One hundred years of return period: Strengths and limitations

E. Volpi, A. Fiori, S. Grimaldi, F. Lombardo, and D. Koutsoyiannis, One hundred years of return period: Strengths and limitations, Water Resources Research, doi:10.1002/2015WR017820, 2015.



One hundred years from its original definition by Fuller [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.

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Our works referenced by this work:

1. D. Koutsoyiannis, Probability and statistics for geophysical processes, doi:10.13140/RG.2.1.2300.1849/1, National Technical University of Athens, Athens, 2008.
2. A. Montanari, and D. Koutsoyiannis, Modeling and mitigating natural hazards: Stationarity is immortal!, Water Resources Research, 50 (12), 9748–9756, doi:10.1002/2014WR016092, 2014.
3. D. Koutsoyiannis, and A. Montanari, Negligent killing of scientific concepts: the stationarity case, Hydrological Sciences Journal, 60 (7-8), 1174–1183, doi:10.1080/02626667.2014.959959, 2015.

Our works that reference this work:

1. E. Volpi, A. Fiori, S. Grimaldi, F. Lombardo, and D. Koutsoyiannis, Save hydrological observations! Return period estimation without data decimation, Journal of Hydrology, doi:10.1016/j.jhydrol.2019.02.017, 2019.
2. T. Iliopoulou, and D. Koutsoyiannis, Revealing hidden persistence in maximum rainfall records, Hydrological Sciences Journal, 64 (14), 1673–1689, doi:10.1080/02626667.2019.1657578, 2019.
3. F. Lombardo, F. Napolitano, F. Russo, and D. Koutsoyiannis, On the exact distribution of correlated extremes in hydrology, Water Resources Research, 55 (12), 10405–10423, doi:10.1029/2019WR025547, 2019.
4. D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 3, ISBN: 978-618-85370-0-2, 391 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2023.

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