Are we fully capturing the potential of solute breakthrough curves?

Several studies have shown that preferential flow is a widespread phenomenon when studying solute transport in soil, but the relationships between this phenomenon, the hydrologic boundary conditions, and site properties are still only moderately understood. Even though a better understanding of these mechanisms is essential to improve predictions of the fate of the contaminants at short and long term time scales. Previous studies used nonparametric indicators characterizing the shape of breakthrough curves issued from Dirac tracer pulses to quantify preferential flow. Breakthrough curves are probability density functions obtained after controlled tracer application to soil columns and they are different for different soil types. Deconvolution techniques have been used to convert these BTC from different types of tracer application to standard transfer functions for which we can estimate and compare shape measures. However, previous studies suggest that the deconvolution used fits the tailing of the BTCs poorly which has an important impact of some of the shape measures used, since some of them are very sensitive to changes in the tailing. This study aims at improving the fit to the tailing of the BTC by using deconvolution techniques more appropriate for probability density functions specific to solute transport without assuming a specific shape of the transfer function. Deconvolution is a minimization of an objective function which is the sum of two terms. The first measures the fit of the solution to the experimental data and the second measures the smoothness of the solution. In this study the Kulblack-Leibler divergence will be applied instead of the widespread Euclidian norm for the first term. Kulblack-Leibler is specified for use with density probability functions and may therefore give a better compromise between fit of the main BTC and fit of the tailing. The innovative aspect of this work is that no a-priori assumptions are made concerning the shape of the BTC through the utilisation of a regularization term. These new convolution techniques will be tested and applied on BTCs from the solute transport data base constructed by Koestel et al. (2012).The expected results are an overview of the the goodness of fit to the probability density function and a quantification of the effect of these improved convolution techniques on the shape parameters. This study is located in the broader context to develop indicators that can predict the preferential flow for certain types of soil.