Determining convective lognormal solute transport parameters from resident concentration data

Time Domain Reflectometry (TDR) has become a popular method to obtain time series of resident concentrations in solute transport studies, so effective interpretation of TDR data is very useful. In this study, we evaluated three procedures to determine the parameters of the convective lognormal transfer function (CLT) model from such time series. In a first approach, the CLT model travel time probability density function (pdf) was related to time series of time-integral-normalized flux concentrations, C-f*(z,t). The normalization was based on mass balance calculations performed with time series of resident concentrations measured at several depths. The C-f*(z,t) data thus obtained were very erratic leading to a high parameter uncertainty. In a second approach, the CLT model travel depth pdf was related to time series of depth-integral- or mass-normalized resident concentrations, C-rm*(z,t). This approach suffered from uncertainty regarding calibration coefficients relating TDR measured impedance to resident concentrations and from uncertainty regarding the solute mass crossing the sampling volume of the TDR probe. The third approach used the relation between travel time and travel depth pdf for a stochastic-convective, transport process to formulate a new expression relating time-integral-normalized resident concentrations, C-rt*(z,t), to the CLT model parameters. No information is needed about calibration coefficients while no a priori assumptions about the solute mass detected by the TDR probe are required. This approach yielded better CLT model fits to observed concentration data, and the variability of parameters fitted at different locations can be related to heterogeneity of solute and water how after averaging across the TDR measurement window.