. A. Timerev [10]. As a result of an analy-
sis of ineasurements of albedo in the polar regions the author drew the
conclusion that within the limits of observational accuracy the change
in reflectivity of the snow-ice surface is caused by a change in the state
of the underlying surface. A definite role in the state of snow and ice
in the change of albedo was also noted in the investigations of M. S. Mar-
shunova and N. T. Chernigovskiy [4, 11]. It can be seen from the data
cited above that in the Arctic with a decrease in air temperature from
4.0 to -6.0�C, when there is a marked change in the state of the ice
cover surface, the albedo increases by approximately SOX (Figures 2, 3).
Although the nature of the dependence of albedo of the ice cover on air
temperature in the regions of both polar caps is identical, we note some
difference in the albedo values in the Arctic and Antarctica with one and
the same sir temperature values and with identical zenith angle values.
The albedo values in Antarctica are usually several percent higher than
in the Arctic, which is probably attributable to the greater dryness of
the snow, the lesser contamination and more even surface of the snow and
ice cover in comparison with the ice cover of the Arctic basin [6, 7].
The mean albedo of the surface of the snow and ice cover in the Arctic
Ocean, determined from the above-mentioned data, is 65%. It is difficult to
determine the similar value for Antarctica due to the lesser volume of ob-
servations made there. However, without queation, the mean albedo of the
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surface of the Antarctic ice cover is considerably greater than the value
cited above. Thus, in particular, the albedo value at Mirnyy station, sit-
uated at the periphery of the Antarctic glacier, during the period from
October through March is 81.4%. On the glacier plateau of Central Antarctica
the albedo is still greater.
In this connection it can be surmised that with an increase in the polar
ice covers the mean albedo of their surface increases. This favors an in-
tensif ication of the positive feedback between air temperature and the
area of the polar ice.
BIBLIOGRAPHY
1. Budyko, M. I., "On the Origin of the Glacial Epochs," METEOROLOGIYA I
GIDROLOGIYA (Meteorology and Hydrology), No 11, 1968.
2. Budyko, M. I., IZMENENIYE KLIMATA (Climatic Change), Leningrad, Gidro-
meteoizdat, 1969.
3. Budyko, M. I., "Semi-Empirical Model of the Thermal Regime of the Atmo-
sphere and Real Climate," METEOROLOGIYA I GIDROLOGIYA, No 4, 1979.
4, Marshunova, M. S., Chernigovskiy, N. T., RADIATSIONNYY REZHIM ZARUBEZH-
NOY ARKTIKI (Radiation Regime of the Foreign Arctic), Leningrad, Gidro-
meteoizdat, 1971.
5. METEOROLOGICHESKIY REZHIM ZARUBEZHNOY ARKTIKI (Meteorological Regime of
the Foreign Arctic), edited by I. M. Dolgin, Leningrad, Gidrometeoiz-
dat, 1971.
6. Romanov, A. A., "Ice Conditions for Navigation in Antarctic Waters,"
'I'RUDY AANII (Transactions of the Arctic and Antarctic Scientific Re-
search Institute), Vol 335, 1976.
7. Rtisin, N. P., METr,OROLOGICHESKIY I RADIATSIONNY.' REZHIM ANTARKTIDY
(Meteorological and Radiation Regime af Antarctica), Leningrad,
Gidrometeaizdat, 1961.
8. SPRAVOCHNIK PO IQ.IMATU ANTARKTIDY. T I. SOLNECHNAYA RADIATSIYA, RADI-
ATSIONNYY BALANS, SOLNECHNOYE SIYANIYE (Handbook of the Climate of
Antarctica. Vol I. Solar Radiation, Radiation Balance, Sunshine), Len-
ingrad, Gidrometeoj.zdat, 1976.
9. SPRAVOCHNIK PO EQ.,IMATU ANTARKTIDY. T II. TEMPERATURA VOZDUKHA, ATMO-
SFERNOYE DAVLENIYE, VETER, VLAZHNOST' VOZDUKHA, OBLACHNOST', OSADKI,
_ ATMOSFERNYYE YAVLENIYA, VIDIMOST' (Handbook on the Climate of Antarc-
tica, Pressure, Wind, Air Humidity, Cloud Cover, Precipitation, Atmo-
spheric Phenomena, Visibility), Leningrad, Gidrometeoizdat, 1977.
~
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10. Timerev, A. A., "Reflective Properties of the Underlying Surface of
the Polar Regions," TRUDY AANII (Transactions of the Arctic and Ant-
arctic Scientific Research Institute), Vol 328, 1976.
11. Chernigovskiy, N. T., Marshunova, M. S., KLIMAT SOVETSKOY ARKTIKI
(RADIATSIONNYY REZHIM) (Climate of the Soviet Arctic (Radiation Re-
gime)), Leningrad, Gidrometeoizdat, 1965.
12. Sellers, W. D., "A Global Climatic Model Based on the Energy Balance r
- of the Earth-Atmosphere System," J. APPL. METEOROL., Vol 8, No 3, 1969.
, 13. Lian, M. S., Cess, R. D., "Energy Balance Climate Models; a Reappraisal
of Ice-Albedo Feedback," J, ATMOS. SCI., Vol 34, No 7, 1977.
72
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UDC 551.509.314
SMOOTHING OF EMPIRICAL HYDROMETEORULOGICAL RELATIONSHIPS BY A CUBIC SPLINE -
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 61-67
(Article by Professor A. R. Konstantinov and N. M. Khimin, Leningrad Hydro-
_
meteorological Institute, submitted for publication 28 February 19801
[Text] Abstract: The authors examine problems in
the theory of splines applicable to an an-
alysis of hydrometeorological processes.
The article farmulates the problem of non-
linear multiple regresaion and existing
solution methods are evaluated. Splines are
regarded as a universal tool for construct-
ing nonlinear relationships between statis-
tically linked variables. Recomnendations
on the use of splines can also he useful in
an analysis of this class of problems in
- other scientific fieldsr but the effective-
ness of their use is demonstrated in stat-
istical problems of a hydrometeorological
nature.
Most hydrometeorological relationships have a nonlinear character. In these
cases the use of the multiple linear regression approach leads to substan- _
tial errors. Accordingly, researchers have been forced to seek new ana-
lytical methods. Among such methods is the "residual method" of statis-
tical analysis, suitable for any form of relationships, including nonlin-
ear relationships. Initially the relationst:ip between the selected func-
tion and the first determining argwnent is taken into account; the residual
value of the function is related to the second argument, etc. This method
has found extenaive application ahraad [4, 10, 11, 13].'During recent years _
it has also heen used in Soviet investigations [5].
In order to realize this method it is necessary to construct graphic re-
gressions of the sought-for relationships. Such a construction sometimes
to one degree or another has a subjective nature, although it is accomplish-
ed using the condition of maximizing of the closQness of the correlation
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between the values of the function for one and the same arguments, deter-
mined by experimental points and regression curves [S, 61. Some problems
in the mathematical approximation of the graphic regression curves were
examined in [6].
The method proposed in this article makes it possible ro construct the me.n--
tioned graphic relationships quite rigorously and objectively. It can also
A
have broader application for consCructing any one-dimensional relationships.
In developing the method it is assumed a priori that the relationship be-
tween the determining factor and the phenomenon is expressed by a smooth
function, whereas the experimental data can have a considerable scatter.
The construction of the smoothing function is an approximation problem.
In this study we give an algorithm for solution of this problem; its real-
ization in some hydrometeorological examples is demonstrated.
- Assume that in the segment [a, b] the grid
W,s - (Q - .Co < .C1 < . . . < �rn -bIr
is stipulated and the values yi, i= 0, 1,...,n are stipulated at thE
points xi. The yi values can be regarded as quantitative characteristics
of some process at the times xi. As an adequately general mathematical ex-
pression we use a model from [2] in the form
yl (xi) (2)
In this model the observed series is regarded as the sum of the determined
sequence [4f(xi)] and the random sequence These companents are usual-
ly computed theoretical values.
It is assumed that at least theoretically it is possible to repeat the ex-
- periment fully as many times as desired, obtaining new sets of observa-
tions. With such repetition the function W(x), called the trend, should
remain one and the same, but the random components would be different as
different realizations of a random process.
The problem of smoothing of experimental data includes the forming of the
~ function f(x), in some sense being the best approximation to the trend
_ 7~(x) in [a, b].
Splines have recently come into wide use for smoothing purposes. We wili
recall the definition of a polynomial spline. The breakdown (1) is stip-
- ulated in the segmenC ja,b]. The function Sm(x) = Sm(x, wn) is called a
polynomial spline in the breakdown wn if:
1 ) = 1 . . .
S. IxI C Pm, - ? X CI�r~, lt+S] , 1 0., , JI ,
~
Z) S. (C) ~ 0T-11 [ar bl,
where Pm is a set of polynomiala of a degree not higher than m, m> 0, but
C(k) [a,h] is a set of functions in [a,h] having a continuous k-th deriva-
tive.
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There i5 a series of approaches to solution of the smoothing problem lead-
ing to splines (see review 112]). A diatinguishing characteristic of all
these approaches is that in actuality for conatructing a smoothing func-
tion it is necessary to know the value af the standard error in measuring
~ the yi value. We will examine one of these problema, the algorithm of
whose solution is given in [14]; we will use it in the text which fol-
lows.
It is necessary to find the function f(x) by which is attained
e
min I(g) = j g" (x)' dx (3)
~
amongst all g(x)E C(2) [a,b] and satisfying the inequality
n .
8 (X) - Yt ~ S. ~ z ) (4)
t-o
fiere ayi>0 and S>0 are stipulated numbers.
In other words, among all the functions �or which the devi.ation from the
measured values with the weigtits S yi2 does not exceed a stipulated value
we seek afunction which is smoothest in the sense (3). The integral in
(3) gives a good approximation for the integral of the square of curva-
ture of the curve y= g(x). If an evaluation of the standard error of the
ordinate y is used as ~'yi, S should fall within the interval (N -(2N)1/2,
N+(2N)1/~), N= n+ 1. A solution of this problem is a cubic spline which
we r'_11 represent in the form 3
f(C)aii (x-x1)I, xI- xEx;- i. (5)
,~o
If yi is the result of a l~~boratory experiment, the 6i values in (2) for
ttie most part are governed by the errors inzroduced by the measuring appar-
atus. These errors can be considered normally distributed random values
with zero mean values and dispersions which are easy to evaluate if infor-
mation on the accuracy of the used instruments is taken into account. In
this case the 6 yi values are known and function (5), being a solution of
' problem (3), (4), serves as a good approximation to the trend 7/f(x).
~ Zde }iave a different situation in an experiment under natural conditions. In
J t}iis case the 61 values are governed by both instrumental inaccuracy and by
the influence exerted on the yi values by external factors, not taken into
account, which caci have a random character. In this case the byi values are
- unknown and the evaluation of "the parameters of the distribution of the Q i
randum values in this case is an extremely complex problem having indepen-
cient importance.
Now we will proceed to r_he prohleln of smoothing from points of view some-
what different than in the studies cited above. Regardless of the nature
of the L1i values, henceforth we will call them errors. We will assume that
the 61 errors are uncorrelated and have a zero mean value. This means that
61 form a purely random process, but the determined dependence of y on x
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is completely determined by the trend Y(x). In this case, according to
[3], the autocorrelation function p(k) of the Q i process is equal to 0
~ for all whole positive k.
Assume that r(k) is a sample autocorrelation function determined by the ex-
pression �_k
- 2: o,, - i(A, -T)
(6)
r(k)
n ~
t-o
where 0 is the sample mean value of the sequence {Q i} . In [3] it was dem-
onstrated that when the nimmher of terms in the series is sufficiently great
it is admissible to assume that r(k) is distributed in conformity to a nor-
mal law with a zero mean value and a dispereion equal to ri 1. This means
that in order for the sequence [4 ij to be conaidered a eample of a set oi
purely random numbers, r(k) must eatiefy the expreasion
JQ
_ ~r(k)~
where q is the selected significance level and uq can be obtained from a
normal distribution law table. In most practical cases the function jr(k)l
is decreasing. Accordingly, hereafter we will limit ourselves to an exam-
ination of the r(1) value, being an evaluation of the first-order autocor-
re?ation coefficient for the series (Qi, , which we will denote by rl. As
the randomness test for the {L1ilsequence we use the expression
uv ~7)
=rv�nYn
Assume that
(8)
;i- -Y-9(X), 9(x) E C(`' (a, hl.
Assume that G is a set of such g(x) for which the sequence {~i3 satisfies
- the randomness test (7), that is
I 1 1 I -
n_1
~z~_ b~ (9)
1 (ar+i -6)
i-o
~ (LI - b)~
1= o
~rq.no
- where T is the sample mean value of the series [Sil .
We will call the f(x) function best with a C(2) [a,b] approximation to
the trend V(x) of the observed yi series if f(x) minimizes the functional
(3) amongst all g(x)E G. Now the problem of smoothing of experimental data
is formulated in the following way.
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It is necessary to find the functio n f(x) with which the minimum of the
functional (3) among all g(x)E C(?) ja,b] ie attained, for which the
conditions (8), (9; are sati.sfied. In other wnrds, among all the tw.ice con-
tinuously differen*iahle functions for which the aeries of residuea (8)
can be considered a sample from a set of purely random numbers it is neces-
sary to find the smoothest in the s enae of the integral (3). - For solution of this problem we will use an algorithm for solution of prob-
lem (3), (4). Iti (4) we will assume that 8 yi =Sy, i= 0, 1,...,n and we
will introduce the parameter (2 y)2S. The inequality (4) will be writ-
ten in the form
n
1: f g' (XI) - v, 1= - Q_ (lo)
o
In accordance with the "existence and uniqueness theorem" [12], each Q cor-
responds to a unique function fQ, b eing a solution of problem (3), (10). We
will use ~p to denote a set of such values Q for which the functions fQ
satisfy coddition (9). The set of f unctions fQ corresponding to XQ will be
denoted FQ.
According to the definition of the b est approximation to the trend yr(x),
- given above, the sought-for function fp(x) minimizes the functional (3) in
the set FQ.
Sinr.e a unique fQ E F corresponds to each Q E}~, We can determine the un-
- ambiguous function q(U -
b
_ 9 (Q) = f fQ (x)2 dx' (11)
a
being, eviaently, a nonincreasing function.
It was demonstrated in [14] that there is such Q'> 0 that for all Q**Q'
the solution of problem (3), (10) is a straight line t(x), constructed
by the least squares method on the basis of observed values (xi, yi)�
We will denote hy r'1 the evaluation of the autocorrelation ceefficient,
- computed using formula (6) with k= 1, for the sequence
A, - N-; - l (xt).
[t is easy to show that r'l with a p robability not less than (1 - q) sat-
isEies the condition ri > = rq~n,
It therefore fo:Llows thzt eitlier rlC rq n and then the Itraight line (x)
is the sought-for appr.oximation co the ~rend 'Y(x) or rl > rq,n. In the
latter case }CQ is a limited set.
tiJe denote (2o = sup {Xi~} . It is evident that QO 30 cm for different h values, cm. normalized (uj) variables (j a 0.
1) curve constructed by author [9], 19, l, 3). -
- 2) trend 4f (X) � - -1) w,lXa, (a�a,. no,): 2�u,,cx,
. (rtl' rlrl' J) U_ (s,). (xw w21);
1) Ue (XI). (xy u31)�
Thus, the solution of the formulated problem ia either a straight line,
constructed hy the least squares method, or a cubic apline (5), being a ~
solution of problem (3), (10) with Q- Qo. In the latter case the solution
of the prohlem is reduced to a determination of Qp and further application ~
of the algorithm represented in [14]. On a practical basis it is neceseary
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to f:ad Q belonging to a quite small neighborhood of the QQ value. _
We wrote the program in ALGOL-60 language, formalized in the form of a
TREND procedure for realizing solution of thia particular problem.
I n order to check the quality of operation of th.e TREND procedure we carr-
ied out a great number of numerical experiments with different mssses of
values yi(i = 1,...,n) which were stipulated by expressian (i)~ where as
y% (x) we tested different s.mooth functions of the type x, x~, sin x,
cos x, eX, and n i were a realization of a random value having a zero
- mean value and distributed either uniformly in [-1, 11 or normally with a
dispersion equal to l. The Ai were generated by a computer, xi were a
x uniform breakdown of the segment [a, b], the a and b values were different
for dif ferent V(x). The experiments were carried out for n= 50, 100, 250.
The f&) function, obtained as a result uf use of the TREND procedure,
in each case Gzas very cloae to the true trend lt((x).
Figure 1 shows the result of one of the experimenta. The values 'V(x) ~
-cos x in 31, Tl n= 100, ai had a normal distribution. The dots in
the figure show the yi values and the solid curve represents the approx-
imation fp (x) to the trend 4/' (x) , obtained as a result of application of ~
the TREND procedure.
We deliberately selected as an illustration of use of the algorithm a case
when the characteristic change in the values of the trend ?/f(x) in [a,b]
is comparable to the mean square error in measuring the Vf (x) values. This
~ case is very characteristic for hyd.rometeorological processes, where quite
- often it is necessary to see{ the rel,ationship between poorly correlated
variab:l Es .
Figure 2 illustrates the application of the algorithm described above in
agrometeorological practice. The example was taken from [9].
As the next example we will demonatrate the possibility of using approxima-
tiou splines in the method of nonlinear multiple regression proposed by
- C> A. Alekseyev [1]. The method is based on the transforma.tion of initial
var.tab? es xj into normalized variables uj. In [1] this transformation is
- accomglis'ed using tabulated values { xji, ujil by means of the. procedure
of smoothing "by hand." For closing the Alekseyev algorithm it is necessary
to carry out this procedure analytically. In our opinian, splines are an
applicablP tool for solving this prohlem primarily because the method for
constructing them is completely "blinc'," that is, is based only on initial
informar_ion, witheut relying on any a priori information o;i the character-
lstic form of tne dependence uj (xj). The latter circuffistance is decisive
for complete automation of the Alekseyev algorithm.
Figure 3 shows the curves for the correlation uj (x3) for the example, pub-
_ lished in [1], of detezmination of the correlation between runoff during
December and precipitation during December, November and Octnber for the
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ttie White Hollow River basin. The constructed curves represent curves of
approximation cuhic splines. �
As indicated at the heginning of the article, the residual deviations meth-
od is an extremely Promising multidimensional statistical analysis method.
At the present time we have developed an algorithm realizing this method .
in analytical f.orm [7]. The central place in the algorithm is occupied by _
the smoothing procedure described in this article.
B.IBZIOGRAPHY
1. Alekseyev, G. A., OB."YEKTIVNYYE METODY VYRAVNIVANIYA I NORMALIZATSII _
KORRELYATSIONDiYKH SVYA?EY (Ohjective Methods for Smoothing and Normal- _
izing Correlations), Leningrad, Gidrometc.oizdat, 1971.
2, Anderson, G., STATISTICHE5KIY ANALIZ VREMENNYKli RYADOV (Statistical An-
alysis of Time Series), Moscow, Mir, 1976.
