-1

. .

FISHERIES RESEARCH BOARD OF CANADA Translation Series No. 1517

• ••■ `-f.. Investigation of water masses of continental water bodies by statistical methods with the use of EDP.

By N.V. Butorin and N.P.. Smirnov

Original title: Issldovaniya vodnykh mass kontinental'nykh - ' vodoemovstatisticheskim metodom.s isporzovâniem EVM. - From: Khimizm vnutrennikh vodoemov i faktory, ikh zagryazneniya i samoochishcheniya (Chemistry of inland waters and factors of their pollution and self-purification), : 86-99, 1968.

Translateu by the Translation Bureau(AM) Foreign.Languages Division' - Department of the Secretary of State of Canada

Fisheries Research Board of Canada Freshwater Institute Winnipeg, Manitoba 1970 .

24 pages typescript .r , f. • i s-/7 • DE'PARTMENT OF THE SECRETARY OF STATE SECRÉTARIAT D'ÉTAT TRANSLATION BUREAU BUREAU DES TRADUCTIONS FOREIGN LANGUAGES DIVISION DES LANGUES DIVISION CANADA ÉTRANGÈRES

TRANSLATED FROM - TRADUCTION DE INTO - EN

Russian . - English

AUTHOR - AUTEUR

Butorin N.V. and N.P. Smirnov

TITLE IN ENGLISH - TITRE ANGLAIS Investigation of water masses of continental water bodies by statistical methods with the use of EDP Title in foreign language (transliterebe foreign chametera) Issldovaniya vodnykh mass kontinentallnykh vodoemov statisticheskim metodom s ispollzovaniem EVM

RÇFRENCE IN FOREIGN 17 ANGUAGE (NAME OF BOOK OR PUBLICATION) IN FULL. TRANSLITERATE FOREIGN CHAIRACTERS. • REFERENCE EN LANGUE ETRANGERE (NOM DU LIVRE OU PUBLICATION) AU COMPLET. TRANSCRIRE EN CARACTERES PHONETIQUES.

Khimism vnutrennikh vodoemov i faktory ikh zagryazneniya i samoochishcheniya.

REFERENCE IN ENGLISH RÉFÉRENCE EN ANGLAIS Chemism of internal bodies of water and faetors in their pollution and self-cleaning.

PUBL ISH ER - ÉDITEUR PAGE NUMBERS IN ORIGINAL DATE OF PUBLICATION NUMEROS DES PAGES DANS Not available DATE DE PUBLICATION L'ORIGINAL

YE'A.R ISSUE NO. VOLUME 86-99 EE NUMÉRO PLACE OF PUBLICATION Anti NUMBER OF TYPED PAGES ' LIEU DE PUBLICATION çs'-g, NOMBRE OE PAG.ES DACTYLOGRAPHIEES Not available 1968

REQUESTING DEPARTMENT Fisheries & Forestry TRANSLATION BUREAU NO. • MIN ISTÉRE-CLIENT NOTRE D6SSIER NO 1()87

BRANCH OR DIVISION TRANSLATOR (INITIALS) AM. DIRECTION OU DIVISION Fisheries Research Board TRADUCTEUR (INITIALES) Dr. Gregg Brundkill, Freshwater PERSON IREQUESTING DATE CpMPLETED AUG 1 9 1910 DEMANDE PAR Institute, Winnipeg, Man. • ACHEVE LE

YOUR NUMBER VOTRE DOSSIER N° 769-18-14 UNEDiTED DRAFT TRANSLATION • Only for infoiniation DATE OF REQUEST 8.5.70 DATE DE LA DEMANDE TRADUCTION NON REVISÉE Infounation. seulement

505.200-10-6 ( R EV. 2/681 e . o IS1i DEPARTMENTOFTHESECRETARYOFSTATE • • SECRÉTARIAT D'ÉTAT TRANSLATION BUREAU • BUREAU DES TRADUCTIONS FOREIGN LANGUAGES DIVISION DIVISION DES LANGUES ÉTRANGÈRES

. CANADA

CLIENTS NO. DEPARTMENT DIVISION/BRANCH CITY No DU CLIENT MINISTERE DIVISION/DIRECTION VILLE 769-18-14 Fisheries & Forestry Fisheries Research Board Winnipeg, Man

