Proceedings of the ASME nd International Conference on Ocean, Offshore and Arctic Engineering OMAE2013 June 9-14, 2013, Nantes, France

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1 Proceedings of the ASME 3 3nd International Conference on Ocean, Offshore and Arctic Engineering OMAE3 June 9-, 3, Nantes, France OMAE3- SWELL GENESIS, MODELLING AND MEASUREMENTS IN WEST AFRICA Marc Prevosto Ifremer - Brest Center 98 Plouzané France Marc.Prevosto@ifremer.fr George Z. Forristall Forristall Ocean Engineering, Inc. Camden, Maine, ME 83 USA george@forocean.com Kevin Ewans Sarawak Shell Berhad Kuala Lumpur Malaysia Kevin.Ewans@shell.com Michel Olagnon Ifremer - Brest Center 98 Plouzané France Michel.Olagnon@ifremer.fr ABSTRACT Swell events show a large variety of configurations when they arrive at sites off West Africa after generation and propagation of waves across the Atlantic Ocean. Within the West Africa Swell Project (WASP JIP), these different configurations have been described and discussed and the ability of numerical models to reproduce faithfully their properties has been assessed from comparisons with in-situ measurements. During the austral winter months, swells approach West African coast from the south to south-westerly direction. These swells are generated by storms in the South Atlantic mainly between S and 6 S. But during austral summer, north-westerly swells are also observed coming from North Atlantic. Typical situations of superposition of these different swells are illustrated in the paper. In spite of a poor overlapping between numerical and insitu measurements databases at the time of the WASP project, and of reduced durations of measurement campaigns, comparisons between in situ measurements and hindcast models permitted identification of the limitations of the different numerical models available. Three sites have been used for this study, one in the Gulf of Guinea with directional Waverider and Wavescan buoys, a second one off Namibia with a directional Waverider and one last instrumented with two wavestaffs off Cabinda (Angola). In addition, the existence of infra-gravity waves in shallow water measurements has been investigated. INTRODUCTION Good knowledge of swell climatology is important to specify the metocean conditions for the design of installations in geographic areas where swell is dominant like West Africa. At the time of the starting of the West Africa Swell Project in, the engineering practices did not integrate sufficiently well the peculiarities of these zones. As more and more installations had started and many were planned, measurements campaigns and sea-state numerical modelling became more numerous, permitting dedicated metocean studies like the WASP project. A general presentation of the project and of its results is given in a companion paper by Forristall et al. []. A complete description of the project is available in [] and details are discussed in two other companion papers, Olagnon et al. [3] which tackles the question of the judicious model to represent the spectral shape of individual swells and Ewans et al. [] in which the sensitivity of structure response to complex swell sea-state representations is studied. Swell events show a large variety of configurations when they arrive at sites off West Africa after generation and propagation across the Atlantic Ocean. During the austral winter months, swells approach West African coast from the south to south-westerly direction. These swells are generated by storms in the South Atlantic mainly between S and 6 S. But during austral summer, north-westerly swells are also observed coming from North Atlantic. Within the WASP Project, these different configurations and their genesis have been analysed and de-

2 scribed and are presented in the first part of this paper. These analyses were mainly based on hindcast wave models. The ability of these numerical models to reproduce faithfully the properties of sea-states dominated by swell in all their complexity has been assessed from comparisons with in-situ measurements and is the object of a second part of the paper. In spite of a poor overlapping between numerical and in-situ measurements databases and of reduced durations of measurement campaigns, comparisons between in situ measurements and hindcast models permitted identification of the limitations of the different numerical models available at the time of the project. Three sites have been used in the project, this paper focuses on a Gulf of Guinea site instrumented with directional Waverider and Wavescan