Evaluation of alternative formulae for calculation of surface temperature in snowmelt models using frequency analysis of temperature observations

The snow surface temperature is an important quantity in the snow energy balance, since it modulates the exchange of energy between the surface and the atmosphere as well as the conduction of energy into the snowpack. It is therefore important to correctly model snow surface temperatures in energy balance snowmelt models. This paper focuses on the relationship between snow surface temperature and conductive energy fluxes that drive the energy balance of a snowpack. Time series of snow temperature at the surface and through the snowpack were measured to examine energy conduction in a snowpack. Based on these measurements we calculated the snowpack energy content and conductive energy flux at the snow surface. We then used these estimates of conductive energy flux to evaluate formulae for the calculation of the conductive flux at the snow surface based on surface temperature time series. We use a method based on Fourier frequency analysis to estimate snow thermal properties. Among the formulae evaluated, we found that a modified force-restore formula, based on the superimposition of the force-restore equation capturing diurnal fluctuations on a gradually changing temperature gradient, had the best agreement with observations of heat conduction. This formula is suggested for the parameterization of snow surface temperature in a full snowpack energy balance model.