Probability plotting position formulas for flood records with historical information

Abstract

For purposes of evaluating fitted flood frequency distributions or for purposes of estimating distributions directly from plots of flood peaks versus exceedance probabilities (either by subjective or objective techniques), one needs a probability plotting position formula which can be applied to all of the flood data available: both systematic and historic floods. Some of the formulas in use are simply extensions of existing formulas (such as Hazen and Weibull) used on systematic flood records. New plotting position formulas proposed by Hirsch and Stedinger (1986) and in this paper are based on a recognition that the flood data arises from partially censored sampling of the flood record. The theoretical appropriateness, bias in probability and bias in discharge of the various plotting position formulas are considered. The methods are compared in terms of their effects on flood frequency estimation when an objective curve-fitting method of estimation is employed. Consideration is also given to the correct interpretation of the historical record length and the effect of incorrectly assuming that record length equals the time since the first known historical flood. This assumption is employed in many flood frequency studies and may result in a substantial bias in estimated design flood magnitudes.