Statistical properties of spatial snowcover in mountainous catchments in Norway Wolf-Dietrich Marchand* and A ˚ nund Killingtveit Department of Hydraulic and Environmental Engineering, Norwegian University of Science and Technology, S.P. Andersensvei 5, 7491 Trondheim, Norway *Corresponding author: Sweco Grøner AS, Olav Tryggvasons gate 24b, 7011 Trondheim, Norway. Tel.: þ 47 73 99 02 00; Fax: þ 47 73 99 02 02; E-mail: wolf.marchand@sweco.no Received 18 June 2002; accepted in revised form 1 September 2003 Abstract The spatial distribution of snowcover in a catchment is determined by complex interactions between meteorological and physiographical factors, integrated over time. The snowcover shows variability over scales ranging from centimeters up to hundreds of kilometers. An important and necessary decision for modelers is to determine spatial resolution in a distributed model. Since the spatial variability in snowcover may be quite large, even within a few meters, it is difficult to use modeling units small enough so that the snow can be assumed evenly distributed within the unit. A possible method to compensate for this is to use larger units, and describe the snow distribution within each unit by a statistical model (e.g. normal, log-normal, gamma, etc). This technique requires information about spatial statistical properties of snowcover within a unit. As many of the distributed hydrological models operate on a grid basis, it would be desirable to find a statistical distribution on a sub-grid scale. However, as an initial approach, the study presented here was done on a catchment scale. The catchment scale presented the possibility of incorporating data from several historical snow surveys. These surveys were taken at the time of maximum snow accumulation in various mountainous catchments in Norway. Comparing empirical distribution functions with different theoretical distribution functions, it was shown that a mixed distribution combining two separate log-normal distributions clearly gave the best fit in most of the catchments. This seems to indicate that a mixture of at least two different populations of SWE values exists. Keywords Hydrological modeling; distribution function; mixed distribution function; snowcover; snow distribution; spatial distribution Introduction In order to model the hydrology of northern areas, it is necessary to acquire data on the snowcover. Such data are traditionally collected manually by measuring with stakes, graduated rods or fixed rulers. The principal uncertainty of the accumulation pattern constructed from point data is that the snow accumulation varies locally over the surface (Richardson et al. 1997). To gain enough information about the actual snowcover variability with traditional means, an extensive measurement design with a large number of snow courses is required. Such measurements are very time-demanding and costly. In many recent approaches, remote sensing data from airborne or satellite platforms are coupled with models of the spatial distribution of snowcover or snow water equivalent (SWE). These techniques are presently not developed enough to give proper results on snowcover properties like depth and density (Elder et al. 1998), but they can give important information on the snow covered area and albedo. In recent years, several authors have described the use of a ground based radar system to measure depth of snow (Andersen et al. 1987; Killingtveit and Sand 1988; Sand and Bruland 1998; Marchand et al. 2001). This technique makes it possible to collect snow depth samples over large areas, spending much less time than with traditional methods. Nordic Hydrology Vol 35 No 2 pp 101–117 q IWA Publishing 2004 101 Downloaded from http://iwaponline.com/hr/article-pdf/35/2/101/363525/101.pdf by guest on 07 April 2023