Articles | Volume 23, issue 6
https://doi.org/10.5194/nhess-23-2053-2023
© 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/nhess-23-2053-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Contribution of solitons to enhanced rogue wave occurrence in shallow depths: a case study in the southern North Sea
Coastal Climate and Regional Sea Level Changes, Helmholtz-Zentrum Hereon, Max-Planck-Str. 1, 21502 Geesthacht, Germany
Markus Brühl
Delft Center for Systems and Control, Delft University of Technology, 2628 CD Delft, South Holland, the Netherlands
Ralf Weisse
Coastal Climate and Regional Sea Level Changes, Helmholtz-Zentrum Hereon, Max-Planck-Str. 1, 21502 Geesthacht, Germany
Sander Wahls
Delft Center for Systems and Control, Delft University of Technology, 2628 CD Delft, South Holland, the Netherlands
Related authors
Ina Teutsch, Ralf Weisse, and Sander Wahls
Nat. Hazards Earth Syst. Sci., 24, 2065–2069, https://doi.org/10.5194/nhess-24-2065-2024, https://doi.org/10.5194/nhess-24-2065-2024, 2024
Short summary
Short summary
We investigate buoy and radar measurement data from shallow depths in the southern North Sea. We analyze the role of solitons for the occurrence of rogue waves. This is done by computing the nonlinear soliton spectrum of each time series. In a previous study that considered a single measurement site, we found a connection between the shape of the soliton spectrum and the occurrence of rogue waves. In this study, results for two additional sites are reported.
Nikolaus Groll, Lidia Gaslikova, and Ralf Weisse
Nat. Hazards Earth Syst. Sci., 25, 2137–2154, https://doi.org/10.5194/nhess-25-2137-2025, https://doi.org/10.5194/nhess-25-2137-2025, 2025
Short summary
Short summary
In recent years, the western Baltic Sea has experienced severe storm surges. By analysing the individual contributions and the total water level, these events can be put into a climate perspective. It was found that individual contributions were not exceptional in all events, and no clear trend can be identified. Often the combination of the individual contributions leads to the extreme events of recent years. This points to the importance of analysing composite events.
Daniel Krieger and Ralf Weisse
EGUsphere, https://doi.org/10.5194/egusphere-2025-111, https://doi.org/10.5194/egusphere-2025-111, 2025
Short summary
Short summary
We analyze storms over the Northeast Atlantic Ocean and the German Bight and how their statistics change over past, present, and future. We look at data from many different climate model runs that cover a variety of possible future climate states. We find that storms are generally predicted to be weaker in the future, even though the wind directions that typically happen during storms occur more frequently. We also find that the most extreme storms may become more likely than nowadays.
Helge Bormann, Jenny Kebschull, Lidia Gaslikova, and Ralf Weisse
Nat. Hazards Earth Syst. Sci., 24, 2559–2576, https://doi.org/10.5194/nhess-24-2559-2024, https://doi.org/10.5194/nhess-24-2559-2024, 2024
Short summary
Short summary
Inland flooding is threatening coastal lowlands. If rainfall and storm surges coincide, the risk of inland flooding increases. We examine how such compound events are influenced by climate change. Data analysis and model-based scenario analysis show that climate change induces an increasing frequency and intensity of compounding precipitation and storm tide events along the North Sea coast. Overload of inland drainage systems will also increase if no timely adaptation measures are taken.
Ina Teutsch, Ralf Weisse, and Sander Wahls
Nat. Hazards Earth Syst. Sci., 24, 2065–2069, https://doi.org/10.5194/nhess-24-2065-2024, https://doi.org/10.5194/nhess-24-2065-2024, 2024
Short summary
Short summary
We investigate buoy and radar measurement data from shallow depths in the southern North Sea. We analyze the role of solitons for the occurrence of rogue waves. This is done by computing the nonlinear soliton spectrum of each time series. In a previous study that considered a single measurement site, we found a connection between the shape of the soliton spectrum and the occurrence of rogue waves. In this study, results for two additional sites are reported.
Daniel Krieger, Sebastian Brune, Johanna Baehr, and Ralf Weisse
Nat. Hazards Earth Syst. Sci., 24, 1539–1554, https://doi.org/10.5194/nhess-24-1539-2024, https://doi.org/10.5194/nhess-24-1539-2024, 2024
Short summary
Short summary
Previous studies found that climate models can predict storm activity in the German Bight well for averages of 5–10 years but struggle in predicting the next winter season. Here, we improve winter storm activity predictions by linking them to physical phenomena that occur before the winter. We guess the winter storm activity from these phenomena and discard model solutions that stray too far from the guess. The remaining solutions then show much higher prediction skill for storm activity.
