Plotting positions for historical floods and their precision

Abstract

Plotting positions are needed for situations where, in addition to a systematically recorded annual flood series, one would have a record of any large floods which occurred during an extended historical period, if they occurred. Many of the published estimators are based on uncensored sampling theory which is not appropriate for such data sets. Here such historical and systematic flood records are viewed as resulting from a partially censored sampling experiment. Plotting positions are derived for such experiments using both classical and Bayesian viewpoints. In general, it is impossible to construct highly accurate estimates of the exceedance probabilities of the largest floods using only their rank, the number of observed historical floods, and the lengths of the historical period and the systematic record. For the largest flood, the coefficient of variation of exceedance‐probability estimators is of the order of 1, as it is for complete systematic records. Examples illustrate the bias and precision of a variety of plotting position formulas. The differences among the different plotting positions are generally small in comparison to the sampling variability. However, plotting positions which are unbiased with uncensored samples are often the most biased when used with a combination of historical and systematic data. Three appendices consider the effect of misspecification of the length of the historical period, the effect of misspecification of the threshold of perception or observation level, and plotting positions for situations with several perception thresholds.