A regression model for computing index flows describing the median flow for the summer month of lowest flow in Michigan

In 2006, Michigan enacted laws to prevent new large capacity withdrawals from decreasing flows to the extent that they would functionally impair a stream's ability to support characteristic fish populations. The median streamflow for the summer month of lowest flow was specified by state decision makers as the index flow on which likely impacts of withdrawals would be assessed. At sites near long-term streamflow-gaging stations, analysis of streamflow records during July, August, and September was used to determine the index flow. At ungaged sites, an alternate method for computing the index flow was needed. This report documents the development of a method for computing index flows at ungaged stream sites in Michigan. The method is based on a regression model that computes the index water yield, which is the index flow divided by the drainage area. To develop the regression model, index flows were determined on the basis of daily flows measured during July, August, and September at 147 streamflow-gaging stations having 10 or more years of record (considered long-term stations) in Michigan. The corresponding index water yields were statistically related to climatic and basin characteristics upstream from the stations in the regression model. Climatic and basin characteristics selected as explanatory variables in the regression model include two aquifer-transmissivity and hydrologic-soil groups, forest land cover, and normal annual precipitation. Regression model estimates of water yield explain about 70.8 percent of the variability in index water yields indicated by streamflow-gaging station records. Index flows computed on the basis of regression-model estimates of water yield and corresponding drainage areas explain about 94.0 percent of the variability in index flows indicated by streamflow-gaging station records. No regional bias was detected in the regression-based estimates of water yield within seven hydrologic subregions spanning Michigan. Thus, the single regression model developed in this report can be used to produce unbiased estimates of index water yield and flow statewide. In addition, a technique is presented for computing prediction intervals about the index flow estimates.