Research papersHershfield factor revisited: Correcting annual maximum precipitation

- Largest empirical analysis on the H-factor ever made; 7127 hourly records studied.
- Updated H-factor values and introduction of new types of H-factors.
- A completely new approach treating H-factor also as a random variable.
- Estimation of the complete distribution of H-factor.
- Results and formulas given are of practical value in hydraulic design.

The Hershfield factor (H) is a multiplier aiming to correct the error between fixed time interval maxima (F-maxima) and sliding maxima (S-maxima) as a direct consequence of temporal discretization of hydrometeorological time series. Rainfall is typically recorded over discrete intervals, e.g., over fixed 24-h intervals, and the historical series express average values over these intervals. This temporal discretization introduces an important systematic error on rainfall characteristics such as the annual maxima. Research to date suggests that our understanding of this error across different time scales is limited. In this study we revisit the probabilistic nature of the H-factor in an unprecedentedly large analysis comprising thousands of up-to-date hourly records across the US. We study the probabilistic behavior of F- and S-maxima of the historical records. We quantify the discretization error of the rainfall maxima and its statistical properties at different time scales. We revisit the classical definitions of the H-factor and we investigate the exact probability distribution of H-factor. We introduce a bounded exponential distribution with an atom at one, which closely depicts the empirical distribution of the H-factor. Notable is the result that the proposed mixed-type distribution is invariant across a range of time scales. This work clarifies the probabilistic nature of the rainfall maxima correction. The results may have wide use across a range of hydrological applications.