A Method Based on Taking the Average of Probabilities to Compute the Flow Duration Curve

Abstract

In this study a method based on taking the average of the probabilities is presented to obtain flow duration curve. In this method the exceedance probability for each flow value is computed repeatedly for all time periods within a year. The final representing exceedance is just simply the average of all these probabilities. The applicability of the method to daily mean flows is tested assuming various marginal probability distributions like normal, Pearson type III, log-Pearson type III, 2-parameter lognormal and 3-parameter lognormal distributions. It is seen that the observed flow duration curves were quite well approximated by the 2-parameter lognormal average of probabilities curves. In that case the method requires the computation of the daily mean and standard deviation values of the observed flow data. The method curve enables extrapolation of the available data providing the exceedance probabilities for the flows higher than the observed maximum flow. The method is applied to the missing data and ungauged site problems and the results are quite satisfactory.