Extreme wave events driven by extratropical ciclones

off the Death Coast

Cintia Bonanad Granero

Curso 2017/2018

Tutor: Germán Rodríguez Rodríguez

Trabajo Fin de Título para la obtención del título de Máster en Oceanografía

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Extreme wave events driven by extratropical cyclones

off the Death Coast

Cintia Bonanad Granero, Máster Interuniversitario en Oceanografía.

Tutor: Dr. D. Germán Alejandro Rodríguez Rodríguez Departamento de Física Grupo de Investigación en Física Marina y Teledetección Aplicadas (FIMATA) Instituto Universitario de Estudios Ambientales y Recursos Naturales (iUNAT)

Líneas de Investigación al que esté vinculado: • Meteorología costera• Hidrodinámica costera

Las Palmas de Gran Canaria, a 23 de Noviembre de 2018

Alumno Tutor

Germán Rodríguez Rodríguez

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ABSTRACT

Extreme wave storms are severe events with low frequency of occurrence, driven by intense, extense and persistent wind fields, and with important implications for offshore and coastal human activities, as well as for the environment. This study examines some relevant characteristics of wave storms and their relation to the driving atmospheric synoptic conditions, for the strongest annual wave events in the period 1998-2018, off the Death Coast (Costa da Morte), northwest coast of Galicia, Spain. Results reveals that this zone is an energetic and swell dominated enduring severe wave conditions, mainly associated to its exposure to deep and persistent extratropical depressions passing through the region, following a clear seasonal pattern.

1. INTRODUCTION

Wind generated surface gravity waves represent the most tangible evidence of the strong atmosphere-ocean coupling, resulting from the exchange of energy and momentum at the sea surface interface. The energetic content of a wind generated wave field grows with the wind speed, the duration of the period during which wind transfers energy and momentum to the sea surface, and the extension of surface over which these fluxes take place, known as fetch. Within this area, sea surface exhibits a very complex and random structure and wave fields are known as wind seas. As waves travel out of the fetch across the ocean basins undergoes important transformations, mainly due to frequency and directional dispersion, giving rise to wave fields that progressively reduce its chaotic aspect, while retaining its random nature, referred as swell waves (e.g. Komen et al., 1994). Since longer waves travel faster than shorter ones, the wavelength and period of the swell gradually increase with time and distance from the fetch, and wave height decreases mainly due to spreading effects. Surface waves at any particular point on the ocean are often a combination of locally generated waves from a local wind and swell generated in more or less remote areas, giving rise to wave conditions known as mixed sea states (Rodríguez and Guedes Soares, 2001). Wind waves and swell transport the energy accumulated during their generation by atmospheric storm events and dissipate it through many processes, whose understanding is of great importance for offshore and coastal engineering activities and for environmental issues. In particular, among other activities and processes, knowledge of wave conditions during intense wave storms is critical to offshore oil prospection, extraction and transportation, offshore wind/wave farms planning, development and exploitation, ship traffic, coastal fisheries, flooding and geomorphology.

In the midlatitudes the daily weather variability is dominated by the passage of high-pressure systems (anticyclones), frequently associated with calm weather, and low pressure systems (cyclones), typically accompanied by mesoscale frontal structures, strong winds, and heavy precipitation (Dacre and Gray, 2009). A cyclone is a synoptic-scale low-pressure system with a closed surface cyclonic circulation, which has counter-clockwise motion of the air in the Northern Hemisphere. Cyclones outside the tropics are usually called extratropical cyclones, and cyclones that form in the tropics, tropical cyclones. A tropical cyclone can transform into an extratropical cyclone at the end of their tropical existence (usually between 30° and 40°). By a strict definition, a cyclone is

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considered a storm when the wind speed reaches the Storm category on the Beaufort Wind Scale, i.e., attains values >24.5 m/s (Bader et al., 2011). Extratropical cyclones are slower, larger, and more frequent than tropical cyclones. In average, more than 200 ETC generate in the northern hemisphere during winter with length scales in the order of 2000 km (Gulev et al., 2001).

Extratropical storms, or midlatitude storms, in the North Atlantic are often formed to the east of the Rocky Mountains, off the east coast of North America, and southeast of Greenland. These storms often move in preferred tracks from the east coast of North America into the North Atlantic, either in a northeasterly direction over the Norwegian Sea, or on a more southerly track, with some cyclone tracks reaching the United Kingdom and northern Europe. This region of maximum track density, extending northeastward along the North Atlantic, is known as the North Atlantic storm track (Dacre and Gray, 2009). Nevertheless, it must be noted that extratropical cyclone tracks exhibit a large variability, but there is a high track density between 40º and 60º N, where cyclones also tend to attain their deepest central sea level pressure (Wernli and Schwierz, 2006).

Extratropical storms travelling along the North Atlantic storm track, covering a large sea surface extension, with associated strong low-level winds, and persisting for at least a few days, often generate wave storms, defined as a period of time during which the wave height exceeds a threshold value, affecting the North Atlantic coasts and leading to a broad range of high damage potential scenarios related to shipping, fishing, offshore operations, and coastal protection activities, among others, triggering operational limitations, structural damages, as well as potential loss of human life. Accordingly, understanding extreme wave events represents a key frontier in science due to the complexity of the underlying physical processes and the large impact they have on human lives, properties and activities, as well as on the environment. In this sense, it worth to highlight that, by definition, extreme events have low frequency of occurrence but important consequences. The term ‘storminess’ is commonly used to include both the frequency of occurrence and the intensity of storms (Carnell et al., 1996).

Extreme wave conditions in a given zone are usually studied without taking into account the characteristics and the dynamic of the generating meteorological processes. In this context, and taking into account the above comments, the main goal of the present work is to examine wave storm properties, as well as the variability of characteristic wave parameters with the storm evolution, in terms of the driving synoptic meteorological conditions during extreme wave storms recorded in deep waters offshore Galicia, NW Spain, in the area known as the Death Coast (Costa da Morte), located within the North Atlantic storm track and well exposed to the effect of extratropical storms.

The paper is structured as follows. The study area is presented in the next section. The main characteristics of wave and meteorological data used in the study are described in section 3. This is followed by the results and discussion, including an analysis of the relationship between meteorological conditions and the resulting wave storms is presented in section 4. Some final conclusions are drawn in section 5.

