Ensemble modeling of E. coli in the Charles River, Boston, Massachusetts, USA

A case study of ensemble modeling of Escherichia coli (E. coli) densities in surface waters in the context of public health risk prediction is presented. The output of two different models, mechanistic and empirical, are combined and compared to data. The mechanistic model is a high-resolution, time-variable, three-dimensional coupled hydrodynamic and water quality model. It generally reproduces the mechanisms of E. coli fate and transport in the river, including the presence and absence of a plume in the study area under similar input, but different hydrodynamic conditions caused by the operation of a downstream dam and wind. At the time series station, the model has a root mean square error (RMSE) of 370 CFU/100mL, a total error rate (with respect to the EPA-recommended single sample criteria value of 235 CFU/100mL) (TER) of 15% and negative error rate (NER) of 30%. The empirical model is based on multiple linear regression using the forcing functions of the mechanistic model as independent variables. It has better overall performance (at the time series station), due to a strong correlation of E. coli density with upstream inflow for this time period (RMSE =200 CFU/100mL, TER =13%, NER =1.6%). However, the model is mechanistically incorrect in that it predicts decreasing densities with increasing Combined Sewer Overflow (CSO) input. The two models are fundamentally different and their errors are uncorrelated (R² =0.02), which motivates their combination in an ensemble. Two combination approaches, a geometric mean ensemble (GME) and an “either exceeds” ensemble (EEE), are explored. The GME model outperforms the mechanistic and empirical models in terms of RMSE (190 CFU/100mL) and TER (11%), but has a higher NER (23%). The EEE has relatively high TER (16%), but low NER (0.8%) and may be the best method for a conservative prediction. The study demonstrates the potential utility of ensemble modeling for pathogen indicators, but significant further research is needed to establish the approach for the Charles River, as outlined in the paper.