Extreme waves in visual wave observations by VOS

Transcription

1 Extreme waves in visual wave observations by VOS Vika Grigorieva and Sergey K. Gulev P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia Being a disastrous phenomenon, extreme waves (including those classified as rouge waves) are critically important for marine structures. Although there are many works on the theory of rogue waves [e.g. 1, 2, 3, 1, 11, 12, 13], their physics of is still poorly understood and they are hardly detectable in different wind wave data. Furthermore, we have very tentative estimates of rogue waves and in most wave data it is hard to discriminate between the observational truth and the measurement artifacts of different nature when very high waves are in question. In this paper we will analyse the collection of visual observations worldwide in order to quantify the most extreme wave cases and to identify their nature. Besides model hindcasts, satellite and buoy measurements Voluntary Observing Ship (VOS) data represent now an important source of global wave information, including that of extreme wave events. There is a general concern that VOS observations are quite inaccurate and, therefore, are hardly applicable for quantitative wind wave analysis. However this concern results primarily from a poor knowledge of the actual errors and uncertainties inherent in the VOS wave observations. This accuracy was more or less quantified during the last years and many errors and uncertainties were either minimized or removed from the VOS collection [5]. Visual wave observations were extensively used for the description of climatological characteristics of wind waves [5, 6, 7] and for the assessment of the long term tendencies in wave parameters [8, 9]. However, they were not yet employed for the analysis of freak waves. We used these data to quantify the highest observed wave cases in the World Ocean during the last century and to further attribute them to the wind storms, potentially freak waves, or observational artifacts. Voluntary observing ships provide massive visual wave information worldwide covering the period from 1885 onwards [14, 15]. Before 195 marine officers reported the highest wave component (sea or swell) and its upper value was limited by 16 m according to the existing coding system. From 195s observers started to report separately wind sea height and swell height estimates. Furthermore, the coding system was changed and allowed for the detection of the maximum wave height up to 25 meters for both sea and swell. From our collection of more than several million reports we selected all cases reporting wave height exceeding 15 meters. Altogether, after 195 there has been found more than 1 of such cases for seas and about 3 cases for swells (Fig.1). Importantly, we considered separately the subsets of reports providing information about all wave parameters (wind sea and swell heights, their periods and directions) and of incomplete reports which provide typically only one wave parameter (e.g. wind sea height). In the first instance we consider wave statistics based on all selected reported without any census wind sea january to to to to swell january Fig.1 Extreme wind sea (left panel) and extreme swell (right panel), m, Northern Hemisphere, January,

2 Figure 2 shows the occurrence histograms of the extreme wind wave and swell heights, their periods, wind speed for all selected extreme cases (i.e. reported wave height is higher than 15 m). Additionally we also estimated the occurrences of wave periods, steepness and wave lengths. Furthermore, wave parameters were analyzed within the radius of 1 km around the location of extreme wave report wind sea height.4.4 wave length max swell height.4.4 wave length (m) (m) (m/s) (m) (m) (m/s) Max wind sea january Northern Hemisphere 667 reports Max swell january Northern Hemisphere 2324 reports.3.2 steepness*1.4.3 wind sea periods.4.3 average wind sea.3.2 steepness* swell periods.3.2 average swell (s) (m) (s) (m) Fig.2 Occurrence histograms for the wind sea (left panel) and swell (right panel), characteristics over the Northern Hemisphere for January (195-26). Preliminary results derived from the subset of all selected extreme cases show quite reliable probability distributions for the whole range of wave parameters implying that the distribution of extreme wave characteristics should now represent the tails of these distributions. Maximum wind speed changes from 5 to 1 m/s, with the wave lengths being about 4 meters for the wind sea and 8-16 m for swell (7% of total subset). Corresponding wave periods change in a wide range from 1 to 25 seconds with the peak of probability at 5 seconds for seas and at 8-1 seconds for swell. We have to note, however, that wave periods are considered to be the most uncertain parameters in VOS and their errors can reach of 3 % from average values. Two-dimensional occurrence distributions of extreme wave cases and speed are presented in Figure 3. They demonstrate the bimodal structure implying 2 maxima of the occurrences at wave heights of m and 2-21 m. Multiply analysis of coding errors nevertheless confirmed the existence of this structure. Very tentatively we can hypothesize that the first maximum is associated with the high waves originating from wind storms and the second one results from the observational artifacts or the freak waves. Analysis of the wave steepness derived from the estimates of wave heights and periods allows for the discrimination of some observational artifacts. Usually wave steepness is defined as δ = H w /λ = 2*π* H w /(g*p w 2 ), where H w is wind sea height, λ is wave length, P w is wind sea period, g is the gravitational acceleration. According to the wave theory δ > 1/7 results in increasing wave steepness and the loss of stability, forcing wave breaking. In the case of multi-system sea, however, wave height and wave length are statistical parameters computed from the wave spectra. This implies some uncertainty in this definition. For instance for some extreme cases identified in the VOS data steepness can reach unrealistic values, particularly due to uncertainties in the estimation of wave periods. For example, for P w = 1 sec δ.64h w. Therefore, we consider this criterion to be effective enough and adopted it for the further analysis.

