Articles | Volume 29, issue 4
https://doi.org/10.5194/hess-29-1159-2025
ยฉ Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-29-1159-2025
ยฉ Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
28 Feb 2025
Research article |
| 28 Feb 2025
| 28 Feb 2025
Non-asymptotic distributions of water extremes: much ado about what?
Francesco Serinaldi
CORRESPONDING AUTHOR
School of Engineering, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK
Willis Research Network, 51 Lime St., London, EC3M 7DQ, UK
Federico Lombardo
Corpo Nazionale dei Vigili del Fuoco, Ministero dell'Interno, Piazza del Viminale, 1, Rome 00184, Italy
Chris G. Kilsby
School of Engineering, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK
Willis Research Network, 51 Lime St., London, EC3M 7DQ, UK
Related authors
Francesco Serinaldi
Hydrol. Earth Syst. Sci., 28, 3191โ3218, https://doi.org/10.5194/hess-28-3191-2024, https://doi.org/10.5194/hess-28-3191-2024, 2024
Short summary
Short summary
Neglecting the scientific rationale behind statistical inference leads to logical fallacies and misinterpretations. This study contrasts a model-based approach, rooted in statistical logic, with a test-based approach, widely used in hydro-climatology but problematic. It reveals the impact of dependence in extreme-precipitation analysis and shows that trends in the frequency of extreme events over the past century in various geographic regions can be consistent with the stationary assumption.
Amy C. Green, Chris Kilsby, and Andrรกs Bรกrdossy
Hydrol. Earth Syst. Sci., 28, 4539โ4558, https://doi.org/10.5194/hess-28-4539-2024, https://doi.org/10.5194/hess-28-4539-2024, 2024
Short summary
Short summary
Weather radar is a crucial tool in rainfall estimation, but radar rainfall estimates are subject to many error sources, with the true rainfall field unknown. A flexible model for simulating errors relating to the radar rainfall estimation process is implemented, inverting standard processing methods. This flexible and efficient model performs well in generating realistic weather radar images visually for a large range of event types.
Francesco Serinaldi
Hydrol. Earth Syst. Sci., 28, 3191โ3218, https://doi.org/10.5194/hess-28-3191-2024, https://doi.org/10.5194/hess-28-3191-2024, 2024
Short summary
Short summary
Neglecting the scientific rationale behind statistical inference leads to logical fallacies and misinterpretations. This study contrasts a model-based approach, rooted in statistical logic, with a test-based approach, widely used in hydro-climatology but problematic. It reveals the impact of dependence in extreme-precipitation analysis and shows that trends in the frequency of extreme events over the past century in various geographic regions can be consistent with the stationary assumption.
Fergus McClean, Richard Dawson, and Chris Kilsby
Hydrol. Earth Syst. Sci., 27, 331โ347, https://doi.org/10.5194/hess-27-331-2023, https://doi.org/10.5194/hess-27-331-2023, 2023
Short summary
Short summary
Reanalysis datasets are increasingly used to drive flood models, especially for continental and global analysis. We investigate the impact of using four reanalysis products on simulations of past flood events. All reanalysis products underestimated the number of buildings inundated, compared to a benchmark national dataset. These findings show that while global reanalyses provide a useful resource for flood modelling where no other data are available, they may underestimate impact in some cases.
Doug Richardson, Hayley J. Fowler, Christopher G. Kilsby, Robert Neal, and Rutger Dankers
Nat. Hazards Earth Syst. Sci., 20, 107โ124, https://doi.org/10.5194/nhess-20-107-2020, https://doi.org/10.5194/nhess-20-107-2020, 2020
Short summary
Short summary
Models are not particularly skilful at forecasting rainfall more than 15โd in advance. However, they are often better at predicting atmospheric variables such as mean sea-level pressure (MSLP). Comparing a range of models, we show that UK winter and autumn rainfall and drought prediction skill can be improved by utilising forecasts of MSLP-based weather patterns (WPs) and subsequently estimating rainfall using the historical WPโprecipitation relationships.
Related subject area
Subject: Global hydrology | Techniques and Approaches: Stochastic approaches
Assimilating ESA CCI land surface temperature into the ORCHIDEE land surface model: insights from a multi-site study across Europe
Deducing landโatmosphere coupling regimes from SMAP soil moisture
Novel extensions to the Fisher copula to model flood spatial dependence over North America
Revisiting the global hydrological cycle: is it intensifying?