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2. STUDY AREA AND DATASETS

2. 1. Study area This study investigates extreme wave storm characteristics in a coastal area located

in the coast of Galicia, in NW Spain. The area corresponds with a southwest–northeast oriented coastline stretching over over more than 100 kilometres along the northwest coast of Galicia. This area is known as the Death Coast, Costa da Morte in Galician, and extends from Cape Finisterre (Land’s End, from Latin finis terrae), in the south, to Cape San Adrian, in the north, facing the North Atlantic Ocean in SW/NE direction (Fig. 1).

The general large-scale atmospheric circulation over this region is dominated by the relative strength and extension of the semi-permanent Azores high-pressure and Icelandic low-pressure centers of action. Furthermore, due to its location within the North Atlantic storm track, close to its southern boundary, it is generally under the influence of extratropical storms several times a year.

Considering that the region's economy is highly dependant on fishing and shellfish-gathering, and that the area is crossed by important shipping lanes, connecting the Mediterranean and the South Atlantic with Northern Europe and the Bay of Biscay, the recurrence of severe wave storms along the history have resulted in frequent shipwrecks, coastal erosion events, storm surges, damage to coastal structures, and many lives lost (Crespo et al 2008; Iglesias and Carballo, 2009). Among the recent disasters, it is remarkable the huge oil spill in November 2002 provoked by the break-up and sinking of the oil tanker Prestige, carrying more than 77 000 tons of heavy fuel oil, causing an environmental and economic catastrophe of enormous proportions, hence the Death Coast name.

Figure 1 Location of the study area in the North Atlantic, northwest coast of Spain, and ubication of the wave buoy in front of Costa da Morte.

2.2. Datasets This study is based on three datasets of different nature. The first dataset includes

experimental wave and meteorological observations recorded in-situ by means of meteoceanic wave buoy, located just in fromt of the study area (see Fig. 1). The second dataset consists of data from a hindcast approach, providing information on meteorological and wave conditions. The third dataset is composed of surface pressure

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and wind analyes. Relevant characteristics of each one of these datasets are presented in this subsection.

2.2.1. Buoy measurements

The measurement device is a SeaWatch buoy equipped with meteorological and oceanographic sensors. It provides hourly information on wind (speed and direction), atmospheric pressure and waves (sea surface elevation and directionality), among others. The buoy is deployed at a point (9.21ºW, 43.50ºN) in deep waters (386 m) in front of near Cabo Vilán, Camariñas, La Coruña (Fig. 1). This buoy, named as Villano-Sisargas buoy, takes part of the deep waters buoy network (REDEXT) managed by the Spanish Port Authority (Puertos del Estado). This measurement device has been operational from April 1998 to the present, but data used in this study covers a time span of 20 years, from April 1998 to April 2018. Currently, the buoy rate of measurement is one data per hour. Nevertheless, the parameters provided are not measured over an hour, but it is an average of the measures taken during a given period which is 26 minutes for wave parameters, 10 minutes for wind speed and direction, and instantaneusly for atmosferic pressure. Meteorological parameters are measured at 3 meters above the sea surface.

Wind-driven waves may be studied at different time scales, depending on the objectives pursued. In practice, two different time scales are commonly considered. The systematic analysis of its structure requires to examine sequences of individual waves, defined from instantaneous values of the sea surface elevation, during the longest possible period of time but fulfilling the stationarity condition. That is, over a time window during which wave properties remain statistically invariant. Each one of these periods is known as a sea state and its lifespan may range from a few tens of minutes to a few hours. In this case, the sea state duration is determined by the buoy rate of measurement (26 minutes). The study of wave conditions during such a period receives the name of short-term analysis. With the information collected during each one of these busts, or sea states, it is possible to define several parameters, regarding wave height, period and direction, which enable their simple characterization. This information, derived from individual sea states, also constitutes the basis for the other time scale of analysis, referred to as long-term analysis. In this approach, the statistical behabiour of the characteristic parameters derived from individual sea states is examined to understand the climatology of wave conditions at a specific site, or wave climate.

Time series of sea surface fluctuations during a given sea state can be analysed in the frequency domain to estimate the directional spectrum, S(f,θ), or more properly the directional spectral density function, which represents the energy contribution of any wave component to the measured wave field in terms of the frequency, f, and propagation direction, θ. Most of the characteristic sea state parameters can be derived from a few statistical moments, named as spectral moments, with the moment of n-th order, mn, defined as

𝑚𝑚𝑛𝑛 = � � 𝑓𝑓𝑛𝑛∞

0

2𝜋𝜋

0𝑆𝑆(𝑓𝑓, 𝜃𝜃)𝑑𝑑𝑓𝑓𝑑𝑑𝜃𝜃 (1)

The most important parameter for the characterization of a sea state is the significant wave height, Hs, defined as the average of the highest third of the individual wave heights

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in a wave record, and is equivalent to four times the square root of the zero-th order spectral moment, m0. That is,

𝐻𝐻𝑚𝑚0 = 4 �� � 𝑆𝑆(𝑓𝑓,𝜃𝜃)𝑑𝑑𝑓𝑓𝑑𝑑𝜃𝜃∞

0

2𝜋𝜋

0�12�

= 4�𝑚𝑚0 (2)

Note that significant wave height is denoted as Hs when estimated from the wave record and as Hm0 when derived from the spectral density function. In the later case it receives the name of spectral significant wave height. Furthermore, it results direct that m0 represents the total energy of the process and, consequently, Hm0 is directly proportional to the energy content of the corresponding sea state. For this and other reasons (Phillips, 1977) this is the parameter used to represent the sea state severity, as a general rule. Another important characteristic wave height is the maximum wave height, Hmax, recorded during a sea state. This parameter cannot be obtained from the wave spectrum but must be obtained directly from the wave record in the time domain.

