| Summary: | 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 (<inline-formula><math display="inline"><semantics><msub><mi>K</mi><mi>f</mi></msub></semantics></math></inline-formula>), main flow zone area (<inline-formula><math display="inline"><semantics><msub><mi>A</mi><mi>f</mi></msub></semantics></math></inline-formula>), storage zone area (<inline-formula><math display="inline"><semantics><msub><mi>A</mi><mi>s</mi></msub></semantics></math></inline-formula>), and storage exchange rate (<inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>); 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 <inline-formula><math display="inline"><semantics><msub><mi>A</mi><mi>f</mi></msub></semantics></math></inline-formula>. Sensitivity analyses of MGGP models showed that the sinuosity is the most influential factor in <inline-formula><math display="inline"><semantics><msub><mi>K</mi><mi>f</mi></msub></semantics></math></inline-formula>, while <inline-formula><math display="inline"><semantics><msub><mi>A</mi><mi>f</mi></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>A</mi><mi>s</mi></msub></semantics></math></inline-formula>, and <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, are more sensitive to <inline-formula><math display="inline"><semantics><mrow><mi>U</mi><mo>/</mo><msub><mi>U</mi><mo>*</mo></msub></mrow></semantics></math></inline-formula>. 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.
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