Articles | Volume 27, issue 24
https://doi.org/10.5194/hess-27-4369-2023
© Author(s) 2023. 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-27-4369-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
14 Dec 2023
Research article |
| 14 Dec 2023
| 14 Dec 2023
Inferring heavy tails of flood distributions through hydrograph recession analysis
Department of Catchment Hydrology, Helmholtz Centre for Environmental Research – UFZ, 06120 Halle (Saale), Germany
Ralf Merz
Department of Catchment Hydrology, Helmholtz Centre for Environmental Research – UFZ, 06120 Halle (Saale), Germany
Institute of Geosciences and Geography, Martin-Luther University Halle-Wittenberg, 06120 Halle (Saale), Germany
Soohyun Yang
Department of Aquatic Ecosystem Analysis, Helmholtz Centre for Environmental Research – UFZ, 39114 Magdeburg, Germany
Department of Civil and Environmental Engineering, Seoul National University, Seoul, 08826, Republic of Korea
Stefano Basso
Department of Catchment Hydrology, Helmholtz Centre for Environmental Research – UFZ, 06120 Halle (Saale), Germany
Norwegian Institute for Water Research (NIVA), Oslo, 0579, Norway
Related authors
Che-You Liu, Jun-Hao Chen, Sung-Ching Lee, Shijie Jiang, Hsing-Jui Wang, and Shao-Yiu Hsu
EGUsphere, https://doi.org/10.5194/egusphere-2026-2483, https://doi.org/10.5194/egusphere-2026-2483, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
Predicting how rainfall becomes streamflow is vital for water and flood management. Traditional models rely on fixed equations that may miss local features, while purely artificial-intelligence models lack physical meaning. We developed a framework that bridges both: it learns catchment characteristics and response patterns from data while remaining physically interpretable. Tested in three Taiwan catchments, it outperformed conventional approaches and revealed meaningful local dynamics.
Hsing-Jui Wang, Ralf Merz, and Stefano Basso
Hydrol. Earth Syst. Sci., 29, 1525–1548, https://doi.org/10.5194/hess-29-1525-2025, https://doi.org/10.5194/hess-29-1525-2025, 2025
Short summary
Short summary
Extreme floods are more common than expected. Knowing where these floods are likely to occur is key for risk management. Traditional methods struggle with limited data, causing uncertainty. We use common streamflow dynamics to indicate extreme flood propensity. Analyzing data from Atlantic Europe, northern Europe, and the US, we validate this novel approach and unravel intrinsic linkages between regional geographic patterns and extreme flood drivers.
Che-You Liu, Jun-Hao Chen, Sung-Ching Lee, Shijie Jiang, Hsing-Jui Wang, and Shao-Yiu Hsu
EGUsphere, https://doi.org/10.5194/egusphere-2026-2483, https://doi.org/10.5194/egusphere-2026-2483, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
Predicting how rainfall becomes streamflow is vital for water and flood management. Traditional models rely on fixed equations that may miss local features, while purely artificial-intelligence models lack physical meaning. We developed a framework that bridges both: it learns catchment characteristics and response patterns from data while remaining physically interpretable. Tested in three Taiwan catchments, it outperformed conventional approaches and revealed meaningful local dynamics.
Hsing-Jui Wang, Ralf Merz, and Stefano Basso
Hydrol. Earth Syst. Sci., 29, 1525–1548, https://doi.org/10.5194/hess-29-1525-2025, https://doi.org/10.5194/hess-29-1525-2025, 2025
Short summary
Short summary
Extreme floods are more common than expected. Knowing where these floods are likely to occur is key for risk management. Traditional methods struggle with limited data, causing uncertainty. We use common streamflow dynamics to indicate extreme flood propensity. Analyzing data from Atlantic Europe, northern Europe, and the US, we validate this novel approach and unravel intrinsic linkages between regional geographic patterns and extreme flood drivers.
Soohyun Yang, Kwanghun Choi, and Kyungrock Paik
Hydrol. Earth Syst. Sci., 28, 3119–3132, https://doi.org/10.5194/hess-28-3119-2024, https://doi.org/10.5194/hess-28-3119-2024, 2024
Short summary
Short summary
In extracting a river network from a digital elevation model, an arbitrary pruning area should be specified. As this value grows, the apparent drainage density is reduced following a power function. This reflects the fractal topographic nature. We prove this relationship related to the known power law in the exceedance probability distribution of drainage area. The power-law exponent is expressed with fractal dimensions. Our findings are supported by analysis of 14 real river networks.