In the case of wave periods there are several optional characteristic periods that can be used in the light of the objectives pursued. Two of those most commonly employed in practice are used in this study. These are, the average wave period, T02, defined in terms of spectral moments as

𝑇𝑇02 = �𝑚𝑚0

𝑚𝑚2�12�

(3)

and the spectral peak period, Tp, defined as the inverse of the frequency at which the spectral density function attains its maximum, fp, (i.e. Tp=1/fp). In other words, Tp is the period associated to the most energetic spectral wave components. It is important to note that, in contrast to T02, Tp is not computed by means of spectral moments but taking into account just only one spectral estimation, so that it shows a larger statistical variability (Rodríguez et al., 1999).

The most common parameters used to characterize the directional properties of a wave field are the mean spectral direction, θm, which represents the mean direction over all the frequency bands in the two-dimensional spectrum, S(f,θ), and is computed as

𝜃𝜃𝑚𝑚 = 𝑎𝑎𝑎𝑎𝑎𝑎 �� � 𝑆𝑆(𝑓𝑓,𝜃𝜃)𝑒𝑒𝑖𝑖𝑖𝑖𝑑𝑑𝑓𝑓𝑑𝑑𝜃𝜃∞

0

2𝜋𝜋

0� = tan−1 �

∫ ∫ sin(𝜃𝜃) 𝑆𝑆(𝑓𝑓,𝜃𝜃)𝑑𝑑𝑓𝑓𝑑𝑑𝜃𝜃∞0

2𝜋𝜋0

∫ ∫ cos(𝜃𝜃) 𝑆𝑆(𝑓𝑓,𝜃𝜃)𝑑𝑑𝑓𝑓𝑑𝑑𝜃𝜃∞0

2𝜋𝜋0

� (4)

The spectral peak direction constitutes the average direction at the frequency associated to the spectral peak, fp, so that θp may be expressed as

𝜃𝜃𝑝𝑝 = 𝑎𝑎𝑎𝑎𝑎𝑎 �� 𝑆𝑆�𝑓𝑓𝑝𝑝,𝜃𝜃�𝑒𝑒𝑖𝑖𝑖𝑖𝑑𝑑𝑓𝑓𝑑𝑑𝜃𝜃2𝜋𝜋

0� = tan−1 �

∫ sin(𝜃𝜃) 𝑆𝑆�𝑓𝑓𝑝𝑝,𝜃𝜃�𝑑𝑑𝜃𝜃2𝜋𝜋0

∫ cos(𝜃𝜃) 𝑆𝑆�𝑓𝑓𝑝𝑝,𝜃𝜃�𝑑𝑑𝜃𝜃2𝜋𝜋0

� (5)

This parameter represents the approaching average direction of the most energetic components in the wave field. Note that, according to its definition, θm estimated for only one frequency, resulting in a parameter with a large uncertainty. As a consequence, with

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the aid of improving its statistical stability, it is usually evaluated by using Eq. 4, but limiting frequency integration to a narrow band around to the peak frequency.

2.2.2. Hindcast data

Missing data occurs in almost any scientific field during the measuring or recording processes. In particular, sea surface wave measuring devices operate in a very hostile medium where sensor or power supply failure are common, so that maintenance operations are frequently required and generate data gaps in time series. Furthermore, while in-situ operating sensors provide accurate information, this kind of experimental measurements are limited in time and space. In this sense, the performance of current atmospheric and wave models has significantly improved, allowing to obtain good quality wind fields and enhancing numerical wave modelling. This fact has been recognised and exploited to develop hindcasting methods for complementing the limited space and time coverage of the available observational data sources. The hindcasting process combines forecasting numerical models and observational information from different sources to generate consistent global estimates of various atmospheric and wave parameters.

In this study, meteorological and wave information derived by means of hindcast approaches has been used. These data belong to SIMAR-44 and WANA datasets, provided by the Spanish government agency Puertos del Estado, and include wind and wave parameters obtained by using the SWAN and WaveWatch-III third generation high resolution numerical models to reconstruct wave conditions, with the input of wind fields produced with the HIRLAM atmospheric model. Wind data are computed at 10 meters level above the sea surface. It is important to mention that hindcast models are not able to estimate individual wave parameters, but just integral parameters derived from the wave spectrum, as explained in section 2.2.1. The SIMAR point used is identified by the number 3007036 and located in the same position as the Villano Sisargas buoy. This hindcast dataset contains data for the period from 1958 to the present, although only data from1998 to 2018 have been processed.

Figure 2 shows, for illustrative purposes, the use of significant wave height data to refill large data gaps in the experimental time series corresponding to a wave storm occurred in February 2016. This example enables to recognize the general good agreement between the observed and hindcast data sets. Nevertheless, it can be appreciated that, while both series display the same general pattern, the experimental signal fluctuates on the hindcast one. This is a common feature, due to the intrinsic smoothing effect of atmospheric and wave models.

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Figure 2: Significant wave height measured by Villano-Sisargas buoy (orange), and hindcast at SIMAR point (blue), for a storm during February 2016.

2.2.3. Synoptic surface weather maps

Surface analysis charts are computer-generated charts representing experimental observations obtained at the same time at different points over a given area. This kind of maps provides a ready means of locating surface weather features, such as pressure systems and fronts, although it can also include an overview of wind fields, or other atmospheric variables. These charts are commonly generated every 3, 6, or 12 hours.

Two surface level pressure analysis maps per day, at 00h and 12h, have been provided by the Spanish State Meteorological Agency (AEMET), for the dates of interest.

3. METHODOLOGY

The most common approach to explore wave storm climatology at a given region consists in examining wave storm activity on the basis of the statistical analysis of observed wave data, defining individual wave storms without considering the generating meteorological processes. A more interesting approximation to study wave storminess integrates the use of experimental information on wave conditions and weather synoptic information, to detect and characterize the atmospheric processes driving the observed wave storm conditions.

This study follows the second methodology by initially analysing the wave observations to detect individual wave storms and some characteristic properties, such as their duration, severity, timing of the storm maximum and possible seasonal pattern, as well as the relationship between two characteristic wave heights, Hm0 and Hmax, of great practical importance. After that, synoptic weather conditions associated to each of the selected storms are screened in attempting to explain the response of wave conditions during these extreme events to the forcing atmospheric processes as they evolve.

The procedures used to extract wave storms from long-term series of significant wave height, and to obtain their characteristic properties are briefly explained in the paragraphs below.

