Large Scale Effects of Seasonal Snow Cover (Proceedings of the Vancouver Symposium, August 1987). IAHS Publ. no. 166

The influence of the variability of snow cover thickness on the intensity of water yield and duration of spring flood on a small river

B . M . DOBROUMOV & A - B . SHUKHOBODSKY State Hydrologiaal Institute 2nd Line, V.O., 23 Leningrad, USSR

ABSTRACT The main factor influencing prediction of maximum spring runoff from snowmelt is the uneven thickness of the snow cover over the drainage basin area. Invest­igations carried out over several small plain drainage basins in a forest-steppe zone with a highly dissected surface showed that the use of standard values of para­meters of the distribution of water equiva­lent of snow over a basin may result in large errors in determining water yield duration and intensity, and hence the maxi­mum runoff for a year or for a long-term period. For practical applications use, it is suggested to use statistical relations between the coefficients of variation of the water equivalent of the snow cover and standard meteorological elements such as the average snow depth over the basin and mean water equivalent of the snow cover. Corre­lations between snow cover distribution parameters with respect to different land­scape types are discussed.

Influence de la variabilité dans l'épaisseur de la couche nivale sur l'intensité du débit spécifique et sur la durée de l'inondation de printemps d'un petit cours d'eau

RESUME L'épaisseur irrégulière de la couche nivale à la surface du bassin versant joue un rôle important dans la formation du débit maximal pendant l'inondation du prin­temps. Des recherches sur quelques petits bassins versants de la plaine à steppe coupée de forêts et ayant un relief raviné, prouvent que l'utilisation, dans les cal­culs, de valeurs typiques des paramètres de la distribution de l'équivalent d'eau de la neige dans les bassins peut être accompagnée

254 B.M. Dobroumov & A.B. Shukhobodsky

par des erreurs importantes quand on estime la durée et l'intensité du débit spécifique résultant et par suite dans le débit maxi­male annuel ou pour une période plus longue. En pratique, on propose d'utiliser les co­efficients de régression entre la variation de l'équivalent en eau de la couche nivale et les caractéristiques météorologiques telles que : l'épaisseur moyenne de la neige sur les bassins versants et l'équivalent en eau de la couche nivale. On discute les corrélations entre les paramètres décrivant la distribution de la couche nivale par rapport à divers types de paysages.

BACKGROUND

Within vast areas, the spring snowmelt flood is a dominating ele­ment of the annual streamflow regime. Thus, it is an important factor to be taken into account in designing hydrotechnical struc­tures and water management projects. To do so successfully, there is an ongoing need for comprehensive research to elaborate on and further improve the methods of snowmelt flood computations. The existing practice of computing maximum snowmelt flood runoff for engineering purposes, as given in Standards document SNiP 2.01.14-83 (1985) and other instructional manuals, is based on semi-empirical relations with only indirect accounting of the flood runoff physical process. However, the ever-growing anthropogenic effect on water resources in well gauged areas and the developments within new regions necessitates methods for computing maximum run­off characteristics in cases of non-homogeneous hydrological time series or where logical data are lacking.

A most promising way of solving the above problems is the development of models describing in detail the snowmelt flood formation process, proceeding from the solution of the balance equation of water input and loss within sub-basins or for the whole drainage basin. In such computation procedures one may make use of different descriptions of the spatial distribution of runoff generation factors over a drainage basin.

The main spring flood runoff generation factor is the income of water to the basin from liquid precipitation and from melt of solid precipitation accumulated over the basin during the antecedent period. As a rule the amount of water resulting from snowmelt sub­stantially exceeds total precipitation during the snowmelt.

The snow cover distribution over the basin area is usually highly uneven depending on the local landscape, on the presence and type of vegetation, on the direction, duration and speed of horizontal snow transport by wind, as well as the amount of solid precipitation.