Detection and attribution of flood trends in Mediterranean basins
Examining the relationship between intermediate-scale soil moisture and terrestrial evaporation within a semi-arid grassland
How streamflow has changed across Australia since the 1950s: evidence from the network of hydrologic reference stations
Investigation of hydrological time series using copulas for detecting catchment characteristics and anthropogenic impacts
Towards observation-based gridded runoff estimates for Europe
Historical land-use-induced evapotranspiration changes estimated from present-day observations and reconstructed land-cover maps
Detection of global runoff changes: results from observations and CMIP5 experiments
Rainfall statistics changes in Sicily
Spatial variability and its scale dependency of observed and modeled soil moisture over different climate regions
How extreme is extreme? An assessment of daily rainfall distribution tails
Impact of climate change on the stream flow of the lower Brahmaputra: trends in high and low flows based on discharge-weighted ensemble modelling
Climate model bias correction and the role of timescales
Streamflow trends in Europe: evidence from a dataset of near-natural catchments
Luis-Enrique Olivera-Guerra, Catherine Ottlรฉ, Nina Raoult, and Philippe Peylin
Hydrol. Earth Syst. Sci., 29, 261โ290, https://doi.org/10.5194/hess-29-261-2025, https://doi.org/10.5194/hess-29-261-2025, 2025
Short summary
Short summary
We assimilate the recent ESA-CCI land surface temperature (LST) product to optimize parameters of a land surface model (ORCHIDEE). We test different assimilation strategies to evaluate the best strategy over various in situ stations across Europe. We also provide advice on how to assimilate this LST product to better simulate LST and surface energy fluxes. Finally, we demonstrate the effectiveness of this optimization, which is essential to better simulate future projections.
Payal R. Makhasana, Joseph A. Santanello, Patricia M. Lawston-Parker, and Joshua K. Roundy
Hydrol. Earth Syst. Sci., 28, 5087โ5106, https://doi.org/10.5194/hess-28-5087-2024, https://doi.org/10.5194/hess-28-5087-2024, 2024
Short summary
Short summary
This study examines how soil moisture impacts landโatmosphere interactions, crucial for understanding Earth's water and energy cycles. The study used two different soil moisture datasets from the SMAP satellite to measure how strongly soil moisture influences the atmosphere's ability to retain moisture (called coupling strength). Leveraging SMAP soil moisture data and integrating multiple atmospheric datasets, the study offers new insights into the dynamics of landโatmosphere coupling strength.
Duy Anh Alexandre, Chiranjib Chaudhuri, and Jasmin Gill-Fortin
Hydrol. Earth Syst. Sci., 28, 5069โ5085, https://doi.org/10.5194/hess-28-5069-2024, https://doi.org/10.5194/hess-28-5069-2024, 2024
Short summary
Short summary
Estimating extreme river discharges at single stations is relatively simple. However, flooding is a spatial phenomenon as rivers are connected. We develop a statistical method to estimate extreme flows with global coverage, accounting for spatial dependence. Using our model, synthetic flood events are simulated with more information than the limited historical events. This event catalog can be used to produce spatially coherent flood depth maps for flood risk assessment.
Demetris Koutsoyiannis
Hydrol. Earth Syst. Sci., 24, 3899โ3932, https://doi.org/10.5194/hess-24-3899-2020, https://doi.org/10.5194/hess-24-3899-2020, 2020
Short summary
Short summary
We overview and retrieve a great amount of global hydroclimatic data sets. We improve the quantification of the global hydrological cycle, its variability and its uncertainties through the surge of newly available data sets. We test (but do not confirm) established climatological hypotheses, according to which the hydrological cycle should be intensifying due to global warming. We outline a stochastic view of hydroclimate, which provides a reliable means of dealing with its variability.
Yves Tramblay, Louise Mimeau, Luc Neppel, Freddy Vinet, and Eric Sauquet
Hydrol. Earth Syst. Sci., 23, 4419โ4431, https://doi.org/10.5194/hess-23-4419-2019, https://doi.org/10.5194/hess-23-4419-2019, 2019
Short summary
Short summary
In the present study the flood trends have been assessed for a large sample of 171 basins located in southern France, which has a Mediterranean climate. Results show that, despite the increase in rainfall intensity previously observed in this area, there is no general increase in flood magnitude. Instead, a reduction in the annual number of floods is found, linked to a decrease in soil moisture caused by the increase in temperature observed in recent decades.
