The sensitivity of snow-surface temperature equation to sloped terrain

SummarySnow surface temperature (SST) is a key component in the calculation of snow-surface energy balance. Common snow models have adapted a specific linearized SST equation that accounts for the energy fluxes at the snow–atmosphere interface. An inspection of this widely used equation reveals that the areal units for three of the energy fluxes disregard the effect of sloped terrain and as a result presents a unit inconsistency in the equation. The objectives of this paper are to: (1) introduce a corrected SST equation; (2) discuss the role of the SST in snow models; and (3) assess the impact of this unit inconsistency on the simulation of snow variables in various climatic conditions. Meteorological observations were used to compare results that were obtained by implementation of the original and the corrected SST equations in a point energy and mass balance snow model. The calculated SST values in the original equation tend to be higher than the calculated value in the corrected equation. As a result when the original equation is used the SST-dependent energy fluxes (i.e. sensible heat, latent heat and net long-wave radiation) into the snow are lower, which yield lower melting rates. In conclusion, while the original SST equation might be applicable in snow models for gentle terrain, it introduces substantial biases in steep terrain. Therefore, it is conservatively recommended to consider the implementation of the corrected SST equation for snow model applications in mountainous terrain that are steeper than 15°.

► Many snow models inadequately treat sloped terrain when calculating snow surface temperature (SST).
► We present SST equation that correctly considers sloped terrain.
► A consideration of sloped terrain substantially impact calculation of SST, SWE and melt.
► The effect of sloped terrain on the calculation of snow variables is cumulative, non linear.
► We recommend using the corrected SST equation for snow models in mountainous terrain.