buoys. Good description of the sea-states has to go through the extraction of wave systems from directional spectra (first swell, secondary swell, wind-sea,...). The tool employed for this extraction is described briefly in this paper. It has been applied systematically to the complete database of the project. To design moored structures, naval architect is interested in low-frequency response generated by nd order wave forces. Through linear transfer, the infragravity waves are another possible source of low-frequency energy. Their climate is not well known and so not yet really employed at the present-day in the design. At the end of the paper, some investigations are presented on the existence of infra-gravity waves in the shallow water measurements of the WASP project. SWELL GENESIS A swell is a series of surface gravity waves that is not generated by a local wind. More precisely, after the generation of gravity waves by a wind field somewhere on the sea, these waves propagate across ocean or sea basins, independently of wind. Characteristics of the swell, then, depends on the generating wind (severity, fetch, duration) and of the distance between the genuine wind-sea and the place of observation of the swell itself. So, if swell waves main peculiarity is to be quasi-harmonic (narrower range of frequencies) long-crested (narrow range of directions) with long wavelength (low frequencies), the range of for example its wavelength can go from several m in sea basins to several m in ocean basins. The swell family is large. Swells arriving on the West African coasts have been created by storms thousands of nautical miles away from there. These distances allows the waves comprising the swells to be better sorted than they were in the wind sea during the generating storm. This is due mainly to the dispersion effect: in deep water the group velocity C of a wave is proportional to its period (and g the gravity), g g C = T = () -- f so, if L is the distance between the storm location and the African coast, the duration D of the travel is L D = --- = Lf () C g and the time lag between two waves separated in frequency by a f is D = Lf (3) g As L corresponds to several millions of meters, a quite short difference in frequency will produce large delay between the waves. For example, a wave with a period of 6 seconds travelling 6 kilometers (the distance between Guinea Gulf and the Roaring Forties) will arrive after 6 days of propagation and 9 hours before waves of seconds Although long waves (low frequency) are generated by the storm later than shorter waves, after travelling on long distances this delay is rapidly compensated by the difference of travelling time. For example, if the in the wind-sea the wave period is proportional to the wind speed U (e.g. Pierson-Moskowitz model) T = U () g the time lag is corrected as D L U = f () g U with U the time derivative of the wind speed. All this makes the swell spectra very narrow in frequency (see Olagnon et al. [3] for more details on the shapes of swell spectra). Equation (3) shows that the analysis of the time evolution of swell frequencies gives information about the location of the generating storm. Interesting animations of swell tracks extracted from satellite SAR [] are available through the web site of the CLS SO- PRANO Project [6]. More details on the generation and propagation of swell and swell climates can be found in numerous papers ([7-9], for example). WAVE HINDCAST DATABASES Two wave hindcast databases have been used in the WASP project. Since that time, improvements in numerical modelling have been realized and all comments and conclusions in this paper must be considered as applying to the state of the art in. Hindcast WANE (West Africa Normals and Extremes) WANE is a wind, wave and current Oceanweather's hindcast for the West Coast of Africa. A -year continuous period, each three hours, and 8 individual storms were hindcast on a.3 by.6 degree grid covering the entire South Atlantic. Wave spectra from the GROW (Global Reanalysis of Ocean Waves) global hindcast were used at the WANE boundaries. All the calculations were made in infinite depth. Ten locations have been considered in the WASP project, from latitude N to 9 S. Three types of data sets have been used:

3 "WANE Storm". Storm spectra time series for the 8 storms that were hindcast in WANE. -hour time step. "WANE OPR". Operational time series for the fifteen years hindcast in WANE. 3-hour time step. "WANE Qscat". Hindcasts assimilating satellite Quik- SCAT scatterometer winds, done for a two-year period. 3-hour time step. For each date the synthetic sea-state parameters and directional spectra (3 freq. x dir.) are given. See Tab. for the periods of time. Hindcast NOAA For some purposes in the project (swell genesis, hindcast vs measurements) the hindcast database "NOAA WAVEWATCH III" has been used. This database was obtained free from the NOAA ftp site. The WASP project used the global model which covers longitudes from 77 S to 77 N. The resolution is. (lon)x. (lat). Each three hours five parameters are given (Tp, Hs, Wave direction at Tp, meter wind speed and direction). The time period used in the project was the eight years 99-. DIRECTIONAL SPECTRUM PARTITIONING Measured or hindcast wave spectra off West Africa are generally multi-modal. In addition to a wind sea peak, more than one swell system is often present. The first step before analyzing directional spectrum is thus to partition it into its components. The partitioning of the spectra into wind-sea and swell partitions was performed using the program APL Waves, developed by the Applied Physics Department of Johns Hopkins University (Hanson and Phillips []). The input to the program is a data file of wave frequency-direction spectra. The program then partitions the 3D spectrum into separate peaks as in the example of Fig. and calculates classical sea-state parameters for each partition. FIGURE. SCHEMATIC WAVE FREQUENCY-DIRECTION SPECTRUM, SHOWING DIFFERENT PARTITIONS. A number of parameters can be set within APL Waves to optimise the partitioning for a particular data set and which influence the result of the partitioning, among them: wave height threshold, to reduce the noise resulting from small isolated peaks. wind-sea multiplier, to determine if a wave system is classified as wind-sea or swell. no. Swells, the number of swells allowed per observation. This value was set to for the analyses in WASP. spread Factor and Swell Separation Angle, which set the directional criteria for combining peaks. If wind data was not available to determine the wind sea component, the wind speed and direction was estimated from the spectrum by means of an iterative process based on the method of Wang and Hwang []. Frequency-direction spectra are required for input to the partitioning analysis. These are directly available in the case of the hindcast dataset, but they must be derived in the case of the point-measured data which provide only the two first pairs of Fourier Coefficients of the directional distribution. For the WASP project, the Maximum Entropy Method (MEM) has been chosen which was found to provide swell sources estimates with the better directional resolution.. Period T (s) Hindcast WANE 873 Wave systems Joint occurences N(T,θ) 3 3 Period T (s) FIGURE. JOINT OCCURRENCE T -DIRECTION Hindcast WANE 873 Wave systems Joint occurences N(Hs,θ) 7 # of sea states 3 # of sea states FIGURE 3. JOINT OCCURRENCE H S -DIRECTION

4 WEST AFRICA SWELL CLIMATE Two geographic zones of swell generation are observed from the Hindcast databases. South swells. During the months of May through October (Austral winter), swells generally approach West African coast from the south to south-westerly direction. These swells are generated by storms in the South Atlantic mainly between S and 6 S. South Atlantic swells, travel sometimes thousands of miles across the ocean before breaking along the West African coast and can produce sea-states up to 7 meters in the South (Namibia) to meters in Angola and 3 meters close to the equator. Northwest swells. During the months of October through April, swells approach West African coast from the north-westerly directions. These swells are generated by big storms that blow off North America and travel first across the North Atlantic Ocean and secondly across the South Atlantic. The wave heights of these swells are obviously lower than for the south swells, with significant wave up to. meters. The locations far north, from Côte d Ivoire to Cameroon are sheltered for these swells. Figure, for the Angola location, the presence of the North- West swells is very clear on the plotting of joint occurrences T-Direction of the swells. Obviously, the number of sea-states with N-W swell is very low (several hundreds during years) and if we look at the joint occurrences Hs-Direction (Fig. 3), we observe that they correspond to very low Hs. Statistics of monthly significant wave height of the sea-states calculated from the years of WANE hindcast is given in Fig. for a point close to Congo. The same plots for the other locations