HomeMy WebLinkAboutSUS153March 1978
CORPS OF EF4GI#EZRS, U,S PRfgiY
CaLa R EGIOP~S RESEARCH AND ENG~NEER~NG LABORATORY
MANOVER* NE\a HBPAPSHiRE
4W(
SEGURETV CLASSSFBCAT 'O6N BF TH$S PAGE We: Dafer E~3&rsdJ
RE PORT DOCUMENTATION PAGE
EXCICZRmS FROM ALL I%WION HYDROMGIGAL GOEGmSS,
1973, VOL. '7
li, S. ?&my Cold Regions Regions and
Approved for public release ; distribution unlimited.
*B5s report contalns 13 articles by various Russian authors on the subjects
of ice jams and iee forecasting, "haracteristics of ice ccrnditjons and how
these condigions lead to problems m forecasting are discussed.
EIJGIGLISH TITLE: EXCER-PTS R8Pi ALL bTION KYDROLOGICAL CONGRESS, 1973, VOL. 7
SOURCE : Leningrad, Trudy, vol. 7, 1973, Gidrologichesklie prcgnozy,
published by Gidrometeoizda", ,9976, p.264-356.
Translated by Sarn Blalock, Kingsport, Tennessee for U.S. Army Gold Regions
Research and Engineering Laboratorq-, 1978, 94p.
The contents of this pbiication have been translated as presen,ted in the
original text. No attempt has been mad:: to verify the accuracy of any
statement contained herein. This translation is published with a minimum
of copy editing and graphics preparation in order to expedite &he disseminatio~
of infomation. Requests for addieional copies of tlxis document: should be
addressed go the Defense Dacmentatrion Cezeer, Cameron Station, Aie,xandria,
Virginia 223$4,
THE TEFIPORAL @JD SPA"E"AL CH&XGEABI&fT'Sr: OF ICE PMEHQMEMA AMD THEEFl EOMG-TERM
FORE CASTS
By: T. N. Makwevich, Z. A. Yefirnova, V. A. Bumyantsev, L. K. Savina, R. Ya.
Uekseyenks, S, V. Shanscthkin
(GGI , Leningrad)
Recently, the practice of long-tern forecasting of ice regime elenents of
rivers has come to include phyzico-statistical methods to a greater and greater
extent. One of these most widely used nethods is the method of forecasti~li: the
characteristics of the ice regime accordini;: to the data fields of meteorological
elentents with the prelimi:lary arrangement of these fields on the natural ortho-
gonal components - this began to be used in 1968 at the Hydrometeorological Center
of the USSR (81, and somewhat later ir, GGI (3). At the same time, the accuracy
of long-term forecasts, part;icularly far rarely repeated years, remains as before
far from satisfying the requiremats of questions. Further research into the
possibilities of perfecting the existing methods and finding new approaches to
solving this problem are necessary.
For this purpose, the authors made a detailed statistical analysis of the
longest series of observations of elements or' the ice regime om rivers with
different types of ice formations: st;able - tkii, northern area rivers (56 moni-
toring stations f , unstable - the Danube River (20 nonitoring stations ) , ad
transitional - the Transbaltic Rivers (27 monitoring s Cations) . By statistical
ks analysis of the temporal. series, one Beans in this ease evaluatting and duplicatiw
the properties of ths initiating process which lies at the bzsis of the series
according ta the available realizations of cha~clacteristics 3le usefilkness ~f
ari such analysis, if it is of course carried out correctly, consists in the possi-
bility of identifying general principles to rqhich all ar part of the Leaporal
series we subordinate. The next stzge consists in the attempt to explain these
principles and to find possibilities of using them for the purpose of prediction.
Knowledge of the basic properties of the temporal series - ckangeabil',ty and ttie
characteristies of its periodic fluctuations - aid one in solvf~ng the primary
problem - predicting the behavior of a temporal series in the future.
The successfulness of employing the most modern methods of? statistically
analyzing time series - spectral and correlation analyses - depends chiefly on
the care taken in selecting data. In order tc use the structuz%di feature3 of
time series of the observations of charaeteris tics of ice phenomena subsequently ,
one should be certain that such series are steady, or, in other* words, that thein
basic statistical parameters do not si~nificantly change in the course of a
certain period of time. ${hen plotting the forecast diagrams, an objective check
or" the series for steadiness has not been nearly carnied out up to this point,
ydhich could not fail to have an effect on the results of emplnqping some parti-
cular forecasting methods ,
*-d
A check or the skeadiness of the mean value of X
where x. is the value of the tine series a'. the j-th moment in time, was carried
out accdrding to the following criterion
2 here sZ and s are the dispersion estimates : 1
The slowly changing trend in the average value leads tq an overage in the
2 estimate of s and has practically no effect on the value 3;. Tb~e series is
recognized as a steady-state series in relation to the average value if the cal-
culated value ofojfalls into the critical region
where n is the length of the series, t is the qumtil cf the normal law. 9
A check on the steady-state nature of dispersions and correlation functions
was made by means of comparing the estimates of dispersion and the autocorrelation
function obtained according to the components of the successiveLy shortening
series (Figure 1). 1x1 order to give an objective aswer to the question of
whether differences betrqeen the selected estimates are significant, with respect
to Chose obtained by the separate components of the series, one uses the Bartlett
criterion in the case of dispersion (6), based on statistics
while in the case of th2 intraseries correlzti~r, function the following statistic
IGas used
Figure I. Autocorrelation functions of the times of appeara2ce of ice on the
Severnaya Dvina River and near Medvedka monitoring station plotted for me en-
tire series and its successively shortening
components I
1 - 70 years, 2 - 60 years, 3 - 50 years, 4 - 40 years, 5 30 years.
Both statistical componen5s are approximately distributed as ~'c N - 1
degrees of freedom. In the cited expressions, N is the nuher of components
into which the series is djvided; ni is the number of members irk the i-th
component of the series; 8' is the selected estimate of dispersion obtained i according to the i-th component;
where (k) is the selected estimate of the intraseries correlation function
upon a shift by k t.lnits, obtained according to the i-th component of the series :
The cited analysis of time series of ice regine characteristics of rivers
with a probability reliability of 95% shored that the number of sections according
to which this hypothesis is net satisfied does not exceed ths permissible value
of 5%. This enables one to ~onsider that the existing series do not contradict
the hypothesis of weak steadiness. In other rmrds, the warming af the climate
observed in the 1930's as tgell as a number of other factors, for example, the
growing role of hwan activity, has not yet led to the appearance of' significaqt
trends in the basic parameters of the ice regi~e of' rivers.
Here it is necessary to provide certain explanations on the subject of .the
unsteady ice regime of rivers averaged in a series of elements and observed
earlier by certain investigators (91, Only a qualitative check of the series
for steadiness was made in the indicated works without using any objective
criteria. We shall also note that one cannot fully rely on the steadiness or
unsteadiness of a series according to selection of' the finite volume. The fact
thht it appeared to be a trend of the average volume of data available at that
time, with the existence of a large number of data, could prove tlo be simply
a branch of a prolonged "cycleH. The cpposite is also possible - the series
that seem to be steady series at a given moment in time will prove to be unsteady
in a different, longer span of tine. 112 both cases there is a certain dmger of
placing too much faith in the results of extrapolation with the nlecessity of
making a decision for a significant period of time into the future.
Unfortunately, in hydrology we are always in a position in which it is
necessary to make a decision using only the available data. Therefore, if all
of the available informztion indicates the absence of significant changes in
series of elements of the ice regime of rivers, our decision sh~uld recognize
the steady-state as reality. Consequently, we have every basis t~o employ dif-
ferent statistical methods not only with respect to an individual component of
the series, beginning in the 193OPs, but also witil respect La the entire series
as a whole, including earlier years, which makes their very application more
well-founded,
A typical feature of a quite long ti~e series of observations of a certain
characteristic of the ice regime of rivers is the presence of prolonged irregu-
lar fluctuations. By studying these fluctuations, one can conclude that they
can be represented as the total of somewhat more or less regular fluctuations.
In order to study this vrr.ixturen of regularity and Frregu2.arity in the series
of river ice regime characteristics, spectral analysis provides the natural
approach from the mathematical viewpoint.
There exist many problems related to obtaining estimates of the spectra
ad of the themes chiefly due to a certain extent to the obvious .fact that it
is not alwaya possible satisfactorrily to describe the infinite se-t when only
a finite nunber of data is given. Hawever, today fuily suitable inethads have
been developed for estimatirig spectral density N.1. These havis the follow in^,
f s~n~ 9
and are only distinguished by the choice of weights Ak, Here m is the point
of truncation or the maximulm number of employed changes, conventionally taken
#I at random from the condition m < (n); R is the estimate af the covariation -
3 (fg)
function taken upon the change in k:
~ The Tfyuka-Xhening estimate was used in the work (10)
As the result of this, we initially obtain the rough estima.tas of the
spectrum
where Lml = Lclt LmWl = L and then by means of smoothing tre shift to the msl "
final estimates or" f (aj)
R.
Spectral analysis provides a quite crude method of determining the reality
or cycles by identifying whether they introduce frequency bands that correspond
to the cycles that make a contribution to the total series dispersion; it is
c!rude in the sense that a precise establishment of this Tact requires that the
length of the series be at Least 7 times longer than the length cf the longest
cycle. Hence, in order to determine, for example, the verity of a 22-year cyele,
one should have data for a ninimum of 150 years, i~hile ta determine the verity
for an 11-year cycle one needs data for 80 ifears. Inasmuch as the reliable
hydrological series are usually muck: shorter, then it is clear that tasking
such cycles according to the separate series requires that we halve more data
than we ds
In order8 to obtain nlcre reliable ideas about the reality of the long cycles,
the single escape, to our view, consists in a joint spectral ana:lysis carried out
according to several 3eries with subsequent averaging of the selected spectra
for a group of rivers that are homogeneous with respect tc the cc3rrelation (spectral.
function1. F1iher! certain conditions of averaging are observed, the estimate is
equivalent !lo an estimate of a spectrum which could be obtained ;2ccording to a
,- significultly larger number of members than the length of each itldividual series.
A check of the intraseries correlation functions *"or homogeneity ms made
in a ~gosk (11,
In the process of the combined statistical analysis of the time series of
the ice formation periods on rivers, covering a quite extensive territory with
varying regimes, a latent quasi-cyclical nature was identified which can provide
a certain effect when plotting the for%ecast links (Figure 2).
Figure 2. Selected estimates of spectral density f(w) of the times of appearance
of ice on rivers,
1 - Severnaya Dvina River - Abramkovo monitoring station, 2 - Vychegda Ziver -
SolFvychegodsk monitoring station, 3 - Danube River - Budapest monitoring sta-
tion (w - frequency, T - period).
It should be noted that the character of this quasi cyclical nature is practically
identical in all three rivers (the northern area, the Danube, the Transbaltie
area). One can identify 21-year and 22-year cycles in the first series; certain
differences pertain to the sh~~ter cycles - the 5 and ?-year ones. The commonality
of the identified cycles indicates a single global principle of their origin.
Relative to the cycle which lasts approximately 11 years, cne can confidently
state that it has a solar nature (4, 7). According to geophysical investigations,
the nature of the 22-year cycle is evidently associated with the variable sign ,nor'
the magnetic field of two 11-year cycles, the even and odd; ad in the meteoro-
logical processes the 22-year cycles frequently appear more noticeably than the
Il-year cycles (5).
We shall exxuoine the use of cyclicity for purposes of forecasting in greater
detail applicable to the Danube River. An analysis of changeability of ice phen-
omena on the Danube demonstrated the most clearly pronounced 22-year cyclicity
in the fluctuations sf the length and onset times of ice phenomena; to a signi-
ficantly lesser degree it appeared in the times of the river's freeing from ice.
An attempt is made in this study to estimate the possible (effect of solar
activity in its 22-year cycle on processes of ice formation. In this case, a
method of analyzing cyclicity for hydrcmeteorologieal forecasts whjch was sug-
gested by V. N. Kupetskiy was used (2). According to the table cf "epoch sppli-
cationH, by knowing three factors - the parity of the 11-year solar cycle, the
phase f rise or fall) ad the value of Wolf sunspat numbers, the correlation
diagrams can be constructed. One can identify certain principles individually
for the odd ad even cycles in the diagrms in the farm sf direct and reverse
links. The value of the Wolf. sunspot nmber is assu~ec! to be the actual value
for the current, year or f~r a foreeast whose validity is quite high. In indi-
vidual years the links are poorly expressed and therefore the forecast for them
should not be ziade according to the submitted method. Such years include the
years following the maximum of the 11-year cycle, before the minimum and the
year of the minimum. Fusthermore, in a number of cases the identified relatien-
ship is vaguely expressed due to the instability of characteristics of the ice
regime and the limited nature of the series - the observations encompass a total
of 3 or 4 22-year cycles, which hinders its statistical basis.
The authors e~mpiled verification forecasts of the times of appearance of
ice for years of the current 20-year cycle (1964 - 1971) during these years in
the region of the even 14, 16, and 18-year cg i . There were un,satisfactory
results from 8 years in 2 instances (1965 and 7.:. in 6 cases the error did
not exceed the pemissible one and of these, it ..ses it was O s 5 days (see
the table)*
O;ne can anticipate phases of development of the Danube ice regime in up-
coming years according to the prediction of the Wolf sunspot numbers. The authar~
have compiled a foreeapt of the length of the ice phenomena and the tines of their
onset for 1973 - 1974 which was fully valid.
Validity of Forecasts of Dates of the Appearance
of Ice an the Dmube River
-- F
Date of Appearan- of Ice
Olir investigations of the character of the relationship of solar activity
with the ice phenomena showed that it is particularly clearly manifested in
the extreme years, with respect to icing.
We shall examine an exmple at a similar relationship of the d~pation cf
the ice phenamena, the greatest assigned value (according to the Danube data)
r.rith the I.301f sunspoC numbers in the current year. As is evident in Figure 3,
the highest correlation coefficients charzcterize ysars whose ic2 phenomena are
prolonged (over 35 - 40 years) and years with nild development of ice phenomena
(duration less than 20 days).
Figure 3. Relationship of correlation ca-
efficiencs r bemeen %he duration of ice
phenomena on the Danube River (Budapest -
Mokhach) , the highest set value Tp, and
the Igalf sunspot number for January of
the current year and the vafue of T P'
The small circles indierate the nunrsber of
years,
With the exception of cases near the average
multiyear value of duration, the carrelation
coefficient sharply increases - from 0.32
to 0,58.
Investigation of the changeability or"
ice phenomena in comparison with cyclicity
made it possible to obtain a certain idea
about the tendency of dsvelopment crf ice
conditilans in succeeding yews, Id is
ana'l;?dtl.ally assumed that for th:is purpose data
on solar activity could be us~ed in addition
to data on atmospheric ciretel.ation, aid in
t this sense the reported resuf.ts are viewed as
the first stage of this kind of investigation,
References
1. Deleur, M. S., A. A. Iva~ova, V. A. Rwyantsev. The Use of Correlation
Analysis to Investigate the Space-Time Chanbeability of Sno1.r < in the Kolyma
River Basin, "Materialy glyatsiologicheskikh issledovaniyn, 19731 No. 22.
2. Kupetskiy, V. N. The Structure of Heiioclimatic Relationships sad the
Possibility of Using Them in Long-tern and Superlong-term Forecasts. "Izv.
VGD", 1969, Vol. 101, No. 4, pp. 289 - 295.
3. Makarevich, T, M. , Z, 8, YeErlmorsa, &, 8 * Savina. A Lung-tiera Foretzas t
iaE the Duratis~n of Ice Phenomena on the Danube River. 'ITr, GCIf7, l972, No,
pa. 3 23.
4. Maksimov, I. V. Geofizicheskiye sily i vody okeana. (Geophysical Forces
and Ocean Idaters) . Lening~ad, Gidrometeoizdat , 1973. iih? pages.
5. OX', A. I. The Mmifestati;3n of the 22-year Cycle of Solar Activity in
the Earth's Climate. "Tr. AANILH ', 1969, Val. 289, pp. 116 - 131.
6. Pusi;yiTnik, Ye. I. Statisticheskiye netody analiw F obra'ootki
nablyudsniy . (Statistical Methods or" Pnalysis and Observation Processing).
t4oscow, "Nauka", 1968. 288 pages.
7. Rubashev, B. $4, ProbLemy solnechnoy aktivnosti. (Problems of Solar
Activity). Moscow - Leningrad, "Nauka", 1964. 362 pages.
8. Savchenkava, Ye. I, Investigating the CharacterLstics of Meteorological
Fields Over 'the Northern Hemisphere, with Respect to Fields Caused by the
Appearance of Ice on Rix~ers of the USSR. "Tr. Gidromettsentra SSSRR, 1969,
No. 40, pp. 47 - 67.
9. Sokolov, A. A. A Change in the Times of Freezing and Thawxng of the
Neva River in Connection with the Warming or" the Climate, nMeteorologiyz i
gidrologiya", 1953, No. 10, p. YO.
10. Statisticheskiye metody v gidrologii . (Statistical Metilads in Hydrology).
Leningrad, Gidrometeoizdat, 1970, 270 pages.
PIOBERN PRINCIPLES OF DEELOPZNG WTdQDS OF LBMG-TEM FORECASTXHG OF
Rf VER FREEZING &"t%D TMhI4EMG
By: Ye. I. Savchenkova, Ye. S. Karakash, N. D. Yefremwa, and
Ye, G* Antipova
(The Hydrometeorologieal Center of tm USSR,
~~OSCQW)
hring the development of a method of long-term fcrecas2ing af the apjearance
of flaating ice, it is expedient to estimate wiien %he iiutum cooling of the water
begins with a high degree of timeliness md how intens,ir.ely it will occur.
course of rater cooling depends in the final analysis on the devel.opraent of at-
mospheric processes, and the frequency and intensity sf w8ves or cold md heat.
Nearly all methods of Long-term forecasting 3.f the times of appearance of ice
are based on an analysis of atmospheric processes in the months that precede
the appearance of the ice,
Btt~rnpts to use statistical methods fir investigating atmafspheric processes
and their interl-elationships have been mde Tor a iang tine, Clo~relation analyses
have usually been used. Many synoptic rules (the method of analogs: rhythuns,
etc.) that are used in long-term weather forecasts have been the result of the
statistical generalization of mterials. Still, their use izl k2ydrology do33 not
always provide good results.
Regional characteristics of the synoptic processes are used duri~4 the
c8eisePopraaen"cf nethods of ice forecasts, Thase characteristics 1p~eB3, refl2ct
the temperature of the air near the ground or its deviation from the normal
value. Thus, for example, the duration of the western shift in November, which
carries heat in the period of Peezing of "ihe upper and middle Volga, depends
upon the developed temperature contrast between the sea and the land. Tkiis
contrast is estimated according to the difference betrqeen the ground and ~gater
surface air temperatures. When the iqesterly ccntra~t shift i.s prolonged but,
not great, this means that the ocean is supercooled ~*.hile thc continent is wsrm
and ",he air moves over the hornog~neous underlyxr~s surface without experiencing
the effect of thermal heterogeneity af the sea and dry land.
Central Asia can serve as another example. The wintsr syoptic processes
of this territory are characterized by predominance on the southrqestern peri-$
phery of the Siberian anticyelone, which can be either cold or :$arm. Depending
upon this factor, the winter in Central Asia is severe, with a prlonged ice
cover on the greater extent of the *hudar yya and Syrdart ya Rivers ~iith floating
ice on rivers in the extreme routi;, or is-so igarm that the ice ccr'iier only
exists in the low water st.reatches or the Syrdartya River, Basw~ch as the
Siberian *nti.cyclone begins to form as early as September, then by Novenber
the distribution of air temperatwe in its 1ricFnit.j reflects the consequences
of tbe predsminant synoptic situation, name2.y the temperature of the invading
ai~ illasses a=nd their tra~sf or~~ati~fi
This process is relatively stabli. a4 the anomaly of atnosphezaic tempera-
tui-e in the western part or" the Siberian =ticyclone in November se v.'; 2s a
Despite the fact that the method of expanding thc meteorological elements
according 'to natural orthogonal functions has a veritable number of valuable
properties which have b~m e3:amined in the literature in sufficie~t- detail (2,
41, still it is very ccjmplex for purposes of computation since it requires
computer calculation, and of course, is aot the only method of obtainiryg meteoro-
logical information. The use of this nebhod in the Laboratory of" Ice Forecasts
of til$ Hydrometeo~ological Center of the USSR began in 1968 to develop long-tern
forecasts of the appearance of floating ice on rivers (5, 6, 8). The concept of
natur;? components for use in long--term foreaasts of ice phenomer~a on rivers:
requiras additional research. Iqith this goal, it is necessary to allalyze atmos-
pheric: processes of the Worthern Hemisphere, and to choose regions above which
the processes determine the developmen% of ice phenomena on the studied rivers;
it is only in this case that the natural compotlents ca? correctljf reflezt char-
a@%er$stics of the syn~pti3 ~POC~SS~S.
ARerward, the pressure and temperature fields as %:ell as the H~QD field
were expanded according to the natural component. The effect of expanding the
field irrto cornponents consists in tk;t the information. about the field component
of a field formed by many points is conce;itraied in a Teig components which ade-
quately fully impart the basic properties of the initial field. During expansion,
a process of successive separation of the field intc totalities of fields occurs;
evidently, those types of circulation which are most f~*equently encountered znd
yield an estimate of the %eights of these fields of the examineti sei;.
The latter circumstance, i.~?., the possibility of presentini; tie inikial
field in the form of a set of a limited nu~ks of fields having a certain type
of circulation, led to the idea of comparing them with sets of fields obtained
when the field of times of ice appearance an the rivers gas expalided. Fields
of anonalies of air temperature for October rere cornpared siith f:ields oi" davia-
tions of the dates of ice appearance after 1 Octobe~ on the Sevel?na!~a Dvina: - Pechora, the upper course of the Kana, the irtysh, the Obs , Yeni:rejr, Lena and
AEU~ Rivers*
Table 1 gives the results of this conipariscn according to tlne anount of
information on the initial field contzined in 1, 2, or inore (up to 10) expansion
fields. It foliows from 'ihe tabular data that already the r'irst 6 components
conkain 91% af fnfor~mation about %he inktial air temperature moenaly field in
October and 95% of ttie date fieids of ice appearace.
Table I
Sumary Znformatior~ ($1 .&bout the Air Temperature iiilonaly for C)cstober and the
Times of Apcesrulcs cf Ice, Contained Successi~alj. ir: the FS.rst Ten Expansion
Fields
ilmber of expansion
Y.ie 9ds 12395678910
AirP tempera%~i~<?
anomaly G3 63 75 83 89 91 93 95 46 96
rn = izmes of ice
appear an ce 80 35 88 92 9-4 95 96 97 98 98
Maps of the eigenvectors of the temperature anomaly field expansion for
October and the dates of ice appearance were drawn. The direction of the iso-
lines which outlirie the uniform values or' natural components are similar.
The first eigenveetor (Xlf of the ice appearance dates eontains 80% of
the information. The region of negative values encompasses the Yenisey Iiiver,
the lower course of tha Obr Rives, the upper course of the Amux3 R:iver and the
fechora River. The zero lin2 runs through the city of Troitsko-Pechorskoye
(the Pechora River), Oktyabrfskoye tributary (the Obv River), the city of
.% /I -.+- abnoyarsk - (the Yenisey River), and through the upper course of the Shilki
and ArenF Rivers. It crosses the USUT River at the city of Vlagoveshchensk.
Such a layout of the zero line corresponds Lo a 90% frequency curve of the
dates of ice appearance on 31 October, cited in a wark (3).
The layout; of the foci of positive and negative values (the points) on
the nap of eigenvector X1 signifies that when the ice appears ftarljr on the
Lena and Yenisey Rivers, as well as on the lower courses of the Obg and
Pecho~a Rivers, it is Bore probable to anticigate the appearance of ice later
than normal on the middle course of the Obg River, on the Irtysih itiver, on
the upper cocsse of the Kama River, and on the Severnaya Dvina Rivers.
In order to obtain a quantitative characteristic of the retlationship
be tween eigenveetors , coefficients of expmsion far a 301-year series of
temperature anomaly fields and dates of ice appearance were corkrelated.
Table 2 gives the values of the obtained correlation coefficients. It is
characteristic that the highest values of the correlation coef t'icients were
obtained with uniform expvlsion coefficients (with the exception of Bg a~d
n 's.
The zero line outlines a region of disposition of the Siberian anti-
cyclone on the mapilaps of anomaly of the x2 temperature field. &I these cases,
the ice appears on the upper courses al the rivers earlier, whi.ch is due to
t-he cold a~tieyclone weather associated with the Siberian antiayclane,
Fieid x3 of the ice appearance dates is characterized by its meridional
nature. The appearance on rivers of this type cul be due to two char'acter-
istic processes: the invasion of vlticyclones from the Barents Sea into the
Obg River basin, and the invasion of anticyclones from the Karsk Sea to the
middle course of the Lena River,
These three fields not only determine the time of appearance of the ice
on the rivers, but also determine to a certain extent thoir distribution for
different rivers in tine. Hencs, in the future during the forecasting of ice
appearance times, the established affinity in the distribution of natural
components of tne eigenvectors of pressur.2 anti temperature anomaly fields for
the month preceding the appearance of the ice and the fields of ice appearanc?
dates can also predict the course of the process of river thawing in time, ~giih
a certain degree of probability.
