Articles | Volume 30, issue 8
https://doi.org/10.5194/hess-30-2301-2026
© Author(s) 2026. 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-30-2301-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Transformed-stationary EVA 2.0: a generalized framework for non-stationary multivariate extremes analysis
Mohammad Hadi Bahmanpour
CORRESPONDING AUTHOR
Department of Physics and Astronomy “Augusto Righi” (DIFA), University of Bologna, Bologna, Italy
Alois Tilloy
European Commission, Joint Research Centre, Ispra, Italy
Michalis Vousdoukas
Department of Marine Sciences, University of Aegean, University Hill, Mytilene, Greece
Ivan Federico
CMCC Foundation – Euro-Mediterranean Center on Climate Change, Lecce, Italy
Giovanni Coppini
CMCC Foundation – Euro-Mediterranean Center on Climate Change, Lecce, Italy
Luc Feyen
European Commission, Joint Research Centre, Ispra, Italy
Lorenzo Mentaschi
CORRESPONDING AUTHOR
Department of Physics and Astronomy “Augusto Righi” (DIFA), University of Bologna, Bologna, Italy
CMCC Foundation – Euro-Mediterranean Center on Climate Change, Lecce, Italy
Related authors
No articles found.
Jacopo Alessandri, Giulia Bonino, Tomas Lovato, Momme Butenschön, Lorenzo Mentaschi, Giorgia Verri, Ivan Federico, and Nadia Pinardi
EGUsphere, https://doi.org/10.5194/egusphere-2026-1119, https://doi.org/10.5194/egusphere-2026-1119, 2026
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
Coastal seas are strongly shaped by complex coastlines, shallow depths, and inputs from rivers, which influence marine life and water quality. This study introduces a new high-resolution modelling system that combines ocean circulation and marine ecosystem processes on unstructured grids. Applied to the northern Adriatic Sea, the model realistically captures seasonal changes in key biogeochemical variables, offering improved tools to support coastal environmental management.
Simona Masina, Andrea Cipollone, Doroteaciro Iovino, Stefania Ciliberti, Rita Lecci, Sergio Cretí, Vladyslav Lyubartsev, Giovanni Coppini, and Emanuela Clementi
EGUsphere, https://doi.org/10.5194/egusphere-2026-887, https://doi.org/10.5194/egusphere-2026-887, 2026
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
The paper presents GOFS16, an eddy-resolving global operational ocean and sea ice forecasting system which provides 6-day forecasts of three-dimensional temperature, salinity, currents, sea level, and sea ice properties. The system assimilates satellite and in situ observations using a 3D variational data assimilation scheme. Validation is conducted routinely using global and regional metrics. Results indicate that GOFS16 performs within the expected range of skill for current global systems.
Italo dos Reis Lopes, Ivan Federico, Michalis Vousdoukas, Luisa Perini, Salvatore Causio, Giovanni Coppini, Maurilio Milella, Nadia Pinardi, and Lorenzo Mentaschi
Nat. Hazards Earth Syst. Sci., 26, 811–825, https://doi.org/10.5194/nhess-26-811-2026, https://doi.org/10.5194/nhess-26-811-2026, 2026
Short summary
Short summary
We improved a computer model to simulate coastal flooding by including temporary barriers like sand dunes. We tested it where sand dunes are built seasonally to protect the shoreline for two real storms: one that broke through the dunes and another where dunes held strong. Our model showed how important it is to design these defenses carefully since even if a small part of a dune fails, a major flooding can happen. Overall, our work helps create better tools to manage and protect coastal areas.
Mahmud Hasan Ghani, Nadia Pinardi, Antonio Navarra, Lorenzo Mentaschi, Silvia Bianconcini, Francesco Maicu, and Francesco Trotta
Ocean Sci., 22, 427–441, https://doi.org/10.5194/os-22-427-2026, https://doi.org/10.5194/os-22-427-2026, 2026
Short summary
Short summary
Using the same sea surface temperature and the same bulk formula but different atmospheric reanalysis and analysis surface-variable datasets, we show that a higher-resolution dataset is crucial for evaluating the heat-budget closure hypothesis in the Mediterranean Sea. For the first time, we investigate the impact of extreme heat-loss events in the Mediterranean Sea by computing the long-term, basin-averaged mean heat budget.