3. Jenkins, H., Watts, D., SPEKTRAL'NYY ANALIZ I YEGO PRILOZHENIYA (Spec-
tral Analysis and its Applicatioi:s), Vol 1, Moscow, Mir, 1971.
4. Yezekiyel, ]i., Foks, K. A., METODY AAIALIZA KORRELYATSII I REGRESSIY
LINEYNYKH I NELINEYNYKH (Methods of Analysis of Correlations and Re-
gressions, Direct and Indirect), Translated from English, Moscow, Stat-
istika, 1966.
5. Konstantinov, A. R., Golitsina, Ye. F., "Ana].ysis of Results of Labor-
atory Investigations of Runoff Losses into Thawed and Frozen Soil,"
TRUDY GGI (Tra:isactions of the State Hydrological Institute), No 250,
1977.
_ 6. Konstantinov, A. R., Serikova, V. V., "Mathematical Approximation of
Graphic Regression Curves for the Correlation Between Runoff Loases
- and Yield and Determining Factors," TRUDY LGMI (Transactions of the
- Leningrad Hydrometeorological Institute), No 42, 1977.
7. Konstantinov, A. R., Khimin, N. M., "Use of the Residual Statistical _
Analysis Method for Inveatigating Hydrometeorological Processes,"
METEOROLOGIYA I GIDROLOGIYA (Meteorology and iiydrology), No 2, 1980.
- 8. Laykhtman, D. L., FIZIKA POGRANICHNOGO 5LOYA ATMU'DFERY (Physics of the
- Atmospheric Boundary Layer), Leningrad, Gidrometeoizdat, 1970.
9. Moiseychik, V. A., AGROMETEOROLOGICHESKIYE USLOVIYA I PEREZIMOVKA OZIM-
YICH KUL'TUR (Agrometeorological Conditiona and the Wintering of Winter
Crops), Leningrad, Gidrometeoixdat, 1975.
10. Panovskiy, G. A., Brayer, G. V., STATISTICHESKIYE METODY V METEOROLOGII
(Statistical Methods in Meteorology), Translated from English, Lenin-
grad, Gidrometeo izdat, 1967. '
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11. Solomon, S., "Statistical Corrplations Between Hydrological Variables,"
STATISTICHESKIYE METODY V GIDROLOGII (Statistical Methoda in Hydrol-
ogy), Leningrad, Gidrometeoizdat, 1170.
12. Stechkin, S. B., Suhbotin, Yu. N., SPLAYNY V VYCHISLITEL'NOY MATEMAT-
IKE (Splines in Computational Mathematics), Moscow, Nauka, 1976.
13. Brandon, D. B., DEVELOPING MATNEMATICAL MODELS FOR COMPUTER CONTROL,
GSA, Vol 7, 1954.
14. Reinsch, H., "Smoothing by Spline Functions," N. M., Vol 10, 1967.
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UDC 556.16"32"
~
DETEtZMINING RUNOFF DURING WINTER AND TRANSITIONAL PERIODS
Moacow METEOROLOGIYA I GIDROLOGIYA in Russtan No 7, Jul 80 pp 68-77
[Article by V. S. Ryazanov, Upper Volga Territorial Administration of Hy-
drometeorology and Environmental Monitoring, submitted for publication 30
October 1979]
[Text] Ahstract: The possibility of using correlation-
hydraulic models based on the Chezy-Manning for-
mula for taking winter runoff into account in
operational work is examined. In the examp'.t~ of
individual hydraulic sraCions, aituated on the
ri-vers of the hasin of the upper Volga and hav-
ing a different character of flow pattern under
winter conditions it is shown that the multiple
regression equations, computed on the basis of
measurements from preceding years, are an objec-
tive basis for routine (operational) determina-
tion of winter water runoff.
At the present time there are no objective methods for routine determina-
tion of river runoff in the absence of an unambiguous.dependence between
water discharges and levels, in particular when ice formations are present
and ice has set in. In actual practice use is made ^f intuitive procedures
for the extrapolation of water diacharges up to the next measurement when
it is possible to correct Lhem. Such procedures lead to considerable errors
in computing daily water discharges, considerably exceeding the admissible
accuracy of t10%. Recently hydraulic models have been proposed for the hy-
drometric determination of runoEf [1]. 'Lheir checlcing and experimental in-
troduction have been carried out at a number of hydraulic stations on rivers
in the Volga basin. The article gives the results relating to models of hy-
drometric determination of winter runoff.
The appearance of ice formations on rivers leads to an increase in hydraulic
resistances to the movement of flow. For this reasor water discharge in the
m
presence of ice formations and setCing-in of the ict (Qwin) differsi~h one
the water discharge when there is a free state of the channel (Qp) W
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and the same river level (H). This difference in the Qwin and Qp values
is evaluated using the cnnversion factor
Kain � Qwin/Qp � &)win vwin/G"O �0' (1)
where WQ and witl are the croas-se5tional areas of the open channel and
the river channel under the ice in m, vp and vwin are the mean current
velocities of the water in the crose section of the open flow and under
the ice in m/sec.
When using the Chezy and Manning formulas expression (1) for determining
Kwin is written in the form of the known formula
K - m (1 _ .~.1513 - ( 3
N� i ` u,u ~ n3xw 7o )0'5 ' ~ 2)
[3 N M= win; 3Z = ice] wherecJicB ia the area of the submerged ice in m2;
edo and no are the cross-sectional area in m2 and the open channel rough-
ness coefficient reapectively; nWin is the generalized coefficient of
roughness of the channel under the ice; IO and Iwin are the hydraulic slopea
of the open and ice-covered river channels; ml is a coefficient taking into
account the relationship between the hydraulic radiua and the geometrical
characteristics of the flow cross section.
For the period of continuous ice cover, when the wetted perimeter (Pwin)
is equal to douhled the wetted perimeter of the channel when in an open
state (PO) and the hydraulic radius is RWin - 0.5 Rp, the coefficient ml
= 0.63. During the transitional periods of freezing and opening-up of the
_ river, when PWin varles in dependence on the degree of coverage of the
_ water surface with ice formationa and is difficult to determine; the coef-
ficient ml is also virtually impossible to determine.
Many autr;ors, including P. N. Belokon', V. N. Goncharov and S. I. Kolu-
paylo, in investigations of the poasibility of applying formulas of the
type (2) for determining ICWin, made the assumption of an equaTity be-
tween Ip and IWin [3]. The same assumption was r3de by I. F. Karasev [1]
iti the multiple correlation equation which he proposed as a computation
model for determining Kwin
- 5 ~
h)N.f = m'-mI m' T e m' W, m m= T,, e- n~'
, ' ~ ~ 3

5 2 T
y ni ~ -2 ~ m ImI w_A f r
'00 01 ~ o '
where TiCe is the duration of ice coverage of the river channel in days,
varying from T= 0 to T� Tice+ m2 ia an empirical coefficient.
Equation (3) in general form descrihes the change in the conversion factor
Kain during the entire period of the winter low water (from Kwin = 1.00
at the heginning of the appearance of ice formations in autumn to Kwin =
1.00 with the clearing of tfie river from ice at the beginning of the spring
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high water). The terms of this equation take into account the influence
of the two principal factors on which the carrying capacity of the chan-
nel is dependent:
the changing roughness of the lower ice surface, represented in depen-
dence on the time T from the time of setting-in of the ice,
degree of restriction of the river channel.
The terms on the right side of expression (3), except for ml, can be re-
garded as variables entering into a regression equation in the form
- - i_N
� y c Qo (Ij lil ~4)
where _ T T
r e 7' e 1 .
- .r~ - , - ,
wo 1'.,
. T
'2 ~ T - 0 -
W 4.1 ~ .I .
x ,I ~ 'C.1 e ~
1 . ~ .1
~nn ~uu
ap, al,...,as are the parameters of the regression equation.
The cross-sectional area of the open channel (WO), entering into equation
(4), on any date is determined from the dependence cJ~ = f(H). The area of
the submerged ice (~ice) is determined using data on the ice thickness
(hice) in a hole:
ej ice T m4hiceBice'
Here B ti Bp is the river channel width at the hydraulic station in m; m4
is a coeTficient taking into account the noncoincidence of the mean thick-
ness of ttte ice in the width of the channel and its thickness measured in
the hole.
5ince :'aily measurements of ice thickness are not made at hydrological posts,
we also tested a model which takes into account the known relationship be-
twPen the increase in ice thickness and the sum of negative air tempera-
tures. Accordin to investigations of different authors, for example, F. I.
Bydin, hice ~,t � According to observations made on the rivers of the
upper Volga basin during the period from 1946 through 1965, Z. S. Surina

[4] obtained the depen ence
hice � 0,97 E t ~)�'S~�
Accordingly, the area of the submerged iee (cJ ice) in equation (3) can be
completely represented by the expression
Wice ' mSBice Iitl' (5)
where m5 is a proportionality factor.
84
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After substituting expressions (5) in place of 4)ice the regression equa-
tion (4) a:; one of the determining factora will take the temperature fac-
tor into account.
Models based on the multiple regreasion equation (4) and using data on the
ice thickness or on ttie sum of negative air temperatures are valid only for
condieions of a stable ice cover without aignificant ice jam - water-under-
snow phenomena during the period of winter low water. Preciaely such a re-
gime is characteristic for most of the rivers in the upper Volga basin. On
the basis of the nature of river freezing in the considered basin, in ac-
cordance with the classification proposed by R. A. Nezhikhovskiy, types I
and II can be distinguished. A fixed ice cover on them is established for
the most part hy a gradual expan8ioa and closing-in of ice forming along
khe s:tore (type I) or hy aimultaneous formation of "bridges" in a number
of places where the ice-tranaporting capacity of the flow is reduced, with
the subsequent filling of the spaces between the ice bridgea with floating
floes (type II).
Z'he entire difficulty in operational determination of runoff is that the
daily water discharges are computed under conditions when there is still
no complete set of ineasurements of diacharges for g particular year. In this
case as a base for the computations it ie poasible to use regression equa-
tions of type (4), derived using the results of preceding measurements
either during periods with winters cloae in severity (WCS) or during the
long-term period as a whole (LTP). Such a type of regression equation with
the use of data on the ice thicknese (WCS-I, LTP-I) and on the sum of neg-
ative air temperatures (WCS-II, LTP-II) was computed for the period 1959
ttirough 1975 for the hydraulic stations Oka River (.Gorbatov), Oka River
(Murom), Oka River (lielev), Vetluga River (Vetluzhskiy) and Mera River (Malo-
IIerezovo), having basin areas from 224,000 to 820 km2.
_ The parameters of the multiple regresaion equations were determined at the
Computation Center Verkhne-Volzhskoye Administration of the Hydrometeorolog-
ical Service by the least squares method using a"Minsk-32" electronic com-
piiter with a standard program developed at the 5tate Hydrological Insti-
tute. The mean air temperature during the time Tice was adopted as the'in-
dex uf winter severity. Winters for whichiz ti/TieE < 7.0 we're classified
_ as mild, withlZtl/Tice � 7�0-9.0 as normal, with J'Ztj/Tice ~>9.0 as
severe.
'Che free term (ap) in the derived regression equations was always close to
1.00, which is natural, hecause with T m 0cAJice � 0 and KWin = 1.00. The
remfiining parameters of the regresaion equations (a1,...,ap) vary in a
rather broad range and reflect the physical conditions of processes of
chunge in KWin�
The de:ived regression equltions in mogt cases have rather high multiple
correl.ation coefficients (Ro = Q.75-0.95). An exceptibn is the regression
equation for the station on the Mera River, Malo-Berezovo, Ro for which
85
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ls only 0.56-0.73. The multiple correlation coefficients as a rule are high-
er for models using data on ice thickness in comparis.on with models taking
into ac count the temperature factor and this is logical. The highest Ro
curresp ond to the regression equstions for severe winters when a stable
ice cover i.s fermed on rivers rapidly and is not impaired by thaws to the
very b e ginning oE the spring higfi water.-The minimum mean square errors
(Q which directly characterize the accuracy of the values computed
from the regression equations, correspond to these same winters. The Rp
values are usually lower for gentle unatable winters when the formation
of the ice cover lasts a long time and is disrupted by thaws leading to
the temporary clearing of ice from the river.
In actual hydrological computations it is necessary to compute the daily
water discharges during years when the measurements of discharges during
the winter low-water period are not made aC a11. The need for thia kind
of cocnp utations arises, for example, in casea of reatoration of winter
runoff on the basis of ineasurements of preceding or subsequent years. In
such c ases it is usually recommended that winter runoff be computed from
the ECwin valuea for the closest years or the means for a number of years.
~ However, such averaged KWin(T) curvea usually do not make it possible to
compute the daily water discharges csi.th sufficient reliability. For this
reaso n the resulta. of such compu*ations of winter runoff during past years
in mo st cases were deemed urlreliable when preparing the handbook SURFACE
WATER RESOURCES IN THE USSR�.
Compar ison of the Kwin values on the baeis of ineasurements and computations
using WCS models, on the assumption that meaeurements were not made, was
carXied out for the posts Oka River (Gorbatov) and Oka River (Murom) in the
years 1958-1959 and 1975-1976, that is, during winters not entering into
- the p eriod adopted for determining the regression equations. Taking into
accoun t that the mean air temperature f.or the winter of 1958/1959 for Gor-
batov was -4.4�C and for Murom was -5.2�C, the KWin values were computed
using the following type of regresaion equatione for 3entle wintere:
1) Oka River Gorbatov
WC5-I Kwin = 0.89-1,63 .r,-3.38.rZ - 10,2 x3-{-8,37 x4+37,7 xs,
WCS-II Kwin = 1,01-}-1,69.r1-0,03.r2-2,05xg-O.OOOIz4+0,14x5;
Z) Oka River Murom
WCS-I Kwin = 0,99-4.62xi-2,72x2-14,7.Y3-}-1,94xA+205xs,
WCS-II ICwin s 1,08-3,01.r,-0,05xz-1,19x3 ; 0,0003x4+0.13x5.
For the winter of 1475/1976 the mean air te.mperature at Gorhat'ov was -7.7�C
and at Murom was --8.6�C. Proceeding on the basis of this value, FCte1in was
comp uted using regression equatiotis for normal winters in the form:
86
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l; Oka River Gorbatov
WCS-I Kwin ' 0,94--7.99x,-6.14.r2 -~-117.r3+2p.4x4-343.r;,
WCS-II Kwin m 1,00-7.45.ri-0.04x:+0,72x3+0,001x4-0.05.r;;
2) Oke River Murom
WCS-I ICwin = 0,95-2,13x,-2,57x2-35,8x9-}-1,34a4+266x5,
WCS-II K4,in a 0,99+0,74x,-{-0,0002x2-1,64x9-0,002x4+0,1Ox6.
Table 1
Results of Computations
of Wa ter Diacharges (WCS Model) for Cases of
Abaence of Meaeurements
3 O7'K310HEHHA BdqNC1!lHBdx 3H8qCBHA Q
llepifo,~
KOAHQCCT80 OT N3M8ptHN61fi,
113MepenNfi
1
2 V J(f= ~ QrtpeAearxoel AeTS
6A10aeAb yPn, y-uTueobwaA aaHHue orOAupHe ,:bao
8 p. OKa - r. I'op6aroe
10 31tWa 1958/59
(
11 8,6 23,4 1 XII 1958
I
3HNia 1975/76
14
10,4 I 22,3 I 17 XII 1975
9 p. OKa - r, MypoM
311M8 1R58!59 I
10 15,1 -28,7 ] 1 XII 1958
- 3N+,a 1975/76 i
15 I 9,1 I 24,7 I 19 X1 1975
7 MoBe.sb
YPlI, y,curaecrayan re.wteparypreaA Oaxrap
_
8 p. Oxe - r. .Tap6aron
311Ma 1958,'59 I
11 I 13,6
45,6
1 XII 1958 -
3i+"a 1975/76
I
I
14 9,0 20,6 17 XII 1975
9 p. Oxa - r. Mypom
3iMS 1958,'59
10 I 10 I-33,4
22 X11 1956
31+M2 1975!76 ~
I
15 12.2 47,3 19 XI 1975
KEY :
1. Period
2. Number of ineasurements
3. Deviation of computed Q values from measured values, %
4. Limit
_ 5. Date
6. WCS model taking into account data on ice thickness
7. WCS model taking into account temperature factor
8. Oka River Gorbatov
9. Oka River Murom
10. IJinter...
87
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The reaulta of comparison of the computed and measured ICWin values are giv-
en in Table 1.
WMMM"
4,~a3laec
~ L ~
9 ~ a ~ ~
a~ o
6CC -
C J a
; u'~ i pi~�,..,__~ � y
Fig. 1. Matching of rLnoff ttydrographs. a) Oka River Gorbatov. Winter
1977/1978; b) Oka River Gorbatov. Winter 1975/1976; c) Vetluga River
Vetluzhskiy post. Winter 1974/1975. 1) According to hydrolopical yearbook;
2) According to WCS model; 3) According to routiue dats; 41/ Measured water
discharges.
The cited data make it possible to draw the preliminary conclusior. that
models of the WCS type are adequately effectivey eapecially models taking
into Rccount data on the thickness of the ice, for the purpases of recon-
structing the winter daily water diacharges during years when no measure-
' ments are made. Howeverr, very high deviatians (AQ) when using models of
the WCS type in individual cases are considerable and uaually correspond
to the characteristic points at the beginning of winter when there is a
minimum Kvin value determining the general form of the Kwin(T) function.
Computed models of the WCS type, when reliable l.ong-tertn weather .forecasts
(of the nature of winter) are available, could also serve as a basis for
routine determination of water runoff. But, unfortunately, hydrologists
for the time being do not have such forecaets. For this reason for opera-
t:.onal purposes at the present time it is possible to u,3e only models
- based on the WCS, obtained on the basis af long-term data for the preced-
ing years of observations.
