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Chapter 8

Wave modelling

CHAPTER
COORDINATORS
Lotfi Aouf and Gabriel Diaz-Hernandez
CHAPTER
AUTHORS
Alexander Babanin, Jean Bidlot, Joanna Staneva, and Andy Saulter

8.5 Data assimilation systems

In a wave forecasting system, data assimilation plays a key role in order to provide the best description of sea state, and also to correct uncertainties related to wind forcing from the atmospheric systems. Since the beginning of the 1990s, with the arrival of altimeter missions such the pioneer one Topex-Poseidon, the assimilation schemes have been implemented to use significant wave height in the WAM model (Janssen et al., 1989; Bauer et al., 1992; Lionello et al., 1992). Basically, the scheme uses an optimal interpolation through a weighted correction of the first SWH guess with that one from altimeters. The correlation model to spread the correction from altimeter SWH to other grid points is essentially a Gaussian function, depending on the distance between the observation and model locations, and a correlation length, which can vary with the wave regime (Greenslade and Young, 2004). The assimilation of SWH corrects the two-dimensional spectrum by introducing appropriate rescaling factors to the energy and frequency scales of the wind sea and swell components of the spectrum, and also updates the local forcing wind speed. The rescaling factors are computed for two classes of spectra: i) wind sea spectra, for which the rescaling factors are derived from fetch and duration growth relations; and ii) swell spectra, for which it is assumed that the wave steepness is conserved. Currently, there is abundant information on SWH (see Figure 8.27), as it is provided by eight satellite missions (Jason-3, Saral/Altika, Cryosat-2, Sentinel-3A and 3B, CFOSAT, HY2B, Sentinel-6MF). This ensures an excellent coverage for open ocean and it is evolving to a good coverage for coastal areas.

A variational technique has been also used in regional wave forecasting (Saulter et al., 2020) to assimilate SWH from altimeters. This scheme is an adaptation of the assimilation code NEMOVAR to wave assimilation.

Figure 8.27. Significant wave height (in meters) observed by altimeter radars of six satellite missions (Jason-3, Saral/Altika, Cryosat-2, Sentinel-3A and 3B, CFOSAT) during the whole day of 11 October 2021 (source: Aouf et al., 2021).

Since the launch of the ERS-1 and 2 and ENVISAT (2002) satellites, the waves are observed with more detailed information (Hasselmann et al., 2013), characterised by the directional wave spectrum that can describe the different dominant wave trains (see Figure 8.28). The assimilation of such observations needs several steps and has been initiated at the end of 1990’s. The method is based on the assimilation of wave systems as derived from a spectral partitioning scheme, which works on the principle of the inverted catchment area (Hasselmann et al., 1997; Voorrips et al., 1997; Breivik et al., 1998; Aouf et al., 2006). The different wave systems are characterised by their mean energy, frequency, and direction. The mean parameters are assimilated using an optimal interpolation (OI) scheme, following a cross-assignment procedure that correlates the observed and modelled wave systems. The analysed spectra are reconstructed by resizing and reshaping the model spectra based on the mean parameters obtained from the OI scheme.

Figure 8.28. Directional wave spectra observed by Synthetic Aperture Radar of Sentinel-1 (source: Derkani et al., 2021).

The SAR, from the ERS, ENVISAT and Sentinel-1 satellites, provides directional wave spectra with a limitation in azimuth direction of detecting waves with wavelength greater than 150 m. Such wave spectra are very useful to describe several wave trains in energy and wave numbers components. MFWAM started to assimilate wave partition parameters, such wavenumber components, by using optimal interpolation. This has provided a significant improvement of long swell propagation, and an assimilation impact which remains efficient at least 3 days in the period of forecast. Figure 8.29 shows the impact of the assimilation of wavenumber components of partitions from ENVISAT on the mean wave period. The different anomalies are strongly correlated with swell track propagation from the Southern Ocean.

Figure 8.29. Difference of mean wave period (in seconds) from the model MFWAM with and without assimilation of wavenumber components of SAR partitions from ENVISAT during the period from September to December 2010; positive and negative values stand, respectively, for overestimation and underestimation of the model, (source: Aouf et al., 2021).

Future wave forecasting systems will be able to assimilate both the wave heights and the directional components represented by the partitions. The impact of these assimilation systems ensures reliable integrated wave parameters in the 3-day forecast. The processing of satellite wave data is evolving rapidly; in a recent study by Wang et al. (2021), it is shown the retrieval of significant wave height on a scatterometer swath by using a deep learning technique. With this type of wave data, the amount of data to be assimilated is significantly increased, which keeps consistent the correction of the model over a swath distance of 200 km. An example of a wide swath SWH obtained from the CFOSAT mission is shown in Figure 8.30. The assimilation of wide swaths of significant wave heights improves the initial conditions of the sea state generated by storms, for instance in the Southern Ocean, and also enhances the impact in coastal regions. Furthermore, with the trend of improved spatial resolution of the wave model, altimeters are providing better sampled wave heights, e.g. 5 hz (~1km), with the ability to correctly describe small scale variations such wave-current interactions.

Figure 8.30. Wide swath significant wave height from the CFOSAT mission. Left: global view. Right: zoom focused on high SWH in Southwest Pacific Ocean (source: Wang et al., 2021).
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