Understanding the Impact of Boundary and Initial Condition Errors on the Solution to a Thermal Diffusivity Inverse Problem

In this work, we consider simulation of heat flow in the shallow subsurface. As sunlight heats up the surface of soil, the thermal energy received dissipates dow nward into the ground. This process can be modeled using a partial differential equation known a s the heat equation. The spatial distribution of soil thermal conductivities is a key factor in the mode ling process. Prior to this study, temperature profiles were recorded at different dep ths at various times. This work is motivated by trying to match these temperature profiles using a simulation-b ased approach and analytic approaches in the context of an inverse problem. Spe cifically we determine soil thermal conductivities using derivative-free optimization to minimize the non li ear-least square errors between simulation and data profile. Here, we conduct two se s f studies, assuming homogeneous and heterogeneous soil envrionments respectively. W e also study how errors in the initial and boundary conditions propagate over time using both a numerica l approach and an analytical method.