Raghavendra B. Jana, Ali Ershadi, and Matthew F. McCabe
Hydrol. Earth Syst. Sci., 20, 3987โ4004, https://doi.org/10.5194/hess-20-3987-2016, https://doi.org/10.5194/hess-20-3987-2016, 2016
Short summary
Short summary
Interactions between soil moisture and terrestrial evaporation affect responses between land surface and the atmosphere across scales. We present an analysis of the link between soil moisture and evaporation estimates from three distinct models. The relationships were examined over nearly 2 years of observation data. Results show that while direct correlations of raw data were mostly not useful, the root-zone soil moisture and the modelled evaporation estimates reflect similar distributions.
Xiaoyong Sophie Zhang, Gnanathikkam E. Amirthanathan, Mohammed A. Bari, Richard M. Laugesen, Daehyok Shin, David M. Kent, Andrew M. MacDonald, Margot E. Turner, and Narendra K. Tuteja
Hydrol. Earth Syst. Sci., 20, 3947โ3965, https://doi.org/10.5194/hess-20-3947-2016, https://doi.org/10.5194/hess-20-3947-2016, 2016
Short summary
Short summary
The hydrologic reference stations website (www.bom.gov.au/water/hrs/), developed by the Australia Bureau of Meteorology, is a one-stop portal to access long-term and high-quality streamflow information for 222 stations across Australia. This study investigated the streamflow variability and inferred trends in water availability for those stations. The results present a systematic analysis of recent hydrological changes in Australian rivers, which will aid water management decision making.
Takayuki Sugimoto, Andrรกs Bรกrdossy, Geoffrey G. S. Pegram, and Johannes Cullmann
Hydrol. Earth Syst. Sci., 20, 2705โ2720, https://doi.org/10.5194/hess-20-2705-2016, https://doi.org/10.5194/hess-20-2705-2016, 2016
Short summary
Short summary
This paper is aims to detect the climate change impacts on the hydrological regime from the long-term discharge records. A new method for stochastic analysis using copulas, which has the advantage of scrutinizing the data independent of marginal, is suggested in this paper. Two measures are used in the copula domain: one focuses on the asymmetric characteristic of data and the other compares the distances between the copulas. These are calculated for 100 years of daily discharges and the results are discussed.
L. Gudmundsson and S. I. Seneviratne
Hydrol. Earth Syst. Sci., 19, 2859โ2879, https://doi.org/10.5194/hess-19-2859-2015, https://doi.org/10.5194/hess-19-2859-2015, 2015
Short summary
Short summary
Water storages and fluxes on land are key variables in the Earth system. To provide context for local investigations and to understand phenomena that emerge at large spatial scales, information on continental freshwater dynamics is needed. This paper presents a methodology to estimate continental-scale runoff on a 0.5ยฐ spatial grid, which combines the advantages of in situ observations with the power of machine learning regression. The resulting runoff estimates compare well with observations.
J. P. Boisier, N. de Noblet-Ducoudrรฉ, and P. Ciais
Hydrol. Earth Syst. Sci., 18, 3571โ3590, https://doi.org/10.5194/hess-18-3571-2014, https://doi.org/10.5194/hess-18-3571-2014, 2014
R. Alkama, L. Marchand, A. Ribes, and B. Decharme
Hydrol. Earth Syst. Sci., 17, 2967โ2979, https://doi.org/10.5194/hess-17-2967-2013, https://doi.org/10.5194/hess-17-2967-2013, 2013
E. Arnone, D. Pumo, F. Viola, L. V. Noto, and G. La Loggia
Hydrol. Earth Syst. Sci., 17, 2449โ2458, https://doi.org/10.5194/hess-17-2449-2013, https://doi.org/10.5194/hess-17-2449-2013, 2013
B. Li and M. Rodell
Hydrol. Earth Syst. Sci., 17, 1177โ1188, https://doi.org/10.5194/hess-17-1177-2013, https://doi.org/10.5194/hess-17-1177-2013, 2013
S. M. Papalexiou, D. Koutsoyiannis, and C. Makropoulos
