An analytical soil thermodynamic model for the diurnal variation of ground surface temperature

An analytical expression is given for time variations of temperature within a model soil slab that is subjected to idealized heating at the supper surface and maintained at constant temperature at the lower surface. Applied at the upper surface, the model temperature may be considered to be the ground surface temperature of the earth. An important feature of this model is that phase-shifted on-linear responses to the forcing are allowed at the upper boundary. The analytical nature of the solution enables us to easily study the relative importance of various physical processes in the model surface energy budget equation. For example, evaporational cooling is found to be an important feedback process under model summer conditions, accounting for a change of about 6K in the daily mean surface temperature; under winter conditions, the change attributable to evaporation is only about 1K. The perturbation method used in our approach to linearize the model upper boundary condition is shown to be applicable to more complicated and more realistic upper boundary conditions.