Basin-wide water equivalent estimation from snowpack depth ...hydrologie.org/redbooks/a107/107069.pdf · Basin-wide water equivalent estimation from snowpack depth measurements L.A

Basin-wide water equivalent estimation from snowpack depth measurements

L.A. Logan Water Quantity Management Branch,

Ontario Ministry of the Environment, Toronto, Ontario

ABSTMCT: tions in an IHD representative drainage basin are analyzed. tical analysis, based on the Sampling Theory for Normal Distribution, is applied to the observations to determine the sampling errors and areal variability of the snowpack parameters.

mulation and a snowmelt period. Based on sampling in specified elevation zones and for each period, sets of regression equations are derived relating snowpack density to logarithm-transformed snowpack depth. These empirical equations are used to predict snowpack density and subsequently to estimate water equivalent from *snowpack depth measurements. The variance explained by each regression is shown to improve with the inclusion of the effect of certain meteorological factors.

ted from regional snow courses are used to demonstrate the applicability of the empirical equations. With the use of these empirical equations to predict density and to estimate water equivalent from measured snowpack depth, it is possible to improve the accuracy of the estimates of the basin water equivalent by increasing only the number of snowpack depth measurements in the study area.

Data on snowpack compiled for four years of snow observa- Statis-

Climatic criteria are used to differentiate between a snow accu-

The snow survey data for the 1971-72 snow season and data selec-

RESUME: neiges tassées d'un bassin type de la DHI. L'analyse statistique, basée sur la théorie des. prélèvements en répartition normale, est appliquée aux observations afin de déterminer les erreurs d'bchan- tillonnage et les variations des paramètres en fonction des lieux.

d'accumulation des neiges de celle de la fonte. En se basant sur des Echantillonnages en des zones d'altitude choisie et durant chaque période, on &rit des équations représentant la régression et étab- lissant une relation logarithmique entre la densité des neiges tassées et leur profondeur. Ces équations empiriques servent à prévoir la densité des neiges qui, avec les mesures de l'épaisseur, permet d'évaluer l'équivalent en eau. Les variations s'expliquant par chac- une des régressions deviennent encore plus claires si l'on tient compte de certains facteurs météorologiques.

Pour montrer que les équations empiriques sont applicables, on utilise des mesures faites sur les neiges en 1971-72 et des donnFes choisies parmi des mesures régionales. grâce à ces équations permettant de prévoir la densité et l'equivalent en eau en partant de la profondeur mesurée, il est possible d'obtenir des valeurs plus précises des équivalents en eau du bassin si l'on augmente uniquement le nombre des points de mesure de la profondeur ..

On analyse les données obtenues pendant quatre ans sur les

Des critères climatiques sont utilisés pour séparer la période

On en tire la conclusion que,

864

INTRODUCTION

Snow cover investigation is one aspect of snow hydrology studies currently being undertaken by the Water Quantity Management Branch, ?.linistry of the Environment of Ontario, in the Bowmanville, Soper, and Kilmot Creeks representative drainage basin. The study forms a part contribution to the International Hydrological Decade (IHD) program.

Snorc surveys in a drainage basin are concerned basically with the determination of the effect of snowpack conditions on basin runoff. The water equivalent of the snowpack is usually determined for Lise in synthesizing or forecasting the total volume of runoff during snomlelt periods. In the general computation of basin snoiimelt, it is usually necessary to consider each melt component, at points under the different local environmental conditions. The collection of data on SnoiC depth, iiater equivalent, and density, therefore, normally are compiled from point measurements taken in areas that are representative of the different vegetative cover and range of topograph!-. The average iiater equivalent determined from these point measurements qenerally represents an estimated value for the areally distributed amounts. Khen dealing iiith average snowpack conditions that vary both in time and space, however, it is usually necessary that changes in the snoiipack be evaluated in conjunction iiith other time dependent variables which are knom to influence these changes. Accounting for changes in the snowpack conditions may be accom!>lished through the use of indices involving meteorological parameters. These indices may be expressed by a simple tiso-variable relationship or through a multi-variate statistical analysis procedure.

survey data in terms of standard errors, areal variabilit?., and reliability of the snowpack parameters; b) to utilize the assessed data in the development of empirical relationships bet\\.een average snoripack density and depth; c) to test the applicability of the prediction equations in the estimation of basin-wide riater equivalent from independent snowpack depth measiirements.