BUREAU NO. LANGUAGE TRANSLATOR (INITIALS) DATE N° DU BUREAU LANGUE TRADUCTEUR (INITIALES) 1087 Russian AM. AUG 1.9 1970

UNI:D;TED DRAFT TRANSLATION 0ny lor information TRADUCTION NON REVISÉE Informaiion seulement

INVESTIGATION OF WATERSASSES OF CONTINENTAL WATT* BODIES BI STATISTICAL METHODS WITH THE USE OF EDP N.V..Butorin and N. P. Smirnov

• The work of Russian and foreign authors has demonstrated conc- lusively that the understanding of "water mass", as the term was defined by A.D. Dobrovollskii (1961), is applicable not only to seas and oceans,

but to large continental water bodies. The distribution of certain phys- ical and chemicalcharacteristics of waters enables the definition within them of water masses, which possess definite physical and chemical prop- erties (Butorin, 1965).

The heterogeneity of the water masses of reservoirs is particularly sharply defined. Thus, in the Rybinsk Reservoir, distincly distinguishable are the water masses of the Volga, Mologa and Sheksna Rivers and that of the central part of this body of water. In general outline, the distrib- ution of thé water masses in the Rybinsk ReserVoir, by season of the year,

Translator's note: The number in the margin refers to the page number of the original text. 2

can be described as follows. In spring, significant regions of the reser-

voir, contiguous with the river areas of the Volga, Mologa and Sheksna,

are filled with Volga, Mologa and Sheksna water masses. In the summer-fall

period the regions occupied by these masses gradually diminish in size,

and in the fall, they can be traced only at their point of exit into the main lake-like body of the reservoir. During these seasons a wide area of

the central part of the reservoir is occupied by a water mass of that name.

In winter the Volga, Mologa and Sheksna masses gradually force out the water mass of the central part of the reservoir and towards the end of winter, they again occupy, along the flooded valleys of the corresponding

rivers, wide areas of the reservoir (Butorin, 1966a).

During the individual seasons significant differences between water masses in the Rybinsk Reservoir can be readily observed even in

limited areas of the water body. Similar phenomena are noted also in

other reservoirs of the Volga watershed (Edeltshtein, 1965).

A basic problem in the analysis of the water masses of any body

of water lies in correctly distinguishing thevarious distinctive features

of the waters, their qualitative and quantitative characteristics. Its

solution can only be realized on the condition of a valid, physically

substantiated selection of criterea or indices, which must constitute

the basis of the definition of the water mass. A decisive role is also

played, at this point, by the selection of a principle for the definition

of a water mass. •

For the definition of water masses in fresh bodies of water, as

it is with marine bodies of water, it is customary to utilize the physical and chemical characteristics of the waters. In different seasons at some

of the bodies of water, it is sometimes possible to establish the distri-

bution of the water masses by as little as one or two indicators, such as,

for example, by the concentration of carbonates and temperature (Schmalz,

1932), turbidity (Atkins and Jenkins, 1955; Ziminova, 1963), the concen-

tration of sulphates (Schrader, 1956), colority and transParency (Fort-

unatov, 1953) and electroconductivity (Kazarovets, 1060). However, the.

possibility of distinguishing water masses in this manner presents itself

extremely rarely. At the present time we are not aware of any one index

or a group of fully définitive indecies, which would be common to fresh

, water bodies and which would permit a direct characterization of their

water masses. •

Up until the most recent times we.utilized, for the definition

of the water masses of Volga River reservoirs, methods borrowed from

oceanology. These methods are based on the analysis of the horizontal

and vertical distribution of the individual characteristics of the medium.

Thus, the basis of one of these methods consists of the analysis of the

spatial distribution .f the magnitudes of the most representative index.

In this method, the boundary between water masses coincides with the line

of the maximum gradients of the given index. Another method permits the

simultaneous utilization of two indicies. It is based on the construction

and analysis of curves of the ITS' type, and triangles of mixing. The

delineation of water masses in this method is Carried out along lines of

their 50% mixing (Butorin, 1966b). Despite a number of positive results which accrue from the application of the methods indicated for - the definition of the water . masses of Volga reservoirs, their utilization is accompanied by defin-

ite difficulties. For example, in utilizing theinethod of.maximuM grad-

ients, the probability is very high of,cases in which the lingesèfièic-..

aration between, a number of fully representative indicies do nOt coin-

cide spatially. In such cases it is difficult to giVe prèference to one

or another index and the selection:of one of them for the delineation

of the water masses becomes, to a certain extent, a subjective matter.