Philipp Heinrich, Stefan Hagemann, Ralf Weisse, Corinna Schrum, Ute Daewel, and Lidia Gaslikova
Nat. Hazards Earth Syst. Sci., 23, 1967–1985, https://doi.org/10.5194/nhess-23-1967-2023, https://doi.org/10.5194/nhess-23-1967-2023, 2023
Short summary
Short summary
High seawater levels co-occurring with high river discharges have the potential to cause destructive flooding. For the past decades, the number of such compound events was larger than expected by pure chance for most of the west-facing coasts in Europe. Additionally rivers with smaller catchments showed higher numbers. In most cases, such events were associated with a large-scale weather pattern characterized by westerly winds and strong rainfall.
Daniel Krieger, Sebastian Brune, Patrick Pieper, Ralf Weisse, and Johanna Baehr
Nat. Hazards Earth Syst. Sci., 22, 3993–4009, https://doi.org/10.5194/nhess-22-3993-2022, https://doi.org/10.5194/nhess-22-3993-2022, 2022
Short summary
Short summary
Accurate predictions of storm activity are desirable for coastal management. We investigate how well a climate model can predict storm activity in the German Bight 1–10 years in advance. We let the model predict the past, compare these predictions to observations, and analyze whether the model is doing better than simple statistical predictions. We find that the model generally shows good skill for extreme periods, but the prediction timeframes with good skill depend on the type of prediction.
Elke Magda Inge Meyer, Ralf Weisse, Iris Grabemann, Birger Tinz, and Robert Scholz
Nat. Hazards Earth Syst. Sci., 22, 2419–2432, https://doi.org/10.5194/nhess-22-2419-2022, https://doi.org/10.5194/nhess-22-2419-2022, 2022
Short summary
Short summary
The severe storm tide of 13 March 1906 is still one of the most severe storm events for the East Frisian coast. Water levels from this event are considered for designing dike lines. For the first time, we investigate this event with a hydrodynamic model by forcing with atmospheric data from 147 ensemble members from century reanalysis projects and a manual reconstruction of the synoptic situation. Water levels were notably high due to a coincidence of high spring tides and high surge.
H. E. Markus Meier, Madline Kniebusch, Christian Dieterich, Matthias Gröger, Eduardo Zorita, Ragnar Elmgren, Kai Myrberg, Markus P. Ahola, Alena Bartosova, Erik Bonsdorff, Florian Börgel, Rene Capell, Ida Carlén, Thomas Carlund, Jacob Carstensen, Ole B. Christensen, Volker Dierschke, Claudia Frauen, Morten Frederiksen, Elie Gaget, Anders Galatius, Jari J. Haapala, Antti Halkka, Gustaf Hugelius, Birgit Hünicke, Jaak Jaagus, Mart Jüssi, Jukka Käyhkö, Nina Kirchner, Erik Kjellström, Karol Kulinski, Andreas Lehmann, Göran Lindström, Wilhelm May, Paul A. Miller, Volker Mohrholz, Bärbel Müller-Karulis, Diego Pavón-Jordán, Markus Quante, Marcus Reckermann, Anna Rutgersson, Oleg P. Savchuk, Martin Stendel, Laura Tuomi, Markku Viitasalo, Ralf Weisse, and Wenyan Zhang
Earth Syst. Dynam., 13, 457–593, https://doi.org/10.5194/esd-13-457-2022, https://doi.org/10.5194/esd-13-457-2022, 2022
Short summary
Short summary
Based on the Baltic Earth Assessment Reports of this thematic issue in Earth System Dynamics and recent peer-reviewed literature, current knowledge about the effects of global warming on past and future changes in the climate of the Baltic Sea region is summarised and assessed. The study is an update of the Second Assessment of Climate Change (BACC II) published in 2015 and focuses on the atmosphere, land, cryosphere, ocean, sediments, and the terrestrial and marine biosphere.
Xin Liu, Insa Meinke, and Ralf Weisse
Nat. Hazards Earth Syst. Sci., 22, 97–116, https://doi.org/10.5194/nhess-22-97-2022, https://doi.org/10.5194/nhess-22-97-2022, 2022
Short summary
Short summary
Storm surges represent a threat to low-lying coastal areas. In the aftermath of severe events, it is often discussed whether the events were unusual. Such information is not readily available from observations but needs contextualization with long-term statistics. An approach that provides such information in near real time was developed and implemented for the German coast. It is shown that information useful for public and scientific debates can be provided in near real time.
Ralf Weisse, Inga Dailidienė, Birgit Hünicke, Kimmo Kahma, Kristine Madsen, Anders Omstedt, Kevin Parnell, Tilo Schöne, Tarmo Soomere, Wenyan Zhang, and Eduardo Zorita
Earth Syst. Dynam., 12, 871–898, https://doi.org/10.5194/esd-12-871-2021, https://doi.org/10.5194/esd-12-871-2021, 2021
Short summary
Short summary
The study is part of the thematic Baltic Earth Assessment Reports – a series of review papers summarizing the knowledge around major Baltic Earth science topics. It concentrates on sea level dynamics and coastal erosion (its variability and change). Many of the driving processes are relevant in the Baltic Sea. Contributions vary over short distances and across timescales. Progress and research gaps are described in both understanding details in the region and in extending general concepts.
