The paper deals with the directional analysis of severe storms in some European locations, in the Atlantic Ocean and North Sea. The analysis is carried out by considering significant wave height and wave direction time series, from the HIPOCAS project database. At each considered location, all storms in the data set are identified. Then, for each storm, variability of direction during sea states is investigated. The results of this analysis show how direction during storms varies within well-defined sectors identified from the main directions from which the strongest storms occur plus or minus a certain angle Δϑ, and from one or more secondary sectors. The variation of direction during storms is evaluated in terms of standard deviation of direction, either by considering all sea states during storm, or only sea states during the part of the storm above a fixed threshold h of significant wave height. The results show that standard deviation of direction decreases as the threshold h increases and it is due to the fact that variability of direction near the storm peak is smaller than in the full storm. Keywords: Sea storm, wave direction, mean wave direction, direction at storm peak, storm duration, storm intensity. Introduction A sea storm is a non-stationary process: the wave spectrum and the significant wave height are not constant in time. A sea storm is defined as a sequence of sea states during which the significant wave height Hs exceeds a given threshold. In general, a storm starts when Hs has an up-crossing related to the given storm threshold and finishes when Hs goes down this
threshold. Following Boccotti’s definition ([1]; see also [2-3]), a sea storm is ‘a sequence of sea states in which the significant wave height exceeds the threshold crith and does not fall
below this threshold for a continuous time interval greater than 12 hours’. This storm definition enables to take into account that a ‘calm’ period may occur even during a storm: if this period, in which Hs is below the threshold hcrit, has duration smaller than 12 hours there is a single storm (Figure 1a). If this time is greater than 12 hours, two different storms (Figure 1b). will be considered. The storm threshold hcrit must depend upon the given location: in the Mediterranean Sea, it may be considered even equal to 1.5m, but this value cannot be considered in most locations in the oceans. Boccotti proposed to use a storm threshold proportional to the average value sH
of the significant wave height in the location calculated from significant wave height time series. A value that may be considered of the threshold is 1.5 times sH .
Storms evolve in space and time often changing direction and thus one can choose an Eulerian or a Lagrangian description to model them as discussed by Bernardino et al. [4]. However it is most common to adopt the Eulerian approach, which is the one considered in this paper. In this paper the variability of the mean wave direction during storms is investigated, by processing significant wave height and wave direction time series coming from the HIPOCAS project [5-6-7], for some European locations in Atlantic Ocean and North Sea (Figure 2). The analysis is carried out by using Boccotti [1] definition of storm to identify storms as the sequence of sea states with significant wave height greater than the storm threshold. Then
Proceedings of the ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering OMAE2014
June 8-13, 2014, San Francisco, California, USA
OMAE2014-24633
the directional analysis is carried out by considering the sequences of significant wave height of sea states during each storm with the sequence of the related wave directions [8, 9]. HIPOCAS project: Wave data Data used for the analysis comes from the studies of the HIPOCAS [5-6-7] project (Hindcast of Dynamic processes of the Ocean and Coastal Areas of Europe). The objective of this project was to provide high-resolution (in space and time) hindcasts of wind, waves and currents for selected European coastal areas. In particular these areas comprise the North Sea, the Irish Sea, the North East Atlantic, south of the United Kingdom including the Azores and Canary Islands and the Mediterranean Sea. It provided a simulation of 44-years (1958-2001) wind, waves, sea level data and current climatology. The hindcast wave model used is the third generation wave model WAM cycle 4 modified for two-way nesting by Gòmez and Carretero [10]. The WAM wave model needs as input wind fields, bathymetric data and the ice fields. The wind field that were used as input to the wave model were calculated using the REMO model which was forced with global data of the 40-years global atmospheric re-analysis carried out by the National Center for Environmental Prediction, Washington, USA (NCEP) and the National Center for Atmospheric Research, Boulder, Colorado, USA (NCAR) [11]. In HIPOCAS the quality of the wind field was improved close to the coast of Europe adopting a technique to obtain small scale analysis from the global re-analysis. It is based on the view that the small scale details of the atmospheric fields are a result of the interaction between the larger scale atmospheric flow and the smaller scale geographic features. The WAM output parameters are the significant wave height Hs, wave direction, mean period Tm, peak period Tp, wind speed, wind direction, Hs for wind sea, direction for wind sea, Tm for wind sea, Hs for swell, direction for swell and Tm for swell with a time step of three hours. 3.Data analysis For the analysis, input data are significant wave height and wave direction time series given by HIPOCAS project for the locations in Figure 2. First, all the storm in the data set have been identified by using Boccotti definition, then the directional analysis has been done by considering the sequence of sea state during each storm with the sequence of the related wave directions (Figure 3). The key parameters of the analysis are: maximum significant wave height which gives the storm intensity, wave direction at Hs max, average direction during storm, storm duration and standard deviation of direction. Figure 4 shows direction at Hs max versus Hs max for the entire storm identified and for each considered location. From these results, it is possible to identify one or more main directional sectors from which the strongest storms come from. Among the considered location two different conditions can be considered: at HIPOCAS(1), HIPOCAS(2), HIPOCAS(5), HIPOCAS(6) there is only one well defined sector from which the strongest storms come from, while for HIPOCAS(3) and for HIPOCAS(4) there is also a secondary direction from which some storms come from. Figure 5 shows average direction during storms versus Hs max. It shows that for
