Internal heat source in the vadose zone: A comprehensive exploration through theoretical spectral analysis and practical application into thermal diffusivity and hydraulic flux in a Quaternary soil water layer

This groundbreaking study introduces a scientifically robust method for assessing internal heat generation in shallow, unsaturated aquifers, highlighting the intricate interplay between internal heat, thermal diffusivity, and hydraulic flux. The research pioneers a novel approach employing time-frequency spectral analysis to address challenges posed by conventional methods that rely solely on prescribed thermal diffusivity and hydraulic flux for evaluating internal heat over time. Rooted in a solid theoretical framework supported by meticulous temperature and heat flux observations, the method adeptly incorporates the concept of an unknown internal heat. The study systematically explores three distinct boundary conditions, showcasing versatility: one with fixed temperatures at the inlet and outlet, another with known temperature at the inlet and no heat flux at the outlet, and a third with a prescribed inlet temperature and constrained outlet heat flux. The estimation of internal heat, coupled with prescribed thermal diffusivity and hydraulic flux, harnesses in-situ temperature and heat flux spectra through an innovative inverse stochastic spectral approach. A notable feature of this research lies in its ability to strategically handle various parameters, including prescribed thermal diffusivity, hydraulic flux, variations in target depth, significant frequency components, and boundary conditions. The variation assessment findings emphasize the diverse range when predicting internal heat generation based on prescribed thermal diffusivity and hydraulic flux. This study facilitates the determination of potential internal heat magnitudes at different depths and provides profound insights into in-situ conditions within the vadose zone.