Where regimes are unstable and in the shoal waters of reservoirs, diff-

iculties are encountered also in the definition of.water masses by type .

ITS' curves, due primarily- to the wide scattering of points, caused both.

by the seasonal variability of indicies 'as well as their unequal repre,

sentability. All'this leads to a certain indefiniteness in' the drawing

of boundaries between water masses. Further,.the methods . indicated do

not allow for an'evaluation of the degree of reliàbility , in the results

• of the definition of water masses. .

From the very meaning of the term water mass it follows, that

it ià most logiCal to define the water masses- of any body of water in

the light of the whole complex of the various indicators of the State .

the mediuM. However,to take seVeral indicators into account at one of

time, for this purpose, is ustially a difficult process, inasmuch as they

all have different units of measurement and degree of variability'. For this reason it is first essential to be able'to express the values of

the indicators in the one system of units. For this it is possible to

to utilize.the method of the standardization of characters (Sokol and Sueath, 1963). The substance of this method consists of the fact that the values of this or that character are examined in the form of a stat- istical series of independent variables and are transformed by the formula

where x is the numerical value of the index; 2 is the mean of the series;

6 is the standard deviation and Si is the standardized value of the index. One of the first attempts at applying the method of the atandard-

ization of characters for the definition of the water masses of shallow e bodies of fresh water, was that of M.G. Ershova (1968). Taking into account that the accuracy of the measurements of the various indicators varies sig- nificantly, Ershova, in ca1cu1atingIS2, introduced a compensating coeffic- ient which depended on the accuracy of the measurement and the degree of variability of the series of the conformable index by which the values of /88 sSi t are multiplied. The formula for the calculation of this coefficient is K 4 T where T is the doubled error of the determination of the index, expressed as parts of the mean (x) 1 , and Cv is the coefficient of the variation of the series. From this formula it will be seen that if the coefficient 'of variation'is fundamentally linked to the accuracy of the determination of

the indéx (T —*Cy), then the value of this index will be very small (K...0) and its specific influence in 'the comparison of characteristics will be insignificant.

1 .Asindicatedbytheresultsofourresearch,thecoefficient•isKp too rigid as a result of the little-substantiated doubling of the error in the determination of the index T. For this.reason, in subsequent employment of the method indicated, T should be taken to be as imply the error in the méasurement or the determination of the index. The whole expression for the calculation of the standardized value is therefore written in the following form

2:1(1 __I) 0 C •

As for the degree of variation 1 dt of any two points In' and IM 8 for a complex of characters, it will be characterized by the expression

d = (S„ — + S where 1 is the number of indicators utilized.

In this way, the employment of this method permits the evaluation of the differences between water masses at two points by any complex of indicators, characterizing not only the physical and chemical, but also the bdological features of the waters.

In utilizing this method with respect to the Rybinsk Reservoir, we attempted to derive the coefficients of variations:Id t between each station in the water body and ai the others, using six indicators: temp- erature, electroconductivity, hardness, colority and the concentrations of hydrocarbonates and calcium, at the surface and near-bottom horizons, in all the synchronous surveys for the years 1960 to 196h. The solution of this problem, given the large number of stations and their frequent repetition, requires a vast amount of calculation. It -is sufficient to mention that with fifty stations in the water body, it becomes necessary to calculate for 1225 values of Id'. Such a volume of work can be carried

out on the Condition that an electronic computer be employed. With this in mind a program was devised, based on the method described, for the electronic computer BESM-2 m, on which the appropriate calculations were

then carried out 2

2 The program was set up by P.S. Gasyukov, to whom the authors empress their appreciation. Programmed into the computer was information on the length of the series (number of stations), the number of indicatore employed, the doubled accuracies of their determinations and series of values of the indicators themselves. The computer print-outs consisted of the values of the coefficients idt - the differences between the water mass at each station and all others, for the entire complex of indicators, the mean value of each characteristic for the whole body of water, the standard deviation, the coefficient of variation and the standardized values of the characteristics.

