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Methods for estimating low-flow frequency statistics, mean monthly and annual flow, and flow-duration curves for ungaged locations in Kansas

September 30, 2021

Knowledge of the magnitude, frequency, and duration of low flows is critical for water-supply management; reservoir design; waste-load allocation; and the preservation of water quality and quantity for irrigation, recreation, and ecological conservation purposes. The U.S. Geological Survey (USGS), in cooperation with the Kansas Water Office, completed a statewide study to develop regression equations for selected low-flow frequency and flow-duration statistics for ungaged streams in Kansas.

The low-flow statistics included the annual and monthly 1-, 7-, and 30-day mean low flow for a recurrence interval of 10 years; flow-duration exceedance probabilities of 0.01, 0.1, 2, 5, 10, 25, 50, 75, 90, 95, 99, 99.9, and 99.99 percent; and mean annual flow. Data used in this analysis were from 254 USGS continuous-record streamgages using data through March 31, 2017, for the regression equation analysis and using data through September 30, 2017, for the flow-duration curve analysis. The streamgages used in the regression analysis of this report are in Kansas and 50 miles beyond the borders of the State. A trend analysis was done because trends can introduce bias into results. Some trends were detected; however, no streamgage was omitted from the analysis because of the presence of a trend. Geographic-information-system software was used to compute 13 basin characteristics for each streamgage.

The State of Kansas was divided into two study areas for the regional regression analysis. Logistic and left-censored regression techniques were used to develop the equations because of the presence of zero flows in the datasets. A collection of performance metrics is provided to estimate the accuracy of each equation. These equations are only applicable to streams in Kansas that are not substantially affected by diversion, regulation, or urbanization. Basin characteristics of these ungaged locations also need to be within the range of the basin characteristics used to develop these equations.

The drainage-area ratio (DAR) method was tested against the regional regression equations using 19 pairs of streamgages. The 7-day annual mean low-flow statistic was estimated using the regression equations and the DAR method. The absolute difference, in percent, was calculated using the observed 7-day annual mean low flow for both methods. The results of the Wilcoxon signed-rank test indicated that the difference between the absolute differences, in percent, for the groups tested was not statistically significant. Previous USGS studies state it is preferable to use the DAR method when the ratio is between 0.5 and 1.5. Some studies offer no scientific basis for these guidelines, whereas other studies have developed different guidelines. In Kansas, the DAR method produced the smallest absolute difference, in percent, when the ratio of drainage areas was between 0.5 and 1.5. The results of this study indicate that the DAR method is appropriate for use in Kansas when estimating streamflow at an ungaged location if there is a nearby streamgage on the same river or stream where the DAR is between 0.5 and 1.5 and the low-flow statistic at the nearby streamgage is not zero.

The regression equations developed in this report will be incorporated into the USGS StreamStats web-based geographic-information-system tool. This will allow users to click on any ungaged location within StreamStats and compute estimates of the selected low-flow frequency and flow-duration statistics. The low-flow frequency and flow-duration statistics for streamgages in Kansas also will be available in StreamStats.