Christina Franziska Radtke, Xiaoqiang Yang, Christin Müller, Jarno Rouhiainen, Ralf Merz, Stefanie R. Lutz, Paolo Benettin, Hong Wei, and Kay Knöller
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-109, https://doi.org/10.5194/hess-2024-109, 2024
Revised manuscript not accepted
Short summary
Short summary
Most studies assume no difference between transit times of water and nitrate, because nitrate is transported by water. With an 8-year high-frequency dataset of isotopic signatures of both, water and nitrate, and a transit time model, we show the temporal varying difference of nitrate and water transit times. This finding is highly relevant for applied future research related to nutrient dynamics in landscapes under anthropogenic forcing and for managing impacts of nitrate on aquatic ecosystems.
Matteo Pesce, Alberto Viglione, Jost von Hardenberg, Larisa Tarasova, Stefano Basso, Ralf Merz, Juraj Parajka, and Rui Tong
Proc. IAHS, 385, 65–69, https://doi.org/10.5194/piahs-385-65-2024, https://doi.org/10.5194/piahs-385-65-2024, 2024
Short summary
Short summary
The manuscript describes an application of PArameter Set Shuffling (PASS) approach in the Alpine region. A machine learning decision-tree algorithm is applied for the regional calibration of a conceptual semi-distributed hydrological model. Regional model efficiencies don't decrease significantly when moving in space from catchments used for the regional calibration (training) to catchments used for the procedure validation (test) and, in time, from the calibration to the verification period.
Felipe A. Saavedra, Andreas Musolff, Jana von Freyberg, Ralf Merz, Stefano Basso, and Larisa Tarasova
Hydrol. Earth Syst. Sci., 26, 6227–6245, https://doi.org/10.5194/hess-26-6227-2022, https://doi.org/10.5194/hess-26-6227-2022, 2022
Short summary
Short summary
Nitrate contamination of rivers from agricultural sources is a challenge for water quality management. During runoff events, different transport paths within the catchment might be activated, generating a variety of responses in nitrate concentration in stream water. Using nitrate samples from 184 German catchments and a runoff event classification, we show that hydrologic connectivity during runoff events is a key control of nitrate transport from catchments to streams in our study domain.
Soohyun Yang, Kwanghun Choi, and Kyungrock Paik
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2022-237, https://doi.org/10.5194/hess-2022-237, 2022
Revised manuscript not accepted
Short summary
Short summary
In extracting a river network from a digital elevation model, one should specify the pruning area. As pruning area grows, the 'apparent' drainage density reduces, following a power function. We suggest that this power-law reflects the fractal topographic nature of a catchment, and indeed follows the exceedance probability distribution of drainage area, a power-law known in earlier studies. We evaluated this theory by analyzing topographies of four study catchments.
Cited articles
Arai, R., Toyoda, Y., and Kazama, S.: Runoff recession features in an analytical probabilistic streamflow model, J. Hydrol., 597, 125745, https://doi.org/10.1016/j.jhydrol.2020.125745, 2020.
Archfield, S. A., Hirsch, R. M., Viglione, A., and Blöschl, G.: Fragmented patterns of flood change across the United States, Geophys. Res. Lett., 43, 10232–10239, https://doi.org/10.1002/2016GL070590, 2016.
Bart, R. and Hope, A.: Inter-seasonal variability in baseflow recession rates: The role of aquifer antecedent storage in central California watersheds, J. Hydrol., 519, 205–213, https://doi.org/10.1016/j.jhydrol.2014.07.020, 2014.
Basso, S., Schirmer, M., and Botter, G.: On the emergence of heavy-tailed streamflow distributions, Adv. Water Resour., 82, 98–105, https://doi.org/10.1016/j.advwatres.2015.04.013, 2015.
Basso, S., Schirmer, M., and Botter, G.: A physically based analytical model of flood frequency curves, Geophys. Res. Lett., 43, 9070–9076, https://doi.org/10.1002/2016GL069915, 2016.
Basso, S., Botter, G., Merz, R., and Miniussi, A.: PHEV! The PHysically-based Extreme Value distribution of river flows, Environ. Res. Lett., 16, 124065, https://doi.org/10.1088/1748-9326/ac3d59, 2021.
Basso, S., Merz, R., Tarasova, L., and Miniussi, A.: Extreme flooding controlled by stream network organization and flow regime, Nat. Geosci., 16, 339–343, https://doi.org/10.1038/s41561-023-01155-w, 2023.
Baudin, M., Dutfoy, A., Iooss, B., and Popelin, A.-L.: OpenTURNS: An Industrial Software for Uncertainty Quantification in Simulation BT – Handbook of Uncertainty Quantification, edited by: Ghanem, R., Higdon, D., and Owhadi, H., Springer International Publishing, Cham, 2001–2038, https://doi.org/10.1007/978-3-319-12385-1_64, 2017.
Bayerisches Landesamt für Umwelt: Abfluss Bayern, Bayerisches Landesamt für Umwelt [data set], https://www.gkd.bayern.de/de/fluesse/abfluss (last access: 26 August 2022), 2022.