During the development or' 3ethods or' long-term forecasts of thl ice
appearance times on rivers of the narthern ETS (the Severnsya Dvina and the
Pechora) , of Siberia (the OW , the Irt:;sh, the Yenisey, the Angara and the
~ena), aqd of the Far East (the knurl, it gas established that obtaining Lhe
foracast indicators for October, Leo, fcr the month in which, as a rule, ice
forrnati~n begins on the iiste3, rivers, ic is best to use the characteristic of
atmospheric circulation for July and August,
Table 2
Value of Cornelation Coefficients Between the Expansion CoePf icients Relevant
t;3 the Naturaal Components of the Air Temperakure Unomaly in October (BI - BX0)
and tho Dates of Ice Appearance (in deviations from 1/X) (B1
-- %a 1
(Note : comrnas should be read as decimals. )
Coefficients of expansiun of the pressure and temperature anomaly fields were
used as this characteristic, according to the natural component in a certain
region of the Northe~n Heuiisphere. This is significant for the given river
basin. The coefficients of expansion of the meteorolcgical element fields for
September for certain rivers, as, for example, the bur, is ir~tiraately related
with the tines of appearance of the ice, which makes it possible to use it to
refine the long-term forecast.
The intimate relatianship of the atmosplle~ic processes of July, as rqell
as those of August and September, with the appearance of the ice on rivers,
which occurs in October, is not racdom, but is confirmed by the investigations
conducted by a number of authors who identified an association between the
temperatures of the air in July (August and September) a~ld Oct:o&!r (7).
The long-term forecast of the times of ice appearance on the Severnaya
Dvina, Peehora, Ob', Trtysh, Yenisay, Angara, Lenaand Amur rivers in~rolved
taking the parameters of ex3ansion as the basic arguments acccrrding to the
natural components of the pressure and temperature ~momsLy fields for July -
September in different secGors of the Northern Henisphere. The characteris tie
sectors were chosen as the result of a careful analysis of atniospheric processes
in these mran"bhs af the year, %hen the appearance of ice was olf)serwd at times
which significantly deviated from the average multiannual times.
In order to obtain the forecasting relationships for the Amur, Ti~nisey
and hgara rivers, it was necessary to use the parameters of e!xpansion of the
pressure and temperature anomaly fields of the air over ea ~te1.n Siberia and
the Pacific Ocean as arguments; for the Pechora River, the lo~~rer course of
the Obt and Lena rivers - those over Canada, while for the micidle and upper
courses of the Lena Rivsr, those over ~ge~tern eastern Sibejria kzad "c be
used. FOP the Severnaya Dvina, %he ObT (excluding the lower course) and the
Irtysh rivelBs, it is necessary to have the parameters of exparksion of the
pressure and temperature anenalies over the Atbantic Ocean, Etkrope, md
western Siberia*
As an exanrpbe, we cite bhe equation which can be used to e~mpile the
fo~eeast of ice appearance dates aceording do the JuZy data far the Severnaya
I'vina River near %he city of Kotlas :
where QD is the deviation af ice appearance times from the naxqmal date near
the city of Kotlas; 91 - Bq are the expansion coefficients of temperature
anomaly fields in July over ETS and tresteuSn Siberia; Sg - BG ;,re the field
expansion coefficients of the pressure anomaly in the same location.
The number of field expansion coefficients over each region was selected
or? the basis of estimating the c~ntribucion of the individual components to
total dispersion. As has been shah3 in mmy ~LUdles~ the prirnary cantribution
fzlls to the first ten members of the expansion, %ini,.ich reflect; tile most sFg-
nificant field characteristics; of these, no more than 7 usually enter the
forecasting equations. This is because when the number of variables increases,
the requirements made upon the volume of initial data rapidly grow and the
styetch where ice formation begins; h and v - respectively, the average depth and
average flow rate on the heat exchange stretch (i.e., on a length lo); k and d -
parameters which characterize heat exchange with the atmosphere; :Lo - wake*.- temp-
erature at the beginning of the stretch; O - temperature of the air averaged over
the stretch; g - influx af beak fram the ground ad subternlaem water over the
stretch,
Sinee most of the initial values are taken as averqes over a stretch whose
length 10 is the sought value, then the calculation is made by t\e method of
successive approximation (3).
2. Improvements have been made in the method of forecasting the dates of
ice cover (the dates of formation of ice necks on rivers). The :relationships
bethleen the critical temperature of ice cover formation @,, , on %he one hand,
and thc totals of negative air temperatures at the point of formation of the neck
fCaM)M) and on the path of movement of the ice (ZN)M), as well as ti3e hydraulic-
morphometrie parametel-s, on the other hand, have been determined by the dimension-
alitiesv method. h%en obtaining the calculation equations, the laaterials of
aviation surveys and special observations carried out by the Gidroenergo-
proyekt were used. The result was obtaining the following twa equations :
A check showed that the accuracy of the calculation made according to the
equatia2s (3) and (4) is signifiemtly higher than chat yielded by the previous
Shulyakovskiy equations (10). The comparison also showed that the equation (41,
despite the fact that it is only slightly simpler, has poorer accuracy than
equation (3). Equations (3) and (4) are identically applicable ;for calculating
the beginning of the ice cover formation on rivers with natural and regulated
water regimes
3, CreaC changes have occurred in the field of short-tern fc1recas"sk sf khe
Spring ice phenomena. A nodel of the debacle process has been dt3veloped which
takes into account the primary property or" the meltigg ice - the reduction in
its strength.
Tile ice cover on tk reservoir is %rimewed as aq infinite OF :semi-infinite
place lying on an elastie base and subject to a vertical \.rind load (1). The
condition of its destruction is the following
here $ is the relative destructive stress of bending, equal to oJc0; a- - des-
tructive stress of the melting ice; a0 - destructive stress for ice nct exposed
to the effect of sunlight and having zero temperature; h - thickness of the
model of the process of destruction of the melting ice which is the basis of the
methods of calcalating and forecasting the dates of debacle of rivers and reservoirs
Id has been established that the strength of the melting ice decreases under
the effect of solar radiation, namely:
3 where S is the amount of heat of solar radiation absorbed by the ice (calicm ;
SO is the mount of heat of solar radiation at which the ice totall;{ loses
strength. On the average for rivers and reservcirs, Sg = 117 cal/cm-3, but it
can fluctuate within broad limits (1) dependi~y upon the structure of the ice.
The amount of heat S over the course of the melting period oontinuously
accuraulates and depends upon the amount of solar radiation that strikes the
ice, the thickness of the ice in which the absorption of solar radiation occurs,
as well as the thermal balance in the upper surface of the ice cover. When
there is a negative therlnal balance, $he heat S accumulated by the ice in the
form of melt water in the ice layer pal-tially and occasionally fully is expended
e the melt water again freezes f .
The value of $ is calculated in parallel with the calculation of ice thick-
ness. A precise determination of + and FA for the given days requires a layer-
by-layer calculation taking into account the distribution of absorbed solar
radiation through the thickness of the ice. Tiis method is laborious without
using a computer, but is preferable if one has a computer, particularly when
establishing the forecasting relationships.
A less laborious method that does not requim a computer but Fs also less
accurate can also be SUCC~SS~L~~~~ used, particularly for corrupiling tbe operating
farecasts (2).
The method of calculating the strength of the melting ice cover made it
possible to issue a new type of forecast, namely a forecast of the thickness
and strength of the ice cover on reservoirs. This forecast is u:;ed to detex--
mine the optimm time of beginning the operation or" lake icebreakers.
5. The trahsiticn from the empirical methods of forecasting to the physico-
statistical ones required refining the physical and mechmical properties of the
ice and snorri as well as the developnent of a method of determining a nunber of
new iee ~haract~eristics. For exa~ple, the albedo of melting ice was refined
(4, 51, md a r'elationship of the ice albedo with meteorological c~ndltions was
established. The concept of the capacity of the ice to absorb solar radiation
(1, 71, etc. $gals expanded.
Btermining the influx of the heat of solar radiation to she ice cover
required reliable information about the albedo of the ice and its absorbing
capacity. It became clear that the albedo of the ice is a variable value as
the result of analyzing aqd generalizing available obser-iation materials. 81-
bedo depends upon the condition 02% the ice surface uld u3on meteorological
conditions. A relztionship of albedo with the course af air temperature, the
type of precipitation md overcast was established for the Lena River. This
maltes it possible quite accurately to calculate albedo for each day of melting
(5). At precisely the same time, the average value of the ice albedo is quite
canstant over the entire melting period (0.30 - 0.35).
fiaabysis of the observation aakerials of different authors rebating to the
absorption of solar radiation by the ice showed that ice absorbs the Sun's rays
selectively and the spectrun of radiation striking the ice surface is extremely
heterogeneous md depends upon the atmospheric hu&di ty , overcast and height of
the Sun. Therefore, the absorption of solar radiation by the iee is not sub-
ordinate to the Buger-Lunbert law, but is approximately dese~ibed by the following
empirical formula
where 10 is the radiation entering the ice; I is the radiation passirlg throwh
ice having a thickness of hi; c is the absorption factor, which depends upon the
structure 0% the ice*
me precise detepminatioa of the abssspt;on factor for -j:!e cGyep of
different water objects ad establishing the principles of the chzmge in z~jr
absorption factor in different physico-geographic regions is a problem for years
ediah ffaat~we,
The caleulatiean of the thermal balance sn th..,e su~face of the water in Autlmn
or on a surface of the melting ice in Spring requires precise values of the meteor-
ological elements over these surfaces. The temperature difference, atmospheric
humidity and wind velocity over the water and ice surfaces and over dry land is
sometimes so great zhat it can tatelly distort the results of calculating ice
melting if the data or' a shore meteorological station are used without raking
the reducing corrections in them. The difference in the value of' meteorological
elcmen+,s is especially high in Spring, after the s~ow h~s aelted away from the
soil. At this time the air temperature over' dry land can be 5 - 70 higher khan
sves %he ice cover*
The observations sho~ed that the difference in temperature and hurcidity of
the air over dry lad and the ice cover depends not only on the abhsllute value
of these elements: but also on the degree of overczst and wind (5). As a rule,
the larger tbe water object, the greater the chap in meteorologi.cal eleaents
above it. Boqiever, these differences ca? be significant even above a compara-
tively small river as a consequence of the de~p cut of the chulnel. or the Level
of protection of the shore meteorological observatistl station. Hence , in order
to obtain reliable data about the thermal balmce, one should establish the
transition coefficient from the shore meteorological station to the examined
object. This is a problem for the Fr~qediate future.
6. The transition to the physico-stztis-lieal ad calculation meihods of
forecasting ice phenomena does not sign20 abandoning the =ore simple forecast
relationships, if they do not contradict the physical concept about the process
and provide accurate results. For exaple, it is knom that the calculation method
of forecasting the Autumn ice phenomena does not ru1.e-out the use of phgsico-
statistical relationships s true Cured on the basis of a multiannual series of
observations. Furthermore, the simple relationships occasionally provide nore
accurate results thbq kth ecalculatian methods. For example, forecasting the
dates of the ice cover according to the total of negative average daily air
tempe~atures md the critical ternperaturn determined on the basis of water
Isvel can be more accurate than that done according to the calculation method
because it is difficult to determine the necessary hydraulic-morphological
characte~istics for the calcuia%ion,
The calculation of ice strength (value 4) is quite laborious md requires
inr"or;nation about neteorological elements. At precisely the sa5e time, when
one is compiling th? debacle forecast (according to the prepared me%thod), par-
ticuiar accuracy in determining ice strength is unnecessary. Therefore, the
possibility of determining the relative sdrength of the ice cover 4) according
to the nmber of days n from %he onset of loelking (frorn the date of the snow's
departing the ice) and the initial ice thickness h~ was investigated, The
fallowing ex2ression was obtained for the Ussuri River (8) :
Equation (11) is also suitable for other rixrers, specifically for regions
where the Spring is usua1l.r sunny (Siberia, the Fa- East).
REFE ZEN CES
1. Bulatov, S. N. Calculating the Strerigth of the Melticg Ice Cover and the
Onset of Wind-Driven Ice Dz-ifting. Leningrad, Gidroaeteoizdat , 1970, L17 pages.
(Tr . Gidromettsentra SSR. No. 74). (Transactions or' the Eydrometeorologica1
Centes of the USSR. Ms. 74).
2. Bulatcv, S. M. Calculating Plelting ol the Ic9 Cover of Rivers aqd Reser-
voirs. "Tr. Gidromettsentra SSRfi, 1072, No. 49, pp. 14 - 29.
3. Yefremovz, N. D. Calculating the "Semperature of Water and ICE Fornation -
V kn, : Sb, dokladov VI konf. pridunayskikh stran pa gidrologich~eskim prognozm.
(In the book: A Collection of Reports aven at the VI Conference of D~inube-
bordering Countries on Hydrological Forbcasts). Book 2, 1972, pp. 291 - 294.
L!. Piotrovich, V. V, Calculations or" the Ice C.sver Thickn~ss on Fieserv~irs
Fade According to Meteorclogical Eieme~ts . Leningrad, Gidrome'ceoizdat , 2.958,
135 pages. (Tr . Gidromettseetra SSR. Mo, 18). (Transactions of the Hydroinetect-o-
logical Center of the USSR. No. 18).
5. Polyakova, K. B. Characteristics of Melting of the Ice Cover and the
Debacle of the Middle Lena, Tr. TSIP!'~ lc.66, go. 151, pp. 149 - 170.
6* Polyakova, K. N. Char2etr*istics of Fo~eeasting the Dates of Appearmen - of Ice on the Lena Xi~ier, Their Probability Distribution ad $he ice Cover
Regime. "Tr. Gidromettsentra SSSR", (Transactions of the Hydrcmeteorclogical
Centes of the USSR), 1974, %ice 117, pp. 6Q - 73.
7. Timchenko, V. M. Calculating the Appearance of Floating Ice on iiivers
of the Ussuri Basin, "Tr. DxmIGM13b, 1972, No. 33, pp. 103 - FI1,
8. Timchenko, V. M. The Question of the Absorption of Solw ]Radiation by
the idle1 king ice Cover of Rivers and Reservoirs. ffMeteorologiya i gidrologiya" ,
1972, No. 8, pp. 97 - 98.
9. Timchenko, V. M., S. t4. Bulatsv. Determining the Stress U~?!nloading Value
for Helting Ice. HCidrotekhnicheskoye stroitelf stvoH, 1973, No. 9 pp. 37 - 38.
10 Shulyakovskiy , L. G. Poyavleniye f da *i naehalo ledostavii ni? rekakh,
ozerakh i vodokhr;milishchakh. (The Appearance of Ice and the Onset of the Ice
Cover on Rivers, lakes, and Reservoirs). Lenir~rad, Cidrometeoizdat, 1960,
216 pages.
11. Shulyakovskiy, L. G. , V. M. Busurina. CalculzCiw the Onset of the Ice
Cover on Rikers Under Natural Conditions an5 Under Regulated Fiow Conditions.
"Tr. Gidrcimettsentra SSSXu, 1967, No. 8, pp, 12 - 2.4.
12. Shulyakovskiy, L. C. 4 Hodel of the River Debacle Process. "Tr. Gid-
romettsentra SSSR8, 1972, No. 49, pp. 3 - 10.
CALCULATICNG THICKNESS OF TBE ICE COVER ON BS/b5',R% AMD RESEZVOHRS FOR
ICE PHDJOMENA FORECASTTMG PURPOSES
Ig: V. V, Piotrovich, V. Ya. Anineva
( The Hy drometeorological Center af the USSR, Noscow )
The accuracy of foreca3ting the thickness af the ice ccver on rivers and
reseriroirs, ar well as the time of debacle and their clearance Troa ice depend
to a significant degree on the correct estimate (diagnosis) of the cusrent ice
thickness. Today, the diagnosis of ice cover thickness is generally based on
standard observation.^ of the water-meteping station. As is knojipn, in a number
af cases these observations poorly characterize the thi2kness of the ies an the
water object in general. The materials obtain3d from ice measuring surveys
carried out on rivkrs in the European Territory of the USSB show that the thick-
ness of the ice at the stations in the initial period of icing is usually less
than the average thickness of the ice on river stretches new the stations, while
in Spring, on the contrary, it is greater. Differences in indirridual years have
reached 10 - 12 cm and mope, The causes of' this zre obvious, In %he WuCmn, t3e
ice Ta~rns near the shore (ashare) earlier; at the end or' Winter- a~d in the period
of the Spring %ha%$ the ice cover is thinner in the shore zone klhm in the middle
of %he river due ks the influx of igapn gx-aund and melt waters from the share.
Tor the Oka River (10), the correlation coefficients of the relationship
sf ice thickness at the stations f1-o~ bhe aibdBe in the stretch of river or an
a stratch of river near the station fluctuate from O.8& to 0.91. Deviations
within limits of 52 cm had a guarantee faceor of 23 - 44% =d within li-~ts of
4- -10 cm - 82 - 91%. The greatest deviation r%&ched 29 cm in tile presence or^
poiynias (stretches of clear water in ice) and the Autun? ice scc&aul2ti~ns.
Measurements aade ;osa a characteristic st~etck sf watzr wid shalfs~s of the
Ok. River near Novinka stction confirmed the astablished opinina regwdir,~ the
thimer ice in stiailorqs. This is explained not only by elevI2ted inrlux of
heat dta the ir:e Sr~m waker in the shallows, but also by the later es%abl<sh-
msnt of the ice cDver and the excessive acca.su9ation of sncw in individual years
on the rough surface of the ice cover
The height or' the snow on the ic~ aeaswsed at stations on the Oka 3ii-er
was most often lawer' fhan its average height cn the hydronetric stretch of
9 t ;~dter (correlation c~efficients of about C. 30). Ti2is iv~3i a24i~zr cna neeesity
of changes in k'ne set-up of observations roade oI" snow at the stati~ss.
P rne people who devised the method or" calculating the thhien5ss of the ice
uhich is presented below have as their goal not only to enhance the accuracy
of dizgnosing the curpent thickness oi" the ice, btt also ~eterni~iag it for a
mul-liannual series ~f past winters. These data are necessary during the
develcpment of a method of long-term farecasting of the dates h-- which the ic5
* *
Y
achiei~es a ce.%sin thickness, the dehc12e kises and the sxiaes a"L wAich u&er
objects am cl-ear of icse, as :$ell as f'sr o$hel-. purposes.
The basis of the method of ealculatin~ the build-up in thickncc~ of the ice
cover from the lower surf;rce is a variation of the known Stephvz forraula. The
fopmula eharacterizas the steady process of bliild-up in the absence of a ready
ice naterial axkd an infXux of heat from the ~ater %o Lkie ice:
where ti,s - temperature of the surface sT the ice or snow on the ice; L -
heat liberated during the crystallization of water (80 cal/g); AT - time;
@ j - density of the ice eover (assumed to be 0 0.91 glcm3) ; HO and h, - thick~ess 2
of the ice coverb and height of snow on the ice (cm); Xi and .\s - respectively,
heat conductivity of the iee cover. (assumed to be 0.0052 cal/(cm deg~;ree ~sec)
sad snow on the icel
In order to det,ermine the rnaximun pre-Spring ice thickness on rivers (2)
uld reservoirs (4), the entire period of ice build-up is divided into cycles
(AT) of varying duration. The bounZlarFes of the cycles are days with snowfalls,
snow drifts arid thaws whinh alter the thermal equivalent of the snow-ice eover
by several tens of centimetars. When the ice is khin and has no s~ow on it,
the duration of the cycles should tie reduced to a day. \$hen one has persistent
anticyclone weakher and a significant layer ol' snow on the ice, one can assme
that AT = 10 days or mare.
After substituting the values. of heat conductivity, density, aid other
constvlts of the ice, forwda (11 acquires the following forn far calculating
ice build-up
whel-e Zt, - the sull of mean daily air teaperat3mns for the mnteorologieal sta-
tion; N - transition coefficient ,"ram air temperature at the metaorologicril
station to temperature cf tkie surace of the ice and snow on the ice;
h - aversge thermal equivalent of the snow and ice cover Z'or the
,a
0 cycle; H- - thickness of the ice eover at the beginaing of the cycle. The
d-
thickness of ihe ice at the erld of the giver? cycle is in fact the initial
thickness for the nest cycle and is assun;& be H? c Ail-.
I f
A comparisc~ of the ;:;eteorological data over %ha ice of' a n2mber or" r~ater
objects and ovPr dry imd has shor2n that- the meteorological statpions on dry
lad a% whieh ~gj-nd ~%re?oci%y 4s similar ta their values over %he water abjec%
%re more representative; i;he distance ta the mneteo~ologieal stabion has less
significance. There l"cre, f hs meteorological statians expcsed to th~ wind are
Coefficient N is aund according to two relationships (Q), which take into
account the relationship betmen air temperatwe at a height of 2 m over the ice
and the %empex*atul"e of khe surface 03 %he ice OP "i;e snow cover on the ice, Heat
conductivity of the snow is determined aceording to its relationship with density
(Lil*
The effect of winter %hags on the height of the snow cover is determiaed
according to the empirically found relationship of the decrease in height with
the total of daily positive aFr tenperaturcs. The density of the snow soaked
by melt water, was taken according to the data of P. P. Kuzqmin (1947).
B more precise calculation of the build-up in thickness of the ice cover
is necesswy for the initial period of icing. The calculation is made for
six-hour time intervals (AT = 00.25 days) according to the follo~ding formula:
where AI" is the influx of heat to the ice from the tiater, in cal/(cm2 days) ;
the other spbo9s ape as before.
The temperatwe of the surface of the ice or "che snow cn the ice t~,~ is
calculated by the method oi thermal. bzlsnce according tc? the meteoroiogieal
elem2nts. For this purpose, effective radiation was calculated after A. P.
Braslavskiy and Z. A. Vikuijna (195'1), heat exchznge resulting from the evap-
oration (condensation) of snow (ice) and convection heat exchmge with the air
were taken acc~rding to B. D. Zaykov (1955 1. The influx of total solar radiation
under condl~ions of cloudless weather rqas determiced according to ri. N. Ukraintsev
(10). Corrections for overcast, albedo, and the absorption of' radiation by the
ice were made according to the at;thcrsP reco~aendations (5).
The sought teaperabuse of the ice or snow surface ent2rs the thermal
balance equation in a power no less than the square, and this complicates
its determination. Therefire, the entire range or" temperatures of the ice
(snow) surface which Fs usually found at the ETS was divided into five components,
for each or" which the surface temperature could be expressed by a first degree
equati.~n after certain sirrzpliTicatitsns
After substituting the values or' t-~,~ ia fornula (3), five equations %$ere
obtained for eaicul9ting the ice build-up !in cm) over a six-hour period:
here, o is the wind velocity at a height of 2 m oxr the surface of the ice cover
(m/sec); tap e - temperature (OC) and absolute lxumidity (mb) of the air at a
height of 2 m over the ice; X = 0.32 cal/(sm X degree min).
The accepted values of the coefficients m, R, P, and q in equation (4) are
given in the table depending on air temperature.
The calculati.on made according to tfie equation (4) is quite laborious, 2nd
therefore special tables were compile2 (9), with whose aid the build-up of
crystalline ice on the lor~er surface of' thc ice cover over six-hour Xime inter-
vals was found aceording ta the separately calculated thermal eciuivalent , the
known daily temperatures of the air, overcast and wind velocity.
The ice thickness %as determined according to the @step-by-stepn system by
totalling the initial thickness of the ice H? at the moment of the ice develop-
ment with the increment over a cycle (AT), in this case over each six-hour period.
With the calculations carried out according to the equations (41, as when
compiling tha tables, a relined relationship of heat conductivity of the snow
with density (cal/(cm - degree * sec) ) was used
The most important factor which determines the intensity of build-up cf the
ice cover is the snow cover, whose heat insulating properties depend on its depth
(height) and density. These characteristics were calculated acc~rding tc the
data or" the neteorological stations and ths precipitation measuring statians.
The mean height of the layer of freshly fsilsn snow on the ice cover with
the absence of emporation and drifting depends on the amount of' incoming snorq
and its density; its amount for narrow water objects was taken according to the
data of the precipitation gauge mounted in locations protected a.gainst the wind
(under the protection of trees in the tieids, in orchards, etc. ). For large
lakes (ILtmen* and others), ZQ~ reservoirs, it is evidently more expedient to
use data on the p~ecipitation measured at seteorological stations open to the
wiild. There under sampling of solid precipitation because of the effect of the
wind reflects the losses of snox to evaporaticn and its driftin@; from the ice
under conditions of strong wind transport to a knawn degree.
The density of the freshly fallen snoig is %~nb in relation to wind velocity
with %he onset time of snowfall to .the tiae of its ~easurement,
When wind velocity is less thm 4 n per second (at the height of the wind
sock), the surfac~ of the ice or ol l snow will be entirely covered by fresh snow
( there is no snow drifting). De~i~ations in' the form of separate accumulations
are observed during snow hrifting (a wind whose velocity is in excess of LI m
per second). The degree of surface caverage depends on the amount of incoming
snow and uind velocity, which characterize the intensity of drifting (5). On
large reservoirs incomplete coverage of the ice by snow (a mottl.ed landscape)
is noted in the course of almost the entire first half of the Winter. In this
instance large fluctuations in tha thickness of the ice over the reservoir's
aquatorium appear.
