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One hundred years of return period: Strengths and limitations
Author(s) -
Volpi E.,
Fiori A.,
Grimaldi S.,
Lombardo F.,
Koutsoyiannis D.
Publication year - 2015
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2015wr017820
Subject(s) - return period , econometrics , probabilistic logic , independence (probability theory) , period (music) , moment (physics) , context (archaeology) , event (particle physics) , statistics , mathematics , computer science , geography , flood myth , physics , archaeology , acoustics , classical mechanics , quantum mechanics
One hundred years from its original definition by Fuller ([Fuller, W., 1914]), the probabilistic concept of return period is widely used in hydrology as well as in other disciplines of geosciences to give an indication on critical event rareness. This concept gains its popularity, especially in engineering practice for design and risk assessment, due to its ease of use and understanding; however, return period relies on some basic assumptions that should be satisfied for a correct application of this statistical tool. Indeed, conventional frequency analysis in hydrology is performed by assuming as necessary conditions that extreme events arise from a stationary distribution and are independent of one another. The main objective of this paper is to investigate the properties of return period when the independence condition is omitted; hence, we explore how the different definitions of return period available in literature affect results of frequency analysis for processes correlated in time. We demonstrate that, for stationary processes, the independence condition is not necessary in order to apply the classical equation of return period (i.e., the inverse of exceedance probability). On the other hand, we show that the time‐correlation structure of hydrological processes modifies the shape of the distribution function of which the return period represents the first moment. This implies that, in the context of time‐dependent processes, the return period might not represent an exhaustive measure of the probability of failure, and that its blind application could lead to misleading results. To overcome this problem, we introduce the concept of Equivalent Return Period, which controls the probability of failure still preserving the virtue of effectively communicating the event rareness.