Mathematical analysis of heat pulse signals for soil water flux determination
 Soil water flux is an important parameter in studies of runoff, infiltration, groundwater recharge, and subsurface chemical transport. Heat pulse sensors have been proposed as promising tools for measuring soil water fluxes. To date, heat pulse methods have required cumbersome mathematical analyses to calculate soil water flux from the measured data. We present a new mathematical analysis showing that a simple linear relationship exists between soil water flux and the natural log of the ratio of the temperature increase downstream from the line heat source to the temperature increase upstream from the line heat source. The simplicity of this relationship makes heat pulse sensors an attractive option for measuring soil water fluxes. In theory, this method is valid for fluxes with magnitudes between 10−4 and 10−7 m s−1. The range of measurable fluxes is defined by temperature measurement resolution at the lower end and by the assumptions used in the analysis at the higher end.
This article is published as Wang, Quanjiu, Tyson E. Ochsner, and Robert Horton. "Mathematical analysis of heat pulse signals for soil water flux determination." Water resources research 38, no. 6 (2002). doi: 10.1029/2001WR001089. Posted with permission.