Sub-grid parameterization of snow distribution for an energy and mass balance snow cover model

Representation of sub-element scale variability in snow accumulation and ab lation is increasingly recognized as important in distributed hydrologic mo delling. Representing sub-grid scale variability may be accomplished throug h numerical integration of a nested grid or through a lumped modelling appr oach. We present a physically based model of the lumped snowpack mass and e nergy balance applied to a 26-ha rangeland catchment with high spatial vari ability in snow accumulation and melt. Model state variables are snow-cover ed area average snow energy content (U), the basin-average snow water equiv alence (W-a), and snow-covered area fraction (A(f)) The energy state variab le is evolved through an energy balance. The snow water equivalence state v ariable is evolved through a mass balance, and the area state variable is u pdated according to an empirically derived relationship, A(f)(W-a), that is similar in nature to depletion curves used in existing empirical basin sno wmelt models. As snow accumulates, the snow covered area increases rapidly. As the snowpack ablates, A(f) decreases as W-a decreases. This paper shows how the relationship A(f)(W-a) for the melt season can be estimated from t he distribution of snow water equivalence at peak accumulation in the area being modelled. We show that the depletion curve estimated from the snow di stribution of peak accumulation at the Upper Sheep Creek sub-basin of Reyno lds Creek Experimental Watershed compares well against the observed depleti on data as well as modelled depletion data from an explicit spatially distr ibuted energy balance model. Comparisons of basin average snow water equiva lence between the lumped model and spatially distributed model show good ag reement. Comparisons to observed snow water equivalence show poorer but sti ll reasonable agreement. The sub-grid parameterization is easily portable t o other physically based point snowmelt models. It has potential applicatio n for use in hydrologic and climate models covering large areas with large model elements, where a computationally inexpensive parameterization of sub -grid snow processes may be important. Copyright (C) 1999 John Wiley & Sons , Ltd.