On the extreme value statistics of spatio-temporal maximum sea waves under cyclone winds
Introduction
Atmospheric storms produce violent winds that force severe sea states, which are the primary cause of severe disasters such as coastal floods, ship accidents, and damages to offshore platforms and coastal structures. One of the sources of such conditions is the tropical cyclones, which are rapidly rotating storm systems characterized by a deep low-pressure centre. In the Northwestern Pacific basin, typhoons and tropical storms are some of the disastrous extreme weather events, causing storm surges with extremely large waves and other destructive impacts along the coasts (Fu et al., 2016, Liu et al., 2009, Wada et al., 2014). In recent years, strong typhoons have been observed with record-breaking waves, such as Kompasu (#1007), Bolaven (#1215) and Sanba (#1216). For instance, Sanba made landfall on the south of the Korean peninsula with peak significant wave heights of 13.4 m measured on the coast and about 16 m hindcasted in the East China Sea (Moon et al., 2016). One or two typhoons per year occur on average in the East China Sea and Yellow Sea (Li et al., 2020, Yu et al., 2020). They tend to be intensified by passing over the area due to regional enforcements such as increased travel speeds by prevailing westerlies and high-temperature seawater. This intensification of typhoons over the area leads to severe coastal disasters by extreme wave events in the Yellow Sea and the southern coast of Korea, causing economic losses in the order of tens of million US dollars per year (Jun et al., 2015, Wang et al., 2020).
Over the global oceans, the characterization of extreme wave events during storms has been an active topic of research for decades because of its importance for marine safety, coastal hazards, offshore design and operations. Significant and valuable efforts have been conducted to understand the likelihood of extreme events, up to the rogue-wave scale (Benetazzo et al., 2017a, Cavaleri et al., 2016, Cavaleri et al., 2012, Dematteis et al., 2019, Donelan and Magnusson, 2017, Dysthe et al., 2008, Fedele et al., 2017, Gemmrich and Garrett, 2011, Janssen et al., 2003, Onorato et al., 2001, Onorato et al., 2013, Slunyaev et al., 2005, Toffoli et al., 2005, Waseda et al., 2011). However, current strategies and forecast capabilities sometimes resulted ineffective in warning seafarers and avoiding structural damage to offshore and coastal facilities (Bitner-Gregersen and Gramstad, 2015, Didenkulova, 2020, Fedele et al., 2017, Mao et al., 2016). In this respect, the characteristics of wind-generated ocean waves under cyclonic storms have been studied extensively with comprehensive understanding (e.g., Liu et al., 2017, Moon et al., 2003, Young, 2017, Young, 1988); this knowledge is not plainly applicable, however, with regard to the formation of individual, extreme waves in these conditions, a process that remains not totally understood. Past observations (Guedes Soares et al., 2004, Santo et al., 2013, Wang, 2005) and spectral wave modelling results (Jiang et al., 2019, McAllister et al., 2019, Mori, 2012) seem to suggest that competing mechanisms may explain the occurrence of single high waves, even exceeding the rogue wave threshold. The question to be addressed is the role of interacting multiple wave systems (i.e., a combination of wind-sea and remotely generated swell, produced by the rapidly varying, spiralling cyclone winds) in enhancing or reducing the probability of encountering high waves.
It is a general feature of translating cyclone winds that the ocean wave directional spectrum's resulting shape and the related bulk parameters vary noticeably around the storm centre. In particular, the maximum significant wave height in such storms can be represented using an extended fetch model (King and Shemdin, 1978, Young, 2017), whose effect is such that the degree of asymmetry of the wind field (stronger winds to the right in the northern hemisphere) is far smaller than the wave field. For the latter, the characterization of Black et al. (2007) distinguished in the geographical space three azimuthal sectors experiencing different types of mixed sea states, with swells and locally generated wind seas travelling in many directions and producing a uni or bimodal shape of the spectra. The work by Holthuijsen et al. (2012) highlighted the swell types in a hypothetical hurricane and the following (angle between the wind and swell < 45°), cross (angle between 45° and 135°), and opposing (angle > 135°) conditions for the swell and the wind sea (see also Hu and Chen, 2011, and Liu et al., 2017). As a result, the resulting sea states produce characteristic patterns for the wave spectrum parameters and surface roughness.
As for the extreme wave generation in general environments, early researches discussed it in the context of nonlinear instability of deep-water waves (Janssen et al., 2003, Mori et al., 2006, Waseda et al., 2011). In nonlinear models that allow for energy focusing due to modulation instability (Benjamin and Feir, 1967), the interaction of two plane-wave systems with different direction of propagation was reported as a possible mechanism for extreme wave formation in deep water (Onorato et al., 2010). However, in the framework of a system of two coupled nonlinear Schrödinger equations (Zakharov, 1968), the crossing angle must be kept smaller than about 60° to 70° (Cavaleri et al., 2012) since, for larger angles, the solution of equations becomes of defocusing type. Indeed, nonlinear Schrödinger type modulational instabilities attenuate as the wave spectrum broadens (Onorato et al., 2009), such that their role in the generation of extreme stormy waves was questioned (see, e.g., Fedele et al., 2016). On the other hand, the constructive interference of 3D elementary waves with random amplitudes and phases enhanced by second-order bound nonlinearities has been proposed as an effective mechanism for extreme and rogue wave generation (Benetazzo et al., 2015, Fedele, 2012). The impact of multiple systems on spatio-temporal maximum wave elevations was firstly analyzed by Baxevani and Rychlik (2004). They proposed that counter-propagating, short-crested (i.e., laterally spread), and uncorrelated sea states with random phases maximize, in Gaussian seas, the likelihood of very high surface elevations.