Beirlant, J., Goegebeur, Y., Teugels, J., Segers, J., De Waal, D., and Ferro, C.: Statistics of extremes: Theory and applications, Wiley, https://doi.org/10.1002/0470012382, 2004.
Bevere, L. and Remondi, F.: Natural catastrophes in 2021: the floodgates are open, Swiss Re Institute sigma research, https://www.swissre.com/institute/research/sigma-research/sigma-2022-01.html (last access: 8 May 2023), 2022.
Biswal, B.: Decorrelation is not dissociation: There is no means to entirely decouple the Brutsaert-Nieber parameters in streamflow recession analysis, Adv. Water Resour., 147, 103822, https://doi.org/10.1016/j.advwatres.2020.103822, 2021.
Biswal, B. and Kumar, D. N.: Study of dynamic behaviour of recession curves, Hydrol. Process., 792, 784–792, https://doi.org/10.1002/hyp.9604, 2014.
Biswal, B. and Marani, M.: Geomorphological origin of recession curves, Geophys. Res. Lett., 37, 1–5, https://doi.org/10.1029/2010GL045415, 2010.
Botter, G., Peratoner, F., Porporato, A., Rodriguez-Iturbe, I., and Rinaldo, A.: Signatures of large-scale soil moisture dynamics on streamflow statistics across U.S. climate regimes, Water Resour. Res., 43, 1–10, https://doi.org/10.1029/2007WR006162, 2007a.
Botter, G., Porporato, A., Rodriguez-Iturbe, I., and Rinaldo, A.: Basin-scale soil moisture dynamics and the probabilistic characterization of carrier hydrologic flows: Slow, leaching-prone components of the hydrologic response, Water Resour. Res., 43, 1–14, https://doi.org/10.1029/2006WR005043, 2007b.
Botter, G., Porporato, A., Rodriguez-Iturbe, I., and Rinaldo, A.: Nonlinear storage-discharge relations and catchment streamflow regimes, Water Resour. Res., 45, 1–16, https://doi.org/10.1029/2008WR007658, 2009.
Botter, G., Basso, S., Porporato, A., Rodriguez-Iturbe, I., and Rinaldo, A.: Natural streamflow regime alterations: Damming of the Piave river basin (Italy), Water Resour. Res., 46, 1–14, https://doi.org/10.1029/2009WR008523, 2010.
Brutsaert, W. and Nieber, J. L.: Regionalized drought flow hydrographs from a mature glaciated plateau, Water Resour. Res., 13, 637–643, https://doi.org/10.1029/WR013i003p00637, 1977.
Bundesanstalt für Gewässerkunde: Global Runoff Database, Bundesanstalt für Gewässerkunde [data set], https://www.bafg.de/GRDC (last access: 29 August 2022), 2022.
Cai, Y. and Hames, D.: Minimum sample size determination for generalized extreme value distribution, Commun. Stat. Simul. Comput., 40, 87–98, https://doi.org/10.1080/03610918.2010.530368, 2010.
Ceola, S., Botter, G., Bertuzzo, E., Porporato, A., Rodriguez-Iturbe, I., and Rinaldo, A.: Comparative study of ecohydrological streamflow probability distributions, Water Resour. Res., 46, 1–12, https://doi.org/10.1029/2010WR009102, 2010.
Clauset, A., Shalizi, C. R., and Newman, M. E. J.: Power-law distributions in empirical data, SIAM Rev., 51, 661–703, https://doi.org/10.1137/070710111, 2009.
Cooke, R. M. and Nieboer, D.: Heavy-Tailed Distributions: Data, Diagnostics, and New Developments, Resour. Futur. Discuss. Pap. No. 11-19, SSRN, https://doi.org/10.2139/ssrn.1811043, 2011.
Cooke, R. M., Nieboer, D., and Misiewicz, J.: Fat-Tailed Distributions: Data, Diagnostics and Dependence, in: Vol. 1, John Wiley & Sons, ISBN 1848217927, 2014.
Cox, D. R. and Isham, V.: A simple spatial-temporal model of rainfall, P. Roy. Soc. Lond. A, 415, 317–328, https://doi.org/10.1098/rspa.1988.0016, 1988.
Cunderlik, J. M. and Burn, D. H.: The use of flood regime information in regional flood frequency analysis, Hydrolog. Sci. J., 47, 77–92, https://doi.org/10.1080/02626660209492909, 2002.
Deutscher Wetterdienst: Climate Data Center, https://cdc.dwd.de/portal/ (last access: 21 August 2022), 2022.
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.
Doulatyari, B., Betterle, A., Basso, S., Biswal, B., Schirmer, M., and Botter, G.: Predicting streamflow distributions and flow duration curves from landscape and climate, Adv. Water Resour., 83, 285–298, https://doi.org/10.1016/j.advwatres.2015.06.013, 2015.