The basic objectives of this study are: a) to evaluate the snoii

STUDY AREA

The study area is the TVilmot Creek basin, a suh-basin of the Bowmanville, Soper and Wilmot Creeks representative drainage basin, located in southern Ontario with a grid location 44" 00' N latitude and 78" 40' IV longitude (see Fig. 1). The drainage area is approximately 88 km2 with surface elevation ranging from 76 m (250 ft) to 373 m (1225 ft) above mean sea level. Floderate and rolling terrain characterizes the lower portion of the basin with increased undul- ation evident above an elevation of 275 m (900 ft). The vegetation consists predomicantly of forage cro2s and k-goved. pstnres, with sparsely distributed productive forested areas, mainly in the. upper terrain,

Snowfall accumulation and complete areal snow cover are normal events in the basin for three to five months of the year, from late November through early April. Annual precipitation, on the average, amounts to 820 mm with approximately 10 to 15 per cent occurring as snowfall. Maximum snowpack accumulation ranges from 25 to 90 cm, and during the snow season daily average temperatures range from -15°C to 2°C. from 0.3 m3/sec during the low flow periods, to 55 m3/scc durjng the

Measured runoff at the basin outlet ranges, on thë average,

865

period of major snow-melt runoff.

DATA COLLECTION

The snow survey sampling network consists of twelve snow courses, each of which was selected to represent a sampling of snowfall in areas with different vegetative cover throughout the range of topography that appears to influence local climatic conditions in the basin. A standard sncw course consists of ten sampling points distributed at regular intervals of 30.5 m. The locations of the snoi$. courses, with the associated hydrometeorological network are shorin in Figure 1. Also, the locations of the courses by arbitrarily chosen elevation zones are indicated on the area-elevation curve of Figure 2.

study area, for four winter seasons, 1968-69, through to 1971-72. During a normal winter season, the routine snow survey commences riith a snow accumulation of depth .? 5 cm and continues throughout the season at regular two-week intervals until snow cover is negligible at the end of the snow season. The point sample observations are sno\\'- pack depth, core length, water equivalent, and. computed density (ratio of water equivalent to depth), using a standard MSC Type-1 tubular snow sampler.

In addition to snowfall, several other meteorological variables (temperature, precipitation, net radiation, sunshine, etc.) are mon- itored continuously in the basin. Similarly, a network of streamflow gauging stations records continuous runoff from several tributary drainage areas and also from the basin outlet.

The network density is approximately one snoii course per 7.3 km'. Snow survey data are compiled, from point observations in the

DATA ANALYSIS

Preliminary analysis of the snow survey data followed a selected statistical analysis procedure [l]. The samples, consisting of independent point measurements, were assumed to be random and normally distributed. meters, in terms of standard error of averages, were c'etermined with the use of statistical techniques of standard applications [2-51. The computations, €or Kean and variance, were carriecl out with the employ o€ a computer statistical package program [6].

The snow courses were evaluated for uniformity in depth of snow cover by a ranking procedure based on the coefficient of variation of average snowpack depth during the melt-free period, Reliability and consistency in sampling were assessed through a simple correlation between the snowpack water equivalent and depth for each snow survey period. The weighted basin-averages of each snowpack parameter, based on the Thiesscn-polygon and the area-elevation-zone methods, were compared with the arithmetic averages. The comparisons indicated negligible differences between individual averages of the different methods. Also, frequency curves, €or the areal distribution of each snowpack parameter, at any given time, indicated a near normal distribution of the average snowpack condition.

Figures 3, 4, and 5 show the time-variation trends of each snow season, 1968-69 to 1971-72, for the basin-wide snowpack average depth, water equivalent, and density. Indicated also is the corresponding standard error of average for each parameter on any given survey date. The time-variation trends for the snowpack depth is observed to be

The confidence and reliability of the snowpack para-

866

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somewhat erratic in distribution, both in magnitude and time; however, the time-variations of the snowpack water equivalent and density followed a corresponding but more consistent trend with accumulation. The density parameter exhibits the most consistent time-variation trends in terms of a minimum of variation between and within snow seasons. Also, areal variability of density is observed to be the least of the three parameters.

SNOWPACK WATER EQUIVALENT ESTIMATION

Estimates of basin-wide water equivalent were to be determined from snowpack depth measurements through a basic empirical relationship between density and depth, developed from the snow survey data collected. Investigations [7] have indicated that, in specified re- gions of Canada, sufficient regional homogeneity of snowpack density at a given period of the snow season exists to allow the use of average densities in combination with regional snow depth values to produce national water equivalent or snow mass maps.