Under typhoon winds, the study by Mori (2012) suggested that long-crested, uni-directional extreme waves resulting from nonlinear instability have a great potential of occurring in the south-east of the storm centre (northern hemisphere), where waves are steep and have narrow frequencies and directional spectra. It is also suggested that in the south and west areas around the storm centre, the large directional spread (resulting from the combination of wind-sea and swell) attenuates the nonlinear four-wave interactions, and the wave field is weakly nonlinear. In that study, at the same time, the role of directionality is not considered as a potential mechanism for the enhancement of the surface elevation. However, as pointed out above, other research indicates that spatio-temporal maxima of short-crested, multi-directional wave trains are enhanced if the energy can spread laterally. This debate provides our principal motivation for studying how the extreme wave generation proceeds under the forcing of multiple wave systems that may maximize the width (frequency and directions) of the resulting sea state. The focus will be on the wave extremes at short term/range by considering the role of the 3D (2D space + time) geometry of the wave field.
Following the summary mentioned above, the present paper will examine the spatio-temporal statistics of maximum waves (crest and crest-to-trough heights) in the Northwestern Pacific under realistic cyclone winds associated with the tropical storm Kong-rey (2018). In situ observations using a stereo wave imaging system and spectral wave model results (from the European Centre for Medium-Range Weather Forecasts, ECMWF) will be used. They allowed us to discuss in detail the cyclone regions where the highest waves are more likely to occur, resulting from dispersive and directional focusing of elementary wave harmonics enhanced by second-order nonlinear effects. The assessment of model directional spectrum estimations (of wave maxima, steepness, frequency and direction widths, significant wave height) with observed wave data will also be discussed.
The arrangement of the paper is as follows. Section 2 introduces the relevant information on the Kong-rey storm, and the basic extreme-value statistical principles used in this paper. Details pertaining to the 3D wave field observation, the wind and spectral wave models are also incorporated in this section. Section 3 is dedicated to comparing model and measurements, and it provides the principal results regarding the geographical pattern of maximum waves and related sea parameters around the storm centre. A discussion and summary of the main conclusions of the study are presented in section 4.
Section snippets
The tropical storm Kong-rey (2018)
The northern hemisphere tropical storm Kong-rey (#1825) developed in late September 2018 as a large and powerful typhoon that was tied with Typhoon Yutu as the most powerful tropical cyclone worldwide in 2018. The twenty-fifth tropical storm, eleventh typhoon and 6th super-typhoon of the 2018 Pacific typhoon season, Kong-rey originated from a tropical disturbance in the open Pacific Ocean; for a couple of days, it went westward, organizing into a tropical depression on 27 September. Then, it
Results and discussion
In this section, we shall focus on analysing the wave fields in the Northwestern Pacific on 5 and 6 October 2018 when the tropical storm Kong-rey translated north towards the Korean peninsula, and measurements from GORS are available, permitting a local assessment and a direct comparison with model results. The objective is threefold. On the one hand, models are used to give an overview of the cyclone and the structure of the sea wave response (intensity and pattern), and, on the other hand,
Concluding remarks
In this study, open-sea measurements of the 3D wave elevation field and spectral-wave model numerical simulations have been used to obtain insights into the short-term/range statistics of maximum waves under cyclone winds (northern hemisphere). We advanced previous investigations on this topic by using, for the first time, spatio-temporal extreme value formulations, which proved to be able to describe the likelihood and amplitude of maximum waves in short-crested, mixed (wind-sea and swell) sea
Funding
The work was supported by the project “Establishment of the ocean research station in the jurisdiction zone and convergence research”, funded by the Ministry of Oceans and Fisheries, Republic of Korea. JY also appreciate partial funding of KIOST (PE99842) and AB by the Copernicus Marine Environment Monitoring Service (CMEMS) LATEMAR project. CMEMS is implemented by Mercator Ocean in the framework of a delegation agreement with the European Union. This work has also been conducted as part of the
CRediT authorship contribution statement
Alvise Benetazzo: Conceptualization, Methodology, Formal analysis, Data curation, Supervision, Project administration, Funding acquisition. Francesco Barbariol: Software, Formal analysis, Investigation, Funding acquisition. Filippo Bergamasco: Software, Investigation. Luciana Bertotti: Investigation. Jeseon Yoo: Resources, Data curation. Jae-Seol Shim: Resources. Luigi Cavaleri: Investigation.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We are grateful to Prof. Miguel Onorato and Dr Silvio Davison for their advice on the statistics of multimodal sea states, and Prof. Antonio Ricchi for the fruitful discussions about atmospheric cyclones.
