Articles | Volume 25, issue 12
https://doi.org/10.5194/hess-25-6479-2021
© Author(s) 2021. 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-25-6479-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
20 Dec 2021
Research article |
| 20 Dec 2021
| 20 Dec 2021
Flexible and consistent quantile estimation for intensity–duration–frequency curves
Felix S. Fauer
CORRESPONDING AUTHOR
Institute of Meteorology, Freie Universität Berlin, Carl-Heinrich-Becker-Weg 6–10, 12165 Berlin, Germany
Jana Ulrich
Institute of Meteorology, Freie Universität Berlin, Carl-Heinrich-Becker-Weg 6–10, 12165 Berlin, Germany
Oscar E. Jurado
Institute of Meteorology, Freie Universität Berlin, Carl-Heinrich-Becker-Weg 6–10, 12165 Berlin, Germany
Henning W. Rust
Institute of Meteorology, Freie Universität Berlin, Carl-Heinrich-Becker-Weg 6–10, 12165 Berlin, Germany
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Cited articles
Agilan, V. and Umamahesh, N. V.:
What are the best covariates for developing non-stationary rainfall Intensity-Duration-Frequency relationship?,
Adv. Water Resour.,
101, 11–22, https://doi.org/10.1016/j.advwatres.2016.12.016, 2017. a
Benestad, R. E., Lutz, J., Dyrrdal, A. V., Haugen, J. E., Parding, K. M., and Dobler, A.:
Testing a simple formula for calculating approximate intensity-duration-frequency curves,
Environ. Res. Lett.,
16, 044009, https://doi.org/10.1088/1748-9326/abd4ab, 2021. a
Bentzien, S. and Friederichs, P.:
Decomposition and graphical portrayal of the quantile score,
Q. J. Roy. Meteor. Soc.,
140, 1924–1934, https://doi.org/10.1002/qj.2284, 2014. a
Bezak, N., Šraj, M., and Mikoš, M.:
Copula-based IDF curves and empirical rainfall thresholds for flash floods and rainfall-induced landslides,
J. Hydrol., 541, 272–284,
https://doi.org/10.1016/j.jhydrol.2016.02.058, 2016. a
Bougadis, J. and Adamowski, K.:
Scaling model of a rainfall intensity-duration-frequency relationship,
Hydrol. Process.,
20, 3747–3757, https://doi.org/10.1002/hyp.6386, 2006. a, b
Brémond, P., Grelot, F., and Agenais, A.-L.: Review Article: Economic evaluation of flood damage to agriculture – review and analysis of existing methods, Nat. Hazards Earth Syst. Sci., 13, 2493–2512, https://doi.org/10.5194/nhess-13-2493-2013, 2013. a
Bücher, A., Lilienthal, J., Kinsvater, P., and Fried, R.:
Penalized quasi-maximum likelihood estimation for extreme value models with application to flood frequency analysis,
Extremes,
24, 325–348, https://doi.org/10.1007/s10687-020-00379-y, 2021. a
Burlando, P. and Rosso, R.:
Scaling and muitiscaling models of depth-duration-frequency curves for storm precipitation,
J. Hydrol.,
187, 45–64, https://doi.org/10.1016/S0022-1694(96)03086-7, fractals, scaling and nonlinear variability in hydrology, 1996. a, b, c
Cheng, L. and AghaKouchak, A.:
Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate,
Sci. Rep.,
4, 1–6, https://doi.org/10.1038/srep07093, 2014. a
Chow, V. T.:
Frequency analysis of hydrologic data with special application to rainfall intensities, Tech. rep.,
University of Illinois at Urbana Champaign, College of Engineering, 1953. a
Courty, L. G., Wilby, R. L., Hillier, J. K., and Slater, L. J.:
Intensity-duration-frequency curves at the global scale,
Environ. Res. Lett.,
14, 084045, https://doi.org/10.1088/1748-9326/ab370a, 2019. a
Davison, A. C. and Hinkley, D. V.:
Bootstrap methods and their application, 1,
Cambridge Univ. Press, Cambridge, 1997. a
DWD:
Kostra-Atlas,
available at: https://www.dwd.de/DE/leistungen/kostra_dwd_rasterwerte/kostra_dwd_rasterwerte.html (last access: 9 June 2021),
DWD, 2017. a
DWD: Deutscher Wetterdienst,
available at: https://opendata.dwd.de/climate_environment/CDC/observations_germany/climate/ (last access: 9 June 2021), n.d. a
Fauer, F. S., Ulrich, J., Jurado, O. E., and Rust, H. W.:
Annual Maxima of Station-based Rainfall Data over Different Accumulation Durations,
Zenodo [data set],
https://doi.org/10.5281/zenodo.5012621, 2021. a, b
Ganguli, P. and Coulibaly, P.: Does nonstationarity in rainfall require nonstationary intensity–duration–frequency curves?, Hydrol. Earth Syst. Sci., 21, 6461–6483, https://doi.org/10.5194/hess-21-6461-2017, 2017. a
García-Bartual, R. and Schneider, M.:
Estimating maximum expected short-duration rainfall intensities from extreme convective storms,
Phys. Chem. Earth B,
26, 675–681, https://doi.org/10.1016/S1464-1909(01)00068-5, 2001. a
Gupta, V. K. and Waymire, E.:
Multiscaling properties of spatial rainfall and river flow distributions,
J. Geophys. Res.,
95, 1999–2009, https://doi.org/10.1029/JD095iD03p01999, 1990. a, b
Hartmann, D., Klein Tank, A., Rusticucci, M., Alexander, L., Brönnimann, S., Charabi, Y., Dentener, F., Dlugokencky, E., Easterling, D., Kaplan, A., Soden, B., Thorne, P., Wild, M., and Zhai, P.:
Climate Change 2013 – The Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M., Cambridge Univ. Press, Cambridge, UK and New York, NY, USA, https://doi.org/10.1017/CBO9781107415324.008, p. 159–254, 2013. a
Koenker, R. and Machado, J. A.:
Goodness of Fit and Related Inference Processes for Quantile Regression,
J. Am. Stat. Assoc.,
94, 1296–1310, 1999. a
Kundzewicz, Z. W., Radziejewski, M., and Pinskwar, I.:
Precipitation extremes in the changing climate of Europe,
Clim. Res.,
31, 51–58, https://doi.org/10.3354/cr031051, 2006. a
Menabde, M., Seed, A., and Pegram, G.:
A simple scaling model for extreme rainfall,
Water Resour. Res.,
35, 335–339, https://doi.org/10.1029/1998WR900012, 1999. a, b
Nguyen, V., Nguyen, T., and Wang, H.:
Regional estimation of short duration rainfall extremes,
Water Sci. Technol.,
37, 15–19, https://doi.org/10.1016/S0273-1223(98)00311-4, use of Historical Rainfall Series for Hydrological Modelling, 1998. a, b
Rust, H. W.:
The effect of long-range dependence on modelling extremes with the generalised extreme value distribution,
Eur. Phys. J.-Spec. Top.,
174, 91–97, https://doi.org/10.1140/epjst/e2009-01092-8, 2009. a
Tank, A. M. G. K. and Können, G. P.:
Trends in Indices of Daily Temperature and Precipitation Extremes in Europe, 1946–99,
J. Climate,
16, 3665–3680, https://doi.org/10.1175/1520-0442(2003)016<3665:TIIODT>2.0.CO;2, 2003.
a
Ulrich, J., Fauer, F. S., and Rust, H. W.: Modeling seasonal variations of extreme rainfall on different timescales in Germany, Hydrol. Earth Syst. Sci., 25, 6133–6149, https://doi.org/10.5194/hess-25-6133-2021, 2021a. a, b
Van de Vyver, H.:
A multiscaling-based intensity–duration–frequency model for extreme precipitation,
Hydrol. Process.,
32, 1635–1647, https://doi.org/10.1002/hyp.11516, 2018. a, b, c
Veneziano, D. and Furcolo, P.:
Multifractality of rainfall and scaling of intensity-duration-frequency curves,
Water Resour. Res.,
38, 42–1, https://doi.org/10.1029/2001WR000372, 2002. a, b, c
Yan, L., Xiong, L., Jiang, C., Zhang, M., Wang, D., and Xu, C.-Y.:
Updating intensity–duration–frequency curves for urban infrastructure design under a changing environment,
WIREs Water,
8, e1519, https://doi.org/10.1002/wat2.1519, 2021. a
Short summary
Extreme rainfall events are modeled in this study for different timescales. A new parameterization of the dependence between extreme values and their timescale enables our model to estimate extremes on very short (1 min) and long (5 d) timescales simultaneously. We compare different approaches of modeling this dependence and find that our new model improves performance for timescales between 2 h and 2 d without affecting model performance on other timescales.
Extreme rainfall events are modeled in this study for different timescales. A new...
