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.

Introduction

Soil thermal properties and soil water flux measurements are desired for understanding water and heat transport phenomena in the vadose zone, quantifying infiltration, runoff and subsurface processes and are of great interest in many scientific and engineering applications where water fluxes and temperatures are required. Over the last decade numerous studies on heat-pulse measurements have shown promise for determination of thermal properties and water flux in soil (Bristow et al., 1993, Bristow et al., 1994; Campbell et al., 1991; Kluitenberg et al., 2007; Olmanson and Ochsner, 2008; Ren et al., 2000; Wang et al., 2002).

Generally, heat-pulse techniques for determination of thermal properties and water fluxes are based on applying a heat pulse to a line source and then measuring temperature rise at thermistor locations 6 mm from the heater. A dual-needle heat-pulse probe (DHPP) having one heater needle and one thermistor needle was presented by Campbell et al. (1991). That design allowed for rapid estimation of bulk heat capacity, specific heat capacity of the solid phase, thermal diffusivity, thermal conductivity, and water content. Subsequent improvements were made by other researchers (Basinger et al., 2003; Ham and Benson, 2004; Kluitenberg et al., 1995; Ochsner et al., 2003; Ren et al., 2003). Similar to a DHPP, a triple-needle heat-pulse probe (THPP) having two thermistor needles (i.e., downstream and upstream) was used for determining uni-directional water flux in soils (Kluitenberg et al., 2007; Ochsner et al., 2005; Ren et al., 2000; Wang et al., 2002). More recently, a penta-needle heat-pulse probe (PHPP) has been developed for estimating water flux in an arbitrary direction within a plane normal to the heater needle (Endo and Hara, 2007). A multi-functional heat-pulse probe (MFHPP) has been developed for simultaneously determining water content, solute concentration and thermal parameters (Mortensen et al., 2006).

The single-point method and inverse method (Bristow et al., 1995) have both been used to infer soil thermal parameters and water flux from temperature measurements of a heat-pulse based probe. The single-point method is based on the analytical solution of heat transport with an infinite line heat source and has been extensively used to estimate bulk volumetric heat capacity, thermal diffusivity, thermal conductivity, water content (Bristow et al., 1994; Campbell et al., 1991; Knight and Kluitenberg, 2004; Ochsner et al., 2003; Ren et al., 2003), and water flux (Gao et al., 2006; Kluitenberg et al., 2007; Ochsner et al., 2005; Ren et al., 2000; Wang et al., 2002). The inverse method involves fitting temperature–time data (T(t)) from heat-pulse based measurements. The advantage of an inverse method is that multi-parameters can be simultaneously estimated and the optimized parameters are extracted based on T(t) data, not simply using a single data point. Bristow et al. (1995) and Welch et al. (1996) fitted temperature measurements of a dual-needle heat-pulse probe using analytical solutions for thermal diffusivity, thermal conductivity, and bulk volume heat capacity. Hopmans et al. (2002) and Mortensen et al. (2006) fitted temperature measurements from a triple-needle heat-pulse probe and a multi-functional heat-pulse probe, respectively, using a numerical model to fit thermal properties, water flux, and water content. The advantage of fitting T(t) data using an analytical solution is that it requires much less computational effort than a numerical model. A finite element method (or finite difference method) is usually used in a numerical model although the heater geometry may be accounted for in the numerical model.

In this study the main objective was to present INV-WATERFLX, a numerical code for simultaneously fitting thermal diffusivity, thermal conductivity, and heat velocities within a plane normal to the PHPP using temperature rise measurements. Subsequently, corresponding bulk volume heat capacity, water content, and water fluxes are calculated. The inverse problem is formulated as the minimization of a generalized least-squares criterion by means of a Gauss–Newton–Levenberg–Marquardt method.