Numerical expe:imenta with the use of auch model.s for the purpoaes of rou-
_ tine computation of daily water diacharges were carried oLt for the posts
- Oka River Gorbatov and Vetluga River Vetltzhskiy poat. Gorbatov post
on the Oka River was of the greatest intereat from the poin.t of siew of
the possibflities of u$e of correlation-hydraulic madels for operational _
determination of runoff: it ts one af the two principal stations for
88
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Table 2
Comparative Results of Operational Computation of Daily Water Discharges
lising LTP Model With Allowance for Temperature Factor
j
OTR.70flCHIlA pacxoaue OT OIt)'61NKUPBHHNX
1
XapaKrepN-
1
d flldpOAUf{I4CCKOM CJKCrUIHIIKe, ~p 3
nCpNO1
CTIih2
4 n
0 MOIlCIIN YPitiI
0 OI1Cp2THBHdM AaHNdM
CTOKa
c
I~~~,
q1IQl1
8 P.
OKd - f. FOP62TOD
7 3~+n+a
j C) TovHdii
8,1
10.5 -31A
- i -
19; 5/76
1AcK81H6fA
7.1
9,8 -25.0
- - -
1 v,ECq4HdA
3,6
4.7 -6,4
- - -
3 11M3
C)T04N14A
6,0
7,8 27,1
11,9 16,1 34,5
14+77/78
aehaaHwA
4,5
5,1 -8,0
11,2 14,3 -21,8
I
'4l'CA4NN11
3,8
4,8 -510
9,6 11,9 -IS,I
9 p Berlyra - p. n. Ber.IyAchi1i:
KEY:
1. Period
2. Runoff characteristic
3. Deviation eF discharges from data published in hydrological year-
book, o
4. Using LTF' mudel
5. Using operational data
6. A Qlim
7. Winter
8. Oka River Corbatov
9. Vetluga Kiver Vetluzhskiy post
10. 24 hours
ll . 10-day period
1'1, month
(letermining the annua.t diacharges of Volga water at Gor'kiy below the con-
fluence of the Uka. Upstream is the post at the Gor'kovskaya Hydroelectric
Power Station, at which r.outine determination of runoff is accomplished
quite reliably. In tile experiments we used the following regression equa-
tions for a long-term period in which the degree of channel restriction
89
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3iiWa CVTCNH611
8,6
11,8
34,5
19,9
21,8
44
4
1973/74 1ch2AHdii
8,4
10.5
21,6
18,4
21,0
,
42,0
I!PCq4H61f1
i 6.1
7,6
11,8
20,4
23,0
31,2
311Ma I cVrovHd~1
4,7
9,9
-26.6
19,4
23
7
51
5
1974/75
:;cKaatdA
2,8
3,9
-19.3
18,4
,
22,5
,
44.7
I
'APCH4Nd1~
2,6
3,1
5,3
16.8
20,5
40,2
3)iMa ' cVT04H61A
6,2
7,1
-35,6
8.8
11,9
-44
7
1975/76 iaeKa,zHdit
4,2
6,4
-15,2
8,7
11,5
,
-31,7
I.:ec941idC~
3,3
3,8
4,5
8,5
10,9
20,4
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_ was taken into account through the sum of negative air temperatures (LTP- _
II):
1) Oka River Gorbatov
Kwin 6 1,0 1 -5,38.Y,-0,04 x2+0,23 x3+0,001 .Y4-0,02 Xs;
2) Vetluga River Vetluzhskiy poat
Kwin � 1,01-4,78.ri-0,03.r2-0,10,r3+0,000003x4=-0,02zs.
The values of the mean daily air temperatures entering into these equa-
tions were used for the post Gorbatov on the Oka River in accordance with
ohservations at Gor'kiy (Stri_.lo) meteorological station and for the poat
Vetluzhakiy on the Vetluga River on the basis of observations at Krasnyye
Baki meteorological station.
Taking into account that in the routine computation of the daily water dis-
_ charges the actual duration of ice phenomena and presence of ice (Tice) is
_ an unknown value, as the computed Tice values it ia desirable to use the
mean for the long-term period of preceding observations. Such an assumption
daea not exert a significant influence on the final results of computations.
In order to tie in the LTP parameters employed in routine computation of
annual water diacharges to the peculiaritiea of the winter for the comput-
ation year we carried out correction of the free term of the equation (Q0)
on the basis of factual ICwin values for the date of each measurement of
water discharge (4) written relative to (ap),
[30M - win ] tio ! _ (KIN.I)i - (11 (xi)r - a, (-C,)i - a7 1X3I1- (l, (aC&)l aa (xs)i� (6) 7-
A coinparison of the data from the hydrological yearbook and the results of
determination of the annual water diecharges by exieting methods and on
the basis of the LTP model is given in Table 2 and in the figure.
The deviations (6Q) show that the values of the daily water discharges,
- computed using the LTP model, for the most part coincide with those pub-
lishri in the hydrological yearbooks and are considerably more exact than
the daily water discharges computed using schematic procedures for the ex-
trapolation of winter water diacharges used for routine purposea at the
present time. However, during the initial period of river freezing, and
~ in individual cases also during the opening-up period, the deviations of
~ the daily water discharges, computed using the LTP model, on individual
days attain 30% or more. Particularly significant errors are observed in
[he initial period of river freezing when a considerable time elapsea
from the date ICWin a 1.00 to the date of the firsC measurement of water
diacharge. An example is the winter of 1975/1976 for Gorbatov post, when
the {.,ossibility of correction of the free term (ap) appeared only after
1 1/2 months from the onaet of setting--in of the ice on the Oka River
lU
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(Fig, Lb). This once a gain confirms the correctness of the requirement
for the need of mPasur ing water discharges during the period of river
freezing as frequently as is practical, taking into account safety con-
ditions in performing the work.
Table 3
Parameters of Regression Equation Based on Logarithmic Model. Mera River
Malo-Berezovo Station, F= 820 1m2
i~.iEivecreo ;
~ I
9E~.t } an~irNn~; u
1ieWCpeHii~ uu ai az ~ a.~ ~ Ra
~
3 YPfI anA mHfKNX JNN I 68
4 YPn a:iH Eiupaia.tbtiaX i
3 HM 103
5 YPII 1.iA cypoeUr 111.%1 , dl
6 YPi%t ea nepiu,2 I
1960-75 rr. ~ :'S?
-0.128 1 0.537 1 0.841 1 0.006 1 0.81
2,372 -0.895 2.4 : Q 0,007 0.89
0.734 I 0.126 1.732 0.110; 0.90
0,841 I 0,064 I 1.661 I 0.006 1 O,a�
KEY:
1. Type of equntion
2. Number of measurements
3. MCS for gentle w inters
4. MCS for normal winters
5. MCS for severe w inters
6. LTP tnodel for period 1960-1975
In cases when additional resistances to flow, caused by ice formations and
an !ce cover, ;are aguravated by any other additional factors, the use of
mociels c,f the type (4) loses physical sense and leads to considerable
errors in computation of daily water discharges. One of these additional
- facturs, distorttng the general fo nn of the function ICwin(T), is water
vegetatiun, whicli, dying otit in the autumn, in many small rivers in the
Volga River basin is nu t carried away by the current, but cnntinues to
exert an addttiunal influence on the relationship between water discharge
,ind l cvel. An exampt e a f this type of river is the Mera River at Malo-Ber-
L'zOvc) statiuu, adopted as one of the analogue rivers in the scheme f.or
uperational comptitation and prediction of Che daily lateral inflow into
Gor'kovskove Reservoir.
'i'he daily water disc}iarges dtir.tng the period of winter low water on the
Mera River a[ Malo-Berezovo, like on most such rivers, are computed vsing
the coef f icient 1Cwit1 pre(T) . Therefore, the WCS and LTP data computed for
,I p:irti~~ulac post us~ng a model of the fortn (4) have low multiple correla-
- _[on coefficients (Ito = 0.56-0.73). The use of these models for operation-
a.l computatioti of wntPr discharges leads to inadmissibly high errors (on
ihe average 25-45% witli values of the limiting errors exceeding 100X).
in such cases when [he Kwin conversion factor loses physical sense, an at-
tempt was made to apply a model for determining water runoff which makes
direct utie of the Chezy-Manning formula
91
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n213
W]NN rt7Al'
-
[3H M - win; 11 = ice Q R3114 c>>
]
transformed by I. F. Karasev [1] into the expreseion
1,41 ~yNy R�aNY V
/ I :~-----5-- 7HV (H)
Q - n., I~~,~
The reduction of expression (8) to logarithmic form makes it possible to
obtain a multiple correlation equation in the forni (4) in which
_ [ 3n M= win; 51= ice ] y= 18 Q; xl _ Ig W~HYxs =~8' R,~~~~
Ig (no) Y 1-?- el'7 h'. Table 4
Comparative Table of Deviations of Computed Discharges From Those
Published in Hydrological Yearbook for
Mera River - Malo-Berezovo Station
ITO AOC8pNQ11tHVlCKOA Ilu oneparstaHdu
Moaenx vPM 4 Aaxedu
KEY:
1.
2.
3.
4.
5.
6.
7.
8.
ilcpxoa 1 haKaxrroKa i
2
~
5 31tN8 1975/76 cyTOVeetA 7,3
1
13.2
8
4
8.0
6
0
10.8
E,6
nexaAHdA 6,
MCCRqHdA 3,3
,
5,0
.
3,9
5,2
311M8 1976i7; cyrovawA 9,3
5
2
12,1
6
8
)2,2
9,6
15,8
12,3
1
IItK1AHdA
NeCR4NdA 3,T
,
4.7
8.4
10,7
Period
12unof f cliaracteristic
According to LPT ].o~arithmic model
According to operational data
Winter
24 hours
Ten-day
Month
The ap, al, a2, a3 values statiatically generalize the parameters of equa-
tion (7), including the canstant slope IWin. The factor xg �or simplifica-
tion of the computations is adopted in the form of the sum of the moduli
- of negative air temperatures (jZtj), which integrally take into account
the degree of channel restriction and roughness.
The equations derived for the Malo-Berezovo post on the Mera River (WSC
and L'rP) with the use of a logarithmic model are given in Table 3.
92
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6 OCTOBER 1980
ME t ' _Ol3 T
NO. 7J JULT 1980
2 OF 2
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Checking of the possibility of use of a multiple regresaion equation (LTP)
for the purpo3e of operational computativn of the daily water diacharge
was carried out during the winter of 1975/1976 and 1976/1977. Data on
air temperature were taken from observations at Ostrovakoye meteorolog-
ieal station, the closest to Malo-Berezovo station.
The correction of the free term of equation (ao) for the purpose of tie-
in of the LTP paramete.rs to the peculiarities of winter of a specific
year was carried out applicable to equation (8) using the expression
(70 1 =(IgQ)r-a, (x, )r-as(X2)t-ax(x,1j� , (9)
The comparative results of the computatione are given in Table 4. The dis-
crepancy of the discharges Q Q cha.racterizes only the degree of coincid-
ence of the data in the hydrological yearboa'c and the results of computa-
tions on the basis of models and does not at all serve as an evaluation
of the accuracy of the Iatter. The deviations Q axe related primarily
to the inadequata soundness o,f the procedures for computing the daily
water discharges contained in the yearbuoks, Accordirg to evaluations
made by the Hydrometry Section at the State Hydrological Inatitute, cor-
relation-hydraulic models ensure a decresse in the errora in operational
determination of runoff by a factor of 1.2-1.5 in comparison with the
methods used.
The results of numerical experiments presented in the article show that ~
equations of the LTP type, taking the teznperature factor into account,
are an entirely objective basis for operational determination of river
runoff during winter on rivers where an increase in hydraulic resistances
to the mocement of the f low is caused only by ice formatione and the ice
cover. In the case of rivers on which additional resiatancea, caused by
ice formations or an ice cover, are complicated by the influence of water
vegetation remaining in the channel, !.t is deairable for operational pur- _
poses to use a logarithmic model for taking winter runoff into account. ~
B IBL IOGRAPHY
l. Karasev, I. F., "Mathematical Models for Hydrometric Determination of
River Runoff," TRUDY GGI (Transactions of the State Hydrological In-
stitute), No 256, 1978.
2. Nezhikhovskiy, R. A. ,"Types of River Freezing and Types of Ice Jams," '
METEOROLOGIYA I GIDROLOGIYA (Meteorology and Hydrology), No 2, 1974.
3. Polyakov, B. V., GIDROLOGICHESKIYE ISSLEDOVANIYA NIZHNEY VOLGI (Hydro-
logical Investigations cf the Low2r Volga), Moacow, Gosstroyizdat,
1938.
4. Surina, Z. S., "Investigation ot Growth and Computation of Ice Thick-
ness on Rivers o� the Upper "lolga Basin," SB. RABOT GOR'KOVSKOY, VOLZH-
i SKOY I RYBINSKOY GMO (Callection of Papers of the Gor'kiy, Volga and r
Rybinsk Hydrometeorological Obser-vatories), Leningrad, Gidrometeoizdat,
1973.
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UDC 556.536
METHOD FOR MAKING OBSERVATIONS OF THE WATER SURFACE SLOPE OF RIVER FLOWS
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 78-83
[Article by Candidate of Technical Sciences V. V. Kovalenko, Leningrad Hy-
' drometeorologica? Institute, submitted for publication 21 January 19811
[Text] Abstract: The author deiines a quantitative
criterion which makes it possible to select
the location of a hydrometric station and the
length of the base for making observations of
the water surface slope of river flowa. The
restrictions on base length which follow from
~ the hydraulic conditions of the water flow cur-
rent are pointed out.
~ The slope of Che free surface of a river flow is one of the most important
hydraulic characteristics [5, 6, 16]. However, the recommendations on the
organization of s'lope observations given in [13, 14] sometimes have a pure-
_ ly qualitative character, which sometime3 leada to subjectivity in siting
a hydrometric station and the choice of the slope base length.
In this article an zttempt is made to define objective quantitative cri-
teria making it possible to regularize slope observations.
The equations of hydromechanics relate the f ield of velocities aud the pres-
sure field. Within the framework of one-dimensional hydraulic idealization
this has the following rESUIt: in principle, on the basis of the measured
pressure differential (or piezometric alope) it is posaible to judge the
discharge passing in the sectioa. In the well-developed countries most of
the industrial �low meters (in Great Britain, for example, 90%) are based
precisely on measurement of the preasure differential (slope).
The principal norm-setting documenta j.n the field of hydrometry of slopes
[13, 141 define the, puxpose of -b'servations of the' longituainal slope
as follows: 1) for estimating the capacity of the channel, determined by the waCer dis-
charge;
2) for ascertaining the value of the Chezy coefficient C, taking into
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- account the hydraulic resistances.
- Taking into account that the water movement in the river flow has a nonuni-
form and nonstationary character, it is natural to generalize the Chezy
formula and obtain a general mathematical model which can be used for the
above purposes and more graphically reflect the role played by the slope
in the solution, possibly, of other hydrometric problems. In order to ob-
tain such a"hydrometric model" it is natural to use hydraulic idealiza-
tion equations, for example, in the following approximation [8]:
dh 1 dU cU dU a- 1 U dF
1 - ' -d -
d�x - j + g� ar ~ g,~ gM F dr
+I ~ d' FRU y2.: FR FRU2 a'` +
g*F ~ dt dz ~ dx dt dx'= ~ dx
+ s, FRU dh(2)

avF aF _ ~
d.r ~ at '
where j is a dissipative term; 0~ ~'1,A2, P3, Aq are coefficients de-
pendent on the velocity distribution in the cross section; the remaining
notations are those in general use in hydrometry.
For a case of practical interest, when information is known on the level
H= f(x, t) and the morphometry of a fixed hydrometric location with the
coordinate xp, after simple transformations of equations (1) and (2) it
is possible to derive an equa.tion in full derivatives [10]

Q ~ fi (xo, t) U" f~ (xn, t) U ~ f,( rol t) l= fa ixo, t~� (3)
In (3) the functions fl, f'1, f2, f 3, with a known morphometry of the hy-
drometric location, are dependent only on the water level and its deriva-
tives in coordinates and time.
If it follows from the Chezy formula for uniform movement that Q= f(H),
then from (3) for smoothly changing movement
Q= f(H, dH, dH 1
- aY vr J~
whereas for a general case dH dN 61-H d~ H
Q- fa , o~ ~ ux- ar~
that is, in the most general case for determining the discharge it is -
necessary to have information not only on the level and slope, but also
on the curvature and derivatives of curvature of the free surface.
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Information on the water surface slope is necessary for the solution of at
least four fundamental problems in hydrometry which in general form can be
solved using equation (3), to wit:
a) indirect measurement (determination) of water discharge,
b) extrapolation of discharge,
c) restoration of the hydrograph;
d) determination of hydraulic resistances (Chezy coefficient).
An investigation of the sensitivity of equation (3), that is, for discharge
or current velocity, to changes in the parameters enrering into it [9], re-
vealed that the free surface slope is the most important.
We note that in the determination of hydraulic resietances from equation
(3) (with measured slope and current velocity) the measurement of convec-
tive acceleration in actuality ia not accompliehed from the difference in
velocities in two sectioas (which in the caee of nonetationary movement
leade to considerable errors), but from the alope and derivative of the
level in time (more detail concerning this is given in [21). In addition
to the piezometric level, which has been discussed until now, a certain
role is played by the inertial and hydraulic (dissipative term in equa-
tion (3)) slopes. For example, in deCermining the additional slope caused
by the difference in dissipation in a uniform flow from that in the case
of nonstationary movement, the piezometric slope is used again [3].
The following points can be noted in comzection with the method for making
slope observatione [13, 14]:
a) choice of site fox a hydrometric post for slope observations;
b) choice of length of segment (base) for measuring slope.
The instructions give quite clear aad sprcif ic recommendations only on the
choice of base length, with accuracy characteristics taken into account;
otherw3.se the instructions are limited to qualitative indications, for ex-
ample, on the unidirectiona.l change in the areas of the cross sections in
- the sector. In order to obtain quantitative criteria for the purpnse of
deaignating the site of the hydrometric post and base length it is natural
to select a criterion which at the most "advantageous" hydrometric post
would assume an extremal value. In obtaining such a criterion it is neces-
sary to take into account the purpose of the slope observations, that is,
on the one hand, at the optimum hydrametric post the measured slope must
_ react well to a change in discharge aad hydraulic resistances, and on the
other hand, with the further use of the slope in computations the dis-
charges and resistances must be adequately sensitive to slope. As such a
criterion we can use the extremum (in the longitudinal coordinate) di the
matrix norm of the corresponding sensitAvity functions Si in some func-
tional space whose metrics is determined by the purpose of the observa-
tions (stationary long-term observations, high-water observations, obserw
- ations of minimum runoff, etc.).
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The sensitivity functions are derived from equations (1) and (2) by known
methods. In particular, the equation for the function of sensitivity of
discharge to slope will be
-F-'C=R dQ-/aBQ=C2 R+gQ'F-~QaC=R rdF
I~)f
S-~- I 1 QIFCIR rt (4)
I z BQ=C=R + 1gF3C=Rl gFaQ G"tR - a BQ3r"-R
a 1) Q=FC=R J S ~ (Q + 1) 2RQ1F. .
The solution of equation (4) with zero "initial" conditions and "freezing-
in" [11] of the coefficients and free term, correspoi;ding to their values
at the hydrometric post, will be
S=(gF3QC=R - z BQIG"R) C- tnC'R Q- I a BQ'C=R + 8Q2F-
- a QzC2R ( dX ) -}-1 a BQ=C'R -I-1gF3C=R)-1 f 1 -exP ((a (5)
+ 1) ~RQ"F)-I F2 CzR ad -~-1 a BQ'Cs R + BQ2F -
- a Q=C=R ( aX ta 13QZC=R -F- IgfBC'R) ' x,}�
*
In a general case the components of the matrix of seneitivity functions
are dependent on the coordinate of the hydrometric post, the extent of
the channel reach (slope base), time and specific realization of the hy-
drological year or observation iaterval. The location of the optimum hydro-
metric poat and the slope base length are not independent of one another,
have a stochastic nature and are determined by the extremum of the norm
of the matrix of sensitivity functions. After designating the location of
the hydrometric post it is necessary to select the length of the base on
which the slope will be deternined. If the equations of hydraulics are
' used as a point of departure, we have aH------p N
dz ~nxj o A x
From the point of view of hydraulics, it would seem that the best base is
a zero base (we note tha*_ there are methods for measuring a slope at a
- point [l, 4]). In actuality, however, this is not the case.
