Multivariate Polynomial Time-Series Models and Importance Ratios to Qualify Fecal Coliform Sources

Sensitivity analysis using importance ratios was applied to multivariate polynomial regression (MPR) models to make inferences about the nature and magnitude of fecal coliform (FC) sources in a combined sewer overflow-impacted stretch of the Passaic River at Paterson, New Jersey. The predictor variables in this study were temperature, discharge, precipitation, and upstream concentrations. The MPR models are applicable only for the current conditions with respect to pollutant sources. New models should be developed in case of any change in pollutant sources, by location or magnitude. This is a limitation that MPR models have in common with any empirical modeling approach, including multilinear regression or artificial neural networks. The performance of the MPR models using R2 was significantly better than simple linear models using the same variables. The importance ratio, a dimensionless measure of model sensitivity, was used for comparison of the effects of different variables. Because model sensitivities, and therefore importance ratios, are not constant in nonlinear models, this work examines their distributions and relates them to system behavior, for example by showing under what conditions dilution does or does not affect FC concentrations in the stream. The analysis showed that MPR models and importance ratios can be used to provide significant information to better understand pollutant sources at a site and the relative importance of various predictor variables in explaining the variability in the FC concentrations.