Wave model
Dansk version
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 DMI-HIRLAM 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.

Daily routine
DMI-WAM is run 4 times a day. The platform is The DMI Cray-XC, a very powerful supercomputer. DMI-WAM uses 144 processors (9 sixteen-core Cray cpus).

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

Wave forecasts
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:

Farvandsudsigter (in danish)
Havprognoser (in danish)

Output parameter table.

Model set-up
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 hirlam SKA
hirlam SKA
boundary JONSWAP nested nested
depth map Rtopo Rtopo/IOW/KDI Rtopo/KDI/GEO


Depth maps
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.

Model boundaries
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.

Energy spectrum
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 7 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 DMI-HIRLAM, version SKA (3 km resolution). Hirlam provides 2½ days of forcing. Forecasts beyond that are based on the ECMWF global weather forecast (16 km resolution). Hirlam wind is available every hour, ECMWF data every 3 hours. To diminish coastal effects, DMI-WAM uses a special HIRLAM '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, ..).

Sea Ice
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 Jcomm (Joint WMO-IOC Technical Commission for Oceanography and Marine Meteorology) home page.

DMI verifikation
Jcomm verifikation

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.

Jacob Woge Nielsen - March 13th 2017