References (115)
- et al.
Maximum wave heights from global model reanalysis
Prog. Oceanogr.
(2019) - et al.
Maxima for Gaussian seas
Ocean Eng.
(2006) Measurements of short water waves using stereo matched image sequences
Coast. Eng.
(2006)- et al.
Towards a unified framework for extreme sea waves from spectral models: rationale and applications
Ocean Eng.
(2021) - et al.
Characterizing the signature of a spatio-temporal wind wave field
Ocean Model.
(2018) - et al.
Offshore stereo measurements of gravity waves
Coast. Eng.
(2012) - et al.
Stereo imaging and X-band radar wave data fusion: An assessment
Ocean Eng.
(2018) - et al.
WASS: An open-source pipeline for 3D stereo reconstruction of ocean waves
Comput. Geosci.
(2017) Catalogue of rogue waves occurred in the World Ocean from 2011 to 2018 reported by mass media sources
Ocean Coast. Manag.
(2020)- et al.
Space–time measurements of oceanic sea states
Ocean Model.
(2013)
Euler characteristics of oceanic sea states
Math. Comput. Simul.
Stochastic Doppler shift and encountered wave period distributions in Gaussian waves
Ocean Eng.
Numerical simulations of ocean surface waves under hurricane conditions: Assessment of existing model performance
Ocean Model.
On estimating extremes in an evolving wave field
Coast. Eng.
Rogue wave statistics in (2+1) Gaussian seas I: Narrow-banded distribution
Appl. Ocean Res.
On the distribution of crest to trough wave heights
Ocean Eng
Rogue waves and their generating mechanisms in different physical contexts
Phys. Rep.
Extreme wave parameters under North Atlantic extratropical cyclones
Ocean Model.
Frequency width in predictions of windsea spectra and the role of the nonlinear solver
Ocean Model.
Modeling freak waves from the North Sea
Appl. Ocean Res.
HF radio measurements of surface currents
Deep. Res.
Comparison and validation of physical wave parameterizations in spectral wave models
Ocean Model.
Statistics of nonlinear wave crests and groups
Ocean Eng.
Towards the identification of warning criteria: Analysis of a ship accident database
Appl. Ocean Res.
On excursion sets, tube formulas and maxima of random fields
Ann. Appl. Probab.
The Geometry of Random Fields
Numerical Modeling of Space-Time Wave Extremes using WAVEWATCH III
Ocean Dyn.
On the shape and likelihood of oceanic rogue waves
Sci. Rep.
Space-time extreme wind waves: Analysis and prediction of shape and height
Ocean Model.
Observation of extreme sea waves in a space-time ensemble
J. Phys. Oceanogr.
Short-Term/Range Extreme-Value Probability Distributions of Upper Bounded Space-Time Maximum Ocean Waves
J. Mar. Sci. Eng.
The disintegration of wave trains on deep water Part 1
Theory. J. Fluid Mech.
Air-Sea Exchange in Hurricanes: Synthesis of Observations from the Coupled Boundary Layer Air-Sea Transfer Experiment
Bull. Am. Meteorol. Soc.
Tropical cyclone wind field forcing for surge models: critical issues and sensitivities
Nat. Hazards
Short-term statistics of waves observed in deep water
J. Geophys. Res.
Wind-Wave Modeling: Where We Are, Where to Go
J. Mar. Sci. Eng.
The Draupner wave: A fresh look and the emerging view
J. Geophys. Res. Ocean.
The Draupner event: the large wave and the emerging view
Bull. Am. Meteorol. Soc.
Rogue waves in crossing seas: The Louis Majesty accident
J. Geophys. Res. Ocean.
Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves
Phys. Rev. X
DNVGL-RP-C205: Environmental Conditions and Environmental Loads
DNV GL Recommended Practice (August)
The Making of the Andrea Wave and other Rogues
Sci. Rep.
“Freak” ocean waves
Oceanus
Oceanic Rogue Waves
Annu. Rev. Fluid Mech.
Part VII : ECMWF Wave Model
IFS Documentation CY45R1.
On the kurtosis of ocean waves in deep water
J. Fluid Mech.
Space-Time Extremes in Short-Crested Storm Seas
J. Phys. Oceanogr.
Cited by (9)
Measurements 2: space-time measurements of freak waves
2023, Science and Engineering of Freak WavesPrediction 2: long-term prediction of extreme waves
2023, Science and Engineering of Freak WavesWave Modulation in a Strong Tidal Current and Its Impact on Extreme Waves
2024, Journal of Physical OceanographyStatistical and Dynamical Characteristics of Extreme Wave Crests Assessed with Field Measurements from the North Sea
2023, Journal of Physical OceanographyCharacterization of extreme wave fields during Mediterranean tropical-like cyclones
2023, Frontiers in Marine ScienceSpace-time statistics of extreme ocean waves in crossing sea states
2022, Frontiers in Marine Science