Under mottled landscape conditions, the mean build-up in the thickness of
the ice AHI is determined accordiw to the following formula
8 where S is the proportion of surface of the %.later ob jeet covered by snow; AH- l. and AH$ are, respectively, the build-up of ice on sectors without a snorg cover
ad under snow,
On the basis or^ using the indicated relationships, as well as faormulas (5)
and (6) and certain assumptions, a number or" relationships of the type (6) was
suggested (5) to calculate the build-up of ice over the course of the entire
period of the mottled landscape. With a continuous cover of the ice by snow,
the intensity of build-up over the aquatorium levels-off and its mean thickness
can be cale7~laf~ited according to the average thernal equivalent of the snow-ice
cover 8
Thaws sigriificantly reduce the depth of the snow cover on the ice and
inc~ease its density. The decrease in the depth of snow due to settling d-wing
a thaw &hs with a density of 0.17 - 0.39 g/en3 comprises approximately 25% of
the calculated tharqing layer and also depends on ';he depth of the snow layer:
here Q is the influx of heat to the surface of the snow during thaving, deter-
mined according to the formulas cited earlier for calculating separate com-
ponents of the thermal balance; PQ and hg are the initial (before the warning
period) density and depth of the snow layer, respectively.
The density or" the snow during the thz%~ increases because of its settling
2nd saturation with water. Befire termination of the rgater retaining capacity
or' the snorq, the density of the snow czn be detemined on the basis of the
mass conservation condition p0hO = pkhkt where pg and ho are the density and
depth of the snow before the thaw, pk and hk are the same characteristics after
the thaw. Thence, according to formula (7); we obtain
The wat
$0 V, D, Kom
snow (lirn),
2 times less
pointed out
capacity of
sn the s true
er retaining capacity of the snow changes significantly and, according
.arov (1957) it c?ompsises less thx 10% on a !'strongly recrystallizedw
and up to 30% on a "finely granularR snow. This is approximately
than the figures provided by P. P. Kuz9min (1947). It should be
that there are no reliable methods of calculating the water retaining
the snow, inasmuch as the water retaining capacity depends strongly
ture of the snow cover and not on density alone.
The excess melt and rain water q, accumulates on the surface of the ice
cover and saturates the snow. After the snow and water mixture freezes, a
snow-ice of the following thickness forms (in cm)
9
3 where p is the amount of solid phase in the snow and iqater mixture (g/cm );
u is the mount of air expressed in proportions of a unit of vola~e of
the mixture (usually 0.02 - 0.05).
The ice material (brash ice, etc.) which lies beneath the ice cover in the
amount K (g/cm3) hastens its b~.ld-up aceording to the follociing equation
where AHI is the calculated magnitude of ice build-up.
Measurements
material ( sludge,
possible ts take
of the ice cover,
material an the b
the following emp
of' the dens
slush, etc.
inta account
In the abz
uild-up in i
irica9 relat
ity of brash ice and accumulations of
made after the establisbent or' iei
its effect on the subsequent build'-up
ence of such measurements the effect o
ce thickness can be taken into account
ionship (2)
other ice
ng, make i%,
in the dep
cf" the ice
according
where AR is the difference between the water le~~ei from the first day of appearan
of ice phenomena and the lowest pre-icing (ser~ies as an indicator of the tor.-
sumption of waker by ice firmation); T - number of days from the (lay of icing to
the date of the ice measl~rement survey. The correlation coefficierlt of tkie actual
ice thickness and that czilculated according to the equation (11) is 0.93 md
mean square deviation is o - 5.3 em.
The snowy ice is widespread
ice cobT?? is overloaded by snon,
ice (7). The thickness of the la
the condition of hydrostatic equi
number of cases this eq~iiibri~
openings in the ice cover as well
on rivers a-~d reserwirs; it forms where the
accompanied by the overflow of water onto the
yer of snowy ice is calculated on the basis of
librim or" tile snow-ice cover (3, 71. In a
is not achieired because or" a defi.ciency or"
as because of freezing of the overflaw water.
Therefore, the following empirical relationship (1) yieids the best results
H field ice = 0.62 (hs --h 1; QS 3
field - ice here, ka is the difference in the depth of the snow in a field s S
(according to the snow survey data) and on the ice (according to a station
measurement ) . The coefficient 0.62 chiefly characterizes the increase in
snow density when the snow thaws because of the water which has entered it
from belaw the ice. The relationship (12) has been obtained according to the
material of ice measurement surveys. Me= square deviation is 4.7 cm.
Fishermen facilitate the formation of snowy ice. One fishing hole nith
a significant overload of the ice by snow can cause the formation of snorgy ice
over an area greater than 1 ha. On small water objects, for example, the
Klyazgminsk reservoir on the Moscow Canal, snow ice of significant thickness
forms almost annually (up to 3'1 cm in the Winter of 1959 - 1960). On the broad
Rybinsk reservoir, relatively less visited by fishermen, the condition of ice
overload by snow frequently remains until Spring and the snorq ice is only noted
in places*
As observations made at the Klyazgminsk reservoir (1956 -- 1959) and on the
Oka River (1970 - 2971) showed, cracks form when a shallow layer of snow exists
with significant Eluctuat ions in air temperature. Through cracks only exist
when the ice is less than 20 cm Chick,
Experience in calculating ice thickness carried out at the Hydrometeorological
Center of the USSR for different rjater objects according ta the "step-by-stepu
cycles have sho~m that this system enables one to take into account the sharply
changing meteorological and hydrological situation. Simultaneously, the need
for future investigations was revealed, particularly in the area of the quanti-
tative determination of the influx of heat f~*om ground water*
1, hiaeva, V. Ya. Experience in Calculating the Thickness of Snow-Ice on
Rivers in the E~iropean Territory of the USSR. Vr. Gibrornettsentra SSSRu,
1972, No. 112, pp. 90 - 99.
2. hineva, ii. Ya. Calculating the Build-Up of Ice Thickness Taking Into
Account Ice Structure, "Tr. Gidromettsentra SSSXo i971?, No. 117, pp. 20 - 38.
3. Feryugin, A. C. Investigating Snow-Ice. ffTt'. GGIfl, 197-1, No. 184,
4. Piotrovich, V. V. A Method of Calculating the Raximun Thickness of the
Ice on a Reservoir. "Tr. "iIIPu, 1963, 80. 130, pp. 3 - 86.
5. Piotrovich, V. V. Calculatians of the Thickness of the Ice Cover on
Reservoirs Carried Out According to Meteorological Elements. "Tr . Gidronet Csentra
SSSR", 168, No. 18. 135 pages.
6. Piotrovich, V. V. Calculating the Build-Up of Crystalline and Snow-Ice
Based on the Exmple of the Kayaa @minsk Reservoir "Tr. Gidromettsestra SSSRff
1970, No. 67, pp. 50 - 38.
7* Piatrovieh 8, Ve The Conditions sf Formation of Snow-Ice 0x1 Reser~oilns~
"W. Gidromettsentra. SSSRvf , 1972, No. 112, pp. 77 - 88.
8. Piotrovich, V. V. The Representativeness of Information About Ice Thick-
ness and Snow Thickness on Rivers, Baed on the Example of the Oka River. "Tr.
Gidromettsentra SSSRH, 1974, No. 117, pp. 3-19.
9. Tablitsy dlya rascheta narastaniya ledyanogo pokrova s nizhney poverkhnosti
i ikh primeneniye. (Tables for Calculating the Build-up of Ice Caver from the
Lower Surface and Their Application). Edited by V. V. Piotrovich. Moscow, Published
by the Hydrometeorological Center of the USSR, 1970, 61 pages.
10. Ukraintsev, V. N. The Approximate Calculation of Sums of Direct and
Scattered Solar Radiation. 9TMeteoroiogiya i gidrologiyafl, 1939, No. 6, pp. 3 - 18.
PROBABILIR CHARACTERISTICS OF FREEZING QJD DEBACLE TIMES OF BIERS &TD
RESERVOIRS OF THE SOVIET UNION
By: B. M. GLnzburg
(The Hydrometeorological Cent,er of the USSR, Moscow)
The freezing and debacle of rivers have a significant effeci; on the activity
or" such branches of the national economy as inland waterway transport and con-
s truction , especially the hydrotechnical and transport types, forestry, energy
generation, etc. Specifically, the beginning and end of the navigation period
will still be determined for many years by the tines of freezing and debacle of
rivers and reservoirs, despite the technical re-equipment of the inlad wsterway
fleet .
In recent years, planning practice has adopted economic calculations for
which data on the probability of times of ice phenomena are necessary. The
development of hydrotechnical construction on river mains requires calculating
the praabability czharac"ceristics of the tims of ice phenomena sn reservoirs..
The improvement in methods of ice forecasts is also linked with studying the
probability charactaristics and space-time relationships of ice phenomena times.
Our investfigations on this problen began in 1964, when characteristics of
the probability of times of ice phenomena on navigable rivers of the SovieQ Unisn
were obtained ~i!i$h the aid of plotbing empirical. curves of the grrarantee rating
of dates of the appearance of floating ice, the beginning of icing and the Spring
debacle (and later, the dates of termination of the Spring debacle and magnitudes
of durauion of the period of the absence of ice as well, called the period of
physical navigation in inland waterway transport). The published tables of times
having frequency ratings of 2, 10, 25, 50, 75, 90 and 98% in a multiannual series
have '=en wide2.y used in practice.
The possibility of approximating their guarantee curves was investigated
(4) r"or purposes of analyzing, swnarizing, md calculating the ],robability
characteristics of the tines of ice phenomena. The Pierson III type (binomial)
equation provedt ta be most suibdble far this purpose and has came f;o be exten-
sively used in hydrological calculations. The use of this equation in the cal-
cula.tians of flow encounters difficulties when extrapolating the values with
very low repetition. In our case such difficulties do not have a significant
ef feet , since i3 the economic calculations, unliice the construct:ion ones, such
an extrapolabj.on is wuallby not required.
A specific characteristic of the calculation of dates is the impossibility
of determining the conventional changeability characteristic - the variation
coefficient C,. In order to calculate it? one ws"Lavve some zb:jolute value
which characterizes the norm, i.e., one must establish the begin12ing of the
time count. Such a beginning will unarroidabiy be arbitrary, and coefficient C
lases the property of =-a indicatar which is comparable L"iJr any statist$cal V
series, Hoa~ever, this circumstance does not prevent "Lhe use of %he "ainomia_?,
equation. The changeability of dates is characterized by the zean square
deviation of the dates from the norm. According to the parameters calculated
from a series of date observations, the average date D, the mean square deviation
o from it and the asymmetry coefr'icient C, - it is eaa to determine the dates of
ice phenomena of any given frequency level p as Dp = D + crQl (CsZa) with the aid
0% the known Fos&er5-Rybkin. tables.
investigation of the accuracy of determining the parameters of the equations
acc~2ding to the actudl series of observations made on rivers showed that the
probable errors for the average dates and the mean square deviations from them,
as a rule, do not exceed one day, e. am within the accuracy limits of the
observations. The changes of average dates caused by climatic f:Luctuations,
with calculation of these dates according to a more than 30-year series, do not
exceed the error limits of the calculation itself. The coefficient of mymetry
is less accurztely determined, but only in very rare cases does 'the error of it,s
calculation cause an inaccurate calculation of the date with the required rrequency
rating af more than one day. Comparing dates of an equal frequerlcy rating obtained
according to the calculation and plotted from the empirical curve demonstrated that
the deviation of these dates in 90 - 95% of the eases do not exa5ed one day, i. e.,
do not exceed the observation accuracy limits.
The parameters of the curves of date frequency of the ice phenomena (and
the dates of varying levels of frequency themselves) have been si a~izeQ in $he
form of maps for the navigable rivers of the USSR. The maps of average dates
(norms) had also been dram earlier according to more or less detailed data.
We shall dwell briefly on the first generalized characteristics of changeability
and asymmetry. The mean square deviations from the norm increase for all ice
phenomena from east to igest, and particulhrly intensive in the western part of
the ETS. Over a greater part of the Territory of the Soviet Union, the change-
ability isolines are nearly perpendicular to the isolines of ice phenomena times.
This is because the ice pkenomena times are decisively influecced by latitudinal
zonality (particularly in Spring, when the proportion of solar radiation is high
in the thermal balance of the snow-ice surr"aee), and changeability increases in
zones of a maritime climate and decreases in zones 0%" the sontin.c?ntal climate,
me basic greaLer as etry zones also tend $sward the extrt2me western and
southern ~egion.~, byhere t boundary of the stable riparian ice regime runs.
Here the Autumn ice formation is occasionally very late and the debacle is
soinetimes very early. This is responsible for the positive asymmetry of the
Aut ice phenomena and the negative asymmetry of the Spring onrzs.
Another highly as etrical zone is Eastern Siberia. The negative as
of the Spring ice phenomena is particularly significant here. These phenomena
occasionally begin significantly earlier than the average times. This is
associated with the high influx of heat from solar radiation md the melting of
the snow cover long bfore the river. debacle.
Other, secondary characteristics of the geographic distribution of change-
ability and asymmetry cf the ice phenomena dates are given a basis during a more
detailed exmienation. The parameters of equations of the frequency curves of
duration of the period of no ice are associated with parameters of the curves of
guasa?,tee of termination sf the Spring debacle and the appewanm of ice, which
are mubually independent, random values
The identified principle of geographic distribution of the paraqeters of
the ice phenomena time guarantee curve equations enables one to use the maps
dram by the author to calculate the guarantee date curves of ice phenomena and
the duration of the period of no ice on stretches of rivers for which observations
are inadequate* In order to test the possible accwacy of such a calculation, the
times of equal frequsr. :y rating have been compiled and calculated according to
parameters taken from maps according to interpolation and taken according to the
empirical frequency curve. The probability deviations for the ice phenomena
dates proved to be close to one day and those for the duration of the period of
no ice were about 1.7 days, i.e., comparable to the accuracy of observatiogs.
Calculating the elements of the ice regime of newly built I-eservoirs has
special significance with the development of hydrotechnical construction on
large navigable primary waterways. The work of I. 11. ~alashovaj- gives a char-
acteri-zation sf the methods and results of' cafculatisns of the zmnuaH dates sf
the onset of icing and clearing the reservoirs from ice. However, when designing
hydrotechnical facilities it is unnecessary to have annual dates in the calcula-
tion - it is adequate to have their frequency curves.
"She author used "the accwuiated data of calculations and observations to
develop a ~ethcd of calculating the parameters of frequency curves.
The aTlerage dates of the onset of icing on a given stretch or' the reservoir
can be calculated according to the sums of average daily negative air. temperatures
which are necessary for freezing of the reservoir CQ (11, and the average depth
of the latter, he It is known fron the more detailez investigations (81, that
the indicated sum is strongly influenced by the current speed as well. Therefore,
the author has taken the lomr envelope of the graph of relationship CB = f(h) -
2s the basis of the calculation, while the deviation in the actual values of
ZO from it is associated with the average current lzelocity in a calculated
stretch v. As a result, the fillowing formula r~as obtained
The date of accumulation - calculated according to this f:o:ormula is con-
sidered to be the onset of icing. One car, make a calculation according to
formula (1) for stretches of a reservoir located 120 - 150 km below the hydro-
electric statiorl. The foxnation of icing occurs later on stretches which are
closer to the lower waters of the hydroelectric power plz~%.
The average dates of ice clearance are determined with the aid of the
relationship of the sum of average daily positive air temperatures Z6+,
necessary for ice clearmee, :k~ith th; sum of average monkilly ne~5ative air
temperatures CO_ oxier the Winter (7), taking into account the effect cf the
---I
%, See this v~~olume.
stability of the reservoir and the influx of heat from solar radiation at the
end of the thaw, which play an important role in the process of ice destruction
(3) - The flaw factor is characterized by the relationship of the volume of
water w that flows through the reservoir over the last two ten-day periods of
"r;he ice men w:ith %.he kotal volume sf &he resermir at the end of its pre-
Spring period of evolution, We The mean daily value of the total influx of
solar radiation 8' was determined for the last ten-day period. of the ice melt.
The eaiculation formula has the following appearance
0 It is valid when 4 80 . The date of accumulation of the total of
positive average daily teroperatures calc~lated according to formula (2) is
taken for the date of reservoir ice clearmce*
Changeability and asymmetry of determining dates of the ice phenom3na
on reservoirs were obtained by comparing their characteristics cf and C, with
those observed on the very same stretches or" the rivers before the construction
of hydrotechnical facilities according to the comparable date series. 1% proved
that freezing dates for the reservoirs, which usualljr fall between the dates of
the appearance of ice and icing on the rive^ have values of cs and C, which are
intermediate ones; they can be determined by interpolation. In this instmce ,
changeability for a reservojr is a lower value than for a river. For the cal-
culation one takes the average reduction coefficient, which is 0.84. The
parameters of changeability and asymxetry for the dates of reservoir ice
clearace were very similar to the parameters for dates of terzination of Spring
icing, which %ere also taken in the calculation directly.
The duration of the period of C,he absence of' ice is determined by the
difference between the dates of the appearace of the ice in the Auturmrn ad
clearance f~om ice in the Spring. The duration of the Spring ice-gmg (debacle)
an a^r;servoPrs is short; fir stmtclraes with li";tba current ad re3servoirs wi"Lhira
the hydroelectric power plant cascade, it averages two days. For the upper
st~etckes 0s" ugsi~gkeg9resennimirs it averzges three days. If one takes "LLs
correction into accounk t"ihn in srde~ ta dete~~ine the pr%ramete;rs of "t;e
equation of the frequency curve of the duration or" the ice-absence period,
one can use the parameters obtained according to the calculatior~ for dates
of the onset of icing (DI, axI CSI) and clearance from ice ( ac, Cs,) of
the mservoirs. As was mentioned, these dates are independent :statistic31
values. Therefore, a composite probability is applicable to it and the
parameters for the difference (T, o~, CsT) are found with parameters for the
initial values in the following relationships (I) :
I_- -- -
T=q-D,. (3)
23")
5 j- -= q-- se (4>
j!l ? * csr -- (-$cJ r- -,>
(5) JcC,&. - J i
"f -
tienee, the frequency curves of the times of icing onset, ice clearance,
ad d9mation of the period of ice absence can be calculated for newly con-
structed reservoirs with the presence of only climatic and projective data.
A check on the accuracy of the calculation delnonstrated that the dates and
values of %qua1 fi-equency (within limits of LO - 90%) according to the cab-
culated and emgirieal curves have probability deviations for ice clearance of
1.3 days, 1.6 days for the onset of icing, and 2 days for the duration of the
ice-absence period. Such values are fully coi~pal-able rqith the accuracy of"
determining the times of ice phenomena on reservoirs.
The investigation of spatial and space-time relationship changeability has
important significance for studying the general principles of propagation of the
ice phenomena and for practical purposes (calculations, and particularly long-
term forecasts ) *
The spatial distribution of the ice phencmena tines ;+as first investigsted
by G. R. Bregman (21, who drew annual maps of" deviations from the norm of dates
of ice phenomena on rivers of the European territory of the LTSSR in the be-
ginning of the L940fs. In order to generalize for the entire terrbitor;i of the
Country, it is more expedient to draw maps of the norealized deviation from the
The exaaination of such maps for a series of characteristic
seiisons has shown that significant anomalies of ies phenomella times enconpass
rivers of exCensive terrif or2 -:.s, but at the saxe tine, in each season, one
invariably traces a signlfirlz~lL difference in these anomalies for rivers in
different parts of the Coui~try. The quantitakive repmsentztion of the general
principles of spatial distribution of normaliz~d deviations of ice phenomena
dates from the average multiannuai ones is provided by comparing t;he "rpatitil"
curves of the frequency of these values ru'i^ih the generalized "kineH frequency
curve. The author has also plotkeg curves similar to the way curves were
plotted by G. P. Kalinin (5) for the nornalized modular coer'ficiex~ts of the
annusl flow. The general character of the spatial and Cine curves is similar,
i.e. , as for the flow, there exists ar? arbitrary ergodicity of distribution of
ice phenomena times , although significa~t differences do exlst in individutii
rr-i* years, obviously due tn the liaitation of area or' the examined territory. Lnence,
the expediency of taking into accounHthe siailarlty of character of the annual
spatial distributions to the generalized time ones during caleuiaQIons and
forecasts is obvious. In order to implement this, regions are det;;?mined in
which the times of iae phenomena are homoge~eous from year to yea+?- and ~rinclples
of relationships Setween the times of ic% phenomena on rivers in ijiffirent regions
hzve been identified.
Regio~s were identified accordifig to th~ sign or' the similar:ity cf deviatisns
from the norm in the times of ice phenomena for all stretches of river in each
year within the boundaries of a regionl. Certainly, the crux of the matter is
the rivers for which such generalization is possible, Fee. , rivers :$hose SasFn
--
lThe wori~s of G. R. Sregman, T. ti. P!a!;arevich, 8. F. Vinogradova uld other
authors were used during the regional work-up.
2 akea is at Peast 30,000 km .
Figure I. Relationship of the normalized :square
values @if deviations in the lacal and "i;rri-
torial charactnris tics oi' ice phenomena t imes
with the distance between the observation -
d
paint and the "center of gra.xri.ityfT of the basin :
1. - for ice appearance ti~e?es; 2 - ,"or onset
times of the Spring debacle.
The regional territorial characteristic is determined for each season in
each region, This is the median value of the times which deviate fi~'lrom the noram,
for example, the appearance of ice in the given year in all obsel-vation point.3
on rivers of the region (ATp). The difference between deviation:s from the ncrrm
in separate points ATi and the territorial characteristic P = &Ti - ATD was
statistically pro~essed. It proved that large deviations h are mope &equenl:ly
observed for stretches or" rivers located r3n the periphery of regions. Fq'his :is
evident from the relationships of the ncr~alized loean square value of devistions
SavrFom the distance 1 betweer, the given point ad the center of gravity of the
0'
region (Figure I). In meaning, this relationship is similar to ithe noraalized
structural function. The minimu value 2 = 0 -2 expresses a devyiation which does
a not depend upon the position of tine observation point. Tb very sarne value of
deviation resulting from distance appears when i % 330 kkm. This also dete~iiiines
the optimum dimensions of the region - the %reatest extent up Go 600 km and :tn
area of about 270 - 300,000 !a2. CercaLnly, such regicinal dimensions are
averased ones; they change depending upon specific co~diti~x~s. Thus, Ln a p:Lain,
the regions cul be greater thm in strongly broken basins; the regions should be
smaller in a zone of unstable climate where interrupkions in the phenoniena
are frequent, etc*
The symbols cn map 62 of the regi~n have been ideatified talking into acccunt
all oT the general arid specific geographical conditions in the territory uf -ihe
Soviet Unior?,, The pmbab-le value of devlatiion A far these regions is abouii; ~5:rie
day, and consequently, the territorial characteristic reliably ref lfs::cts the Siick-
ground of ice phenomena times on rivers of %lit region.
The use or" territorial regional charac terls tics of the f ree.zing and debac:le
times cf rivers in investigations conducted by the method of lonlg-term forecasts
or" these phenomena has an ii;i.portank adratage: the $zeneral conditicns of appear-
ace of a~oroalies relating to ice phenornei:~ times - atrocspheric macroprocesses -
aye associated uit!. the territo~ialiy general characterist:lcs of these times for
vast territories. It ha-, been established that in crdnr to enscri? satisfactory
firecasts for all rivers of a region, it is necessary that the florecast relatit2n-
R?- ship identified for the generalized tiaes AT correspond to the criterion q (L). [>. P It is necessary to make such assumption in the effective :'rules fix; a
&ha forecast se~wice"",
T Figure 2. Relationships of the correlation
as caeffici,encs of the ice phenomeana kimes
with the disdmee be ti~en fegio~zs a
~2 6 1 - in the direction c~E the isorzkrbones of
the times of appearvlce af floating ice;
2 - in the direction of the spatial appear-
ance of flaating ice; 3 - in the direction
of isochrclnes of the anset t:mes 02' &he
Spring debacle; 4 - in the directi~n of
propagation of the Spring debacle.
The csrslela.tion bet~qeen "i;e terri"torial characteristics oar" tlaesf2 .e;L%es in
different regions was used to investigat principles or" the space--time reiztion-
ships of ice phenomena times in an extensi~re tqrritory. The values of AT, ibr
pairs of regions located along the isochrones Mere correlated, i-e., for rivers
where the ice phe~omena occur., on the average, at similar tines, as well as for
pairs of regions located iti the direction of the progagation of the ice phen-
omena. Figure 2 shows a measurement of correlation coefficients depending upon
the distance b@t.~geen regio:-ns
The graphs primarily show tile anisotropicity of the a~omaly field of the
ice phenomena times. The correlatior, coefficients dininish proportional to
distance, rgith respect to those loczted along the isochrones, sig~nificantly
mope slowly than for the similar pairs located in the direction o.P propagation
_if the ice phenomena. The cause cf this diflference is that. in this firmer case
",e reduction ia %he eori-eiatisn csefficiesst is due to a difference in csnditians,
chiefly meteorological conditions in space, vhiie in the latter case one adds
stFll the inI=?uer,ee of the change in these conditions in Cime.
Differevces in the type of the relationship r : f(L) are also significant
for dirferent. seasons. The decrease in r prcpsrtional "L ddistancfs (=~c@L~s mare
slowly for the tilnes cf ap:>earance of ice. A steeper drcp ir. r with distance
along the isochrones z~d a lesser effect of the difference ir. time are char-
acteristic fkr %he onset times of the %ring debacle.