Hydrol. Earth Syst. Sci., 17, 851โ862, https://doi.org/10.5194/hess-17-851-2013, https://doi.org/10.5194/hess-17-851-2013, 2013
A. K. Gain, W. W. Immerzeel, F. C. Sperna Weiland, and M. F. P. Bierkens
Hydrol. Earth Syst. Sci., 15, 1537โ1545, https://doi.org/10.5194/hess-15-1537-2011, https://doi.org/10.5194/hess-15-1537-2011, 2011
J. O. Haerter, S. Hagemann, C. Moseley, and C. Piani
Hydrol. Earth Syst. Sci., 15, 1065โ1079, https://doi.org/10.5194/hess-15-1065-2011, https://doi.org/10.5194/hess-15-1065-2011, 2011
K. Stahl, H. Hisdal, J. Hannaford, L. M. Tallaksen, H. A. J. van Lanen, E. Sauquet, S. Demuth, M. Fendekova, and J. Jรณdar
Hydrol. Earth Syst. Sci., 14, 2367โ2382, https://doi.org/10.5194/hess-14-2367-2010, https://doi.org/10.5194/hess-14-2367-2010, 2010
Cited articles
Allamano, P., Laio, F., and Claps, P.: Effects of disregarding seasonality on the distribution of hydrological extremes, Hydrol. Earth Syst. Sci., 15, 3207โ3215, https://doi.org/10.5194/hess-15-3207-2011, 2011.โa
Arnold, B. C., Balakrishnan, N., and Nagaraja, H. N.: A First Course in Order Statistics, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, ISBN 978-0-89871-648-1, 1992.โa
Balkema, A. A. and de Haan, L.: Residual Life Time at Great Age, Ann. Probab., 2, 792โ804, 1974.โa
Beck, C.: Dynamical Foundations of Nonextensive Statistical Mechanics, Phys. Rev. Lett., 87, 180601, https://doi.org/10.1103/PhysRevLett.87.180601, 2001.โa
Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J., De Waal, D., and Ferro, C.: Statistics of Extremes: Theory and Applications, Wiley Series in Probability and Statistics, Wiley, Chichester, England, ISBN 0-471-97647-4, 2004.โa
Bernardara, P., Mazas, F., Kergadallan, X., and Hamm, L.: A two-step framework for over-threshold modelling of environmental extremes, Nat. Hazards Earth Syst. Sci., 14, 635โ647, https://doi.org/10.5194/nhess-14-635-2014, 2014.โa, b, c
Bernardo, J. M. and Smith, A. F. M.: Bayesian Theory, John Wiley & Sons, New York, ISBN 0-471-92416-4, 1994.โa
Botto, A., Ganora, D., Laio, F., and Claps, P.: Uncertainty compliant design flood estimation, Water Resour. Res., 50, 4242โ4253, 2014.โa
Boulesteix, A., Binder, H., Abrahamowicz, M., Sauerbrei, W., and for the Simulation Panel of the STRATOS Initiative: On the necessity and design of studies comparing statistical methods, Biometrical J., 60, 216โ218, 2018.โa
Bunde, A., Eichner, J. F., Havlin, S., and Kantelhardt, J. W.: Return intervals of rare events in records with long-term persistence, Physica A, 342, 308โ314, 2004.โa
Bunde, A., Eichner, J. F., Kantelhardt, J. W., and Havlin, S.: Longโterm memory: A natural mechanism for the clustering of extreme events and anomalous residual times in climate records, Phys. Rev. Lett., 94, 048701, https://doi.org/10.1103/PhysRevLett.94.048701, 2005.โa
Burnham, K. P. and Anderson, D. R.: Formal inference from more than one model: Multimodel Inference (MMI), in: Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, edited by: Burnham, K. P. and Anderson, D. R., Springer New York, New York, NY, 149โ205, ISBN 0-387-95364-7, 2002.โa
Caldwell, P. C., Merrifield, M. A., and Thompson, P. R.: Sea level measured by tide gauges from global oceans as part of the Joint Archive for Sea Level (JASL) since 1846, NOAA National Centers for Environmental Information [data set], https://doi.org/10.7289/v5v40s7w, 2001.โa, b
Cook, N. J.: Rebuttal of โProblems in the extreme value analysisโ, Struct. Saf., 34, 418โ423, 2012.โa
Cox, D., Hunt, J., Mason, P., Wheater, H., Wolf, P., Cox, D. R., Isham, V. S., and Northrop, P. J.: Floods: some probabilistic and statistical approaches, Philos. T. Roy. Soc. A, 360, 1389โ1408, 2002.โa
David, H. A. and Nagaraja, H. N.: Order Statistics, Wiley, Hoboken, New Jersey, ISBN 0-471-38926-9, 2004.โa
