Estimation of regional flow-duration curves for Indiana and Illinois

Flow-duration curves (FDCs) of daily streamflow are useful for many applications in water resources planning and management but must be estimated at ungaged sites. One common technique for estimating FDCs at ungaged sites in a given region is to use equations obtained by linear regression of FDC quantiles against multiple basin characteristics that can be computed by means of a geographic information system (GIS) computer program. In this study, such regional regression equations for estimating FDC quantiles were computed at the 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 25, 30, 40, 50, 60, 70, 75, 80, 90, 95, 98, 99, 99.5, 99.8, and 99.9-percent exceedance probabilities for rural, unregulated streams in Indiana and Illinois with temporally stationary records, using data through September 30, 2007. The approach used accounts for censored values below 0.01 cubic feet per second, which are observed at exceedance probabilities as low as 70 percent (that is, occurring at least 30 percent of the time). The basin characteristics used are suitable for computation by the USGS Web-based application, StreamStats, and are available for all U.S. Environmental Protection Agency (EPA) Region V states and the larger Great Lakes area, with some specific local exceptions. Indiana and Illinois were each divided into three regions, and a different set of equations for estimating FDC quantiles was computed for each region.

The error of estimation of the FDC quantiles, measured as the mean square residual in log space converted to a percentage of the quantile, varies somewhat among regions and varies strongly with exceedance probability, with a minimum error of 10 to 20 percent at an exceedance probability of 5 or 10 percent, but rises to 17 to 38 percent at the high-flow end of the FDCs (the 0.1-percent quantile) and 100 to 745 percent at the low-flow end. For comparison, errors of estimation also were computed for FDC quantiles estimated by linear regression on drainage area alone and by using the drainage-area ratio (DAR) method. Three criteria, the nearest basin centroid and two others termed “strict” and “broad”, were used to select index stations for the DAR method. The “strict” and “broad” criteria put conditions on the basin centroid distance and the range of their drainage-area ratios, and the errors were averaged for all index station pairs satisfying each criterion. The use of the simpler DAR method usually resulted in higher errors of estimation compared to the linear regression equations with multiple basin characteristics, except occasionally in the case of the DAR method with the strict index station selection criterion, a criterion that is rarely possible to satisfy in practice.

An example application of the estimated equations to one gaged and a few ungaged locations in a watershed in the study area is included to illustrate the steps required. These steps are the computation of the basin characteristics and, using those characteristics together with the estimated equations, the computation of the FDC quantiles and their uncertainties.