Elsevier

Progress in Oceanography

Volume 197, September–October 2021, 102642
Progress in Oceanography

On the extreme value statistics of spatio-temporal maximum sea waves under cyclone winds

https://doi.org/10.1016/j.pocean.2021.102642Get rights and content

Highlights

  • Spatio-temporal maximum wave heights occur to the north-east of the cyclone’s eye, where sea states are more energetic.

  • Individual waves with normalized extreme heights are met to the south/south-west of the moving cyclone.

  • Directional spread and bound nonlinear interactions play a significant role in producing extreme waves.

  • Different physical mechanisms can trigger high waves in the sea regions under cyclone winds.

Abstract

Principles of the spatio-temporal statistics are used to investigate the characteristics of short-term/range extreme sea waves and related sea-state parameters under cyclone winds (northern hemisphere). We base our analysis upon consistent stereo-imaging observations of the 3D (2D space + time) sea surface elevation field, and spectral wave model results in the Northwestern Pacific during tropical storm Kong-rey (2018). The focus is on the extreme value analysis of individual maximum sea surface elevations (crest heights) and maximum crest-to-trough wave heights. Results highlight the sea areas around the storm centre where the spatio-temporal highest waves are more likely, and, via scale analysis, the principal mechanisms responsible for the occurrence of extreme conditions in bimodal (composed of wind-sea and swell) and short-crested storm seas. We find that individual waves are the highest to the north-east of the translating cyclone, where sea states are more energetic. However, in the south/south-west of the centre, where opposing wind-sea/swell sea states dominate, directional spread and bound nonlinear interactions are enhanced. In this area, more extreme waves may occur, having the maximum crest and wave heights mean values in excess of 1.3 and 2.1 times the significant wave height, respectively. This set of results provides insights into the role of the dispersive and directional focusing enhanced by nonlinearities up to the second order as an effective mechanism for the formation of extreme waves under cyclone winds. To examine what physical mechanism is behind the generation of extreme waves in different regions around the cyclone, we also explore for comparison areas where nonlinear four-wave interactions are more likely to occur.

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.

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