Parameter Estimates of Field Solute Transport Models Based on Time Domain Reflectometry Measurements

Abstract A new technique using vertically installed time domain reflectometry (TDR) probes can be used to measure the mass flux of solute past the ends of the TDR probes and characterize the probability density functions of travel times. The procedure is applicable for a conservative tracer under steady‐state leaching conditions of constant surface volume flux density of water. The procedure is, however, limited to soils low in salts where the addition of a solute spike will cause a measurable reduction in the TDR signal. We developed the transport equations used to analyze the breakthrough data and obtain the appropriate parameters of two steady‐state models, the convective dispersion equation and the convective lognormal transfer function, as well as a moment analysis. Other models could also have been used. The TDR measurements (reduced in terms of the maximum measured value) for a Dirac‐delta function (spike) input of solute are shown to be equivalent to the solution of a step function input of pure water at the surface to a soil containing unit concentration to infinite depth, i.e., the complement of the flux‐averaged reduced concentration for a step function input of solute. Nonlinear curve‐fitting techniques were used to obtain the transport parameters. Fitting the measured TDR readings to the two models for both field and laboratory data gave good estimates of the transport parameters. The moment analysis, however, reflected the early breakthrough and tailing of the solute, resulting in a doubling of the variance. In addition, variances at the averaged field scale were found to be slightly more than double those at the local scale. The field TDR procedure is fast, inexpensive and nondestructive; the analysis presented yields needed parameters for model predictions.