Flood frequency analysis – Part 2: Development of a modified plotting position

Abstract

The original plotting position concept was suggested more than a century ago. Since then, many alternative plotting position approaches have been developed. Despite a general lack of agreement around which plotting position is theoretically ‘correct’ and the ‘best’ to use, all plotting positions fail to adequately address outliers and data of similar magnitude. Hydrologists generally fail to acknowledge that the plotting position primarily offers an informative display of data, against which distributions can be compared, rather than an absolute measure of probability. This paper does not intend to challenge any of the many lengthy theoretical mathematical arguments, utilised to ‘prove’ why one plotting position is superior to the others. These theoretical arguments may very well be valid for a ‘population’ of flood peaks – the reality, however, is that hydrologists are confronted with the challenge of analysing very limited ‘samples’ of the population. Consequently, the plotting position issue demands a more pragmatic approach, rather than a purely theoretical approach. This paper illustrates various problems with existing plotting position techniques in use and offers an alternative approach and a more sensible plotting position technique, using Z-scores and referred to as the Z-set PP, against which distributions can be checked. The study further illustrates how effectively the Z-set PP deals with outliers and its robustness with various record lengths. Although derived from a study of flood peak data obtained from South African flow-gauging sites, it is deemed that it will be universally applicable.