Modeling Snowmelt Over an Area: Modeling Subgrid Scale Heterogeneity in Distributed Model Elements
We analyze the parameterization of sub-grid scale variability in snow accumulation and melt models from a physical perspective considering the causes of the variability and the effect on snowpack energy exchange. The source of temporal changes in spatial variance of snow water equivalent is the covariance between snow water equivalent and the accumulation or melt rate at each point. Variability caused by drifting and differential solar radiation can be effectively parameterized with areal depletion curves relating snow covered area to basin average snow water equivalent. As a first approximation, depletion curves may be estimated from the distribution of snow at peak accumulation. Improvements can be made to the depletion curve by using the joint distribution of solar radiation and snow water equivalent at peak accumulation. Consideration of how distributions may change as the model element size increases provides insight into how this conceptualization may be applied to scaling up snowmelt models.