Stochastic Spectral Analysis of Heat Transfer in the Soil Water Layer: Simultaneous Consideration of Hydraulic Flux and Thermal Diffusivity With Estimation of Hydraulic Flux by Prescribed Thermal Diffusivity

This study presents a novel and scientifically robust approach for evaluating hydraulic flux in shallow unsaturated aquifers, emphasising its interaction with thermal diffusivity. Traditional methods that assess temperature fields in the soil water layer rely solely on predefined hydraulic flux or prescribed thermal diffusivity, posing significant challenges in capturing the inherent spatial and temporal variability. To address these limitations, this study employs a time-frequency spectral analysis framework, integrating theoretical derivations with observed temperature spectra. This approach effectively estimates hydraulic flux while maintaining a prescribed thermal diffusivity, offering a refined methodology for vadose zone investigations. The study examines two distinct boundary conditions: one with fixed inlet and outlet temperatures and another with a prescribed inlet temperature and a constrained outlet heat flux. Hydraulic flux is estimated through an inverse stochastic spectral approach, leveraging observed in situ temperature spectra. By systematically evaluating key parameters—including thermal diffusivity, target depth, domain length, dominant frequency components, and boundary conditions—the proposed methodology demonstrates a robust capability to quantify hydraulic flux variability. Notably, the results under the second boundary condition (prescribed inlet temperature, constrained outlet heat flux) align with temperature spectral observations, reinforcing the validity of this spectral-based approach. This research enhances the ability to resolve hydraulic flux in heterogeneous subsurface environments, providing insights into its potential range and uncertainty at varying depths. The findings offer a practical and adaptable framework for characterising vadose zone dynamics, with implications for subsurface hydrological modelling and environmental management.