Cited articles
Ablowitz, M. J. and Kodama, Y.: Note on Asymptotic Solutions of the Korteweg-de Vries Equation with Solitons, Stud. Appl. Math., 66, 159–170, https://doi.org/10.1002/sapm1982662159, 1982. a
Ablowitz, M. J. and Segur, H.: Solitons and the Inverse Scattering Transform, Society for Industrial and Applied Mathematics, https://doi.org/10.1137/1.9781611970883, 1981. a, b
Ablowitz, M. J., Kaup, D. J., Newell, A. C., and Segur, H.: The Inverse
Scattering Transform-Fourier Analysis for Nonlinear Problems, Stud.
Appl. Math., 53, 249–315, https://doi.org/10.1002/sapm1974534249, 1974. a
Akhmediev, N., Ankiewicz, A., and Taki, M.: Waves that appear from nowhere and disappear without a trace, Phys. Lett. A, 373, 675–678,
https://doi.org/10.1016/j.physleta.2008.12.036, 2009. a
Baschek, B. and Imai, J.: Rogue Wave Observations Off the US West Coast,
Oceanography, 24, 158–165, https://doi.org/10.5670/oceanog.2011.35, 2011. a, b, c
Benjamin, T. B. and Feir, J. E.: The disintegration of wave trains on deep
water, J. Fluid Mech., 27, 417–430,
https://doi.org/10.1017/s002211206700045x, 1967. a, b
Bitner, E. M.: Non-linear effects of the statistical model of shallow-water
wind waves, Appl. Ocean Res., 2, 63–73,
https://doi.org/10.1016/0141-1187(80)90031-0, 1980. a
Bitner-Gregersen, E. M. and Gramstad, O.: Rogue waves. Impact on ship and offshore structures., in: R+I Position Paper, DNV GL, https://www.dnv.com/Publications/rogue-waves-60134 (last access: 23 May 2023), 2016. a
Bolles, C. T., Speer, K., and Moore, M. N. J.: Anomalous wave statistics
induced by abrupt depth change, Phys. Rev. Fluids, 4, 011801,
https://doi.org/10.1103/PhysRevFluids.4.011801, 2019. a
Brühl, M.: Direct and inverse nonlinear Fourier transform based on the
Korteweg-deVries equation (KdV-NLFT) – A spectral analysis of nonlinear
surface waves in shallow water, PhD thesis, Technische Universität Carolo-Wilhelmina zu Braunschweig, https://doi.org/10.24355/DBBS.084-201411210916-0, 2014. a
Brühl, M. and Oumeraci, H.: Analysis of long-period cosine-wave dispersion in very shallow water using nonlinear Fourier transform based on KdV equation, Appl. Ocean Res., 61, 81–91,
https://doi.org/10.1016/j.apor.2016.09.009, 2016. a, b, c
Brühl, M., Prins, P. J., Ujvary, S., Barranco, I., Wahls, S., and Liu, P. L.-F.: Comparative analysis of bore propagation over long distances using conventional linear and KdV-based nonlinear Fourier transform, Wave Motion,
111, 102905, https://doi.org/10.1016/j.wavemoti.2022.102905, 2022. a, b
Calini, A. and Schober, C. M.: Characterizing JONSWAP rogue waves and their
statistics via inverse spectral data, Wave Motion, 71, 5–17,
https://doi.org/10.1016/j.wavemoti.2016.06.007, 2017. a
Casas-Prat, M., Holthuijsen, L., and Gelder, P.: Short-term statistics of
10 000 000 waves observed by buoys, Proceedings of the Coastal Engineering Conference, Hamburg, Germany, 31 August–5 September 2008, World Scientific, 560–572, https://doi.org/10.1142/9789814277426_0047, 2009. a
Cattrell, A. D., Srokosz, M., Moat, B. I., and Marsh, R.: Can Rogue Waves Be Predicted Using Characteristic Wave Parameters?,
J. Geophys. Res.-Oceans, 123, 5624–5636, https://doi.org/10.1029/2018jc013958, 2018. a, b
Chabchoub, A., Hoffmann, N. P., and Akhmediev, N.: Rogue Wave Observation in a Water Wave Tank, Phys. Rev. Lett., 106, 204502, https://doi.org/10.1103/physrevlett.106.204502, 2011. a
Christou, M. and Ewans, K.: Field Measurements of Rogue Water Waves, J. Phys. Oceanogr., 44, 2317–2335, https://doi.org/10.1175/jpo-d-13-0199.1, 2014. a, b, c, d
Christov, I.: Internal solitary waves in the ocean: Analysis using the periodic, inverse scattering transform, Math. Comput. Simulat., 80, 192–201, https://doi.org/10.1016/j.matcom.2009.06.005, 2009. a
Costa, A., Osborne, A. R., Resio, D. T., Alessio, S., Chrivì, E., Saggese, E., Bellomo, K., and Long, C. E.: Soliton Turbulence in Shallow Water Ocean Surface Waves, Phys. Rev. Lett., 113, 108501,
https://doi.org/10.1103/PhysRevLett.113.108501, 2014. a
Dean, R. G. and Dalrymple, R. A.: Water Wave Mechanics for Engineers and
Scientists, World Scientific, https://doi.org/10.1142/1232, 1991. a
Didenkulova, E.: Catalogue of rogue waves occurred in the World Ocean from 2011 to 2018 reported by mass media sources, Ocean Coast. Manage., 188, 105076, https://doi.org/10.1016/j.ocecoaman.2019.105076, 2020. a