Rodrigo Campos-Caba, Paula Camus, Andrea Mazzino, Michalis Vousdoukas, Massimo Tondello, Ivan Federico, Salvatore Causio, and Lorenzo Mentaschi
EGUsphere, https://doi.org/10.5194/egusphere-2025-5313, https://doi.org/10.5194/egusphere-2025-5313, 2025
Short summary
Short summary
We assess the ability of machine learning emulators, from Multivariate Linear Regression to Long Short-Term Memory (LSTM) networks, to reproduce storm surge dynamics in the northern Adriatic Sea. Using the corrected Mean Absolute Deviation squared (MADc²) loss function, we demonstrate that data-driven models can match high-resolution hydrodynamic simulations in representing extreme surge events with greatly reduced computational cost.
Seimur Shirinov, Ivan Federico, Simone Bonamano, Salvatore Causio, Nicolás Biocca, Viviana Piermattei, Daniele Piazzolla, Jacopo Alessandri, Lorenzo Mentaschi, Giovanni Coppini, Marco Marcelli, and Nadia Pinardi
Nat. Hazards Earth Syst. Sci., 25, 3737–3758, https://doi.org/10.5194/nhess-25-3737-2025, https://doi.org/10.5194/nhess-25-3737-2025, 2025
Short summary
Short summary
This research investigates how seagrass meadows attenuate coastal waves. Our methodology integrates site measurements with numerical simulations, revealing that plant flexibility and seasonal growth cycles are crucial factors that enhance model fidelity for predicting wave damping. These insights aid ecosystem-based coastal protection and conservation of these vital habitats. Future work should address current–sediment–vegetation interactions for a more complete hydrodynamic understanding.
Salvatore Causio, Seimur Shirinov, Ivan Federico, Giovanni De Cillis, Emanuela Clementi, Lorenzo Mentaschi, and Giovanni Coppini
Ocean Sci., 21, 1105–1123, https://doi.org/10.5194/os-21-1105-2025, https://doi.org/10.5194/os-21-1105-2025, 2025
Short summary
Short summary
This study examines how waves and ocean currents interact during severe weather, focusing on Medicane Ianos, one of the strongest storms in the Mediterranean. Using advanced modeling, we created a unique system to simulate these interactions, capturing effects like wave-induced water levels and wave-induced effects on the vertical structure of the ocean. We validated our approach with ideal tests and real data from the storm.
Aloïs Tilloy, Dominik Paprotny, Stefania Grimaldi, Goncalo Gomes, Alessandra Bianchi, Stefan Lange, Hylke Beck, Cinzia Mazzetti, and Luc Feyen
Earth Syst. Sci. Data, 17, 293–316, https://doi.org/10.5194/essd-17-293-2025, https://doi.org/10.5194/essd-17-293-2025, 2025
Short summary
Short summary
This article presents a reanalysis of Europe's river streamflow for the period 1951–2020. Streamflow is estimated through a state-of-the-art hydrological simulation framework benefitting from detailed information about the landscape, climate, and human activities. The resulting Hydrological European ReAnalysis (HERA) can be a valuable tool for studying hydrological dynamics, including the impacts of climate change and human activities on European water resources and flood and drought risks.