For this analysis, density, the parameter with the most consistent time trend and least areal variation, was considered as the dependent variable in the development of the empirical relationship with depth. The snow survey data for 1968-69 to 1970-71 were used in the development of the empirical equations and the 1971-72 data were used in testing their applicability. Further improvement in the empiricisms was envisaged with the consideration of certain meteorological parameters.

Density and. Depth Regression

The concurrent series of average densities and depths of the snowpacks observed throughout the several winter seasons were assumed to be mere permutations from the same population. The relationship:

P (t) = f ID It) 1 (1 1 in which,

proposed for relating the two parameters through a least-square regression technique [8].

increase in density with an increase in the accumulation of the snowpack (Fig. 3). The density continues to increase gradually, however, to a maximum bcyond the point of maximum depth and into the period when the snowpack was obscrved to be depleting. It seems reasonable, therefore, that different empirical derivations of equation (1) would be appropriate: one for the accumulation period and one for the melt period. From climatic observations and knowledge of the meteorological parameters known to influence snowmelt, it is assumed that the accumulation period would be dictated largely by the fo1lov;ing arbitrarily selected climatic criteria:

P (t) = average snowpack density in gm/cm3 and D (t) = average snowpack depth in cm; at any time, t, was

The density time-variation curves (Fig. 5) indicate a general

- DI< D2; Tmax.<- O°C; Rn%I langley and P / < 0.5

ps

where Dl and D2 are the snowpack depths observed on each snow course for two successive temperature for the time interval between surveys; Rn is the avcrage daily net radiation for the same time interval and Pr and Ps are the

snow surveys; Tmax is the average dai ly maximum

867

amount o€ liquid precipitation and snowfall, respectively, also for the same time interval. Without performing claborate computations [9] on daily snowmclt to obtain a refined demarcation of a melt period, judicious application of thc climatic criteria above permits the grouping of the snow survey data into the two appropriate series. When two or more of the critcria above hold for a particular survey interval, the data are grouped into the accumulation period. That is, the accumulation period was charactcrized by a general increase in D for a Tmax I_ 0°C and/or Rn 5 O langley; the added assumption on Pr/Ps was that a rain-snow ratio of less than 0.5 would have limited effect on the snowmelt process.

used in test graphical plots and trial regressions, relating density with depth and density with log-transformed depth. The latter analysis indicated the more significant relationships. It was observed further that on a particular snorn' survey during the accumulation period the snowpack depth increased with samples for the higher elev- ations, although there were no definite changes in the density. Pre- suming that elevation does influence the density-depth relationship, separate sets of regression equations were developed for each elevation zone €or the accumulation and melt period. The following linear regression was fitted to each set of data:

The grouped data, for the accumulation and melt period, were

where pet) z,T is the average snowpack density in gm/cm3 for a given elevation zone, Z, and a given snow season period, T; a and b are the regression constant and coefficient, respectively, and X(t) is the logarithm of the average snowpack depth in log D10 (cm) ; at any time, t.

Tables 1 and 2 show the result of the regression analyses for the accumulation and melt period. All sets of equations for each p(t)Z,T are significantly linear as indicated by the large F-values (variance ratio for the regression and deviations from the regression based on the "null hypothesis" Ho:ß = O) and the t-ratio for the regression coefficients are all significant, at least at the 95% confidence level [4, 81. The coefficients of determination, r2, all of acceptable significance, indicate the proportion of variance reduced by each regression. regression appears reasonable, as the snowpack density will likely be influenced by other time-dependent factors, notably meteorological variables, which were not considered in these first approximate relationships. However, additional reduction in variance in each regression would be desirable.

The proportion of variance explained by each

Density, Depth, and MeteoroZogicaZ Parameters Regression

Certain meteorological parameters were considered as an additional influence on the snowpack density. Liquid precipitation, temperature and barometric pressure, in addition to snowpack depth, were considered as the independent variable in a multiple regression with snowpack density as the dependent variable. These meteorological variables are known to be some of the major factors that influence snow metamorphosis and snowmelt [9], which often cause changes in the snowpack density.

mined from the records of fous climatological stations in the st,udy Relative estimates of temperature and precipitation were deter-

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area. Typical time-variation curves of daily maximum temperatures and daily precipitation amounts, observed in the basin, are demon- strated by the records of climatological station (1) shown in Figure 6. Barometric pressure data, at a given time and elevation were in- terpolated from general barometric-pressure curves developed from records at selected regional climatological stations [lo] adjacent to the study area.

