Thermal conductivity in a vadose zone: a novel spectral solution and application by the implication of significant coherence of thermal condition in the shallow gravel formation

Abstract Due to the heterogeneity in the unsaturated or vadose zone, it is challenging to represent the analytical mechanism and actual in-situ water content in the soil layer. However, in the shallow layers, thermal conditions quickly change with surface temperature evolution. It expects that the water content can, more or less, be affected by the in situ heat mechanism. This research, therefore, suggests a novel design to theoretically discover the thermal conditions, such as soil temperature, soil temperature gradient, and heat flux in the shallow Quaternary gravel layer at various depths using spectral analysis of temporal observations. This research primarily proposes a stochastic inverse solution for estimating thermal conductivity using spectral analysis of soil heat flux and temperature gradient. It suggests that the thermal condition exhibits the most periodic fluctuations during the diurnal process over a 24-hour period. The soil temperature gradient and heat flux at depths of 10, 30, 60, and 120 (cm) can capture changes in soil temperature and air temperature to a certain extent in the frequency domain. The thermal conductivity within the soil-water system is determined across soil depths ranging from 10 to 120 cm using the derived inverse spectral solution. Consequently, the utilization of spectral analysis makes it feasible and attainable to assess the thermal conductivity of the soil layer in conjunction with the heat flux and temperature gradient.