Dralle, D. N., Karst, N. J., Charalampous, K., Veenstra, A., and Thompson, S. E.: Event-scale power law recession analysis: Quantifying methodological uncertainty, Hydrol. Earth Syst. Sci., 21, 65–81, https://doi.org/10.5194/hess-21-65-2017, 2017.
Durrans, S. R., Eiffe, M. A., Thomas, W. O., and Goranflo, H. M.: Joint Seasonal/Annual Flood Frequency Analysis, J. Hydrol. Eng., 8, 181–189, https://doi.org/10.1061/(asce)1084-0699(2003)8:4(181), 2003.
El Adlouni, S., Bobée, B., and Ouarda, T. B. M. J.: On the tails of extreme event distributions in hydrology, J. Hydrol., 355, 16–33, https://doi.org/10.1016/j.jhydrol.2008.02.011, 2008.
Eliazar, I. and Sokolov, I.: Gini characterization of extreme-value statistics, Physica A, 389, 4462–4472, https://doi.org/10.1016/j.physa.2010.07.005, 2010.
Embrechts, P., Klüppelberg, C., and Mikosch, T.: Modelling extreme events for insurance and finance, Springer, Berlin, Heidelberg, https://doi.org/10.1007/978-3-642-33483-2, 1997.
Fiorentino, M., Manfreda, S., and Iacobellis, V.: Peak runoff contributing area as hydrological signature of the probability distribution of floods, Adv. Water Resour., 30, 2123–2134, https://doi.org/10.1016/j.advwatres.2006.11.017, 2007.
Fischer, S. and Schumann, A.: Robust flood statistics: comparison of peak over threshold approaches based on monthly maxima and TL-moments, Hydrolog. Sci. J., 61, 457–470, https://doi.org/10.1080/02626667.2015.1054391, 2016.
Gioia, A., Iacobellis, V., Manfreda, S., and Fiorentino, M.: Influence of infiltration and soil storage capacity on the skewness of the annual maximum flood peaks in a theoretically derived distribution, Hydrol. Earth Syst. Sci., 937–951, https://doi.org/10.5194/hess-16-937-2012, 2012.
Godrèche, C., Majumdar, S. N., and Schehr, G.: Statistics of the longest interval in renewal processes, J. Stat. Mech. Theory Exp., 2015 P03014, https://doi.org/10.1088/1742-5468/2015/03/P03014, 2015.
Hall, J., Arheimer, B., Borga, M., Brázdil, R., Claps, P., Kiss, A., Kjeldsen, T. R., Kriaučiūnienė, J., Kundzewicz, Z. W., Lang, M., Llasat, M. C., Macdonald, N., McIntyre, N., Mediero, L., Merz, B., Merz, R., Molnar, P., Montanari, A., Neuhold, C., Parajka, J., Perdigão, R. A. P., Plavcová, L., Rogger, M., Salinas, J. L., Sauquet, E., Schär, C., Szolgay, J., Viglione, A., and Blöschl, G.: Understanding flood regime changes in Europe: A state-of-the-art assessment, Hydrol. Earth Syst. Sci., 18, 2735–2772, https://doi.org/10.5194/hess-18-2735-2014, 2014.
Hodgkins, G. A., Whitfield, P. H., Burn, D. H., Hannaford, J., Renard, B., Stahl, K., Fleig, A. K., Madsen, H., Mediero, L., Korhonen, J., Murphy, C., and Wilson, D.: Climate-driven variability in the occurrence of major floods across North America and Europe, J. Hydrol., 552, 704–717, https://doi.org/10.1016/j.jhydrol.2017.07.027, 2017.
Hu, L., Nikolopoulos, E. I., Marra, F., and Emmanouil, N. A.: Toward an improved estimation of flood frequency statistics from simulated flows, J. Flood Risk Manage., https://doi.org/10.1111/jfr3.12891, in press, 2023.
Jachens, E. R., Rupp, D. E., Roques, C., and Selker, J. S.: Recession analysis revisited: Impacts of climate on parameter estimation, Hydrol. Earth Syst. Sci., 24, 1159–1170, https://doi.org/10.5194/hess-24-1159-2020, 2020.
Jarvis, A., Reuter, H. I., Nelson, A., and Guevara, E.: Hole-filled SRTM for the globe Version 4, CGIAR CSI [data set], https://cgiarcsi.community/data/srtm-90m-digital-elevation-database-v4-1 (last access: 8 August 2022), 2022.
Jepsen, S. M., Harmon, T. C., and Shi, Y.: Watershed model calibration to the base flow recession curve with and without evapotranspiration effects, Water Resour. Res., 52, 2919–2933, https://doi.org/10.1002/2015WR017827, 2016.