can be found in []. Sea state Hindcast WANE 699 max quantile 99% quantile 9% median month FIGURE. SEA-STATE HS, WANE HINDCAST, CONGO Typical situations of swell Three typical situations have been extracted from the NOAA hindcast database, focusing on the Angola point. the biggest South-South-West swell system (Hs= meters), completed with a South-West example; the biggest 3 wave systems ( examples are given); the biggest North-West swell system (Hs=.3 meters). First the sea-state field of the Atlantic at the dates of interest (called afterwards "date of analysis") is given (Figs., 8, and ). They show Hs on the left, focusing on the highest values, and on the right the peak period, focusing on the long waves. As it is a peak period, when we observe a front of swell at s as in Fig., it is obvious that before this front longer waves with amplitudes lower than the global spectral peak have already arrived. Colorbars indicate the scales of Hs and Tp. Animations of these Hs and Tp fields, which are not possible to show in a paper, are very instructive. Secondly, the time evolution of the triplet (Hs, Tp, Direction) for each wave system of the sea-states at a chosen location (here the Angola point) is plotted, from several days before the "date of analysis" of the sea-state field to just after (Figs. 6, 9, and, black arrows). The "date of analysis" is indicated by two blue dash-dotted lines. The wave systems come from the partitioning of the directional spectra of the WANE Operational hindcast. The ordinate indicates the peak period, given by the dot of the arrows. The length of the arrows gives Hs (the scale is given top-left by the maximum Hs of the figure). The direction is given by the direction of the arrows. A theoretical wind-sea calculated from the local wind used in the WANE Operational hindcast is given by red arrows (Eq. (6)). The model comes from Carter [] and corresponds to a duration-limited sea. Hs =.6D 7 U 9 7, T m =.D 3 7 U 7 (6) with U the wind speed in m/s, and D the duration of the wind in hours. Here an empirical choice of 8 hours has been made for D. The direction of the wind-sea is put to the direction of the wind. The point and directional spectra corresponding to the "date of analysis" at the Angola point, are given in Figs. 7,, 3 and 6. South-South-West swell. The biggest swell (in Hs) encountered, May 6, 997, during the 8 years of the NOAA database is a south-south-west swell (the red swell front is south of Guinea Gulf on Fig. -right). It has not been generated by the biggest storms of the South Atlantic, but by a "moderate" storm (Hs~8m) closer to the West coast of Africa. It is a very pure swell (see Fig. 7) with a mild slope in high frequencies, due to the vicinity of the storm. It could be called a "young swell". South-West swell. This is the swell front visible in the middle of Atlantic on Fig. -right. This is an example of a South-West swell generated by a very severe storm. A storm travelling from West to East between and West latitudes, is now South of Africa (Fig. -left). All along its travel, with first a Hs of 3m close to South America which decreased to 8m South of Africa. The first waves of this swell begin to appear at the end of the history (Fig. 6), with very long periods (s), not yet visually observed in spectra in Fig. 7. This swell did not generate later Hs higher than.m.

5 NOAA WAVEWATCH III 997//6 : Tp (s) FIGURE. SOUTH-SOUTH-WEST SWELL SYSTEM, OCEANIC WAVE FIELD. 3 Hs from wind Hs max = 3.9 m.3.. Peak period (s).. /8: /8: /: /: 6/: 6/: 6/: 7/6: 7/6: date (997//dd/hh) FIGURE 6. SOUTH-SOUTH-WEST SWELL SYSTEM, HISTORY OF WAVE SYSTEMS. Multiple swells. We have selected two examples of multiple wave systems. The first sea-state, May, 997 (Figs. 8-) is composed of very long waves (Tp=s), the first waves from the last South Atlantic storm, a second swell system (Tp=s), and a last one (Tp=6s) which seems to be a wind sea when considering its time evolution and comparing to a theoretical wind sea coming from model (Eq. (6)). The three systems are well observed in point spectrum Fig.. The second situation, May 6, 998 (Figs. -3) clearly also has three wave systems, but here, the one with the shortest waves (Tp=7s) seems, looking at the time history of the peak period, to be the tail of one of the swells propagating from South-West, perhaps mixed with a local wind-sea. This situation shows the difficulty in some cases to distribute wave systems between swell and wind-sea psd (m /Hz) 3 Hs =. m FIGURE 7. SOUTH-SOUTH-WEST SWELL SYSTEM, DIRECTIONAL AND POINT SPECTRA.