Still =atk.,e;~ cha~ac"sekistic is also significant: &he type of curve for &he
Autxm? debacle ice pnenomevla is tndif f erent r-iith respect to the geographical
localization of regions. Fe'cr the Sprir,g phen-,mer.a themselvzs, the cclrve r = f(i)
drops particularly steeply, falling to signifiil~~t negative values of r' if one
*. region is in the European tlrritor'y of the USST, zqd the other 1s XI: the Asiatic
territory.
80th thz gefieral aspects and ike spec;;'ic fsatures of the ;"'elSs of tiyaes
of ice phenomena are basically associated with the character of rnet2anologic;l
flG: I-ds9 primarily teaperaturn ones. T'i:is is c~nfirned by the simila~it;r
of the sbi;ained curves of the relatiorship r = f(L) with their methodologically
1 * similzr manner of ~e~aini~g tehe norEA zed a~t~corre3atio functions of air
temperature cited in works of meteoruicgists (6, others).
the scale and seasonal characteristics of atmospheric macroproc5sses, Thus, when
the diaensi~~~ sf lqish crests ad troqhs in the troposphere axe extensive,
the zone sl id91itlcai direction of the transfer from the axis of %he depression
to the axi, of i:~e cresf occupies nearly 2 - 3 thcusand hem. The meaningful
es~re2-ati~~ eoefficie-IC is also eonserved at such a dista~ee With a fiirther
inczxease in distulce, the relationship is either fully lost or even becomes an
inverse re,atlonship, but at a distance of 5,000 - 7,000 kn, i.e. , wi3en the
drop is into a sjmilar branch of an ,-dja5ent deformation field, the correlation
coefficients again become pcsitive ones.
In Autumn, the No~thern Hemisphere is characterized by the developiilent of a
zmal circulation whiie in Spring it is characterized by enhancerneat of the meri-
dioaal one. Therefore, stable contrasts of the anomalies with respect tc latitude
are not typical for But but they appear frequently in Spring. In this case,
both basic fa~ms of meridional circulation (according to Vmgengeym and Girs) are
characterized by the geographical localization of altitudinal troughs and crests
which causes the opposite signs of anomalies in air temperature over the Eurvpean
part of the USSR and Siberia.
14 zones were identified on the basis of this aqaLysist taking into account
the specific geographical conditions - orography , the flow directions of rivers,
tke alternation time of swoptic seasons - within which a stable. relationship
exists =ong the times of ice phenomena (r 3 0.6). One can take the original
dates of Fee phenomena with identical frequency for rivers of each zone in the
calculations to back-up the times or' navigation other similar calculations.
Xt is expedient to develop a method of long-term ice firecasts for these rivers
based or! taking into account the identical characteristics oP atmospheric cir-
culabion
EFI- me principal chsracter of changes 2 2 the correlation coefficients cf times
or" ice phenonnena, depending upon the dis~azce and difference in average dates
of their appearance among regions can be used in calculations and forecasts.
Thus, i.f a vast deviation of these times froa the norm occurs in one or' the
regions (or is a~ticipated), one can caiculat? their most probable deviations
from the nrjrm in other regions. These ttrpes of calculatio~s can b~ useful rrihen
matching long-term forecasts ovPr an extensive territory.
One can also assign =y pzrticular data as initial ones, for example, un-
favorable times of ice phenomena in any particular importmt region with respect
to the economic considerations. Accomplished exmales of such calculations harre
~laal~~ that their application during navigation glanning on rivers enconpassing
zri extensive territory can provide a noticeable savings.
In conclusion, one should nota that everything that has been done in the
realm of analyzing the statistical structure of fields of ice phenamena times
is the first step on the pathway to creating new methods of long-term forecasts
based upon the in~~estigation of structural associations bz trgeen atmospheric and
hydrological processes over vast areas.
2. Aleicseyev, G. A, i;brrfi:oulas .Tor Detsrmining Sti3ndard P ira.meters or Dis-
tribution Cur~res of he Sum, Diffe~*ence st~d Leriva'cive of 1ndeper.clen-L Statistical
Values. "Sb. rabot po gidrologiiu, 1959, Mo: l, pp. 128 - 133.
2. Bregman, G. R. The kletilod of Background Forecasts or" River Debacle.
"Tr. NIU GUMS. Series lilt, 1941, No. 3, pp. 3 - 55.
3. Bulatov, S. N. Calculating the Stability of a Helting Ice Cover and
the Onset of Wind-driven Ice Drift. Leningrad, Gidrometaoizdat, 1979 118 pages.
(Tr. Gidromettsentra SSSR, No. 7h)*
0. Ginzburg, B. He Probability Chazactel-istics of the Times of Freezing
and Debacle of Rivers and Reservoirs of the Soviet Union. Lening:rad, C-idrometeo-
izdat, 1973, 112 pages. (Tr. Gidromettsentra SSSX. No. 118).
5. Kalinin, G. P. Problemy global nay gidrologii. (Problems of Global
Hydrology) . Leningrad, Gidrorneteoizdat , 1968. 375 pages.
6. Meleshko, V. P., I. P. Guseva, Calculating Certain Statistical Char-
acteristics for Fields of Temperature and Iiu?iidity. ffTr. GGOn, 19611, No. 165,
pp. 40 - 46.
7. Piotrovich, V. V. Obraaovaniye i staivarliye l'da na ozerakh - vodo-
khranilishchakh 1 raschet srokov ledostava i ochis'ncheniya. (For~ation and
Melting of Ice on Reservoir Lakes and Calculating the Times of Icing and Clear-
ance ). Moscow, Gidrometeoizdat , 1958, 192 pages.
3. Shulyakovskiy, L. G. Poyavleniye lf da i nachalo ledostava na rekakh,
nzerakh i vodokhrmilishchakh. (The Appearance of Ice and the Onset of Icing
on Rivers, Lakes, and Reservoirs) , Moscow, Gidro~eteoizdat , 1960, 216 ?ages.
CHARACTERISTICS 0%" Tm ICE REGImS OF RIVERS
By: M. V. Korbutyak
(UkrNIIG, Kiev)
The process of formation of the ice regime of rivers under different cli-
matic and synoptic conditior,~ is realized with the complex interaction of such
faeta~s as the inflow of ground water, the water bearing content, extended slopes
and the morphology cf channels, the convolution and orientation of the river
network, human economic activity, etc. One frequently observes peculiarities
in the development of ice phenomena along the length of water courses and the
methods of their calculation do not practically exist through the present.
It is known that freezing, debacle and build-up in the thickness of ice
are the result of heat exchange of the water flow with the environment. Climate
plays an important role in this process. The characteristics of certain components
of the ice regime of large and meditlm size rivers were compiled according to the
data of observations of water measuring stations (3, -. , and others) (times of
debacle and freezing of rivers in the USSR, the ice thickness an rivers in the
European part of the USSR, etc. ) . Investigations carried out by L. G. Sh?dy~k~l.kov-
skiy (101, Ya. I. Narusenko (9, I... G. Glazacheva (1) and other authors ~hoxed
that in a number of cases the accuracy of such gene~alizations is inadequate
for estimating the ice regime of specific stretches of rivers, particularly small
ones. The lrarying intensity of subterranean in-flow along the length of rilrers,
variations in the longitudinal slopes and the convolution of the channel, which
determine the low velocity regime, as reil as other factors lead to a large
territorial changeability in the times of onset of different ice phenomena and
the thichess of the ice cover,
The author developed a method of determining characCeristics of the ice
regime for stretches of rivers that had not been covesgd by hydrological ob-
servations based on the example of small rivers of the middle Volga area (T).
The m~thod includes calculating the components of the thelmal balance ..nd
p1ottir.g graphic relationships, analyzing the geographic distribution of
causative factors, mapping characteristics of the ice regime, and checking the
calculation data by means af full-scale obsermtions.
The intensity and developmei~cal trend of the ice processes are determined
by the relationship of heat losses and heat influx. Beat losses (heat exchange
by convection, evaporation and the radiation balance) are derivatives of meteoro-
logical conditions and change throughout the territory in accord+ance with the
geog~kphic zonality. The components of heat inflw (the heat of subterranean
water, from dissipation of flow energy), on the contrary, are chiefly determined
by azonal factors. Therefore, their territorial (and l2ngth-wise with respect
to rivers) distribution is extremely uneven.
Heat losses, as well as the heat of energy dissipation, were calculated
according to a method presented in the work of 3. V. Donchenko (2). The mean
nultiannual values of heat losses from the water's surface uoder conditions of
the middle Volga &rea are 250 - 8CO oal/(enZ day) in Nuvtmber - February.
Determination of the amount of heat supplied with subterranean wzter on a
given stretch j.s a complicated task in most cases because of khe difficulty of
calculating the subterranean supply. L. G. Shulyakovskiy (10) assumed that the
3ingle method of detemining the in-flow or" subterranean water to rivers is
' comparing the f1ci.1 rates of water or the flaw volumes over a certain span of
time on two stretches located at the beginning and end of the investigated
stretch. The location of the stretches is usually predetermined by the hydro-
logical stations, which are located at distances of tens and hundreds of kilo-
meters apart, as a rule. The Shulyakovskiy calculations for the Volga and .
certain of: its tributaries demonstrated that the specific influx for both large
and sinall rivers averages 3.0 - 6.0 cm3/day per 1 cm2 of water sttrfzice.
It should be pointed out that the specific influx along the length of the
river Fs very unequal and on small rivers this inequality is more strongly
pronounced than on large ones. For example, on the Kazanka River, whose length
becanie approximately 150 la following the construction of the Kuybyshev reservoir,
the average value of the subterranean Fnf lux comprises approximately 6.0 cm3/cay
and on certain stretches ranges from O to 400 cm3iday and more per 1 cmz of water
surface (Table 1). Therefore, at individual points on this river the formatian
of the ice regime occurs without being influenced by the heat of subterranean
water while in other places the influx of heat exceeds 200 cal/day per 1 cm2
and the ice csvler does no$ form at allD
Experience in investigating the characteristics of the ice regime of middle
Volga rivers has sho~q2 that a realistic evaluation of the ize phenomena along
stretches of the river requires differential data about the influx of subterranean
water, and not data averaged over its entire length (or a significant part of it).
Ir. order to deteraine the magnitude of subterranean supply and to clarify its
role in the formation of charactaris'cics of the ice regime, the author used the
material of a hydrometric survey of rivers. The method of making the survek is
presented in a study (6). It war noted in 1!)65 at an interdepartmental seminar
conducted in June at the GGI that the hydrometric swvey, in combination with
the hydrogeological analysis, is a reliable method of estimating the subterranean
flow in the river. The latter is calculated according to the increments in the
aqverage mrxll;iannua% low-water level flow ra%es or" water between the trkibutar%es
or the influx and the water rrionitsring staticn. One calculates the specific in-.
f' 1 uT x of subterranean water y (cm3/day per 1 cm2) sn tile stretches according to
the fillasring relatLonshig
3 where q is the influx of subterra~ean water on the stretch, m /set; s is the area
of the water surface Tn the stretch, m2.
Table 1 gives the results of calculating the specific in-flow of subterra~ean
wat,er on stretches of the bzanka Ri.ser, Sia~ilar 621.wlations 1g2.re made for BOS~
rivers of the niddio Voiga area and a map of changes in the specific it,-l"low along
their length was dratin (53. This map serves as the primary source for identifying
stretches with partic~ilar conditions of development of the ice phencmena. Eigh
values of the specific ifi-flow magnitud~s are most often encountered on rivers
up to 50 km Lung; (Table 21, particularly in their upper wates t;reas located within
the confines or" the iiytsko-Kma, the near-Volga and BwuLTmino-5e.lebeyevsk highlands.
I
3
9 9 9 c'! 9 a+ 9 9-T q C.! ??Om 9 q'q c?c3" iyO!? qq 6", ?e= P-
~3 ~i o 10 PJ 3 o o- a a mcro t mw rii.o or-. t*- g 0"" f- 2 2 PC4 - d
,3:
(0 c3*-pt6 -c2$3 C:f- ? qccq 9 99 9 ? 90-q 9 0-q 99 c?".". c 9 9 2 o a o d d c oo o o ooo o oo oo ooc ao a o r, -
I 1 I
f-f 0.l e9"i
continuation of key for Table 1:
4 - Width of stretch, m
5 - Mirror area, m2 % l~-~ 3 6 - Influx of subterranean water, m /sec
7 - Specific influx, cm3/(cm2 - day)
8 - Source - Apaykino spring
9 - Apaykino spring - first left tributary (left tributary)
10 - First left tributary - second right tributary (right tributary)
11 - Second right tributary - fourth left tributary (Urnyak)
12 - Fourth left tributary - fifth right tributary (Pshalym)
13 - Fifth right tributary - sixth right tributary (Meteska)
14 - Sixth right tributary - seventh left tributary (~is*rnes' )
15 - Seventh left tributary - eighth left tributary (Chekurcha)
16 - Eighth left tributary - Arsk water station
17 - Arsk water station - tenth right tributary (Verezi)
18 - Tenth right tributary - eleventh left tributary (Ghdpanovo)
19 - Eleventh left tributary - twelfth right tributary (Subash-Aty)
20 - 12th right tributary - 14th left tributary
21 - 14th left tributary - Kurkachi water station
22 - Kurkachi water station - 15th right tributary (Krasnaya)
23 - 15th right tributary - 19th right tributary (Serda)
24 - 19th right tributary - Bimeri water station
25 - Bimeri water station - 21st right tributary (Sd-a)
26 - 21st right tributary - 2Qth left tributary
27 - 24th left tributary - 25th left tributary (Kinderka)
28 - 25th left tributary - 26th right tributary
29 - 26th right tributary - 27th right tributary
30 - 27th rigfit, tributary - 28th right tributwy (Solona)
31 - 28th right tributary. - 29th left tributary
32 - 29th left tributary - BolFshiye Derbyshki water station
33 - Bolfshiye Derbyshki wat&r station - 31st left tributary (Noksa)
34 - Note. The stretches are located between the mouths of permanent
the parentheses enclosed names designate the lat'er.
tributaries,
At the Same time, in the lower water stretches or" comparatively large rivers such
as the Iletr , Kazanka, the Sviyaga and others as veli, in places one observes
very high values of the subterranean in-flow xhich e:cceed 100 cm:j/day per 1 cm 2
of water surface. These tend toward the stretches where the cop:ious wzter-bearing
strata of the Kazanp and Cretaceous deposits drain.
When Table 2 was being compiled, rivers of the investigated region Mere grouped
accordi:lg to the cited gradations of length. Within the limits of each gradation
the number of stlretcbes xith the assigned values cf the specific in-flow or' sub-
tesranean water b$as counted a
The amount or' heat supplied with the subterranean water is equal to ttie
product of the vsl IAe of thpir in-flow atld water temperature. On the basis of
observations made by the author and investigations carried out by V. V. Piotrovich
(81, a temperature of ~OC was accepted as the calculated one.
Ray fcss Table 2 ;
1 - Table 2. The Repetition of Cif'ferent Values of the Specific 2:n-flow ~f
Subterranean Maker on Rivers of the Mirldla Vohga l@ea
2 - specific inflow, cm3iday per L cn2
3 - repetition (5) af values of specific in-flobi on rivers of' the r"oilawiq,
lengths
4 - up to 20 krn
5 .- Rota1
The influx of heat with subterranean water along stretches of the river ranges
from O to 5,000 edl/cm2.
Because of the dissipation of flow energy, the heat influx fluctuates within
limits of 0.0 - 50.0 cal/(em2 day), while the heat influx from the river channel
soil averages 20 czl/em2 * day. The total heat influx with the subterranean water,
from the dissipation of flow energy and from floi~ channel soil on different stretche:
of rivers fluctuates, therefore, from 20 to 5,000 cal/(em2 day).
The times and character of freezing of different river stretches depend on
the total influx of heat and the slopes, as well as the fLow rate of water. These
factors usually change little in time, but are very unequally distributed along
the length of rivers. Graphs which enable one to determine the dates of the
appearance of ice and freezing of individual stretches of rivers and which take
these factors into account according to the transition of the mean daily temp-
eraturn of the air through O'C, we cited in a study (4) *
specific years, the characteristics or' freezing a:^ stretch23 of rivers
are determined by the synoptic-meteorologicit1 conditions. kTn:~nen there is an
intensive incr9ase in negative temperatures, the sums of thermal losses build-
up rapidly and universally, and therefore difrarences in the times of freezing
of rivers of the middle Volga aerea do not exceed 5 - 10 days. On the other hanil,
the frequent alternation of air masses ad the unstable negative ai~ tsmperatu-e-
cause differences in fre3zing tirnes of up to 1.5 - 2.0 njonths ",hrbou;rh the gix~en
territory and aloag the length of the rivers.
The thickness of the ice cover depends upon the sum af negative ai~ de~p-.
eratures over the period of ice build-up and the SuiLd-up in the s~ecific heat
infl~. frs~n .*raker (see the figure).
According to the data of the author's investigation and cn the basis of
%aterial in the literature and on background, one caz establish Che following
crcrnditiorts sf ice formation on rive~*s:
a) rapids stretches or stretches with a specific heat ififlur, in excess of
500 cal/(cm2 * day) do not freeze;
b) stretches with slopes of 1 - 5$ mind a specific heat influx in excess
of 100 cal/(crnz day) are ~hasacterized by unstable icing with stretches of
open water and ice crusts;
C) ill places that have snow slides as $ell as stretches without tributaries,
which are quite long and have flow rates of water less than 1.0 m3/see, ice
crusts whose th-ichess reaches 1,s m form ( for example, the Tumbarlinka River ) ;
d) on marshy stretches of the river channel the ice thickness is usually
13 - 2.0 tines less than on stretches sf ~ater; in individual cases stretches
af' water f~ee of ice form (the tributaries of the Shoshmy River); the ice is
turbid and contains a great deal of air and organic material;
e) :he discharge of warm waste leads to the formation of stretches of water
that are free of ice and non-freezing stretches (the Ik iiiver below the Urussinsk
combined heat and power plant), while ncn-unifirm releases from reservoirs favor
the fornation nf ice crusts (the Staryy Zay Rive;' below garabash).
River debacles ase esharacr3terize by the fa%lowing featwes :
a) stretches with unstable ice phenomena become clear of local ice a month
before the background times ;
b) stretches of rivers with an unstable ice cover, in which the heat influx
with suDLesranean water exceeds 200 cal/(cm2 * day) and whose longitudinal slopes
arc greaher than 10/00 undergo debacle J, -. 2 igeeks befoe-e "cke backgrowd time31
3 c) rivers whose $later flag rates are no more "cm 1,0 dsec wLth a 701.6
ice tJiii,ck~ess (35" lsqder Lhe conditions sf' pvledomivaance of southern expastrre of
the slopes undergo debacle 2 - days Ssfsre the Szbirgro~nd times. The very
3aae rivei9s with thick ice crusts and a px*edoain~~tly nwtherr~ slow expasexre,
an the contiqary, undergo debacle 2 - 3 days later tnan the background times;
d) sn small rivers, particslariir Lz the presence of ice crusts, the ice
tml..i;s place ~l?e O$S@~V~S 3 rw~ dab:-- q,le at flostlf "cia~ae, \lih!en there is
i;fr,t~nsbve ~xi.1 erosi~n $he ice crusts becone aud caked and the ice in "Lhese
places cccasicnally remains mtil. Jiine;
e) a:-: stretches of rivers whose convolution factor exceeds 1.6, in channel
nzrrowz , sur brancF5,ed stretches and in zones sf ~-es?rvsi,- pressure tapering, ice
jams systemiiatical2y forn.
The relationship of ice thickness with the sum of negative air temperatures
C - tbC and the specific heat influx from water y.
The ambers next to the points are values of observed ice thick-
nesses, cm.
kbeezine; maps, ice thickness maps and debacle Eaps of rivers of the middle
Volga area were drawn on the basis of all material (4, 71, For purposes of
clarity, the dates of ice set-in, the length of the period of ice formation,
etc. are shown on maps along the rivers. The types of ice phenomena, the thick-
ness of ice at the end of Winter, places of formation of ice crusts and stretches
of open wster, ice jans and ice daas, debacle dates, and the duration of the
debacle zre also shown. The reliability of the depicted characteristics gas
checked by observations at water stations and on monitoring stretches during
the ice surveys. Deviations of dates of the arbset of ice phases Eron! those
cited usually do not exceed 1 - 3 days, while the locations of ioe crusts,
stretches of open water and unfrozen stretches, the i"ormatFon of ice jams and
ice dams, coincide as a rule,
I. Glazacheva, L, I. Ledovyy i termicheskiy rezhim rek i ozer Latviyskoy .
SSR. (The Ice and Thermal Regimes or' Rivers and Lakes of the Latliian SSR),
Riga, "Zvaygznefl, 1965. 232 pages.
2. Donchenko, Re V. A. Kethod of Calculating Heat Losses fron~ a Water
Surface in Winter. "Tr. GGIu, 1960, No. 72, pp. 42 - 60.
3. Donchenko, R. V. The Intensity of Build-up in the ice Thi.ckness on
Rivers and Reservoirs. Yr. GGIt3, 1968, No. 159, pp. 42 - 55.
Y. Korbutyak, M. V. ; G. N. Petrov. Methods of Draiging Maps or' Ice Phenonena
on Rivers for Regional Atlases. V kn.: Materialy 111 nauebi. konf. p~ kompleksnom~
kartografirovaniy~. (In the Book: Material of the III Scientific Conference on
Combined ~apping). First Edition, Kiev, "Haukova duukaW, 1970, PFI. 279 - 285.
5. Marusenko, Ya. 1. Ledovyy rezhim rek basseyna Tomi. (The ice Regime of
River's of the Tcma Basin). Tomsk, Published by Tomsk University, 1962, 215 pages.
6. Petrov, G. N. The Low Water Flow and its Study. "Tr. KFAN SSSX. Ser.
energetiki i vodn. khoz-va", 1956, No. 1. 143 pages.
7. Petrov, G. N., M. V. Korbutyak. Experience in Studying and Mapping Ice
Phencmena Based on the Example of Middle Volga Area Rivers. "Tr. koardinatsionnykh
sovoshchaniy po gidrotekbaiken, 1968, No. 42, pp. 171 - 181,
8. Piodrovich, V. V. The Results of Ten-Year Observations of Water Temp-
erature in Springs Near the City of Moscow. "Tr. TsIPU, 1965, hs. 151, pp. 93 -
148,
9. Sroki zanerzaniga rek i vodokhranilishch SSSF (veroyatnostnyye kharakte-
ristiki). (Freezing Tines of Rivers and Reservoirs of the USSR (prilbability
characteristics). Plascow, Tubxished by the Hydrometeorological Ce~ter. of Che USE,
99 70, 121 pages,
10. Shulyakovskiy, L. G. Poyavleniye 18da i ~dchalo ledostava na rekakh,
ozeraki: i vodckhranilishchakh. (The Appearance of Ice and the Beginning of
Icing on Rivers, Lakes, and Reservoirs) . Moscocr, Gidrometeaizdat , 1960. 216 pages.
THZ USE OF EXSCRIMINANT MALYSXS FOR LONG-TERM mRECASTIN@ OF AUTUPN ICE
PHASES IN THE LOVER REACHES AN3 MOUTHS OF RIJJERS IN "FW ARCTIC L0N:E OF SIBERIA
Bg: Xu, V. Nikolayev, G, Ye- Usankina
( AANII , Leningrad)
Many branches of the national economy (inlad trulspcrt, hgdroenergetics,
the forestry indu"try, and others') are interested to one degree or aother in
kno~~ing the eeezing times of streas, in connection with which the ice regips
of rivers and the study of the principles which cause fluctuations in these
dates in tine and space are extremly pressing ones. It is knokln that the
freezing times of rivet-s are affected by various factors in combination ad the
contribution of each of these factors to the general course of 'the process is
non-uniform. Therefore, the identificati~n af individual f acto~rs that have the
greatest effect Qn the predicted process is one of the primary problems &hat
arises during the development of forecast sys tens.
Investigations of the ice regirnes af rivers in the Arctic zone of SiOeria
have been carried out, at the AANII since 1933 by A. P. Burdykina, who exmined
nacrocircaati~n atmospheric processes in detail. Such processes affect the
free :j . times of rivers (2, a3 others 1. Zn analyzing tiie rnultiannual flue-
tur" .IS of ice rormation dates, Burdyktna concluded that the 3ackgrour.d of the
fore^-abed phenomenon is determi~ed by the predominant types of atmospheric
circulation over the investigated territory (according to Vangex~geyn?). Burdykina
suggested forecast relationships of freezing tines with some particular char-
acteristic of atmospheric circul.ation. The conclusion tllat atmospheric pro-
cesses have a signir'icact effect on freezing of rivers ir, the Arctic zone of
Siberia was confirnned by an malysis of tke spatial statistical structure or"
the ice formation dat.2 fields, which have a signifi~znt (about 1,000 b) scale.
The purpose of this study w~.s to Zaprove the existing methods of forecasting
the ice regime of Siberivl rivers. For this purpose, the effect of macrocireu-
lation processes of the atmosphere on the *enzing ti~es of IOKG?~ reaches and
mouths of rivers in the Ob4-Yenisey regian was ex
over the Northern Hernisphe~e *om 40° north latitude ar.d further to the north
was used as the circula2ii.g index.