Tiberiu-Eugen Antofie, Stefano Luoni, Aloïs Tilloy, Andrea Sibilia, Sandro Salari, Gustav Eklund, Davide Rodomonti, Christos Bountzouklis, and Christina Corbane
Nat. Hazards Earth Syst. Sci., 25, 287–304, https://doi.org/10.5194/nhess-25-287-2025, https://doi.org/10.5194/nhess-25-287-2025, 2025
Short summary
Short summary
This is the first study that uses spatial patterns (clusters/hotspots) and meta-analysis in order to identify the regions at a European level at risk of multi-hazards. The findings point out the socioeconomic dimension as a determining factor in the potential risk of multi-hazards. The outcome provides valuable input for the disaster risk management policy support and will assist national authorities on the implementation of a multi-hazard approach in national risk assessment preparation.
Rodrigo Campos-Caba, Jacopo Alessandri, Paula Camus, Andrea Mazzino, Francesco Ferrari, Ivan Federico, Michalis Vousdoukas, Massimo Tondello, and Lorenzo Mentaschi
Ocean Sci., 20, 1513–1526, https://doi.org/10.5194/os-20-1513-2024, https://doi.org/10.5194/os-20-1513-2024, 2024
Short summary
Short summary
Here we show the development of high-resolution simulations of storm surge in the northern Adriatic Sea employing different atmospheric forcing data and physical configurations. Traditional metrics favor a simulation forced by a coarser database and employing a less sophisticated setup. Closer examination allows us to identify a baroclinic model forced by a high-resolution dataset as being better able to capture the variability and peak values of the storm surge.
Roderik van de Wal, Angélique Melet, Debora Bellafiore, Paula Camus, Christian Ferrarin, Gualbert Oude Essink, Ivan D. Haigh, Piero Lionello, Arjen Luijendijk, Alexandra Toimil, Joanna Staneva, and Michalis Vousdoukas
State Planet, 3-slre1, 5, https://doi.org/10.5194/sp-3-slre1-5-2024, https://doi.org/10.5194/sp-3-slre1-5-2024, 2024
Short summary
Short summary
Sea level rise has major impacts in Europe, which vary from place to place and in time, depending on the source of the impacts. Flooding, erosion, and saltwater intrusion lead, via different pathways, to various consequences for coastal regions across Europe. This causes damage to assets, the environment, and people for all three categories of impacts discussed in this paper. The paper provides an overview of the various impacts in Europe.
Dominik Paprotny, Belinda Rhein, Michalis I. Vousdoukas, Paweł Terefenko, Francesco Dottori, Simon Treu, Jakub Śledziowski, Luc Feyen, and Heidi Kreibich
Hydrol. Earth Syst. Sci., 28, 3983–4010, https://doi.org/10.5194/hess-28-3983-2024, https://doi.org/10.5194/hess-28-3983-2024, 2024
Short summary
Short summary
Long-term trends in flood losses are regulated by multiple factors, including climate variation, population and economic growth, land-use transitions, reservoir construction, and flood risk reduction measures. Here, we reconstruct the factual circumstances in which almost 15 000 potential riverine, coastal and compound floods in Europe occurred between 1950 and 2020. About 10 % of those events are reported to have caused significant socioeconomic impacts.
Panagiotis Athanasiou, Ap van Dongeren, Maarten Pronk, Alessio Giardino, Michalis Vousdoukas, and Roshanka Ranasinghe
Earth Syst. Sci. Data, 16, 3433–3452, https://doi.org/10.5194/essd-16-3433-2024, https://doi.org/10.5194/essd-16-3433-2024, 2024
Short summary
Short summary
The shape of the coast, the intensity of waves, the height of the water levels, the presence of people or critical infrastructure, and the land use are important information to assess the vulnerability of the coast to coastal hazards. Here, we provide 80 indicators of this kind at consistent locations along the global ice-free coastline using open-access global datasets. These can be valuable for quick assessments of the vulnerability of the coast and at data-poor locations.