Didenkulova, I., Nikolkina, I., and Pelinovsky, E.: Rogue waves in the basin of intermediate depth and the possibility of their formation due to the
modulational instability, JETP Lett.+, 97, 194–198, 2013. a
Dingemans, M. W.: Water Wave Propagation Over Uneven Bottoms, World Scientific Publishing Company, https://doi.org/10.1142/1241, 1997. a
Doeleman, M. W.: Rogue waves in the Dutch North Sea, Master Thesis, Delft University of Technology, Delft, the Netherlands, 2021. a
Dudley, J. M., Genty, G., Mussot, A., Chabchoub, A., and Dias, F.: Rogue waves and analogies in optics and oceanography, Nat. Rev. Phys., 1,
675–689, https://doi.org/10.1038/s42254-019-0100-0, 2019. a
Dysthe, K., Krogstad, H. E., and Müller, P.: Oceanic Rogue Waves, Annu. Rev. Fluid Mech., 40, 287–310, https://doi.org/10.1146/annurev.fluid.40.111406.102203, 2008. a
Dysthe, K. B. and Trulsen, K.: Note on Breather Type Solutions of the NLS as Models for Freak-Waves, Phys. Scripta, T82, 48,
https://doi.org/10.1238/physica.topical.082a00048, 1999. a
Fedele, F., Brennan, J., de León, S. P., Dudley, J., and Dias, F.: Real
world ocean rogue waves explained without the modulational instability,
Sci. Rep., 6, 27715, https://doi.org/10.1038/srep27715, 2016. a
Fedele, F., Herterich, J., Tayfun, A., and Dias, F.: Large nearshore storm
waves off the Irish coast, Sci. Rep., 9, 15406,
https://doi.org/10.1038/s41598-019-51706-8, 2019. a, b
Fernandez, L., Onorato, M., Monbaliu, J., and Toffoli, A.: Modulational instability and wave amplification in finite water depth, Nat. Hazards Earth Syst. Sci., 14, 705–711, https://doi.org/10.5194/nhess-14-705-2014, 2014. a
Forristall, G. Z.: On the statistical distribution of wave heights in a storm, J. Geophys. Res., 83, 2353, https://doi.org/10.1029/jc083ic05p02353,
1978. a, b
Fu, R., Ma, Y., Dong, G., and Perlin, M.: A wavelet-based wave group detector and predictor of extreme events over unidirectional sloping bathymetry, Ocean
Eng., 229, 108936, https://doi.org/10.1016/j.oceaneng.2021.108936, 2021. a, b
Gardner, C. S., Greene, J. M., Kruskal, M. D., and Miura, R. M.: Method for
solving the Korteweg–deVries equation, Phys. Rev. Lett., 19, 1095-7, https://doi.org/10.1103/PhysRevLett.19.1095, 1967. a
Garett, C. and Gemmrich, J.: Rogue waves, Phys. Today, 62, 62–63,
https://doi.org/10.1063/1.3156339, 2009. a
Gemmrich, J. and Garrett, C.: Unexpected Waves, J. Phys. Oceanogr., 38, 2330–2336, https://doi.org/10.1175/2008jpo3960.1, 2008. a
Glukhovskiy, B.: Investigation of sea wind waves, Gidrometeoizdat, Leningrad, 1966 (in Russian). a
Gramstad, O., Zeng, H., Trulsen, K., and Pedersen, G. K.: Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water, Phys. Fluids, 25, 122103, https://doi.org/10.1063/1.4847035, 2013. a, b
Grinevich, P. and Santini, P.: The finite gap method and the analytic
description of the exact rogue wave recurrence in the periodic NLS Cauchy
problem. 1, Nonlinearity, 31, 5258–5308, https://doi.org/10.1088/1361-6544/aaddcf,
2018. a
Häfner, D., Gemmrich, J., and Jochum, M.: Real-world rogue wave
probabilities, Sci. Rep., 11, 10084, https://doi.org/10.1038/s41598-021-89359-1,
2021. a
Haver, S.: Evidences of the existence of freak waves, in: Proc. Rogue Waves,
Brest, France, 29–30 November 2000, IFREMER, ISBN 2-84433-063-0, 2000. a
Haver, S. and Andersen, O. J.: Freak waves: rare realizations of a typical
population or typical realizations of a rare population?, in: The Tenth
International Offshore and Polar Engineering Conference, Seattle, USA, 27 May–2 June 2000, International Society of Offshore and Polar Engineers, ISBN 978-1-880653-46-3, 2000. a, b, c, d, e
Huntley, D. A., Guza, R. T., and Bowen, A. J.: A universal form for shoreline
run-up spectra?, J. Geophys. Res., 82, 2577–2581,
https://doi.org/10.1029/jc082i018p02577, 1977. a
Islas, A. L. and Schober, C. M.: Predicting rogue waves in random oceanic sea
states, Phys. Fluids, 17, 031701, https://doi.org/10.1063/1.1872093, 2005. a
Its, A. and Kotlyarov, V.: Explicit formulas for solutions of the
Schrödinger nonlinear equation, Doklady Akad. Nauk Ukrainian SSR, ser. A, 11, 965–968, 1976. a
Its, A. R. and Matveev, V. B.: Schrödinger operators with finite-gap spectrum and N-soliton solutions of the Korteweg-de Vries equation, Theor. Math. Phys.+, 23, 343–355, https://doi.org/10.1007/bf01038218, 1975. a
Janssen, P. A. E. M. and Onorato, M.: The Intermediate Water Depth Limit of the Zakharov Equation and Consequences for Wave Prediction, J. Phys.