Karlsen, R. H., Bishop, K., Grabs, T., Ottosson-Löfvenius, M., Laudon, H., and Seibert, J.: The role of landscape properties, storage and evapotranspiration on variability in streamflow recessions in a boreal catchment, J. Hydrol., 570, 315–328, https://doi.org/10.1016/j.jhydrol.2018.12.065, 2019.
Kousar, S., Khan, A. R., Hassan, M. U., Noreen, Z., and Bhatti, S. H.: Some best-fit probability distributions for at-site flood frequency analysis of the Ume River, J. Flood Risk Manage., 13, 1–11, https://doi.org/10.1111/jfr3.12640, 2020.
Koutsoyiannis, D.: Statistics of extremes and estimation of extreme rainfall: I. Theoretical investigation, Hydrolog. Sci. J., 49, 575–590, https://doi.org/10.1623/hysj.49.4.575.54430, 2004a.
Koutsoyiannis, D.: Statistics of extremes and estimation of extreme rainfall: II. Empirical investigation of long rainfall records, Hydrolog. Sci. J., 49, 591–610, https://doi.org/10.1623/hysj.49.4.591.54424, 2004b.
Koutsoyiannis, D.: Stochastics of Hydroclimatic Extremes – A Cool Look at Risk, in: 2nd Edn., Open Academic Editions, Athens, https://doi.org/10.57713/kallipos-1, 2022.
Krakauer, N. Y. and Temimi, M.: Stream recession curves and storage variability in small watersheds, Hydrol. Earth Syst. Sci., 15, 2377–2389, https://doi.org/10.5194/hess-15-2377-2011, 2011.
Kumar, M., Sharif, M., and Ahmed, S.: Flood estimation at Hathnikund Barrage, River Yamuna, India using the Peak-Over-Threshold method, ISH J. Hydraul. Eng., 26, 291–300, https://doi.org/10.1080/09715010.2018.1485119, 2020.
Laio, F., Porporato, A., Fernandez-Illescas, C. P., and Rodriguez-Iturbe, I.: Plants in water-controlled ecosystems: Active role in hydrologic processes and responce to water stress IV. Discussion of real cases, Adv. Water Resour., 24, 745–762, https://doi.org/10.1016/S0309-1708(01)00007-0, 2001.
Lang, M., Ouarda, T. B. M. J., and Bobée, B.: Towards operational guidelines for over-threshold modeling, J. Hydrol., 225, 103–117, https://doi.org/10.1016/S0022-1694(99)00167-5, 1999.
Lehner, B., Liermann, C. R., Revenga, C., Vörömsmarty, C., Fekete, B., Crouzet, P., Döll, P., Endejan, M., Frenken, K., Magome, J., Nilsson, C., Robertson, J. C., Rödel, R., Sindorf, N., and Wisser, D.: High-resolution mapping of the world's reservoirs and dams for sustainable river-flow management, Front. Ecol. Environ., 9, 494–502, https://doi.org/10.1890/100125, 2011.
Lins, H. F.: Challenges to hydrological observations, WMO Bull., 57, 55–58, 2008.
Lombardo, F., Napolitano, F., Russo, F., and Koutsoyiannis, D.: On the Exact Distribution of Correlated Extremes in Hydrology, Water Resour. Res., 55, 10405–10423, https://doi.org/10.1029/2019WR025547, 2019.
Lu, P., Smith, J. A., and Lin, N.: Spatial characterization of flood magnitudes over the drainage network of the Delaware river basin, J. Hydrometeorol., 18, 957–976, https://doi.org/10.1175/JHM-D-16-0071.1, 2017.
Malamud, B. D. and Turcotte, D. L.: The applicability of power-law frequency statistics to floods, J. Hydrol., 322, 168–180, https://doi.org/10.1016/j.jhydrol.2005.02.032, 2006.
Marani, M. and Ignaccolo, M.: A metastatistical approach to rainfall extremes, Adv. Water Resour., 79, 121–126, https://doi.org/10.1016/j.advwatres.2015.03.001, 2015.
Marra, F., Nikolopoulos, E. I., Anagnostou, E. N., and Morin, E.: Metastatistical Extreme Value analysis of hourly rainfall from short records: Estimation of high quantiles and impact of measurement errors, Adv. Water Resour., 117, 27–39, https://doi.org/10.1016/j.advwatres.2018.05.001, 2018.
Martinez-Villalobos, C. and Neelin, J. D.: Climate models capture key features of extreme precipitation probabilities across regions, Environ. Res. Lett., 16, 024017, https://doi.org/10.1088/1748-9326/abd351, 2021.
McCuen, R. H. and Smith, E.: Origin of Flood Skew, J. Hydrol. Eng., 13, 771–775, https://doi.org/10.1061/(asce)1084-0699(2008)13:9(771), 2008.
McDermott, T. K. J.: Global exposure to flood risk and poverty, Nat. Commun., 13, 6–8, https://doi.org/10.1038/s41467-022-30725-6, 2022.
