Spectral coherence of soil thermal conditions and a stochastic inverse solution for thermal conductivity in the shallow vadose zone of Quaternary gravel formation

Abstract

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. In addition, this research proposes a stochastic inverse solution of thermal conductivity using spectral estimation of soil heat flux and temperature gradient. It suggests that the most apparent periodic fluctuations of the thermal condition are in the diurnal process for 24 hours. The soil temperature gradient and heat flux at 10, 30, 60, and 120 cm depths can catch soil temperature and air temperature changes to some degree in the frequency domain. The thermal conductivity ranges from about 5.44 to 0.41 W/(m°C) for the soil depths from 10 to 120 cm using the spectral inversed solution. Thus, using spectral analysis, assessing the soil layer's thermal conductivity and other thermal conditions becomes feasible and achievable.