A computer statistical package, stepwise-multiple-regression, routine [6], was used to perform several trial computations with the array of snowpack and metenrological data. In the final analyses, the most significant regression fitted to the data in all cases for both the accumulation and melt period was of the form:

p(t1 z,T = a + blX (t) + b2 P (t3 (3)

where, P(t) is the accumulated liquid precipitation in cm at any time, t, are the regression constant and coefficients, respectively. Precip- itation, D, proved to be the only variable to result in a greater additional reduction in variance. The inclusion of accumulated nax- imum daily temperature above O°C and average barometric pressure (mb), in the regression, did not result in an additional significant reduction of variance above that obtained by equation 3.

the accumulation period and melt period, respectively. All the regressions were significant and indicated sone degree of improvement above the regressions of equation (2). Improvements were in terms of smaller standard error of estimates, larger coefficients of determination, in general accounting for a greater proportion of variance in the regressed estimates.

AppZication of Regression Equations

p(t)Z ~ and X(t) are previously defined, and a, and bl and b2

Tables 3 and 4 show the result of the regression analyses for

The empirical regression equations derived are first approximations of a type of relationship that may be used, in combination with measured snowpack depths, to predict estimates of snowpack water equivalent. The equations are assumed to be applicable in the study area, adjacent to the study area, and in remote areas within the same climatic region.

The snow survey data, for the 1971-72 snow season, from the study area and from selected regional watersheds [ll] were used to test the applicability of the regression equations. Table 5 shows a listing of some of the watersheds in southern Ontario, with records of snow survey data, selected for the test applications. The data on snow depth and water equivalent are compiled from core sampling of snowpack in 10-point snow courses. arbitrarily, with a range of elevation similar to that of the study area.

applied to the defined elevation-zones and the basin as a whole. Figure 7 shows the time-variation trends, based on the 1971-72 data, for the observed and predicted snowpack density and the observed and estimated water equivalent, with the application of the basin regression equations of Tables 1 and 2 and Tables 3 and 4, respectively. A reasonably good fit was obtained by each set of regressions as indicated by the large correlation coefficients.

The watersheds were selected,

For the study area, the appropriate empirical equations were

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Table 5 Selected Watersheds with Snow Survey Data in Southern Ontario

Elev. * Nearby Watershed Lat. N Long. W m-a.m.s.1. Climat. Stn.

Gananoque River 44" 30' 76" 08' 99 Brockville Bue11 Creek 44" 38' 75" 43' 107 Brockville Moira River Plainf ield 44" 17' 77" 21' 107 Belleville Actinolite 44" 33' 77" 20' 168 Belleville Ontonabee River 44" 11' 78" 20' 190 Pet erborough Indian River 44" 28' 78" 08' 228 Peterborough Grand River 43" 06' 80" 27' 276 Brantford Muskoka Rosseau Falls 45" 15' 79" 37' 244 Hunt svi 1 1 e Norway Point 45" 13' 79" 02' 336 Huntsville

Terra Cotta 43" 43' 79" 57' 343 Georgetown Orangeville 43" 56' 80" 06' 426 Orangeville Beaver River 44" 16' 80" 32' 440 Owen Sound

Credit River

*Snow course elevation in metres above mean sea level

The results of the application of the empirical equations in the selected watersheds gave a reasonably good comparison between observed and predicted values. data with the application of the empirical equations for the corresponding elevation-zone of Tables 1 and 2. Figure 8 shows the graphical comparison for the observed and computed water equivalent for the 1971-72 winter season in the selected watersheds.

The tests were made on the snow survey

CONCLUSIONS

The snow survey observations for three winter seasons provided for the determination of the confidence and reliability of the data used in the development of empirical regression equations between average snowpack density and depth. Because of the implicit assumption that some refinement in the prediction equations would be achie- ved by considering separate empirical relationships for defined sub- divisions of the topography and for an accumulation and melt period, the equations developed to take into account these factors. equations derived were all statistically significant while accounting for, in each case, a reasonable proportion of variance in the regressed estimates. only variable, of the meteorological factors considered, to cause significant additional reduction in variance.

