An analytical solution for estimating percolation rate by fitting temperature profiles in the vadose zone

We present a simple analytical solution for one-dimensional steady heat transfer with convection and conduction through a multilayer system such as a vadose zone. We assume that each layer is homogeneous and has a constant thermal diffusivity. The mass/heat flow direction is perpendicular to the layers, and the mass flow rate is a constant. The analytical solution presented in this study also assumes constant known temperatures at the two boundaries of the system. Although the analytical solution gives the temperature as a function of a few parameters, we focus on the inverse application to estimate the percolation rate in a vadose zone. Example applications have shown that with reliable field observation data, the solution can be used to determine the percolation rate to high degree of accuracy (e.g., to mm/year). In some other cases, the solution may also be helpful in characterizing potential lateral flow along layer divides.