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Representation of sub-element scale variability in snow accumulation and ablation is increasingly recognized as important in distributed hydrologic modelling. Representing sub-grid scale variability may be accomplished through numerical integration of a nested grid or through a lumped modelling approach. We present a physically based model of the lumped snowpack mass and energy balance applied to a 26-ha rangeland catchment with high spatial variability in snow accumulation and melt. Model state variables are snow-covered area average snow energy content (U), the basin-average snow water equivalence (W a), and snow-covered area fraction (A f). The energy state variable is evolved through an energy balance. The snow water equivalence state variable is evolved through a mass balance, and the area state variable is updated according to an empirically derived relationship, A f W a †, that is similar in nature to depletion curves used in existing empirical basin snowmelt 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 the distribution of snow water equivalence at peak accumulation in the area being modelled. We show that the depletion curve estimated from the snow distribution of peak accumulation at the Upper Sheep Creek sub-basin of Reynolds Creek Experimental Watershed compares well against the observed depletion data as well as modelled depletion data from an explicit spatially distributed energy balance model. Comparisons of basin average snow water equivalence between the lumped model and spatially distributed model show good agreement. Comparisons to observed snow water equivalence show poorer but still reasonable agreement. The sub-grid parameterization is easily portable to other physically based point snowmelt models. It has potential application 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.

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