6 NOAA WAVEWATCH III 997// : Tp (s) Hs from wind Hs max =. m 8 6 FIGURE 8. MULTIPLE SWELL SYSTEM, 997, OCEANIC WAVE FIELD..3.. Peak period (s)...3 8/: 9/8: 9/8: /: /: /: /: /: /6: date (997//dd/hh) FIGURE 9. MULTIPLE SWELL SYSTEM, 997, HISTORY OF WAVE SYSTEMS. North-West swell. During winter, some North Atlantic storms generate swell sufficiently powerful to travel to the West African coast (see Fig. ). As it can be observed in Fig., some locations as Guinea Gulf are sheltered from this swell. During the 8 years of the NOAA database, the biggest Hs corresponding to these swells was.3m. Of course these swell are much less severe than the South swell, but they arrive abeam to floating systems oriented to the main swell directions. We have here again an example of superposition of three to four wave systems. These five examples illustrate the diversity of the situations (type and number of wave systems, Hs, period, direction, genesis) and show the difficulty of a detailed statistical description of the swell climatology in West Africa. psd (m /Hz) Hs =. m FIGURE. MULTIPLE SWELL SYSTEM, 997, DIRECTIONAL AND POINT SPECTRA.

7 NOAA WAVEWATCH III 998// 6 : Tp (s) Hs from wind Hs max =. m 8 6 FIGURE. MULTIPLE SWELL SYSTEM, 998, OCEANIC WAVE FIELD. Hindcast WANE Peak period (s) /: /8: /8: /: /: 6/: 6/: 6/: 7/6: date (998//dd/hh) FIGURE. MULTIPLE SWELL SYSTEM, 998, HISTORY OF WAVE SYSTEMS. HINDCAST-MEASUREMENT COMPARISONS Comparisons between in situ measurements and hindcast models are not always very easy for two reasons. First, the periods of time of the in situ measurements (often relatively short) do not coincide with the period of time of the hindcast databases; secondly the short durations of the in situ measurements do not permit accurate statistical comparisons. The choice in this project has been to compare qualitatively and simultaneously the sea-states parameters extracted from the measurements and the hindcast data to establish some features of the differences. However, statistical information in term of quantile/quantile plots are given for the global sea-state Hs. psd (m /Hz) Hs =.7 m FIGURE 3. MULTIPLE SWELL SYSTEM, 998, DIRECTIONAL AND POINT SPECTRA.

8 NOAA WAVEWATCH III 998/3/ : Tp (s) Hs from wind Hs max =.9 m 8 6 FIGURE. NORTH-WEST SWELL SYSTEM, OCEANIC WAVE FIELD. Hindcast WANE Peak period (s) /: /: /: /8: /8: 6/: 6/: 7/: 7/: 7/: date (998/3/dd/hh) FIGURE. NORTH-WEST SWELL SYSTEM, HISTORY OF WAVE SYSTEMS. The aim would be, to validate the swell information given by the hindcast models, in order to give confidence in the statistics that could be calculated from large time duration databases. More statistical comparisons with scatter plots are available in [] (chapter 8). Three sites have been used for this study, Bonga ( 33 N, 36 E) with a directional Waverider and Wavescan, 8m water depth, Kudu (8º38 S,º3 E) with a directional Waverider, 8m water depth and Cabinda, hereafter called Chevron (º S,º E and º3 S,º E) with two wavestaffs, 8m and 8m water depth. The overlaps of hindcast periods and measurement periods are given in Table. More details on the measurements are given in a companion paper [] psd (m /Hz) Hs =. m FIGURE 6. NORTH-WEST SWELL SYSTEM, DIRECTIONAL AND POINT SPECTRA.

