Stochastic Upscaling for Snow Accumulation and Melt Processes with PDF Approach
Publication: Journal of Hydrologic Engineering
Volume 13, Issue 12
Abstract
Although the importance of subgrid variability in the snow model has been recognized, only a few modeling studies on the parameterization of subgrid effects have been performed. This study proposes a new upscaling approach from a single-layered point-scale snow model toward a finite-scale model, using the probability density functions (PDF). The Fokker-Planck equation (FPE) for the snowmelt process is formulated in a two-dimensional probability domain for snow temperature versus snow depth. This Fokker-Planck equation, governing the evolution of the probability density of the snow temperature–snow depth bivariate state variable, can describe the subgrid effects of the snow process. The numerical solutions of the FPE are validated with Monte Carlo simulations. It is demonstrated that the derived FPE can express the spatial variability of the snow process sufficiently well once the necessary information on the spatial variation in shortwave radiation and snowfall are given. The validation results are encouraging and point toward potential use of this PDF model as an engine for large-scale grid-based modeling to capture the subgrid variability of snow processes.
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Published In
Journal of Hydrologic Engineering
Volume 13 • Issue 12 • December 2008
Pages: 1103 - 1118
Copyright
© 2008 ASCE.
History
Received: Mar 28, 2006
Accepted: Jan 10, 2007
Published online: Dec 1, 2008
Published in print: Dec 2008
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