In the first phase analysis was carried out on twelve surveys, conducted in 1960-1961. Table 1 presents the number of stations in the survey and the accepted accuracies of the determinations of the elements, as well as the mean values of the indicators utilized, for the entire body /89 of water, and the values of te .and lav robtained from an'analysis of four surveys carried out in various seasens during the 1960-61 hydrological year.

The data in this table reflects well the seasonal variations of

the indicators of the waters of the Rybinsk Reservoir and their , statis- tical characteristics. As it can already be seen from the table, the greatest heterogeneity of the waters of the reservoir.are observed in the spring period and their greatest homogeneity is characteristic of the fall-summer period. The results of the analyses of the remaining surveys cohform well with the data presented.'

Prior to going on to the definition of the water masses of the

Rybinsk Reservoir with the aid of the coefficients of variations Id',

Table 1 Mean values, standard deviations and the coefficients of variation from data of surveys carried out in various seasons of 1960-1961

. •. : : •. • :Accepted . May, Indicators 9 M 160 : 9 28 July, 1960 : 4 October, 1960 : 14 November,1961 :accuracy : •. •. . . . .• : . . •. •. :of deter- Mean : « : Cv : Mean : 6 : C • Mean : 6 : C : Mean : 6 : C :mination V • V V • . • • • . : .• :of indic.

Temperature, °O : 5.61: 2.44: 0.43: 23.71: 0.44: 0.02: 9.03: 0.53: 0.06: 0.15: 0.17: 1.09: 0.01

Electroconductivity:157 : 57 : 0.36:161 : 19 : 0.12:170 : 30 : 0.18:194 : 29 : 0.15: 0.03 micro-Siemens/cm

Concentration of : 1.39: 0.52: 0.38: 1.40: 0.21: 0.15: 1.44: 0.35: 0.24: 1.64: 0.28: 0.17: 0.01 hydrocarbonates, mg-equ/1

Hardne5s, mg-equ/1 : 1.65: 0.56: 0.34: 2.15: 0.26: 0.12: 2.16: 0.31: 0.111:2.38: 0.38: 0.16: 0.01 Concentration of calcium, mg-equ/1: 1.22: 0.41: 0.33: 1.34: 0.13: 0.10: 1.51: 0.25: 0.16: 1.72: 0.25: 0.15: 0.01

Colority, deg. : 38 : 14 : 0.37: 26 : 7 : 0.28: 30 : 4 : 0.14: 38 : 15 : 0.39: 0.12

No. of stations : h5 : 60 : 54 : 39

OD 9 derived from the analyses, it is essential to solve the problem of the selection of the criteria for the values of Idl, that is, to determine the magnitude of the "variations" of characters which would be sufficient to ascribe the water masses at two points to different cpmplexes.

We will examine this problem in greater detail. Let us assume that we have an aggregate of points characterized by only. one indicator. Let us accept as significant euch a variation of the values of the indicator as would satisfy the probability of random deviation from the mean of the whole complex, equal to 0.01, that is, a probability, normally acceptable in mathematical statistics, sufficient to ascribe a point to another com- plex. A variation of values of the indicators equal to 2.6d complies with this value of probability.

Bil =xn= 2.6.

We will convert this expression in the following manner:

x • 2. fia =_- a a- •

In the event that K= 1, /90

Ç and a .n'

.Then

(S.— Sm ),„ =-- 2,.6 and d..= (S S =(S S„.)-= 2.6.

Now let us take the aggregate of points characterized by two independ- ent indicators. The probability of random deviation for one and the same value for both proper -ties will be equal to the product of the probabilities 10 of the random deviation of each of them for this value,

P • • • • '

If '131,2 ' is taken, as in the first case, to be equal to 0.01, then the significant variations of the values for the indicators will be equal to 1.76. If

TO clau =----\/(S„—,.9„ig+ (S.— S \ 1(1.7)2 + (1.7)2 =2.4.

Considering, in the mame way, the case. of a complex characterized by three independent properties, we derive a d. 2.2 and four • a. d=-- 2 .0 . • •

In praCtice, it is very seldom, in the hydrological research of continental water bodies, that it becomes necessary to deal with.more than three or four'independent indicators characterizing the State of the water masses, and for this reason, with a certain error in the'selection of the criterion of.probability, Id' can be taken to be from 2.0 to 2.4.

