Analytical Solution for Inverse Estimation of Groundwater Recharge from Transient Thermal Response in Stratified Media

Understanding transient heat transport in a layered subsurface media is essential for applications ranging from groundwater recharge estimation to climate signal detection in soil. This study presents an analytical model for 1D transient heat transfer in an N-layered soil system, accounting for realistic surface temperature variations induced by diurnal, seasonal, and long-term climatic trends. The governing advection-conduction equation is solved using the generalized integral transform technique, which inherently enforces interfacial continuity of temperature and heat flux across soil layers without the need for recursive matching or numerical Laplace inversion. The proposed solution is validated against existing analytical and numerical models, demonstrating excellent agreement in homogeneous and stratified domains. A local sensitivity analysis identifies key hydrothermal parameters influencing subsurface temperature behavior. The model’s inverse capability is further demonstrated through integration with a genetic algorithm, enabling the estimation of vertical water flux from synthetic temperature-depth data and observed field measurements. This work provides the first fully analytical, scalable, and computationally efficient framework for simulating and interpreting subsurface temperature dynamics in stratified systems. Its flexibility and robustness also make it readily applicable to other diffusion-driven transport processes, such as solute and vapor migration in layered geological formations, thereby enhancing its interdisciplinary relevance.