Mathematical models of a melting snowpack at an index plot

Abstract A detailed model, based on present knowledge on snow-melt processes, was first developed. This model was calibrated and tested on the data of two lysimeter sites, located in the north French Alps, one in an open area and one in a forested area. The assumptions required are extensively discussed and have been sustained by further measurements, particularly the surface temperature, computed by an iterative technique, which is the key variable of the energy budget at the air-snow interface. Using a 3-h time step, this model appears to be very satisfactory in simulating meltwater outflows during the whole melt period. In addition, the computation, on a continuous basis, of the temperature profile and cold content of the snowpack proves to be sufficiently accurate and very useful for hydrological purposes such as determining the beginning of outflows after cold spells. In order to enable the model to be fitted to the data usually available in mountainous regions, the model structure was then slightly altered and the missing data have been replaced by various estimates. The effects on the accuracy of prediction are briefly considered. It appears that a subroutine with a time step of 12 h is sufficiently accurate for the majority of watershed-model requirements. Such a subroutine, which can easily be integrated in a complete watershed model, is finally presented.