Oceanogr., 37, 2389–2400, https://doi.org/10.1175/jpo3128.1, 2007. a, b
Johnson, D.: DIWASP, a directional wave spectra toolbox for MATLAB®: User Manual, Centre for Water Research, University of Western Australia, Tech. Rep., Research Report WP-1601-DJ (V1.1), 2002. a
Jorde, S.: Kinematikken i bølger over en grunne, Master thesis, University of Oslo, Oslo, Norway, 2018. a
Karmpadakis, I., Swan, C., and Christou, M.: Assessment of wave height
distributions using an extensive field database, Coast. Eng., 157,
103630, https://doi.org/10.1016/j.coastaleng.2019.103630, 2020. a, b
Kashima, H., Hirayama, K., and Mori, N.: Estimation Of Freak Wave Occurrence From Deep To Shallow Water Regions, Coastal Engineering Proceedings, 1, 36, https://doi.org/10.9753/icce.v34.waves.36, 2014. a
Kharif, C. and Pelinovsky, E.: Physical mechanisms of the rogue wave
phenomenon, Eur. J. Mech. B-Fluid., 22, 603–634,
https://doi.org/10.1016/j.euromechflu.2003.09.002, 2003. a, b, c, d
Korteweg, D. J. and de Vries, G.: XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves,
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of
Science, 39, 422–443, https://doi.org/10.1080/14786449508620739, 1895. a, b
Kotlyarov, V. and Its, A.: Periodic problem for the nonlinear Schroedinger
equation, arXiv [preprint], https://doi.org/10.48550/ARXIV.1401.4445, 17 January 2014. a
Lawrence, C., Trulsen, K., and Gramstad, O.: Statistical properties of wave
kinematics in long-crested irregular waves propagating over non-uniform
bathymetry, Phys. Fluids, 33, 046601, https://doi.org/10.1063/5.0047643, 2021. a
Lenau, C. W.: The solitary wave of maximum amplitude, J. Fluid Mech., 26, 309–320, https://doi.org/10.1017/s0022112066001253, 1966. a
Li, Y., Draycott, S., Zheng, Y., Lin, Z., Adcock, T. A., and van den Bremer, T. S.: Why rogue waves occur atop abrupt depth transitions, J. Fluid Mech., 919, R5, https://doi.org/10.1017/jfm.2021.409, 2021. a
Longuet-Higgins, M. S.: On the Statistical Distribution of the Height of Sea
Waves, J. Mar. Res., 11, 245–266, 1952. a
Ma, Y., Dong, G., and Ma, X.: Experimental Study Of Statistics Of
Random Waves Propagating Over A Bar, Coastal Engineering
Proceedings, 1, 30, https://doi.org/10.9753/icce.v34.waves.30, 2014. a
Majda, A. J., Moore, M. N. J., and Qi, D.: Statistical dynamical model to
predict extreme events and anomalous features in shallow water waves with
abrupt depth change, P. Natl. Acad. Sci. USA, 116,
3982–3987, https://doi.org/10.1073/pnas.1820467116, 2019. a
Massel, S. R.: Ocean Surface Waves: Their Physics and Prediction, World
Scientific, https://doi.org/10.1142/2285, 2017. a
MATLAB: version 9.6.0.1072779 (R2019a), The MathWorks Inc., Natick,
Massachusetts, 2019. a
McCowan, J.: VII. On the solitary wave, The London, Edinburgh, and Dublin
Philosophical Magazine and Journal of Science, 32, 45–58,
https://doi.org/10.1080/14786449108621390, 1891. a
Mendes, S. and Scotti, A.: The Rayleigh-Haring-Tayfun distribution of wave
heights in deep water, Appl. Ocean Res., 113, 102739,
https://doi.org/10.1016/j.apor.2021.102739, 2021. a
Mendes, S., Scotti, A., Brunetti, M., and Kasparian, J.: Non-homogeneous
analysis of rogue wave probability evolution over a shoal, J. Fluid
Mech., 939, A25, https://doi.org/10.1017/jfm.2022.206, 2022. a, b
Middleton, D. and Mellen, R.: Wind-generated solitons: A potentially
significant mechanism in ocean surface wave generation and surface
scattering, IEEE J. Oceanic Eng., 10, 471–476,
https://doi.org/10.1109/JOE.1985.1145130, 1985. a
Müller, P., Garrett, C., and Osborne, A.: Meeting report: Rogue waves – The Fourteenth 'Aha Huliko'a Hawaiian Winter Workshop, Oceanography, 18, 66–75, https://doi.org/10.5670/oceanog.2005.30, 2005. a