Davison, A. C. and Smith, R. L.: Models for exceedances over high thresholds, J. Roy. Stat. Soc. B Met., 52, 393โ442, 1990.โa
De Michele, C.: Advances in Deriving the Exact Distribution of Maximum Annual Daily Precipitation, Water, 11, 2322, https://doi.org/10.3390/w11112322, 2019.โa
De Michele, C. and Avanzi, F.: Superstatistical distribution of daily precipitation extremes: A worldwide assessment, Sci. Rep., 8, 14204, https://doi.org/10.1038/s41598-018-31838-z, 2018.โa, b
Deidda, R.: A multiple threshold method for fitting the generalized Pareto distribution to rainfall time series, Hydrol. Earth Syst. Sci., 14, 2559โ2575, https://doi.org/10.5194/hess-14-2559-2010, 2010.โa
Dimitriadis, P. and Koutsoyiannis, D.: Climacogram versus autocovariance and power spectrum in stochastic modelling for Markovian and HurstโKolmogorov processes, Stoch. Env. Res. Risk A., 29, 1649โ1669, 2015.โa
Dimitriadis, P. and Koutsoyiannis, D.: Stochastic synthesis approximating any process dependence and distribution, Stoch. Env. Res. Risk A., 32, 1493โ1515, 2018.โa
Dimitriadis, P., Koutsoyiannis, D., Iliopoulou, T., and Papanicolaou, P.: A Global-Scale Investigation of Stochastic Similarities in Marginal Distribution and Dependence Structure of Key Hydrological-Cycle Processes, Hydrology, 8, 59, https://doi.org/10.3390/hydrology8020059, 2021.โa
Eichner, J. F., Kantelhardt, J. W., Bunde, A., and Havlin, S.: Extreme value statistics in records with long-term persistence, Phys. Rev. E, 73, 016130, https://doi.org/10.1103/PhysRevE.73.016130, 2006.โa, b, c
Eugene, N., Lee, C., and Famoye, F.: Beta-Normal distribution and its applications, Commun. Stat. Theory, 31, 497โ512, 2002.โa
Fisher, R. A. and Tippett, L. H. C.: Limiting forms of the frequency distribution of the largest or smallest member of a sample, Math. Proc. Cambridge, 24, 180โ190, 1928.โa
Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B.: Bayesian Data Analysis, 2nd ed., Chapman and Hall/CRC, Boca Raton, FL, ISBN 1-58488-388-X, 2004.โa
Giorgi, F. and Mearns, L. O.: Calculation of average, uncertainty range, and reliability of regional climate changes from AOGCM simulations via the โReliability Ensemble Averagingโ (REA) Method, J. Climate, 15, 1141โ1158, 2002.โa
Gnedenko, B.: Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire, Ann. Math., 44, 423โ453, 1943.โa
Gumbel, E. J.: Statistics of Extremes, Columbia University Press, New York, USA, ISBN 9780231891318, 1958.โa
Hisakado, M., Kitsukawa, K., and Mori, S.: Correlated binomial models and correlation structures, J. Phys. A Math. Gen., 39, 15365, https://doi.org/10.1088/0305-4470/39/50/005, 2006.โa
Hosseini, S. R., Scaioni, M., and Marani, M.: Extreme Atlantic hurricane probability of occurrence through the Metastatistical Extreme Value distribution, Geophys. Res. Lett., 47, 2019GL086138, https://doi.org/10.1029/2019GL086138, 2020.โa
Iliopoulou, T. and Koutsoyiannis, D.: Revealing hidden persistence in maximum rainfall records, Hydrolog. Sci. J., 64, 1673โ1689, 2019.โa
Iliopoulou, T., Papalexiou, S. M., Markonis, Y., and Koutsoyiannis, D.: Revisiting long-range dependence in annual precipitation, J. Hydrol., 556, 891โ900, 2018.โa
Jenkinson, A. F.: The frequency distribution of the annual maximum (or minimum) values of meteorological elements, Q. J. Roy. Meteor. Soc., 81, 158โ171, 1955.โa
Kantelhardt, J. W., Koscielny-Bunde, E., Rybski, D., Braun, P., Bunde, A., and Havlin, S.: Longโterm persistence and multifractality of precipitation and river runoff records, J. Geophys. Res.-Atmos., 111, D01106, https://doi.org/10.1029/2005JD005881, 2006.โa
Karlis, D. and Xekalaki, E.: Mixed Poisson distributions, Int. Stat. Rev., 73, 35โ58, 2005.โa
Koutsoyiannis, D.: Stochastics of hydroclimatic extremes โ A cool look at risk, third edn., Kallipos, Open Academic Editions, Greece, ISBN 978-618-85370-0-2, 2023.โa
