Estimating the mean areal snow water equivalent from satellite images and snow pillows

Abstract

By modelling the snow accumulation process in time and space as sums of random gamma distributed variables, the mean areal snow water equivalent (SWE) can be estimated. In the methodology we make use of the fact that sums of gamma distributed variables with a certain set of parameters also are gamma distributed variables with parameters being functions of the original and the number of summations. The measured snow/SWE at a point at a certain time t, can thus be seen as the accumulation, or the sum of the snowfall process from the beginning of the snowfall season up to t. The integration of these points, which give an area, can be seen as another summation. From snow pillows and precipitation gauges the value of daily accumulated precipitation/snow has been found to be well represented by a two parameter gamma distribution. This distribution has been found to be representative for large areas. The number of events where the precipitation was accumulated can be estimated from snow pillows situated in the area. The mean snow coverage over an area, which represents the summation of the individual points over an area, can be derived from satellite images represented in a GIS. The methodology is tested for two nested catchments of size 4723 km' and 19832 km' in a mountainous area in Southern Norway for eight satellite scenes. The results are compared with simulated snow reservoirs using a rainfall-runoff model, and found to agree well. Large discrepancies in the snow reservoirs between the proposed method and the rainfall runoff model are found in late spring and are probably due to errors in the estimated mean snow coverage.