However, in the analysis of the Water masses of the rn of the Volga we utilize a complex of characters among whiph are several which depend on one another, and in this instance Kp yi 1.

In - this case the formula for the calculation of le in its general form will be written in the following manner:. '

p. 11-1 (K p) V 11

where lut represents the value of the excess over tol, and which must. be selected depending on the number of independent characters Its that are utilized in the analyses (t=2, u=1.7; t=3, 11=1.31 t=4, u=1.0), and on the condition that 9,0.50. In order that the role of the dependent characters may somehow be taken into account in the determination of tut, the establishment of the number It' can be carried . out by the following formula:

1— t t = to + (1 — r) o:

where to is the'number of truly independent characters, and r is the coefficient of correlation between the dependent characters. However, with a certain error in the direction of understating

the probability of the .random derivation of 14Se! it can be taken that

Having calculated 'dui, in accordance with the analysis of the • given twelve hydrological surveys'ef the Rybinsk Reservoir, utilizing the characters listed earlier, we derived the mean value oe,..= 2.4*0.3. /91 With the probability . of random excess lying within the limits of O.0-

0.01, this mean value of Idj can be accepted as significant in ascribing two stations to different water masses, in all samplings of the Rybinsk Reservoir, regardless of the season of the year. ey way of an example of the use of the statistical method indic- ated, for the definition of the water masses of the Rybinsk Reservoir,

let us examine the results.of thé analysis of four synchronous samplings carried out during various hydrological seasons during the course of One 12 hydrological year. The mean values of the indicator characters, the standard deviations and the coefficients of variations for each indiv- idual.indicator in' the survey are presented in Table 1. •

As it has been shown, the value of 2.4 should be accepted for the criterion of the significance of Ids, that is, it can be assumed, with a high degree of probability (0.95-0.99) that with the variation Id' throughout the complex of characters equal to and greater than 2.4, the stations under examination belong to two different complexes or to two different water masses.

The examination of the results of the analysis of the materials taken during the synchronous surveys is best started in the spring per- bd since, as it has been demonstrated earlier (Fishing Industry Atlas,

1963, Butorin, 1965, 1966a) and as it can be seen from the data in Table 1, it is during this period that the greatest heterogeneity of the water masses of the reservoir is to be observed.

In previous studies (Butorin, 1965, 1966) it had been established that, in spring, the areas of exit of thé main river flow into the reser- voir are filled with the water masses of the corresponding rivers. For this reason Station 1 in the Vega flow, Station 36 in the Mologa and Station 23

In the Sheksna were taken as base line stations, characterizing the water masses of the corresponding rivers in a more or less pure'form. Then, from these points (fig. 1,a) lines were drawn, with the values of ids inscribed on them, to the entire aggregate of stations àdjacent to the base line stations. In cases when the value Id' between two stations under study would be less than 2.4, it was considered that they were situated in 13 one and the same water mass. If however, Id' was more than or equal to 2.4, then it would be considered that the water masses at the two stations were different.

As a result of this treatment, as can be seen from fig.'1, it was possible to clearly distinguish the regions with specific water masses, from a complex of properties. Relative to this, it was found that the variations fdl for the river waters and the waters of the central part of the reservoir reach values of 5-6. By virtue of its greater value of WI, the survey centre of the waters of the central part of the reservoir was established at Station 14 (fig. 1,b). The analysis of the magnitudes of Id' at Station 14 with the entire aggregate of surrounding points, enabled the definition of the nucleus of the water mass of the central part of the reservoir, which by its porperties, was most sharply distinct from the water masses of the rivers. During the summer period, as it can be seen from fig. 2,a, the study sampling did not make it possible to define the water masses of the Volga and Sheksna in the areas in which the observations were made, and only at Station 36 and 37 was there a sharp identification of the water of the Mologa River. During this period a large part of the reservoir was filled with the transformed waters of the spring high water, quite homogeneous throughout the basin of the reservoir. No nucleus-of waters, with sharply distinguishable properties, were observed in the central part of the reservoir during the period of this survey (fig. 2,b). The high degree of homogeneity of the waters of the reservoir in the summer of 1960, and the lack of Volga and Sheksna river waters 5

in the vicinity of the exita of the corresponding flows, is apparently

linked to the exceptionally small summer rUn- off, which in the case of -

the Volga, consiated of only 0.2 km., . - •

In ,the fallthoUgh, not only are the river waters of the Môloga

clearly distinguishable, but also those of the Volga, which are obser-

vable even in the region:of the Shumarovskii Islands (fig. 3,a). This

is a result of the fact that during the fall period the Volgalncreased .

its . flow significantly, which consisted,'in September-October, of 1.9 kM3 :

A large part of the reservoir during this season, as in summer, was filled

with a relatively homogeneous wster mass (fig. 3,b).