NLWKN: Tideaußenpegel, NLWKN [data set], https://www.pegelonline.nlwkn.niedersachsen.de/Pegel/Tideau%C3%9Fenpegel/ID/452
(last access: 23 December 2021), 2021. a
Onorato, M., Osborne, A. R., Serio, M., and Bertone, S.: Freak Waves in Random Oceanic Sea States, Phys. Rev. Lett., 86, 5831–5834,
https://doi.org/10.1103/physrevlett.86.5831, 2001. a
Onorato, M., Osborne, A., Serio, M., Cavaleri, L., Brandini, C., and Stansberg, C.: Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves, Eur. J. Mech. B-Fluid., 25, 586–601, https://doi.org/10.1016/j.euromechflu.2006.01.002, 2006. a
Onorato, M., Cavaleri, L., Randoux, S., Suret, P., Ruiz, M. I., de Alfonso, M., and Benetazzo, A.: Observation of a giant nonlinear wave-packet on the surface of the ocean, Sci. Rep., 11, 23606, https://doi.org/10.1038/s41598-021-02875-y, 2021. a, b
Orzech, M. D. and Wang, D.: Measured Rogue Waves and Their Environment, Journal of Marine Science and Engineering, 8, 890, https://doi.org/10.3390/jmse8110890, 2020. a, b
Osborne, A.: The inverse scattering transform: Tools for the nonlinear fourier analysis and filtering of ocean surface waves, Chaos Soliton. Fract., 5, 2623–2637, https://doi.org/10.1016/0960-0779(94)e0118-9, 1995. a
Osborne, A. and Bergamasco, L.: The solitons of Zabusky and Kruskal revisited: Perspective in terms of the periodic spectral transform, Phys. D, 18, 26–46, https://doi.org/10.1016/0167-2789(86)90160-0, 1986. a, b
Osborne, A. R.: Behavior of solitons in random-function solutions of the
periodic Korteweg–de Vries equation, Phys. Rev. Lett., 71,
3115–3118, https://doi.org/10.1103/physrevlett.71.3115, 1993. a, b, c
Osborne, A. R. and Petti, M.: Laboratory-generated, shallow-water surface waves: Analysis using the periodic, inverse scattering transform, Phys.
Fluids, 6, 1727–1744, https://doi.org/10.1063/1.868235, 1994. a, b
Osborne, A. R., Segre, E., Boffetta, G., and Cavaleri, L.: Soliton basis states in shallow-water ocean surface waves, Phys. Rev. Lett., 67, 592–595,
https://doi.org/10.1103/physrevlett.67.592, 1991. a, b, c
Osborne, A. R., Onorato, M., and Serio, M.: The nonlinear dynamics of rogue
waves and holes in deep-water gravity wave trains, Phys. Lett. A, 275,
386–393, https://doi.org/10.1016/s0375-9601(00)00575-2, 2000. a
Osborne, A. R., Resio, D. T., Costa, A., Ponce de León, S., and
Chirivì, E.: Highly nonlinear wind waves in Currituck Sound: dense
breather turbulence in random ocean waves, Ocean Dynam., 69, 187–219,
https://doi.org/10.1007/s10236-018-1232-y, 2019. a
Pelinovsky, E. and Sergeeva, A.: Numerical modeling of the KdV random wave
field, Eur. J. Mech. B-Fluid., 25, 425–434,
https://doi.org/10.1016/j.euromechflu.2005.11.001, 2006. a
Pelinovsky, E., Talipova, T., and Kharif, C.: Nonlinear-dispersive mechanism of the freak wave formation in shallow water, Phys. D,
147, 83–94, https://doi.org/10.1016/s0167-2789(00)00149-4, 2000. a, b
Peterson, P., Soomere, T., Engelbrecht, J., and van Groesen, E.: Soliton interaction as a possible model for extreme waves in shallow water, Nonlin. Processes Geophys., 10, 503–510, https://doi.org/10.5194/npg-10-503-2003, 2003. a, b
Prevosto, M.: Effect of Directional Spreading and Spectral Bandwidth on the Nonlinearity of the Irregular Waves, in: Eighth ISOPE conference, Montreal, Canada, 24–29 May 1998, International Society of Offshore and Polar Engineers (ISOPE), ISOPE-I-98-212,
https://onepetro.org/ISOPEIOPEC/proceedings-abstract/ISOPE98/All-ISOPE98/ISOPE-I-98-212/24544 (last access: 23 May 2023), 1998. a
Prins, P. J. and Wahls, S.: Soliton Phase Shift Calculation for the
Korteweg–De Vries Equation, IEEE Access, 7, 122914–122930,
https://doi.org/10.1109/access.2019.2932256, 2019. a
Prins, P. J. and Wahls, S.: An accurate 𝒪(N2) floating point algorithm for the Crum transform of the KdV equation, Commun. Nonlinear Sci., 102, 105782, https://doi.org/10.1016/j.cnsns.2021.105782, 2021. a, b, c
