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Simple linear model for calibration of time domain reflectometry measurements on solute concentration

Abstract:

The lack of an adequate method for calibration of time domain reflectometry (TDR) measurement on bulk soil electrical conductivity is a limiting factor, especially for field-scale solute transport study. This study investigated an appropriate calibration method that can be applied to horizontally positioned TDR probes in situ. A nonlinear model (RM) has been proposed assuming a two-pathway conductance. Using the quadratic form, the RM equated electrical conductivity in the immobile phase of soil solution (EC(ws)) in a series-coupled pathway with electrical conductivity in the mobile phase of soil solution (EC(wc)) in a continuous pathway. We related bulk soil electrical conductivity (EC(a)) to electrical conductivity of soil water (EC(w)), assuming constant EC(ws) during breakthrough. This resulted in a linear relationship between EC(a) and EC(w). The linear relation, termed here simple linear model (SLM), was tested using experimental data obtained from soil columns. Laboratory breakthrough experiments were performed on short and large columns by applying a pulse input of solute. At the end of breakthrough, separate calibration experiments were performed using a step input of solute. Both RM and SLM were compared with the step input calibration method (SIM) as a reference method. Results show that the SLM is better than RM in terms of mass recovery. In addition, parameters of the solute transport model were not affected within 20% of uncertainty in the slope coefficient of the SLM when compared with the reference method. Advantages of the SLM are that it has an identical equation form to the SIM but less effort is required, especially for soil columns showing preferential flow, and it can be readily applied to field conditions.