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.

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Sediment transport load monitoring is important in civil and environmental engineering fields. Monitoring the total load is difficult, especially because of the cost of the bed load transport measurement. This study proposes estimation models for the suspended load to total load ratio (Fsus) using dimensionless hydro-morphological variables. Two prominent variable combinations were identified using the recursive feature elimination procedure of support vector regression (SVR): (1) W/h, d*, Reh, Frd, and Rew and (2) Reh, Fr, and Frd. The explicit interactions between Fsus and the two combinations were revealed by two modern symbolic regression methods: multi-gene genetic programming and Operon. The five-variable SVR model showed the best performance (R2=0.7722). The target dataset was clustered by applying a self-organizing map and Gaussian mixture model. Through these steps, Reh and Frd are determined as the two most influential variables. Subsequently, the one-at-a-time sensitivity of the input variables of the empirical models was investigated. By referring to the clustering and sensitivity analyses, this study provides physical insights into Fsus controlling relationships. For example, Fsus is proportional to Reh and is inversely related to Frd. The empirical models developed in this study are applicable in practice and easy to implement in other real-time surrogate suspended-sediment monitoring methods, because they only require basic measurable hydro-morphological variables, such as velocity, depth, width, and mean bed material grain size.