Canopy radiation transmission for an energy balance snowmelt model
To better estimate the radiation energy within and beneath the forest canopy for energy balance snowmelt models, a two stream radiation transfer model that explicitly accounts for canopy scattering, absorption and reflection was developed. Upward and downward radiation streams represented by two differential equations using a single path assumption were solved analytically to approximate the radiation transmitted through or reflected by the canopy with multiple scattering. This approximation results in an exponential decrease of radiation intensity with canopy depth, similar to Beer's law for a deep canopy. The solution for a finite canopy is obtained by applying recursive superposition of this two stream single path deep canopy solution. This solution enhances capability for modeling energy balance processes of the snowpack in forested environments, which is important when quantifying the sensitivity of hydrologic response to input changes using physically based modeling. The radiation model was included in a distributed energy balance snowmelt model and results compared with observations made in three different vegetation classes (open, coniferous forest, deciduous forest) at a forest study area in the Rocky Mountains in Utah, USA. The model was able to capture the sensitivity of beneath canopy net radiation and snowmelt to vegetation class consistent with observations and achieve satisfactory predictions of snowmelt from forested areas from parsimonious practically available information. The model is simple enough to be applied in a spatially distributed way, but still relatively rigorously and explicitly represent variability in canopy properties in the simulation of snowmelt over a watershed.