A Modified Force-restore Approach to Modeling Snow-surface Heat Fluxes

Accurate modeling of the energy balance of a snowpack requires good estimates of the snow surface temperature. The snow surface temperature allows a balance between atmospheric heat fluxes and the conductive flux into the snowpack. While the dependency of atmospheric fluxes on surface temperature is reasonably well understood and parameterized, conduction of heat from the snow surface into the snowpack depends on a complex history of previous heat exchanges and surface temperatures and can be somewhat more difficult to model. A variety of schemes ranging from multiplayer finite difference models to simple approximations based on air temperature exist to estimate snow surface temperatures and conductive fluxes. Previous research has suggested that single layer models are incapable of dealing with the complexity of the heat flow calculations within a snowpack. In this paper, we explore the idea of describing heat fluxes into the snowpack based on knowledge of the diurnal forcing. We examine observations of snow temperatures within a snowpack in detail and compare heat fluxes estimated from a linear equilibrium approach, a force restore approach, and a modification of the forcerestore approach that estimates the effects of lower frequency temperature variations on the surface heat flux. The modified force restore model shows the best agreement with observations.