Flood peak regionalization using mixed-mode estimation of the parameters of the log-normal distribution

Abstract

Most hydrologic design problems occur at sites where stream-gage data are not available. At these ungaged locations, therefore, it is, necessary to use either an uncalibrated estimation method or an empirical equation that is based on a regionalization of peak-discharge estimates from gaged data. Traditionally, empirical equations have been calibrated by regressing estimated peak discharges, which have been obtained from a log-Pearson Type-III analysis of gaged data, on watershed and precipitation characteristics. This method is sensitive to both extreme events and small sample sizes. In an effort to minimize the problems with outliers and data variance, we derived a particular form of the three-parameter log-normal distribution by utilizing a variate transform of the annual peak-flow series for fitting to a histogram. This mixed-mode fitting uses nonlinear least squares to optimize on the class errors between the observed and computed histograms of the data. The sample variability is controlled by using a fixed probability range rather than the sample range. The mixed-mode estimator technique was used to derive parameters for 132 gaged sites in Pennsylvania. Using the mixed-mode parameters for a log-normal probability density function, peak discharges of five different exceedance probabilities were computed for each station and then regionalized for use at ungaged sites. Regression techniques were used to relate the peak discharges to watershed and precipitation characteristics; drainage area was the only predictor variable that was necessary for accurate estimates. The significant predictor variable in a log-form was drainage area. For comparative purposes, the log-Pearson Type-III peak-discharge estimates were also regionalized. The average error for the mixed-mode log-normal method did not differ significantly from the log-Pearson Type-III regionalized equation error. The mixed-mode method provided correlation coefficients ranging from 0.91 to 0.94, whereas the traditional method provided correlations ranging from 0.88 to 0.96 for different return periods.