Refinement of regression models to estimate real-time concentrations of contaminants in the Menomonee River drainage basin, southeast Wisconsin, 2008-11

In 2008, the U.S. Geological Survey and the Milwaukee Metropolitan Sewerage District initiated a study to develop regression models to estimate real-time concentrations and loads of chloride, suspended solids, phosphorus, and bacteria in streams near Milwaukee, Wisconsin. To collect monitoring data for calibration of models, water-quality sensors and automated samplers were installed at six sites in the Menomonee River drainage basin. The sensors continuously measured four potential explanatory variables: water temperature, specific conductance, dissolved oxygen, and turbidity. Discrete water-quality samples were collected and analyzed for five response variables: chloride, total suspended solids, total phosphorus, Escherichia coli bacteria, and fecal coliform bacteria. Using the first year of data, regression models were developed to continuously estimate the response variables on the basis of the continuously measured explanatory variables. Those models were published in a previous report. In this report, those models are refined using 2 years of additional data, and the relative improvement in model predictability is discussed. In addition, a set of regression models is presented for a new site in the Menomonee River Basin, Underwood Creek at Wauwatosa.

The refined models use the same explanatory variables as the original models. The chloride models all used specific conductance as the explanatory variable, except for the model for the Little Menomonee River near Freistadt, which used both specific conductance and turbidity. Total suspended solids and total phosphorus models used turbidity as the only explanatory variable, and bacteria models used water temperature and turbidity as explanatory variables.

An analysis of covariance (ANCOVA), used to compare the coefficients in the original models to those in the refined models calibrated using all of the data, showed that only 3 of the 25 original models changed significantly. Root-mean-squared errors (RMSEs) calculated for both the original and refined models using the entire dataset showed a median improvement in RMSE of 2.1 percent, with a range of 0.0–13.9 percent. Therefore most of the original models did almost as well at estimating concentrations during the validation period (October 2009–September 2011) as the refined models, which were calibrated using those data.

Application of these refined models can produce continuously estimated concentrations of chloride, total suspended solids, total phosphorus, E. coli bacteria, and fecal coliform bacteria that may assist managers in quantifying the effects of land-use changes and improvement projects, establish total maximum daily loads, and enable better informed decision making in the future.