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3.1. Wave storm concept and definition Conceptually, a wave, or sea, storm may be understood as a situation in which wave

energy is significantly higher than that normally observed at a given place. That is, a period of intense wave activity. Nevertheless, from a practical viewpoint, it is more appropriate to consider a wave storm in terms of the time pattern of the significant wave height, as the parameter commonly used to assess the severity of wave conditions. Accordingly, a wave storm can be roughly defined as a period of time during which the significant wave height exceeds a threshold value. This simple definition is very loose and a more strict definition is necessary to remove possible ambiguities and facilitate its practical implementation.

On the basis of the foregoing comments, a variety of alternative definitions have been proposed. In general, although there is no a fully accepted definition, most of them are based on the peaks over threshold (POT) approach, introduced in the context of the statistical theory of extreme value analysis, and also known as partial duration series. In this methodology, Pickands’ theorem, (Pickands, 1975) states that, given a sample of independent and identically distributed values, the distribution of the data exceeding a given threshold converges to a Generalized Pareto Distribution (GPD). Nevertheless, a sequence of significant wave height values constitutes an auto-correlated time series. Then, some criterion is necessary to generate a sample of statistically independent values from the available information. Moreover, it is necessary to chosee an optimal threshold for ensuring the convergence toward the GPD.

Following this approach, a wave storm is commonly considered as sequence of sea states during which the significant wave height excedes a fixed constant threshold, Ht. The storm starts when the significant wave height goes above this threshold and finishes when it falls below it, for a continuous time interval greater than a preset minimum period, which set the minimum time interval between statistically independent storms. From a physical perspective, this minimum temporal distance between successive wave storms ensures their meteorological independence. That is, the time interval between wave storms, known as inter-storm period, has a minimum value that ensures that they are generated by independent synoptic systems, such as a tropical or extratropical cyclones. Furthermore, since wave height can fluctuate for a brief period above, or below, the threshold, a minimum storm duration, Dmin, is set to include only storm events of a significant duration. Nevertheless, the minimum inter-storm period set by the meteorological independence criterion also ensures that brief crossings below the storm threshold during a single storm event are included within the same event.

Some other important factors in the charecterization of wave storms are the timing of the storm peak significant wave height, (Hm0)max, and the duration of the event, D, defined as the length of time between an up-crossing and subsequent down-crossing of the storm threshold. The time of occurrence of the maximum storm wave height represents the moment of maximum intensity of the event. Its knowledge allows to explore possible coincidences with other meteocean phenomena and the likelihood of ocurrence for exceptionally high water levels in coastal areas. Similarly, storm duration affects the probability of occurrence of extremely high water leves, but also the total load exerted on marine structures, the probability a ship encountering a severe storm and so on. Dolan and Davis (1994) found that storm duration as well as maximum significant

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Figure 3: Definitio sketch of wave storm, illustrating two successive independent storms, including a fall bellow the threshold level shorter than the minimum inter-storm period required for independence.

storm wave height plays a significant role in determining beach morphodynamic variability.

The storm threshold, Ht, is a critical value which depends upon the geographical location, and should be related in some way to the average significant wave height in that area. This threshold is the key parameter allowing to distinguish stormy from mild and light wave conditions for a particular marine area.

Figure 3 displays, for illustrative purposes, two successive storms. During the first one the significant wave height stays always above the threshold fixed. By contrast, in the second storm Hm0 falls bellow Ht during a period smaller than the minimum inter-storm period set and, consequently, that brief crossings below the threshold is included within the same storm.

3.2. Wave storm severity There are different ways to quantify the wave storm strength. The total wave power

(TWP) is a parameter introduced by Dolan and Davis (1992) as an indicator of the severity of a given wave storm. This parameter multiplies the time increment between observations, ∆t, by the sum of the squared values of Hm0, a quantity proportional to the wave energy. Thus, total wave power can be expressed as

𝑇𝑇𝑇𝑇𝑇𝑇 = � 𝐻𝐻𝑚𝑚02(𝑡𝑡)

𝑡𝑡𝑓𝑓

𝑡𝑡𝑖𝑖 𝑑𝑑𝑡𝑡 ≈ ∆𝑡𝑡�𝐻𝐻𝑚𝑚0

2

𝑡𝑡2

𝑡𝑡1

(6)

where ti and tf are the starting and ending times of the storm event, determined by the up and down-crossings of the storm threshold, Ht, respectively. Then, storm duration, D, is given by D= (tf - ti).

It interesting to note that TWP is not really a measurement of wave strom severity but of wave activity during the storm duration. Thus, it does not allow to compare the severity of different storms because total duration is not taken into account in its definition. In line with this, it is interesting to standarsize this value with respect to the storm duration to obtain the storm energy (Lin-Ye, et al. 2018), denoted as E and given by

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𝐸𝐸 =1𝐷𝐷� 𝐻𝐻𝑚𝑚0

2(𝑡𝑡)𝑡𝑡𝑓𝑓

𝑡𝑡𝑖𝑖 𝑑𝑑𝑡𝑡 ≈

∆𝑡𝑡𝐷𝐷�𝐻𝐻𝑚𝑚0

2

𝑡𝑡2

𝑡𝑡1

(7)

Wave storm intensity is quantified in this study by means of TWP (m2h) and E(m2), with ∆t=1h, since this is the cadence of the data in the available significant wave height data time series.

3.3. Wave storm seasonality To assess the existence of seasonal variations in the timing of wave storms along the

year, it is interesting to note that any circular temporal measure can be translated into angles. Thus, for example, it is possible to consider the day of the year at which the maximum of a storm occurs, d, as a circular random variable which can be converted to a angular value, θ, in radians, by

𝜃𝜃 =2𝜋𝜋

365𝑑𝑑 (8)

where d is the day of the calendar year on which the maximum significant wave heigh of a given storm (the storm peak) occurred. It is assumed that the number of days per year is 365, so that it ranges between 1 and 365. In leap years, the data corresponging to 29 February have been removed, accepting that February months have only 28 days (Rodríguez et al, 2014).