The longitudinal coordinate x explicitly enters the sensitivity function
S. Theoretically S attains its maximum value when x=00. On a practical
basis, as has been done in an investigation of dynamic systems [9], it is
reasonable to limit ourselves to those x= L values for which the exponen-
~~ial term in S attains the level 0.63. Using (5), taking into account the
principal hydraulic characteristics and channel morphometry, we derive a
formul.a for base length
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h4f3F
L=
' gn2F- 0,;> h4/3 dF
~ dx (6)
The restrictions on base length, following from formula (6), are related to -
the inertial effect in water flow movement. However, there is still another
restriction associated with the correctness of the one-dimensional hy- `
draulic idealization itseZf. The H level, figuring in the equations of '
hydraulics, naturally differs from that level z which in actuality is ob-
served in a real flow and with which the relief of the free surface is
associated. The difference between the averaged (hydraulic) and actual
levels also dictates the choice of the slope measurement base from zhe con- _
dition that the drop of the averaged slope be at least an order of magnitude
greater than the level drop as a result of its random variations, that is
aJit'li-. dx ~ dx, (7)
4 ax `
~
where f is the norm of level variatinns not taken into account by the
one-dimensional idealization. At the present time only estimates of the
systematic level deviations in width from a horizontal position as a re-
sult of rounding-off of the flow, Coriolis force of the earth's rotation
and relief of the channel cross sect3on are real. At Che present time
nothing is known about the dependence of this same systematic deviation
on the phases for the hydrological year, and also about the distribution
of water volume in the long-term section. It is reasonable to adopt the
following hypothesis: _ . . . .
yEf B12,B121I H-zi.
M'lx
The slanting of the free surface due to Che enuoonerated factors can be de-
termined using the known formul.as [7]. U.sing the mean value theorem, from (7) we obtain an estimate of the slope
measurement base length
lo Ilfii
f (8)
where the hottom slope can be taken approximately as I.
The instructions [13, 14] recommend a formula for designating the base
length, using as a point of departure the accuracy in measuring water
level and the leveling of poats, that is, the determination of L is re-
lated only to the possibilities.for technical outfitting of the hydrolog-
ical network. However, the reetrictions corresponding to formulas (6) and
(8) have a fundamental character and cannot be elim4.nated b,y any tech-
nical means. Taking into account that when making alope observations
in the network use�is made of a'etandard program and technical means, the
errora in leveling and level measurement can be conaidered identical. Then
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the base length, accord4_nq to [13, 14], will be determined only by the flow
slope. m
o, t
0,
~
L _ L
p'� h ~
Fig. 1. Results of analysis of field daza. 1) theoretical curve, 2) data
from yearbooks.
On the other hand, the bilinear symmetric functional corresponding to the
scalar product of the sensitivity vector in measurements and the aensitiv-
ity vector in computations and relating the meaeured and computed para-
meters, is dependent not only on the slope, but also (in the simplest case
of a quasisteady regime) on channel roughness, depth of filling and the
value ( d F/ a x),t.
However, the instructions do not fix the base length in dependence on chan-
nel fi?ling and roughneas, but only in inverse dependence on slope, which
should lead to a decrease in the correlaCion of the measured slopea and
discharges with an increase in roughness and a decrease in filling. In
order to check this assumption we made an aaalysis of 1,500 measured dis-
charges (on the basis of data frvm the yearbooks) at 78 hydrometric posts
located on diiferent rivers in the USSR. The results of computations are
shown in Fig. 1(significance level SX). Taking into account the measure-
ment errors and the fact that data from standard observations cited in
yearbooks cannot be used in calculating the'above-mentioned functional at
each point in the observation interval, with allowance for sensitivity to
the Chezy coefficient, along the y-ardiaate we plotted the product of the
discharge-to-slope and slope-to-discharge regression coefficients m. An
evaluation of statistical homogeneity was made using the Fisher test [15].
The figure shows that the representativeness of the observations is leas
than is theoretically possible. The dropoff of the theoretical curve from
their point of intersection is attributable to the fact that with a zero
base a zero sensitivity is adopted.
S ummary
1. The official norarsetting documents dealing with slope observations have
a q_ualitative character, which can reduce the representativeness of ineas-
urements.
2. The site for a hydrometric post and slope base length are not mutually
independent.
99
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3. An objective method for designating the hydrometric post coordinate in-
volves finding the extremum of the norm of the matrix of sensitivity func-
- tions within the li.mits of the channel resch in which the caxrying out o�
hydrometric observations is planned.
4. The slope measured at a point, that is, on a zero base, m3y or may not
characterize the discharge acually passing through the hydrometric post. D
Due to the explicit dependence of the sensitivity function on the longitud-
inal coordinate there is a finite length of the base in which the measured
slope 4zi11 determine discharge. This base is dependent for the most part
on channel filling, roughness and morphometry of the channel reach.
5. The base Iength should be such that th.z drop of the averaged (hydraulic)
level not only substantially exceeds the error in determining slope, but
also is an order of magnitude grsater than the level drop as a result of
its random variations (wind waves, etc.) or the systematic deviations as-
sociated with incorrectness of the one-dim2nsional hydraulic idealization
(water surface slanting in the case of ehannel curvature or in the case of
a nonuniform distribution of diFCharge in the cross section).
6. At the 5% significance level there are systematic deviations of field
data from the theoretical data, which indicates a nonrepresentativeness of
the measured slopes at a number of posfis in the network and the deairabil-
ity of taking into account the results cited above when organizing si;,pe
observations.
BIBLIOGRAPHY
1. Arbuzov, I. A., Kovalenko, V. V., "Device for Measuring the Longitud-
inal Slope of the Free Surface of a Watercourse," Author's Certif-
icate USSR 535456, OTKRYTIYAO IZOBRETENIYA, PROMYSHLENNYYE OBRAZTSYO
TOVARNYYE ZNAKt (Discoveries, Inventions, Industrial Models, Trade-
marks), No 42, 1976.
2. Kovalenko, V. V., "Method for Determining Convective Acceleration in
Open Channels," Author's Certificate USSR 606135, OTI:RYTIYA, IZOBRET-
ENIYA, PROMYSHLENNYYE OBRAZTSY, TOVARNYYE ZNAKI, No 17, 1978.
3. Kovalenko, V. V., "Method for Determining Additional Hydraulic SZope
of a Nansteady Open Flow,",Author's Certificate USSR 605085, OTICRYT-
IYA, IZOBRETENIYA, PROMYSHLENNYYE OBRAZTSY, TOVARNYYE ZNAKI, No 16,
1978.
4. Kovalenko, V. V., "Method for Aetermining the Longitudinal S?ope of a
Water Surface," OTKRYTIYA, IZOBRETENIYA, PROMYSHLENNYYE OBRAZTSY,
TOVARNYYE ZNAKI, No 19, 1978.
5. Zheleznyakov, G. V., Danilevich, B. V., TJCHNOST' GIDROLOGICMSKIKH
IZMERENIY I RASCHETOV (Accuracy of Hydrological Measurements and Com-
putations), Leningrad, Gidrometeoizdat, 1966.
100
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6. Karasev, I. F., Chizhov, A. N., "Cr iteria in Measuring the Accuracy
of Water 'A'Ievels on Rivers and Reservoirs," TRUDY GGI (Transactiona
of the State Hydrological institute No 150, 1968.
7. Karaushev, A. V., RECHliAYA GIDRAVLIKA (Fluvial Hydraulics), Leningrad, -
Gidrometeoizdat, 1969.
8. KartvelishviZi, N. A., NEUSTANOVIVSHIYESYA OTKRITYYE POTOKI (Uneteady
Open Flows), Leningrad, Gidrometeo i zdat, 1968.
9. Katys, G. P., ELEMENTY SZSTEM AVTQMATICHESKOGO KONTROLYA NESTATSION-
ARNYKH POTOKOV (Elements of Systems for Automatic Monitoring of Non-
stationary Flows), Moscow, Izd-vo AN SSSR, 1959.
- 10. Kovalenko, V. V., "Measurement of the Hydraulic Characteristics of
Nonsteady Open Flows," SBORNIK RABOT PO GIDROLOGII (Collection of
Papers an Hydrology), No 12, 1977.
11. Kovalenko, V. V., Varyshnikov, N. B., "On the Problem of the Extrapo-
lation of the Diechargea Curve in a Case of Unstegdy Movement of an
Open F].ow," MEZINUZOVSKI'Y SBORNIK (Intercollege Collection of Ar-
ticles), No 63, 1977.
12. Kovalenko, V. V., Stolyar, S. Ye.. "Some Problems in Hydrometry of
Unsteady Open Flows," IIROBLEMY ARMrIKI I ANTARRTIKI (Problems of the
Ar;:tic and Antarctica), No 53, 1978.
13. METODICHESKIYE UKAZANIYA UGMS No 81. ORGANIZATSIYA NABLYUDENIY NAD
PRODOL'NYM UKLONOM VODNOY POVERKHIJOSTI (Systematic Instructions of
the Main Administration of the Hydrometeorological Service No 81.
Organization of Obaervations of the Longitudinal Slope of a Water
Surface), Leningrad, Gidrometeoizdat, 1971.
14. NASTAVLENIYE GIDROMETEOROLOGICHESKIM STANTSIYAM I POSTAM, I'YP 6, CA I
(Instructions to Hydrometeorological Stations and Posts, No 6, Part
I, Leningrad, Gidrometeoizdat, 1978.
15. Rozhdestvenskiy, A. V., Chebotarev, A. I., STATISTICHESKIYE METODY V
- GIDROLOGII (Statistical Methods in Hydrology), Leningrad, Gidrometeo-
izdat, 1974.
lb. Shestakova, R. A., "Choice of the Reach for Measuring the Slope of a
Water Surface in Channels Without Floodplains," TRUDY GGI, No 164,
1968.
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UDr, 556.(536+537)
STUDY OF KINEMATIC STRUCTURE OF r'LOW IN RIVER MOUTH REACH MODEL
Moscow METEOROLOGIYa t GIDROLOGIYA in Russian No 7, Jul 80 pp 84-89
[Article by Candidates of Physicsl and Mathematical Sciences N. A. Mikhayl-
ova and V. P. Petrov, 0. P. Petrosyan, Moscow State University, submitted
for publication 25 October 1979]
= [Text] Abstract: Data from laboratory investigations
are compared with the energy spectra of tur-
bulence in the main channel and in the mouth
reach of a river. It is shown that the dimen-
sions of the eddies in the thiclcness of the
flow co:incide with the dimensions of the macro-
scale channel formations at the bottom of the
flow.
Despite the fact that the problem of formation of the mouth reaches of
rivers has long attracted the attention of researchers, until now there
has been no clear understanding of the mechanism of this process and its
quantitative evaluation. The mouths of rivers are characterized by all the
peculiarities of channel flow determined by the principle of interaction
between channel and flow forunulated by M. A. Velikanov. But at the same
time there are additional difficulties associated primarily with consider-
able horizontal broadening o� the channel,including with depth. All the
mentioned circumstances determine the specific structure of flow in mouth
reaches, which as of yet has noti been adequately studied. In analyzing the
considered flow it is evidently desirable to apply the method already de-
veloped for the investigation of channel flows [3, 41. To be sure, it is
necLasary to take into account the peculiarities of movement of sand waves
and bars under conditions of nonuniform movement of the flow [2].
The investigations described in this article were carried out under labora-
tory conditions in the hydrophysics laboratory of the Department of Physics
of the Sea and Waters of the Land of the Physics Faculty at Moscow State
University. The model of a microriver with a mouth reach was formed in a
channel flume 21 m in length, 4 m wide and 1 m high using sand 0.2 mm in
diameter. The initial groove was linear longitudinally and in cross section
had a tragezoidal configuration with the �ol.lowing river parameters: width
at iw ttom 30 cm, side slope coeff9.cient 1:2, longitudinal bottom slope
0.001.
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Flow Characteristics
10 K 1 1 8016
I
I I
II
(
I I
II
h cx
11,6
17.8
10,5
11,4
2 1' c4c
41,1
37,1
37,6
38.7
Fr
.0,15
0,09
0,13
0,13
Re
0,48�105
0,67�106
0,38�105 I
0,44�106
KEY:
l. hours
2. cm/sec
y`
q0 .

~
a1
JO
1
d cm/sec
~
10
10 1. 1 1 . , I . . a~~r
100 � 110 940 1Q0 140 100IiM
Fig. 1. Transverse sections of channel (uP.tQ its~midpoint along the right
bank) at post I 10 (curve 1), 50 (curve 2) and 80 (curve 3) hours after on-
set of experiment (a) and distribution of inean velocity in depth of flow at
post 7 10 hours after onset of experiment (b).
In the mouth reach the horizontal configuration persisted but the bottom
slope changed sharply and was equal to 0.01. The banks of tne model, which
were horizontal in the river reach, had a slope 0.015. The length of the
- microriver was 16.5 m; the remaining part of the model was accounted for
by the mouth reach of the river and sea. The microriver was formed with
a water discharge Q= 44 liters/sec. The experiment lasted 82 hours. During
this time the channel of the microriver and its mouth reach were re�ormed;
the intensity of the process gradually attenuated with transition from the
river to the mouth, where there was a marked broadening of the flow.
In order to ,judge the temporal change of characteristics of the channel and
flow along the length of the model we selected characteristic control points
at distances of 14 m, 17.5 m and 18 m from the entry into the flume. Point
( ?I post") I was in the channel reach of the model where there was no influ-
ence from the broadening and deepening of the flow, points II and III were
in the moizth reach. Table l gives the flow characteristics at points I and
II 10 a.r~d 80 hours after onset of the experiment. All the characteristics
relate ro the vertical on the flow axis. When carrying out the experiment
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observations were made of formation of bottom relief in the channel and
mouth. At the indicated moment in time the mean length of the sand waves
in the channel was 12 cm and their rate of mAVement was 5 cm/sec. Measure-
ments of the bottom profile were made systema tically at the control points.
Figure la shows cross sections at point I 10 (curve 1), 50 (curve 2) and
30 (curve 3) hours after onset of the experimPmi. Tne sections were run
to the midpoint of the channel along the righ t bank. The cited curves
show that with the course of time the shore slope becomes more gentl.e and
the channel is widened. In this process ttie bottom readings in the middle
' of the channel increase, whereas on the slope they decrease.
As a characteristic of the degree of formation of the channel we used the
flow width B at point I, which was measured each 5-F hours. With the course
of time the B value first increased rapidly and after attaining some value
during the time t= 55 hours then remained essentially constant. By thie
time the bottom relief in the channel (point I) had already formed. In
the mouth reach (points II, III) the formation of a bar was ot,served.
Two series of ineasurements of the mean and fluctuating characteristics of
velocity at points I and II on the vertical in the middle of the channel
were carried out for a comparison of the kinematic and etiergy characteris-
tics of the flow in the channel and mouth in the scage of formation and in
a formed state. The first series of ineasurements was made after 10 hours
and the second was made 80 hours after onset of the experiment. At these
same moments in time we measured the bottom p rofile along the axis of
channel symnetry (see Fig. 2c,f). Measurements of the mean velocities
were made with a vane. As an example, Fig. lb shows the velocity curve at
point I 10 hours after channel forma.tion. The origin of the coordinate
system was matched with a point on the�bottom through which the control
vertical passed, where measurements were made. Both in the initial stage
- of channel formation and in the c_.se of a forming channel it was found that
the velocity gradients in the bottom region at point I were greater than
at point II. However, the elevation of the bottom region, where the mean
velocity varies substantially, at point II is greater; this is attribut-
able to broadening and deepening of the flow.
- Fluctuations of the vertical and horizontal velocity components were regis-
- tered using a thermohydrometer with a compe.nsating resistor [5]. Registry
- was with an N-327 automatic recorder; a UT-401B amplifier with a microcir-
cuit was used. At each point registry was for 1 min. Since the water dis-
charge did not change in the course of the experiment, and channel dEforma-
tion was insignificant during the time of registry,-during this time inter-
- val the flow movement can be considered steady. In processing these records
we applied a theory developed for stationary random processes [1]. Each
record was represented in the form of a series of 600 points; the dis-
' creteness'interval was Q t= 0.1 sec and the corresponding Nyquist fre-
quency was
' fN = 1/2A t = 5 Hz,
104
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which is less than the limiting frequency transmitted by the recording
instrument. The duration of the record (1 min) imposes a limitation on
the minimum frequency
fmin = 1
= O, 16
.
T
where T is the length
of
the record.
-
- - -
Y`M
~
a
42
Q 1~ CM/G C
W
10
S
n d
~e ~ a)
zy , cui/sec
cn/c
Hz,
O) b
cm/sec
; 4, wr/c
e
a~ z
6a ~ t~1/c
- 74 i5 16 17 10 X M
Fig. 2. Vertical distribution of standard deviations of horizontal (1)
and vertical (2) velocity components at posts .(points) I(a, d) and II
- (b, e) after 10 and 80 hours and also longitudinal section of channel
after 10 and 80 hours (c, f) from onset of experiment.
Thus the range of investigated frequencies falls in the limits
0.16 Hz4 f S 5 Hz.
On the basis of the results of statistical processing we obtained data
on the distribution (in the depth of the flow) of the standard devia-
tions of fluctuations of the horizontal O' and vertical O'y velocity
components at points I(Fig. 2a,d) and II ~Fig. 2b,e) 10 and 80 hours
after onset of rhe experiment. At point I the O'u and ~ values in both
cases have a maaimum at the bottom, where the main zone of production of
turbulent energy is situated. Then, beginning with a distance of 0.4 H
from the bottom, the intensity of the turbulence remains constant, which
agrees with the investigations in [4]. - At point II, with an unformed mouth (10 hours.after onset of the experi-
ment) O'u has a ma.ximum at the bottom and the elevation of the region
with an increased Q v value is greatly increased. However, when the
mouth is formed, the O"u and f)"v distiribution curves, together with the
maxima at the bottom, have a tendency to an increase in the values of
the mentioned characteristics at the midpoint of the flow as weZl.
In order to evaluate the contribution of velocity fluctuations of differ-
ent frequency to the energy of turhulent fluctuations we examined the
correlation functions and the spectral density functions. These were
105
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computed from numerical series, processed in accordance with a program
prepared by V. R. Nikitin applicable to tne problems described in [3].
In order to reduce the record to a stationary form we employed the
- "moving average with a Tukey cosine-kernel" operation. In this case the
"moving" mathematical expectation for the i-th term of the series was
determined by the expression
Ui ' 2 11 1 ~ Ut+' (1 4- Cos 2~ z I.
