Symbolic Regression of Upstream, Stormwater, and Tributary E. Coli Concentrations Using River Flows

Symbolic regression was used to model E. Coli concentrations of upstream boundary, tributaries, and stormwater in the lower Passaic River at Paterson, New Jersey. These models were used to simulate boundary concentrations for a water quality analysis simulation program to model the river. River flows from upstream and downstream boundaries of the study area were used as predictors. The symbolic regression technique developed a variety of candidate models to choose from due to multiple transformations and model structures considered. The resulting models had advantages such as better goodness-of-fit statistics, reasonable bounds to outputs, and smooth behavior. The major disadvantages of the technique are model complexity, difficulty to interpret, and overfitting. The Nash-Sutcliffe efficiencies of the models ranged from 0.61 to 0.88, and they adequately captured the upstream boundary, tributary, and stormwater concentrations. The results suggest symbolic regression can have significant applications in the areas of hydrologic, hydrodynamic, and water quality modeling.