Mejía, A., Daly, E., Rossel, F., Javanovic, T., and Gironás, J.: A stochastic model of streamflow for urbanized basins, Water Resour. Res., 50, 1984–2001, https://doi.org/10.1002/2013WR014834, 2014.
Merz, B. and Thieken, A. H.: Flood risk curves and uncertainty bounds, Nat. Hazards, 51, 437–458, https://doi.org/10.1007/s11069-009-9452-6, 2009.
Merz, B., Blöschl, G., Vorogushyn, S., Dottori, F., Aerts, J. C. J. H., Bates, P., Bertola, M., Kemter, M., Kreibich, H., Lall, U., and Macdonald, E.: Causes, impacts and patterns of disastrous river floods, Nat. Rev. Earth Environ., 2, 592–609, https://doi.org/10.1038/s43017-021-00195-3, 2021.
Merz, B., Basso, S., Fischer, S., Lun, D., Blöschl, G., Merz, R., Guse, B., Viglione, A., Vorogushyn, S., Macdonald, E., Wietzke, L., and Schumann, A.: Understanding heavy tails of flood peak distributions, Water Resour. Res., https://doi.org/10.1029/2021wr030506, in press, 2022.
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, 1–18, https://doi.org/10.1029/2019WR026535, 2020.
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.
Morrison, J. E. and Smith, J. A.: Stochastic modeling of flood peaks using the generalized extreme value distribution, Water Resour. Res., 38, 41-1–41-12, https://doi.org/10.1029/2001wr000502, 2002.
Müller, M. F., Dralle, D. N., and Thompson, S. E.: Analytical model for flow duration curves in seasonally dry climates, Water Resour. Res., 50, 5510–5531, https://doi.org/10.1002/2014WR015301, 2014.
Müller, M. F., Roche, K. R., and Dralle, D. N.: Catchment processes can amplify the effect of increasing rainfall variability, Environ. Res. Lett., 16, 084032, https://doi.org/10.1088/1748-9326/ac153e, 2021.
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.
Mushtaq, S., Miniussi, A., Merz, R., Tarasova, L., Marra, F., and Basso, S.: Prediction of Extraordinarily High Floods Emerging From Heterogeneous Flow Generation Processes, Geophys. Res. Lett., 50, 1–10, https://doi.org/10.1029/2023GL105429, 2023.
Mutzner, R., Weijs, S. V., Tarolli, P., Calaf, M., Oldroyd, H. J., and Parlange, M. B.: Controls on the diurnal streamflow cycles in two subbasins of an alpine headwater catchment Raphael, Water Resour. Res., 51, 3403–3418, https://doi.org/10.1002/2014WR016581, 2015.
Németh, L., Hübnerová, Z., and Zempléni, A.: Trend detection in GEV models, arXiv [preprint], arXiv:1907.09435 [stat.ME], 1–13, https://doi.org/10.48550/arXiv.1907.09435, 2019.
Nerantzaki, S. D. and Papalexiou, S. M.: Tails of extremes: Advancing a graphical method and harnessing big data to assess precipitation extremes, Adv. Water Resour., 134, 103448, https://doi.org/10.1016/j.advwatres.2019.103448, 2019.
Pall, P., Aina, T., Stone, D. A., Stott, P. A., Nozawa, T., Hilberts, A. G. J., Lohmann, D., and Allen, M. R.: Anthropogenic greenhouse gas contribution to flood risk in England and Wales in autumn 2000, Nature, 470, 382–385, https://doi.org/10.1038/nature09762, 2011.
Pan, X., Rahman, A., Haddad, K., and Ouarda, T. B. M. J.: Peaks-over-threshold model in flood frequency analysis: a scoping review, Stoch. Environ. Res. Risk A., 36, 2419–2435, https://doi.org/10.1007/s00477-022-02174-6, 2022.
Papalexiou, S. M. and Koutsoyiannis, D.: Battle of extreme value distributions: A global survey on extreme daily rainfall, Water Resour. Res., 49, 187–201, https://doi.org/10.1029/2012WR012557, 2013.
Papalexiou, S. M., Koutsoyiannis, D., and Makropoulos, C.: How extreme is extreme? An assessment of daily rainfall distribution tails, Hydrol. Earth Syst. Sci., 17, 851–862, https://doi.org/10.5194/hess-17-851-2013, 2013.
Pauritsch, M., Birk, S., Wagner, T., Hergarten, S., and Winkler, G.: Analytical approximations of discharge recessions for steeplysloping aquifers in alpine catchments, Water Resour. Res., 51, 8729–8740, https://doi.org/10.1002/2015WR017749, 2015.
Porporato, A., Daly, E., and Rodriguez-Iturbe, I.: Soil water balance and ecosystem response to climate change, Am. Nat., 164, 625–632, https://doi.org/10.1086/424970, 2004.