In order to select the optimum value of the filter parameter we carried
out a methodological study similar to that described in [3]. In all the
investigated cases for both velocity components the spectral density
functions S(f) are multimodal and the main energy of the turbul.ent fluc-
tuations is concentrated in the region of low frequencies. As a sample,
Figure 3 shows the energy spectra of fluctuations of the horizontal (a)
and vertical (b) velocity components at point II 10 hours after onset of
the experiment at a distance of 0.05 H from the bottom. The maximum of
the S(f) functions, obtained for point I 10 hours after onset of channel
formation,falls at one and the same frequency fur the vertical and hori-
zontal velocity components. At points situated at a distance of 0.05 H and
0.15 H from the bottom the spectral functicns have a clearly expressed
maximum at a frequency of 0.3 Hz. With increasing distance from the bot-
tom the intensity of this maximum decrea.ses for both the vertical and hor-
izontal components, remaining graater for the horizontal component. How-
ever, at the su-rface, at a distance 0.8 H from the bottom, once again
there is a marked increase in the intensity of the first maximum, evi-
dently caused by the presence of an interface. With increasing distance
from the bottom of the flow the spectra become more broad-banded.
s(f;
1,0
QB
0, 6
Ry
41
o z 4 o z OFrK gz
Fig. 3. Energy spectra of fluctuations of horizontal (a) and vertical (b)
velocity components at point II 10 hours after onset of experiment at
distance 0.05 H from bottom.
In order to estimate the degree of concentration of'energy at a particular
frequency we used the characteristic fo/Af, sinilar to the quality of the
vibrational system CJO/2 a'il in radiophysics. Here 0 f is the width of the
spectral curve at tfie 0.7-level from the maximtnn value, fp is the fre-
quency which.corresponds to the maximum. An increase in the fp/pf charac-
teristic witfi.an identical fo value is evidence of a clearer definition
of structural formations in the flow. The maximum values of the fp/,&f
parameter are observed at the bottom and at the surface of the flow and
are equal to 3 and 2.5 regpectively.
106
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On the assumpt.ion of correctness of the hypothesis of "frozen-in" turbu-
lence we made an evaluation of the size of an eddy using the expression
L~UT,
where U is the maan velocity at a point, T is the characteristic period,
obtained using the spectral function.
The characLeristic size of the eddies, correspending to a frequency f= 0.3
I?z, is 1.1-1.4 m, which is 13 H.
At this same vertical with forming bottom relief 80 hours after onset of
the experiment the main energy of the turbulent fluctuations is also con-
centrated in the low-frequency region. However, in this case the spectra
become wideribanded. For both velocity components the spectral density
functions have maxima at one and the same frequeneies and the first maximum
falls at a frequency of 0.2 Hz. In contrast to the initial stage in channel -
formation, the first maximum for the vertical velocity component is every-
where more intensive than for the horizontal component. The characteristic
size of the eddies corresponding to a frequency of 0.2 Hz is 1.4-1.9 m,
which is 20 H and is equal to the size of macroscale formations at the
bottom of the flow. 'I'he maximum values of the fp/Q f parameter, the same
as in the initial stage of formation, are observed at the bottom and at
the surface of the flow.
In spectra obtained 10 hours after the onset of formation of tre mouth at
the bottom at dis tances 0.05 H and 0.15 H from the bottom, the first maxi-
mum falls at a frequency of 0.4 Hz. The fp/L1f value attains a maximum val-
ue at a distance 0.05 H.; 0.4 H; 0.98 H from the bottom. Both'the spectral
components have maxima at the same frequencies. The main energy of the tur-
bulent fluctuations is concentrated in the lcw-frequency region. The char-
- acteristic dimensions of the eddies present in the bottom region of the
mouth and corresponding to a frequency of 0.4 Hz are equal to 0.14-0.27 m,
which corresponds to a dimension of the order of the depth of flow at this
vertical. The formation of such eddies is evidently associated with a mark-
ed deepening of the flow at the investigated point. In addttion to these
eddies, in the upper part of the flow there are eddies measuring about 6 H.
_ Thus, the eddies arising during the passage of the flow in the channel
also persist in the mouth reach.
The spectra obta ined at this same vertical af ter 80 hours, when the mouth
- has been formed, and the bar has already been formed, are wider-banded. The
main energy of the turbulent fluctuations is also concentrated in the low-
_ frequency region. The maximum values of the f0/Q f parameter are attained
at the bottom and 3t the surface. 'I'he chara.cteristic sizes of the eddies
corresponding to a frequency of 0.3 Hz, at.which the first S(f) maximum
falls, are equal to 1.1-1.3 m, which corresponds to 12 H, that is, we again
observe eddies existing also at (in the channel.) with a formed
~ bottom.
107
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Summary
1. The kinematic structure of the flow in the mouth reach was governed by
the broadening and deepening of the channel and differs from the structure
of the flow in the channel. The hottom region, where there is a substantial
- change in velocity in the depth of the flow in the mouth reach is greater
than in the main channel.
2. Energy spectra in the main channel and in the mouth reach are multimodal
- for different moments of channel formation. The main part of the energy in
all cases is concentrated in the region of low frequ2ncies. However, if the
main frequency in tfie channel persists in the entire depth, in the mouth
reach it hecomes lower wiCfi an increase in elevaCion.
3. In the channel reach there are eddie5 of about 10-13 H which also persist
in the upper part of the flow in the mouth reach. The indicated sizes of
eddies coincide with Che sizes of the macroscale channel formaticns on the
bottom of the flow.
4. The standard deviations of the velocity fluctuations have maxima at the
bottom, which indicates the existence of a region with an increased turbu-
lence intensity. In the m+outh.rea.ch the distribution of the standard devia-
tions has a tendency ta an increase in the middle of the flow.
BIBLIOGRAPHY
l. Jenkins, H., Watts, D., SPEKTRAL'NYY ANALIZ I YEGO PRILOZHENIYA (Spec-
tral Analysis and its Applications), Vol 1, Moscow, Mir, 1972.
2. Mikhaylov, V. N., DINAMIKA POTOKA I RUSLA V NEPRILIVNYKH UST'YAKH REK
(Flow and Channel Dynamics in Nontidal River Mouths), Moscow, Gidro-
meteoizdat, 1971.
3. Mikhaylova, N. A., Shevchenko, 0. B., "Laboratory Investigations of the
Characteristics of Channel Turbulence and Channel Deformation in the
Coastal Region," METEOROLOGIYA I GIDROLOGIYA (Meteorology and Hydrol-
ogy), No 4, 1976.
4. Mikhaylova, N. A., Kharchenko, I. P., "Laboratory and Field Investiga-
tions of Turb.ulence in Channel Flows in the Low-Frequency Part of the
Spectrum, VESTNIK MGU. FIZIKA, ASTRONOMIYA (Herald of Moscow State
University. Physics, Astronomy), No 6, 1976.
5. Petrov, V. P., "Instrumentation, Method and Results of Investigation
of Turb.ulent ii4:.tuations of Concentration and Velocity in a Sediment-
Transporting Channel Flouz," Aurhor's Summary of Dissertation for the
Award of the Degree of Candidate of Physical and Mathematical Sciences,
Moscow, Moscow State University, Physics Faculty, 1971.
108
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UDC 551.5:633.14
EFFECT OF WINTERING ON THE YIELD ANb GR05S HARVEST OF WINTER RYE
Moscow METEOROLOGIYA I GIDRQLOGIYA in Ruseian No 7, Jul 80 pp 90-96
[Article by V. A. Shavkunova, US3R Hydrometeorological Scientific Reaearch
Institutey submitted for publicatiou 27 E'ebruary 19801
[Text] Abstract: The authox cites the results of in-
vestigations of the effect of wintering condi-
_ tiiona on the yield and gross harvest of winter
rye. The change in the yield of winter rye dur- -
ing the last 20 yeare is inveatigated. Equations
reflecting the trend of this change with time
are derived for obZasts, republics and economic -
regions in which plantings of winter rye are for
the most part concentrated.
The principal grain crop in the Noncher-nozem zone is winter rye. About 80%
of the entire area of wintar rye in the USSR is located in this zone. Due
- to the climatic characteristics in the Nonctternozem zone ita yields are
more atable than in a number of other agricultural regions in the country.
However, even here there are variationa in yield by years. For example,
during the periad from 1958 through 1978 the maximum yield of winter rye
in a ninnber of regions was 22-25 Centners/hectareo whereas the minimum
yield was 5-9 centner s /hectare. (Table 1).
Many researchers have dealt with the problems relating to the influence of
agrometeorological conditions on the yield of winter crops in our country
[1, 3, 4, 6]. They determined the influence of wintering on the yield of
winter crops on the basis of the state of sown-crops in spring (using the
= number of plants and stems per 1 m~ or using the thinness of plantings
after wintering).
The investigations of V. A. Moiseychik [3] have demonatrated that with a
decrease in the number of stems in apring in comparison with their number F
in autumn as a result of damage to the sown areas during the wintering per-
iod the yield is reduced with one and the same state of the winter crops
in autumn. The correlation between the yield and the percentage of intact
109
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stems hy spring is linear. However, its dependence on the degree of bushi-
ness of planta in autumn has a nonlinear character. For winter rye of the
Vyatka and Vyatka 2 varieties the dependence of yield on the state of the
- sown crops in autumn and spring is expreased by the equation
-
Y= 0,063 9P; r = 0,84 � 0,04,
where y is the yield, centners/hectare, K is the mean bushiness of the sown
crops in autumn, P is the percentage of intact stems by the time of renew-
al of the spring growing season of plants.
Table 1
Yield of Winter Rye (Centners/Hectare) During Period 1958-1978
8
9
io
11
12
14
15
16
Teppxropl+A ~
CPCAH z
MSKCH-
M8JI6Hq~
roA 4
MNHN�
M8JI6li8R
5
I r0�~ 6
KOjie68-
IIEPHO,q
JIeHitcrpaltcxaa o6n
15,4
24,4
1973
7,2
1961
17,2
MocKOSCxaA 06a.
14,3
23,9
1973
8,2
1964
15,7
BopoxeHCCtcaii 06.1.
14,9
23,0
1973
6,6
1963
18,4
KyA6dweBCxaA o6n.
12,9
24,5
1975
7,0
1967
17,5
CaparoecxaA o6n.
12,0
22,4
1978
5,4
1963
17,0
6amKxpcttaa ACCP
13,8
22,3
1978
9,3
1964
13,0
,Opex6yprcxa� o6n.
11,8
25,7
1978
4,6
1975
21,1
5eaopyCCKBA CCP
14,6
26,7
1978
6,8
1958
19,9
Tlarauescxas CCP
14,9
25,1
1976
7,8
1962
17,3
KEY:
1.
Territory
9.
Moskovskaya Oblast
2.
Mean
10.
Voronezhskaya Oblast
3.
Maximum
11.
Kuybyshevskaya Oblast
- 4.
Year
12.
Saratovskaya Oblast
5.
Minimum
13.
Bashkirskaya ASSR
6.
Year
14.
Orenburgskaya Oblast
7.
Variation during period
15.
Belorussian SSR
_ 8.
Leningradskaya Oblast
16.
Latvian SSR - As indicated by an analysis of the data for the last 20 years which we made,
the yield of winter rye, despite the increased intensification of agricul-
ture during recent years, increases more slowly than the yield of winter
- wheat. In order to clarify the trend in the increase in the yield of winter
rye we constructed curves of the dynamics of its yield from 1958 through
1978 and derived equations for the trend lines for 37 oblasts, 5 economic
regions, the Baltic region and Belor;issia, where the sowings of winter rye
for the most part are concentrated. Table 2 gives these equations for econ-
omic regions.
The change in the yield of winter rye during the last 20 year~., without al-
lowance for the influence of weather during individual years, can be traced
from the position of the trend line at the beginning (1958) and at tlLe end
110
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of the period (1978). The greateat increase in the yield of winter rye
as a reault of an increase in the level of agricultural techniques and
the introduction of new varieties into production, judging from the trend
lines, was in the Belorussian SSR, Lithuanian SSR and Estonian SSR (16.5-
18.5 centners/hectare). in the Latvian SSR the yield of winter rye in-
creased by 11.9 centners/hectare, in the Northwestern and Central Regions
by 7 centners/hectare. Its minimum increase wae in the Volgo-Vyatskiy,
Tsentral'nochernozemnyy and Povolzhskiy Regions (3-4 centners/hectare).
However, in individual years favorahle for wintering (1973, 1978), the
yield of winter rye in the Tsentral'nochernozemnyy Region attained 22 cen-
tners/hectare, and in PovoJ_zhskiy Region 19 centners/hectare:
Table 2
Equations for Trend Lines for Yield of Winter Rye t
the Period 1958 to 197$
1(03(04)H-
TeppNropiR YPaBHE'HkfA J1HHN11 L(HCH'f
TpCHAOB KOpP!?fA-
1 2 uxln 3
8 Ceaepo-3anaAHWN pai'+oK
9 L(P_HTP8A6HW{i P2FtOH
10 BOJIfO�HUCKHA p3fCON
11 UeHTpB:IbH04epH03Q5tHb1lt
- paNUtt
12 IIOBOlIMCCKNR p8t(()H
1 6enopycctcas CCP
1~ :IE[TOecxaR CCP
15 JlaraHAcKax CCP
- 16 3CTOHCK2R CCP
KEY :
1.
2.
. 3.
4.
5.
6.
7.
8.
9.
>y Economic Regione for
YpoxcaAxocTb no rpex,zY,
4 4/za
Hfl 5 ea 6 yeeaN4e?
H148A0 KOHELj HFlC 3fl
uepNOua nepiloAa aepHOA
y=0.327 T+6.066
0,836
6,4
13,0
6,6
yz0,343 T+6,198
0,850
6,5
13,4
6,9
y=0,151 r+7,614
0,492
7,7
10,8
3,1
y=0,193 T+ 11.874
0,313
12,0
16.4
4,4
y=0,1i1 T+9,914
0,379
10,0
i3,1
3,1
y-1,174T+7,395
0,771
7,3
23,8
16,5
y=0,891 T+5,444
0,889
6,3
24.2
11,9
Y=0.697 T+7,481
0,822
8,1
22,0
11,9
y=0.917 T+8,382
0,849
9,2
27,7
18,5
17 II P{{ !4i Q y 8 H ff e. tf - YPOiiC241HOCTb I70 TfeHAY, T- IIOPAzKOBWIt xoKep COAg� C4H-
TaA c 1958 r., HOMep KOTOpOfO 839T 3d eAHHHL1y (1I:ISi TCCP - 1963 C.).
Territory
Trend line equa.tions
Correlation coefficient
Yield according to trend,
centners/hectare
At onset of period
At end of period
Increase during period
Severo-Zapadnyy Reg:ion
Tsentral'nyy Region
- [Severo-Zapadnyy - Northwest-
ern; Tsentral'nyy = Centrsl]
10. Volgo-Vyatakiy Region
11. Tsentral'nochennozemnyy Region
12. Povolzhskiy Region
13. Belorusskaya SSR
14. Lith;ianian SSR
15. Latvian SSR
16. Estonian SSR
17. Note. y is the yield according
to the trend, T is the sequence
number of the year, reckoned from
1958, the number of which was
used as unity (for the Belorus-
sian SSR 1963)
111
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~
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KE" TO TABLE 3
1. Oblast
3. ndices, %
4. Vologodskaya
5. Fskovskaya
6. Voronezhskaya
7. Lipetskaya
8. Tambovskaya
9. Kuybyshevskaya
10. Saratovskaya
In the trend line equations the regression coefficients characterize the
mean year-by-year tendency of increase in the yield of winter rye. Their
analysis by individual oblasts and republ ics of the European USSR indicat-
ed that the hi.ghest trend in increase in the yield of winter rye was observ-
ed in Leningradskaya (0.747 centner/nectare) and Moskovskaya (0.811 centner/
hectare) Oblasts, Belorussian SSR (1.174 centner/hectare), Lithuanian SSR
(0.891 centner/hectare), Latvian SSR (0.697 centner/hoctare) and Estonian
SSR (0.917 centner/hectare) . -y u%ia -c
y en~ne"rafhecfa_ro
10
0
Fig. 1. Dependence of yield on area
the Northwestern Economic Region.
~ !W~ , .
~
~ 20 4o s~ i Sdead� T
with dead plantings of winter rye in
The deviations of yield �rom the trend line, which characterize the degree
of stability of yields, during the cou~se of the entire analyzed period by
oblasts, regions and republics consistently fell in a large range (�15-30%),
but in a number of regions during the last decade even increased Co 1-50-60%
of the yield according to the trend. In Leningradskaya, Novgorodskaya and
Pskovskaya Oblasts in the Northwestern Region, in all oblasts of the Central
ReEion, in Gor'kovskaya, Voronezhskaya, Kurskaya and Ul'yanovskaya Oblasts
and Chuvashskaya ASSR, in the yea.r 1972/73, which was favorable for the
wintering and growth of crops, the positive deviations of yield from fihe
trend ware 25-50%. In years with unfavorable wintering conditions, when
the plantings of winter rye in the course of 120-160 days were under a
thick snow cover with weak freezing of the soil and soil temperature at the
depth of the tillering node of about 0�C (1965/66, 1977/78) or were subject-
ed to the harmful influence of strong freezes or a thin snow cover (1968/
69, 1971/72), the deviations of yield from the trend attained -30 and -50%.
In a comparison of the deviation of yield and the extent of the area with
plantings of winter rye killed during the autumn-winter period it was es-
tablished that there is a nonlinear inverse relationship between them (Fig.
1). As a rule a large area with dead plantings of winter ryP corresponds
to a minimum value of its yteld. We also discovered similar dependences of
the yield of winter rye on the area witFi planting3 which had perished by
spring for other economic regions. This pattern was violat2d only fn indi-
vidual years with unfavorable wintering conditions, but very good
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conditions for yield formation during the spring-surmner period. Table 3
shows that in 1968/69 winter rye perished over great areas as a result of
winterkilling and was resown with spring crops; its yield in Kuybyshevsk-
aya asd Lipetskaya Oblasts was somewhat higher than the yield according
to the trend. A positive deviation from the trend was observed in Kuyby-
shevskaya and Saratovskaya Oblasts in 1475/76 as we11, when due to an aut-
umn drought a considerable part of the area of winter rye was resown in
spring.
As indicated by an analysis of data for the last 17 years, a decrease in
the yield and a decrease in the harvested area of winter rye also lead to
a decrease in the gross grain harvest.
Figure 2 shows the change in the gross yield of winter rye and the area of
its perishing by years for the period from 1961/62 through 1976/77 for
- Novgorodskaya, Tul'skaya and Penzenskaya Oblasts. For the c:omparability of
data for different years the gross yield of winter crops was reduced to a
_ unit planted area (mean for the period) and was given in percent of its
mean value. Figure 2 shows that the gross yield decreases considerably
with an increase in the area of perished winter rye. In years with poor
- winterir.g conditions (Novgorodskaya Oblast 1965/66, 1976/77, Tul'skaya
Oblast 1963/64, 1974/75, 1976/77, Penzenskaya Oblast 1962/63, 1968/
69, 1974/75, 1976/77),with the perishing of crops over an area equal to
20-50% of the total area of sown winter rye, jt decreased to 50-70%. In
years with favorable weather conditions for the autumn growing season and
the wintering of crops (Novgorodskaya Oblast 1966/67, 1970/71, 1972/73,
Tul'skaya 1969/70, 1972/73, I975/76, and Penzenskaya 1969/70, 1973/
74, 1975/76), when the death of winter rye was not great, the gross yield
was 110-170% of the mean.