Koutsoyiannis, D. and Dimitriadis, P.: Towards Generic Simulation for Demanding Stochastic Processes, Sci, 34, https://doi.org/10.3390/sci3030034, 2021.โa
Koutsoyiannis, D. and Montanari, A.: Statistical analysis of hydroclimatic time series: Uncertainty and insights, Water Resour. Res., 43, W05429, https://doi.org/10.1029/2006WR005592, 2007.โa, b
Kuczera, G.: Comprehensive at-site flood frequency analysis using Monte Carlo Bayesian inference, Water Resour. Res., 35, 1551โ1557, 1999.โa
Labat, D., Masbou, J., Beaulieu, E., and Mangin, A.: Scaling behavior of the fluctuations in stream flow at the outlet of karstic watersheds, France, J. Hydrol., 410, 162โ168, 2011.โa
Leadbetter, M. R.: Extremes and local dependence in stationary sequences, Z. Wahrscheinlichkeitstheorie, 65, 291โ306, 1983.โa
Leadbetter, M. R., Lindgren, G., and Rootzรฉn, H.: Extremes and Related Properties of Random Sequences and Processes, 1 edn., Springer-Verlag, New York, US, https://doi.org/10.1007/978-1-4612-5449-2, 1983.โa, b
Lombardo, F., Volpi, E., and Koutsoyiannis, D.: Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades, Hydrolog. Sci. J., 57, 1052โ1066, 2012.โa
Lombardo, F., Volpi, E., Koutsoyiannis, D., and Papalexiou, S. M.: Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrology, Hydrol. Earth Syst. Sci., 18, 243โ255, https://doi.org/10.5194/hess-18-243-2014, 2014.โa
Makkonen, L.: Problems in the extreme value analysis, Struct. Saf., 30, 405โ419, 2008.โa
Makkonen, L., Pajari, M., and Tikanmรคki, M.: Closure to โProblems in the extreme value analysisโ (Struct. Safety 2008:30:405โ419), Struct. Saf., 40, 65โ67, 2013.โa
Markonis, Y., Moustakis, Y., Nasika, C., Sychova, P., Dimitriadis, P., Hanel, M., Mรกca, P., and Papalexiou, S. M.: Global estimation of long-term persistence in annual river runoff, Adv. Water Resour., 113, 1โ12, 2018.โa
Marra, F., Amponsah, W., and Papalexiou, S. M.: Non-asymptotic Weibull tails explain the statistics of extreme daily precipitation, Adv. Water Resour., 173, 104388, https://doi.org/10.1016/j.advwatres.2023.104388, 2023.โa, b
Miniussi, A. and Marani, M.: Estimation of daily rainfall extremes through the Metastatistical Extreme Value distribution: Uncertainty minimization and implications for trend detection, Water Resour. Res., 56, e2019WR026535, https://doi.org/10.1029/2019WR026535, 2020.โa
Miniussi, A., Marani, M., and Villarini, G.: Metastatistical Extreme Value Distribution applied to floods across the continental United States, Adv. Water Resour., 136, 103498, https://doi.org/10.1016/j.advwatres.2019.103498, 2020.โa
Mood, A. M. F., Graybill, F. A., and Boes, D. C.: Introduction to the Theory of Statistics, third edn., McGraw-Hill, New York, ISBN 0-07-042864-6, 1974.โa
Moran, P. A. P.: An Introduction to Probability Theory, Oxford science publications, Oxford University Press, New York, ISBN 0-19-853242-3, 1968.โa
Morrison, J. E. and Smith, J. A.: Stochastic modeling of flood peaks using the generalized extreme value distribution, Water Resour. Res., 38, 41.1โ41.12, 2002.โa
Mushtaq, S., Miniussi, A., Merz, R., and Basso, S.: Reliable estimation of high floods: A method to select the most suitable ordinary distribution in the Metastatistical extreme value framework, Adv. Water Resour., 161, 104127, https://doi.org/10.1016/j.advwatres.2022.104127, 2022.โa, b
Papalexiou, S. M.: Rainfall generation revisited: Introducing CoSMoS-2s and advancing copula-based intermittent time series modeling, Water Resour. Res., 58, e2021WR031641, https://doi.org/10.1029/2021WR031641, 2022.โa, b, c
Papalexiou, S. M. and Serinaldi, F.: Random fields simplified: Preserving marginal distributions, correlations, and intermittency, with applications from rainfall to humidity, Water Resour. Res., 56, e2019WR026331, https://doi.org/10.1029/2019WR026331, 2020.โa, b, c