A common question when dealing with angular random data is whether a data sample is, or not, distributed uniformly around the circle. This means that the uniform distribution is usually considered as the null hypothesis. Then, to know if wave storms at a given region are uniformly distributed through the year (null hypothesis), or there is one or several time periods during which storms are more frequent (alternative hypothesis), is necessary to know if the time of occurrence of wave storms along the year follows a uniform distribution. Note that uniformity represents the situation in which probability is spread out uniformly on the circumference. The chi-square test, adapted for circular variables, is the most frequently used to assess the goodness of fit between the empirical and the uniform distributions (Vega et al. 2013 and references therein) and is applied in this study to test potential seasonality in wave storm occurrence through the year.

The above described approach is used in this study to evaluate the potential existence of seasonal variations in the time of occurrence of storm peaks along the year.

3.4. Abnormality index Most information available to characterize wave fields is given in terms of the

significant wave height, Hm0, (Eq. 2), which represents a measure of the average sea state severity. However, in practice, the hydraulic design of coastal and offshore structures depends on the input of extreme values for Hm0 and Hmax. Furthermore, Hmax is the most pertinent parameter to explore and describe the risk associated with operability and stability of ships and marine structures (Goda, 1999). The value of both parameters, Hm0 and Hmax, increases with wind speed, fetch, and wind duration. However, while Hm0 is determined by the average conditions which can be estimated from a sequence of successive individual wave heights, or from the corresponding spectral density function,

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the behaviour of Hmax is not fully controlled by the mean meteorological conditions generating the wave field, but is a single random value affected by local conditions. Thus, it is common to observe wave records with the same Hm0 and different Hmax.

Regretfully, information on the individual wave with greatest impact, Hmax, is not usually available. In particular, large databases obtained through hindcast approaches, where wave characteristics are derived by integrating the wave spectrum, does not include values of this important parameter. The deterministic computation of Hmax, or the ratio between this and Hm0, for a given sea state is not possible, due to its random nature, and must be estimated based upon the use of theoretical statistical distributions of individual wave heights (i.e., Longuet-Higgins, 1952; Feng et al, 2014) or by means of empirical relationships derived from experimental measurements. In this regard, it is important to stress that the ratio of these two parameters is used to detect the existence of transient very high waves in relation to the sea state in which they occur. These waves are referred to as freak waves, rogue waves, monster waves, or king waves. The most common criterion used to define a freak wave is named as abnormality index (Dean, 1990) and expressed as AI=Hmax /Hm0 > 2.

Although the deterministic computation of this ratio for a given sea state is not possible, Longuet-Higgins (1952) provides a formulation for estimating this ratio, by assuming that a record of individual wave heights represents a sample drawn from a population governed by a Rayleigh distribution. The most probable value of the ratio is given by

𝜇𝜇 �𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚

𝐻𝐻𝑚𝑚0� =

√ln𝑁𝑁

√ln 3 + 3√𝜋𝜋2 𝜀𝜀�√ln 3�

= �√ln𝑁𝑁

2�

12�

(9)

That is, the abnormality index depends on the number of waves in the record, N. It is evident that the expected value tends to 2, approximately, when the number of waves is large, above 2000.

In this study, the statistical relationship between Hm0 and Hmax,

𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑐𝑐 𝐻𝐻𝑚𝑚0 (10)

is examined, through the analysis of in-situ wave records using a linear regression approach between both variables, and compared with other theoretical and empirical results. Two assess the possible change of this ratio during storm conditions, it is evaluated for the full data set (sea states recorded during 20 years), for sea states belonging to the selected extreme storms, and for the sea states corresponding to the peak for each of these extreme events.

4. RESULTS AND DISCUSION

A preliminary study of the wave conditions in the study area by analysing the full data set corresponding to the period from April 1998 to April 2018, with the goal of providing a basic knowledge of the wind and wave climate in the study area.

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Wind rose (Fig. 4, left) presents a clear bimodal structure with modes in almost opposite directions. The most frequent winds blow from the NNE-ENE directional sector, which accounts for more than 25% of the observations. The secondary mode represents winds blowing from the WSW-S sector. It is interesting to highlight that winds from this sector has a lower frequency of occurrence but can be very intense, with episodic events of wind speed higher than 20 m/s. Another interesting feature is the relative low frequency of winds flowing in the land-sea (seaward) direction, especially from the fourth circular quadrant. On the contrary, wave rose (Fig. 4, right) reveals a distribution with a single mode containing sea states travelling from the W-NNW sector and including the most severe wave conditions. Thus, almost 70% of the sea states with Hm0 higher than 4 meters reach the buoy from this sector. Naturally, waves approaching the measurement point from the ENE-SW are restricted by fetch limitations between this point and the coast.

The clear difference between the dominant directions of the local wind and that of the observed wave conditions reveals the low relationship between both phenomena and makes evident the dominance of swell wave fields approaching mainly from the second directional quadrant.

Directional distributions, of mean and peak periods are shown in Fig. 5. It can be observed that more than 60% of the sea states approaches the buoy from the W-N. In particular, about half comes from the WNW-N directional sector with mean period, T02, larger than 6 s, and more than 10% with T02 > 8 s (Fig. 5, left). Regarding the peak period (Fig. 5, right), almost 40% of the observations have Tp > 10 s and concentrate on the WNW-N sector. Sea states travelling from ENE-N and SSW-W sectors constitute a very small relative amount over the total, and the associated peak periods are very short, lower than 6-8 s.

These results evidence the dominance of energetic swell wave fields approaching from the WNW-N, while sea states reaching the study area from ENE-N and SSW-W sectors are locally generated wave fileds with short period and small height. In brief, regarding wave conditions, the study area may be considered as an energetic and swell dominated area with large and high waves coming from the second circle quadrant.

Figure 4: Wind (left) and wave (right) roses in the study area for the (1998 - 2018) period.

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Figure 5: Directional distribution of mean wave period (left) and peak wave period (right) in the study area for the (1998 - 2018) period.

