A novel stochastic method to determine thermal diffusivity for a shallow vadose zone: the theoretical derivation and application adopting the spectral analysis of temperature

Spatial heterogeneity and temporal variability are typical features of the heat transfer properties, including thermal diffusivity, in the shallow vadose zone. Assessing the heat transfer property, particularly in the context of time-dependent observations, may pose challenges in achieving effective evaluation. This study aims to analyze the dominant frequency in the temporal evolution of temperature within a shallow unsaturated soil zone system. The thermal diffusivity of the zone profile can be determined by employing temperature auto and cross-spectral density in the frequency domain. The study presents a theoretical spectral representation of an analytical system that combines temperature and thermal diffusivity considering two boundary conditions: (1) temperature at the inlet and outlet and (2) temperature at the inlet while ensuring no heat flux at the outlet. Subsequently, an inverse method is employed to estimate the thermal diffusivity by utilizing observed in situ temperature spectra. By selecting the domain length, significant frequency component, and boundary types of the designed elements, the study assesses the uncertainty of the system by examining the cross-variation of thermal diffusivity at different target depths. The study also examines the validity of the derived thermal diffusivity values for the proposed soil layer. The innovative research demonstrates the feasibility and applicability of using stochastic time-frequency spectral analysis to accurately determine the thermal diffusivity in the soil-water layer of a shallow vadose zone.