INV-WATFLX, a code for simultaneous estimation of soil properties and planar vector water flux from fully or partly functioning needles of a penta-needle heat-pulse probe

Abstract

Soil thermal properties and water fluxes are fundamental for understanding water and heat transport phenomena in the vadose zone. Processes of interest include quantifying infiltration and runoff in addition to solute transport rates, which are of great interest in many scientific and engineering applications where water flux and temperature are key parameters. In this study, INV-WATFLX was developed for simultaneously fitting thermal diffusivity, thermal conductivity and heat velocities in a plane normal to a penta-needle heat-pulse probe (PHPP) using temperature rise measurements in a porous medium. The inverse problem is formulated as the minimization of a generalized least-squares criterion by means of a Gauss–Newton–Levenberg–Marquardt method. Fitted temperature measurements following a heat-pulse injection were calculated from an analytical solution of temperature rise derived at the four thermistor positions of the PHPP. The INV-WATFLX code was tested with a set of synthetic simulations using CORE 2D V4. Relative errors of thermal diffusivity, conductivity, bulk volume heat capacity, and water fluxes estimated in INV-WATFLX to their prescribed values in the synthetic simulations were smaller than 3%. We also evaluated the ability of INV-WATFLX to provide estimation of thermal properties and fluxes from temperature rise measured by a sub-set of the four thermistors. INV-WAFLX was applied to laboratory column flow experiments for water flux estimation using a PHPP. Water fluxes estimated using INV-WATFLX was comparable to independently measured fluxes. The new code provides reliable estimation of soil thermal properties and water fluxes from temperature rise using heat-pulse measurements.