In the Nonchernozem zone one of the principal reasons for the decrease in
the yield of winter rye is a weakening of the crop:; and the death of a
great number of stems as a result of their prolonged presence under a thick
snow cover with only a slight rreezing of the soil. The area with the dead
plantings may be small, but in the remaining part of the plantings of win-
ter rye the plants are damaged. In winter the apical cone grows without be-
coming differentiated, as a result of which in spring some of the sprouts
completely die off o.r the ears are shortened, with a lesser number of
grains. �
We determined the dependence of thP gross yield of winter rye for the ter-
ritory of different oblasts on the area with dead crops in winter. The
method cited in [S] was used in the computations.
For the oblasts of the Northwestern economic region the dependence is ex-
pressed by the equation " - W- 235.5 e'0'os sB 32,4;
(1)
[B = dead] r~ =0,671 + 0,082; Ew 1
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for the oblasts of the Tsentral'nochernozemnyy (Central Chernozem) econ-
omic region
W= 171,8 e o.a{s sa + 3,5;
(2)
~1= 0,781 � 0,058; Ea. l i,9�/0;
[B = dead ]
for the oblasts for the Volgo-Vyatskiy economic region
w- 168,7 e- 0. 055 ss +29,5~ (3)
~ =11,762 t 0,102; Ew - � 17,70l0;
for the oblasts of the Ural'skiy economic region
W- 150,7 e-o.089 Ss + 20,0; (4)
r~ - 0,717 -4- O,Otil; Em = t 22,10/0;
for the oblasts of the Tsentral'nyy (Central) economic region
- -
[Y~ = 222,8 e'o,osa sa + 21, 1~ -
(5)
i= 0,547 � Q,091; E w_ -T- 23,4�/0� -
' Here W is the gross yield of winter rye grain over the territory of the
oblasts, reduced to a unit planted area in pezcent of its mean value; Sdead
is the area with dead plantings of winter rye; '1'1 is the correlation ratio;
EW is the error of the equation.
wr., s11% Sdead o x
sso r, 'A
~ I
1#o
1?o I ! i I ~
1on
v
BO 1 r~ vX
I 1,I ~ I ~j 19
/
so ~\1
yo
n i A~
20 r / !
. \ ;
. �r-rar :
r .9sr162 W/66 � ~s69no ~9TJ,~~y
�
1M164 ~967/6D 1911/77 7975/16
, Fig. 2. Change in gross yield W and area with dead plantings of winter rye
Sdead in Novgorodskaya (1), Tul'skaya (2) and Penzenskaya (3) Oblasts.
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The carrelation hatween the gros.s yield of winter r}e and the area with _
dead plantings is nonlinear. It is expresged-with particular clarity in
- the case of an area with dead plantings in apring equal to 15% of ita sown area or more. In years with conditiona favo:.ahle for wintering, when
the area of death of the plantings is less than 10% cf the sown area, the
gross yield of grain as a rule ts determined by the conditions of the
spring-summer period and the level of agricultural engineering. An ex-
ception is the years when a considerable percentage of the stems of win-
ter rye in the Nonchernozem zone perished as a result of rotting (1966/
67, 1467/68). The correlation between the gross yield of winter rye and
the area of destruction of plantings during the winter period, as can be
seen from the cited equations., for the Volgo-Vyatskiy, Ural'skiy and Tsen-
tral'nochernozemnyy econonomic regions was closer (rJ= 0.72-0.78) than in
the Central and Northwestern regions (YZ = 0.55-0.67). This can be attrib-
uted, evidently, to the more favorable conditions for the wintering of
winter rye in the Central and Northwestern regions in comparison with the
Volgo-Vyatskiy region, where rye is frequently subjected to rotting, and
in the Ural'skiy and Tsentral'nochernozemnyy regions where it frequently
freezes out.
V. A. '.�;oiseychik [3] earl:ier obtained a quantitative dependence of the
gross yield on the area with dead plantings as a whole for winter crops for
1950-1970. It revealed that each percent of area with dead plantings of
winter crops in spring reduces the gross yield as a whole for the USSR on
the average by 1.7%.
The introduction of more winter-resistant varieties, an increase in the
level of agricultural techniques for the cultivation of plants and the
timely adoption of ineasures for the care of plantings during the early
spring period in many regions to a definite degree can reduce the yield
losses due to unfavorable agrometeorological conditions during the winter
period.
BIBLIOGRAPHY
1. Kulik, M. S., METODICHESKIYE UKAZANIYA PO SOSTAVLENIYU DOLGOSROCHNYKH
AGROrIETEOROLOGICHESKIKH PROGNOZOV SREDNEY OBLASTNOY UROZHAYNOSTI
OZIMYKH ZERNOVYKH V NECHERNOZEtQ10Y ZONE (Systematic Instructions on
Preparing Long-Range Agrometeorological Forecasts of the Mean Oblast
Yield of,Wiater Grain Crops in the Nonchernozem Zone), Moscow, Gidro-
meteoizdat, 1976.
2. Kuperman, F. M., Moiseychik, V. A., VXPREVANIYE OZIMYKH KUL'TUR (Rott-
ing of Winter Crops), Leningrad, Gidrometeoizdat, 1977.
3. Moiseychik, V. A., AGROMETEOROLOGICHESKIYE USLOVIYA I PEREZIMOVKA OZIM-
YKH KUL'TUR (Agrometeorolagical Conditions and Wintering of Winter
Crops), Leningrad, Gidrometeoizdat, 1975.
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4. Obukhov, V. M., UROZHAYNOST' I METEOROLOGICHESKIYE FAKZORY (Y1e1d and
Meteorological Factors), Moscow, Gosp.lanizdat, 1949.
5. Semendyayev, K. A., EMPIRICHESKIYE FORMULY (EmFirical Formulas), Mns-
cow-Leningrad, Tekhteoretizdat, 1933.
6. Ulanova, Ye. S., AGROMETEOROLOGICHESKIYE USLOVIYA I UROZHAYNOST' OZIMOY
P5HENITSY (Agrometeorological Conditions and Yield of Winter Wheat),
Leningrad, Gidrometeoizdat, 1975.
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UDC 551.(576.1+509.334-513)
INVESTIGATION OF A CLOUD ENSEMBLE MODEL ON THE BASIS OF GATE DATA
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 97-108 _
[Article by Candidate of Physical and Mathematical Sciences A. I. Fal'-
kovich, USSR Hydrometeorological Scientific Research Center, submitted
�or publication 15 January 1480]
[Text] Abstract: The author has formulated a cloud
ensemble model for tfie purpose of parameter-
ization of the moist convection processes in problems of general circulation of the atmo-
sphere and long-range weather forecasting. The
investigation is carried out on the basis of
observation phase III in GATE polygon A/B. A
study is made of the spectrum of the cloud
. ensemble, the distribution of entrainment and
expulsion of mass, heat and moisture balance
in the cloud ensemb.le, heating function as a
result of condensation. A new principle for
- the parameterization of moist convection is
proposed.
~
In the numerical integration of the equations of hydrotherigodynamics a part
of the spectrum of movements (so-called subgrid processes) is cut off. Due
to the nonlinearity of the equations its influence on the remaining part _
must be parameterized, that is, must be expressed quantitatively through
parameters described by the grid, the redistribution of energy and momentum
among these parts of the spectrum. Here it should not be thought that if we
integrated the weather forecasting equations with a very small interval it
would be possible to describe the life cycle of each cloud separately and
- that the parameterization is governed only by the technical possibilities
of modern computers. This is not so. First, for the time being there is
still no satisfactory cloud model, and second, even if it was, at the ini-
- tial moment in time we will never know with the required accuracy the
necessary characteristics of the cloud. The model of an individual cloud
is described by a complex system of equations in hydrothermodynamics. A
- very important role in its development is played by microphysical processes,
whose description in weather forecasting problems is impossible.
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In this connection clouds in Weather forecasting must be regarded stat- _
_ istically as a cloud ensemble, investigating its total influence on the
change on the macroscale characteristics of the atmosphere. In this case
it is necessary to make abstraction from the nature of an individual cloud,
introducing some stylization of this cloud, and no longer model a cloud, _
but the entire cloud ensemble corresponding to some macroscale disturbance.
There are several different approaches to solution of this problem. For ex-
ample, Fraser [6] in 1968 attempted to describe the mechanism of the life
cycle of a cloud. He regarded the cloud as a"white box," consisting of
the cloud proper, a homogeneous sphere-i occupied by an ascending current,
and the cloud "jacket," where the temperature can not only be below the
temperature of the cloud, but also below the ambient temperature. The tem-
perature minimum is attained at the visible boundary of the cloud (where
the liquid water content becomes equal to zero). Writing the equation for
the first law in thermodynamics for the iaixture of cloud sir and ambient
air, Fraser finds the temperature distribution with increasing distance
from the core of the cloud. As the horizontal coorainate here use is made
of the ratio of the mass of cloud 3ir to the mase of the mixture. The par-
ticles, entering into the cloud "Jacket," have a negative buoyancy force
relative to the ambient air. They descead first in conformity to the moist
adiabat, for the time being without evaporation of all the liquid water,
and then in conformity to the dry adiabat, and for the time being their
temperature is not comparable to the ambient temperature. Computing the
flow of mass in the settling region, it is possible to relate it to the
upward transport in the cloud core and thereby compute the total vertical _
_ transport of mass generated by the "white tax" at any level. It is true
that for this it is samehow neceseary to parameterize precipitation. Many
unclear points remain in this cloud atylization. For example, it is not
clear how to stipulate the cloud boundaries vertically. In this connec-
- tion it is unclear whether the continuity equation is satisfactory here.
The third equation of dynamics is used only qualitatively: it is assumed
that the particle descends (rises) if its temperature differa from the am-
bient temperature to the point where these temperatures are comparable.
- Another approach is based on the use of the theory of a turbulent noniso-
thermic jet for the mo deling of a cloud [1].
Here the cloud is a jet with characteristics homogeneous along the section
and is entrained into homogeneous surroundings. In the model of ajet use
is made of the third equation of motion, in which an allowance is made for
the buoyancy force, the weight of the liquid water in the jet, entrainment
of ambient air into the jet and the resistance of the ,jet to the external
flow. Use is also made of the equations for conservation of energy, specific
liquid water content and ice content. Precipitation does not fall and ice
content is parameterized by the introduction of the radius of the cloud
particles. It is asstnned that the pressure in the jet and in the surround-
ing atmosphere is identical. The entrainment is stipulated inverse propor-
tional to the radius of the jet, which can change with altitude. The
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expulsion of mass and radiation cooling at the tops of the clouda are
neglected. The model is stationary. The cloud top is situated where the
vertical velocity becomes equal to zero. We note that it follows from the
condition of stipulation of entrainment that the vertical velocity can be-
come equal to aero only where the jet under the influence of the external
flow turns and becomes completely horizontal. The slope of the jet is de-
termined by the effect of aerodynamic @rag forc:es; difficulties arise in
the choice of the aerodynami c drag coefficient.
. This cloud model was used in [2] for computing some properties of the en-
semble of convective clouds on the basis of aerological sounding data. At
the levEl of the cloud base it was assumed that the overheating of the
~ cloud relative to the surrounding air was 0.1�C and W= 1 m;sec for all
clouds. The distribution function for clouds was stipulated on the basis
of horizontal dimensions, fo llowing Plgnk [8]:
- 1V (D) ~ jVo e-Q o
Here 0< D- O
> rl
U
cd
rl

q th
cd cC
00
�r1
9: uS 00
co
�rl
9
v7 OD
cd -H
c
~
~
~
~
~
H
HO
A U~
A U~
P

W
~

A
0-
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Tahle 2 shows Lhat the quantity of precip itation determined in a season
with a field rain gauge installed at a height of 0.35 m, that is, dire ct-
ly at the ground surface, in both places of comparative observatione, ex-
ceeded the amount determined by a similar instrument at a heigY:t of 1.5 m
f rom 3. 8 to 8. 2%.
It should be neted that the seasons of comparative observations in 1977
and 1979 were arid and the shortage of precipitation was 40 and 24% re-
spectively; 1978 was overmoist, with the quantity of falling p recipita tion
exceeding the norm by 32%.
After summarizing the results of the comparative observations cited above
thE preliminary conclusion can be drawn that a field rain gauge installed
at a height of 0.35 m more completely determines tfie quantity of falling
precipitation than one installed at the standard height 1.5 m.
It is also interesting to note Chat when uaing a field rain gauge in the
surface variant of the apparatus (0.35 m) there is a greater degree of
concealment and a ccordingly it is more secure, which is a condition of more
than a little importance when it is emplo yed under field conditions.
Such investigations of the Davitaya field rain gause, carried out in dif-
ferent regions of the country, make it possible to draw final conclus ions
concerning the feasibility of its installation in the surface variant.
BIBLIOGRAPHY
1. Podgayskiy, N. N., "Use of the Davitaya Field Rain Gauge as a Total
Instrument," rIETEOROLOGIYA I GIDROLOGIYA (Meteorology and Hydrology),
No 2, 1975.
2. Podgayskiy, N. N., "Tota1 Measurement of Precipitation in Rotated
Fields," METEOROLOGIYA I GIDROLOGIYA, No 10, 1977.
3. RUKOVODSTVO DLYA AGROMETEOROLOGICHESKIKH POSTOV, MTS, KOLKHOZOV I SOV-
KHOZOV (Manual for Agrometeorological Posts) Machine Tractor Stations,
Kolkhoz and Sovkhoz Enterprises), Leningrad, Gidrometeoizdat, 1955.
149.
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~
REVIEW OF MONOGRAPH BY I. D. KOPANEV: $NEZHNYY POKROV NA TERRITORII SSSR
(SNOW COVER OVER THE TERRITORY OF THE USSR), LENINGRAD, GIDROMETEOIZDAT,
1978, 180 PAGES
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 119-120
[Review hy Candidates of Geographical Sciences A. I. Voskresenskiy and
N. N. Bryazgin]
[Text] The author of this neuily published bouk, I. D. Kopanev, is one of
the outstanding specialists in our country in the field of study of the
~ snow cover. The new monograph which he has writCen contains a scientific
generalization of an enormous volume of long=term observations of the
snaw cover by more than 600 hydrometeorological stations and posts in the
USSR.
' The reviewed book is distinguished by its practical nature. It is intend-
- ed for a broad circle of readers, not only professional climatologists
and geographers, but also workers in agriculture and transportation, and
also those at planning and construction agencies. The monograph includes
extensive, well-selected reference material and also the results of anal-
ysis necessary for solving scientific problems related to the climatology
of the snow cover.
Much attention is devoted to the stochastic analysis method, by means of
which it is possible to take into account the entire statistical total-
ity of initial information. This enabled the author to obtain some char-
acteristics of the snow cover with a st3.pulated guaranteed probability
for most of the stations in the USSR (excluding mountain and arctic sta-
tions).
The book gives a concise history of the method for making snow-measuring
observations since 1892 and its changes during subsequent years. The
author feels that at the prPSent time the method for carrying out snow-
measuring observations in general has been considerably improved. How-
evez, it should be noted that the last review of the method for snow-meas-
uring ohservations, made in 1965 and directed to a decrease in the volume
150
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of observations (a changeover from snow surveys every 10 da;s to monthly
surveys only) reduced the information yield of data on the snow cover.
This applies, in particular, to the northern regions, where as a result
of frequent blizzards there is a considerable horizontal redistribution
of the snow cover.
In the monograph considerable attention is devoted to an investigation of
the accuracy of standard snow-measuring observations. Using the mathemat-
ical statistics approach, the author defined the most advantageous solu-
tions of the evaluation of errors in snow-measuring observations and a
method for computing the temporal characteristics of the snow cover. The
conclusion is drawn that the maximum admissible error in snow-measuring
observations (5-10%) in different regions of the USSR requires a differ-
ent choice of the number of ineasuremenC points, the time interval, length
and form of the route. In connection with the change in the mEthod for mak-
ing snow-measuring observations the author draws attention to the neces-
sary evaluations of homogeneity of series of snow-measuring observations.
One of the sections of the mnograph is devoted to this problem. Here the
author has established that the inhomogeneity in the series of snow-meas-
uring observations at most hydrometeorological stations in the USSR is in-
significant and is within the limits of ineasurement error.
In a number of sections in the monograph the author also gives the climatic
aspects of the snow cover. For example, the duration of the snow cover., the
dates of formation and destruction of the snow cover, are presented in the
form of maps and tables giving the characteristics of their spatial and -
temporal variabiZity over the territaiy of the USSR. ,..ies? results will be
useful in solving a number of practical and methodologicat prL,lems.
- In the monograph the information on the depth of the snow cover is given
in the greatest detail. Its mean chara^teristics are given for the terri-
' tories of the administrations of the Hydrometeorological Service, separate-
ly for the Baykal-Amur Railroad snd the entire Soviet Union in the form of
monthly maps and also maps of the mean maximum and extremal depths of the
snow cover on the basis of data from snow-measuring surveys. As new inform-
ation the author gives the variability of the depth of the snow cover in
the course of winter and also evaluations of changes in its depth in field
and forest sectors in comparison with observational data obtained using
_ permanent rods. However, it must be admitted that the problem of the non-
representativeness of observations with permanent rods at meteorological
stations in arctic and probably subarctic regions remains timely. In such
areas these observations possibly should be abolished since they do not
- reflect the real distribution of the snow cover and accordingly cannot be
used for practical and scientif ic purposes.
The computations of the probabil.ity of distribution of the snow cover by
regions and individual stations ma.de by the author make it possible to _
satisfy more completely and on a modern level the requirements of many
- branches of the national economy. Using the tables and nomograms presented
in the monograph practical workers can independently obtain the necessary
information. The same purpose is solved by the ma.terial, presented for
151
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the first time, on the spatial and tempoial variabj.lity of depth of the
snow cover. The author established a considerable year-to-year variabil-
ity of depth of the snow cover (on the basis of data for stations with
long series of obssrvations), dependent on the combinations of conditions
of circulation of the atmosphere and local physiographic conditions.
- In the monograph considerably less attention is devoted to two other char-
acteristics of the snow cover density of the snow cover and water re-
serve in the snow cover. However, the author has been able to supplement
considerably the materials contained in handbooks on the climate of the
USSR. In addition to variability of density of the snow cover, the author
also examined the characteristics of blizzard activity, and also the cor-
relation between data on water reserves in the snow cover and precipita-
tion, etc. The results of investigations described in this section can be
used for solving different practical problems, in particular, in computa-
- tions of snow transport during blizzarda and computations of the water bal-
ance.
