Abstract: Based on the Phillips & Vriès' theory, we have suggested a coupling model for simulating water-heat movement in the sand soil with vegetation. The effects of temperature and vegetation roots on the exchange of water and heat between atmosphere and land are firstly analyzed. Then, we have provided the formulae to estimate soil evaporation, canopy transpiration, water-absorbing rate of root system and heat flux in soil. A Crank-Nicolson difference scheme is constructed to solve nonlinear diffusion equation to...