Marc Igigabel, Marissa Yates, Michalis Vousdoukas, and Youssef Diab
Nat. Hazards Earth Syst. Sci., 24, 1951–1974, https://doi.org/10.5194/nhess-24-1951-2024, https://doi.org/10.5194/nhess-24-1951-2024, 2024
Short summary
Short summary
Changes in sea levels alone do not determine the evolution of coastal hazards. Coastal hazard changes should be assessed using additional factors describing geomorphological configurations, metocean event types (storms, cyclones, long swells, and tsunamis), and the marine environment (e.g., coral reef state and sea ice extent). The assessment completed here, at regional scale including the coasts of mainland and overseas France, highlights significant differences in hazard changes.
Giovanni Coppini, Emanuela Clementi, Gianpiero Cossarini, Stefano Salon, Gerasimos Korres, Michalis Ravdas, Rita Lecci, Jenny Pistoia, Anna Chiara Goglio, Massimiliano Drudi, Alessandro Grandi, Ali Aydogdu, Romain Escudier, Andrea Cipollone, Vladyslav Lyubartsev, Antonio Mariani, Sergio Cretì, Francesco Palermo, Matteo Scuro, Simona Masina, Nadia Pinardi, Antonio Navarra, Damiano Delrosso, Anna Teruzzi, Valeria Di Biagio, Giorgio Bolzon, Laura Feudale, Gianluca Coidessa, Carolina Amadio, Alberto Brosich, Arnau Miró, Eva Alvarez, Paolo Lazzari, Cosimo Solidoro, Charikleia Oikonomou, and Anna Zacharioudaki
Ocean Sci., 19, 1483–1516, https://doi.org/10.5194/os-19-1483-2023, https://doi.org/10.5194/os-19-1483-2023, 2023
Short summary
Short summary
The paper presents the Mediterranean Forecasting System evolution and performance developed in the framework of the Copernicus Marine Service.
Martin Morlot, Simone Russo, Luc Feyen, and Giuseppe Formetta
Nat. Hazards Earth Syst. Sci., 23, 2593–2606, https://doi.org/10.5194/nhess-23-2593-2023, https://doi.org/10.5194/nhess-23-2593-2023, 2023
Short summary
Short summary
We analyzed recent trends in heat and cold wave (HW and CW) risk in a European alpine region, defined by a time and spatially explicit framework to quantify hazard, vulnerability, exposure, and risk. We find a statistically significant increase in HW hazard and exposure. A decrease in vulnerability is observed except in the larger cities. HW risk increased in 40 % of the region, especially in highly populated areas. Stagnant CW hazard and declining vulnerability result in reduced CW risk.
Panagiotis Athanasiou, Ap van Dongeren, Alessio Giardino, Michalis Vousdoukas, Jose A. A. Antolinez, and Roshanka Ranasinghe
Nat. Hazards Earth Syst. Sci., 22, 3897–3915, https://doi.org/10.5194/nhess-22-3897-2022, https://doi.org/10.5194/nhess-22-3897-2022, 2022
Short summary
Short summary
Sandy dunes protect the hinterland from coastal flooding during storms. Thus, models that can efficiently predict dune erosion are critical for coastal zone management and early warning systems. Here we develop such a model for the Dutch coast based on machine learning techniques, allowing for dune erosion estimations in a matter of seconds relative to available computationally expensive models. Validation of the model against benchmark data and observations shows good agreement.
Umesh Pranavam Ayyappan Pillai, Nadia Pinardi, Ivan Federico, Salvatore Causio, Francesco Trotta, Silvia Unguendoli, and Andrea Valentini
Nat. Hazards Earth Syst. Sci., 22, 3413–3433, https://doi.org/10.5194/nhess-22-3413-2022, https://doi.org/10.5194/nhess-22-3413-2022, 2022
Short summary
Short summary
The study presents the application of high-resolution coastal modelling for wave hindcasting on the Emilia-Romagna coastal belt. The generated coastal databases which provide an understanding of the prevailing wind-wave characteristics can aid in predicting coastal impacts.