Figure 1. a) Upper panel - Example of actual storm with a calm period and two peak of significant wave height, at Azores; b) Lower panel - example of two successive storms with calm period greater than 12 hours, at Azores. the strongest storms average wave direction is within well-defined sectors. A comparison between Figures 4 and 5 suggests that for the strongest storms direction at Hs max and average wave direction are very close for most of the storms (Figure8) and are within well-defined sectors. As it is possible to see from Figure 8 that the couple (average direction, direction at maximum significant wave height) are centered around the bisecting graph. Figures 6 and 7 show respectively direction at Hs max versus storm duration and average direction versus storm duration. By a comparison between figure 4 and figure 6 it is possible to understand that the strongest storms both in term of intensity and duration come from the same directional sectors. Figure 9 shows a comparison between wave direction associated to the storm begin and wave direction associated to the storm end. For most of the storms these directions are different to each other. For each storm identified, the standard deviation of mean direction has been calculated (Figure 10) and it is less than 40º. Finally, for the strongest storms, standard deviation of direction has been calculated by considering only the part of storm above a fixed threshold of significant wave height (from 0.5 Hs max to Hs max) (see Figure 3) at each considered location. The result for HIPOCAS(4) is shown in Figure (11). From these figures it can be seen that the standard deviation of
Figure 4.Wave direction at the maximum significant wave height during actual storm versus maximum significant wave height, at each considered location (the direction the waves are coming from is considered).
HIPOCAS(1)
HIPOCAS(3) HIPOCAS(6) HIPOCAS(5)
HIPOCAS(1) HIPOCAS(1)
Figure 5. Average wave direction during actual storm versus maximum significant wave height, at each considered location. CONCLUSIONS In the paper a directional analysis has been proposed of ocean storms, by considering the variability of wave direction in the sea states during each storm. It has been found a certain variability of wave direction during storms: the analysis done by calculating standard deviation of wave direction has revealed that this variability is quite larg in correspondence of
storm queues and it is strongly reduced near storm peaks. Furthermore it has been shown that the strongest storms both in terms of intensity and duration come from well defined directional sectors. The results are of interest for a deepest analysis of directional storms, to determine design criteria that take into account effects of wave direction.
REFERENCES [1] P. Boccotti, “Wave Mechanics for Ocean Engineering”.
Elsevier Science, New York, 2000. [2] Arena, F., Pavone, D., The return period of non-linear
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[3] Arena, F., Pavone, D., A generalized approach for the
long-term modelling of extreme sea waves. Ocean Modell., 26, 2009, pp. 217-225.
[4] Bernardino, M.; Boukhanovsky, A., and Guedes Soares, C. 2008; Alternative Approaches to Storm Statistics in The Ocean. Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2008); Estoril, Portugal. New York, USA: ASME; OMAE2008-58053.
Figure 6. Direction at Hsmax versus duration of actual storm, at each considered location.
Figure 7. Average wave direction during actual storm versus duration of actual storm, at each considered location.
Figure 8.For each storm identified with Boccotti criterion, average direction during actual storm versus direction at maximum significant wave height during actual storm, at each considered location.
HIPOCAS(1) HIPOCAS(2) HIPOCAS(3)
HIPOCAS(6) HIPOCAS(4) HIPOCAS(5)
Figure 9.Wave direction at the end of the storm versus wave direction at the beginning of the storm, at each considered location
Figure 10. Standard deviation of direction versus average direction during storm, at each considered location.
Figure 11. For the strongest storms standard deviation of direction versus average direction during storm, calculated by considering only the part of storm above a fixed threshold (from 0.5 Hsmax to Hsmax) at HIPOCAS (4).
[5] Guedes Soares, C., Weisse, R., Carretero, J.C., Alvarez,
E., 2002. A 40 years hindcast of wind, sea level and waves in European waters. Proceedings of the 21st International Conference on Offshore Mechanics and Arctic Engineering (OMAE'02), ASME Paper OMAE2002-SR28604.
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Environmental Sciences and Environmental Computing, Vol. 2, P. Zanetti, Ed., EnviroComp Institute, 2004, 1-50.
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[10] Gómez Lahoz, M., Carretero Albiach, J.C., 1997. A two-way nesting procedure for the WAM model: application to the Spanish coast. J. Offshore Mech. Arct. Eng. 119, 20–24.
[11] Weisse, R., Feser, F., 2003. Evaluation of a method to reduce uncertainty in wind hindcasts performed with regional atmosphere models. Coast. Eng. 48, 211–225.