In a general form (not taking account of phase and structural snow modifications) the water equivalent of the snow cover for a*ny elementary site within a drainage basin at time "t" may be express­ed by the following equation:

Snow cover and water yield 2 5 5

wn = w no + / * t p i d t + rQi d t -r%^ -ftf±dt+rEcdt -

Jo Jo Jo Jo Jo

f\dt + Tssidt - A s ^ t , (1)

where: wno is the initial water equivalent of the snow cover (̂fc 0 in case of snow storage remaining from the previous winter period); Pj_ is the precipitation intensity (solid and liquid); Qi and Q0 are the rates of moisture inflow and outflow during thaw periods, respectively (horizontal component); f̂ is the infiltration rate into soil; Ec is the rate of condensation of moisture on the snow surface; Es is the rate of evaporation from the snow; SS^ and SS0 are snow transport by wind to and from the given site per time unit, respectively. Actually, it is very difficult at present to determine snow storage in a basin by measuring the components of the above equation; therefore, simpli­fied methods are applied in practice. According to Kopanev (1971) the basic techniques of determining snow storage over a drainage basin are the following: measurements by snow stakes and precipi­tation gauges, and snow surveys. In addition, in some countries gamma-surveys of the snow cover are applied. Parshin (1953) , Kuzmin (1960), Shpak (1954), Kopanev (1971, 1978) and other authors have provided good evidence that the most accurate way to determine snow storage of a drainage basin is to carry out snow surveys along the snow courses covering the most typical land forms and various kinds of landscapes. Besides this, the statistical treatment of snow survey data suggested by Velikanov (1940) and later improved by Komarov (1959) has made it possible to include in computations and predictions not only the average water equivalent of the basin snow cover, but also the uneven distribution of the snow cover using the coefficient of variation, Cv.

Thus, proceeding from the analysis of snow surveys of 1938-1945 carried out at 23 drainage basins of the forest, forest-steppe and steppe zones ranging in area from 0.11 to 889 km^, Kovzel (1956) computed standard Cv values in relation to basin landscape char­acteristics: 0.15-0.30 for basins with 80-100% forest area; 0.30-0.50 for steppe basins with gentle and long slopes or with 0-80% forest area; 0.50-0.80 for open steppe basins with steep topo­graphy. Kuzmin (1960) summarized previous work and determined the range of Cv of water equivalent of snow: 0.10-0.90 in open localities; 0.05-0.50 in forests. Komarov (1957) analyzed snow surveys for 1939-1954 conducted within the steppe and forest-steppe zones having areas ranging from 6.2 to 892 km^, and concluded there was considerable stability of snow storage within a basin from year to year. This finding made it possible to develop for practical use in the steppe and forest-steppe zones, binomial asym­metric probability curves of water equivalent of the snow cover using standard parameters CS=2CV and Cv=0.45. Later, Kuzmin (1960) gave a similar recommendation for river basins of the forest zone for which 0.23 was adopted as a standard Cv value. Applica­tion of standard values of Cv of snow water equivalent led to

256 B.M. Dobroumov & A.B. Shukhobodsky

developing snowmelt computations where both the average snow stor­age and the uneven snow depth distribution are taken into account. Zhidikov et al. (1977) showed, however, that the adoption of standard values of snow storage in a river basin leads to consider­able error in determining the rate and timing of the snowmelt which results in erroneous values of both the volume and peak maximum flow. In view of the above, it was recommended that the optimal value of Cv should be determined from analysis of data. In studies aimed at the modelling of the spring flood runoff formation process, Kuchment et al. (1986) and MDtovilov (1986) arrived at similar conclusions and in their work along with the calibration of Cv values these authors used empirical relationships for evaluating Cv.

METHODOLOGY AND ANALYSIS

In statistical processing of the snow survey data carried out at Nizhnedevitskaya Water Balance Station from 1954 to 1983 an attempt was made to obtain quantitative estimates of the main characteris­tics of distribution of snow water equivalent over small river basins of the forest-steppe zone as well as their influence on the rate and duration of the snowmelt.

In the region of Nizhnedevitskaya WBS, .snow surveys were made along representative snow courses in 12 basins with areas ranging from 0.05 to 103 km^ and having forest percentages from 0 to 60% over highly dissected relief. According to the data of Dmitrieva (1956) , basin gullies in the River Devitsa compose 7 to 8% of the basin area.

