The Hershfield Factor Revisited

Abstract:

This study deals with the celebrated Hershfield factor. Rainfall is typically recorded over discrete time intervals, e.g., over fixed 24-hour intervals, and thus the recorded measurements express average values over these intervals. This temporal discretization may introduce a systematic error on rainfall characteristics such as the annual maxima, which are inferred usually from records of average values. The error depends on the recording time intervals of the measurement system and on the time scale under study. For instance, Hershfield and Wilson in 1958, based on the analysis of 1-min measurements, were the first to propose a multiplier of 1.13 to correct the discretization effects on the annual daily maxima. Since then, several studies closely or approximately agree with this result. Yet all of these empirical studies are based on limited datasets in terms of number of stations and of record lengths. Furthermore, the methodological framework implemented in some studies was later questioned. Here we perform an unprecedentedly large empirical analysis of thousands of up-to-date hourly records across the US in order to quantify the effect of discretization on the rainfall maxima by assessing the Hershfield's factor value. Moreover, we further explore linkages between the Hershfield's factor and other rainfall characteristics such as the probability dry. Clarification on the effects of temporal discretization can be crucial for quantifying better rainfall extremes and for assessing their statistical behavior.