In winter the heterogeneity of the water masses of the Rybinsk

Reservoir again increases. Regretably, material on winter observations

is extremely limited. Thus for example, in February 1961, no sampling

was carried out at the stations of customary synchronous surveying in .

the region of the exit into the reservoir of the Mologa River flow, and

the same was true at Stations 1 and 2'in the Volga River flow. Since we

did not have the material for this survey.from the base line points, we

were unable to define the Mologa water mass in the Mologa flow, and with-

respect to -the Volga water,'we were obliged to designate Station 3 as the

baseline reference station.(fig. 4). This,•evidently, had an influence in widening the range of distribution of these two masses and, further,

had an adverse effect, as will be seen later, on the evaluation'of the

statistical validity of their definition for the winter period (Table 2).

In Figure 4,a it can be Seen that the Volga water mass, in February

of 1961, occupied a.Significant area of the reservoir and its boundary With 5

the water mass of the central part of the reserVoir - can be traced quite • clearly. The considerable increase in the vOlume of the, Volga waters.in winter, by comparison with the preceding season (fig. 4,a), is explained' -by the heavy winter run-off of the Volga, which., for the period November, 1960 to March, 1961, consisted of 7 ..4 km3 , that is, 15 times in excess of the summer, flow and 1.7 limes that of the fall. During the winter it was found possible to . alsO define the Sheksna .water mass. Despite the fact that the winter run-off of the Sheksna was . smaller than that of the summer and fall, it was clearly distinguishable in the region of the reference statien, 4,e . It is meat probable • that'this is promoted by thelaek of a wind mixing.action on-the waters in the winter period, as à result of which .the river water masses are more clearly defined than in the summer-fall period, and have sharply expressed boundaries with the water mass of the central part of the reservoir.- This is particularly clearly visible in Figure 11.,b. In winter, as was'the case with the spring period, it waS possible to distinguish the nucleus of the waters of the central part of the reservoir with their sharply expressed properties,forming and receiving its greatest devel- opment as it does, precisely during this . season.

In this way, with the aid of the method under study, it is possible, in all seasons of the year, to define the river water masses in the Rybinsk Reservoir, associated with the regions of entry of their parent rivers, and the water mass of the central part of the reservoir, in which, in

winter and in the spring, a sharply expressed water nucleus is observed. The .results, derived by the statistical method, confirm, in general, the 16

Fig. 1. Diagram defining the water masses in the Rybinsk Reservoir in the spring. a - River water masses; b Water mass of the central part of the reservoir. 1 - Volga River water mass; 2 - Mologa River'water Mass; 3 - Sheksna River water mass; 4 - waters of the Ukhra and Sogozhà Rivers; 5 - Nucleus of the - waters of the central part of the reservoir; 6 - Numbers of the. reference stations. 17

Fig. 2. Diagram defining the water masses of the Rybinsk Reservoir in the summer.

Legend same as in Fig. 1. ;

23

a

ti • il 3s ibr ,Se

Fig. 3. Diagram defining the water masses of the Rybinsk Reservoir in the fall. Legend same as in Fig. 1. r

19

g, %IL veit,wie

%.WM1 MAIO» UM», lelbelL1%.

Int\ I • Sae° II 3N.. 1

Fig. h. Diagram defing the water masses of the Rybinsk Reservoir in the winter.

Legen same as inirig. conclusions with respect to the presence and distribution of water masses in the Rybinsk Reservoir which have been arrived at through the use of other methods (Butorin, 1965, 1966).

