Indirect estimation of soil thermal properties and water flux using heat pulse probe measurements: Geometry and dispersion effects

Traditionally, analytical solutions for heat transport in soils have been used in combination with heat pulse probe (HPP) measurements to estimate soil thermal properties. Although the analytical method has resulted in accurate estimation of soil thermal properties, we suggest that parameter estimation using inverse modeling (IM) provides new and unique opportunities for soil thermal characterization. Moreover, we show that the IM approach provides accurate estimation of soil water flux density in both unsaturated and saturated soil conditions for a wider range of water velocities than originally thought possible. Specifically, we show that accurate soil water velocity is obtained, simultaneously with soil thermal properties, if heat dispersion is included in the heat transport equation. The requirement for including heat dispersivity depends on the value of the newly defined dimensionless Keith Jirka Jan (KJJ) number, which is equal to the ratio of thermal dispersion to thermal conductivity. For example, when KJJ > 1, ignoring thermal dispersivity leads to errors in the water flux density which can exceed 10%. By including thermal dispersivity, water flow velocities were accurately determined for water flux densities ranging from 1.0 to >10 m d'1. We also demonstrate the general application of inverse modeling to estimate soil thermal properties and their functional dependence on volumetric water content in a separate numerical experiment. We suggest that inverse modeling of HPP temperature data may allow simultaneous estimation of soil water retention (when combined with matric potential measurements) and unsaturated hydraulic conductivity (through water flux estimation) from simple laboratory experiments.