The appearance of the new publication must be regarded as an important con-
tribution of hydrometeorology to supporting the needs of the national econ-
ony of the country.
152
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REVIEW OF MONOGRAPH BY A. P. FEDOSEYEV: AGROTEKHNIKA I POGODA
(AGRICULTURAL TECHNIQUES AND THE WEATHER), LENINGRAD, GIDROMETEOIZDAT,
1979, 240 PAGES
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No Jul 80 pp 120-121
[Review by Candidate of Geographical Sciences V. N. Strashnyy and G. Z.
Goloverdyuk]
[Text] In this book by A. P. Fedoseyev, which was edited by Academician
I. S. Shatilov of the All-Union Academy of Agricultural Sciences, agricul-
tural specialists will find information on the influence of agrometeoro-
logical conditions on agricultural production, and also on different agri-
cultural engineering methods which make possible more effective use of the
potential natural resources uf a territory and favor obtaining higher and
more stable yields.
The author demonstrates the results of investigations of the inf luence
' of differentia*..ed agricultural techniques for the cultivation of agricul-
tural crops on their yield in relation to climatic and agrometeorological
cotiditions. The author sets forth the essence of recommendations on taking
into account existing and anticipated weather conditions in determining
the desirable struc-,ure of sown areas, methoda and times for working the
soil, determining the vptimum times and doses of application of mineral
fertilizers, times for the sowing of grain crops, and also for the care
for sown areas and carrying out the harvest.
It was established as a result of the investigations that with deviation
of the times for the sowing cf spring and winter grain crops from the op-
timum times a noncorrespondence arises between the biological needs of
plants and the prevailing meteorological conditions and this leads to a
decrease in crop yield. The possibility of selecting the optimum times for
sowing and the optimum seeding norms for grain crops in each specific year
in dependence on meteorological conditians and the climatic probability
of different gradations of precipit3tion in .Tuly is made clear.
It is demonstrated on the basis of extensive experimental data that with
- allawance for the state of grain crop sprouts and.prevailing agrometeor-
ological conditions it is possible to select the corresponding agricultur-
al techniq~:c,; for caring for sown areas favoring an increase in crop yield.
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The agrometeorological criteria of desirability of packing the soil and
harrowing sown areas are given.
The influence of unfavorable agrometeorological conditions during the cold
season of the year on the state of winter grain crops and methods for pro-
tecting sown areas from tfieir ef�ect is considered.
The hook gives the agrometeorolog:_,:al indices for the beating down of the
principal regionalized varieties of harley and a method for predicting
the beating down of crops and the effectiveness of their processing with
TUR preparation are examined in dependence on weather conditions.
The author attaches much importance to the choice of the optimum techniques
o� harvesting work, taking into account the influence of agrometeorolog-
ical conditions on the magnitude of the grain losses.
Zn the book special attention is devoted to the effectiveness of mineral
fertilizers in dependence on weather conditions. Among the agrometeorolog-
ical factors. determining the effectiveness of fertilizers the author in-
cludes the level of the exposure of plants to light, temperature, air and
soil moisture content. In the clima.tic aepect, a decrease in the annual
quantity of precipitation from the northern to the southern agricultural
regions of the European USSR by 100 mm causes a decrease in the effective-
ness of moderate doses of fertilizers on the average by 1.1 centner/hectare
of grain for grain crops as a whole and by 1.9 centner/hectare for winter
crops. A decrease in the reserves of productive moisture in the soil dur-
_ ing the growing season for grain crops by 10 mm results in a decrease in
the effectiveness of fertilizers on the average by 0.1-0.2 centner/hectare
of grain. It is shown that the content of nitrates in the soil in spring is dependent
on the quantity of precipitation during the winter period and the nature of
snow melting. With precipitation of 190-200 mm or more the content of ni-
- trates decreases sharply, which predetermines the high effectiveness of
nitrogen fertilizers.
The author has proposed equations for computing evaluations of the effect-
iveness of fertilizers as a function of ineteorological factors and indi-
vidual agrochemical properties of the soil.
Maps of the average effectiveness of fertilizers for grain crops jn depen-
dence on agroclimatic conditions are given. Methods are proposed for de-
termining the precipitation for the autumn-winter period in ascertaining
the optimum doses of nitrogen fertilizers for grain crops in each specific
year. Agrometeorological recommendations are given for optimizing the doses
of nitrogen topdressing for grain crops in dependence on meteorological
conditions. It is shown that allourance for the quantity of falling precipit-
ation or soil moisture content during the autumn period makes it possible
to make a correct decision concerning the advantage of sowings of winter
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or spring grain crops for the purpose of obtalning the maximum yield in
each specific year.
In the author's opinion, allowance for agrometeorological conditions when
using differentiated agricultural techniques for the cultivation of agri-
cultural crops and the making of optimum agricultural engineering decisions
constitutes a significant, but for the time being a poorly used reserve
for the increasing of crop yields.
The book also gives exampJ_es of computations of the economic effectiveness
of different agrometeorological recommendations.
The book has individual shortcomings. For example, there is inadequate
discussion of the matters of using two- and three-day weather forecasts
and also predictions of air temperature and precipitation anomalies for
5 and 10 days for the making of economic decisions in agricultural produc-
tion. References are made to long-range predictions of the time of onset
of the summer precipitation maximum, climatic stochastic forecasts, sto-
chastic synoptic forecasts of moistening conditions despite the fact that
such forecasts are not made in the system operated by the State Committee
on Hydrometeorology.
In general the book merits a high evaluation because a study of this type
has appeared for the first time and its publication must be regarded as
a significant contribution to solution of the problem of introduction of
hydrometeorological information iiito agricultural production. It will be
a valuable aid for a wide range of specialists in agriculture and agro-
meteorologists. Without question, it will be read with interest and profit.
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SIXTIETH BIRTHDAY OF SAMUIL r10ISEYEVICH SHUL'MAN
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 122-123
[Article by members of the Board of the USSR State Committee on Hydro-
meteorology and Environmental Monitoring]
[Text] Samuil Moiseyevich Shul'man, Director of the West Siberian Regional
~ Scientific Research Institute and Chief of the West Siberian Territorial
Administration of Hydrometeorology and Environmental Monitoring, marked
his 60th birthday on 20 July 1980.
Samuil Pioiseyevich began his work activity in the Hydrometeorological Ser-
vice in 1944 after graduation from the Higher Military Hydrometeorological
Institute in the post of ineteorological engineer at the polar station Am-
derma. During the period 1945-1947 he worked as a meteorological engineer
at the aviation meteorological station Sofia in Bulgaria. In May 1947, af-
ter demobilization from the ranks of the Soviet Army, Samuil Moiseyevich was
sent to Austria, where until November 1949 he worked as chief of the for-
eign aviation meteorological station in Vienna. The next five years he
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headed prognostic subdivisions at the Administration of the Hydrometeor-
ological Service of the Karelian-Finnish SSR.
Beginning in 1954 and to the present time the work activity of S. M. Shul'-
man has been associated with the West Siberian Tei�ritorial Administration
of Hydrometeorology and Environmental Monicoring, whlch he has headed
since 1959. Samuil Moiseyevich is devoting much effort Lo the development
and improvement of a system of prognostic agencies and a network of sta-
tions in the administration. He is devoting great attention to improve-
ment in the forms and methods for hydrometeorological support of Party and
soviet agencies in Western Siberia, which has led to an increase in the ef-
fectiveness of operation of the service in the national economy.
The broad development of scientific research in the subdivisions of the
- administration led to the organization in 1968 of the Novosibirsk Affil-
iate of the USSR Hydrometeorological Center and its subaequent transforma-
tion in 1970 into the jdest Siberian Regional Scientific Research Institute.
14hile combining the tasks of chief of the administration and director of
the institute, S. M. Shul'man exhili.ts 2oncern about the development of a
broad complex of scientific investigations in the field of the hydrometeor-
ology of Siberia, an increase in the scientific potential of the institute
and the creation of a progressive scientific atmosphere there.
_ The activity of S. M. Shul'nan, directed to the universal development and
strengthening of creative contacts with the key institutes of the Siberian
Division USSR Academy of. Sciences and the Siberian Division of the All-
Union Agricultural Academy, has been of great importance in establishing
the institute and ensuring a high level of investigations by its workers.
Samuil Moiseyevich made a definite contribution to the creation and suc-
cessful operation of the West Siberian Regional Computation Center, the
- Novosibirsk Service of the Automated System for Data Transmission and the
Center for the Reception and Processing of Satellite Information. Under
his direction and with his direct participation work is bei.ng successfully
done on the organization of a national service of observations and mon-
itoring of environmental contamination. During the time of his work at
- the Administration of the Hydrometeorological Service he has done much
work on the introduction of modern technical equipment in the network of
stations in the administratior_, on the development of an automated system
for the processing of hydrometeorological information at the West Siberian
Regional Hydrometeoralogical Center, and in compiling and issuing regime
and reference materials.
Samuil Moiseyevich is carrying out much wcrk for strengthening the opera-
tional and observation agencies of the West Siberian Territorial Adminis-
tration of Hydrometeorology and Environmental Monitoring.
In addition to his great routine productive activity and organizational
work, S. M. Shul'man is actively participating in public 1if.e. The busi-
nesslike and personal qualities of Samuil Moiseyevich have won him merited
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authority in the organizations of the State Committee on Hydrometeorol-
ogy, among subordinates, and also in the organizations of other depart-
ments.
The services of S. M. Shul'man in the development of the Hydrometeorolog-
- ical Service, as well as active participation in public life, have been
recognized by government awards the "Emblem of Honor" and medals.
In warmly congratulating the veteran of the Hydrometeorological Service on
his noteworthy anniversary, we wish him long and productive years of life,
strong health and new work successes.
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AT THE USSR STATE COMMITTEE ON HYDROMETEOROLOGY AND ENVIRONMENTAL MONITORING
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 p 123
[Article by V. N. Zakharov]
[Text] During the period 25-27 March 1980 the State Hydrological Institute
held a coordination conference on the draft of a plan for scientific-re-
search and experimental des ign work for 1981-1985 in the field of hydrol-
ogy of the land.
A numher of scientific reports were presented prior to discussion of the
draft of this plan. The mos t important scientific and technical problems
in the field of hydrology of the land in the Eleventh Five-Year Plan were
discussed by the conference chairman, the director of the State Hydrolog-
ical Institute A. A. Sokolov. Reporta were presented on the present sta-
tus and tasks of hydrological investigations in the Ukraine (A. V. Shch-
erhak), in Central Asia (Yu. N. Ivanov), in the Far East (V. N. Glubokov),
in Kazakhstan (V. V. Golubtsov), in Transcaucasia (V. Sh. Tsomaya), on
the prospects for the devel opment of investigations for study of the mouth
reaches of river.s (M. M. Ro gov) and on the atatus and prospects for devel-
opment of investigatians for study of the quality of water resourcea (L. V.
Brazhnikova).
Communications of the scientific directors nf the corresponding sections
were presented in relation to the draft plau presented for consideration.
The draft plan was approved after taking into account the comments and
additions expressed or proposed in the course of the discussion.
The pl.an dealt with such themes as changing the water balance, hydrological
regime and surface water resources, hydrometeorological basis for the ter-
ritorial redistribution of water resources, water balance, water regime
and hydrological computations, channel processes, erosion and sediments,
and also on some other sections.
In addition to the scientis ts and specialists of the State Hydrological
Institute, the conference was attended by representatives of the State
Oceanographic and Hydrochemical Institutes, Far Eastern Scientific
Research Institute, Transcaucasian Scientific Research Institute, Kazakh
Scientific Research Institute, Central dsian Scientific Reaearch Institute,
Ukrainian Scientt,fic Research Institute, Institute of Water Problems USSR
Academy of Sciences. 159
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AT THE ALL-UNION EXHIBITION OF ACHIEVF.MENTS IN THE NATIONAL ECONOMY
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 123-125
[Article by S. B. Iokhel'son, I. A. Koloskov and M. M. Novikov]
[TextJ The problem of preaervation of the environment occupies one of the
first places among the vitally important problems exciting mankind today.
In our country the preservation of the environment has been elevated to
a constitutional issue and it is being devoted great attention on an-
everyday basis.
A special exhibit entitled "The Environment Reliable Monitoring" was
opened on 10 January 1980 in the pav3lion "USSR Hydrometeorological Ser-
vice" at the All-Union Exhibition of Ach3evements in the Natienal Economy.
This exhibit reflected the achievements brought about in this field. The
exhibit consiated of five main sections: State System for Observing and
Monitoring the State of the Environment; Instruments and Methods for Study-
ing and Monitoring the Environment; Methods for Routine and Long-Range Fore-
casting; Scientific Research Work; International Activity of the Institu-
tions of the State Committee on Aydrometeorolo gy in the Field of Preserva-
t.ion of the Environment.
In the Soviet Union a National Service for Ob.serving and Monitoring the
Level of Environmental Contamination has been established with the direct
paxticipation of the key scientific research institutes of the State Com-
mittee on Hydrometeorology (Institute of Applied Geophysics, Main Geophys-
ical Observatory, State Hydrochemical and Oceanographic Institutes, and
Institute of Experimental Meteorology). Its activity can be characterized
by the following data: the state of the air basin ia monitored in 350 cit-
ies in our country, including at stationary observation points in 250 cit-
ies; each year laboratories make more than 3 million analyses of aerosols
and gases in the atmosphere; monitoring of contamination of waters of the
land is carried out in 1,900 rivers, lakes and reservoirs and in 14 seas;
observations in fresh-water bodies are carried out at 4,000 pointso and
in sea waters - at 1,800 stations; the total number of analyses of water
samples annu:uly exceeds 2 million. The netwnrk for the monitoring of soil
contamination, organized four years ago, even now monitors the content
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of pesticides and metals at 1,700 points in the Soviet Union.
Water quality is monitored with respect to hydrobiological indices in 170
rivers, lakes and seas.
The effectiveness of ineasureQ for preventing the contamination of the en-
- vironment is dependent to a high degree on the inatsvments and equipment
used in monitoring. The wide variety of instrwnentation shown at the ex-
hibit shows that the main direction in developments in the field of anal-
ytical instrument making is directed to ensuring the reliability, opera-
bility and effectiveness of monitoring of the state of the environment. The
exhibit familiarizes visitors with new instruments, standard-produced by
industry, introduced in the system of the State Committee on Hydrometeor-
ology and other ministriea and departments, and also new inatrument devel-
opments in this f ield.
During recent years automatic eyatems for observation, collection and pro-
cessing of information have been auccessfully introduced into the monitor-
ing network. The Central Design Bureau of Hydrometeorological Instruments,
together with other organizations, ia demonatrating an automatic station
for the monitoring of atmospheric contamination ASKZA - avtomaticheskaya
stantsiya kontrolya zagryazneniya atmosfery. It makes possible snnitoring
and transmission of data on contamination of atmoapheric air with CO and
S02.
The Hydrochemical Inatitute is exhibiting an automatic station for the mon-
itoring of surface waters of the land ASKPV avtomaticheskaya stants-
iya kontrolya poverkhnostnykh vod sushi. The station makes ppssible the
simultaneous collection of information on seven parameters (oxygen content,
turbidity, pH, and others).
~
Among the most interesting instruments shown at the exhibit we can mention
the following:
the "Atmosfera II" truck laboratory, intended for carrying out exped-
- itionary work and routine monitoring of air contamination (Safonovskiy
Plant) ;
the "Komponent" sampling apparatus, making it possible to take 32 gas
samples from the air in accordance with a stipulated program (Leningrad
_ Saecial Design Bureau of Thermophysical Instrument Making);
portable sensitive instruments for continuous measurement of the atmo-
spheric dust content (Leningrad Instrument of Aviation Instrument Making);
a complex of laboratory equipment, including the S 112 atomic absorption
spectrophotometer, the APV-102 automatic photocolorimetric analyzer and the
S603 spectrophotometer for determining organic and inorganic contaminants
in objects in the environment (Tbilisi Scientific-Production Combine "Ana-
litpribor"). The S 112 instrument has a large range of lamps, attachments
and auxiliary devices and in its sensitivity is equal in every way to sim-
ilar foreign spectrophotometers;
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experimental model of the "Khrustal' 4001" two-channel gas chromatograph;
the ins trument is supplied with four detectors for the registry or a wide
range of organic compounds (Hydrochemical Institute and Moscow Special De-
sign Bureau of Gas Chromatography).
In addition, at the exhibit there was demonstration of standard samples of
soil and water intended for the calibration of instruments fabricated at
the Moscow Soil Institute imeni V. V. Dokuchayev and the Odessa Physico-
chemical Institute. In the soil samples it was possible to certify the
presence of 34 elements, in the water samples 17 elements, including
mercury, lead, cadmium, antimony and other toxic elements.
The experimental operational system for the collection and proce,_,sing of
daily informa*_ion arriving from the atmospheric monitoring network, devel-
- oped at the Institute of Applied Geophysics, is of great practical impor-
tance. The information analyzed and generalized on the "Minsk-32" elec-
tronic computer is transmitted on the very same day to interested organ-
izatioxis for the adoption of the corresponding decisions.
In one of the sections of the eahibit information was given on the USSR
State Standards, prepared with the direct participation of the Main Geo-
physical Observatory, intended for safeguarding the purity of the air
basin of our country:
GOST 17.2.1.04-77 "Meteorological Aspects of Contamination and Indus-
trial Wastes. Principal Terms and.Definitions";
GOST 17.2.3.01-77 "Rules for Monitoring the Quality of Air of Populat-
ed Places";
- GOST 17.2.3.02-78 "Rules for Setting the Admissible Wastes of Harmful
Substances by Industrial Enterprises."
_ The Central High-Elevation Hydrometeorological Observatory presented a
method for computing the admissible load of waste waters in watercourses
- and regulation of their discharge. The introduction of this method in the
purif ication structures of the Kurovskiy Melange Combine and the Orekhovo-
Zuyevskiy Plant "Karbolit" considerably improved the quality of water in
the rivers of the Moscow region.
A section of particular interest was that telling of the scientific re-
search work carried out in the field of monitoring of contamination of
the environment. At the Institute of Applied Geophysics specialists have
developed a mathematical model for routine computation of the transport
of contaminating substances across USSR national boundaries. Data on the
fluxes of transported substances are regularly transmitted to internation-
al organizations. Using a flying laboratory created at the Institute of
Applied Geophysics, a study was made of the distant transPort of sulfur
compounde, nitrogen oxides, mercury vapors, hydrocarbons, pesticides and
metals in the atmosphere. The collected data made it possible to formulate
models of behavior of inercury in tha biosphere.
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The Institute of Applied Geophysics is presenting a method which makes -
it possible to use standarr.i network snow-measuring surveys for determin- -
ing contamination of the snow cover by the fallout of heavy metals, sulfur
compounds, pesticides, benzapyrene, etc. This makes it possible, without -
significant additional expenditures, to determine the wastes expelled by
individual enterprises and to study the distant transport of contaminat-
ing subs tances . .