In order to demonstrate the statistical reality of the variations of the characters of the water masses defined by us in the Rybinsk Reser- voir, we made use of the t-distribution (Student distribution) for a case of the comparison of the means of two independent samples (Bruks and Karu - zers, 1963) *. The null-hypothesis in this case lies in the fact that the samplings represent the very same complex, and we wish to evaluate the significance of the variations which exist between their means. If 'n1' and In2 1 constitute the scope of these two selections, and

8 141' and 1142 1 , their mean values, then

M, -- M 2 t ' 0 n 2 Y n1 • n2 where dris the . evaluation of the quadratic deviation of the complex from which the sampling was taken. In our case 'n1' is the number of stations related to the waters /98 of the central part of the reservoir, while In2 1 is the number related to. the river waters. IM1 1 and 'M2 1 represent the appropriate mean . values of the ,indicators of these water masses. The values of Atel are given in

Table 1. The calculated values of ItI in comparison with the theoretical. values, reflecting the definite probability Of the reality of the null- hypothesis accepted by us, are Presented in Table 2. As has already been indicated earlier, during the summer season in the case under study, we

* Translatorls note: Probably "Brooks and Carruthers". 21 were unable to define the Sheksna and Volga water\masses, and for this reason, for comparison in carrying out the calmulations for • t', we took, for the former, the characteriatics of the' water observed at Stations 23,

24 and 25, and for the latter, those of Stations 1,2 and 3. The same was done for the Sheksna water mesa for the fall period. - As it can be seen from Table 2, in all cases in which we define the water masses in the:Rybinsk Reservoir with the aid of the criterion of variation tdi, with its accepted magnitude of value equal to 2.4, for most of the indicators, and with a probability exceeding 0.05, and in a number of cases 0.01, it can be considered that our null-hypothesis is incorrect and that the water masses that we defined are specifically different; Comparison of the calculated values of Itl with the theoretical also shows that the criterion of sighificahee for ldcwas established sufficiently objectively by us, since in the contrary case (for example, where d<2.14), an opportunity was afforded to define the Volga and Sheksna river waters in the summer period, and the Sheksna in the fall. However, as can be seen from Table 2, in this case we would have had differences between the indicators of'the river water masses and those of the waters of the central part of the reservoir, in the absolute-majority of cases statistically unreliable. The data in this table also show that the more characteristic and conservative indicators of the water masses in the Rybinsk Re'servoir are electroconductivitir, hardness and the concentrations of hydrocarbonates and calcium. The temperature of the water is useful to some extent in this respect.only in the spring period. • •

Table 2

Calculated values of ttl in comparison with the theoretical, reflecting the definite ,probability that defined waters belong to one water mass

. . VoI Fa,„ waters •. Mologa waters . •. Sheksna waters . .• : • .

Indicators : • • • • • • • • • • • : 9 May 28 Jul: 4 Oct:14 Feb: 9 May 28 Jul: 4 Oct:14 Feb: 9 May 28 Jul: 4 Oct:14 Feb: : 1960 : 1960 : 1960 : 1961 : 1960 : 1960 : 1960 : 1961: 1960 : 1960 : 1960 : 1961:

Temperaiure, 0C : 3.13 :0.08 : 0.65 : 1.75 : 4.15 : 0.44 : 0.74 : : 1.04 : 1.46 : 1.2 . : 1.00 :

Electroconductivity, : 2.69: 1.16 :3.62 : 2.71 : 3. J4 :2.33 : 3.43 : 3.41 : 0.72 : 0.11 : 3.43 : micro-Siemens/cm

Concentration of hydro- : 3.15 : 0.83 : 2.76 ; 2.54 : 3.50 : 2.53 : 3.36 : : 3.97 : 0.33 : 0.33 : 1.83 : carbonates, mg-equ/1

Hardness, mg-equ/1 : 2.70 : 0.53 : 1.94 : 1.78 : 3.13 : 2.00; 3.27 : : 3.37 : 0.07 : 0.72 : 2.72 :

Concentration of calcium, : 2.77 : 0.88 : 3.53 : 1.50 : 2.41 : 3.78 : 3.50 : : 3.18 : 1.50 : 0.47 : 3.04 : mg-equil

• Colority, deg. : 2.11 : 1.70 : 2.08-: 2.23 : 3.42 :2.86 : 0.69 : : 3.03 : 1.70 : 2.08 : 0.93 :

