Advantages of analytically computing the ground heat flux in land surface models

Abstract. It is generally accepted that the ground heat flux accounts for a significant fraction of the surface energy balance. In land surface models, the ground heat flux is typically estimated through a numerical solution of the heat conduction equation. Recent research has shown that this approach introduces errors in the estimation of the energy balance. In this paper, we calibrate a land surface model using a numerical solution of the heat conduction equation with four different vertical spatial resolutions. It is found that the thermal conductivity is the most sensitive parameter to the spatial resolution. More importantly, the thermal conductivity values are directly related to the spatial resolution, thus rendering any physical interpretation of this value irrelevant. The numerical solution is then replaced by an analytical solution. The results of the numerical and analytical solutions are identical when fine spatial and temporal resolutions are used. However, when using resolutions that are typical of land surface models, significant differences are found. When using the analytical solution, the ground heat flux is directly calculated without calculating the soil temperature profile. The calculation of the temperature at each node in the soil profile is thus no longer required, unless the model contains parameters that depend on the soil temperature, which in this study is not the case. The calibration is repeated, and thermal conductivity values independent of the vertical spatial resolution are obtained. The main conclusion of this study is that care must be taken when interpreting land surface model results that have been obtained using numerical ground heat flux estimates. The use of exact analytical solutions, when available, is recommended.