Randoux, S., Suret, P., and El, G.: Inverse scattering transform analysis of
rogue waves using local periodization procedure, Sci. Rep., 6, 29238,
https://doi.org/10.1038/srep29238, 2016. a, b
Randoux, S., Suret, P., Chabchoub, A., Kibler, B., and El, G.: Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments, Phys. Rev. E, 98, 022219, https://doi.org/10.1103/physreve.98.022219, 2018. a
Raustøl, A.: Freake bølger over variabelt dyp, Master thesis, University of Oslo, Oslo, Norway, 2014. a
Sergeeva, A., Pelinovsky, E., and Talipova, T.: Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework, Nat. Hazards Earth Syst. Sci., 11, 323–330, https://doi.org/10.5194/nhess-11-323-2011, 2011. a, b, c, d
Shannon, C.: Communication in the Presence of Noise, P. IRE, 37, 10–21, https://doi.org/10.1109/JRPROC.1949.232969, 1949. a
Sievers, J., Rubel, M., and Milbradt, P.: EasyGSH-DB: Themengebiet – Geomorphologie, Bundesanstalt für Wasserbau [data set], https://doi.org/10.48437/02.2020.K2.7000.0001, 2020.
Slunyaev, A.: Nonlinear analysis and simulations of measured freak wave time
series, Eur. J. Mech. B-Fluid., 25, 621–635,
https://doi.org/10.1016/j.euromechflu.2006.03.005, 2006. a, b, c
Slunyaev, A.: Persistence of hydrodynamic envelope solitons: Detection and
rogue wave occurrence, Phys. Fluids, 33, 036606,
https://doi.org/10.1063/5.0042232, 2021. a
Slunyaev, A., Sergeeva, A., and Didenkulova, I.: Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth, Nat. Hazards, 84, 549–565, https://doi.org/10.1007/s11069-016-2430-x, 2016. a
Slunyaev, A. V.: Analysis of the Nonlinear Spectrum of Intense Sea Wave with the Purpose of Extreme Wave Prediction, Radiophys. Quant. El.+,
61, 1–21, https://doi.org/10.1007/s11141-018-9865-8, 2018. a
Slunyaev, A. V. and Shrira, V. I.: On the highest non-breaking wave in a group: fully nonlinear water wave breathers versus weakly nonlinear theory, J. Fluid Mech., 735, 203–248, https://doi.org/10.1017/jfm.2013.498, 2013. a
Soares, C. G., Cherneva, Z., and Antão, E.: Characteristics of abnormal
waves in North Sea storm sea states, Appl. Ocean Res., 25, 337–344,
https://doi.org/10.1016/j.apor.2004.02.005, 2003. a
Soomere, T.: Rogue waves in shallow water, Eur. Phys. J.-Spec. Top., 185, 81–96, https://doi.org/10.1140/epjst/e2010-01240-1, 2010. a, b
Soto-Crespo, J., Devine, N., and Akhmediev, N.: Integrable Turbulence and Rogue Waves: Breathers or Solitons?, Phys. Rev. Lett., 116, 103901,
https://doi.org/10.1103/physrevlett.116.103901, 2016. a
Stansell, P.: Distributions of freak wave heights measured in the North Sea,
Appl. Ocean Res., 26, 35–48, https://doi.org/10.1016/j.apor.2004.01.004, 2004. a, b, c, d
Stansell, P., Wolfram, J., and Linfoot, B.: Effect of sampling rate on wave
height statistics, Ocean Eng., 29, 1023–1047,
https://doi.org/10.1016/s0029-8018(01)00066-x, 2002. a
Sugavanam, S., Kopae, M. K., Peng, J., Prilepsky, J. E., and Turitsyn, S. K.:
Analysis of laser radiation using the Nonlinear Fourier transform, Nat. Commun., 10, 5663, https://doi.org/10.1038/s41467-019-13265-4, 2019. a, b
Tayfun, M. A.: Distributions of Envelope and Phase in Wind Waves, J. Phys. Oceanogr., 38, 2784–2800, https://doi.org/10.1175/2008jpo4008.1, 2008. a
Tayfun, M. A. and Fedele, F.: Wave-height distributions and nonlinear effects, Ocean Eng., 34, 1631–1649, https://doi.org/10.1016/j.oceaneng.2006.11.006,
2007. a
Toffoli, A., Fernandez, L., Monbaliu, J., Benoit, M., Gagnaire-Renou, E., Lefèvre, J. M., Cavaleri, L., Proment, D., Pakozdi, C., Stansberg, C. T., Waseda, T., and Onorato, M.: Experimental evidence of the modulation of a plane wave to oblique perturbations and generation of rogue waves in finite water depth, Phys. Fluids, 25, 091701, https://doi.org/10.1063/1.4821810, 2013. a