4.1. Wave storms definition and selection The methodology exposed in section 3.1 has been used to detect storms in the time

series of significant wave height. The minimum interstorm period has been set in 24 hours, and the wave height threshold has been chosen in terms of two different approaches. First, some percentiles of the full data set were computed. In particular, the quartiles Q1=1.6 m, Q2=2.2 m (median) and Q3=3.1m. Thus, the higher 25% of the observations are above 3 meters, approximately. In this connection, a more pragmatic approach that intrinsically takes into account the modal wave conditions is to set the threshold according to the 90th percentile of the significant wave height dataset, wich is D9=4.2 m. Secondly, Hm0 values were fitted to a three parameter Weibull probability distribution, given by

𝐹𝐹(𝐻𝐻) = 1 − exp �− �𝐻𝐻 − 𝛽𝛽𝛼𝛼 �

𝛾𝛾

� (11)

where α, β and γ are the shape, location and scale parameters, respectively. These parameters have been estimated by using the maximum likelihood metod and the values for the optimal fit are: α=1.93, β=0.60, and γ=1.30. With these parameters is simple to estimate the value of Hm0 associated to a probability of exceedance of 0.1. The resulting value is Hm0 ≈ 4 m, which represents de wave height with a return period of 10 years, and is almost equal to the 90th percentile. Then, the wave height threshold is established as Ht=4 m. Nevertheless, wave storms for a threshold equal to Q3 (3 meters) were also selected.

4.2. Annual extreme wave storms Using the above criteria, the total number of storms detected were 523 for Ht=3 m

and 431 for Ht = 4 m. Naturally, the number of storms and their duration increases by decreasing the threshold because more events are taken into account, but if the threshold

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is too low the quality of the estimate is compromised because the resulting events may no longer be statistically independent. These results demonstrate the importance of the threshold selection and make evident the severity of the wave climate in the study area. However, the main goal of the study is to examine wave the storm properties, as well as the variability of characteristic wave parameters with the storm evolution, in terms of the driving synoptic meteorological conditions during extreme wave storms. Accordingly, after evidencing the great importance of determining the optimum threshold and highlighting the severity of the wave climate off Costa da Morte, the largest annual wave storms during the1998 – 2018 period have been selected for a detailed study. The evolution of Hm0 during each one of these storms is shown in Fig. 6. It is important to stress that some storms considered as a single event could have been separated in various individual storms by increasing the threshold wave height.

Table 1 compilates the main characteristics of the annual extreme storms storms analyzed in the present study. These events are named by Stx, with x representing the chronological order of the storm (St). Column 3 indicates the value of the storm peak significant wave height, (Hm0)max. In column 4, the time of occurrence stands for the timing of this value. Storm duration estimated for the thresholds Ht=3m and Ht=4m, are given in columns 5 and 6, respectively. Total wave power and Storm Energy, estimated for Ht=4m, are shown in columns 7 and 8, respectively.

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Figure 6: Significant wave height evolution during maximum annual wave storm recorded at Death Coast

during the (1998 - 2018) period.

Observation of Table 1 reveals that storm St02 does not occur for Ht=3m. This is because storms St01 and St02 occurs just a few days apart at the end of 1998 and beginning of 1999. Thus, reducing the threshold, the duration of the storm increases and both storms merge into a single storm whose peak occurs at the end of 1998. It is also worth to note that the storm St16 occurs between the end of 2013 and the start of 2014 and represents a single storm, even for Ht=3m. It should also be noted the extremely large duration of this storm, starting in December 2013 and ending in January 2014, lasting for more than 25 days.

Values of storm duration and TWP for a threshold Ht=4m are represented in Fig. 7 (left). The scatter diagram reveals a clear and expected trend of TWP to increases with the storm duration. A similar trend, but with a larger dispersion, is observed between the storm duration and the significant wave height at the peak of the storm (Fig. 7 left). In both cases, it is striking the presence of an outlier, highligthted with a red square, far from the average trend. This value corresponds to the above mentioned storm St6, occurred

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Table 1: Characteristic parameters for largests storms in the period 1998-2018 in the Death Coast

Storm number

Year Max [Hm0]

(m) Time of peak occurrence

Duration(h) (Ht 3m)

Duration (h) (Ht 4m)

TWP (m2h) (Ht=4m)

Storm Energy (m2) (Ht=4m)

St01 1998 9.51 30/12 01:00 743 371 8489.4 22.88

St02 1999 8.97 17/01 13:00 --- 253 4657.0 18.40

St03 2000 7.99 20/04 10:00 307 46 1408.2 30.61

St04 2001 7.67 06/02 12:00 131 113 3294.0 29.15

St05 2002 7.50 22/05 05:00 179 66 1699.3 25.74

St06 2003 10.22 31/10 20:00 165 125 4631.5 37.05

St07 2004 8.21 26/12 03:00 209 56 2076.3 37.07

St08 2005 10.61 18/01 20:00 178 58 3008.1 51.86

St09 2006 10.88 08/12 16:00 759 267 8139.7 30.48

St10 2007 10.12 09/12 20:00 242 142 4408.5 31.04

St11 2008 12.55 10/03 19:00 170 133 4486.1 33.73

St12 2009 13.46 24/01 01:00 655 297 1480.8 4.98

St13 2010 11.73 09/01 03:00 325 135 5411.8 40.08

St14 2011 10.01 17/02 01:00 673 200 8192.5 40.96

St15 2012 8.30 18/04 17:00 66 45 1665.8 37.01

St16 2013-2014 12.41 06/01 13:00 694 615 2300.4 3.74

St17 2015 10.38 24/02 10:00 468 64 2497.0 39.01

St18 2016 9.58 08/02 16:00 242 227 7760.7 34.18

St19 2017 11.46 02/02 15:00 320 307 9.509,6 30.97

St20 2018 10.31 24/03 10:00 56 32 1.709,9 53.43

during more than 25 days in winter 2013/2014 Note that, despite being the storm with longest duration, and having one of the higher maximum significant wave height, it shows one of the lowest TWP and the lowest value of the storm energy. This particular storm will be examined in detail later.

4.3. Seasonality of extreme wave storms To explore the existence of a seasonal pattern in the timing of wave storms along the year, the date of occurrence of the maximum significant wave height (storm peak) of every annual extreme event is transformed into an angular value by means of Eq. 8. Figure 8 shows the date of occurrence of the largest storms for each year from 1998 to 2018 in

Figure 7: Scatter diagram for storm duration and TWP (left), and storm duration and (Hm0)max (right).