The analysis of the spatial unevenness of snow storage was undertaken by plotting empirical probability curves of snow water equivalent for the date preceeding the beginning of melt. These curves are well approximated by the binomial probability curves. A typical feature of the basins of Nizhnedevitskaya WBS is a consi­derable increase in the variation coefficients of snow water equi­valent for the basins that are not completely covered with snow (An < 100%). Figure 1 shows typical probability curves of water equivalent of snow on Log Tatyanin drainage basin with An=100% in 1961 and An=51% in 1962.

More than 200 probability curves were developed, and the values of the variation coefficients of snow water equivalent for open terrain in the forest-steppe zone ranged from 0.13 to 2.30. The upper limit is more than two times greater than earlier estimates. The information on the uneven depth of the snow cover in a basin is highly important for obtaining more accurate spring flood runoff estimates. Since standard observations on snow cover do not provide such information and in view of the high variability of snow stor­age distribution in a basin from year to year, it was decided to assess the possibility of indirect determination of Cv of snow water equivalent in a river basin. Using the work of Parshin (1953), who developed the relationship between the coefficient of variation of snow storage distribution over an area and the average

Snow cover and water yield 2 5 7

snow storage in a basin, the present authors plotted similar graphs both for individual basins and for the whole region. Despite the fact that the relationship between Cv of snow water equivalent and the average depth of snow in a basin appeared to be improved, the relationship between snow water equivalent and the average snow storage in a basin, shown in Fig. 2, seems to be more applicable for practical use.

Wn mm

400 \ J

\

\ \

\ :

• 1961

A 1962

1 ' p% 1 5 10 60 90 99 99,9 99,99

FIG. 1 Probability eurves of water equivalent of snow cover on Log Tatyanin basin

0,5 4

• - 9 6 % = A n ^ 1 0 0 % I - A n i - 9 5 %

- Wn Basln.mm

FIG. 2 Relationship between Cv and average snow storage for Nizhnedevitskzya WBS

One can see that relationships between Cv and the snow cover depth, and Cv and the average snow storage in a basin are non­linear; and the same values of snow storage correspond to different coefficients of variation which depend on the extent of snow cover in a basin.

258 B.M. Dobroumov & AB. Shukhobodsky

Testing of the hypothesis of the va l id i ty of adopting CS=2CV as standard (see Fig. 3) shows that for a snow cover extent ranging from 76 to 100%, CS=2.3CV may be accepted as standard for th i s region, and for An< 75%, Cs = 1.6Cv-0.64.

FIG. 3 Coefficients of asymmetry versus coefficients of variation of water equvalent of snow at Nizhnedevitskzya WBS

Wn Basin.mm

FIG. 4 Correlations between the average snow storage in the basin and the average snow storage in (a) fields and (b) the forest in the river basins of Nizhnedevitshzya WBS

Snow cover and water yield 259

In view of the lack of data it was impossible to develop a sep­arate relationship for snow cover extent ranging from 76 to 95%.

Correlations between snow storage values and different kinds of landscape are shown in Fig. 4. The curves were plotted using all data on average snow storage in the field and in the forest at Nishnedevitskaya Water Balance Station. It is clear from Fig. 4 that snow storage in the fields is practically a function of the snow storage of the whole basin, though the area of the fields varies from 40 to 90% of the total basin area. The lack of a good relationship for forest suggests that snow storage in the forest depends not only on its location, but also on its density, age and the type of vegetation. The data on the distribution of the snow cover in the forest is available only for Devitsa River basin up to the village of Tovarnya with the forest area being 14%. Figure 5 shows the correlation between Cv of snow storage over the whole basin and in the forest for this basin.

C y Basin

0,7

0,6

0,5-

0,4

0,3

0,2

0,1

0,1 0,2 0,3 0,4

FIG. 5 Correlation between Cv of snow water équivalent accumulated over the whole basin and in the forest in the River Devitsa basin up to Tovarnya

One can see from Fig. 5 that the unevenness of snow distribution in the forest is much lower than the unevenness of snow storage distribution in the field basin which is physically reasonable.