3 5 wind sea Jan 5 5 swell Jan W I N D (m/s) H E I G H T S (m) 5 5 wind sea Jul H E I G H T S (m) 5 5 swell Jul W I N D (m/s) Fig.3 Two-dimensional probability distributions of the wind sea heights and wind speed for January and July over the Northern Hemisphere.4.3 Hmax/Hmean Fig. 4 Histogram of the ratio η for the Northern Hemisphere, January One of the key parameters used for the detection and quantification of the rogue waves is the ratio between maximum and the averaged wave height in the record. We used this criterion, taking the average value from all observations within the radius of 1 kilometers from location of maximum. In this case we consider the ratio η=h max /H mean where H max is the reported extreme wave height and H mean is the average over all simultaneous reports within 1 km radius. Occurrence histograms for these mean estimates are presented in Figure 4. Usually the threshold of η=2 is considered for the detection of extreme cases, the values of η>4-5 are

4 identified very seldom. The occurrence histogram of η (Fig.4) show that the ratio varies from 1 to 25 with the peak values of 8-9. Thus, this ratio is not effective enough for the detection of the observational artifacts and we need another criterion to check our data quality. In the next step we performed an accurate quality control of the selected extreme wave cases. First, we selected only the reports providing information about all wave parameters (wind sea and swell heights and periods) and excluded incomplete reports which provide frequently only one wave parameter. This census resulted in the reduction of the number of reports by about 3%. Then we excluded the reports without wind speed and reports which give suspicious characteristics of the wave steepness. We used the threshold of.2 for wind sea steepness and of.15 for swell steepness. This limitation broke up to 8% reports. Finally 129 extreme wind sea cases and about 8 extreme swell cases were left for the further analysis. The frequency distributions derived from this subset show already quite significant differences from those derived from the whole census (Fig.5). For the wind waves they show one major maximum at m with the smaller secondary one at more than 2 meters. Remarkably the wind speed distribution is represented by the wide plato with the modal values varying within 5-35 m/sec. However, when we consider the extreme swells, the two maxima in the distributions remain, being still centered at the same values (15-16 and 2-21 meters)..6 max wind sea.3.3 wind sea steepness* (m) (m/s) max swell height.3.3 swell steepness* (m) (m/s) Fig.5 Occurrence histograms after the quality control for the wind sea (upper pictures) and swell (down pictures) parameters, Northern Hemisphere, January In the next instance we analyzed individual cases in order to attribute extremes to the storm conditions, artifacts or freak waves. For the seas we requested that storm wind speed for all cases exceeds at least 1 m/sec and that the sea level pressure should be deeper than 12 hpa. These requirements eliminated about 98% of all reports which can be with a high probability associated with severe storms. After that the rest consisted of few cases (e.g. 19 cases for January). They are located in the Northern hemisphere mid latitudes and few in the Atlantic tropics where then are likely associated with the tropical cyclone development. All these cases report wind waves higher than 16 meters with the highest waves (of 22 meters and more) identified in the eastern mid-latitudinal Atlantic and northeast Pacific. The data from these reports were further analyzed with respect to the wave age [4]: a = Cp / Vef, where Cp is deep water phase speed at spectral peak, which is derived from the peak wave period P w as Cp = (g/2π) P w.

