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<p>Spatial heterogeneity and temporal variability represent intrinsic attributes of heat transfer properties, encompassing thermal diffusivity within the near-surface unsaturated zone. Evaluating such properties, especially within a time-evolving context, presents intricate challenges that demand nuanced approaches. This investigation is devoted to scrutinizing the dominant temporal frequency governing temperature dynamics within the confines of a shallow unsaturated soil domain. By utilizing the frequency domain, the thermal diffusivity of the soil profile is determined through skillful employment of temperature auto and cross-spectral density. The study introduces an analytical framework encompassing temperature and thermal diffusivity, considering two distinct boundary conditions: (1) prescribed temperatures at the inlet and outlet and (2) inlet temperature with outlet heat flux constraint. A subsequent inverse method is deployed to estimate thermal diffusivity, capitalizing on observed in situ temperature spectra. By judiciously delineating domain extents, key frequency components, and boundary conditions for the prescribed elements, the study systematically explores the uncertainty embedded within the system. This exploration entails an examination of cross-variations in thermal diffusivity across varying target depths. By employing diverse scenario manipulation strategies, the thermal diffusivity is resolved across the order of 1.0E−07 to 1.0E−06&#xa0;m<sup>2</sup>/s. Impressively, about 95% of the estimated thermal diffusivity values converge closely around their mean via cross-grouping, showcasing robust consistency under fixed scenarios. This innovative study underscores the feasibility and practical utility of harnessing stochastic time–frequency spectral analysis as a potent tool for precisely determining thermal diffusivity within the soil–water stratum of the shallow vadose zone.</p>

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

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • David Ching-Fang Shih

摘要

Spatial heterogeneity and temporal variability represent intrinsic attributes of heat transfer properties, encompassing thermal diffusivity within the near-surface unsaturated zone. Evaluating such properties, especially within a time-evolving context, presents intricate challenges that demand nuanced approaches. This investigation is devoted to scrutinizing the dominant temporal frequency governing temperature dynamics within the confines of a shallow unsaturated soil domain. By utilizing the frequency domain, the thermal diffusivity of the soil profile is determined through skillful employment of temperature auto and cross-spectral density. The study introduces an analytical framework encompassing temperature and thermal diffusivity, considering two distinct boundary conditions: (1) prescribed temperatures at the inlet and outlet and (2) inlet temperature with outlet heat flux constraint. A subsequent inverse method is deployed to estimate thermal diffusivity, capitalizing on observed in situ temperature spectra. By judiciously delineating domain extents, key frequency components, and boundary conditions for the prescribed elements, the study systematically explores the uncertainty embedded within the system. This exploration entails an examination of cross-variations in thermal diffusivity across varying target depths. By employing diverse scenario manipulation strategies, the thermal diffusivity is resolved across the order of 1.0E−07 to 1.0E−06 m2/s. Impressively, about 95% of the estimated thermal diffusivity values converge closely around their mean via cross-grouping, showcasing robust consistency under fixed scenarios. This innovative study underscores the feasibility and practical utility of harnessing stochastic time–frequency spectral analysis as a potent tool for precisely determining thermal diffusivity within the soil–water stratum of the shallow vadose zone.