Using in-situ temperature measurements to estimate saturated soil thermal properties by solving a sequence of optimization problems

We describe an approach to find an initial approximation to the thermal properties of soil horizons. This technique approximates thermal conductivity, porosity, unfrozen water content curves in horizons where no direct temperature measurements are available. To determine physical properties of ground material, optimization-based inverse techniques are employed to fit the simulated temperatures to the measured ones. Two major ingredients of these techniques are an algorithm to compute the soil temperature dynamics and a procedure to find an initial approximation to the ground properties. In this article we show how to determine the initial approximation to the physical properties and present a new finite element discretization of the heat equation with phase change to calculate the temperature dynamics in soil. We successfully apply the proposed algorithm to recover the soil properties for the Happy Valley site in Alaska using one-year temperature dynamics. The determined initial approximation is utilized to simulate the temperature dynamics over several consecutive years; the difference between simulated and measured temperatures lies within uncertainties of measurements.