5 Here g is the gravitational acceleration, Vef = V 1 *Cos θ is the component of the wind in the wave direction, θ is the angle between wave and wind directions (in 95% cases those angle are equal), V 1 is the wind at 1 m anemometer height and neutral stability. For all extreme seas wave age a > 1.2. So, those reports are either observational artifacts or swell, which was reported as wind sea. Furthermore, we performed a detailed synoptic analysis of all cases with extreme wind waves using SLP and wind speed data from the NCEP/NCAR re-analysis. Reanalysed winds and SLP also do not hint on the extremes in the VOS data. Thus, extreme heights which passed the quality control of wind waves can not be attributed to the freak waves. Similar analysis of extreme swells is much more complicated, since swell does not depend on the local wind and, thus, local wind cannot be used as additional information for the analysis. We first limited our analysis to the cases when extreme swell is associated with wind sea height smaller than 5 meter. This is reasonable, because high wind seas of 1-15 meters are unlikely to be associated with simultaneously high swells. In other words, sailors cannot accurately identify these cases and discriminate high wind seas and high swells. Secondly, we eliminated from the analysis all cases of extreme swells identified in the marginal seas or in the regions where the fetch is short enough to provide swell growth up to extreme values. Next, for every report of extreme swell we analyzed visual swell reports in the vicinity of about 2 km from this point. We required that the neighboring swell reports should imply swells of at least higher than monthly mean values. All these procedures filtered out substantial amount of reports and left for the further analysis about 1% cases of extreme swells. In the Northern Hemisphere about 5% of extreme swell cases were identified in the North Atlantic and North Pacific mid latitudes and subtropics where they can be attributed to the propagation of the swell parcels from storms. Tropical cases can be associated with the propagating swells form the tropical cyclone systems. For the Southern Hemisphere the number of extreme wind sea and swell cases is generally smaller than for the Northern Hemisphere (Fig.6). This can be reasonably explained by generally smaller number of observations here compared to the Northern Hemisphere. Altogether there have been identified 86 cases of extreme wind seas of which the quality control procedures left 9 cases to be further considered with confidence. For swell data we first selected 227 extreme cases of which only 7 cases were left after the critical analysis to to 2 max seas , Aug,m 2-8to to 25 max swell , Aug,m Fig.6 Extreme wind sea (left panel) and extreme swell (right panel), m, Southern Hemisphere, January, The further analysis of wave age and synoptic situations revealed that all extreme wind seas in the South Ocean can be attributed to either severe storm conditions or observational errors. None of the remained 7 extreme swell reports was found to be suspicious. This work was focused on the explanation of extreme waves in the VOS-collection. These waves do not influence the global climatology, but may play an important role in the extreme wave statistics. We tried to find signatures of the known freak events in VOS data and to show that not all 25 meter heights are the observational artifacts. The VOS collection does not include any reports to be verified with such events as the New Year Wave and the extreme wave in the south-east Africa region. Nevertheless, one report was found near the location of the catastrophe

6 on 15 February 1982 near the Grand Banks of Newfoundland (Lawton G.) This report fits to all our requirements. Remarkably, it reports swell with the height of 15 meters, period of 15 sec and the length of 351 m implying steepness of.4. The sea height was 5 m with the period being 6 sec. We also analyzed wave reports over all well-known banks with specific topography and wave regime. Only the data from the Dogger Bank and Chatham rise (Fig. 7) have been accepted for analysis after the quality control. We have to stress, however, that the period reported (about 17 seconds), should be considered with caution. Although the analysis of synoptic situation shows strong gradients of sea level pressure in this location, we do believe that wind sea of 15 meters height and 9 sec period can be considered as a reliable indication of the storm in this area H=16m P=9s V=9.8 m/s to to to to P=1s V=3 m/s Dogger bank H=16m P=1s V=13m/s H=18.5m P=1s V=1m/s a>5! H=18.5m P=17s V=3 m/s H=2m P=1s V=3 m/s H=15m P=17s V=7m/s a>3! H=15m P=8s V=9.9 m/s H=2.5m P=1s Fig. 7 Left panel: Extreme cases on the Chatam rise. Wind sea data are shown on the top and swell data are in the bottom panel. Right panel: extreme cases on the Dogger-bank. Blue color indicates wind sea, red color stands for the swell data. Considering Chatham rise, we can conclude that extreme wind sea estimates are quite reliable for this region, although extreme swells are likely overestimated. However, we can argue that South Ocean provides conditions for long enough fetch and, therefore, hypothesize that extreme swell can also contribute to the freak events. Our analysis of extreme wave heights in the VOS collection over the last several decades shows that VOS data when properly quality controlled and pre-processed can be capable of capturing even single extreme wave events. Among all extreme wind waves in the VOS collection about 2% can be attributed to wind wave storms and more than 8% are considered as observational artifacts. Frequency distributions of extreme wave heights clearly show maxima peaked at meters and 2-21 meters and these maxima hold even after very strict quality control, indirectly hinting on the existence of freak events in the VOS records. At the same time we have to stress that all data reporting extreme swells are highly doubtful. However, few cases (about 1-2% of identified events) can really be considered as confirmation of extremely high swells, potentially of the freak nature.

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