On the exact distribution of correlated extremes in hydrology

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.

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[English]

The analysis of hydrological hazards usually relies on asymptotic results of extreme value theory (EVT), which commonly deals with block maxima (BM) or peaks over threshold (POT) data series. However, data quality and quantity of BM and POT hydrological records do not usually fulfill the basic requirements of EVT, thus making its application questionable and results prone to high uncertainty and low reliability. An alternative approach to better exploit the available information of continuous time series and non-extreme records is to build the exact distribution of maxima (i.e., non-asymptotic extreme value distributions) from a sequence of low-threshold POT. Practical closed-form results for this approach do exist only for independent high-threshold POT series with Poisson occurrences. This study introduces new closed-form equations of the exact distribution of maxima taken from low-threshold POT with magnitudes characterized by an arbitrary marginal distribution and first-order Markovian dependence, and negative binomial occurrences. The proposed model encompasses and generalizes the independent-Poisson model and allows for analyses relying on significantly larger samples of low-threshold POT values exhibiting dependence, temporal clustering and overdispersion. To check the analytical results, we also introduce a new generator (called Gen2Mp) of proper first-order Markov chains with arbitrary marginal distributions. An illustrative application to long-term rainfall and streamflow data series shows that our model for the distribution of extreme maxima under dependence takes a step forward in developing more reliable data-rich-based analyses of extreme values.

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Our works referenced by this work:

1. D. Koutsoyiannis, Statistics of extremes and estimation of extreme rainfall, 1, Theoretical investigation, Hydrological Sciences Journal, 49 (4), 575–590, 2004.
2. D. Koutsoyiannis, Statistics of extremes and estimation of extreme rainfall, 2, Empirical investigation of long rainfall records, Hydrological Sciences Journal, 49 (4), 591–610, 2004.
3. 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.
4. 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.
5. 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.
6. 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.
7. P.E. O’Connell, D. Koutsoyiannis, H. F. Lins, Y. Markonis, A. Montanari, and T.A. Cohn, The scientific legacy of Harold Edwin Hurst (1880 – 1978), Hydrological Sciences Journal, 61 (9), 1571–1590, doi:10.1080/02626667.2015.1125998, 2016.
8. D. Koutsoyiannis, and S.M. Papalexiou, Extreme rainfall: Global perspective, Handbook of Applied Hydrology, Second Edition, edited by V.P. Singh, 74.1–74.16, McGraw-Hill, New York, 2017.
9. F. Lombardo, E. Volpi, D. Koutsoyiannis, and F. Serinaldi, A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall, Water Resources Research, 53 (6), 4586–4605, doi:10.1002/2017WR020529, 2017.
10. 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.
11. 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.