In order to solve the task oF the investigztian, a method of discrlmicant
analysis of the atmaspheric pressure fields wad used.
The method sf discsriairaali",analysi.s had also been used before ~QP. fore-
casts cf hydrometeorologic21 phenomena (1, 3, ar.3 others). In :L966, N. A.
Bagrov (1) predicted the rnean a~nthly anolmL of precip :.tation according to
air temperature fields, represented with the aid of discriminant analysis in
the forn of ~aeffieie~~t~ 02 linear expansion. LQ 1459, YE. V. Mikolayev obtained
forecast equations for pre-calcuiati.on of Lhe total icing of' the Arctic Ccem
in August as the result of a separate analysis of the ~ir pressure ard air
temperature fie hds over the Northern Hemisphere,
Th2.s investigation included the following: 1) the identif icaticn or' cpti-
mum regions in whicn the atmospheric processes most affect the freezing ti~es
of rivers; 21 the identif:'ication of data on pressure in optinu3 regions of
infcrmative forecasts, re2resenting comparati~jely small nultlbers of poLnts
f~om %he arch.ives,
The identification of optimm regiai3s from the pred2ctc.r fields igas
carried out on the basis of analyzing %he value dr2 (i = 1, 2, . . . , n), xql2ich
characterizes the distance between classes along the axis cf the coordinates
of the n-mdirnenslonal space. For this purpose, the predictor fields iqere divided
into classes in accordance with the classes of the fgreeasted phencnenon "above
the norm'kand "below thd normu. in the presence of two classes, the 'lalue d72
is calculated according to the following farmula -A
-9 -3 - -. d12=p; (h)+P; (Bj -- ZP, (J 4 Pi (El,
where B acd B are classes of the atmospheric pressure fields.
%2 The maximum sqilare of distance bet:geen classes di indieate3 the :?FghesS;
information content of the given point in spzce. In order ';o e:xclude tl2e sf :"ec t
of air pressure dispersion, it is expedient to use the relst,ionsi-.ip d"^ .& the 1
3 analysis, where 3- is dispersion at t3e i-th point. i
Tho task of ide;:ti@il~g the io;.'ormatlve redictions using discrininan-l
analysis is analogous t~ the task cf expvldinq fields actcordirig to the nat?w;tl
? ra orthogonal ccmpcnent , during which the first rrcriables PI, P2, .. . . , P, &,re
represented in the fdrm of secondary ria-iables Pi, Pi, . . . . P9 as the resu' t
of 2 linear trasform, wher~ an
The difference i1;:thqser! the scpzrate ar,?lysis and e)~~msion of fields
according ta the nztural or t'nogocal component consists in the aodas of deter-
mining the transform coefficients u+ (i = 1, '
dr*
, ..., n). As was shoi~r. in a
8 .? study i~), durFng discriminant z~alysis the determination of 0p';imm co-
ef ficients is associated xith sclving thi I'cil3uing aquztion
%&ere: R is a mztrix ehapactarizing the dir'fsrencss bet5~een classe; F1 is 2
"orrariation matrix for the entir~ set; u is the eiger, VIICCOF; X 23 the e-i -~3 sen
.s;.al.kae,
Tine original information was r5prese;ited by ~~alues aE the mean ~ionthly
pressure at 27 points over the per'iod fro^ 1935 through 1968 (Figure 1). The
dates of onset of stable ice rorm~t$~on of rivers in the Obf -Yenisey region
served as the characteristic of fre~zing times,
The ~~Xakionships obtained for each month were averaged by seasons
a i
(Fall, JJinter, Spring, Sumar). A series of points with roaxim~m values of
32 dr" was C~OJWI to identie the optimum regions hr each season. :L*k.,e other
2 c7 i points were excluded *om the mafysis.
The original infomation about pressure in the opttimum re6;ions obtai~ed
by linea~ orthogonal trvlsform was represented in the fornt of the first expansion
coefficients PI for each month (Sep'camber - December of the preceding year and
January - August of the c~i-~~?nt year).
Figure 2 shows the curve of correlation coefficient modul~kses r Setveen
the obtained predictions and the onset dakes of stable icing. Data on the
in formatior, content of the predictions lor individual months can already be
obtained according to the value of t he first eigen values A, whose course
coincides basically with the course of vdue r.
Hcwaver, the use of cne month alone for forecasting the piaedictors can
lead to signifi~~t errors ad it is therefore more expedient to construct
forecast diag~~ams using several predictors. In this comectiora , regression
equations (see the table) were compiled which make it possible to give fore-
casts with a timeliness faetor ranging from 1. to il months.
Figure I. Dlqgraa of points
used during discriminvlt
malysis af piresswe fields,
Figure 2, Moduluses of ccr~ef,atEan co-
efficients r bemeen the dates af stable
icing end the predictor Pqlm) and the
first eigen values h (2).
?,
Coefficients of Regression Equations
(Note : camr.as shcule be read as decimals. )
Figure 3 sho~~s chs~ges in the ~olf ficients ~r" multiple eorn$lation dqending
on the forecast timeliness. The coefficie~ts of rr.ultip2e eorreii3tion have vaiues
of greater - thm 9.89 ai~eady :-$hen fareca%irg with a ti~eiiness ractop of 9 - 7
months
The regression equai;ions, which make it possible to predict the dates of
stable ice formation or" rivers in the Obt-Yenisey region with a timeliness
factor of L and 7 months were -~erifiad using independently obtained material
covering 4 years (1969 - 1972). The estimate was made ac~ording to two C.20 A
criteria (amplitudes) and 0.674 o. The verification forecasts were valid
according to both criteria.
8 6 e
ID- Timeliness, man ~hs
Figure 3. Change in the coefficients of multiple correlation of regression
equations depending on forecast timeliness.
Hence, opti~ntum regions were determined as the result of discriminant analysis
of presstlre fields over the Northern Hemisphere and then the most iYrfarmsrtive
predictors of the ice fornabion dakes of lower reaches and msmth:s of rivers in
- the Obg-Yenisey reginn were identified. The predictolas served as the basis for
compiling the regressl3n equations. Foreclsts have been given accordl.ng t,o the
obtained eq'ilations or, the basis of an inde~~endently obtained material. Such
forecasts ijere totally valid,
Of course, four years do not enable one adequately fully to judge the
validity of the method, but taking into account the quite high coefficients
of multiple correlation, one can assume that the given forecast systems we
promising.
~ REFERENCES
1. Bagrov, N. A. Forecasting the Monthly haunt of Precipitation. @Meteo*-
rologiya i gidrologiya9*, 1966, No. 7, pp. 3 - 12.
2. Burdykina, A. P. Seeking a Method of Forecasting Freezing of Mouth
Stretches of the Lena, Oienek md Yma Rivers with Good "T"i.meLine:;s. "Tr,
AAHIu'lIS, 1959, Vol. 209, pp. 69 - 108.
3. Gruza, G* V. Certain Practical Methods of Discriminant il.lalysis. "Tr.
SANIGMi", 1967, N 23 (4) pp. 160 - 156.
4. Nikolayev, Yu. V. Preobrazovmiye infirrnatsii v prilclzherlii k zadacham
gidrome teorologii . (The Transf ormatior, af information As Applied to Hydro-
meteorological Problems). Leningrad, Gidroaeteoizdat, 1969. 63 pages.
5. Ter-Mkrtchym, ??. G. A New Method of Realizing Discriminant ;ir,d Regyes-
sjon Systems. wiYeteorologiya i gidrologiyaw, 1969, No. 7, pp. 44 - 55.
WE EFFECT OF THZ L~QL,GOGRAD WESERVOIR ON ICZ APPEARANCE aaxEs ATD TTSZ DURATION
OF DEBACLE QN THE I!OLGA RIVER BELOW VOLGOGRAD axbib IN THE VOLG52 DELTA&
By: A, K, Bwabash
(The Astrakhan ' GMO)
The flow regulation of the Volga River by the Volgograd dam (hydrotechnical.
facility) caused significant chaqges in its ice rvtgime blou the city or' ~.\lgograd
and in the delta. Over the 1941 - 1958 period, under natural conditions loaticg
ice appear3ed in the northern Volgograd-Verkhnelebyazhtya stretch ad extetlded to
the south (Table 1). The difference beti-~sen the average dates of' ice appearaace
in the north ad south of the stretch of river was 4 days. This difference com-
prised 7 days with early dates of ice appearance and 3 days with later ones.
In the delta the ice usually forms earlier on the eastern streams, and then
on the Bakhtemir stream. The earliest ice appearance on the eastern streams is
explained by the fact that the flaw rates are Ic~~~er in them thm in the Bakhteair
strean *
Under condl tions of regulation af tke Volga flow by the Volgograd dm (accord-
ing to data for 1959 - 1912), ir~ating ice appears in all eases to the south of
the examined stretch. The diifference in average dates of ice appearance between
the south and nor-ih of this stretch of khe river cozrapi..ises 3 days* The difference
for the early dates is 4 days and is 2 days for the later ones. The sequsnce of
dates is csns2~ved in the delta.
The sverage rnultiannual ice appearance date under natural conditions in the
Chernyy Yar following the average rcultianr.ual date of air temperature transition
via oOC to negative values is 7 days later, is II days later at Astrakhan* , and
6 days later at Zeienga. The average date of ice appearance over the 1959 -
1972 period is 25 days Later ihw- the average ~ultiamnual date of' air temperature
transition through OoC to negative valu2s at Chernr~ Yapr, 23 days later at
Astrakhan\ and 17 days later at Zelenga,
m iaking into acwunk the fa& that over the 1959 - 1972 period the transiticn
of average daily air teoiperatur:; through OOC to negative values %;as later', on
the average, than the multiulnual dates at Cherllyy Yar by 13 days, by 11 days at
Astrakhanf, and 8 days at Zelenga, one can co~sider that the ice appears later
at Chernyy Yar as the result of the hzrming effect of tha iiolgog~srd reservoir
than izrder natural conditions, averaging 5 dsys there and 1 - 3 days in the delta.
P1?I ihe warning effect of the reservoir is well ncticezble according to the
empirical rela'cionships 28- = f where CB- is the sun of negative air
temperat~~~es from the date of' air temperature transition via O'G 1x1 the date
of ice appearznce ; 3 is the temperature of the mter Lc~~ediaCely befire the
G sir tsmperatu~e crosses O i: to negative val'.es accorbing to the corresp~rding
199 staticr, on the stretch of river. ine relationships have been canpilee according
.a- LO observational daSa at stations called the Chernyjr Yar, lferM3nelebya~i?~ji~,
Astraichant 2nd Zelenga oirer the period fro3 i91!1 tbrougi? 1972 (see the figure).
Key for Table 4 :
1 - Table 1. Dates of Appearance of Floating Ice on a Stretch of the Volga River
Between iiolgograd and Verkhnelebyazh'ye and in the 'Jolgs! Delta Under Natural
and Regulated Cariditions
2 - river, tributary
3 -- point
4 - date of' appearance of floating ice
5 .- natural eornditions
6 - regulated conditions
7 - early
8 -- medium
9 -- late
10 - Volgci
.I1 ..- Ruzan
12 -. Balcht enir
13 - Kamyzyak
I4 - Znlenga
15 - Nikitinskiy bank
-+ P AD - Volgograd
17 - Chernyy Yar
I8 - Yenotayevsk
continuation of key for Table l:
19 - Verkhneiebyazhfye
20 -. Astrakhan
23 - Krasnyy Yar
22 -. fk~ly~qt4
23 - 0iya
23 - Kmyzyak
25 - Zelenga
25 - KaraulBnoye
m4 ih.3 .relatianship of the sua of aveyage daily neuative air J, ~emperatures ZO-
a P
necessary for the appearsfice of floating ice 5:ith the initial %iater temperature
s."*
40 *
;. - Chernyy Yar, b - Astrakhan" c - ~ielenga. The n-,~~bers next ts the pnLnts
are years*
A greater sum or negaGive air temperatures is necessary in the relationship
f'or Chernyy Yar i.n most cases for ice to appear when the water kemperature is
ediately before the air tenperature crosses OQC in years with a
regulated flow. The difference be tweer? the sums of negative air temperatures
necessary for the appearance of ice in regulated flows and mder natural con-
ditions is less for iTelerkhnelebyazhgye than at Chernyy Yar, and is less for
Astrakhanq than for Verkhnelebyazh9ye. There is no difference in the temperai;ure
totals for Zelenga.
Hence, the wvrming effect of the Volgograd reservoir gradudlly decreases
proportional to distance from the dam downstream. In the lower reaches of the
delta its effect totally vanishes.
Calculation of dates of ice appearance fol Chernyy Yar, Xenotayevsk, Astra-
khan" Krrasyyy Yar, Ikryanyy and Kmyzyak were made for years with a regulated
flow according to the method of L. Go ~hul~akovski~l. 111 all 60 cases, the
calculation errors did not exceed 1 - 2 days.
On the Vol!sograd-Verkfinele byazh' ye stretch, under natural conditions and
mder conditions of regulated flow, the duration of icing decreases from north
to south, while in the delta iQ decreases from the soutfawest to t+he northeast
(Table ?) . The averwe duration of debacle under regulated conditiilns near
Volgograd and Chernyy Yar is 6 days greater than under natural conditions, while
on the Yenotayevsk-VerkPaelebyazhTye stretch and in the delta it is practically
the same as usndf>pl natural conditionso
The longest duration of debacle under natural and regulated conditions is
observed in years with a 'iresterly movement of the air masses. The shortest
duration of debacle is caused by cold air mass penetrations from the Barents
ad Kara SeasB
A shorter duration of the ice gaqg tha under conditions of regulated flow
corresponds to ident ieal totals of negative avttr%e daily air temperature near
Chernyy Yar. At identical duration of the ice gang corresponds to a similar
total near Astr*akhanf under natural and regulated conditions.
Hence, the warming effect of the reservoir arfects the duration of the ice
gang on the stretch of river fron Volgograd to Chernyy Yar but is not refleeted
in the delta*
In Autumn, navigation is practically terminated with the beginning of f ce
gang formation. Under natural conditions or. the Volgograd-Astrakhanq stretch
the closure of navigation occurred on 24/XI, when the ice gang near Volgograd
began, on the average. Under conditions of regulated flow, navigation terminated,
on the average, on 13/XLI, when the ice gan began to forrn at Verkhnef ebyazhg ye.
'3hulyakovskiy, L. G. Poyavleeiye 1' da i rlachalo ledostava na rekakh, ozerakh
i vodokhranil ishchakh (raschety dlya tseLey prcgnozov) . (The @pearanee of Ice
and the Beginning of Icing on Rivers, Lakes, and Reservoirs f Calculations for
Forecast Purposes) ). Hoscow, Gidrometeoizdat, 1960. 216 pages.
Key for Table 2:
1 - Table 2. Duratior, of' Che Autuinn Ice Gang o;l a Stretch of the Volga River at
" w Volgoprad-VerekhneIS.ebysi.zh~ ye and in the Volga Delta under ?jatural Con2itions
and Conditions of Regulated Flow
2 - river, tributary
3 - station
4 - duration of Autunn ice gang, days
5 - natural conditions
6 -- maxixila3
7 -- medZue
8 - minimm
9 - regulated conditions
10 - Voolga
_k% - Ba,ta;aq
12 - Bakhtemir
13 -- Kamyzyak
14 - Zslenga
15 - Nikitinskiy bank
16 - Volgograd
21 -- Chernyy Yar
O
1$d - Yenotayevsk
l.9 - Verkhne1eDyazh"ye
20 - Astrakhan
3-r 21 - hrasnyy Yar
22 - Ii<wyanoye
23 .- Olya
24 - Ramyzyak
25 - Zelenga
26 - Krauiqnoge
Hence, over the 1959 - 1972 period, the closure of navigation occtrred an
average of 19 days later than under natural conditions.
With the exception of the climatic factor, one should consider that the
cLosure of navigation on the V~lgograd-Astrakhan' stretch of' river today,
resulting from the warming efrect of the Volgograd reservoir, occurs an average
of 9 - 12 days later than under natural conditions, and an average of 1 - 3
days later on the delta than under natun-a1 conditions.
THE ICE REGIME OF THE SOVIET STIiETCH OF TEE DANUBE, CH*MACTERISTICS OF ICE
FORMATION, AND THE POSSIBILITY OF COPIPILING SHORT-TERM FORECASTS
By: A. V. Shcherbak, L. I, Solopenko
(The Gkrainian MICMI, Kiev)
The Danube River, flowing through the territory of eight nations in central
and southeastern Europe, has important significance as a transpol-tation main and
as a source of hydronlectr~c power and land '.rrigatFon.
"She work of T. 3, P1aL:arevich and Z, A. Yefinova (5) has keen devoted to
analyzing md surmnarizing available data on the Autmkn-lv'inter ice regime of the
Danube over the 1900 - 1955 period for the purpose of identifying the possibility
of predicting its characteristics. However, the above authors did not exmine
the characteristics of ice formation on the Soviet stredeh of the Dmube, Tpee
ice regime of the Danube delta has been d2scribed in works (1, 3) and in scientific
reports of the Danube GNO*
- 0% *P In 1969 - 1972, investigations were carrieci out at the Ukra:inim* N~brii. of
conditions of ice a"clz%sr?atisn on the Soviet stretch of the Danratj.;?. fan: the purpose
of developing a method of short-tern forecasts of the beginning of separate phases
of the ice regime and the degree of blockage hazard (2, 6, 8 - 10). The invzsti-
gations were carried out on the basis of dzta obtained from hydrdmeteorologicai
observations over the 1935 - 1970 period, for which data are available 03 air 2nd
water temperature. Data on ice phenomena iron? 1931 through 1944, taken from a
study (3), were additionally used to ob'iain quantitative characteristizs of the
ice regime,
The investigated stretch of the river is located in the extreme soutbgestern
part of the European territory of the USSB, which is characterized by an unstable
temperitture regime in the Autilm and Winter. The unique nature of the ice regiae
on this stretch sf "%he river is also associated with this faet-lor: the first
appelrance of the icz can be observed here from the middle of December to the
beginning cf February , although the ice formations are cccasion&lly e~tirely
absent. Thus, over a period rangins fram 19a through 1978 s"s%S:Le ice phenomena
in the lower reaches of the &nube existed in 22 of the 3 yeaps, itrhich coaprises
56% of the time?. In ten years (or 26% of the time), ice phenomena were either
absent or were extremely brief (up to 3 days). In the remaining years, periods
with unstable i.ce phensmena ldepe observed when ice b"clma"i;ion %as int2rpotrpted and
renewed over the course of the Winter 2 or 3 times. The tdtal psobabilli-ly of the
appearanc-. of ice or? the investigated stretch of the Dan~be compris2s 82% am3 the
establishment of icing totals S&$.
As on the entire lower Daub- (5), the a~kplitude of dates o? the appearance
of ice and establishment of an ice cover is very lsrge - it rescues 5$ ta 58 days.
On the So~liiet s,treLcch of the Danube the ice appears aimllast simtr-tl;ane~usly ogsep
i&s entire extend* The earliest appearance of ice was nobd dn the s'tr?eCch an
12 - 13/XII (1945), and the latest was observed on 7 - 8/11 (1965). Th3 average
date of ice appearance is u - 5/I.
T%.e stationary ice cover on the lower reaches of the Danube is estabiishc?d
becz~se of the fo~mation of ice necks and the freezing of floes comtng dokn-
stream. The early establishment of ice on the Soviet strnCch of the Dulube waa
noted on 17 - ZO/XII (19481, the late one on 9 - 11/11 ( f 956 2, whll~? the average
dates are 12 - 14/Ia The average duration of the pel-iod with ice is 20 days,
ranging from 2 to 79 days in separate years.
Depending on the times of onset of tile ice-mrrning processes, four groups of
gears have been identified on the Soviet s$retch of the Danube:
9. Years of early ice appearance - the onset of ice phenolaena was observed
no later thvn 25/XII (1945 - '16, 1946 - 47, 19&8 - 49, 1953 - 54, ;:I61 - 62,
1962 - 63, 1969 - 70).
2. Years in which the first appearance of ice was noted on dates siniilar to
the average matiannual ones, i.e., frcn 26/XII through 1991 (1344 - 45, 19'19 - - 50, 1356 - 57, 1963 - 64, 1965 - 66, 1967 - 68, 1968 - 69).
3. Years of a late (after 19/11 onset of ice phenomena (1950 - 51, 1955 - - 56, 1959 - 60, 1960 - 61, 1964 - 65).
4. Years when the ice phenomena were absent or short-lived (up to 3 days)
(1947 - 118, 1951 - 52, 1952 - 53, l05Q - 55, 1757 - 58, 1958 - 59).
Under conditions of mild winters with I'requent warming spells, when the sun
of negative air temperatures over the period of icing basically comprises 80 - - 1300, the averaLe tliickness of the ice an the stretch of Saviet Dzmuh does not
exceed 25 - 30 cm and can reach 50 - 70 cm only dwing rare, severe winters.
Despite such instability or' the ice regime, the development of ice -nation
on the Soviet stretch of Dmube in the Autmn and Viinter and the dekiaele in the
\$linter - Spring are frequently accompanied by ice barrier and ice da~ phenonena.
The thick barriers ad ice dam occasionally cause catastrophic elevations in
water level. Mul"siafinual observations of ice phenomena on the Saviet stretch of
the Dwiube show that the formation of ice barriers and ice dams usually occurs
on the sme stretches of the river (l - 3), $$here the water surface slope sharply
drops iind one notes sharp bends, channel constrictions, islmds and shallow bar
stretches af delta rivulats,
.Small ice barriers and ice dams usually form during the htum - Winter ice
gang. Their thickness chiefly depends upon the water level cf the river and the
ints~qsity of cooling, i*e. , on factors that determine the intensity of ice forma-
tion, The Autum Swrier-dam qhenomena can be subdivided into two groups depending
upon this factor:
1) those that form during sharp cooling a~d a high water level of the river
at the beginning of ice formation ;
2) those famed by sharp fluctuations in air temperature over the course of
a long period of ice formatian*
Ice dm9 aekfieve extensive develcspme~t on the Scaviet skrstcll of the 'am*3be
in the period of debacle and the Spring debacle. Particularly thick ice jarrs
;$ere observed in the Spring of 19511, 1967, and 1969. The formation of Spring
ice jams is determined to a significant extent by the severity or' the Winter,
the nat,u-e of establishzent of icing in the previous Aut -Winter period, the
intensity of development of the Spring processes md the condition of the ice
on the river shoreline,
&pending upon the degree of influence of scir.e particular factor, one cm
isolate two types of ice jams:
1. Jams that form as the result of rnechznical deslructi~n ai? a fim ice
cover by a water wave; these appear after severe vinters, when a significantly
thick ice cover farms on the Sower reaches ai"" the Danuk* If %he ice co%er
proves to be mildly brokext .;p by the theraal factors by the tille of debacle,
then during debacle large ice fields of fi~n ice ia~edge in betwecr? the barks,
creating favorable conditions for vast ace~auiatloss or" ice ~rhich continr.ously
come in Prom ug~stx*eaa.
2. The ice jzms which are due to the character of establishnent of :he ice
cover in the previous Autumn-Winter period. These form in years when ther~al
factors predoninate in destructian of the ice cover. Ice jams or ice dms sre
ssually observed 053; river stretches %$here the thlcgmess sf the ice in th3 Axt
Winter period is 30 - 40% greater than on the upper and lower stretches of the
river. Therefore, the S~ring debacle is retarded in this spot and the ics coning
dokn From upstream, in piling ~p Ln the edge of the ice, bl~cks the _rloirii,zg
section of the rives channel,
In addition to the indicated types of ice jms, cambination types of ice
j~ms can exist on the investigated stretch of' the D.nutie, when their i"orn2ition
is Pdeilitated by sea ice which closes the mouth of delta rivulets during
driving winds, as was observed in 1367, and pjr+.icularly in the SprL~g of 1969.
L~vestigations of &he syxaptic processes which determine weakher conditions
snd cause ice formation and debacle acquire inportant significance duping the
analysis of the devclupmentai course of indixridual ice regime ph{sncmena, p;%rt,i-
cularly when they are highly unstable.
An malysis of atmaspheric processes (j!, sho~2d that signiflcarit cooling
in the exzmined pegion occurs when the brznches cf anticyclones foraed in aasses
of Arctic or cooled contiwntal polar air move in from the north, tha corthgest
7- or the northeast. cz!qever, in ordsr to identily the conditions or" fornatio~l oL"
the indicated local sjmoptic processes one must refer to the investigation crf
the characteristics of total atmospkerie eireulation in the Auiut3am-gintar period
Fshi~ii cause their appearance.
Fer this purpose, the classification of nacroprocesses according to circe-
lation indices, suggested by 4. L. Kats (4) was used. It was establFshnd that
cooling in the exmined region is mast often r?ua to meridionax precesses ~+ith
the circulation forms YJ, 3, and C, and that cooling very rarely occurs duris?~
atmospheric! prbocesses due to the easterly pcsif ion of the ridge, i. e. , cf rct2-
Lation of ifarm 9. This made it possible to EisstAYe that the tstaliity of cir-
culation processes of the indicated forms Ls also a cornbination of macrcprocesses
aqder whose influence tlne weather csnditions fka~w which deke~mine my 9af Lhe pw-
titular dates of ice appearance on the ~nvestigated s&ret+ch of the river (6).