Aircraft investigations of aerosol effluent are made by the Institute of
Applied Geophysics. Interesting data have been obtained on the f ractional
composition of smoke discharged at the Shchekinskaya State Regional Elec-
tric Power Station.
The Northwestern Administration of the Hydrometeorological Service, in col-
laboration wj.th the Botanical Institute imeni Komarov USSR Academy of Sci-
ences, has developed an experimental method for the joint monitoring of
atmospheric contamination in Leningrad on the basis of chemical and biolog-
ical indices. Several types of ferns have been used in carrying out bioin-
dication monitoring, since these have increased sensitivity to contamina-
tions.
Specialists at the Institute of Applied Geophysics have created a remote
apparatus on the basis of a COZ laser for highly sensitive monitoring Af
- the atmospheric content of ozone, ammonia, ethylene and other coritaminat-
ing gases. An operational model of the apparatus is being demonstrated.
At the Institute of Applied Geophysics specialists have also developed a
method for determining the mass concentration of aerosol on the basis of
the results of multifrequency laser sounding which is undergoing testing.
Specialists at the Main Geophysical Observatory have developed methods for
numerical modeling for studying the patterns of dispersal of impurities
and establishing the admissible discharge into the atmosphere. These
methods served as a basis for the INSTRUCTIONS ON COMPUTING THE A`iTiOS_ HERTC
SCATTERING OF HARMFUL SUBSTANCES PRESENT IN THE EFFLUENT OF ENTERPRISES
SN369-74.
One of. 012 sections at the exhibit was devoted to methods for predicting
the levels of environmpntal contamination.
_ A method for long-range prediction of the effect of economic activity on
the state of the environment has been created under the direction of sci-
entists at the Institute of Applied Geophysics. Methods for meteorological
prediction of high levels of atmospreric contamination have been developed
at the Diain Geophysical Observatory. In 1979 warriings concerning an anti-
cipated high atmospheric contamination were prepared for 103 cities.
The Hydrochemical Institute and the Institute of Applied Geophysics for
_ the first time have developed a method for the routine predictio n of con-
tamination of river water. The method developed by the State Hydrochemical
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Institute has undergone practical testing at a number of ,3dministrakions
- of the Hydrometeorological Service. The results of the checking were en- -
tirely satisfactory. -
- During recent years the NorLhern Administrati.on of the Hydrometeorological
Service has begun to predict the oxygen regime of rivers. The measures
taken on the basis of the forecast prevented the freezing-in of fish in
the rivers of the Severnaya Dvina basin during the severe winter cold of
1977 and 1979.
In conclusion we should note the exhibit devoted to international coopera-
tion in the field of monitoring the state of the environment. The Soviet
Union is taking an active part in all the principal interna.tional programs.
Particularly important is realization of a global system for monitoring the
enviranment. The member countries of the Socialist Economic Bloc are par-
tj.cipating in solution of this problem, together with other countries. The
- first joint expeditionary experiment of the member countries of the Social-
ise Ecar..::nic Bloc on the problem of the global system for monitoring the
environment was carried out in the autumn of 1979 in the territory of the
Hungarian People's Republic. Specialists of the Laboratory for Monitoring
- the Environment and Climate of the State Committee on Hydrometeorology and
the USSR Academy of Sciences participated in the experiment from the USSR.
The program of the experiment (observations under the background monitor-
- ing program, intercalibration of inethods and instruments, mutual training
of specialists) was completely c3rried out. As a result of implementation
' of the program it was possible to obtain new and interesting data on the
background state of the environment in the central European region.
The speci"l exhibit entitled "Environment - Reliable Monitoring" objective-
ly reflects the activity of the State Committee on Hydrometeorology in the
field of preservation of the environment. The successes attained in the
Soviet Union in this f ield were possibl.e due to the everyday attention
given to these problems by the Party and the government.
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CONFERENCES, MEETINGS AND SEMINARS
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Ju1 80 pp 125-127 _
[Article by I. A. Yankovskiy]
[Text] Scientific-methodological seminars were held in 1979 for examining
ways to increase the effectiveness and quality of work on monitoring and
predicting air contamination, the inventorying of harmfnl effluent.
~ Field seminars were held at the Central Asian Scientific Research Insti-
tute (Tashkent) during the period 28 May through 2 June, at the Verkhne-
Volzhskoye Te�rritorial Administration of the Hydrometeorological Service
(Gor'kiy) during the period 1 through 5 October,at the Far Eastern Sci-
_ entific Research Institute (Vladivostok) during the period 15 through 20
_ October 1979. These seminars were attended by representatives of 36 admin-
_ istrations of the Hydrometeorological Service and scientific research in-
_ stitutes, a number of organizations of the USSR Health Ministry, planning,
industrial and public service organizations, the type of whose activity is
- related to preservation of the environment. Altogether more than 360 repre-
sentatives of 160 organizations and departments participated in the sem-
inars.
In opening the seminars, N. N. Aksarin, director of the Central Asian Sci-
entific Research Institute, V. S. Ryazanov, chief of the Verkhne-Volzhsk-
oye Administration of the Hydrometeorological Service and Yu. P. Kovtan-
yuk, deputy director of the Far Eastern Scientific Research Institute,
presented reports on the tasks of the National Service for Observing and
Monitoring the Environment (SKZA Sluzhba Nablyudeniy i Kontrolya
Okruzhayushchey Sredy) and on the tasks of the seminar. The speakers told
about the status of work on investigation of contamination of atmospheric
air, stated some shortcomings in the activity of network subdivisions of
the SKZA and brought artention to the need for further development and inr-
provement in operation of the network for monitoring contamination of the
air medium. They demonstrated that strengthening of the relationships be-
tween scientific ins*_itutes and practical workers and creative cooperation
of the personnel of the administrations of the Hydrometeorological Service
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and scientific research centera is, under present-day conditions, a
highly important factor in increasing the quality and ensuring the maximum
effectiveness of operation of network suhdivisions in the service.
The reports and communications of specialists in the Administration for
Observing and Monitoring the Environment (V. V. Chelyukanov), Main Geophys-
ical Observatory* (I. A. Yankovskiy, L. R. Son'kin, I. A. Solomatina, E. Yu.
' Bezuglaya, N. S. Vol'berg, Ye. A. Shaykova, Ya. S. Kanchan, M. N. Zashikh-
in), USSR Hydrometeorological Center (L. M. Neronova and I. A. Tikhomirova)
were devoted to:
analysis of the status of definite types of work for studying atmospher-
ic contamination;
prospects for the development of ineans and methods for analysis of con--
tamination of atmospheric air, taking into account the off:Lcial new "Manual
on Monitoring Atmospheric Contamination;"
automatic methods for analysis of atmospheric contamination;
analysis and generalization of data on the discharge of harmful sub-
stances into the atmosphere;
organization of work on the inventorying of harmful discharges;
- examination of norms for the maximum admissible discharges into the at-
mosphere and implementation of the plan for measures for the introduction
of GOST [State Standard] 17.2.3.02-78, a method for avaluating the quality
and effectiveness of operation of the network for observing and monitoring
atmospheric contamination;
status of work for predicting air contamination;
introduction of new methods for analysis of air contamination;
examination of ways to improve operation of new technical means, such
as automatic gas analyzers, computations of the norms for maximum admis-
sible discharges;
coordination of schemes for siting and plans for the construction of
industrial facilities;
- computation methods for determining the harmful substances expelle3 in-
to the atmosphere by industrial sourcea, proposals on the sequence for
monitoring sources of contamination of the air medium.
V. V. Chelyukanov, a specialist of the Administration for Monitoring Con-
taminants of the State Committee on Hydrometeorology, discussed the prob-
lems facing republic and territorial administrations of the Hydrometeorolog-
ical Service. He noted that the local subdivisions of the SKZA have done
much for the development and improvement of monitoring of atmospheric con-
- tamination, but can do far more. The most important task of each subdiv-
ision is intensifying attention to improvement iu the quality ot work and
increasing its effectiveness. He also emphasized the need for the speediest
possible introduction of new gas analysis apparatus and new methods for
analysis of air contamination, rapid mastery of new manuals and State Stan-
dards. In conclusion the apeaker mentioned the need for improving the rou-
- tine servicing of Party and state agencies and organizations dealing with
the national economy.
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The communications of specialists of the republic and territorial adminis-
trations of the Hydrometeorological Service and scientific research insti-
tutes noted the positive results obtained in the course of investigations
of atmospheric contamination. TheGe investigations are being made by spec-
ialists under thE direction of M. Ye. Berlyand with the broad participa-
tiorl of specialists in network subdivisions of the service. A high evalu-
ation was given to the "Method for Evaluating the Quality and Effective-
ness of Network Operation," developed on the basis of an analysis of the
activity of the existing network and allowance for the requirements set
forth in the "Manual on Montitoring of Atmospheric Contamination," as well
as GOST [State Standard] 17.2.3.01-77 "Preservation of the Environment.
Atmosphere. Rules for Monitoring Air Quality of Populated Places" and in-
cluding use of data from an experimental evaluation of the quality of work
performed by specialists of republic (territorial) administrations of the
Hydrometeorological Service and scie4tific research institutes, It is as-
sumed that the use qf this method will favor a further improvelqent in the
effectiveness of servicing of the national economy.
An equally important effect can be obtained from the introduction of the
"Methodological Instruction~ on the Prediction of Air Contamination in
Cities," also developed at the Main Geophysical Observatory, which were
publistied and disseminated to all 3dministrations of the Hydrometeorolog-
_ ical Service and scientific research institutes. This has created the pre-
requisites for the organization of work on protecting the atmosphere
against contamination during periods of dangerous meteorological condi--
- tions. It was noted in a report by L. R. Son'kin that at the present time
pr.edictions of air contamination are prepared for more than 100 cities
in the country. Warnings are transmitted to several hundred industrial,
power and transport organizations. It was noted that a good effect was ob-
tained by the specialists of the Central Asian Scientific Research Inst-
_ itute, West Siberian Scientific Research Institute, Azerbaydzhan, Irkutsk,
- Kazakh, Kirgiz, Krasnoyarsk (Noril'sk), Northern, Northwestern and North-
ern Caucasus Administrations of the Hydrometeorological Service. The
greatest number of cities was supplied with prognostic information on at-
mospheric contamination by the Ural, Volga Region, Upper Volga, Northern
Caucasus Adminl.strations of the Hydrometeorological Service and the Cen-
tral Asian Scientific Research Institute.
In ttte seminars an important place was devoted to a discussion of the prob-
lems involved in the sequence of development and examination of the norms
for maximum admissible levels in the atmosphere and implementation of the
plan for measures for introducing GOST [State Standard] 17.2.3.02-78 en--
titled "Preservation of Nature. Atmosphere. Rules for Setting Admissible
D.ischarges of Harmful Substances by Industrial Enterprises." Revealing
the essence of these important steps in the field of improvement of work
in the field of scientific expertise, the speakers M. N. Zashikhin and Ya.
S. Kanchan emphasized the necessity for both coordination of the schemes
for distribution and the plans for construction of industrial facilities
and also for computing the norns for maximum admissible discharges.
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As indicated in the reports of N. S. Vol'berg and Ye. A. Shaykov, great
- possibilities for a substantial improvement in the quality of collection
of informa*ive data are being afforded by the introduction of the "Manual
on Monitoring of Atmospheric Contamination," the new methods and technical
means for analysis of the state af the air set forth in this manual. The
objective is to make fuller allowance for the peculiarities of analysis
of atmospheric air for its content of harmf ul substances by manual and
automatic methods and make more extensive use of already available auto-
matic methods recommended by the Administration for Monitoring Contamina-
tion of the State Committee on Hydrometeorology. However, at some admin-
istrations of the Hydrometeorological Service and scientific research in-
_ stitutes automatic gas analyzers are being introduced into the practical
work of the SKZA very slowly.
Exceptional importance has been given to the organization and development
of forms of operational servicing of Party and soviet agencies and organ-
izations ser.vicing the national econotuy. A good basis for increasing tl-.e
effectiveness of operational servicing of users is the use of information
accumulated in the experience of specialists of a number of administra-
tions of the Hydrometeorological Service in close collaboration with the
prognostic agencies of the service (report of I. A. Yankovskiy).
A particular place was devoted to an analysis and generalization of data
on the discharge of harmful substances into the atmosphere and also to
an examination of the organization of inventorying work. These and other
aspects of this problem were covered in the reports of I. I. Solomatina,
which were read in the plenary and section sessions.
It was demonstrated in a report by E. Yu. Bezuglaya entitled "Study of
Climatic Conditions of Scattering of Impurities in the Atmosphere" that
this matter is closely related to the quality and effectiveness of servic-
ing of interested organizations.
D. V. Vinokurova told about the results of work on complex themes related
to the study of the climatic conditiona of transport and scattering of
impurities in the atmosphere and to the development of a method for eval-
uating the quality of operation of the network for the monitoring of at-
mospheric contamination. There has been considerable work on the plan for
scientific-methodological direction of the network. Among the many forms
of information on the state of atmospheric air a leading place at the ad-
ministrations of the Hydrometeorological Service is occupied by graphic
information. Maps, photographs, graphs and figures have been produced and
beautifully finalized; these reflect the nature and tendency of atmospher-
ic contamination and illustrate the principles and methods for analysis
of the state of the atmosphere.
The resolutions adopted by participants in the seminars formulated spe-
cific proposals on the further improvement of operation of network subdiv-
isions of the SKZA and improvement in methodological leadership on the
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part of the central agencies of the service. Particular attention was de-
voted to the need for a highly speedy introduction of new technical appar-
atus, preparation of inethodological aids for carrying out expert examina-
tion of projects, preparation of a plan for the section "Preservation of
the Air Basin" and determination cf the discharge of harmful substances
into the atmosphere and computation of the maximum admissible discharge
levels,
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NOTES F2tOM ABROAD
Moscow METEOROLOGIYA I GIDROLOGIYA in Russian No 7, Jul 80 pp 127-128
[Article by B. I. Silkin]
[Text] As reported in SCIENCE NEWS, Vol 115, No 24, the American meteor-
ologist W. A. Lyons has carried out an analysis of daytime space photo-
graphs taken in June 1979 from aboard meteorological satellites situated
in an equatorial orbit at an altitude of about 46,000 km above the earth's
surface. On a series of photographs it is possible to distinguish a thick
zone of haze which extends over a considerable part of the United States
from Kentucky to Maryland and which then extends 1,300 k~n to the
east of the shore, reaching the central part of the Atlantic Ocean.
The analysis revealed that this haze is a dense air mass saturated with sul-
fates released into the atmosphere as a result of combustion of great tnass-
es of coal at electric power stations in industrial regions of the basin
of the Ohio River and New England (the northeastern states in the United
States situated along the Atlantic coast of the country). The sulfates
are condensation nuclei for the naisture droplets which form the haze and
usually reduce visibility by more than half. Such haze can persist in one
- place for several weeks. The rain "washes away" the haze, but absorbing
sulfuric acid, the precipitation acquires toxic and corrosive properties.
The investigations of W. A. Lyons also indicated that within the limits of
_ the haze there is a high ozone concentration. Within this air mass it at-
- tains 91 parts per billion, whereas outside this mass it is only 69 parts
per billion. As demonstrated by recent studies in the field of agrometeor-
ology, such an ozone concentration is extremely harmful for plantings of
soy beans and legumes.
As reported in NATURE, 31 May 1979, and in SCIENCE NEWS, Vol 116, No 1,
~ 1974, the American chemist and meteorologist J. 0. Nriagu carried out an
investigation of the intensity at which contamination of the earth's air
envelope with metals is transpiring at the present time.
According to his conclusions, during the last decade approximately 74 mil-
lion lcilograms of cadmium, 585 million kilograms of copper, 4.3 billion
kg of lead, 4.5 million kilograms of nickel and 3.3 billion kilograms of
zinc have entered the atmosphere.
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The estimate of the quantity of inetals entering into air space was made
separately for natural sources (eruptions of volcanoes, forest fires,
erosio n, rising duat particlea and salts expelled from the surface of
seas and oceans) and for sources associated with man's activity (mini.ng
industry, metallurgy, combustion of coal in different fields of produc-
a~ tion, combustion of firewood and wastes, blowing away of fertilizers,
etc. ) .
As might be expected, human activity was a much more important source of
agents contaminating air than natural processes. For example, in 1975
the combustion of liquid fossil type of fuel (including gasoline) led to
the entry of 273 million kilograms of lead into the atmosphere. At the
Game time, eruptions of all the earth's volcanoes, being highly important
natural sources of lead, introduced only about 6.4 million kilograme of
this metal into the atmosphere.
The h igh lead content in air apace ie a relatively new phenomenon. In
the decade 1910-1920 its total quantity in the atmosphere did not exceed
493 million kilograms. During the next decade alone it attained 1.1 bil-
lion kilograms. J. 0. Nriagu attributes such a rapid increase to the
large-scale use of automotive vehicles and the appearance of gasoline with
lead additives in 1923. As reported in CHEMICAL WEEK, 21 February 1979, and in THE SCIENCES, Vol
19, No 16, 1979, on the request of the US Environmental Protection Agency
a group of TVA specialists, headed by the geochemist and soil scientist
G. S. Loggle, carried out an investigation, lasting two years, of the in-
fluence exerted on vegetation by sulfur present in the air.
The s tudies were made in greenhouses into which no air could penetrate from
thP outaide. Ttie inside atmosphere was purified from the sulfur whictn it
usual ly contains by means of charcoal filters. In addition, in order to
determine the quantity of sulfur absorbed by vegetation from the soil and
from *_he air, the radioactive tracer S35 was used under the open sky.
It wa s established that with a reduction in the content of sulfur in the
soil the plant increases its absorption from the air medium. Cotton, hay
and o ther plants cultivated in the alkaline soils of the southeastern
United States satisfy a considerable part af their needs for sulfur from
the air.
' ldith an increase in the combustion of fossil fuel, increasing the sulf ur
content in the atmosphere, there was an approximate coincidence in time
with the decrease in the quantity of fertilizers containing sulfur which
is applied to the soil. Sulfur increases the content of chlorophyll in
plants and thereby facilitates. the processes of photosynthesis and growth.
Thus, the dependence of vegetation on chemical substances in the atmoaphere
_ has recently increased.
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In the opinion of G. S. Ploggle, if the present-day efforts for air purif-
ication are crowned with success, in the territory of the Tennessee River
valley, covering seven states in the United States, there will be a de-
crease in crop yields by app roximately 10%. In order to make up for the
loss of sulfur from the air here it will be r.er_essary ta apply fertilizer
at a cost up to 7.6 million dollars.
Although it still has not been possible to establish a difference between
the sulfur "naturally" pr_esent in the atmosphere and the sulfur ejected in ~
the course of industrial activity, it is nevertheless clear that the con-
tamination of air by sulfur has some unquestionable positive aspects in
addition to negative aspects.
- COPYRIGHT: "Meteorologiya i gidrologiya," 1980
[11-5303]
5303 -END-
CSO: 1864
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