Analytical and Invertible Model for Transient Heat Transport in Layered Subsurface Media

 Abstract

Accurate characterization of transient heat transport in layered subsurface media is fundamental to a wide range of environmental and hydrological applications, including groundwater recharge assessment, land-atmosphere interaction analysis, and climate signal detection in soils. This study presents a fully analytical solution for one-dimensional transient heat transfer in a two-layer soil system subjected to realistic, time-dependent surface temperature forcing associated with diurnal variations. The governing advection-conduction equation is solved using the Generalized Integral Transform Technique, which enables an exact treatment of interlayer thermal interactions while avoiding numerical inversion or interface-matching complexities. The resulting formulation yields a computationally efficient and stable solution that is well suited for both forward simulation and inverse analysis. The analytical solution is rigorously validated through comparison with high-resolution numerical simulations, demonstrating excellent agreement for both homogeneous and stratified soil configurations over a wide range of hydrothermal conditions. The inverse modeling capability of the framework is further demonstrated by coupling the analytical solution with a genetic algorithm to estimate vertical water flux from field-measured temperature data, highlighting its potential for non-invasive hydrological characterization. This work introduces a scalable, computationally efficient, and physically consistent framework for simulating and interpreting transient heat transport in layered subsurface systems. Owing to its generality, the proposed methodology is readily extendable to other diffusion-dominated transport processes, such as solute transport in stratified geological media, thereby enhancing its applicability across a broad range of geoscientific problems.

Keywords: Transient heat transport, Layered subsurface media, Analytical solution, Generalized Integral Transform Technique, Inverse modelling