Papalexiou, S.-M., Koutsoyiannis, D., and Montanari, A.: Can a simple stochastic model generate rich patterns of rainfall events?, J. Hydrol., 411, 279โ289, 2011.โa
Papalexiou, S. M., Serinaldi, F., and Porcu, E.: Advancing space-time simulation of random fields: From storms to cyclones and beyond, Water Resour. Res., 57, e2020WR029466, https://doi.org/10.1029/2020WR029466, 2021.โa, b, c
Papalexiou, S. M., Serinaldi, F., and Clark, M. P.: Large-domain multisite precipitation generation: Operational blueprint and demonstration for 1,000 sites, Water Resour. Res., 59, e2022WR034094, https://doi.org/10.1029/2022WR034094, 2023.โa
Pickands III, J.: Statistical Inference Using Extreme Order Statistics, Ann. Stat., 3, 119โ131, 1975.โa
Popper, K. R.: The logic of scientific discovery, Hutchinson & Co., Ltd., London, UK, ISBN 0-203-99462-0, 1959.โa
Porporato, A., Vico, G., and Fay, P. A.: Superstatistics of hydro-climatic fluctuations and interannual ecosystem productivity, Geophys. Res. Lett., 33, L15402, https://doi.org/10.1029/2006GL026412, 2006.โa
R Development Core Team: R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0, http://www.R-project.org/ (last access: 31 October 2023), 2023.โa
Renard, B., Sun, X., and Lang, M.: Bayesian methods for non-stationary extreme value analysis, in: Extremes in a Changing Climate: Detection, Analysis and Uncertainty, edited by AghaKouchak, A., Easterling, D., Hsu, K., Schubert, S., and Sorooshian, S., Springer Netherlands, Dordrecht, 39โ95, https://doi.org/10.1007/978-94-007-4479-0, 2013.โa, b
Salvadori, G., De Michele, C., Kottegoda, N. T., and Rosso, R.: Extremes in nature: An approach using copulas, Springer, Dordrecht, the Netherlands, ISBN 978-1-4020-4414-4, 2007.โa
Serinaldi, F.: Use and misuse of some Hurst parameter estimators applied to stationary and nonโstationary financial time series, Physica A, 389, 2770โ2781, 2010.โa
Serinaldi, F. and Kilsby, C. G.: Simulating daily rainfall fields over large areas for collective risk estimation, J. Hydrol., 512, 285โ302, 2014a.โa
Serinaldi, F. and Kilsby, C. G.: Rainfall extremes: Toward reconciliation after the battle of distributions, Water Resour. Res., 50, 336โ352, 2014b.โa
Serinaldi, F. and Kilsby, C. G.: Stationarity is undead: Uncertainty dominates the distribution of extremes, Adv. Water Resour., 77, 17โ36, 2015.โa
Serinaldi, F. and Kilsby, C. G.: Understanding persistence to avoid underestimation of collective flood risk, Water, 8, 152, https://doi.org/10.3390/w8040152, 2016b.โa
Serinaldi, F. and Lombardo, F.: BetaBit: A fast generator of autocorrelated binary processes for geophysical research, Europhys. Lett., 118, 30007, https://doi.org/10.1209/0295-5075/118/30007, 2017a.โa, b
Serinaldi, F. and Lombardo, F.: General simulation algorithm for autocorrelated binary processes, Phys. Rev. E, 95, 023312, https://doi.org/10.1103/PhysRevE.95.023312, 2017b.โa, b
Serinaldi, F., Bรกrdossy, A., and Kilsby, C. G.: Upper tail dependence in rainfall extremes: would we know it if we saw it?, Stoch. Env. Res. Risk A., 29, 1211โ1233, 2015.โa
Serinaldi, F., Lombardo, F., and Kilsby, C. G.: All in order: Distribution of serially correlated order statistics with applications to hydrological extremes, Adv. Water Resour., 144, 103686, https://doi.org/10.1016/j.advwatres.2020.103686, 2020b.โa, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r
Serinaldi, F., Briganti, R., Kilsby, C. G., and Dodd, N.: Sailing synthetic seas: Stochastic simulation of benchmark sea state time series, Coast. Eng., 176, 104164, https://doi.org/10.1016/j.coastaleng.2022.104164, 2022a.โa
Skellam, J. G.: A probability distribution derived from the binomial distribution by regarding the probability of success as variable between the sets of trials, J. Roy. Stat. Soc. B Met., 10, 257โ261, 1948.โa
