Battle of extreme value distributions: A global survey on extreme daily rainfall

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.

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[English]

Theoretically, if the distribution of daily rainfall is known or justifiably assumed, then one could argue, based on extreme value theory, that the distribution of the annual maxima of daily rainfall would resemble one of the three limiting types: (a) type I, known as Gumbel, type II, known as Fréchet and, type III, known as reversed Weibull. Yet, the parent distribution usually is not known and often only records of annual maxima are available. Thus, the question that naturally arises is which one of the three types better describes the annual maxima of daily rainfall. The question is of great importance as the naïve adoption of a particular type may lead to serious underestimation or overestimation of the return period assigned to specific rainfall amounts. To answer this question, we analyze the annual maximum daily rainfall of 15 137 records from all over the world, with lengths varying from 40 to 163 years. We fit the Generalized Extreme Value (GEV) distribution, which comprises the three limiting types as special cases for specific values of its shape parameter, and analyze the fitting results focusing on the behavior of the shape parameter. The analysis reveals that: (a) the record length strongly affects the estimate of the GEV shape parameter and long records are needed for reliable estimates, (b) when the effect of the record length is corrected the shape parameter varies in a narrow range, (c) the geographical location of the globe may affect the value of the shape parameter, and (d) the winner of this battle is the Fréchet law.

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See also: http://dx.doi.org/10.1029/2012WR012557

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, doi:10.1623/hysj.49.4.575.54430, 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, doi:10.1623/hysj.49.4.591.54424, 2004.
3. S.M. Papalexiou, and D. Koutsoyiannis, Entropy based derivation of probability distributions: A case study to daily rainfall, Advances in Water Resources, 45, 51–57, doi:10.1016/j.advwatres.2011.11.007, 2012.
4. 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.