Giorgio Micaletto, Ivano Barletta, Silvia Mocavero, Ivan Federico, Italo Epicoco, Giorgia Verri, Giovanni Coppini, Pasquale Schiano, Giovanni Aloisio, and Nadia Pinardi
Geosci. Model Dev., 15, 6025–6046, https://doi.org/10.5194/gmd-15-6025-2022, https://doi.org/10.5194/gmd-15-6025-2022, 2022
Short summary
Short summary
The full exploitation of supercomputing architectures requires a deep revision of the current climate models. This paper presents the parallelization of the three-dimensional hydrodynamic model SHYFEM (System of HydrodYnamic Finite Element Modules). Optimized numerical libraries were used to partition the model domain and solve the sparse linear system of equations in parallel. The performance assessment demonstrates a good level of scalability with a realistic configuration used as a benchmark.
Aloïs Tilloy, Bruce D. Malamud, and Amélie Joly-Laugel
Earth Syst. Dynam., 13, 993–1020, https://doi.org/10.5194/esd-13-993-2022, https://doi.org/10.5194/esd-13-993-2022, 2022
Short summary
Short summary
Compound hazards occur when two different natural hazards impact the same time period and spatial area. This article presents a methodology for the spatiotemporal identification of compound hazards (SI–CH). The methodology is applied to compound precipitation and wind extremes in Great Britain for the period 1979–2019. The study finds that the SI–CH approach can accurately identify single and compound hazard events and represent their spatial and temporal properties.
Piero Lionello, David Barriopedro, Christian Ferrarin, Robert J. Nicholls, Mirko Orlić, Fabio Raicich, Marco Reale, Georg Umgiesser, Michalis Vousdoukas, and Davide Zanchettin
Nat. Hazards Earth Syst. Sci., 21, 2705–2731, https://doi.org/10.5194/nhess-21-2705-2021, https://doi.org/10.5194/nhess-21-2705-2021, 2021
Short summary
Short summary
In this review we describe the factors leading to the extreme water heights producing the floods of Venice. We discuss the different contributions, their relative importance, and the resulting compound events. We highlight the role of relative sea level rise and the observed past and very likely future increase in extreme water heights, showing that they might be up to 160 % higher at the end of the 21st century than presently.
Cited articles
Acero, F. J., Parey, S., Hoang, T. T. H., Dacunha-Castelle, D., García, J. A., and Gallego, M. C.: Non-stationary future return levels for extreme rainfall over Extremadura (southwestern Iberian Peninsula), Hydrol. Sci. J., 62, 1394–1411, https://doi.org/10.1080/02626667.2017.1328559, 2017.
Bevacqua, E., Maraun, D., Hobæk Haff, I., Widmann, M., and Vrac, M.: Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy), Hydrol. Earth Syst. Sci., 21, 2701–2723, https://doi.org/10.5194/hess-21-2701-2017, 2017.
Bevacqua, E., Maraun, D., Vousdoukas, M. I., Voukouvalas, E., Vrac, M., Mentaschi, L., and Widmann, M.: Higher probability of compound flooding from precipitation and storm surge in Europe under anthropogenic climate change, Sci. Adv., 5, eaaw5531, https://doi.org/10.1126/sciadv.aaw5531, 2019.
Bender, J., Wahl, T., and Jensen, J.: Multivariate design in the presence of non-stationarity, J. Hydrol., 514, 123–130, https://doi.org/10.1016/j.jhydrol.2014.04.017, 2014.
Burek, P. A., van der Knijff, J., and De Roo, A.: LISFLOOD, distributed water balance and flood simulation model: revised user manual 2013, Publications Office of the European Union, https://doi.org/10.2788/24719, 2013.
Cannon, A. J.: A flexible nonlinear modelling framework for nonstationary generalized extreme value analysis in hydroclimatology, Hydrol. Process., 24, 673–685, https://doi.org/10.1002/hyp.7506, 2010.
Cheng, L., AghaKouchak, A., Gilleland, E., and Katz, R. W.: Non-stationary extreme value analysis in a changing climate, Clim. Change, 127, 353–369, https://doi.org/10.1007/s10584-014-1254-5, 2014.