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polar coordinates. As expected, it is observed that extreme storms occur mainly during winter, between December and March, with a substantially lower probability of presentation during spring and autumn, that becomes null in summer. Accordingly, the Chi-squared test, adapted for circular variables, clearly rejects the hypothesis of uniformity at any level of significance. That is, extreme storms are not randomly distributed around the circle (i.e. along the year) but concentrates during the the end in late autumn, winter, and spring, with the more intense conditions observed during winter. Accordingly, the test allows to accept the existence of a seasonal pattern in the timming of extreme annual storms on a statistical basis.

Figure 8: Polar plot of the maximum Hm0 and its occurrence time for the period 1998-2018.

4.3. Variability of the abnormality index

As discussed in the previous section, there is not a precise theoretical relationship governing the ratio between the significant wave height for a given sea state, Hm0, and its corresponding maximum wave heigh, Hmax, except under restrictive assumptions. Therefore, due to their practical importance, it is relevant to determine this relationship for each area of interest.

Two assess the possible change of this ratio during storm conditions, the statistical relationship between Hm0 and Hmax, has been evaluated for the full data set (sea states recorded during 20 years), for sea states belonging to the selected extreme storms, and for the sea states corresponding to the peak for each of these extreme events.

Results of the regression analysis of the Hmax against Hm0 for the full dataset (1998-2018) are presented in Fig. 9, where the solid line indicates the mean ratio between both parameters and the dashed lines are the associated 95% confidence intervals. The resulting mean ratio is given by

�𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚

𝐻𝐻𝑚𝑚0�

����������= 1.523 ± (1.521, 1.525)

Figure 10 shows the results of the linear regression between Hmax and Hm0 for every sea state included in some of the 20 selected annual extreme storms. The solid line

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indicates the linear regression between both parameters and the dashed lines are the associated 95% confidence intervals. The corresponding mean ratio is given by

�𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚

𝐻𝐻𝑚𝑚0�

����������= 1.493 ± (1.474, 1.513)

Regression analysis of Hmax against Hm0 for sea states corresponding to the peak for each of these extreme events is shown, as a scatter plot of both variables, in Figure 11, where the solid line denotes the linear regression between both parameters and the dashed lines the associated 95% confidence intervals. The linear regression obtaines is

�𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚

𝐻𝐻𝑚𝑚0�

����������= 1.526 ± (1.065, 1.987)

Figure 9: Scatter plot of Hmax versus Hm0 for the whole period 1998-2018. The orange line indicates the

linear regression and dashed blue lines are the 95% confidence intervals.

Figure 10: Scatter plot of Hmax versus Hm0 for every sea sate in the selected extreme wave storms. The

orange line indicates the linear regression and dashed blue lines are the 95% confidence intervals.

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Figure 11: Scatter plot of Hmax versus Hm0 for peak storm values. The orange line indicates the linear

regression and dashed blue lines are the 95% confidence intervals.

A remarkable feature in the above figures is the outlier corresponding to a maximum wave height of 27.8 m, while its significant wave height is 12.41. In this case, ocurred during the event St16, the the Abnormality Index, AI (=Hmax/Hm0), is 2.24. That is, the largest wave in the record associated to the peak in the strom St16 was a freak wave. The second highest Hmax was recorded in November 9st, 2010, which reached 21.87m, while the significant wave height was 11.73m (AI=1.86). The smallest Hmax, 10.7 m, was registered in February 6st 2001, when Hm0 was 7.67 m heigh (AI=1.39). Nevertheless, it is also interesting to observe that the above cited freak wave did not occur during the event with a highest storm peak, that was St 12, with a maximum significant wave height of 13.46 m but a maximum wave height of 19.4 m (AI=1.44).

Feng et al (2013) analysed data recorded in the Norwegian Sea by a Ship-Borne Wave Recorder and obtained a mean value of 1.53, with lower and upper 95% confidence limits (1.27, 1.89). Myrhaug and Kjeldsen (1986) obtained a mean ratio for sea states with Hmax>5 m for experimental observations in the Norwegian Sea. On the other hand, from an operational point of view, Goda (1999) points out that this ratio generally falls within the range (1.6 – 2.0). In particular, the upper limit, or even a higher value, is chosen in the design of offshore structures. Accordingly, values of the AI for any of the three cases considered are well within the interval (1.40-1.75) predicted by the Rayleigh method (Longuet-Higgins, 1952) and the correction suggested by Forristal (1978), without considering spectral bandwidth and non-linear effects, and are fully consistent with those obtained by other authors. Furthermore, results support the hypothesis that the ratio Hmax/Hm0 remains almost invariant during stormy and normal conditions.

While site-specific, mean values of Hmax/Hm0 do provide a better approximation of the relationship between both parameters than a universal coefficient. However, the dependence on the record length and seasonal climatology should not be ignored when predicting maximum wave height for practical applications.

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4.4. Storm event analysis With a view to examine the variability of wave conditions during extreme wave

storms with the progress of the meteorological conditions inducing the extreme wave storms, the behavior of the main characteristic wave parameters in terms of meteorological conditions have been explored, with the help of the meteorological information provided by the meteocenic buoy and synoptic weather maps. The wave parameters used are significant wave heigh, maximum wave heigh, peak period, mean period, wave peak direction, mean wave direction, derived from the directional wave spectrum and given in Eqs (2-5). Recorded meteorological variables are, atmospheric pressure, wind speed and direction.

After examining the evolution of the characteristic wave parameters for all the annual extreme wave storms in the period 1998-2018, in terms of the atmospheric conditions, as general comment it may be pointed out that all of these storms have been generated by extratropical cyclones passing more or less close to the Galician coast. Generally, these extratropical storms generate in the east coast of North America, specially in the southern part, and travel in north-east direction towards the Norwegian Sea, passing over the British Isles. However, some of these mesoscale perturbations remain stationary at the southwest of Ireland, covering a large oceanic extension. The resulting wave storms duration and severity are linked mainly to the intensity, steadiness (persistence), extension, and proximity of the low pressure centre to the area.

For simplicity, only two illustrative examples are presented. The selected storms are:

1- St13 (winter 2010) - Start time (08/11/2010 06:00) end time (13/11/2010 21:00)

2- St16. (winter 2013/2014) -Start time (14/12/2013 01:00) end time (08/01/2014 16:00).

