Coupling diffusion and maximum entropy models to estimate thermal inertia

Abstract

Thermal inertia is a physical property of soil at the land surface related to water content. We developed a method for estimating soil thermal inertia using two daily measurements of surface temperature, to capture the diurnal range, and diurnal time series of net radiation and specific humidity. The method solves for soil thermal inertia assuming homogeneous 1-D diffusion of heat near the land surface. The solution uses a boundary condition taken as the maximum likelihood estimate of ground heat flux made by a probabilistic uncertainty model of the partitioning of net radiation based on the theory of maximum entropy production (MEP model). We showed that by coupling the 1-D diffusion and MEP models of energy transfer at the land surface, the number of free parameters in the MEP model can be reduced from two (P — soil thermal inertia and I — thermal inertia of convective heat transfer to the atmosphere) to one (P is defined by I). A sensitivity analysis suggested that, for the purpose of estimating thermal inertia, the coupled model should be parameterized by the ratio P/I. The coupled model was demonstrated at two semi-arid sites in the southwest United States to estimate thermal inertia and these thermal inertia values were used to estimate soil moisture. We found 1) parameterizing the MEP model with a constant annual P/I value resulted in surface flux estimates which were similar to those made when daily P and I parameters were derived directly from measurements of ground heat flux (Nash-Sutcliffe efficiency>0.95); 2) estimates of P made using the coupled model were superior to those made using the diffusion model with a common linear approximation of the ground heat flux boundary condition; and 3) thermal inertia was a better predictor of soil moisture in moderately wet conditions than in dry conditions due to a lack of sensitivity of thermal inertia to changes in soil moisture at low moisture contents.