Coles, S.: An introduction to statistical modeling of extreme values, Springer, https://doi.org/10.1007/978-1-4471-3675-0, 2001.
Dosio, A., Mentaschi, L., Fischer, E. M., and Wyser, K.: Extreme heat waves under 1.5 °C and 2 °C global warming, Environ. Res. Lett., 13, 054006, https://doi.org/10.1088/1748-9326/aab827, 2018.
Dottori, F., Mentaschi, L., Bianchi, A., Alfieri, L., and Feyen, L.: Cost-effective adaptation strategies to rising river flood risk in Europe, Nature Clim. Change, 13, 196–202, https://doi.org/10.1038/s41558-022-01540-0, 2023.
Genest, C., Rémillard, B., and Beaudoin, D.: Goodness-of-fit tests for copulas: A review and a power study, Insur. Math. Econ., 44, 199–213, https://doi.org/10.1016/j.insmatheco.2007.10.005, 2009.
Hamed, K. H.: Trend detection in hydrologic data: The Mann–Kendall trend test under the scaling hypothesis, J. Hydrol., 349, 350–363, https://doi.org/10.1016/j.jhydrol.2007.11.009, 2008.
Hamed, K. H. and Rao, A. R.: A modified Mann-Kendall trend test for autocorrelated data, J. Hydrol., 204, 182–196, https://doi.org/10.1016/S0022-1694(97)00125-X, 1998.
Jane, R., Dalla Valle, L., Simmonds, D., and Raby, A.: A copula-based approach for the estimation of wave height records through spatial correlation, Coast. Eng., 117, 1–18, https://doi.org/10.1016/j.coastaleng.2016.06.008, 2016.
Jiang, C., Xiong, L., Xu, C.-Y., and Guo, S.: Bivariate frequency analysis of nonstationary low-flow series based on the time-varying copula, Hydrol. Process., 29, 1521–1534, https://doi.org/10.1002/hyp.10288, 2015.
Jiang, S., Bevacqua, E., and Zscheischler, J.: River flooding mechanisms and their changes in Europe revealed by explainable machine learning, Hydrol. Earth Syst. Sci., 26, 6339–6359, https://doi.org/10.5194/hess-26-6339-2022, 2022.
Joe, H.: Multivariate Models and Multivariate Dependence Concepts, Chapman and Hall/CRC, https://doi.org/10.1201/9780367803896, 1997.
Li, H., Wang, D., Singh, V. P., Wang, Y., Wu, J., Wu, J., Liu, J., Zou, Y., He, R., and Zhang, J.: Non-stationary frequency analysis of annual extreme rainfall volume and intensity using Archimedean copulas: A case study in eastern China, J. Hydrol., 571, 114–131, https://doi.org/10.1016/j.jhydrol.2019.01.054, 2019.
Manning, C., Widmann, M., Bevacqua, E., van Loon, A. F., Maraun, D., and Vrac, M.: Increased probability of compound long-duration dry and hot events in Europe during summer (1950–2013), Environ. Res. Lett., 14, 094006, https://doi.org/10.1088/1748-9326/ab23bf, 2019.
Mentaschi, L. and Bahmanpour, H.: menta78/tsEva: tsEva 2.0 (tsEva-2.0), Zenodo [data set], https://doi.org/10.5281/zenodo.19087463, 2026.
Mentaschi, L., Vousdoukas, M., Voukouvalas, E., Sartini, L., Feyen, L., Besio, G., and Alfieri, L.: The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis, Hydrol. Earth Syst. Sci., 20, 3527–3547, https://doi.org/10.5194/hess-20-3527-2016, 2016.
Mentaschi, L., Vousdoukas, M. I., Voukouvalas, E., Dosio, A., and Feyen, L.: Global changes of extreme coastal wave energy fluxes triggered by intensified teleconnection patterns, Geophys. Res. Lett., 44, 2416–2426, https://doi.org/10.1002/2016GL072488, 2017.