These wave storms have been chosen on the basis of their severity and duration. Note that both storms have substantially high maximum significant wave heights (peak storm), with 11.73 m and 12.41 m, respectively. However, their characteristics are notably different in terms of their duration and severity. Thus, St13 have an average duration (135 h) but a large severity, expressed in terms of the total wave power (5411.8 m2h) and the energy storm (40.08 m2). On the contrary, St16 presents the largest duration (615 h) but very low severity, with total wave power (2300.4 m2h) and the the lowest energy storm (43.74 m2). Additionally, these two extreme wave events, share the characteristic of having been considered as a single event by using a threshold wave height Ht=4m, but could have been separated in various individual storms.

Storm St13 (Winter 2010)

The evolution of the characteristic wave and wind parameters during extreme wave storm St13 is summarised in Figure 12, while the progress of the synoptic sea level pressure and wind field structure is documented in Figure 13.

The largest values of wave height occur during day 8, when the center of the cyclone es placed east of the UK with a very low pressure center (958 Hpa) and its outer border affecting the Death Coast with winds from the west. Next day the center of the synoptic systems slightly weakens but shift down towards the southern side of the UK, affecting more intensively the Galician coast with NW strong winds. Day 10 the storm has

24

dissipated, but another low-pressure system begins to approach from the NW and progressively intensifies reaching very low pressure values (952 Hpa) during day 11. However, this new storm is centered further north and, as a consequence, affects the study area less strongly. Subsequently, this extratropical cyclone follows its path northeastward.

This atmospheric scenario reflects in the pressure time series (Fig. 12) with two abrupt drops, the first more intense, in addition to other less intense pressure drops after day 16. Naturally, the inverse effect is observed in wind speed time series. Likewise, wind and wave directions experiment similar changes. Wind and waves travel from NNW during the most intense phase of the storm and their direction fluctuates between tNNW and W after that. The almos coincident pattern of the mean and peak wave directions reveal the existence of a principal wave field that, observing the large values of the mean and peak period, correspons to a swell component generated in the more intense region of the cyclone and irradiated towards the study area, combined with a less energetic locally generated wave field.

Figure 12: Time evolution of wind and wave conditions during the storm St13. Start time (08/11/2010

06:00) end time (13/11/2010 21:00) (Wind direction not available).

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Figure 13: Daily synoptic mean surface level pressure and 10 m wind maps during the storm St13. Start

time (08/11/2010 06:00) end time (13/11/2010 21:00).

Storm St16 (Winter 2013/2014)

The period from December 2013 to February 2014 was meteorologically speaking anomalous, with an atmospheric activity highly atypical. A series of unusually strong low-pressure systems traveling from the west North Atlantic and impacting northern Europe, resulted in exceptional storminess, causing this winter to be ranked as the stormiest on record for the Ireland–UK domain (Matthews et al. 2014). The formation of low-pressure systems far to the west, and their intensification as they crossed the Atlantic, caused many low extense and persistent pressure systems driving extreme wave conditions.

Note that, instead of consider just a single event, by using a threshold wave height Ht=4m, clearly this storm could have been separated in various individual storms, just as revealed by the progression of the atmospheric pressure curve (Fig. 14).

The synoptic weather charts reveal the existence of a series of low-pressure systems with asimmilar behaviour to those comented for the storm St13, but travelling along a more zonal track. These systems do not have a very low pressure center but are very extense, affecting a large part of the European coast. However, around Sunday 5 and Monday 6 January a very deep and extense cyclone is installed east of the British Isles, transferring a large amount of energy to the sea surface over a long fetch. As a result, the Death Coast experiences the arrival of a very long swell, with peak periods above 15 s, and reaching 20 s during the most intense moment of the storm, with maximum wave heights above 15 meters and reaching the historical maximum of 27.8 m, with an

27

associated significant wave height of 12.41 m, and an Abnormality Index of 2.24, corresponding to a freak wave. This extremely severe event is that appearing in figures (9-11) as an outlier.

Figure 14: Time evolution of wind and wave conditions during the storm St16. Start time (14/12/2013

01:00) end time (08/01/2014 16:00).

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Figure 15: Daily synoptic mean surface level pressure maps during the storm St16. Start time (14/12/2013 01:00) end time (08/01/2014 16:00).

5. CONCLUSIONS

The following conclusions can be drawn from the results obtained by means of the analysis of wind and wave data during extreme wave storms off Costa da Morte:

Costa da Morte is an energetic and swell dominated area with large and high waves coming from the WNW-N, while locally generated sea states are much less frequent and approaches the area from ENE-N or SSW-W sectors. It experiences severe meteorological and associated wave conditions, due to their exposure to the long Atlantic fetch and to deep extra tropical depressions passing through the region.

Storm duration exhibits a direct relationship with the total wave power and the significant wave height at the peak of the storm, although in the latter case there is a larger dispersion in the data.

Extreme storms time of occurrence is not randomly distributed along the year but concentrates during the the end in late autumn, winter, and spring, with the more intense conditions observed during winter. The existence of a seasonal pattern in the timming of extreme annual storms can be accepted on a statistical basis.

Observed values of the Abnormality Index are well within the interval (1.40-1.75) predicted by theoretical models, despite their obvious limitations, and are fully consistent with those obtained by other authors. Furthermore, results support the hypothesis that the ratio Hmax/Hm0 remains almost invariant during stormy and normal conditions.

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The annual extreme wave storms observed during the period 1998-2018, have been generated by extratropical cyclones passing more or less close to the Galician coast. Generally, these extratropical storms generate in the east coast of North America, specially in the southern part, and travel in north-east direction towards the Norwegian Sea, passing over the British Isles. However, some of these mesoscale perturbations remain stationary at the west or southwest of Ireland, covering a large oceanic extension, and irradiating long and energetic swell towards the Death Coast, where it is common to observe mixed sea state conditions by the superposition of the remotely generated swell with comoonly weaker locally generated wave fields.

6. AKNOWLEDGEMENTS I am indebted both to the government agency Puertos del Estado, for providing

the wave buoy and hindcast data sets, and to the State Meteorological Agency (AEMET), for supplying synoptic weather maps. I would like to offer my special thanks to Prof. Germán Rodríguez for his effort to make this study possible, as well as his patience and motivation during the months of work.

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