9 TABLE : HINDCAST AND MEASUREMENT PERIODS WANE OPR WANE QUIKSCAT NOAA BONGA Waverider st BONGA Waverider nd BONGA Wavescan Chevron Wavestaff 8m & 8m Kudu Waverider Hs,Tp comparisons Bonga. In looking at the frequency of the spectral peak (Fig. 7), some differences can be observed between the hindcasts and the measurements (blue & black). First, WANE OPR (green) and QSCAT (yellow) hindcasts give a denser region between.hz and. Hz compared to measurements and NOAA hindcast (red). At the opposite end, agreement at frequencies higher than.6hz is poor, specifically for WANE OPR. This is certainly due to an underestimation of local wind in WANE, partially corrected in QSCAT BONGA Peak frequency NOAA (red) WANE (green) WANE QSCAT (yellow) WAVESCAN (black) WAVERIDER (blue) comparisons, perhaps due to improvements in the numerical model. The same comments globally apply for Chevron and Kudu sites. Peak frequency time series Bonga. As it has been observed on the sea-state Hs, the time history of the frequency of the spectral maximum, shows that hindcast models simulate well the swell event (Fig. ). However the frequency seems to be slightly higher with the hindcast models. The typical characteristic of swell frequency evolution explained before, increasing from low to high frequencies is clear. WANE follows the swell system longer because NOAA and buoy switch to the wind sea system at some Hs level, whereas WANE underestimates wind sea..6. WANE OPR Waverider fp (Hz) / 96/ 98/ 99/ / /7 /9 3/ date (yy/mm) FIGURE 7. PEAK FREQUENCY AT BONGA In Fig. 8, the time series of sea-state Hs given by WANE and the Waverider measurements are compared. If, more or less, the "storm" events observed by the buoys are present in the hindcast, the hindcast gives "storms" of lower severity. NOAA hindcast (Fig. 9), gives results more in agreement with the Waverider in amplitude and in shape. But, it misses again some events (swell or wind sea?). The scatter plots are much better than for WANE but the quantile-quantile plots show for NOAA an - cm offset of underestimation. This offset disappears in Waverider nd phase and Wavescan buoy vs NOAA hindcast /9 7/7 7/6 8/3 8/ 8/ 8/8 9/ 9/ 9/ date (998/mm/dd) FIGURE 8. H S WANE VS WAVERIDER AT BONGA Peak frequency of the wave systems. The time histories of the peak frequency of the wave systems obtained after partitioning of WANE (green dots) and buoys (black dots) directional spectra are plotted Fig. for Bonga and Chevron sites. The conclusions are the same for all sites. Compared to the partitioning in wave systems obtained from buoy measurements, the hindcast

10 gives more complete information on the superposition and evolution of swell systems (up to four systems, e.g. at the beginning of the Bonga series). In most of these situations the energy in the satellite swell systems (one young, the other old) are much lower than the energy in the main swell system. So the quality of the spectrum estimated from the buoy measurements does not permit extraction of the satellite swell systems. On the other hand, the wind sea wave systems are practically absent in the hindcast. This is not due to a problem of partitioning, but to an underestimation of the local wind field by WANE. Peak frequency (s) Hindcast WANE 8793 vs Bonga measurements Wave systems Bonga WANE.6. NOAA Waverider... 7/ 7/9 7/7 7/6 8/3 8/ 8/ 8/8 9/ date (998/mm/dd) Chevron WANE /9 7/7 7/6 8/3 8/ 8/ 8/8 9/ 9/ 9/ date (998/mm/dd) FIGURE 9. H S NOAA VS WAVERIDER AT BONGA Peak INFRA-GRAVITY WAVES The infragravity waves are not directly generated by the wind, but instead are generated in shallow water through nonlinear mechanisms from "short-period" waves (>.Hz) as they impinge on the coast. As a matter of fact, second order, difference frequency effects in the wind-wave field produce long-period waves (<.Hz) that are bound to the wave group and produce wave set-down. When the wave field impinges on the coast, the short-period energy is lost in wave breaking at the shore, while the long-period waves are reflected.. fp (Hz) WAVERIDER (blue) NOAA (red) WANE (green) 7/8 7/6 7/ 8/ 8/ 8/9 8/7 date (998/mm/dd) FIGURE. F P BUOY VS NOAA VS WANE AT BONGA / / / / /3 / / date (99/mm/dd) FIGURE. F P WAVE SYSTEMS, BUOY VS WANE AT BONGA (TOP) AND CHEVRON (BOTTOM) In most cases, offshore, the wave spectrum (hindcast models or buoy measurements) do not contain energy in the very low frequency band. In that case, for structural responses, the estimates of the lowfrequency spectrum is based only on nd order calculations from the "short-period" frequency band of the wave spectrum and the energy calculated in this way will account only for the component that is bound to the wave group and not the freely propagating (infragravity) part that is reflected from the coastlines of the entire ocean.anyway, it is a very difficult problem and most of studies have been based on measurements. Unfortunately it is climatology and site (bathymetry) dependent. Most of infragravity waves generated in surf zone are trapped in shallow waters and their intensity offshore is very difficult to evaluate as most of measurements available come from buoys which filter the infragravity frequencies. In shallow water (water depth 3 m) the studies of Herbers et al. ([3],[]) show that, (IGW stands for InfragGravity Waves, BW stands for Bound Waves): the energy ratio IGW/BW goes from 3 to ; when the swell energy is increasing, IGW/BW is decreasing; the energy of IGW are measured between.* - m and 6* -3 m.

