Gene expression models for prediction of longitudinal dispersion coefficient in streams

- Developed more accurate gene expression model for longitudinal dispersion.
- The trained and tested model using 150 published international datasets.
- Model variables included Froude number, aspect ratio, and the bed roughness.
- Prediction errors of GEP models were smaller than existing regression models.
- The exponents in GEP models are not constant but a function of Froude number.

SummaryLongitudinal dispersion is the key hydrologic process that governs transport of pollutants in natural streams. It is critical for spill action centers to be able to predict the pollutant travel time and break-through curves accurately following accidental spills in urban streams. This study presents a novel gene expression model for longitudinal dispersion developed using 150 published data sets of geometric and hydraulic parameters in natural streams in the United States, Canada, Europe, and New Zealand. The training and testing of the model were accomplished using randomly-selected 67% (100 data sets) and 33% (50 data sets) of the data sets, respectively. Gene expression programming (GEP) is used to develop empirical relations between the longitudinal dispersion coefficient and various control variables, including the Froude number which reflects the effect of reach slope, aspect ratio, and the bed material roughness on the dispersion coefficient. Two GEP models have been developed, and the prediction uncertainties of the developed GEP models are quantified and compared with those of existing models, showing improved prediction accuracy in favor of GEP models. Finally, a parametric analysis is performed for further verification of the developed GEP models. The main reason for the higher accuracy of the GEP models compared to the existing regression models is that exponents of the key variables (aspect ratio and bed material roughness) are not constants but a function of the Froude number. The proposed relations are both simple and accurate and can be effectively used to predict the longitudinal dispersion coefficients in natural streams.