Prediction of Ground Surface Temperature and Soil Moisture Content by the Force‐Restore Method

Abstract

The parsimony and computational efficiency offered by the force‐restore approximation of the diffusion equation have motivated its widespread application in modeling ground surface temperature. Different assumptions regarding the definition of ground surface temperature have resulted in different versions of the force‐restore method. Here, four existing versions of the force‐restore method for ground surface temperature are compared and contrasted. An improved version of the force‐restore method is developed by minimizing the error produced by the force‐restore approximation of the heat diffusion equation. The proposed model performs well for the physically realistic ranges of scaled soil thickness and reproduces amplitude and phase that are quite close to the exact solution of the diffusion equation under a single periodic forcing. It is shown that neglect of higher harmonics can produce appreciable errors in the force‐restore method if the upper soil thickness is less than the damping depth of the diurnal forcing. The success of the force‐restore approximation in modeling ground surface temperature has prompted its application in the prediction of soil moisture content. However, extension of the force‐restore method for the prediction of soil moisture content is not straightforward. There are two major difficulties in modeling soil moisture content by the force‐restore method. One is the situation‐dependent relative importance of the suction term and gravity term in the Richards equation and the other is the choice of state variable, moisture content versus suction head, in the solution of the force‐restore method for soil moisture prediction. Both of these could produce appreciable errors in the force‐restore treatment of soil moisture evolution.