The Remarkable Generality of the Transient Storage Model with Residence Time Dependence: Temporal Moments.

<p>Several distinct approaches to the one-dimensional modeling of river corridor transport at the macroscale have been developed as generalizations of the original Transient Storage Model (TSM).  We show that essentially all of them can be captured by simply restructuring the TSM so that the exchange coefficients are functions of residence time, because doing so converts the TSM to a general memory function form.  We use this generalized TSM approach to find novel closed-form expressions for the temporal moments of breakthrough curves resulting from river corridor tracer tests, when hyporheic zone exchange is governed by a memory function.  These expressions are useful because they can be used to test different hypotheses about the hyporheic zone residence time distribution based on analyses of the temporal moments of the tracer test breakthrough curves prior to detailed modeling work.  We demonstrate the application with a case study, and present extensions of the notion of making rate coefficients depend on residence time.</p>

Multi-Gene Genetic Programming Regression Model for Prediction of Transient Storage Model Parameters in Natural Rivers

A Transient Storage Model (TSM), which considers the storage exchange process that induces an abnormal mixing phenomenon, has been widely used to analyze solute transport in natural rivers. The primary step in applying TSM is a calibration of four key parameters: flow zone dispersion coefficient (Kf), main flow zone area (Af), storage zone area (As), and storage exchange rate (α); by fitting the measured Breakthrough Curves (BTCs). In this study, to overcome the costly tracer tests necessary for parameter calibration, two dimensionless empirical models were derived to estimate TSM parameters, using multi-gene genetic programming (MGGP) and principal components regression (PCR). A total of 128 datasets with complete variables from 14 published papers were chosen from an extensive meta-analysis and were applied to derivations. The performance comparison revealed that the MGGP-based equations yielded superior prediction results. According to TSM analysis of field experiment data from Cheongmi Creek, South Korea, although all assessed empirical equations produced acceptable BTCs, the MGGP model was superior to the other models in parameter values. The predicted BTCs obtained by the empirical models in some highly complicated reaches were biased due to misprediction of Af. Sensitivity analyses of MGGP models showed that the sinuosity is the most influential factor in Kf, while Af, As, and α, are more sensitive to U/U*. This study proves that the MGGP-based model can be used for economic TSM analysis, thus providing an alternative option to direct calibration and the inverse modeling initial parameters.