Generalized skew coefficients of annual floods in the United States and their application

Abstract

Generalized skew coefficients for use in defining flood-tYequency curves that tbllow log Pearson type 3 distributions are shown by isopleths on a map of conterminous United States. The generalized logarithmic skew coefficients range from 0.6 along the eastern seaboard to -0.5 in Indiana and Illinois.West of the one-hundredth meridian the coefficients range from -0.3 to 0.2 except for a small area in Nebraska where the generalized skew goes as high as 0.4. The validity of the map values is verified by a split-sampling procedure. In the west the discharge of 50-and 100-yr peaks. computed by using map values of skew is more accurate than that computed by using the observed skew of a sample of 30 annual peaks. East of the Mississippi River the accuracy is even higher and approaches the equivalent of 60 annual peaks along the east coast. An equation gives the adjustment by which a T-yr peak computed by using map skew would have to be increased to give a discharge that has an average exceedance probability equal to I/T. Flood-frequency curves are commonly computed by fitting a Pearson type 3 distribution to the logarithms of annual peak discharges observed over a period of years. Such a curvedepends on the mean, the standard deviation, and the skew coefficient computed from the logarithms of the annual peaks and is subject to the error inherent in estimating the population parameters from the sample statistics. The Water Resources Council [1967] recognized that the skew coefficient has greater variability between samples than the mean and the standard deviation do and suggested the possibility of using a regional value of skew coefficient in place of that based on a short record of annual peaks.

Technique for estimating magnitude and frequency of floods in Kentucky

“…The ratio Ks at the site is given by equation : Sm""""n"~mmm"""in ~m""n" ~"~ m""ml � � � DRAINAGE AREA, IN SQUARE KILOMETERS 100 1,000 10,000 � � � � � DRAINAGE AREA, IN SQUARE KILOMETERS 100 1,000 5,000 100,000 � � � � (Hardison, 1974) were in general agreement with graphical plots in most cases .…”

“…The second line (Assigned) shows the assigned skew (Hardison, 1974) In summary, the recommended procedure for estimating flood discharge for a desired frequency is outlined below .…”

Log Pearson type 3 quantile estimators with regional skew information and low outlier adjustments

“…As noted above, À1.4 is a realistic lower bound. The range [À1.4, +1.4] is certainly within the distribution of site-to-site variability observed in Hardison's [1974] estimates and substantially larger than that suggested by MSE G % 0.100 as reported by Tasker and Stedinger [1986] and Reis et al [2003]. Thus it is certainly reasonable to place bounds of ±1.4 on generated population skews so as to restrict the analysis to reasonable values.…”

“…[9] The regional skew may be obtained from the skew map provided in B17, which was originally developed by Hardison [1974]. The standard error of the map is reported to be 0.55, indicating that MSE G is approximately 0.302.…”

Analyzing the effects of excess rainfall properties on the scaling structure of peak discharges: Insights from a mesoscale river basin

“…In the United States, the U.S. Geological Survey (USGS) pioneered the methodology used for regionalization of flood frequencies in the 1960s [Benson, 1962[Benson, , 1964[Benson, , 1968, and the method has subsequently undergone several refinements [e.g., Hardison, 1974;IACWD, 1982;Tasker and Stedinger, 1986]. Regional flood-frequency equations relate peak discharge quantiles to rainfall and catchment descriptors such as drainage area, slope of the main channel, longest stream length, soil type, land use, and mean annual precipitation.…”