The multiple of the n~unber of days with circulation fom B ad of the total nmber
of days with circ-fiation of the other forms over the course of a certain period
is accepted as the indicator of this cnmhinati~n "I. mis ix2dieatar, determined
according to the indices of atmspheric circulation, is calculateck accordug to
the folicrqing formula :
in accordance with the meL,hod presented in gatst% i~ork I&).
The annual course of monthly ialues of t5~ index N averaged for t43e gro8tps
of years calculated aceording to LQe dates of ice appeayamce shows tikat the
greatest diflerences in the course of the curves for different groups observed
in A~.',xst - October. In the course of thiv period, each group of years hw its
awn inherent character of formation of the 34-optic processez fr31~~ month to month.
m he course of index N i2 time in indibr.tuai years does not fully dup~icate
the course of its average values. However, the signs referred to above a= main-
tained for years of ",he early and late ice t"ormation by valses, respectively, of
89 and 80$, while fop years i~ith normal dates of appear== of the: ice phenorne~a
and years of no ice phenom?aa, the magnitude of conformance is TO$;. Cansequently,
on the basis of the si.gns already identified at the end of October, one can state
with a probability indicated above whethey the ice formation in the cwmrent seasen
w%Pl be e~zfy, I:2"Le, near $he normal date, sr um%icip~*ced altogether,
Tae estiaa&(s ar" the forecast canclusions "ssased on the material sf d969 --. 197C
anmd 1970 - 1979, t~hich did not enter into khe selection, deerror,strseted khat they
eouid be utilized to compile approximate firecasts of the onset of ice famation
on the %vieL stretch of the Danube X%7y"era The develapment of a ~i~eth~d of ahor%-
tera $losacash sf the '=ginning of ice faraaticn is necessmy to reer"he these
qualitative predictions,
Today, such forecask-s are clampiled according to em~irical rel,,akionships ax*
by meaqs of calclala&ion* The cs~?stl..uction r;-lf "te empirical assocj.a%iollis is
based an establishi~g kmal relz";,ionships of kbhe dates of appe.ir=kcs of ice with
certain factors. The latter j.nclude the total of negative air temperatures
necessary for the appearaqce of ice, the temperature of the 5qater sad the uater
Level of tha river by the tine air temperature cr9sses OOC.
The indica bed empisical relationship for establishing the title of appearance
or' ice on tie Da7ube fliver near the city of Izmail, cited ir, a wor3k (81, ca be
represented in the f oliowing form:
kbe~e (EO-1 Is the total of riegative avesage &ily air tempe~atuses needed ain fi for the ons'ec of ice fornation;vis trater temperature near Izinail Chatal imediately
befoz*e air temperature crosses OaC. The value of parz~etar 4. is (3eterrnined depending
ol*
upon ths flow rates of water: when Q > 4500 m"isec, A = 10.5; wllelen Q = 4500 - - 3500 m3/sec, A = 7.2, an6 when Q < 3500 m3/sec, A : 'reg.
Calctllation of the dates of sppearance ~f ice made with the use of this
relaGionship yields fully satisfactory results: the er rors of the veriried fore-
casts for the 1946 - 1967 period do not exceed 2 days in 94% of the casesI
Applicable to the conditions of the extreme southwestern part oi' the European
territory or" the USSR (taking into account features of the examined stretch of
the Dvlube River associated with the presence of an extensive deitaf, a calculation
was made of the time of ice appearance according to the nethod of L. G. Shulyakovskij
(7). The results of 2a:c~~lations of the times of ice appearu2ce nea- the city of
lzmail showed that on 19 of the 23 calculations for dates that were carried out
(83$), the erpo.or rjaj zero. The f~equency of error was no more thlm ul day, con-
prising e?%, while an error frequency or" no nore than 2 days ccmprised 97% (9).
It is known that the characteristic of Winter severity, and consequently,
the indieator cf development or the ice-fo~ming processes can be "5he anomaly
of air temperature in idinter. Comparing these anonalies in ihe siouthrgestzrn part
~f ;? Europeu~ territory of the USSR (zTXII-II) and the average duration of ice
cover on the Soviet stretch of the Danube showed that a quite intizate relation-
U-
-
ship exists Oetrseen the indicated characteristics. in seasons with AT,,, -3 lo3 ~a9-$1
in 93% of the cases the ice cover in the loiqer reaches of the Daube was practically
-rpa
absent, and when there was a negative anomaly (AT.- ,< -lo), in 86% of the cases n%%-.II - L! ---- one noted a2 ice cover Lasting over 20 days. In cases ~~hen -1 < AT, 0 <+I, &If -Hi
the air temperature anomaly in Mintzr was not intensive enowh to be a reliable
characteristic of he anticipated duration of the ice cover; the latter in such
years is determined by the distribution dpamic (al~ernation emaoic) of c~4d and
warn waves daring Winter' and by the effect of+ a n~qber of cther factors, T'or
example the water level of the river*
In this investigatia~, the at2CI;ors iitte~pted to estimate the hypothetical
severity of Winter by using the magnitude of the average air ulomaly. In
analyzing the course cr" the indicator cf the eombincition of macro)processes N,
the authors succeeded in identifying con tras king periods, rghose process dif -
ferentiiil indicators could serve as the forecast signs of' the average air
temperature anomaly sign in Winter in the southwestern part of the USSR. The
basic farecasting sign of the investigated phenomek%on %as the transformation of
circulation in the troposphere from August ta September: %ken there :gas a
positive difference in the macroprocess indicators fram Aug;~st to September
( i'dTT- 0, one should anticipate a cold i8iinter or a \$inter ne;;r the norr; - - a~ I I" IX
AT, -- O (frequency 92%) ; when NVIII-N < O One should m..titzipate a warm ~~LL-II EX
.. *v a wxnter at least in the soutk~~esterr, part of' the European territory of the USSB -
n*Mlg
AT,.,,- > O (frequency 86%). A~L-XT
fiaalysis of the hydrometeorological and synoptic conditions of ice jz?
fc~za'cion was mada far the purpose of date~minlng the degree ol" ice jzvaiag ad
to identify the possibllitg or^ comparing the xsarnings of the appearance of
dangerous ice jams and ice d=ras in the Low ~.da"ater reaches of %he Banuam* Over
ti2e 11945 - 1970 period, there were no more than 5 - 6 such jam-dam phenomena
on individual sdt~e%cehes sf the river, %ikh such a linited ass~r%mer$% 02' ori-
ginal data, one can only discuss the approximate estimate of the degre aE
ice jam hazard and the probability ai? the formation of dangerous ice jam-ice
dan ph,, aaomena.
It was established that the following are the criteria of ice jam hazard
which make it possible to issue warnings about the probable formatiorl of dm-
gerous ice jam-ice dam phenomena on the Soviet stretch of the Danube:
0 a) seT$r?re (up to =15 and below) cooling at the beginning of ice formtion
wit'n a high water level (the water level no lo~~erer than 200 cm at the Rent water
monitoring station) ;
b) ice thickness on the stretch in excess of 40 cm at the time of debacle ;
ckcases when the d.irec+, astablishnent of ice cover in the Buturn w;nd
%$inter tras preceded by ice jam-ice dam phenorne~a;
d) the presence of stable northeasterly or easterly winds during the ice
gang period and the presence of adhssive or floating ice in the western part
sf the Black Sea.
The obtained conclusions have satisfactory accuracy for use in working
practice, despite the fact that some of the= are approxinate and rough. Tbeir
further refinement and improvement are possible proporGional to the accumulation
of original data based on analyzing the entire eomSination of hydroaeteorologica1
a~d synoptic conditions which determine the developmental character of ice-forming
prseesses on the?: Soviet stretch af the Danube *
1. Vagin, N. Fa Principles of Ice Processes in Deltas (based on the example
of the mouth of the Danube). "Sb, rabot Kievs~oy CbfOw, 1971, No. '7, pp. 7 - 13.
2, Vagir%, FP X1 A= Kcrvernyy, 8, Ve Sncherbak, Chasac%erPi,strics of Ice
Jao; Formation on the Soviet Stretch of the Danube. "Tr. UkrNIGMIT*, 2972, No. 112,
pp. 57 - 68.
3. Gidrologiya ustgyevoy oblasti Dunapa. (Eyiydrology of the D3nube Mouth
Area). Moscow, Gidroneteoizdat , 19 63. 383 pages. s
4. Kats , A. L. Sezonnyye izmeneniya obshchey tsirkulyatsii atmosfery i
dolgosl-ochnyye p-ognozy. (Seasonal Changes in Czneral Atmospheric Circulation
and Long-Term Forecasts), Leningrad, Cidrometeoizdat, 1960. 270 pages.
Mak~~e~~ick~ Th XP Z. A- Yefim~va. Characteristic Features af the Autmn
Ice Regime of the Danube River. "Tr. GCIR , 1962, No. 80 pp. 126 - 170.
6. Solopenko, L. I. Circulation Investigations of Ice Formetior, on the Soviet
Stretch of the Danube. "Tr. UkrgIC$.IIw, 1970, Eo. 97, pp. 63 - 69.
7. Shulyakovskiy , L. Go Poyavle~iye l 'da i nachalo ledostava na rekakh
i vodokhranilishchakh. (The Appearance of Zce and the Beginning or" Icing on
Riirers and Reservoirs). P!o.ioscow, Gidrometeoizdat , 1860, 216 pages.
8. Shcharbak, A. IJ. , L. I. Solopenkc. Autumn-TN'inter Ice Regime of the
Soviet Stretch of the Danube River. "Tr. UkrNIGMIvt, 1970, No. 97, pp. 70 - 83.
9. Shcherbak, A, V. Calculating the Time of Floating Ice Appearance on
the Soviet Stretch of the Danube River. "Tr. UKRNIGMIH, 1971, I.Io. 104, pp. 57 -
- 68,
10. Shcherbak, A. V. L. I. Sologenko. Conditions of Formation of Ice Jam-
Ice Dam Phenomena on Lower \$ater Reache2 cf the Datlube River. "Tr. UkrNIGMI" ,
1972, No. 116, pp. 131 - 138.
By: M. M. Beylinson, A. D. Mimzhanov, B. R. Abdykazymova, A. K. Dosymbetov
(The Kazakh Educational Institute, Alma-Ata)
Tne thermal and ice regimes of rivers, lakes, and reservoirs of ICazaWlsta
are extremely varied. One can identify the following groups of rivers and their
stretches according to the Winter regime :
1 - rivers with a stable ice cover;
II - rivers with a predominantly unstable and inte ttent ice cover;
III - rivers with ice phenomena but without a continuous ice cover or with
an ice cover only during particularly severe winters;
IV - river stretches witho~~t ice phenomena.
All of these groups of rivers are encountered in the southeastern regions of
the K;zakh SSR; over the gl-eater part of Kazalchstan, one has rivers with a stable
ice cover and they frequently freeze to the bottom even in open stretches. &?
exceptionally lo%$ water content .is a feabre of maTy of the Kazakhstan rive~s.
Some rivers in &he morthejssn ad middle noegioss af the republic dry-up in the
er arad &turn1 ad represent a system of disparate stretches of' water which
fl-eeze in a fashyeon similar tea small lakesr
The aqueous mass of the large rivers cools mre slowly than that of the
small ones. This retards the appearance of ice on large rivers by an averwe
of 3 - 7 days. The Autumn ice gang is only observed on the large rivers (Irtysh,
Ural, Syrdar'ya and the Ili; it is less ~"requently observed on the Karatal, the
Lepsy and others). It is usually accompanied by the formation of large ice piles
011 the shares. 140sb crfcen the Autum ice gmg is associated with the break-
"trough of ice Ji2a~ ace iee dans. Sub-swface lice whose formation. is the maat
characteris"%i feature of znoun.tain rivers in Winter plays the pri~ia~y role in
the ice regime of the mountain rivers. ?he amount ar' brash ice transported by
some rivers reaches a high value, particularly on the Irtysh, tkie SyrdarFya and
ti3e Xli*
Ice dm phersomena zre frequently observed saa nomtain s"swrg,3s These in-
flict great lasses or. inland waterway management and hydrotecMica.1 facilities.
Brash ise-ice conglomerations are frequerltiy obse~ved during the break-through
of ice darsjs.
The formation process of the ice cover on Kazakhstan rivers takes up a long
period (on the average, _From the ZII decade of October to the I decade of December
up to the TI. decade of November to the %I decade of January). A number or" rivers
in the southern regions of the republic does not _fi-eeze every year. Tne esta-
blishinent of an ice cover along the length of a rive: depends on the flow
dlresti~i~.
In tbz first half of the Winter one observes an intensive build-up of the
ice cover and already in the first half or December the rapids on emany plain
rivers freeze down to the bottom. By the end of December the average ice thick-
ness is 15 - 75 cm and the maximum ice thickness is 40 - 95 cm. 'The highest
values (up to 40 - 220 cm) of ice thichess are reached at the end of Februa-y -
Mrrch. In individual years, because of thick accumulations of sub-surface ice
and the fomaticn of ice piles, the thickness of the ice can reach 4 - 5 m (4).
The ice piles are responsible for the stratified character of the ice cover.
The ice cover on Kazakhstan rivers averages a duration ranging from 35 to 175
days (the longest duration runs from 95 to 195 days).
The beginning of debacle generally falls to the I decade of January -
the middle of April (the latest dates of river cleara~ce from ice rmge from
the III decade of February to the I decade of May), In connection with the
increase in solar radiation, the ice cover on the Kazdkhstan rivers begins to
break-up still before the onset of stable positive air temperatures. The ri~zer
debacle occurs under the effect of both therzal and mechanical faetcbrs.
The average duration of the period with ice phenomena on rivers with a
stable ice cover is 105 - 190 days (the shortest is 45 - 175 days and the
longest is 140 - 215 days). In the southern regions of the republic, the
length of the period with ice phenomena are significantly shorter (up to
70 - 150 days). The debacla2 ad clearance of rivers from ice is somewhat less
extended in time than their freezing process.
The ice regime of the rivers changes sharply when the flow is regulated.
The process of ice cover formation ad its destruction on many reservoirs in
Kazakhstan are similar to the analogous processes that occur on rivers wder
natural conditions. On comparatively large reservoirs, the ice cover is
established earlier and more rapidly an stretches wilere the abutment wedges out
into the stream and somewhat later (by 20 - 35 days) directly adjacent to dans
(41, where open stretches of water frequently do not freeze over the e2tire
lu'inter. investigations conducted on the bngirsk, Ust ' -Kamenogorsk and Bukh-
ta~zlinuk reser~rcrirs demonst rated that under the conditions of Kazakhstan the
change in the dates of onset cf ice formation and the establishment of the
continuous ice cover on regulated rivers can be calculated with sufficient
accuracy according to the method of L. G. Shulyakovkiy (7, 8), using the formulas
of A. P. Braslavskiy and Z. A. !rikUina (1954) for calculating the thermal
balance components.
The construction of the Kapchagaysk i3:~ilroelectrie power plant on the
I11 Rives and the reservoir, which is a combination water managen~knt object,
is solT$ing problems of the developmen t of energy generation, qriculture
an-d fish management, was completed in the Ninth Five-Year Pian, llne operation
of the Kapchagaysk hydroelctric power plant strongly depends 0.2 the ice regime
or" the reservoir. The functioning of' a number of econodc organizations which
capitalize on the waCer riches of the reservoir, the developnent of inland
~zater~qay transport, and other brdanches of the national economy also depend
up03 %he ice situatione
In order to service the m~nagement ~r~gmizations in !$inter, the authors
beg= to study the ice regime of the Kapchagaysk reservoir in addition to
investigating the ice regimes of existing bzakhstan reservoirs. Formulas
rqere chosen for the thermal balance calclllations ( 5) , and a method of fore-
casilng the dates of onset of different phases of the ice phenomena ~jas
developed,
The basis of calculating ice formation on reservoirs in Kazakhskan was
the f ollowi~g inequality
where b is the averag ter temperature according to depth at the end of' the
n-th interval or" time; - the depthwavepage water temperature at the tima of
Q n beginning of ice formation, i.e., the temperature at which the beginning of ice
formation is possible under the given meteorological conditions; Bn is the speci-
fic heat yield of the water surface at the time of beginnix of ice formation;
a is the coefficient of heat yield from the water mass to the supface of the n water-air interface at the time ice formation begins. The calculatians =re
made with the aid of nomograms plof,ted for the conditions of Kazakhstan,
The inequality (1) was verified or? the basis of full-scale data for Lake
Balkhash, the Kengirsk, Ustt-Kaqenogorsk and Bukhtarminsk reservoirs, as well
as the Ili River along the free course, taking into account the annual and
averaged hydrological data, since for the bpchagaysk reservoir one cannot take
into account hydrological data for past years (the reservoir did not exist).
In 77% of the cases, the error of calculation for the Ili River over a 35-year
period in the region where the reservoir was built is 21 day and comprised 77%.
It was 83% r"or 22 days and 94% for *3 days. The maximum calculation error was
6 days (1,956). In the Winter of 19110 - 1941, there was no ice cover. This was
in fact obtained as the result of calculation. The preliminary calculations
made it possible to represent th anticipated process of' Autumn ice firmation
on the Kapchagaysk reservoir. Freezing of reservoir stretches with an average
depth of 3 m and a current velocity of 0.1 m/sec is anticipated one day earlier,
on the average, than on the Ili River with a free flow. The averaas date of
freezing of these stretches is 13/XII according to the calculation and the
earliest date is 23/XI, while the latest is 18/I. The appearance or^ floating
ice is vlticipated on 5/XII, on the average, according to the calculations.
This is 8 days before reservoir freezing (the exlirerne dates of floating ice
appearance are 18/XI, 1972, and 3/I, 1942).
These same stretches f 3 m deep) with a flow velocity of 0.2 - 0.3 m/sec
on the average, should freeze one day later than the Ili River :in this region
with free flow, according to the calculation. The extreme date23 fluctuate
from 23/XI through 19/I. The appearance of floating ice (without taking into
account transit brash ice) is also anticipated an average of 7 8 days before
the formation of the continuous ice cover. In separate years this period can
also extend for more than a month (1939).
Th:? freezing cf stretches of the Kapchagaycsk reservoir with an average
depth of 5 m, according to the calculation, is expected 7 - 9 days later than
that of the Ili River to the point of its regulated flow. The extreme dates
fluctuate fr30m 27 - 29/XI tllrough 16 - 2311. The appearance of floating ice is
expected 3 - 6 days earlier, on the average.
Stretches of the reservoir with an average depth cf 7 m are expected to
freeze, on the average, 11 - 13 days later thar! the Ili River under natural
conditions, according to the calculation. On stretches of the reservoir with
an average depth of 5 m or more, large stretches of open water slnould be ob-
served in individual Winters. Thus, in the \$inter of 1939 - 1940 the ice cover
was absent, according to the calculation, on stretches of river whose average
depth is 5 - 7 rn. It is vlticipated that the ice regime of the Ili River in
the lower reach of the Kapchagaysk reservoir will be unstable. Here favorable
conditions are created %"or the accumulation of bras11 ice md the B"o!raation sf
ice dams,
According to the calculation, the for~ation of a continuous ice cover
through the Kapehagaysk reservoir aquatorim will occupy a long period of time. - It will mach an average of over 16 days (from 4 to 57 days) for stretches whose
depth ranges from 3 to 7 m alone. 8 - 10 days after stretches of the reservoir
3 m deep have frozen, one anticipates freezing of stretches with an average
dept21 of 5 m, then, in 12 - 14 days, freezing of stretches whose depth is 7 n.
Deper stretches of chz reservoir should freeze significantly later.
Sharp periods of nocturnal cooling can cause the metal components of the
hydrotechnical facilities imersed in the water to freeze (gratings, shields,
spillway structures, etc. 1. This can occur priar to the appearance of particles
or^ floating brash ice on the water surr'ace.
Freezing maps have been #!ram for the large Kazakhstan reservoirs (Lake
Balkhash and the Bukhtarminsk reservoir) according to the meteorological data..
These maps enable agencies of the hydrometeorological service to provide service
to fishing industry regions which are remote from the water monitoring stations
(3). The inequality (1) also forms the basis of the calculation. In order to
test the calculations of freezing dates of different little-studied reservoLrs
in Kazakhstan, the materials of ice aviation survcjis xere csed. These ape gen-
erally in good agreement :~ritt; the maps dram according to the calculation data
(11,
The generalized nultiannual maps of the average, early, and late reservoir
freezings provide a complete charac t~rizakion of the regime of Autumn ice
formation. Thus, the formation of the continuous ice cover for the Lake Balkhash
aquatorim according to aaps draym on the bzsis of calculation da,ta, occurs on
the average in 36 days (from 16 to 67 days). On the average, stretches of the
lake about 10 m deep freeze 7 - 8 days after stretches 4 - 6 m deep freeze.
Stretches about 15 n; deep freeze 15 days after the latter and those about 20 m
deep freeze abost 20 days later. The Zaysansk stretch of the Bukhtarminslr
reservoir freezes much quicker. Comparing the freezing maps drz~dn according to
the data of ice aviation surveys and the meteorological data showed that one
ca? forecast "the reserx~air fi-eezing dates in ay%y pa&.% of the reservoir with a
ti~eliness factor of 3 - 5 days, using the leather forecasts. Tie rjorking
short-tern forecasts of freezing of separate regions of Lake Balkhash Ibr
servicing the transport and fishing fleet in the hazardous period of ice forma-
tion produced a good monetary savings. Such forecasts made it possible to in-
crease the fishing times and navigation period and also made it possible timely
to prepare for fishing and to remove the fleet to wintering berths in timely
fashion without loss of working days.
Methods of long-term forecasting the beginning of ice cover on Kazakhstan
reservoirs have been developed on the basis of malyzing the sgnoptic processes
of the preceding period, specifically, as well as for stretches for which hydro-
logical data are unavailable for past years, as well as for newly created reser-
voirs (2).
The fornation of the Siberian anticyclone over the western horn of Kazakhstan
is a significant feature of atmospheric processes of the cold half-year. The
Siberian anticyclone is frequently a continuous strip of high pressure which
intersects the examined territory along its medial latitudinal zone and has a
significant effect on climate and weather. Its extent and break-up determine
the nature of the Autumn aqd Spring ice phenomena. The movement of anticylcones
along meridional trajectories is also very signi,ficant for the circulation pro-
cesses and climate of Kazakhstan. Analysis has shown that the intensive forma-
tion of ice in rivers and reservoirs here most frequently occurs with pre6odnance
of the eastern type of atmospheric circulation, according to G. Ya. Vmgengeym.
The predominance of the meridional type of circulation, as a rule, causes later
ice formation at the end of November and in December in the central regions of
Kazakhstan and at the end of Decernbel- and in Julumy in the southlem regions.
The ice debacle is most often observed when the cyclones extend from the south-
west. The earliest dates of river debacle in the southern regions of Kazakhstan
are due to the sauthwesterlg movement of air; nlasses in February in the absence of
northwesterly incursions, and in March for the rivers in Central Kazakhstan. The
late dates of debacle are observed when there are northern and nortkdesterly in-
cursions of anticyclones in March and April.
The inverse relationship which exists between processes in S~eptember and
November, identified by the authors and other investigators, is a fezture of
the synoptic processes that exist above the examined ferritory . Different
characteris tics of atmospheric processes used for long-term forecasting of ice
phenomena have been identified by analyzing the synoptic conditions which cause
ice formation on rivers, lakes, and reservoirs in Kazakhstan. According to the
authorsg investigations, an inverse relationship exists between the temperature
of the air during warm half of the year and the onset of icing. Thus, reservoirs
in the southeastern part of Kazakhstan usually freeza earlier with a comparatively
high air temperature in August and September, while later ice r"or.mation frequently
exists during predominance of low temperature at this tinie. A comparatively close
association has been identified between the calculated dates of freezing of the
newly built Kapchagaysk reservoir and the total of average daily air temperatures
h ilug~st.Zfl-~~~~, which are less thvl the average decade multimmual ones for this
month (see the figtire). In the figuret one clearly traces three directions of
points due to the different types of synoptic situations (meridional C, s~esterly
W easterly, E types of circulation), The farecast relationships which exist
between the SUA~ CO-VIITt characterizes cooling in August and is due to the various
m
atmospheric processes, aqd the beginning of ice formation and have been identified
for Lake BaSkhasi2*
The relationship be tween the beginning of icing on the Kapchag-. ,.sk -i+eservoir
(h = 3 a, u = 0.1 m/sec) and the total of low air temperatures m August during
varying synoptic situations in the previous Winter.
I - predominance of the meridional type of circulation; XI - predominance of the
westerly type of circulation; JII - preeominance of the easterly type of circula-
tion a
Tlne forecast relationships which exist betieen tk indices of atmospheric
circulation on 1 September, calculated according to maps of barometric topograpkf
ATSOD and freezing of Lake fblkhash (11 yield good resfits. This index char-
acterizes both the meridional airstreams in the troposphere and, to a certain
extent, the latitudinal ones.
The development of methods of forecasting the beginning, development, and
end of ice phenomena with a high timeliness factor under the conditions or"
Kazakhstan is a complicated problem. A number of the developed methods for long-
term forecasting of the onset of icing in southeastern Kazakhstan is used in the
practical work of the UGPfS, KazSSSR and has been since 1060. Experience gained
in compiling the long-term ice phenomena forecasts for Lake Balkhash with a time-
liness factor of 1.5 - 2 mnths have yielded positive results far this period (6).