Mentaschi, L., Vousdoukas, M. I., García-Sánchez, G., Fernández-Montblanc, T., Roland, A., Voukouvalas, E., Federico, I., Abdolali, A., Zhang, Y. J., and Feyen, L.: A global unstructured, coupled, high-resolution hindcast of waves and storm surge, Front. Mar. Sci., 10, https://doi.org/10.3389/fmars.2023.1233679, 2023.
Naumann, G., Cammalleri, C., Mentaschi, L., and Feyen, L.: Increased economic drought impacts in Europe with anthropogenic warming, Nat. Clim. Change, 11, 485–491, https://doi.org/10.1038/s41558-021-01044-3, 2021.
Nelsen, R. B.: An introduction to copulas, Springer, https://doi.org/10.1007/0-387-28678-0, 2006.
Parey, S. and Gailhard, J.: Extreme Low Flow Estimation under Climate Change, Atmosphere, 13, https://doi.org/10.3390/atmos13020164, 2022.
Parey, S., Hoang, T. T. H., and Dacunha-Castelle, D.: Different ways to compute temperature return levels in the climate change context, Environmetrics, 21, 698–718, https://doi.org/10.1002/env.1060, 2010.
Parey, S., Hoang, T. T. H., and Dacunha-Castelle, D.: The importance of mean and variance in predicting changes in temperature extremes: J. Geophys. Res. Atmos., 118, 8285–8296, https://doi.org/10.1002/jgrd.50629, 2013.
Parey, S., Hoang, T. T. H., and Dacunha-Castelle, D.: Future high-temperature extremes and stationarity, Nat. Hazards, 98, 1115–1134, https://doi.org/10.1007/s11069-018-3499-1, 2019.
Ribeiro, A. F. S., Russo, A., Gouveia, C. M., and Pires, C. A. L.: Drought-related hot summers: A joint probability analysis in the Iberian Peninsula, Weather Clim. Extrem., 30, 100279, https://doi.org/10.1016/j.wace.2020.100279, 2020.
Salvadori, G., Durante, F., de Michele, C., Bernardi, M., and Petrella, L.: A multivariate copula-based framework for dealing with hazard scenarios and failure probabilities, Water Resour. Res., 52, 3701–3721, https://doi.org/10.1002/2015WR017225, 2016.
Sarhadi, A., Burn, D. H., Concepción Ausín, M., and Wiper, M. P.: Time-varying nonstationary multivariate risk analysis using a dynamic Bayesian copula, Water Resour. Res., 52, 2327–2349, https://doi.org/10.1002/2015WR018525, 2016.
Serinaldi, F.: Dismissing return periods!, Stoch. Environ. Res. Risk Assess., 29, 1179–1189, https://doi.org/10.1007/s00477-014-0916-1, 2015.
Shooter, R., Ross, E., Ribal, A., Young, I. R., and Jonathan, P.: Spatial dependence of extreme seas in the North East Atlantic from satellite altimeter measurements, Environmetrics, 32, e2674, https://doi.org/10.1002/env.2674, 2021.
Sklar, A.: Fonctions de répartition à n dimensions et leurs marges, Publications de l'Institut de Statistique de l'Université de Paris, 8, 229–231, 1959.
Sklar, A.: Random variables, joint distribution functions, and copulas, Kybernetika, 9, 449–460, 1973.
Stagge, J. H., Tallaksen, L. M., Gudmundsson, L., van Loon, A. F., and Stahl, K.: Candidate distributions for climatological drought indices (SPI and SPEI), Int. J. Climatol., 35, 4027–4040, https://doi.org/10.1002/joc.4267, 2015.
Tilloy, A., Malamud, B. D., Winter, H., and Joly-Laugel, A.: Evaluating the efficacy of bivariate extreme modelling approaches for multi-hazard scenarios, Nat. Hazards Earth Syst. Sci., 20, 2091–2117, https://doi.org/10.5194/nhess-20-2091-2020, 2020.
