Hershfield factor revisited: Correcting annual maximum precipitation

S.M. Papalexiou, Y. Dialynas, and S. Grimaldi, Hershfield factor revisited: Correcting annual maximum precipitation, Journal of Hydrology, 542, 884–895, doi:10.1016/j.jhydrol.2016.09.058, 2016.



The Hershfield factor (H) is a multiplier aiming to correct the error between fixed time interval maxima (Fmaxima) and sliding maxima (Smaxima) as a direct consequence of temporal discretization of hydrometeorological time series. Rainfall is typically recorded over discrete intervals, e.g., over fixed 24h 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 Hfactor in an unprecedentedly large analysis comprising thousands of uptodate hourly records across the US. We study the probabilistic behaviour of F and Smaxima 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 Hfactor and we investigate the exact probability distribution of Hfactor. We introduce a bounded exponential distribution with an atom at one, which closely depicts the empirical distribution of the Hfactor. Notable is the result that the proposed mixedtype 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.

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Our works referenced by this work:

1. S.M. Papalexiou, D. Koutsoyiannis, and C. Makropoulos, How extreme is extreme? An assessment of daily rainfall distribution tails, Hydrology and Earth System Sciences, 17, 851–862, doi:10.5194/hess-17-851-2013, 2013.
2. S.M. Papalexiou, and D. Koutsoyiannis, Battle of extreme value distributions: A global survey on extreme daily rainfall, Water Resources Research, 49 (1), 187–201, doi:10.1029/2012WR012557, 2013.
3. A. Efstratiadis, Y. Dialynas, S. Kozanis, and D. Koutsoyiannis, A multivariate stochastic model for the generation of synthetic time series at multiple time scales reproducing long-term persistence, Environmental Modelling and Software, 62, 139–152, doi:10.1016/j.envsoft.2014.08.017, 2014.

Tagged under: Extremes, Rainfall models