1. Beylinson, N. M. Calculating a~d predicting the Dates of Ice Cover
Fctrm~tion an Lab Balkhash. "Tr. TsIPH, 1965, Mo. 151, pp. 46 - 54.
2. Baylinsor., M. PI. Using Meteorological and Synoptic Characteristics for
Short--Tenn and Long-Term F~recasts of Freezing Dates of Lakes arid Reservoirs
of Kazakhstan in the Absence of Hydrological Data. "Tr. I(azNIGt4I:", 1966, No. 25,
pp. 127 - 134.
3. Beylinson, M. Me Maps of the Average, Early, and Late Fx%eezing of Lake
Balkhash, Calculated According to Meteorological Data. "Tr . KazNiGMIu , 19 67,
4. Beylinson, 81. M. character is ti.^^ of the Ice-Thermal. Regime of Kazakhstan
Rivers. "Tr. koordinatsion!iykh soveshchmiy po gidrotekhnii:eff, 1968, Nc. 42,
pp. 144 - l64.
- 2. Beylinson , M. M. , L. Ya. Pavlenko . Basic Features of the Thermal Balance
of the Kapchagaysk Reservoir* "Sb. rabot Alma-Atinskoy GMOR, 1970, No. 5, pp.
23 - 29,
6. Beylinson, M. M. Experience in Compiling Long-Term Ice Forecasts in
Southern Kazakhstan. I'Tr. KazHIGMIv , 1971, No. 41, pp. 124 - 128.
7. Shulyakovskiy, L. G. Poyavleniye 18da i nachalo ledostava na rekakh,
ozerakh i voookhrmilishchakh (raschetg dlga tseley progn~za). ('rhe Appearance
of Ice and the Beginning of IcFng on Rivers, Lakes, and Reservoirs (Calculations
for Forecast Purposes ) . Moscow, Gidrometeoizdat , 1960, 216 pages.
8. Shulyakovskiy , L. G. , V. M. Busu~ina. Calcula-Lion of the Beginning of
Icing on Rivers Under Natural Conditions and Under Conditions of Flow Regulation.
"Tr. Gidromettsentra SSSR", 1967, No. 8, pp. 12 - 24.
CAL;CULBTIONS AND FORECASTS OF FREEZING DATES ATID ICE CLEBR4&VCE DATES OF THE
VOLGA RIVER RESERVOIRS
(A Method and Experience in Practical Support of the Inland Itaterway
Fleet)
By: Ee V, Balashova
(The Hydrometeorologica1 Center of the USSR,
Moscow)
The grandiose hydrotechnical constr~ction which has unfalkled since the
beginning of the 1950's on the large rivers in the USSR has faced forecast
hydrologists with the necessity cf issuing forecasts for new objects that have
still unknoymA ice regimes.
As the result of investigations conducted at the Hydrometeorological Center
of the USSR, L. G. Shulyakovslxiy, V. V. Piotrovich and S. N. Eulatov (3, 8, 9)
have obtained nethads which enable one to calculate the annual dates of freezing
of reservoirs and ",heir ice clearance in the absence of obserrrction data. !$ith
the aid of these methods, meteorological data for past years and the hydraulic
and aorphome tric characteristics of reservoirs are used to calculate the a~innual
dates of freezing and ice clearance of practically all newly created reservoirs
as provided by the project. This primarily includes the Volga River reserxioirs,
which are used to provide for a significant fraction of the carago turnover of
the inlaild watermy fleet of the USSR. Calculations of the multim-nual series
=re carried out for the Gortkiy, KuySyshev, Saratov and llolgograd reservoirs
(2, 6). Moreover, the curves of frequency of the dates of ice phenomena %+ere
calculated for the Gheboksarsk hydroelectric power plmt reservoir, which is
under construction (7).
Tile obtained mltiannual series encompassed various conditions, in~luding
the extreme ones. The series make it possible to ootain the regime character-
istics of freezing and clearance of reslrvoirs according to 2 probability t30"orm,
to identify chaqges in the ic regime in comparison with the river under naturzl
conditions , ukd to deternine the effect of the mcrphometric an",yydraulic r"actors
on these changes. Furthermore, these series served as the regime basis for
developing methods of long-term forecasts.
A foreca~it %$as prepared by carrying out. the indicates operations by the
ki~e or" sta.rtup of eaci; reservoir (the forecast :.ias the probability character-
istic). 'i'his forecast dealt wit11 the ice regime, 2nd beginning with the first
year oi' existence of the ri.servoir long-term and short-terrr, f'orecasts of freezing
a?b ice clearance were r3egularlg issued.
NOW) when certain data of Pull-scale obser:.atians made on reservoirs hzve
been accumulated, one can attempt to test our assumptions about the chmga in
t.he dates of ice phenomena resulting from reguistion. The largest series of
observ~tions is available for the Gor'kig, Kuybyshev (17 years) 2nd the 'loigc-
grad (14 years) reservoirs. The d3-k~~ of Ice phenomena observed on the reservoips
%ere plotted by tile authors on apprasriate frequzney curves %zhich liere in turn
plotted according to the series calculated earlier. Certainly, such a comparison
is nat very valid since one is comparing series of difi'erent length, ad more-
over, irihen climatic characteristics of a period can influence the accurac:y of
the c~mparisoni if the series is short,
Figure 1. A comparison of the freezing dates of reservoirs rjith the frequency
curve obtained aceorbing to the calculation.
i - Ruybyshev reservoil-, upper slope ; XI - Gor "ciy reservoir, K~ostroma-Pur yevets
stret~h.
%%e freezing dates of the limitiw stretches of the Gwr'ki:y and Kupbyshev
resarvsiirs ovar the 1956 - 1972 period are superimposed quite satisfact urily
(Figure 1) on the frequency curves of the calculated dates for 1925 - 1355.
Ose can only izcite a slight tendency toward deviation of the actual dates -50
the early side, whieh is evidently explained by predominance cf the lorgt2red
wa"s;e reeve bbaicg~ound on the ?Jolga River at that tine. The c',h;rigeabil:ity of
dates on the C-or'kiy ~eservoir aver the years of' its existenca was sonelhat
greater than according tu the caleulatiain. The calculated chagezbilitlr is
probably toc low, in..-smch as the annual fluctuations in flo:j mt:: in t4ke intake
atretch %ere not taken inGo BC.&;LQU~$,
ma Lne ic2 cleara~urce dates of the Kapbysker reservoir lie precisely on tk:e
fr%quenc;~ curv3 abtained from the calculatiot? ~eries (Figure 2) . The ob sar8ved
dates of clearance ofa the Gor'kiy reservoir are 2x30 near the curve. Ti243
greawest deviatiotls here are noted in the late dates, with a frequency o:? nore
than 80% Reservoir ice clcarmces were not obse~ved after iO/ir cver the! years
of existence of khe reser'voir, while according to the cal.culatin8 sucn dates
could appear once eTJerg 10 - 15 years. The observed t.js of c:learw2ce or' the
V~lgograd reservoir lie noticeably earlier than the calculation curve. K~re
one patently has it certain spstenatie error in "she ealcillatioa ol 3 - 5 days
5qhich evidenkly appeared as a consequence of falling to consider the flow rate
af the reserqroir in the calculations ;;nd the influx of heat to the lower 5:urI'ace
of the ice, which clin be significant in the southern regions,
Figure 2. A comparison of dates of reservoir clearance from ice with the **"re-
quency curve obtained according to the calculation. 1 - Kuybyshev reservoir,
I1 - Volgograd reservoir.
'T;he probable deviation in the observed dates of ice phenomena from the
curve calculated before does not exceed 2 days for all reservoilrs with the
exception of the Volgograd one.
t&.ihile recbkoning with the insufficient strictness of the ci'ted comparison,
we sGill consider it possible t.o cqnclude :hat the concepts eo~cerning the
change in the ice regim of the L'olga River obtained aceording to the caleulatlon
data were basically cur~e-ect .
One can state the following in suraarizing the results of the calculations
a~d observations.
mx ine chulge in the freezing dates of reservoirs in conparisun with the river
is determined by the change in Oepths, flow velocities ai~d the gssitian of the
reservoir in the hydroelectric power pia~ t cascade. an &he Kuuybyshev reservoir,
above which (on the Volga and Kama ctnttches) the Volga Rixre~ is in a relatively
a naCural state, the first ice necks r~hich limit navigation ~orn in ti..e zolle of
hydroelectric power plant abutment ~dedqing, whare a sharp drop in flow velacity - occurs ad the lowest depths mt? observed. Ace zppears here j -- 5 days later
thm on the same stretch of the _river under natural conditions, while the ice
cover fornis 10 - 15 days earlier.
On the Gorgkiy, Saratov, ad Volgograd reservoirs, ~qhose uI:per part is
under the el';2cl; of the hydroelectric parer plant located upstream, the locat-ioa
or^ the first ice neck shifts slightly be lor^ the zone of abu-lme~?t b&edging r;nd
araually chan--~s 0-- depending upon tkie magnitude of %he flow rates 0;' water thrcugh
the hydro2lectric power plant. The ice appears 6 - 10 days latt:s i~ere thzn daaes
r'lnatlng ice on the river, and the ice cover begins to form 10 - 12 days later
thm fl~aiing ice.appears or. the river, and totals 2 - 5 days before the river
freezes under natural conditions. The new Cheboksarsk reservoir will be in-
clude[$ among the same group of reservoirs ( 7). Hence, a compariscn of the
nature of freezing of single reservoirs md those locaged in the hydroelectric
power plant cascade shows the advantage of %he latter from the standpoint of
ti2e durai;i.oa% of the Au% navigation period.
Comparing the frequency curves of+ dates of ice appearance a~d the anset of
the ice cover or, the river and on the reservoirs shows that the probability of
early ice fornation noticeably diminished over all stretches of reservoirs. One
also notes a general decrease in changeability of dates of the iZut:
ornena proportional to river ~egulation. On the ane hand, the letter is associated
with the more rigid freezi~g at khe late dates, and on the othe3- is associated
with the greater equalization of the aqueous regime under regulated conditions.
The effect of flow rates of water flowing through the reservoir on tile onset dates
of icing is extrcin@Ly significait, particularly during unstable wt -ther at the
time of i%.eezing. Ir, individual years the increase in the f1or.r rr of water
by 30 - 508 can lead to retardation ia the case& of icing on the Vo~ga stretch
of the Kuybyshev reser~~oir or in the upper part of the Voigograd reservoir by
8 - 12 days (I, 6). This ci~cmstance can and should be used to extend navigation
into ths l\ut.mnlBc
In Spring, the ice cover is preserved longest cn the widest stretches of the
reservoir and in the stagamt, closed coves. The clearvlce of these stretches
from ice limits the &ginning of nomi navigation. On the Voigograd reservoir,
which is sharply elongated along the meridian, the difference in conditLons of
the influx of heat i?as a noticeable ef act on t3e break-up of ice. The lower,
southern part af the reservoir clears of ice significantly earlier thvl the upper
part, although its width in the part near the dam is greater but the velocity
I.s 318%geP dD
The change in the dates on xhich tjle reservoirs are clear of ice, in com-
parison with the dates observed on the same stretches of the river under natural
conditions, is ehinily determined by the direction of flow of tk~e river, the
dwation or' %he Spring debacle ad the flow or' the rese~7~criir. Based on %he
ermple of the Vofga iiiver) this is trs~ed pi?i~ti~ularly cL+~~P~J. All I.C;IS~~VO~PS
Inca"ied on the upper course qf the river, &ere the debacle was brief under
natural conditions, frpe fram ice significantly later tha the river itself.
The @i-fferenoe is ~ost noticeable on the n~iy dates. The dates of clesrwce
or" reservoirs with a frequency of 10% are noted 11 - 14 days later tha2 the
correspondislg dab23 on the river. For %he late dates (dates ijith a freqllency
of 90$f, this difference shortens ta 6 - 8 dzys and even to 3 days in the
Ugiichsk rese~voir, which has a strong cwrent. In the Kdybyshev reservoir,
wi3ere tk duratior;. rif the Spring de baele kcreased under natural conditions
due t:, the transport of ice frofn the Lma Ri.rer, the differetlce in cleara~ce
dates comprises a total of 2 days for she mlie~ate datz~.
Prior to regulation, the lorqel- Volga opened from downstream to upstream.
Eere the consequence of the in-flow of ice frurc the upper: more northerly
stretches of the river was a prolonged ice gring, first of the Valga ice, then
the Kma ice; the total duration or" the Spr1r.g debacle, the maxim~m one of all
the rivers the USSR, averaged to 15 days. After regulation of the river at
the Saratov and Vofgograd reservoirs, 3nly the "localu ice melts. 16s rapid
dostruetion is facilitated by the southerly posit,ion of the Volgograd reservoir
and by the rapid flow of the Saratov reservoir. As a result, the ice now dis-
appears here 1 - 4 days earlier than under natural conditions. As the investi-
gatiolls of B. 24. Ginzburg showed (7), on the whole the changes in the duration
of the period of absence of ice cn the Volga resulting from regulation are
favorable for inlad waterway transport.
The character of chances in different reservoirs varies. The most favorable
ohages occurred on the lower Volga* Here navigation can last ;in average of
17 - 19 days longer than before construction of the Volgograd and Saratov hydro-
electric powel- plats. On the Volga from Rybinsk to Kuybyshev, changes in the
duration of the iceless period are slight. It (the iceless period) dininished
significantly only on the upper Volga and at Sheks~a follociing filling of the
Rybinsk reservoir, respectively by 2 - 3 and ? days.
The conclusion that the effect of regulating the Volga is favorable wi2h
respect to the duration of navigation is the mgre correct because under the
conditions of the reservoirs the extension of navigation into both the Spring
and Aut periods is significantly facilitated, In Aut the ships trar sit
stretches of the first cover ice with the aid of icebreakers. This is parti-
cularly effective in years with a broken course of freezing, when the cold
waves alternate with prolonged periods BZ warming and the extension of ice phen-
omena ts the deeper skretches of the reservoirs is retarded. In Spring the ice-
breakers force a navigable channel in the ice long before the complete break-up
of the iceo
Presently, investigations of the build-up in the thickness of the ice in
the initial period of icing and losses of stability of the ice cover in Spring
are underway at the Hydrometeorological Center of the USSR for purposes of
identifying the possibility of long-term forecasting of the dates of onset aad
termination of' navigation in the ice (4). The work will continue, but one can
already draw e1er"Lai r;@oncZusions.
The investigations and practical experience derived in the inland waterway
fleet demonstrate that modern icebreakers comparatively easily cross ice up to
ZT - 20 cm thick, HMis difficult to determine the dates af onset sf this
thickness according to data of available full-scale observations md therefore
the authors have proceeded along the path of calculating the daily build-up of
ice thickness* The calculation !$as made for a stretch of f~rrnafiion of the first
ice neck on the Kuybyshev reservoir (the Verkhnyy Uslon region) or. the computer,
using the method of ShulyaL;ovskiy. 6s the result, a multiannilaL series \+as
obtained (since 1940) of the dates when the ice thickness reaeited 10, 15, and
20 can
013 the av.!3~2ge, the ice reaches a Lhiekness of 10 cn on t-he fourdfi day aE
j-cing, 15 cm on the eighth day; the thiclrness of ice measuring 20 cul is observed
in 15 days, 23 cases of piir"i;i~Larly severe c~ld, the ice thickness reached
20 cm in only I) - 6 days, but during ~;n extended Autumn this per*iod can even
extend to 30 - QO days.
The Freqtiency curves of the dates ~crH%en. a certain thicbess sf' the ice is
reached run in parallel with the curve of dates of the icing and deviate only
in the late cases. A build-up of ice to a thickness of 20 cm is observed in
a period from the middle of November to the end of Decenber, on the average to
7/5II. Analysis of the probability of ice build-up showd that one can plan
navigation in &he ice wtil the end of Noveaber.
A system of methods was developed for operational support of opening and
closing navigation on the Volga reservoirs. With the aid of this systern
(methods) , long-term forecasts of freezing and clearance of the reservoirs are
issued with a timeliness factor of 1.5 - 2 months and is then refined by fore-
casts with a lower timeliness rating (10 - 20 days) and by short-term forecasts
(over 3 - 5 days).
The long-term forecast methods (5, 6) are based on the use of the relation-
ship of ice phenomena dates with the development of atm~sphe~sic processes in the
preceding period. The quantitative indicators of the condition and tendency of
seasonal restructwings of temperature fields and their pressure fields are taken
intc account, as well as the characteristics of the flow rate of water rurlning
throupa the r~?servai.r and %he ice "cfnichess,
The long-term forecasts are issued in a probabilistic form which makes it
possible re!alistically to estimate the degree of industrial risk in resolving
specific management problems. Unfortunately, the probabilistic rorm or fore-
casts has still not r'ound extensive application in planing the pera at ion of
inland waterway transport.
The general justification of the long-term forecasts over the time or"
existence of the Volga reservoirs has been 76%. The forecasts of reservoir
clearance from ice and forecasts of the early and nearly normal beginning of
the icing hav$$ been most successfully justified. The forecasts of" late *enzing
are clearly justified: the ice cover formed much later than the anticipate3
dates. "i'e latter is due to the fact that during development cf We method and
issuance sf the fo~ecasts the techicia23 inv~fved skrrove to avoid the most
hazardous error for inland waterway transport - unvlkicipated early freezing.
Such errors, and consequently, the associated disruption of accomplishing the
plans of transport, accidents and material losses did not occur on the Volga
reservoirs. The long-term forecasts and their verifications mde it possible
nearlg- always fully to utilize the navigation period. Long-term forecasts of
reservoir freezing mre particulzrly effective in recent years, when the method
(for the first time in the practice of long-t*erm ics forecasts) made it possible
to foresee the disparate, intermittent character of ice formaticn. Taking the32
forecasts into account, the intensive operation ol the inland watert~ay fleet,
particularly the self-propelled vessels, continued 15 - 20 days after the
formation or" the first ice necks in 1969 - 1972. The additional tine could not
be successfully used to the fullest extent for navigation only in cases cf a
predicted, very late freezing (1962, 1967, 19691, when navigation terlcinated
before the beginning of icing despite the issuance of verifications of the long-
texm forecasts, since during planning carried out according to the long-term
forecast neither the dispatch or" cargoes nor the maintenance of the waterimy had
been planned much 3-ater than the dates.
The short-term forecasts, upon which operating decisions concek-ning opening
a~rad terminating, navigation are based, Ere eompi&sd on the basis of calculation
methods with the use of forecasts of air temperature and, sometimes, wind and
overcast. The timeliness of the Autumn forecasts averages ?! days and that of the
Spring olles is 6 days. The high accuracy of calculations (for the Kuybyshev
and Volg~grad reservoirs, for example, the errors of calculating the beginning
of icing did not ever exceed 1 day) ensures adequate reliability of short-ters
forecasts despite the error of weather forecasts. In 93% of the cases their
errors did not exceed the accepted permissible ones.
The immediate prospective for significantly improving the ef fefztiveness of
ice phenomeria forecasts on Volga River rese~voirs is seen in devisin.3 methods of
forecasting navigation conditicns in the ice. The first steps in this direction
have already been taken. These are the short-term forecasts of ice cuild-up
issued in 1971 and 1972. These were noticeably useful. Presently, afthods of
forecasting dates when the thickness and strefigth of' the ice render the movement
of ships th~3ugh the reservoir possible are under development.
iin important condition of the successfulness of' hydrological support for
inland waterway transport is the constant contact or" spnrational agencies of
the firecast service with management of the inland :datergay fleet. The close
cooperation of the Hydrometeorological Center of the USSR with the operating
directorates of MRF, RSFSR, the GorTkiy Weather Bureau with VORP and the Volga
BUP, the Kuybgshe~ Weather Bureau with the "Volgotanker" shipping line, esta-
blished in recent years, has improved the eifectiveness of service, mind in many
cases has made it possible to make correct operating decisions in a complicated
ad unfavorable situation, Such decisions have ensured the sucsessfu$. accom-
plishment of improtant economic tasks.
We consider it expedient to extend cooperation in carrying out investlgatio~s
ained at identifying methods cf optimua plaqning of' fleet operations jointly iqith
the scientific institutions of MRF, taking into account the probabilistic char-
acter of ice phenomena forecasts. Conducting such investigations, in addition
to improving methods of forecasting ice phenomena and developing methods of
fcrecasting the zonditions of ice navigation, will make it possible ts improve
the support of inl.and waterqday transport, one hopes, by providing ice r'crecasts
at a new, higher level,
1. Balashova, I. V., D. N. Yefremova. Freezing Dztes af Nekly Created
Reservoirs. "Tr. koordinatsionnykh scveshchxliy po gidrotekhnikew, 1968, No. 42,
pp. 230 - 236.
2. Balasbova, I. V., V. P. Sklabinskiy. Freezing Dates of the Swatov
and Volgograd Reservoirs. ffTr. Gidromettsentra SSSRn, 1972, Mo. 49, pp. 70 - 82.
3. Sulatov, S. MI, V, V, Pistrovich. Calculations ad Forecasts OF Icz
Clearance Dates of Reservoirs. "Tr, koordinatsionnykh soveskchaniy po gidro-
tekhnikev, 1968, No. &2, pp. 222 - 229.
4. Bulatov, S. N* Calculating the Strength of the Melting Ice Cover and
the Beginning of Wind Ice Drift, Leningrad, Gidrorneteoizdat, 1970, 118 pages.
(Tr, Gidromettsentra SSSR. No. 74.).
5. Ginzburg, B. M., I. V. Balashova. A Method of Calculating and Fcre-
casting Ice Break-up on Reservoirs. "Tr. TsIPfl, 1963, No. 100, pp. 3 - 65.
6. Ginzbwg, B. M., Ye. C. Antipova, 1. V. Balashova. A Metilod of Fore-
casting the Beginning of Icing on the Volga River Cascade. "Tr. Gidromet tsentra
SSSRB, 1968, No. 17, pp. 3 - 19.
7. Ginzburg, E, M. Probabilistic Characteristics of the Dates of Freezing
and Debacle of Rivers and Reservoirs in the Soviet Unior;. Leningrqad, Gidro-
meteoizdat, 1973, XI1 pages. (Tr. Gidromettsentra SSSR, No. 118.1.
8. Pio trovich, V. V. Obrazovaniye i s*taivaniye 1' da na ozerakh-vodokkira-
nilishchakh i raschet srokov ledostava i ochnshcheniya. ( Formation and Melting
cf Ice on Lakes and Reservoirs and Calculating the Dates of Icing and Clearance).
Leningrad, Gidromteoizdat , 1958. 192 pages.
9. Shulyakovskiy, L. G. Poyavleniye lgda i nachalo ledostava na rekakh,
ozerakh i vodokhranilishchakh. (The Appearance of ice and the Begj-nning of Icing
on Rivers, Lakes, and Reservoirs). Halascow, Gidrorneteoizdat, 1960. 216 pages.
FQSECASTS OF YL~.WIMW ICE JAM WATER LEVELS IN LOCAXIONIS WITH &W%\SffAL ICE JA$l
FO&\lATf 0@
By: 3. .Ab Nezhikhovskiy, N. P. Sakovskaya, G. ST. Ardasheva
- Ace jams have been studied veq little. Only the qualitative featwres of
the process are Bore or less know. The quantitative evaluation, and specifically
calculating and forecasting the maximum ice jam level, is possible in a fit+ cases.
Such a state of' this problem is due to many objective i'aet6rs: the ccnplexity
of the process, the high cost and laboriousness of field observations, and finally,
the impossibility of accurately duplicating the phenomenon under laboratory con-
ditions. Subjective factors also play a certain role. Until recently, inves ti-
gations of ice jails were dominated by the so-called hydrodynamic trend, which
clearly does not correspond to the moclerll stage of hydrological science.
The presently actit~e stationary system of hydrometric observation stations
on rivers does not correspor,.' the requirements of studying ice jruns. The
mil-scale data obtained by this system are cxtremeiy incompiets and disp~rate,
and therefore it is extremely important in analyzing them ti. he governed by
certain general principles regarding the essence of the process (1, 3, 4). With-
out this, conclusions may be random ar,d even erroneous.
Ice jam formation is an obligatory component of the debacle process oI" naay
rye In the period from thd tine the ice c~ver achieves its rnaximuan thick-
ness over the Winter and befire the beginning of the massive Spring debacle,
two groups of factors are simultaneously active:
a) a gradual weakening of the ice cover under the effect, of warm air and
solar radiation, as well as the heat of nelted snow water;
b) an increase in the tractive force of the water stream on the oaundary
of the water - ice interface resulting fron; an increase in the flow rate of'
water in &he ~iver*
For the sake of brevity, we shall tern the first group or' factcrs thermal
factors and the second group or" factors mechanical factors. Obviously, the
break-up of the ice cover into individual nasses and the break-up or' the field
will occur at the time when stress in the ice cover exceeds its strength limit.
