A Linear Analysis of Thermal Effects on Evaporation From Soil

Evaporation of water from a soil surface is a complex process that can be strongly tied to the distribution of temperature in the soil. One way of examining this coupling is through linearization and analytic solution of the partial differential equations and boundary conditions that govern the distributions of moisture and temperature. The solution for a step change in temperature and matric head at the surface of a soil that is initially isothermal and uniformly wetted suggests that evaporation can be calculated accurately by neglecting the dependence of moisture content on temperature, even when the associated “thermal liquid flux” is the largest moisture flux immediately beneath the soil surface. The resulting error decreases with the hydrothermal diffusivity ratio η , which is the ratio of soil moisture diffusivity to soil thermal diffusivity, and increases with the thermal liquid force ratio ξ , which is proportional to the poorly understood temperature coefficient of matric head. In contrast, the solution for diurnally varying evaporation from a relatively dry soil shows that the relative error induced by neglecting vapor diffusion due to thermally induced vapor concentration gradients is approximately equal to the relative magnitude of the neglected flux itself. This error is roughly equal to ση ½ , where the thermal vapor force ratio σ ; is the ratio of characteristic thermal to isothermal driving forces. Furthermore, when ση ½ is large, the daytime switches from a time of maximum evaporation to a time of minimum. This behavior is not reproduced if the thermal vapor flux is ignored.