Our works that reference 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. 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.
3. S.M. Papalexiou, and D. Koutsoyiannis, A global survey on the seasonal variation of the marginal distribution of daily precipitation, Advances in Water Resources, 94, 131–145, doi:10.1016/j.advwatres.2016.05.005, 2016.
4. 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.
5. 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.
6. H. Tyralis, P. Dimitriadis, D. Koutsoyiannis, P.E. O’Connell, K. Tzouka, and T. Iliopoulou, On the long-range dependence properties of annual precipitation using a global network of instrumental measurements, Advances in Water Resources, 111, 301–318, doi:10.1016/j.advwatres.2017.11.010, 2018.
7. Y. Markonis, Y. Moustakis, C. Nasika, P. Sychova, P. Dimitriadis, M. Hanel, P. Máca, and S.M. Papalexiou, Global estimation of long-term persistence in annual river runoff, Advances in Water Resources, 113, 1–12, doi:10.1016/j.advwatres.2018.01.003, 2018.
8. G. Papaioannou, A. Efstratiadis, L. Vasiliades, A. Loukas, S.M. Papalexiou, A. Koukouvinos, I. Tsoukalas, and P. Kossieris, An operational method for Floods Directive implementation in ungauged urban areas, Hydrology, 5 (2), 24, doi:10.3390/hydrology5020024, 2018.
9. I. Tsoukalas, C. Makropoulos, and D. Koutsoyiannis, Simulation of stochastic processes exhibiting any-range dependence and arbitrary marginal distributions, Water Resources Research, 54 (11), 9484–9513, doi:10.1029/2017WR022462, 2018.
10. T. Iliopoulou, D. Koutsoyiannis, and A. Montanari, Characterizing and modeling seasonality in extreme rainfall, Water Resources Research, 54 (9), 6242–6258, doi:10.1029/2018WR023360, 2018.
11. 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.
12. G. Papacharalampous, H. Tyralis, D. Koutsoyiannis, and A. Montanari, Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: A large-sample experiment at monthly timescale, Advances in Water Resources, 136, 103470, doi:10.1016/j.advwatres.2019.103470, 2020.
13. T. Iliopoulou, and D. Koutsoyiannis, Projecting the future of rainfall extremes: better classic than trendy, Journal of Hydrology, 588, doi:10.1016/j.jhydrol.2020.125005, 2020.
14. P. Dimitriadis, D. Koutsoyiannis, T. Iliopoulou, and P. Papanicolaou, A global-scale investigation of stochastic similarities in marginal distribution and dependence structure of key hydrological-cycle processes, Hydrology, 8 (2), 59, doi:10.3390/hydrology8020059, 2021.
15. 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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1. Cleverly, J., N. Boulain, R. Villalobos-Vega, N. Grant, R. Faux, C. Wood, P. G. Cook, Q. Yu, A. Leigh and D. Eamus, Dynamics of component carbon fluxes in a semi-arid Acacia woodland, central Australia, Journal of Geophysical Research: Biogeosciences, 10.1002/jgrg.20101, 2013.
2. Dyrrdal, A. V., A. Lenkoski, T. L. Thorarinsdottir and F. Stordal, Bayesian hierarchical modeling of extreme hourly precipitation in Norway, Environmetrics , 10.1002/env.2301, 2014.
3. Ahammed, F., G. A. Hewa and J. R. Argue, Variability of annual daily maximum rainfall of Dhaka, Bangladesh, Atmospheric Research, 137, 176-182, 2014.
4. Serinaldi, F., and C. G. Kilsby, Rainfall extremes: Toward reconciliation after the battle of distributions, Water Resources Research, 50 (1), 336-352, 2014.
5. Roth, M., T. A. Buishand, G. Jongbloed, A. M. G. Klein Tank and J. H. van Zanten, Projections of precipitation extremes based on a regional, non-stationary peaks-over-threshold approach: A case study for the Netherlands and north-western Germany, Weather and Climate Extremes, 10.1016/j.wace.2014.01.001, 2014.
6. Kochanek, K., B. Renard, P. Arnaud, Y. Aubert, M. Lang, T. Cipriani and E. Sauquet, A data-based comparison of flood frequency analysis methods used in France, Nat. Hazards Earth Syst. Sci., 14, 295-308, 2014.
7. Bolívar-Cimé, A. M., E. Díaz-Francés and J. Ortega, Optimality of profile likelihood intervals for quantiles of extreme value distributions: applications to environmental disasters, Hydrological Sciences Journal, 10.1080/02626667.2014.897405, 2014.
8. Jagtap, R. S., Effect of record length and recent past events on extreme precipitation analysis, Current Science, 106 (5), 698-707, 2014.
9. Serinaldi, F., and C. G. Kilsby, Simulating daily rainfall fields over large areas for collective risk estimation, Journal of Hydrology, 10.1016/j.jhydrol.2014.02.043, 2014.
10. Naveau, P., A. Toreti, I. Smith and E. Xoplaki, A fast nonparametric spatio‐temporal regression scheme for Generalized Pareto distributed heavy precipitation, Water Resources Research, 10.1002/2014WR015431, 2014.
11. Panthou, G., T. Vischel, T. Lebel, G.Quantin and G. Molinié, Characterizing the space–time structure of rainfall in the Sahel with a view to estimating IDAF curves, Hydrol. Earth Syst. Sci. ,18 (12) 5093-5107, DOI: 10.5194/hess-18-5093-2014, 2014.
12. Dyrrdal, A. V., T. Skaugen, F. Stordal and E. J. Førland, Estimating extreme areal precipitation in Norway from a gridded dataset, Hydrological Sciences Journal, 10.1080/02626667.2014.947289, 2014.
13. Serinaldi, F., A. Bárdossy and C. G. Kilsby, Upper tail dependence in rainfall extremes: would we know it if we saw it?, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-014-0946-8, 2014.
14. Cheng, L., A. AghaKouchak, E. Gilleland and R. W. Katz, Non-stationary extreme value analysis in a changing climate, Climatic Change, 10.1007/s10584-014-1254-5, 2014.
15. Caloiero, T., A.A. Pasqua and O. Petrucci, Damaging hydrogeological events: A procedure for the assessment of severity levels and an application to Calabria (Southern Italy), Water, 6 (12), 3652-3670, 2014.
16. Serinaldi, F., and C.G. Kilsby, Stationarity is undead: Uncertainty dominates the distribution of extremes, Advances in Water Resources, 77, 17-36, 2015.
17. Cannon, A.J., An intercomparison of regional and at-site rainfall extreme value analyses in southern British Columbia, Canada, Canadian Journal of Civil Engineering, 42 (2), 107-119, 2015.
18. Smith, A., C. Sampson and P. Bates, Regional flood frequency analysis at the global scale, Water Resources Research, 51 (1), 539-553, 2015.
19. Marani, M., and M. Ignaccolo, A metastatistical approach to rainfall extremes, Advances in Water Resources, 79, 121-126, 2015.
20. Basso, S., M. Schirmer and G. Botter, On the emergence of heavy-tailed streamflow distributions, Advances in Water Resources, 82, 98-105, 2015.
21. Cavanaugh, N.R., A. Gershunov, A.K. Panorska and T.J. Kozubowski, The probability distribution of intense daily precipitation, Geophysical Research Letters, 42 (5), 1560-1567, 2015.
22. Cheng, L., T.J. Phillips and A. AghaKouchak, Non-stationary return levels of CMIP5 multi-model temperature extremes, Climate Dynamics, 44 (11-12), 2947-2963, 2015.
23. Alam, M.S., and A. Elshorbagy, Quantification of the climate change-induced variations in Intensity–Duration–Frequency curves in the Canadian Prairies, Journal of Hydrology, 527, 990-1005, 2015.
24. Ganora, D. and F. Laio, Hydrological applications of the Burr distribution: practical method for parameter estimation, J. Hydrol. Eng., 10.1061/(ASCE)HE.1943-5584.0001203, 04015024, 2015.
25. Boers, N., B. Bookhagen, N. Marwan and J. Kurths, Spatiotemporal characteristics and synchronization of extreme rainfall in South America with focus on the Andes Mountain range, Climate Dynamics, 10.1007/s00382-015-2601-6, 2015.
26. Tenório da Costa, K., and W. dos Santos Fernandes, Evaluation of the type of probability distribution of annual maximum daily flows in Brazil [Avaliação do tipo de distribuição de probabilidades das vazões máximas diárias anuais no Brasil], Revista Brasileira de Recursos Hídricos, 20 (2), 442 – 451, 2015.

Tagged under: Extremes, Rainfall models