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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

8.7 Validation and calibration strategies

For all operational ocean forecast systems, verification of wave models is dependent on the choice of metric, sampling strategy, and parameter(s) to be verified. Verification and measurement of model uncertainty include describing the difference between the model and observed conditions and their statistical properties; assessing the value of the model in accurately predicting specific ocean conditions for user decision making; providing a long term view of performance and measuring the impact of model changes; and/or investigating the model’s ability to represent particular ocean processes or conditions. As with any statistical analysis, it is useful to frame the question or hypothesis that the verification should answer and ensure that the metrics provided are appropriate to the expertise of the audience.

For the verification, it is fundamental the sampling strategy applied to both model and observations. Sampling should consider spatial and temporal correlations with respect to data to be verified. These correlations will be dependent on the verification setting, for example in the open ocean wave fields may be well correlated over scales of hundreds of kilometres and several hours, whilst in coastal settings with a strong tidal component correlation in wave conditions, scales can diminish about tens of kilometres and periods of less than an hour (Saulter et al., 2020). The degree of correlation between data affects the sample size required to consider robust statistical verification. The verification can be affected if scales represented by models and observations are substantially different. In-situ observations tend to sample on scales equivalent to approximately 5-20 km depending on dominant wave periods, whilst a 1 Hz altimeter observation of significant wave height is derived over a spatial footprint that covers approximately 6-7 km in the along-track direction with a diameter 2-10 km increasing with the sea-state (since the backscatter increases as waves get bigger and wavelengths longer). Wave models can generally be considered to scale at a factor of 3-4 times of either the wave or forcing atmospheric model horizontal grid and integration time step (Janssen et al., 2007). It is recommended to define a benchmark representative scale for comparison with the data processed to that scale, as well as metadata describing this processing supplied alongside with metrics. It may also be important to communicate limitations in the data, for example in the case in which the available observations and processing methods cannot be extended to a full coverage of the model domain, such as coastal zones.

Figure 8.36. Top: variation of scatter index of SWH in a forecast compared to wave buoys from June to August 2021, colours stand for operational centres names (source: WMO/LC-WFV). Bottom: map of scatter index of SWH from Global Ocean Wave Reanalysis (WAVERYS) compared to altimeter HY2A during the 2013-2018 period - source: CMEMS-GLO-QUID-001-032 https://catalogue.marine.copernicus.eu/documents/QUID/CMEMS-GLO-QUID-001-028.pdf

Existing standards for baseline performance metrics can be found via the WMO/LC-WFV established at ECMWF (Bidlot, 2016), and Product Quality Dashboard of the Copernicus Marine Service (🔗8). Left panel in Figure 8.36 shows an example of scatter index of SWH monitoring provided by different operational centres in the framework of the WMO/LC-WFV. As illustrated by the Copernicus Marine Service global wave reanalysis (right panel in Figure 8.36), the altimeters have the advantage of covering all ocean basins, allowing the monitoring of the spatial variation of wave models errors.

Standards will continue to evolve with the increased use of ensemble forecast systems and reductions in horizontal scales of wave, atmosphere, and ocean models. However, model performance is better described by metrics that exploit the uncertainty in forecasts, either from the ensemble (Pezzutto et al., 2016) or using variability in spatial neighbourhoods surrounding an observation point (Ebert, 2008; Mittermaier and Csima, 2017). For long-term monitoring, an important ensemble prediction metric is the Cumulative Ranked Probability Score (Hersbach, 2000),which can be directly compared with Mean Absolute Error for deterministic predictions, therefore enabling the benefits of transition to high resolution or ensemble models from lower resolution or deterministic systems to be measured.

Wave observational data are dominated by SWH measurements available from in-situ sources and remote sensing via satellite missions and HF radar. SWH data are a primary health indicator for the wave model, describing the wave energy of the surface ocean as a response to momentum supplied by the atmosphere and redistributed through wave dispersion. SWH is often the main parameter of interest for users and decision makers about sea-state conditions (see also Chapter 4). However, to properly verify a wave model’s performance at a process level, observations of further parameters describing the distribution of wave energy within the two-dimensional frequency-direction spectrum should be also used. Full spectral coverage in the frequency (period) domain of ocean surface waves is currently obtained only by in-situ measurements. Attention is needed to understand the limitations imposed by a given platform’s response to wave action, which determines a high frequency cut-off, and the distinction between directional spectra derived from the ‘first five’ approach used by in-situ data (Swail et al., 2010) versus the full frequency-direction distributions generated from models and remote sensing. Remote sensed data are strongly affected by frequency (wavelength) cut-off constraints as , for example, SAR will capture long period swells but not short wind-waves. From a verification perspective, it can be difficult obtaining a sufficient sample of data across the full directional wave spectrum to enable a robust statistical analysis over multiple frequencies and directions, and hence it is often preferable to compare wave heights, periods, and directions integrated over a reduced number of partitioned regions of the wave spectrum (Ardhuin et al., 2010). Since wave models are strongly influenced by the uncertainty inherited from the forcing atmosphere (Cavaleri et al., 2018), when evaluating wave models at the process level, it is recommended to verify wave parameters alongside contemporary measures of wind speed or stress.

A useful tool in the verification process is the wave rose analysis. Figure 8.37 shows a comparison between the directional wave properties by the Copernicus Marine Service WAVERYS and the buoy 51202 deployed by the NOAA NDBC at Oahu (Hawaii, USA).

Figure 8.37. Left: wave rose for Copernicus Marine Service WAVERYS. Right: wave rose at NDBC buoy 51202 (Hawaii, USA).
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