11 psd (m /Hz) 3 3 measurements bounded waves psd (m /Hz) Ekoundou measurements bound waves measurements bounded waves Frequency (Hz) the total energy measured by the wavestaff (practically invisible on the graph). This could indicate low frequency free waves..the same processing was applied to the complete database of Ekoundou. Figure shows the energy calculated in the band [Hz-.Hz], bound and total waves, for the 3 sea-states. The total low frequency energy values are included in the range [.* - m -6* -3 m ] indicated by Herbers et al ([3],[]), and the comparison with second order bound waves confirms the comment that forced (bound) infragravity waves are consistently much less energetic than free infragravity waves. 7 x 3 Ekoundou 6 [,.Hz] [,.Hz] measurements [,.Hz] bound waves [,.Hz] total bounded energy/ waves total energy/ Frequency (Hz) FIGURE. MEASURED VS SECOND ORDER SPECTRUM () Low frequency energy and second order bound waves Measurements from a wavestaff at Ekoundou ( 7 N,8 3 E) have been used to compare second order bound waves energy calculated from the free short waves and low frequency energy estimated from the measured spectra. Complementary results using a pressure probe at Malabo (3º7 N,8º E) will be found in []. psd (m /Hz) 6 3 measurements bounded waves psd (m /Hz) Ekoundou measurements bound waves Frequency (Hz) Frequency (Hz) measurements bounded waves FIGURE 3. MEASURED VS SECOND ORDER SPECTRUM () At Ekoundou, the water depth is 8 m. A wavestaff can measure low frequency waves (free or bound). To calculate the energy of the second order bound waves, the spectra have been filtered to keep only the "short-waves", [.Hz-Hz], and then the second order bound waves have been calculated in using the classical second order transfer functions (see for example []). Figure shows a first example of comparison. The second order part is plotted in black. When we compare, in the pop-up window, the low frequency part, [Hz-.Hz], we observe very comparable energy. No additional energy coming from free propagating long waves is visible. A second example, Fig., with swell and a wind-sea, corresponds to a less steep sea-state, and so weaker second order effect. On the other hand, here in the pop-up window, the second order low frequency energy is much lower than energy (m ) # time series FIGURE. MEASURED VS SECOND ORDER ENERGY CONCLUSIONS The West Africa Swell Project, initiated in, has permitted improvement in the knowledge of swell climatology in West Africa. The complexity of the sea-states, superposition of several swells and wind-sea, has been explained and analysed physically and statistically. The quality of the hindcast numerical models to reproduce faithfully the properties of sea-states dominated by swell has been assessed from comparisons with in-situ measurements. These models were not, at the time of the project, of sufficient quality to accurately track all the swell events, but the model estimates appeared richer in information on superposition of multiple swell systems than directional buoys. Since the end of the project the hindcast models have been improved by the integration of new dissipation and non-linear interaction source functions and also by the addition of buoy and altimeter data assimilation (see for example Cavaleri et al. [6] and more recently Ardhuin et al. [7]). Some analyses of shallow water measurements have shown the presence of low-frequency components that could be due to the presence of infra-gravity waves. Much more work is needed to furnish to the engineer metocean specifications on the low-frequency energy generated by these types of waves. ACKNOWLEDGEMENTS We thank the participants of the WASP Joint Industry Project for their financial support and technical input. The partici-

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