The topographical, hydrometric and other materials needed in analyzing the
process of ice jzm formation on a river are extrenely varied. Certainly, the
most valuable ones are the frequent observations af i.rater levels ind ic~ phases
on adjacent water monitoring station positions and the longitudiijal prcfiles of
the water surface of the river over charactsristic moments in time plotted on
their basis,
During the analysis of the indicated rrateriai for a number of rivers, one
can draw cestain important concl~~ions:
- one should distinguish locations of the annual formation of ice jams and
stretches of the river with vareiable foci of ice jilms which are in~o~~lstant and
meander from year to year. As it is case now that forecasbs alee only possible
for places where ice 3 appear almost annually, if only becawe long- term
observations of the water bevel made in the statisnary water mesuring system
are indicative for them, then the following hold;
i
- as a rule, the location of the annudi formation of '.ce jams tends toward
the break in the longitudinal profile of the river frcm a stretch with a sharp
slope (which rneans a rapid current) toward a stretch with a Low slope (and con-
sequently, with a slow current). Such stretches include the areas where reser-
. voir abutments wedge into the stream, the v:sxtths of rivers when they enter a
sea or lake, areas of transition from rapids (semi-mountainous ) stretches of
rivers to plainz . In some cases, the location of annual ice jam formation can
be on a stretch of river where several types of channel obstacles Eire combined,
for example, a sk:.,rp bend (over LLO - i20°) with an alluvial fan.
Applicakz~e to the sat task, one should also include stretches where the
locations ef ice jams are located a short distance apart among the stretches
with nearly annual formation of ice j with a known cause. Of cowse, the
magnitude or" the observed ice jam maximum at the water monitoring station
will depcnd upon where, in fact, %he ice jam has formed below the station in
a given year, but this difference is not so important if one takes into account
the entire value of the ice Jan] level increase and the fict of a noticeable drop
in slope in the area or" the abutment from the ice jam.
Ice jam formation is a multifactorial process in whose course the cause and
efl"ect frequently alternate. The existing concepts about the natural essence
of the process of ice jam formation are incomplete. Current information about
the basic factors of this process is inadequate. At present, in forecasting ice
jams, one must first be satisfied with taking one or two integral indices of
the process into account, and second, one must bear in mind the specific features
of the aqueous and ice regimes of tine river in the debacle period. The magnitude
of the average flow rate of water Q,, at the edge of the ice cover along the path
or' its movement within limits of the ice collecting stretch (as the character-
istic of mechanical factors of the process) can be an integral indicator for
locations where the ice jams fom annually or nearly annually. Another integrd
indicator is the strength of ;:he ice cover at the time of river debacle ah; , as
the result of thermal factors ' (2). &
~ We shall further make a nmber sf partial remarks.
ed rivers (stretches of rivers), the debacle front always propagate
downstreun. In the debacle process the mechanical factors predominate ovel* the
thermal factors. Consequently, one should pay chief attection to estimatirig the
magnitude of flow rate Qav=
The 1engt;h of the ice collecting stretch is apprcximately found as a deri-
vative of the af,rer%ge swface velocity of water fla~q over the duration of the
period of the dense, and sometimes, average Fee gang, more accurately, when
at a given point the surface coverage of the river with floating ice diminishes
from 1.O to 0.3, The sparse ice gang subsequent to this on the river has alrezdy
nearly been universally due to the transport of ice from secondary streans aid
tirbutaries, the ice trash-out from shore build-ups during. the rise in watw
level?, etx,
The flow rate of water at the edge of the ice cover during movement of the
ice down the river, of course, does not stay eonstant. Inasmuch as the high
water moves more rapidly down the river than the debacle front, then the flow
rate of water at the edge gradually increases both on the non-flog and, parti-
cularly, on the main strean! stretch of the river. It is signif~cant that the
indicated average Plow rate at the edge of the ice Q,, emerges as the direct
and indirect characteristic of the process of ice jan! _formation.
The direct effect of the flow rate*Qa, is quite obvious. The greater Qav2
then the higher the maximum ice jam level when all other conditions are eqi;al.
The flow rate increases with the increase in Q,,, which means that the forces
which lead to .hu%mocking, floes, layered ice, etc. grow stronger.
The indirect effect of flow rate Qav is less obvious, but is also g~eat.
Thus, r&en the flow rate of water is hi&q the debacle front adva12ces do~~nsbreax
comparatively rapidly, without halts and ice dms. As the result) large masses
of firm ice participate in the farmation of the ice jam in locations i~here the
ice jam occurs annually. \$hen Qav is small, the edge of the ice cover advances
slowly, with partial halts in locations of temporary ice jams. In such places
a great deal of ice remains in jams on the shores. Small masses of ~eak ice
approach the location of the annual formztion of ice jams.
It is sigr,ir'icar,t that both integral indices of the process or' ice jam
formation - flow rate Qav and the destructive stress cjhi - are fl-equently
interrelated. If in my given year the river has undergone debacle at n Lou
level Hdeb (consequently, at z low flow rate Qav), t3en this means that ice
cover was not stabbe, ad, vice versa. -
For confirmation, we refer to works (2, 91, whose authors suggest identir'ying
empirical relationships of the type cshl pC f (Hdeb)-
We shall assme that hydrographs of the Spring high water period have already
been pre-calculated in some fashion for several stretches of the ice collecting
region, for example, the upper, middle, and lower. We shall further assume that
dates of the debacle in these stretches are kno~m in advance. Then, by 9
the Slow rates in these str~tches on the day of debacle and by averaging them,
we obtain the value of the integral characteristic Qav. The difficulties consist
in the ract that presently there is no precise method of predicting the dates of
a river % debacle, specifically on a dammed region. Furthermore, in the exmined
period the water levels in the river are distorted by the ice phenomena, which
sharply reduces the accuracy of calculating flow. Finally, the course cf the
river debacle process to a great extent depends upon fclture weather conditions,
which are known to the forecaster only within the most general outlines. For the
reasons given above, unique nethods of directly or indirectly estilnating flow
rate Qav are used for each river, in additicn to carefully taking iinto account
the specific features of its water and ice regimes.
A description of local methods of forecasts of the ice dam mavilna for certain
rivers is given in the works of authcrs (5, 7). Here we shall limit oursel~~es
solely to presenting general conclusions relevant to the accomplished work.
It follows from the purely fundamental concepts that the relationships ar
predicting the ice dam maxima of levels should only be identified for those years
when ice dams were noticed. However, in this case it is necessary to introduce
a criterion of whether or not there will. be a daa. In a practical regard, it is
more c~rrect to use all years of observations (more accurately, all instances of
debacle). If there was no ice dam, then one can accept, for exaolple, the highest
level over the period of the thick ice gaqg as the ice dam maximum.
When establishing local forecast relationships of? the following type
primary significance attaches to choosing the moment of issuing tile forecast. The
unique feature consists in the fact that the indicated moment should be unLrorm
fron year to yeas both xith respect to the water and ice regimes of the river.
On those rivers (stretches) there the high water wave runs in a transit,
or where the edge of the ice cover always moves from upstream to tlomstream,
it is simplest to ijijight the forecast issuance time to the day of debacle at
the point of observations near the upper boundary of' the ice colle5cting stretch.
Flow rate Q,, is arbitrarily assumed to equal the total af Qup + Qlate In order
to increase the accuracy af determining flow rate in the upper stretch Qup and
flow rate of a lateral tributary Qlr;tr one can put off issuing the forecast until
later, fir example, until the day the thick ice gang on the upper stretch terminates.
A method of forecasting the maximum ice dam level of the Severnays Dvina River
near the city of ArkhangeL'sk was devised according to the system described above
(6).
On rivers ~~ihere the high waterway uithin the aonfines of the ice collecting
stretch forms equally as ?;he result of both the flow via the upper stretch or" the
sector and the latepal in-flo:+ *om the psrtial. basin, it is convenient to wait
$he foreaasb yelease toward the time of oazse6 of' tAe maseim~m 50cttal sP flow pates
(QuP_+ Qla)max* An example can be the mjnestr River on the Mogil-eii-Podol' skiy-
pgt hamenka stsetch (7). Characteristic for such stretches is the fact that
in certai~ years the debacle occurs chiefly because of the flood from the partid
basin. Zn this instance, the motion of the edge of the ice cover is accelerated
ad "Lhe timeliness of the forecast correspondingly drops.
There are ri~el-s and river basins where the Spri.ng flood on the ice collecting
stretch form? by means of interference of the flood waves of individual rivers.
Figure 1. The relationship ii = f (Q ) for the Severnaya Dvina River max* ztr av
new the city of Arkhangel sk.
i - on the day of rel2xse of the forecast the edge of the ice ccver is above the
Zvoz village; 2 - the same, below Zvoz villzge.
f-7 7 The debacle process occurs differently frca yesr to year, ine forecast release
tends toward the timn of peak onset or^ the flood on small rivers. According to
the data on the distribution of water in the channel system (8) (or by other
aeans), ane calculates the course cf ih1att.r flow rates for the stretch in the
rniddle part of the ice collecting pwt or^ the river. Then the calculated flo~+
rates are averaged for a certain interval of time to the peak (usually, two
r-7 or three days, including the peak day). Ihe relationships Emax. zgr f(Qav)
were obtained by the descriptive method for the Velika River nenr the city of
Pskov (5) and for the Severnaya Dvina River near the city of Arickangel'sk (Figure
1). We note that the selected mcment for issuing the foreeast is insufficiently
homogeneous from year to year with reupecz to the ice situation. Therefore,
one must additionally take into account, far example, the position or' the debacle
front or the strength of the ice cover on the day cf compiling the forecast in
the form etf a third vwiable,
The sciution to this problen for zones xhere the abutmen$ of reservoirs
wedges into the piver, on the one hand, is chiefly complicated due to the
varying p~e-fhsd developmerii, and, sn the ocher nand, is ficilltated Seceuse
of the vlnual repetitinn of the phenonenon. The diagram of the solution to
the problem is the follorging. One of the existing netbods predicts Eiow szte
Bay. For the condition of an open channel, a curve of %he flow rate of water is
established in the form of a function of three variables Q(H, Z), rqhere Z is the
water level in the central part of the reservoir. According to the precalculated
flow rate Qav and the level Zini observed on the day of compilirlg the forecast
with the aid of finction Q(H, Z) , one finds the level according to the observation
statian in the area where the abutment wedges in which exists in the absence of
an ice cover 'ini ) Finally, one constructs the following empirical
relationship Qav
H =r(s ,z ma, ztr
Q,
ini
Figure 2. The relationship H = fm 9 Z+qL for the upper. part or" the max, atr Q,, --
Kaunass reservoir near Birshtonas village.
The open circles shox years uhen an ice neck existed near Birshtonas village at
&he Lime o? forecast issuance,
Far exaple, such a relationship was obtained Tor the area of abu'cmsnk
wedging of the Kaunass reservoir on the Neman River - Birshtonas village
stretch (Figure 2).
In same cases, the magnitude of khe anticipated level H is sig- max, zLr
nificmtly influenced by other factors that hwe still not been taken into
account, primarily the residual iqinten ice jans 2nd coaling at the time cf
debacle,
In regions with u~stable Winter weather, the river freezes and thaws
several tilles in certain years. The debacle usually does not encawass the - entire river at the same time, but only a certain stretch of the river. in
-7. places where the debacle front hts stabilized in wxnter, ice barriers remzin
in the river channel on the shores. In r'reezifig, they create additional ob-
sheles ts ms3tement -of the debacle front, At the location of the iginter ftr;si--
dual ice jm the thickness of the Spring ice jam increases. One can approximately
estimate the effect of the residudi ice jam by the magnitude of trje initial level
at the point of observations H. ie the level on tine day of compiling the xn;' forecast. During this process, he forecast relationship vill have the fillowing
form for the river in the case of the prtsenee of an additional series or" ob-
servations
and in the case of a short s~ries of observations (taking into account non-
linearity of the relationship bet~~een H may, zky md Q 1 av
whekqe E is the level that correspolnds to the i'lor; rate Q aieeordi~g i;s tile
Qav 8V
curve $(h) ; ci and 5 are parameters.
Similarly, for zones where the reservsir abutnent wedges in,
~gh~re GZini is the drop along tke length of the raservcir on the day of -iss~ip+;
L P - bne forecast (the level differential 1. in certain reservoir cii;tnnels, the drop
value 6Zini itself, being a function of the flo:g rai;= r;! as.d the ma-k l*:,.ater
at the ba~ z, fluctuates within q~izz sigcificat liniks. havnng -- . pio&t?d
r\, -%f
the eurva of flow ratas Q(H, Z) in the function 62 ='f(Q, Z), it 5s not dFffi-~lt
tmd to obtain the valbe of drop according to the difference 6Z - 6Z- when ne12-
ini ini
essary, Zki.s drop is due solely to the residual ice Jan.
We note r,fist preeiction relationships of the -Ly$;.e (4) have bsen es-tablisf:ed
2"cir the Dnestr River near &l.logilev-?odoit skiy city and at the Ky~enic pgt , rihlle
the type (6) has been established far the abutmen-l vedgi~g zone oZ the Duboss2rsk
reservoir ( the cities of Rybnitsa and Rashkov) .
The debacle of large rivers is a prolonged process during :~hicl! eo~li3g f!.oa
CC
P1? a?. air te~perature of -4, -6OC and ic:.~or ezq occur. ina debacle g~adiualiy siahrs
and then totally cfases because of frcnt movement. In the halting ooir,t of
%d r,
edge of the iee cover, the naximun ice jan level additiccally rises 100 - 153
cm on the Dnestr a~d Nerna~ Ri-~ers, and can drap belosi t;lis spct (by Ffi ,G - P";I? ~cm),
It is at present difficult ta say where the debade front will in fact halt*
Local methods of short-term forsoasts of the ice jam maximum water levels
have been developed for 11 stretches on four rivers (the Velikabra, the Neman,
the Severnaya Ilvina and the Dnestr). Investigations are being carried out on
the Low water reach of the Yenisey River (the Turukhansk-Ust '-Port stretch).
Depending upon the size of the river and characteristics sf its aqueous regirne,
the average timeliness of the forecast fluctuates from 1 - 2 to 6 - 8 days ad
tne accuracy criterion s ranges from 0.35 to 0.70.
0- A
1. Berdennikov, V. P. Dynamic Conditions of the Formation of Ice J
Rivers. "Tr. GGI", 1954, No. 110, pp. 3 - 11.
2. Bulatov, S. N. The Question of Melting of the Ice Cover of Rivers and
Reservairs. "Tr. GGIR, 1970, No. 49, pp. 14 - 29.
3. Liser, I. Ya. ilesenniye zatcry lfda na rekakh Sibiri. (Spring Ice Jams
on Rivers of Siberia). Leningrad, Gidrometeoizdat, 1967. 104 pages.
4. Metodicheskiye rekomendatsii po sostavleniyu qfKataloga zatornykh i
sazhornykh uchas tkov rek SSSRH . (Methodological Recommendations for Compiling
the "Cktalog of Ice 3 ed ad Ice D eb stretches of Rivers $a $he USSRtP).
Leningrad, Published by GGI, 1971, 44 pages.
5. hiezhikhovskiy, R. A., L. K., Nekipelova, G. V. Ardasheva. Forecasting the
Maximum Ice Jam Le~rel of the Veiikaya River Near the City of Pskov. "Tr. GGIu ,
1971, No. 193, pp. 108 - 118.
6. Nezhlkhovskiy, R. A., N. P. Sakovskaya. Forecasking the Maximum Ice Jam
Level of Water in the Severnaya Dvina River Near the City of Arknange18sk.
"Tr. GGI", 1972, No. 197, pp. 68 - 83.
7. Nezhikhovskiy, H. A., G. V. .kdasheva, N. P. ~&ko~ska~;i. Forecasting
Maximu Ice Jam Water Levels in the Dnestr Rivzr on the Hllogilev-Podolfskiy-
Dubossary City Stretch. "Tr. GGIu, 1973, No. 218, pp. 9 - 43.
8. Posobiye po kratkosrochnp prognozam pavodochogo stoka rek, (A Nanual
on Short-term Forecasts of River Flaod Flow a Leningrad, Cidroroeteoizdat ,
1973, 148 pages,
9. Shulyakovskiy, I;. G. Conditions or^ Formation and the Possibility of
Forecasting Ice Jams During 3i.6er Debacle. "Tr. koordinatsionnykh soveshchaniy
po gidrotekhnikeH, 1970, Ho. 56, pp. 13 - 211.
PREDICTING ICE JAM WATER LEVELS ON TW LEE15 HVEE
By: A, Se Rudnev
(The Yakutsk UG1dIS)
Ice jam formation on the Lena River is a characteristic featux-e of the ice
regime of this river. The thickness of the ice jms fluctuates from year' to
year and along the length of the river within broad limits (3, md others). .
The elevated ice jam frequency of the Lena River is due to the heterogeneity of
ice thickness and to the change in morphometric conditions along the length of
%he rE"j~ex"~
The wave of the Spring flood, in forxing in the south of the river basin,
moves downstrea~~ encountering a more and nore solid ice cover in its pathrqay.
The ice cover is predominantly broken up under the ~2echanieal action of the
large mass of wa tsr .
The formation of ice jzms 021 the Lena 3iver tends toward certain locations -
foci of ice jan formation - which are located, as a rule, on stre-iches that are
characterized by reduced slope steepness (at the open stretch-rapids confluence),
a sharp change in the directian of the channel or its fai-way, by widening or
consstructiorr of the main channel, as well, as the appearance of channel fom-a-iisns -
islands, shoals, bars, and holes. A change in channel morphology on any particular
stretch of the river resuLts in a sharp change in the f4o~ velocity regime, anb
consequently, in the tr~ssporting capacity of the river, In this case the capa-
city of the river also changes, diminishing in places where the channel branches-
off into a number of secondary streas an6 an stretches where there are sharp
bends in Lhe ehmnef.
The flood %j;ive, in :gashing against the riTv.erts ice cover, transports a large
mass of ice to the ice jam for~ation focus, where the unbroken ice cover is
usually preserved, On the approach to the focus of ice jam formation, the ice
gradually fills the entire free surface of the water, after which the ice begins
to pack and forn Layers. The sr?as"iiratensit.e ice fragmenzka"tio (~abv-irausly occurs
in that part of the channel where the greases& drop in levels 6s noted at that
ti~e and .,.ahere the Slow velocity has i"t saximu~ values* The increase in xater
level resulting from the head caused by -k"n short-term reductiorl in ice packing
continues simuitaneously with accwulation of ice in the jam, This leads to
ice advznces into the jam, Still further ice packing occurs because o-the
advances of ice, %he ice mss increases, the free ~_ross-se@-l;ian of the channel
builds-up into several layers. This causes an additional elevation in water
level zbove the ice jar, (3, and others). .
The cited descripti'on of ice jm formation is not typical .Tor the rivers
of Yakutiya alone. In this regard, it is appropriate here to cite some genpral
conclusions dragn by Ye. G. Popnv ~qhich are specifically arid fu:liy spplicable
ta tth Lena River: @TZlj,s obvious mechanism sf bex~~;1apment and autoliquida";ir>rcstia~
of ice jamas wi..$hia its general outline, ac-luaiky represents in each specific:
case an exceptionally complex and theore"iic;afly ursduplicatable system of
i~teraction of forces aqd factors srhich it does nc t seem practically possibis
to take into accountu. And further: "Various combinations introduce a sig-
nificant element of chance into the locations of jam formation and the rising
height of the level which they cause. The indicated circumstance deprives one
in many cases of the possibility precisely to foresee these two impartant
characteristics of the ice jam" (2). The random nature of the phenomenon
worsens the inconstancy of the locations r~here ice jms form, a fact to which
i. G. Shulyakovskiy paid attention in pointing out that !'on a morphologically
homogeneous stretch of a river, among the many stretches of transition from
rapids to operl waters, there are also others where the farmatian of an ice jam -
is equally probable because of hydraulic, morphological, and eliinatic condi-
tionsgs (5 3
A large r,umber of foci of ice jam formation (about 180) have been identified
on the Lena River (see the drawing), where Shulyakovsltiy's referenced opinion
is confirmed, as never before, with respect to the possibility lor" appearace
of 2qually probable conditions for the formation of an ice jam in several foci
of jam formation. Obviously, on the strength of this hct, the fr9quently ob-
served movement of' an ice jam from one ~OCW to another also occurs with brief
halts at any one of the aforementioned locations. If one takes into account that
the distance between the identified foci of ice jam formation on the Lena River
comprises an average or" 20 - 25 km, and the length of the stretich of ice jun ice
accumulation in the case of thick ice jams reaches 170 - 180 km, then the cause
of the annually observed intensive rise in water level at the water monitoring
stations during the river debacle becomes comprehensible.
Despite the fact that ice jam for~ation has been studied by many invlsti-
gators, until now there have been no generally accepted schemes far calculating
and forecasting ice jam levels. The meritas and shortccmings of the different
methods of determining the arlnual values of' ice jan rises in water Level have
been examined in sufficient detail by M. A. Zhukova (1).
We shall point out that the maximum annual levels in the mFddle and lower
cocrse of the Lena River pertain to its debacle period. This makes it possible
to consider both the ice jm maxima and the niaximum levels homogeneous, iae*
those that are observed during the debacle, since the latter, like the ice jam,
causes an additional rise in water level as the result of construction of the
free river cross-sections by ice.
Analysis of observation materials obtained in the period of Lena River
debacl~ demonstrated the possibility of using the water level irarnediately
before the ice movement zs an indirect characteristic or" the readiness of the
river's ice cover for debacle. It was noticeable that high water levels
imediately before ice movement correspond to the best readiness of the ice r'or
debacle and the thinnest condition of the for~ed jms. At prec:isely the same
tine, when water levels are low before ice movement on the Lena River, ice jams
of varying thickness are possible:
a) significant thickness, if the ice formed during high ;~ater and the
Winter was a severe one;
S) then, if the ice formed at a low water level ad the Winter i~jas a mild
oneB
A map diagram of ice jam formation foci an the rivers of Yakutlya. 1. - ice Jan;
farmation focus.
Key:
1 - th~ tap%ev Sea
2 - the Ea~"i^Lern. Siberian Sea
3 - baabar
4 - Saskylakh
5 - Ofsnsk
6 - 0lenek
7 -. Sukhana
6 - Zhigansk
9 - Piarkha
10 - Vi3 yuy
Il - Nyuya
12 -.-. Oleki~insk
13 - Vilyny~.sk
Ih - Yakutsk
15 -- Sinyaya
I6 - Vuyqa
l"7 - Ofekma
18 - Tinpton
continuation of key for diagram on p. 92:
19 - hga
20 -- Tommob
21 - Ustv-Maya
21a - Maya
22 .- Lena
23 - Kyusyur
24 - Dzhangky
24a -. Yma
2% - Vorsplbnt~ov~~
26 -. Ymsfc
27 - ddycha
28 - Bldm
29 - Indigirka
30 - Us%?-Nera
31 - Moaa
32 - Ozhogina
33 - Srednekolpsk
It seemed possible to use the water level irrsnediately before the ice movement
as an indirect characteristic of the water level during this time and as ;in. arbi-
trary reckoning measure during the determination of the ice jam rise in the water
level. The ice jam level rises on the river Lena AHZ were calculated as the di-f-
ference between the rcaxinum ice jm level H and tlie level imediately before sax, Z ice movement H H. pee
With respect to the thickness cf the ice Jans, then the typification of ice
jams (31, suggested befire by the authors, was used as its charzcteristic, In
accordance with this typification, an ice jan of the I type (the blind ice jam)
is thickest. The moderately thick ice jm is of the I1 type (the dm-jam) and
the thin one is ul ice jam of the III type (the plug ice jam),
Each tyge of ice jam corresponds to a certain value of water level increase
in the river, which is the greater, the thicker the ice jam. The excesses in
maximum ice jam ~qater level were divided into three gradations according to the*
magnitude: Lhcse with a Pequency of less than 25%, those whose frequvrncies
zqange from 25 to 75%, and those greater thzq 77%. It is conventionally assumed
that ice jam level rises igith a frequency or" Less than 25% we caused by 1 type - jams; ice jams with a frequency raging from 25 to 75% - LI type janis, and those
%hose frequency is greater thm 75- 111 type ja~s. The average value OH,,
has been calculated for each of these groups of ice jam water level rises.
The forecast of the highest ice jam water level is compiled zfter carrying
out aviation reeonnai.ssance of the ice condition of the Lena River in its debacle
period. Having established the type of formed ice jam, one determines the
possible magfiitude of the highest ice jam later level at the closest water
monitoring station by means of adding HH*, AHav. This pertains to the
L
monitcring station located above the ice jam which corresponds ta an ice ja2 of
the established type.
1. Zhukova, M. A. The Question of ijetemining Ica Jam Rises in Water Level.
"Tr. koordinatsionnyk;? soveshchaniy ps gidrotekbaikew, 1970, No. 56, pp. 129 - l38.
2. Popov, Ye. G. Ice Jams ad Problems 31" CombarLting Them. qtPleteoroiogiya
i gidrologiyaH, 1963, !do. 8, pp. 52 - 60.
-=. 3. Rudnev, A. S. The Typification of ice vTms on the Idens River. "Sb. raboi;
Yzkutskoy Gt4h,Of?, 1969, M3. 2, pp. 63 - 69.
'I. R~dnev, 3. S. Experience in Ccmbatting Ice Jaas an the Lena River. "Tr.
koordinatsionnykh soveshchaniy po gidrotekhikeH, 1970, No. 56, pp. 82 - 90.
5. Shulyako~sk3.y~ L. G. Conditions of Formation and the Possibility of
Predicting ice Jms During Riv~r Debacles. Tr* koordinatsionnykh soveshchaniy
po gidrotekhaike8, 1970, No. 56, pp. 13 - 24.