A study of the uneven distribution of the snow cover with respect to the duration and rate of the water yield was made by modelling the snowmelt process over 2-3 hour intervals for the whole melt period. Meteorological data and the average values of snow water equivalent were used as the model input.

C . P/-II-QO +

260 B.M. Dobroumov & A.B. Shukhobodsky

The depth of melt water (mm h_1) was estimated by means of the slightly modified formula developed by Kuzmin (1961):

= a [(T200- Ts) + 1.75 (e200- es)] (1 + 0.547u) + b(l - r)

(1 - 0.14N - 0.53NL)Rlo- e[(Ts+ 273.15)4 - (T200+ 273 .15)

4

(0.61 + 0.045e2D5^)(l + 0.12N + 0.12NL)] (2)

where a is a geographical parameter equal to 0.0366; T 2QO

and e2Q0 a r e the air temperature (°C) and humidity (mb) at

the height of 200 cm, respectively; Ts is snow surface tempera­ture (°C); es is the mean vapour pressure at the snow surface (mb) ; u is the wind speed at the height of the vane (m s--'-); b is a parameter equal to 7.5; r is the albedo of the snow cover (expressed as a decimal); N and N^ are total and lower-level cloudiness, respectively (expressed as a decimal); R̂ 0 is the total solar radiation intensity with the cloudless sky (cal cm~2 min--'-); e is St ef an-Bo ltzmann1 s constant for black-body radiation equal to 8.14 x 10 (cal cm min degree) .

Non-uniform process of water yield from snow was taken into account according to the method suggested by Kovzel (1962). Com­putations were made for variation coefficients from 0.2 to 0.8, that for the values typical for snow cover extent equal to 100%, and for Cs close to 2CV. Computations for basins not completely covered with snow were not made because the statistical parameters pertinent to the given case did not correspond to those used in the method suggested by Kovzel. Figure 6 shows the results of computing water yield in 1960 from the Devitsa River basin, at Nizhnedevitsk. These results illustrate well enough the influence of the uneven distribution of the snow cover on the rate and duration of the water yield. Experimentation showed that the change of Cv of the snow water equivalent from 0.2 to 0.8 leads to an increase of the water yield duration by 30% on the average and to the exceedance of the maximum water yield intensity (during the period without liquid precipitation) for 2-3 hour intervals by 100% and even more. In the case of a daily computation interval, the influence of the uneven snow depth distribution over a basin on the maximum does not exceed 30 to 40%. Thus, the errors in estimating maximum spring snowmelt flood runoff that result from neglecting spatial distribution of the snow cover alone may reach 30% and even more.

CONCLUSION

In conclusion, it should be mentioned that the coefficient of vari­ation of the snow water equivalent on a basin is only a statistical characteristic of the distribution of snow storage over a basin. It does not take into account the actual distribution of snow water

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262 B.M. Dobroumov & A.B. Shukhobodsky

equivalent with regard to stream channel, slope aspect, landscape and microforms of relief, which makes the efficiency of its use in the models considerably lower. One of the ways to overcome this drawback is to use subsets of variation coefficients of snow water equivalent for different landscape forms. Where observational data are lacking, practical estimates of the parameters of the probabi­lity curves of water equivalent of the snow cover may be obtained by using the relationships discussed in this paper.

REFERENCES

Dmitrieva, N.G. (1956) Nekotorye osobennosti obrazovania i stekania taloi vody y rayone Nizhnedevitskoi stokovoi stansii. (Some peculiarities of snow melt water formation and runoff in the region of Nizhnedevitskaya runoff station). In: Sneg i tatye vody, ikh izuehenie i ispolzovanie, 157-173. Izdatelstvo AN SSSR, Moscow, USSR.

Komarov, V.D. (1957) Voprosy teoril i rascheta (prognoza) snegovogo polovodia nebolshikh ravninnykh rek. (Problems of theory and computation (prediction of a snowmelt flood of small plain rivers). Trudy TsIP 50, 3-39, Leningrad, USSR.