The prediction equations derived for the basin as a whole provided for a probable increase in the accuracy of estimating areal distribution of snowpack water equivalent with an increase in number of measurements of only one, depth, of snow survey observations. It is reasonable to believe that further improvements in the regression will result with the inclusion of future snow survey data into the regression analysis and the utilization of more refined climatic criteria.

874

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Accumulated liquid precipitation was deduced to be the

Within the limitations of the investigations, the empirical equations derived in combination with independent snowpack depth measurements were applicable, as first approximations, for estimating water equivalent in areas of similar elevation-zones and with large- scale snowfall and climatic experiences similar to those of the study area. However, the applications are recommended for shallow snowpacks of depths 5 cm to 100 cm.

scale, in a homogeneous climatic region. Regional snow survey data could be used to develop the basic empirical relationships; also aerial photographic surveys could provide the necessary additional snowpack depth measurements for the evaluation of regional water equivalent values.

Conceivably, the method of analysis could be applied on a larger

REFERENCES

LOGAN, L.A. (1971). Snow Survey Report, East and Middle Oak- ville Creeks Drainage Basin 1968-69. OWRC Water Resources Bulletin 4-1, Climatic Series.

FISHER, R. (1958). Statistical Methods for Research Workers. Hafner Publishing Co. Inc., New York.

RIGGS, H.C. (1968). Some Statistical Tools in I-lydrology. Techniques of Water Resources Investigation of the U.S.G.S. Book 4, Chapter Al, U.S. Department of the Interior.

SNEDECOR, G. and COCHRAN, W. (1968). Statistical Methods. Iowa State University Press, Iowa.

THOM, H. (1966). Some Methods of Climatological Analysis. lVM0 - No. 199, TP103 Technical Note No. 81.

IBM (1970). CALL/360: Statistical Package, Version 2. IBN Data Processing Division, New York.

McKAY, G.A. and FINDLAY, E.F. (1971). Variation of Snow Resources with Climate and Vegetation in Canada. Proceedings of the Western Snow Conference, 39th Annual Meeting; pp. 17-25.

EZEKIEL, M. and FOX, K.A. (1967). Methods of Correlation and Regression Analysis - Linear and Curvilinear. 3rd Edition, John Wiley E Sons Inc., New York.

U.S. Army Corps of Engineers (1959). Snow Hydrology. OTS-US Department of Commerce Pß 151-660.

Canada Department of Transport - Metcorological Branch (1968- 1971). Monthly Records : bleteorological Observations in Canada

Ontario Department of the Environment - Conservation Authority Branch (1971-72). Snow Survey Data.

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Fig. 6 . Tine-variation of daily maximum temperature and daily precipitation amount €or the winter seasons

1965-69 to 1971-72 observed at the climatological station Ill

881

20.0 I I I I I

15.0

10.0

5.0

o. o

o. 5

0.4

O3

0.2

O1

0.0

I I I I I ~ I I I I I ~ I I I I I I I I

I I I I I I I I I I

r (eq. 6) i. 0.98

r (oq.9) = 0.99

I I I I I I I I I I I I

3.0

8.0

C

C

- .-

t *.o

.- a u

L e +

2.0

0.0

Fig. 7. Time-variation of observed and predicted basin-wide

1971-72 winter season: Nilmot Basin. snowpack density and water equivalent for the

882

20.0

IS. o

10.0

E' 5.c o c .- c U c

a

s 0.1 4- - s 20.c O > =I u .-

% c P 15.0

I0.C

5. (

O.(

o o

MELT PERIOD

-

-

-

0.0 5.0 10.0 15.0 20.0

Water equivalent (observed) in cm.

Fig. 8. Comparison of observed and computed snowpack water equivalent in selected watersheds in Southern Ontario,

for the 1971-72 winter season.

88 3

DISCUSSION

H.I. Hunter (Canada) - I assume that your basin is not too isolated and I wonder if you have looked at payer? Dublished on areal snow markers?

L.A. Logan (Canada) - I have examined many references on this subject. Ilowever, the idea in this study was to economize on field activity. Ille wished to utilize existing data and data easily obtwin- able, and, by taking point measurements over the entire area, we hoped to obtajn the water equivalent of the snowpack in the basin.

884

Documents

Basin-wide water equivalent estimation from snowpack depth ...hydrologie.org/redbooks/a107/107069.pdf · Basin-wide water equivalent estimation from snowpack depth measurements L.A