Smith, J. A., Villarini, G., and Baeck, M. L.: Mixture distributions and the hydroclimatology of extreme rainfall and flooding in the Eastern United States, J. Hydrometeorol., 12, 294โ309, 2011.โa
Smith, J. A., Cox, A. A., Baeck, M. L., Yang, L., and Bates, P.: Strange floods: The upper tail of flood peaks in the United States, Water Resour. Res., 54, 6510โ6542, 2018.โa
Smith, R. L.: Threshold methods for sample extremes, in: Statistical Extremes and Applications, edited by: Tiago, O. J., Springer Netherlands, Dordrecht, Springer Netherlands, Dordrecht, the Netherlands, 621โ638, https://doi.org/10.1007/978-94-017-3069-3, 1984.โa
Stedinger, J. R.: Design events with specified flood risk, Water Resour. Res., 19, 511โ522, 1983.โa
Tahir, M. H. and Cordeiro, G. M.: Compounding of distributions: a survey and new generalized classes, Journal of Statistical Distributions and Applications, 3, 1โ35, 2016.โa
van Montfort, M. A. and van Putten, B.: A comment on modelling extremes: Links between Multi-Component Extreme Value and General Extreme Value distributions, Journal of Hydrology (New Zealand), 41, 197โ202, 2002.โa
Volpi, E., Fiori, A., Grimaldi, S., Lombardo, F., and Koutsoyiannis, D.: One hundred years of return period: Strengths and limitations, Water Resour. Res., 51, 8570โ8585, 2015.โa
Volpi, E., Fiori, A., Grimaldi, S., Lombardo, F., and Koutsoyiannis, D.: Save hydrological observations! Return period estimation without data decimation, J. Hydrol., 571, 782โ792, 2019.โa
Von Mises, R.: La distribution de la plus grande de n valeur, Rev. Math. Union Interbalcanique, 1, 141โ160, in: Selected Papers of Richard von Mises: Volume II. Probability and Statistics, General, American Mathematical Society, Providence, Rhode Island, edited by: Frank, P., Goldstein, S., Kac, M., Prager, W., Szegรถ, G., and Birkhoff, G., 271โ294, Library of Congress Catalog Number 63-18572, http://alexander.shen.free.fr/vonMises_64_SelectedPapersVol2OCR.pdf (last access: 25 February 2025), 1936.โa
Wang, W., Van Gelder, P. H. A. J. M., Vrijling, J. K., and Chen, X.: Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes, Hydrol. Earth Syst. Sci., 11, 851โ862, https://doi.org/10.5194/hess-11-851-2007, 2007.โa
Wood, E. F. and Rodrรญguez-Iturbe, I.: Bayesian inference and decision making for extreme hydrologic events, Water Resour. Res., 11, 533โ542, 1975.โa
Yadav, R., Huser, R., and Opitz, T.: Spatial hierarchical modeling of threshold exceedances using rate mixtures, Environmetrics, 32, e2662, https://doi.org/10.1002/env.2662, 2021.โa
Zorzetto, E. and Marani, M.: Extreme value metastatistical analysis of remotely sensed rainfall in ungauged areas: Spatial downscaling and error modelling, Adv. Water Resour., 135, 103483, https://doi.org/10.1016/j.advwatres.2019.103483, 2020.โa
Zorzetto, E., Botter, G., and Marani, M.: On the emergence of rainfall extremes from ordinary events, Geophys. Res. Lett., 43, 8076โ8082, 2016.โa
Short summary
Non-asymptotic probability distributions of block maxima (BM) have been proposed as an alternative to asymptotic distributions from classic extreme-value theory. We show that the non-asymptotic models are unnecessary and redundant approximations of the corresponding parent distributions, which are readily available, are not affected by serial dependence, have simpler expression, and describe the probability of all quartiles of the process of interest and not only the probability of BM.
Non-asymptotic probability distributions of block maxima (BM) have been proposed as an...
Similar articles
Assimilating ESA CCI land surface...
Olivera-Guerra et al.
Deducing landโatmosphere coupling ...
Makhasana et al.
Novel extensions to the Fisher copula to...
Alexandre et al.