The DMI operational wave forecasting service DMI-WAM uses the 3rd generation spectral wave model WAM Cycle4.5 [Günther, Hasselmann and Janssen, 1992], forced by DMI's numerical weather prediction (nwp) model Harmonie and the global nwp model ECMWF/GLM .

WAM Cycle4.5 solves the spectral wave equation. It calculates the wave energy as a function of position, time, wave period and direction. 'Real' wave parameters are calculated as suitable integrals of the wave energy spectrum.

The energy source is the surface wind. The sink terms are wave energy dissipation through wave breaking (white capping), wave breaking in shallows, and friction against the sea bed. Depth-induced wave breaking is only considered in model domains of high spatial resolution. The wave energy is redistributed spatially by wave propagation and depth refraction, and spectrally by non-linear wave-wave interaction.

Interaction with sea ice is included, while interaction with sea current is not. Effects due to varying sea level caused by tides or storms are also not incorporated.

DMI-WAM is run 4 times a day. The platform is The DMI Cray-XC50, a very powerful supercomputer. DMI-WAM uses 144 processors (4 36-core Cray cpus).

DMI-WAM runs
Analysis	00z	06z	12z	18z
Forecast range	132 hours
Forcing	Harmonie ECMWF
Run time	45 min

The DMI-WAM output is hourly maps of wave height, direction, and period, plus a number of other wave parameters. All forecasts are archived on tape in GRIB format.

DMI web pages broadcast the most recent forecast:

Main page (in danish, only 2 days ahead)
ocean.dmi.dk

Output parameter table.

DMI-WAM has three geographical domains at present: North Atlantic, North Sea / Baltic Sea, and Transition Area (Danish Waters) (see figure and table below).

A Red Sea set-up was terminated March 2014 A North West Pacific / Yellow Sea set-up was terminated July 2014 A Mediterranean set-up was terminated December 2016

model n.atlantic n.sea-baltic transition area space step 1/4° (ca. 25 km) 1/20° lat 1/12° lon (ca. 5 km) 1/100° lat 1/60° lon (ca. 1 km) advection time step 2 min 30 sec 10 sec source term time step 6 min number of directions 36 number of frequencies 35 sea points 47457 92314 139639 long 69W-30E 13W-30E 7E-16E lat 30N-78N 47N-66N 53N-60N forcing ECMWF GLM Harmonie NEA ECMWF GLM Harmonie NEW ECMWF GLM boundary JONSWAP nested nested depth map Rtopo Rtopo/IOW/KDI Rtopo/KDI/GEO

Revisions.

The basic depth map is the Rtopo 30" by 30" global bathymetry. This is used in the North Atlantic. In high-resolution domains, rtopo is combined with local depth information from various sources.

The North Atlantic model uses the JONSWAP wind-sea spectrum along open model boundaries. The fine grid North Sea - Baltic model is nested into the North Atlantic model, and uses time/space interpolated boundary wave spectra calculated by that model. The Transition Area model is further nested into the North Sea - Baltic model.

The wave energy is discretized into 36 directions (10° resolution), and 35 frequencies ranging from 0.04177 Hz to 1.06417 Hz in 10% steps. That corresponds to wave periods of 0.94-23.94 seconds, and wave lenghts of 1.37-895 meters (in deep water). To avoid excessive shadow effects from islands, the spectral directions are shifted away from the major compass directions. To speed up wave growth from calm sea, the spectral energy has a lower limit corresponding to a wave height of 11.3 cm. This parameterises capillary waves. Depth-induced wave breaking (method taken from the SWAN wave model) is used in the North Sea - Baltic Sea and Transition Area models only. In the North Atlantic model, the depth maps are not detailed enough for activation of this effect.

DMI-WAM is coldstarted once and for all using fully developed sea. Subsequent model runs are initialised using the sea state at analysis time, calculated by the previous run as a 6 hour forecast.

The 10 meter wind forcing is provided by DMI's limited area nwp model Harmonie, version NEA (2½ km resolution). Harmonie provides 2½ days of forcing. Forecasts beyond that are based on the ECMWF global weather forecast (9 km resolution). Harmonie wind is available every hour, ECMWF data every hour until 2½ day forecast range, 3-hourly beyond. To diminish coastal effects, DMI-WAM uses a special Harmonie 'water-wind', in which the surface roughness everywhere is assumed to be that of water. This enhances the wind speed in the coastal zone, most important in semi-enclosed areas (bays, fjords, ..).

The ice concentration is daily OSISAF (radar-based) maps in ~10 km resolution. The maps are preprocessed to weather model grids, and then further onto wave model grid. A grid point is considered ice-covered when the concentration exceeds 0.3. The ice cover is kept constant thru each model run.

DMI technical report DMI-WAM Version 4 (pdf) of May 2003.

DMI-WAM is verified on a daily and 6-monthly routine basis versus buoy data, and on a 6-monthly routine basis versus satellite altimetry data. DMI-WAM further takes part in a comparative validation exercise, that is updated automatically every month at ECMWF and published on the LC-WFV (WMO / ECMWF : Leading Center for Wave Forecast Verification) project home page.

DMI verifikation
LC-WFV project description

DMI-WAM was first put to use medio 1999. Output has been archived since April 2000. Some model domains were not implemented until later years. For some model domains, an 11 year re-run has been carried out using the most recent version of DMI-WAM. This archive contains the years 2003-2013.

A frequency distribution analysis of wave height has been carried out, based on 1-7 years of DMI-WAM output. Please refer to the wave statistics page.