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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

8.6 Ensemble modelling

Forecasts are subject to uncertainty by their nature. Some of the uncertainty is due to errors in model parameterizations of real-world processes, while some others can be attributed to observation errors. However, a significant amount of uncertainty is also introduced as a result of small differentials between the analysis and the state of environmental conditions at forecast initiation. These differences can lead to much wider discrepancies between the forecast and actual state at longer lead times, depending on the stability of the background meteorological conditions. One approach to forecasting is attempting to quantify the uncertainties, and view the forecast as sampling from a probability distribution of likely conditions rather than as a single “deterministic” outcome. Continuing increases in computing resources have enabled modelling centres to adopt a probabilistic forecasting approach based on running wave EPSs.

The aim of an EPS is to provide forecasters with a measure of model and climatic uncertainty associated with a given forecast. The ensemble will indicate lower forecast uncertainty in well- specified and stable weather conditions than in unstable conditions, where the present weather state might be poorly analysed and weather system development is more dynamic. As a forced-dissipative system, wave-forecast uncertainty is mostly determined by variations in the driving atmospheric data. Thus, the requirement for a complex EPS based on data assimilation, using perturbed initial conditions to generate starting conditions for ensemble members as in ensemble weather prediction, is limited. Pioneering applications have been developed for global medium-range forecasts (1-4 weeks ahead) at centres such as the ECMWF (Molteni et al., 1996; Saetra and Bidlot, 2004), NCEP (Chen, 2006), and FNMOC (Alves et al., 2013). Research into short-range regional ensemble systems, which have a stronger requirement for uncertainty to be well specified at forecast initialization, is ongoing at the UKMO (Bunney and Saulter, 2015), the Italian Meteorological Service (Pezzutto et al., 2016), and the Australian Bureau of Meteorology (Zieger et al., 2018).

Figure 8.31. Point time-series ensemble wave forecast product by ECMWF. Top two panels: direction variability and wind speed. Lower three panels: forecast of total wave parameters. In this instance, a high-resolution deterministic model and the ensemble control are overlaid using the blue and red lines, respectively (source: WMO, 2020).
Figure 8.32. Ensemble forecast charts. Top: ensemble mean significant wave height (contours) and spread (shading). Bottom: probability of significant wave height exceeding 4 m (source: WMO, 2020).

The data provided by an ensemble (see Figures 8.31 and 8.32) allow more than one approach to be adopted when interpreting and issuing a forecast. For example: i) individual members can be identified and used to describe alternative forecast scenarios deterministically; ii) dynamic changes in ensemble spread can be used to estimate the uncertainty associated with a deterministic product derived from the ensemble; or iii) probability information about a given outcome (for instance, the probability of wave height exceeding a certain operating threshold) can be used directly. The choice of approach requires an understanding of the end-user requirements and of the ensemble’s performance.

However, a well-specified ensemble should show a good reliability relationship. Similarly, a good ensemble will show a strong correlation between spread in the EPS forecast and error in the ensemble control/mean forecast and observations. All these behaviours are fundamentally reliant on the quality of the underlying model. In the example in Figure 8.33, reliability is shown to be significantly affected for a short-range ensemble forecast when an underlying bias is corrected. A recommended practice when assessing probability of threshold exceedance is to evaluate the probability and also the quantity by which the threshold is exceeded. For example, a forecast where 90% of ensemble members exceeded a threshold by 1 m Hs should be given a stronger level of confidence than a forecast with a similar probability of 90%, but which threshold exceeds by only 10-20 cm.

Figure 8.33. Reliability diagram for two wave EPS forecasts of significant wave height above 6 m at a forecast range of 2 d (blue: Atlantic regional model; red: regional model of the United Kingdom). The forecasts are considered reliable when the forecast probability and frequency of subsequent observations are similar (the data fall onto the 1:1 line). In this example, the effect of bias correcting the forecast is significant; in the bottom panel, the lines representing forecasts after bias correction are much closer to the 1:1 line than the raw forecasts in the top panel (source: WMO, 2020).

One aspect of ensemble prediction that may have particular application is the identification of low-probability, high-impact occurrences of a “dangerous” sea state within the ensemble at long range (Petroliagis and Pinson, 2012). In extreme cases, the accuracy of the underlying model may be more questionable than everyday forecasting, but this can be mitigated using a background model climatology. Lalaurette (2003) described the ECMWF EFI methodology for wind, temperature, and precipitation parameters, in which forecast members were compared against a model climate. This EFI has also been extended to waves. Figure 8.34 shows an example in which the figure on the left is EFI (with range -1 to 1) for significant wave height, with values nearing 1 over the Norwegian Sea. The figure on the right is the corresponding 99th percentile of the wave height distribution for that day. Therefore, EFI indicates that the model is predicting wave heights above 4 m and that this is not usual for that time of the year.

Figure 8.34. Extreme Forecast Index (left) and associated 99th percentile of significant wave height derived from the model’s long-term climate simulation (right panel) (source: WMO, 2020).

A computationally cheaper version of a full ensemble system is the so-called “poor man’s ensemble” (Ebert, 2001), which combines some independent model forecasts from several operational centres. The availability of such a set of forecasts can also contribute to a “consensus forecast” in which the forecasts are weighted and bias corrected according to past performance to produce an “optimal consensus forecast”, which typically outperforms any of the individual model forecasts (Durrant et al., 2009).

An example is given below for the interest of using a wave ensemble in the frame of emergency and wave submersion warning. Figure 8.34 right panel shows the high uncertainty between members on the location of the strong wave area generated by a storm event. The propagation of the storm is observed differently. Several members, including the deterministic forecast, estimate SWH of 10m on Brittany coasts at 102-hour forecast (06:00 UTC), as illustrated in Figure 8.35 left panel. In fact, the wave submersion warning in this case was triggered for the evening. It can be seen that about 20% of the members considered a probability of waves with SWH greater than 10m near the analysis. Uncertainty was also related to the location of the storm on the North-South axis.

Figure 8.35. Left: probability (in %) of SWH exceeding 10m at 102-hour forecast from the wave ensemble system. Right: standard deviation of SWH (in metre) between ensemble members, 30 January 2021 at 06:00 UTC (courtesy: A. Dalphinet, MeteoFrance).
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