Pumo, D., Viola, F., La Loggia, G., and Noto, L. V.: Annual flow duration curves assessment in ephemeral small basins, J. Hydrol., 519, 258–270, https://doi.org/10.1016/j.jhydrol.2014.07.024, 2014.
Rahman, A. S., Rahman, A., Zaman, M. A., Haddad, K., Ahsan, A., and Imteaz, M.: A study on selection of probability distributions for at-site flood frequency analysis in Australia, Nat. Hazards, 69, 1803–1813, https://doi.org/10.1007/s11069-013-0775-y, 2013.
Rajah, K., O'Leary, T., Turner, A., Petrakis, G., Leonard, M., and Westra, S.: Changes to the temporal distribution of daily precipitation, Geophys. Res. Lett., 41, 8887–8894, https://doi.org/10.1002/2014GL062156, 2014.
Rentschler, J., Salhab, M., and Jafino, B. A.: Flood exposure and poverty in 188 countries, Nat. Commun., 13, 3527, https://doi.org/10.1038/s41467-022-30727-4, 2022.
Resnick, S. I.: Heavy-Tail Phenomena: Probabilistic and Statistical Modeling, Springer US, New York, https://doi.org/10.1007/978-0-387-45024-7, 2007.
Rodriguez-Iturbe, I., Porporato, A., Rldolfi, L., Isham, V., and Cox, D. R.: Probabilistic modelling of water balance at a point: The role of climate, soil and vegetation, P. Roy. Soc. A, 455, 3789–3805, https://doi.org/10.1098/rspa.1999.0477, 1999.
Rogger, M., Pirkl, H., Viglione, A., Komma, J., Kohl, B., Kirnbauer, R., and Merz, R.: Step changes in the flood frequency curve: Process controls, Water Resour. Res., 48, 1–15, https://doi.org/10.1029/2011WR011187, 2012.
Roques, C., Rupp, D. E., and Selker, J. S.: Improved streamflow recession parameter estimation with attention to calculation of
Rossi, M. W., Whipple, K. X., and Vivoni, E. R.: Precipitation and evapotranspiration controls on daily runoff variability in the contiguous United States and Puerto Rico, J. Geophys. Res.-Earth, 121, 128–145, https://doi.org/10.1002/2015JF003446, 2016.
Saf, B.: Regional flood frequency analysis using L-moments for the West Mediterranean region of Turkey, Water Resour. Manage., 23, 531–551, https://doi.org/10.1007/s11269-008-9287-z, 2009.
Santos, A. C., Portela, M. M., Rinaldo, A., and Schaefli, B.: Analytical flow duration curves for summer streamflow in Switzerland, Hydrol. Earth Syst. Sci., 22, 2377–2389, https://doi.org/10.5194/hess-22-2377-2018, 2018.
Sartori, M. and Schiavo, S.: Connected we stand: A network perspective on trade and global food security, Food Policy, 57, 114–127, https://doi.org/10.1016/j.foodpol.2015.10.004, 2015.
Schaefli, B., Rinaldo, A., and Botter, G.: Analytic probability distributions for snow-dominated streamflow, Water Resour. Res., 49, 2701–2713, https://doi.org/10.1002/wrcr.20234, 2013.
Seckin, N., Haktanir, T., and Yurtal, R.: Flood frequency analysis of Turkey using L-moments method, Hydrol. Process., 25, 3499–3505, https://doi.org/10.1002/hyp.8077, 2011.
Sharma, A., Wasko, C., and Lettenmaier, D. P.: If Precipitation Extremes Are Increasing, Why Aren't Floods?, Water Resour. Res., 54, 8545–8551, https://doi.org/10.1029/2018WR023749, 2018.
Sharma, D., Kadu, A., and Biswal, B.: Universal recession constants and their potential to predict recession flow, J. Hydrol., 626, 130244, https://doi.org/10.1016/j.jhydrol.2023.130244, 2023.
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, 6510–6542, https://doi.org/10.1029/2018WR022539, 2018.
Spearman, C.: The proof and measurement of association between two things, Am. J. Psychol., 15, 72–101, https://doi.org/10.2307/1412159, 1904.
Székely, G. J., Rizzo, M. L., and Bakirov, N. K.: Measuring and testing dependence by correlation of distances, Ann. Stat., 35, 2769–2794, https://doi.org/10.1214/009053607000000505, 2007.
Tarasova, L., Basso, S., Zink, M., and Merz, R.: Exploring Controls on Rainfall-Runoff Events: 1. Time Series-Based Event Separation and Temporal Dynamics of Event Runoff Response in Germany, Water Resour. Res., 54, 7711–7732, https://doi.org/10.1029/2018WR022587, 2018.