Value of t with probability 2.05 : 2.00 : 2.01 : 2.04 : 2.06 : 2.00 : 2.01 : : 2.06 : 2.00 : 2.01 : 2.04 : of null-hypothesis 5:100

Value of t with probability 2.76 : 2.66 : 2.68 : • 2.75 : 2.79 : 2.66 : 2.68 : : 2.79 : 2.66 : 2.68 : 2.75 : of null-hypothesis 1:100

IN) ro •

• 23

All this attests to the fact that the statistical method under discussion is fully suitable for the definition of water masses in the reservoirs of the Volga watershed. The superiority of this method over others lies primarily in the fact that, for the definition of water masses, it permits the simultaneous use of a complex of different indicating prop- erties, and has a statistically substantiated calculational base which enables the evaluation of the degree of reliability of the results. Besides this, it makes possible the application of modern computer technology to the problem of defining the water masses of continental bodies of water. The positive results obtained with the statistical method in the definit- ion of the water masses of these bodies of water afford grounds to assume that it could be employed for similar purposes in oceanology. BIBLIOGRAPHY

Bruks K. and N. Karuzers. » 1963. Primene nie statisticheskikh metodov v meteorologii. (The application of statistical methods in meteorology), State Scientific and Technical Hydrometeorological Publishing House, Leningrad, . Butorin• N.V. 1965. K izucheniyu vodnykh mass Rybinskogo vodokhranilishoha. V sb.: Dinamika vodnykh mass vodokhr. (Contributions to the study of the water masses of the Rybinsk Reservoir). n the review, The dynamics of water masses of reservoirs). Trudy of the Institute of the Biology of internal Waters, Iss. 7. Butorin N.V. 1966a. Sezonnoe izmenenie kharakteristik vodnykh mass i ras- predelenie ikh v Rybinskom vodokhranilishche. V sb.: Plankton i bentos vnutrennikh vodoemov. (Seasonal changes in the characteristics of water •masses and their distribution in the '.4binsk Reservoir). (In the review: Plankton and benthos o internal water bod es . u.yof the institute of

the Biology of- Internal Waters, Iss. • 12.. • Butorin N.V. 1966b. 0 vertikaltnoi neodnorodnosti vodnykh mass.Rybihskogo • vodokhranilishcha. (The vertical heterogeneity of the water massee of the Rybinsk ReserVoir). In the review: Plankton and bent bodies, Truày of the Institute of the Biology of Internal Waters, Ise. 12. • Dobrovoltskii A.D.•1961. Ob opredelenii vodnykh mass. .(Thedetermination • • of-water masses). Oceanology, Ise. 1.. • • Ershova M.N. 1968. 0 . primenenii.statisticheskikh metodov k vydeleMiyu Z2.2 vodnykh mashv vodokhranilishobath.(The employment of statistical - methods in the definition of the water masses of reservoirs). Bulletin of the Institute of the Biology of Internai Waters, No. 2. - • 2iminova N.A. 1963. Kolichestvennaya kharakteristika vzvecei Rybinskogo.. vodokhraniliecha. (Quantitiative characteristics of the suspended matter of the Rybinsk Reservoir). Trudy of the Institute of the Biology. of Internal Waters, Iss. 6. Kazarovets N.M. 1950. frimenenie konduktometricheskogo métoda . k izucheniyu paspredeleniya vodnykh mass Rybinskogo vodokhranilishcha; (The application of conductometric'methods.to the study of the. distribution of,water Masses - in the Rybinsk Reservoir). Bulletin e the Inatitute of the Biology of- Internal Waters, No. 7. •

• Fortunàtov M.A. 1959. Tsvetnoett i prozrachnostt vody Rybinskogo vodo- . khranilishcha kak pokazatelt ego rezhima.. (COlority and tranIparency of the water of the Rybinsk Reservoir ie an indicator of ità regime). Trudy of the . of the Biology of -Internal Waters. Academy of Sciences of the USSR, Institute Isà. 2. • .A tkins .W. R. G. a; P. G. 1enkin 5.7 1955. Identification of Water-Masses by ' . their Suspentled Matter. Nature, v. 175, ,34 4495. Schrader T. 1956. Talsperren. Urania, 11. , 2. • Sek al R. 11. a. Sueat h. 1963. Principles of Nuinerical taxonomy. ,London.