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Flood Frequency Relationships for Small Watersheds in Kansas

This report presents some new flood-frequency equations for Kansas that combine the best features of the Rational method and traditional regression equations. These equations provide estimates of discharges with recurrence intervals of 2, 5, 10, 25, 50, and 100 years for unregulated rural streams with drainage areas under 30 square miles. The inputs to these equations are the drainage area, the mean annual precipitation, and rainfall intensity. The rainfall intensity is the average intensity over the drainage area for a duration equal to the watershed’s time of concentration and the same recurrence interval as the desired discharge. Two sets of equations are presented. The equations in the first set are termed Extended Rational equations because the discharge is directly proportional to both rainfall intensity and drainage area, as in the Rational formula. The equations in the second set are power-type equations developed by traditional multiple-regression analysis. The two sets of equations are quite similar, with nearly identical standard errors. Both sets of equations were developed from data for 72 USGS stream-flow gaging stations on unregulated rural streams with drainage areas under 30 square miles and record lengths of 20 years or longer. Two-year through 100-year discharges for each station were computed from the annual peak-flow data by the most recent USGS method for Kansas. The time of concentration for each watershed was estimated from the channel length and average channel slope with the KDOT-KU equation for rural watersheds in Kansas. Point-rainfall intensities for these times of concentration were interpolated from KDOT’s rainfall tables. Corresponding area-average rainfall intensities were determined from the precipitation depth-area-duration relationship in the U.S. Weather Bureau’s Technical Paper No. 40. The runoff coefficient (C) for each recurrence interval was backed out from the Rational formula (Q = C i A) using the discharge from the frequency analysis, the area-average rainfall intensity and the drainage area. Predictive equations for the 2-year through 100-year runoff coefficients were developed by regression analysis. Many physical and climatic characteristics of the watershed were considered as possible explanatory variables. The recommended equations relate the runoff coefficients to mean annual precipitation (MAP). Maps illustrate the geographic variation in C, as predicted from MAP, across Kansas for the six recurrence intervals. The Extended Rational equations for the 2-year through 100-year discharges were obtained by substituting the recommended equations for C into the Rational formula. The report includes step-by-step instructions for applying the new equations and an example application.