Estimation of Vadose Zone Water Flux from Multi‐Functional Heat Pulse Probe Measurements

Abstract

A small multi‐functional heat pulse probe (MFHPP) was applied to further develop measurement methodologies to improve on water flux estimations for unsaturated soils. The temperature responses of four thermistors surrounding a central heater in a 2.7‐cm diam. probe were analyzed by the heat transport equation to estimate thermal properties and convective heat flow. Volumetric heat capacity, water content, and thermal diffusivity were estimated from the horizontally placed thermistors, neglecting the convective flow effects in the transverse direction, whereas the water flux density was estimated from the temperature responses to the vertically placed thermistors. A parameter optimization technique was employed to fit the most likely parameters to the relevant analytical solutions. Falling head and multi‐step outflow experiments yielded independently obtained water flux measurements. Results showed that the estimated volumetric water content corresponded well with independent gravimetric measurements with a RMSE of 0.0056 m3 m−3, across a wide range of water fluxes smaller than 0.5 m d−1 Thermal diffusivity values as obtained with the MFHHP also agreed well with independently measured thermal diffusivity values, for water flux density values smaller than 2 m d−1 For saturated conditions, the estimated water fluxes from the MFHPP measurements were accurate in the range between 0.056 and 27.0 m d−1, with a R of 0.995 and RSME of 0.0952 log(m d−1) (0.52 m d−1). For unsaturated flow, MFHHP estimations significantly overestimated water flux density for flux values smaller than 0.10 m d−1 Within these limitations, we conclude that MFHPP methodologies are now available, making possible simultaneous estimation of thermal diffusivity and water flux density in unsaturated soils.