Trillo, S., Deng, G., Biondini, G., Klein, M., Clauss, G., Chabchoub, A., and
Onorato, M.: Experimental Observation and Theoretical Description of
Multisoliton Fission in Shallow Water, Phys. Rev. Lett., 117, 144102,
https://doi.org/10.1103/physrevlett.117.144102, 2016. a
Trulsen, K., Zeng, H., and Gramstad, O.: Laboratory evidence of freak waves
provoked by non-uniform bathymetry, Phys. Fluids, 24, 097101,
https://doi.org/10.1063/1.4748346, 2012. a
Trulsen, K., Raustøl, A., Jorde, S., and Rye, L. B.: Extreme wave statistics
of long-crested irregular waves over a shoal, J. Fluid Mech.,
882, R2, https://doi.org/10.1017/jfm.2019.861, 2020. a
Ursell, F.: The long-wave paradox in the theory of gravity waves, Math. Proc. Cambridge, 49, 685–694, https://doi.org/10.1017/s0305004100028887, 1953.
a
Wahls, S., Chimmalgi, S., and Prins, P. J.: FNFT: A Software Library for
Computing Nonlinear Fourier Transforms, Journal of Open Source Software, 3,
597, https://doi.org/10.21105/joss.00597, 2018. a
Wahls, S., Chimmalgi, S., Prins, P. J., and Brehler, M.: FastNFT/FNFT: Development Version (Commit 681191c), Zenodo [code], https://doi.org/10.5281/zenodo.7991180, 2021. a
Waseda, T., Hallerstig, M., Ozaki, K., and Tomita, H.: Enhanced freak wave occurrence with narrow directional spectrum in the North Sea, Geophys. Res. Lett., 38, L13605, https://doi.org/10.1029/2011gl047779, 2011. a, b
Zabusky, N. J. and Kruskal, M. D.: Interaction of “Solitons” in a Collisionless Plasma and the Recurrence of Initial States, Phys. Rev. Lett., 15, 240–243, https://doi.org/10.1103/physrevlett.15.240, 1965. a, b
Zakharov, V. E.: Stability of periodic waves of finite amplitude on the surface of a deep fluid, J. Appl. Mech. Tech. Ph.+, 9, 190–194, https://doi.org/10.1007/bf00913182, 1968. a
Zeng, H. and Trulsen, K.: Evolution of skewness and kurtosis of weakly nonlinear unidirectional waves over a sloping bottom, Nat. Hazards Earth Syst. Sci., 12, 631–638, https://doi.org/10.5194/nhess-12-631-2012, 2012. a, b
Zhang, J. and Benoit, M.: Wave–bottom interaction and extreme wave statistics due to shoaling and de-shoaling of irregular long-crested wave trains over steep seabed changes, J. Fluid Mech., 912, A28,
https://doi.org/10.1017/jfm.2020.1125, 2021. a, b
Zhang, J., Benoit, M., Kimmoun, O., Chabchoub, A., and Hsu, H.-C.: Statistics
of Extreme Waves in Coastal Waters: Large Scale Experiments and Advanced
Numerical Simulations, Fluids, 4, 99, https://doi.org/10.3390/fluids4020099, 2019. a
Zheng, Y., Lin, Z., Li, Y., Adcock, T. A. A., Li, Y., and van den Bremer, T. S.: Fully nonlinear simulations of unidirectional extreme waves provoked by strong depth transitions: The effect of slope, Phys. Rev. Fluids, 5, 064804, https://doi.org/10.1103/physrevfluids.5.064804, 2020. a, b
Zou, L., Wang, A., Wang, Z., Pei, Y., and Liu, X.: Experimental study of freak waves due to three-dimensional island terrain in random wave, Acta Oceanol. Sin., 38, 92–99, https://doi.org/10.1007/s13131-019-1390-x, 2019. a
Executive editor
I agree with handling editor
Short summary
Rogue waves exceed twice the significant wave height. They occur more often than expected in the shallow waters off Norderney. When applying a nonlinear Fourier transform for the Korteweg–de Vries equation to wave data from Norderney, we found differences in the soliton spectra of time series with and without rogue waves. A strongly outstanding soliton in the spectrum indicated an enhanced probability for rogue waves. We could attribute spectral solitons to the measured rogue waves.
Rogue waves exceed twice the significant wave height. They occur more often than expected in the...
Altmetrics
Final-revised paper
Preprint