Concept of Threshold in the Estimation of Probable Maximum Precipitation: Hershfield’s Method Revisited

Abstract

Hershfield’s statistical procedure is recognized by the World Meteorological Organization (WMO) and widely used for estimating probable maximum precipitation (PMP). It uses the frequency factor formula, where the frequency factor K is derived empirically. The procedure always treats the largest observed event in a sample as an outlier and as the only outlier. This is not necessarily true, for a sample could contain multiple outliers or be devoid of outliers. This is a vital issue which has thus far not received the attention of researchers. Outliers are identified by a threshold which is determined using the interquartile range (IQR) test, which is nonparametric. The test revealed that nine stations had multiple outliers numbering between 2 and 5, while four stations did not have any outliers. In the presence of multiple outliers, Hershfield’s PMP results are seen to be as much as 45% higher than those obtained by the improved method, which gives results that are also consistent with the hydrometeorological method. The analysis considers 19 rainfall stations in Sri Lanka covering several different climatic zones. The modified method is efficient and reliable for estimating PMP and can be used as a tool in hydrological design.