Configuring Maximum Entropy Deconvolution for the Identification of Residence Time Distributions in Solute Transport Applications

Abstract

The advection-dispersion equation (ADE) or aggregated dead zone (ADZ) models and their derivatives are frequently used to describe mixing processes within rivers, channels, pipes, and urban drainage structures. The residence time distribution (RTD) provides a nonparametric model that may describe mixing effects in complex mixing contexts more completely. Identifying an RTD from laboratory data requires deconvolution. Previous studies have successfully applied maximum entropy deconvolution to solute transport data, with RTD subsampling used for computational simplification. However, this requires a number of configuration settings which have to date not been rigorously investigated. Four settings are investigated here: the number and distribution of sample points, the constraint function, and the maximum number of iterations. Configuration options for each setting have been systematically assessed with reference to representative solute transport data by comparing the goodness-of-fit of recorded and predicted downstream profiles using the Nash-Sutcliffe efficiency index, evaluating RTD smoothness with a measure of entropy, and through consideration of the mass-balance of the RTD. New methods for defining sample point distribution are proposed. The results indicate that goodness-of-fit is most sensitive to constraint function and that smoothness is most sensitive to the number and distribution of sample points. A set of configuration options that includes a new sample point distribution is shown to perform robustly for a representative range of laboratory solute transport data.