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 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 two sink terms are wave energy dissipation through wave breaking (white capping), and friction against the sea bed. Depth-induced wave breaking is not considered. Interaction with sea ice is included, while interaction with sea current is not. The wave energy is redistributed spatially by wave propagation and depth refraction, and spectrally by non-linear wave-wave interaction.

DMI-WAM is run 4 times a day. The platform is The DMI Cray-XT5, a very powerful supercomputer. DMI-WAM uses 88 processors (11 eight-core Cray cpus).

DMI-WAM runs
Analysis	00z	06z	12z	18z
Forecast range	132 hours	132 hours	132 hours	132 hours
Forcing	Hirlam ECMWF	Hirlam ECMWF	Hirlam ECMWF	Hirlam ECMWF
Run time	75 min	75 min	75 min	75 min

The model output is hourly forecasts of wave height, direction, and period, plus a number of other wave parameters. The full forecast is archived on tape in GRIB format.

Go to the DMI web pages to view the most recent forecast:

Farvandsudsigter (in danish)
Havprognoser (in danish)
ocean.dmi.dk

Output parameter table.

DMI-WAM has five geographical domains: the North Atlantic, the North Sea and Baltic Sea, the Transition Area (Danish Waters), the Mediterranean and the Red Sea (see figure and table below).

model	n.atlantic	n.sea-baltic	transition area	mediterranean	red sea
space step	1/2°	1/10° lat 1/6° lon (ca. 10 km)	1/50° lat 1/30° lon (ca. 2 km)	1/6° (ca. 20 km)	1/15° (ca. 7.5 km)
advection time step	3 min	1 min	20 sec	45 sec	30 sec
source term time step	12 min	12 min	12 min	12 min	12 min
number of directions	24	24	24	24	24
number of frequencies	32	32	32	32	32
sea points	11955	62863	31362	9513	13085
long	69W-30E	20W-30E	7E-16E	6W-36E	32.33E-50.13E
lat	30N-78N	36N-75N	53N-60N	30.5N-46N	10.47N-30N
forcing	hirlam T15 ECMWF GLM	hirlam T15+S03 ECMWF GLM	hirlam S03 ECMWF GLM	hirlam T15 ECMWF GLM	hirlam A ECMWF GLM
boundary	JONSWAP	nested	nested	closed	JONSWAP
depth map	Etopo5	Etopo1-2	DMI/BSH/KDI/FRV/Etopo1-2	Etopo5	Etopo2

(May 2005: North Atlantic model extended from 75N to 78N. Latitude resolution of North Sea - Baltic and Transition Area models increased.) (August 2005: Sea ice included.) (November 2006: 60 hour forecast range (was 54h).) (September 2008: New model code cycle 4.5) (July 2009: Hirlam E forcing (3km) replaces Hirlam S (5km)) (August 2009: New Red Sea model domain) (November 2009: 00z forecast extended to 5 days using ECMWF GLM forcing.) (November 2009: Frequency spectrum extended to cover 1.2-24s, 7 more frequencies) (December 2009: Forecast range extended to 5½ day) (December 2009: Test of depth-induced wave breaking started) (February 2011: Depth-induced wave breaking implemented in transition area. New depth maps, based o a number of sources) (February 2011: Depth-induced wave breaking implemented in North Sea - Baltic area. New depth maps based on Etopo1, pathced with Etopo2 in a coastal strip)

The depth maps are subsets of the Etopo5 5' by 5' global bathymetry. For the Red Sea model, the Etopo2 2' x 2' bathymetry is used. For the Transition Area model, the 1 n.m. Dynocs bathymetry is used.

The North Atlantic and Red Sea models use 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 Mediterranean is treated as a closed basin, assuming no wave energy exchange with the Atlantic or the Black Sea.

The wave energy is discretized into 24 directions (15° resolution), and 32 frequencies ranging from 0.04177 Hz to 0.80180 Hz in 10% steps. That corresponds to wave periods of 1.2-24 secs, and wave lenghts of 2.25-900 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 switched off at present, since it leads to severe underprediction at a few near-shore buoys. Depth maps must be revised before this mechanims is switched on.

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 taken from DMI's limited area numerical weather prediction model DMI-HIRLAM, versions S03 (3 km resolution) and T15 (15 km resolution). Forecasts beyond 2-2½ days (depending on model domain) use the ECMWF global weather forecast. Hirlam wind is available every hour, ECMWF data every 3 hours. T15 is used in the DMI weather forecasting service since July 2004. S03 replaced the former 5km version S05 medio 2009. To diminish coastal effects, DMI-WAM uses a special HIRLAM 'water-wind' where the surface roughness everywhere is that of water. This enhances the wind speed in semi-enclosed areas (bays, fjords, ..).

The ice concentration is daily NCEP 12z analysis in 0.5 deg. resolution. A grid point is considered ice-covered when the concentration exceeds 0.3.

See also the 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