MFWAM

Météo-France's wave model

MFWAM, for Météo-France WAve Model, is the operational global wave system of Météo-France, the French weather service, and the one that Copernicus Marine distributes as its global wave analysis and forecast. It is a third-generation wave model, which describes the sea state as a spectrum of waves, 24 directions by 30 frequencies, rather than as single waves.

Its code is ECWAM, the wave model of the Integrated Forecasting System (IFS) of ECMWF. The product description names the version ECWAM-IFS-38R2, with a dissipation term developed by Ardhuin et al. (2010), and tells that the model was upgraded in November 2014 with the improvements of the European research project MyWave (Janssen et al. 2014). The quality document adds that the code moved to ECWAM-IFS-41R2 in December 2020, with no change in the wave physics.

The system has been renewed several times since. Its version 4, in January 2018, brought the computing grid down to 10 km, the minimum water depth from 10 m to 5 m, adjusted dissipation terms to improve the surface stress at the air-sea interface for high and intermediate winds, and a diagnostic Phillips spectrum for the high-frequency part of the spectrum. In December 2020 the forecast was extended to 10 days, and in September 2022 the assimilation took in the wave heights of Sentinel-6A and the directional wave spectra of the SWIM instrument of CFOSAT. The delivery has been twice daily since December 2021.

Copernicus Marine publishes it as the product GLOBAL_ANALYSISFORECAST_WAV_001_027, with one dataset of 3-hourly fields and a rolling archive of two years. Besides the integrated parameters of the whole spectrum (significant height, periods, direction, Stokes drift, maximum wave height), it provides the partitions of the spectrum into wind waves and primary and secondary swell.

Winds in, a regular grid out

Waves are driven by the wind, so the winds that force the model set much of the quality of its waves. MFWAM takes those of ECMWF's IFS, 6-hourly analyses and 3-hourly forecasts at 1/10°, together with the sea ice fraction. The quality document adds that the upgraded system is forced by the surface currents of Mercator's global PSY4 ocean forecasting system, updated daily.

The model's own grid is irregular: the distance between its points in longitude decreases toward the poles, and is about 1/10° at the equator. The sea floor comes from the 2-minute ETOPO2 topography of NOAA. The wave parameters are then interpolated onto the regular 1/12° grid of 4320 × 2041 points on which the product is published.

Of the product's many fields, Saily WR keeps three: VHM0, the spectral significant wave height, in metres; VMDR, the mean direction the waves come from, in degrees, as for the wind; and VTPK, the period at the peak of the spectrum, in seconds. The same model also computes the Stokes drift that the SMOC current adds to the ocean's circulation.

The fields are instantaneous, not averaged, every 3 hours, at 00, 03, 06, 09, 12, 15, 18 and 21 UTC, so the sea state between two of them is not described.

Altimeters and wave spectra, twice a day

MFWAM is corrected by observations from space. The manual lists the significant wave heights of the altimeters Jason-3, Saral, Cryosat-2, Sentinel-3A and 3B, CFOSAT and Sentinel-6, and the wave spectra of the radar (SAR) of Sentinel-1, assimilated by optimal interpolation in a daily cycle.

The SWIM instrument of CFOSAT gives directional wave spectra for wavelengths from 60 to 500 m. The quality document reports that using them reduced the bias of wave height in the Southern Ocean, because they better scale the growth of wind waves in storms over an unlimited fetch.

Analyses are made four times a day, at 00, 06, 12 and 18 UTC, with updated ECMWF forcings. The product itself is updated twice a day, at 00:00 and 12:00 UTC, each time with the analysis of the production day and a forecast up to 240 hours ahead.

Copernicus Marine keeps two years of the series on its data store, and deletes the obsolete forecasts as new ones arrive.

At sea

The quality document scores the analysis. Against buoys of the US National Data Buoy Center, mostly in North America, from January to May 2020, the wave height has a bias of 2 cm and a scatter index of 13.8%, the peak period a bias of 0.33 s and a scatter index of 12.6%. Against the independent altimeters HY-2B and HY-2C, in June 2022, the scatter index of the wave height is 7.9% on average, with a bias of 3 cm.

The errors are not the same everywhere. The scatter index stays below 8% in the open ocean and increases in coastal areas; the bias is small, but larger near the coasts and in regions affected by sea ice. The document gives no figure for the 10-day forecast: for the forecast of the first day, it reports a scatter index of 10.2% in February 2020, against altimeters.

A wave model on a 1/12° grid describes the sea state of an area several kilometres wide, not what a headland, a shoal or a narrow pass does to it close to shore, where the document finds its errors larger; and the model stops at 5 m of water depth. At sea, it tells the height, the direction and the period of the waves a route is likely to meet, to be read as a forecast, not a measurement.

MFWAM in Saily WR

Saily WR shows MFWAM's waves along a computed route: a chart of their height, direction and period along the route, and the highest waves it meets in the summary. They are shown, never used: the route is computed from the wind, and from the current if one is chosen, and the waves do not slow the boat. The same waves go with the route of every wind model, so that the routes stay comparable side by side.

A server downloads each new run as soon as it is published, and the Data page shows live which run MFWAM is on, its horizon and its coverage. Its row there is of the Waves kind, after the currents. As the model is global, it has no footprint to draw on the map.

As the Copernicus Marine licence requires, the data are credited wherever they are shown: "E.U. Copernicus Marine Service Information (CMEMS)". That licence is free and lets anyone build and share products derived from the data, for any purpose, on that one condition.