Komarov, V.D. (1959) Vesennii stok ravninnykh rek Yevropeiskoi ohasti SSSR, uslovia ego formirovania i metody prognozov. (Spring flow of the plain rivers of the European part of the USSR, the conditions of its formation and prediction methods). Gidrometeoizdat, Moscow, USSR.

Kopanev, I.D. (1971) Metody izuahenia snezhnogo pokrova. (Methods for studying snow cover). Gidrometeoizdat, Leningrad, USSR.

Kopanev, I.D. (1978) Snezhnyi pokrov na territorii SSSR. (Snow cover over the USSR area). Gidrometeoizdat, Leningrad, USSR.

Kovzel, A.G. (1956) 0 raspredelenii snegozapasov v rechnykh basseinah. (On the distribution of snow storage in river basins). In: Sneg i talye vody, ikh izuehenie i ispolzovanie, 135-156. Izdatelstvo AN SSSR, Moscow, USSR.

Kovzel, A.G. (1962) Uproschennaya skhema rascheta vodoodachi iz snega. (Simplified procedure for computing water yield from snow). Trudy GGI 99, 141-176, Leningrad, USSR.

Kuchment, L.S., Demidov, V.N., Motovilov, Yu.G. & Smakhtin, V.Yu. (1986) Sistèma fiziko-matematicheskikj modelei gidrologicheskikh protsevov i opyt yeyo primenenia k zadacham formirovania rechnogo stoka. (A system of physical-mathematical models of hydrological processes and experience in its application to the problems of river-runoff formation) . Vodnye reswsye, 5, 24-36, Moscow, USSR.

Kuzmin, P.P. (1960) Formirovanie snezhnogo prokrova i metody opredelenia snegozapasov. (Snow cover formation and methods for determining snow storage). Gidrometeoizdat, Leningrad, USSR.

Kuzmin, P.P. (1961) Protsess tayania snezhnogo pokrova. (metody issledovania i raseheta) . (Snow cover melting process methods of investigation and computation). Gidrometeoizdat,

Snow cover and water yield 2 6 3

Leningrad, USSR. Motovilov, Yu.G. (1986) Fiziko-matematicheskaya model formirovania

t a l ogo s toka . (Phys ica l -mathemat ica l model of snowmelt runoff fo rmat ion) . In: Tezisy dokladov V Vsesoyuznogo gidrologiohes-kogo siezda. Sektsia teorii i metodov gidrologiaheskikh rasahetov, 90-91, Gidrometeoizdat , Leningrad, USSR.

Pa r sh in , V.N. (1953) Tochnost ucheta snegozapasov v bas se ine i yeyo v l i a n i e na tochnost prognoza obiema polovodia. (Accuracy of account ing snow s to rage in a b a s i n and i t s i n f l u e n c e on the accuracy of f lood volume f o r e c a s t s ) . Trudy TsIP 30(5 7 ) , 3 -51 , Leningrad, USSR.

Shpak, I . S . (1954) 0 t o c h n o s t i nab lyuden i i nad snezhnym pokrovom p r i snegosiemkakh. (On the accuracy of obse rva t ions on snow cover d u r i n g snow s u r v e y s ) . Trudy GGI 4 5 ( 9 9 ) , 3 1 - 4 7 , Leningrad, USSR.

SNiP 2.01.14 - 83. Opredelenie rasahetnykh. gidrologiaheskikh kharakteristik (1985) ( C o n s t r u c t i o n Norms and Code of P r a c t i c e . Determinat ion of Design Hydrologica l C h a r a c t e r i s e s ) . S t r o i i z d a t , Moscow, USSR.

Velikanov, M.A. (1940) Vodnyi balans sushi. (Water ba lance of l a n d ) . Gidrometeoizdat , Leningrad, USSR.

Zhidikov, A .P . , Levin, A.G., Nechaeva, N.S. & Popov, E.G. (1977) Metody rasaheta i -prognoza polovodia dlia kaskada vodohranilish i reehnykh sistem. (Methods of computation and f o r e c a s t i n g of snowmelt f loods for r e s e r v o i r s and r i v e r sys t ems) . Gidrometeoiz­d a t , Leningrad, USSR.