The Coupled Transport of Water and Heat in a Vertical Soil Column Under Atmospheric Excitation

Abstract

The purpose of this work is to develop a detailed, physically-based model of the response of the land surface to atmospheric forcing. The coupled, nonlinear partial differential equations governing mass and heat transport in the soil are derived. The theory of Philip and de Vries is re-cast in terms of the soil water matric potential, accounting for soil inhomogeneities and hysteresis of the moisture retention process. An existing model of hysteresis is modified to incorporate the effect of temperature and to facilitate numerical analysis. The Galerkin finite element method is applied in the development of a numerical algorithm for the solution of the governing equations. The numerical procedure is coded in FORTRAN for computer solution and several examples are run in order to test the method. The various modes of mass and heat transport are simulated accurately. A proposed procedure for the evaluation of non-linear storage coefficients in the numerical scheme yields excellent mass and energy balances.