Tarasova, L., Basso, S., and Merz, R.: Transformation of Generation Processes From Small Runoff Events to Large Floods, Geophys. Res. Lett., 47, e2020GL090547, https://doi.org/10.1029/2020GL090547, 2020.
Tashie, A., Pavelsky, T., and Band, L. E.: An Empirical Reevaluation of Streamflow Recession Analysis at the Continental Scale, Water Resour. Res., 56, 1–18, https://doi.org/10.1029/2019WR025448, 2020a.
Tashie, A., Pavelsky, T., and Emanuel, R. E.: Spatial and Temporal Patterns in Baseflow Recession in the Continental United States, Water Resour. Res., 56, 1–18, https://doi.org/10.1029/2019WR026425, 2020b.
Troch, P. A., Berne, A., Bogaart, P., Harman, C., Hilberts, A. G. J., Lyon, S. W., Paniconi, C., Pauwels, V. R. N., Rupp, D. E., Selker, J. S., Teuling, A. J., Uijlenhoet, R., and Verhoest, N. E. C.: The importance of hydraulic groundwater theory in catchment hydrology: The legacy of Wilfried Brutsaert and Jean-Yves Parlange, Water Resour. Res., 49, 5099–5116, https://doi.org/10.1002/wrcr.20407, 2013.
Vázquez, A., Oliveira, J. G., Dezsö, Z., Goh, K. I., Kondor, I., and Barabási, A. L.: Modeling bursts and heavy tails in human dynamics, Phys. Rev. E, 73, 1–19, https://doi.org/10.1103/PhysRevE.73.036127, 2006.
Villarini, G. and Smith, J. A.: Flood peak distributions for the eastern United States, Water Resour. Res., 46, 1–17, https://doi.org/10.1029/2009WR008395, 2010.
Villarini, G., Smith, J. A., Baeck, M. L., Marchok, T., and Vecchi, G. A.: Characterization of rainfall distribution and flooding associated with U.S. landfalling tropical cyclones: Analyses of Hurricanes Frances, Ivan, and Jeanne (2004), J. Geophys. Res. Atmos., 116, D23116, https://doi.org/10.1029/2011JD016175, 2011.
Vogel, R. M., McMahon, T. A., and Chiew, F. H. S.: Floodflow frequency model selection in Australia, J. Hydrol., 146, 421–449, https://doi.org/10.1016/0022-1694(93)90288-K, 1993.
Volpi, E., Fiori, A., Grimaldi, S., Lombardo, F., and Koutsoyiannis, D.: Save hydrological observations! Return period estimation without data decimation, J. Hydrol., 571, 782–792, https://doi.org/10.1016/j.jhydrol.2019.02.017, 2019.
Wang, H., Merz, R., Yang, S., Tarasova, L., and Basso, S.: Emergence of heavy tails in streamflow distributions: the role of spatial rainfall variability, Adv. Water Resour., 171, 104359, https://doi.org/10.1016/j.advwatres.2022.104359, 2022.
Wietzke, L. M., Merz, B., Gerlitz, L., Kreibich, H., Guse, B., Castellarin, A., and Vorogushyn, S.: Comparative analysis of scalar upper tail indicators, Hydrolog. Sci. J., 65, 1625–1639, https://doi.org/10.1080/02626667.2020.1769104, 2020.
Wilson, P. S. and Toumi, R.: A fundamental probability distribution for heavy rainfall, Geophys. Res. Lett., 32, 1–4, https://doi.org/10.1029/2005GL022465, 2005.
Wittenberg, H.: Baseflow recession and recharge as nonlinear storage processes, Hydrol. Process., 13, 715–726, 1999.
Yunus, R. M., Hasan, M. M., Razak, N. A., Zubairid, Y. Z., and Dunne, P. K.: Modelling daily rainfall with climatological predictors: Poisson-gamma generalized linear modelling approach, Int. J. Climatol., 37, 1391–1399, https://doi.org/10.1002/joc.4784, 2017.
Zhang, X. S., Amirthanathan, G. E., Bari, M. A., Laugesen, R. M., Shin, D., Kent, D. M., MacDonald, A. M., Turner, M. E., and Tuteja, N. K.: How streamflow has changed across Australia since the 1950s: Evidence from the network of hydrologic reference stations, Hydrol. Earth Syst. Sci., 20, 3947–3965, https://doi.org/10.5194/hess-20-3947-2016, 2016.
Short summary
Accurately assessing heavy-tailed flood behavior with limited data records is challenging and can lead to inaccurate hazard estimates. Our research introduces a new index that uses hydrograph recession to identify heavy-tailed flood behavior, compare severity, and produce reliable results with short data records. This index overcomes the limitations of current metrics, which lack physical meaning and require long records. It thus provides valuable insight into the flood hazard of river basins.
Accurately assessing heavy-tailed flood behavior with limited data records is challenging and...