Tilloy, A., Paprotny, D., Grimaldi, S., Gomes, G., Bianchi, A., Lange, S., Beck, H., Mazzetti, C., and Feyen, L.: HERA: a high-resolution pan-European hydrological reanalysis (1951–2020), Earth Syst. Sci. Data, 17, 293–316, https://doi.org/10.5194/essd-17-293-2025, 2025.
Vousdoukas, M. I., Mentaschi, L., Voukouvalas, E., Verlaan, M., Jevrejeva, S., Jackson, L. P., and Feyen, L.: Global probabilistic projections of extreme sea levels show intensification of coastal flood hazard, Nat. Commun., 9, 2360, https://doi.org/10.1038/s41467-018-04692-w, 2018.
Vousdoukas, M. I., Mentaschi, L., Hinkel, J., Ward, P. J., Mongelli, I., Ciscar, J.-C., and Feyen, L.: Economic motivation for raising coastal flood defenses in Europe, Nat. Commun., 11, 2119, https://doi.org/10.1038/s41467-020-15665-3, 2020.
Wahl, T., Jain, S., Bender, J., Meyers, S. D., and Luther, M. E.: Increasing risk of compound flooding from storm surge and rainfall for major US cities, Nat. Clim. Change, 5, 1093–1097, https://doi.org/10.1038/nclimate2736, 2015.
Wang, R., Liu, J., and Wang, J.: The extremal spatial dependence of significant wave height in the South China sea, Ocean Eng., 295, 116888, https://doi.org/10.1016/j.oceaneng.2024.116888, 2024.
Yan, L., Xiong, L., Guo, S., Xu, C.-Y., Xia, J., and Du, T.: Comparison of four nonstationary hydrologic design methods for changing environment, J. Hydrol., 551, 132–150, https://doi.org/10.1016/j.jhydrol.2017.06.001, 2017.
Yue, S. and Wang, C.: The Mann-Kendall test modified by effective sample size to detect trend in serially correlated hydrological series, Water Resour. Manag., 18, 201–218, https://doi.org/10.1023/B:WARM.0000043140.61082.60, 2004.
Zhang, X.: A dataset of monthly SPI and SPEI derived from ERA5 over 1959–2022, Figshare [data set], https://doi.org/10.6084/m9.figshare.24485389.v1, 2023.
Zheng, F., Westra, S., Leonard, M., and Sisson, S. A.: Modeling dependence between extreme rainfall and storm surge to estimate coastal flooding risk, Water Resour. Res., 50, 2050–2071, https://doi.org/10.1002/2013WR014616, 2014.
Zscheischler, J., Westra, S., van den Hurk, B. J. J. M., Seneviratne, S. I., Ward, P. J., Pitman, A., AghaKouchak, A., Bresch, D. N., Leonard, M., Wahl, T., and Zhang, X.: Future climate risk from compound events, Nat. Clim. Change, 8, 469–477, https://doi.org/10.1038/s41558-018-0156-3, 2018.
Zscheischler, J., Martius, O., Westra, S., Bevacqua, E., Raymond, C., Horton, R. M., van den Hurk, B., AghaKouchak, A., Jézéquel, A., Mahecha, M. D., Maraun, D., Ramos, A. M., Ridder, N. N., Thiery, W., and Vignotto, E.: A typology of compound weather and climate events, Nat. Rev. Earth Environ., 1, 333–347, https://doi.org/10.1038/s43017-020-0060-z, 2020.
Short summary
As natural hazards evolve, understanding how extreme events interact over time is crucial. While single extremes have been widely studied, joint extremes remain challenging to analyze. We present a framework that combines advanced statistical modeling with copula theory to capture changing dependencies. Applying it to historical data reveals dynamic patterns in extreme events. To support broader use, we provide an open-source tool for improved hazard assessment.
As natural hazards evolve, understanding how extreme events interact over time is crucial. While...