Robust Estimation of the Generalized Solute Transfer Function Parameters

Abstract

A method is presented to mathematically characterize a wide range of solute transport processes in soils from time‐domain‐reflectometry (TDR)‐based breakthrough curve (BTC) measurements. To do this, we combined the flexible generalized transfer function model (GTF) with the definition of the time normalized resident concentrations Crt* The GTF is a four‐parameter flexible transfer function able to describe both the convection‐dispersive (CD) and the stochastic‐convective (SC) process of dispersion in a soil. In addition, it allows other dispersion processes typical for heterogeneous soils to be modeled. To obtain robust estimations of the GTF model parameters, closed‐form expressions of the GTF time normalized resident concentrations Crt* and temporal moments of Crt* were defined. These expressions allow the transport parameters to be estimated from TDR‐based BTCs without relying on problematic probe calibrations and mass recovery assumptions. Since GTF is a four‐parameter model, the robustness of the parameterization procedure was tested by fitting the Crt* of the GTF model to numerically generated, error‐contaminated BTCs. Using the least‐square optimization technique, robust estimates of the GTF parameters could be obtained from TDR observations at two different soil depths. Application of the proposed method was also tested for a real undisturbed sandy subsoil and compared with the convective lognormal transfer (CLT) and CD models. For this case, it was shown that the GTF model improved greatly the goodness of prediction of the BTCs. The proposed method offers a new powerful tool for analyzing transport processes of nonreactive solutes in soil.