Advancing the physical basis of depletion curves to improve curve estimation and snowmelt modeling

The spatial distribution of snow on the landscape is a fundamental control on meltwater inputs to basins. The effects of the spatial variability in snow accumulation and melt are commonly parameterized through the use of some version of a depletion curve, relating the snow covered area to time, accumulated melt, or the remaining snowpack on the ground. Depletion curves are generally estimated empirically through calibration against basin outflows, limiting their application in ungaged basins. Understanding the physical basis of depletion curves can provide valuable insights to improve curve estimation; provide utility for remote sensing of snow water equivalent; and improve the parameterizations in physically based models. To a first approximation, depletion curves can be derived as a function of the variability of snow water equivalent in the basin. In this respect, the coefficient of variation of spatially sampled snow water equivalent at peak accumulation is a good predictor of the depletion curve. A second approximation to the depletion curve can be derived from the spatial covariation of snow water equivalent at peak accumulation with energy inputs for snowmelt. While both approximations can be derived from spatially sampled snow water equivalent, such data are rarely available over large areas. Temporal sampling of remotely sensed snow covered area combined with estimates of snowmelt is an alternative that remains true to the second approximation. This approach opens the possibility to large scale estimation of depletion curves, with the potential for estimating the fraction of the seasonal maximum snow water equivalent remaining on the ground for a given remote sensing scene or to improve data assimilation procedures. Both of these approaches only estimate the snow covered fraction of a given unit. Further using the correlation between snow water equivalent and exposure to melt energy, we can estimate the relative energy exposure of the remaining patches, providing greater utility of the depletion curve concept for hydrologic modeling applications