Methods for estimating regional skewness of annual peak flows in parts of the Great Lakes and Ohio River Basins, based on data through water year 2013

Bulletin 17C (B17C) recommends fitting the log-Pearson Type III (LP−III) distribution to a series of annual peak flows at a streamgage by using the method of moments. The third moment, the skewness coefficient (or skew), is important because the magnitudes of annual exceedance probability (AEP) flows estimated by using the LP−III distribution are affected by the skew; interest is focused on the right-hand tail of the distribution, which represents the larger annual peak flows that correspond to small AEPs. For streamgages having modest record lengths, the skew is sensitive to extreme events like large floods, which cause a sample to be highly asymmetrical or “skewed.” For this reason, B17C recommends using a weighted-average skew computed from the station skew for a given streamgage and a regional skew. This report generates an estimate of regional skew for a study area encompassing most of the Great Lakes Basin (hydrologic unit 04) and part of the Ohio River Basin (hydrologic unit 05). A total of 551 candidate streamgages that were unaffected by extensive regulation, diversion, urbanization, or channelization were considered for use in the skew analysis; after screening for redundancy and pseudo record length greater than 36 years, 368 streamgages were selected for use in the study. Flood frequencies for candidate streamgages were analyzed by employing the Expected Moments Algorithm, which extends the method of moments so that it can accommodate interval, censored, and historic/paleo flow data, as well as the Multiple Grubbs-Beck test to identify potentially influential low floods in the data series. Bayesian weighted least squares/Bayesian generalized least squares regression was used to develop a regional skew model for the study area that would incorporate possible variables (basin characteristics) to explain the variation in skew in the study area. Twelve basin characteristics were considered as possible explanatory variables; however, none produced a pseudo coefficient of determination greater than 5 percent; as a result, these characteristics did not help to explain the variation in skew in the study area. Therefore, a constant model having a regional skew coefficient of 0.086 and an average variance of prediction (AVP_new) (which corresponds to the mean square error [MSE]) of 0.13 at a new streamgage was selected. The AVP_new corresponds to an effective record length of 54 years, a marked improvement over the Bulletin 17B national skew map, whose reported MSE of 0.302 indicated a corresponding effective record length of only 17 years.