Helmholtz-Zentrum Geesthacht, 2014-09-19

WAM Cycle 4.5

A Wave Prediction Model for Global and Regional Scales

Example 1 Example 1

Basic Characteristics

The WAM model is

  • a 3rd generation non-stationary surface wave prediction model
  • based on the energy density balance equation
  • in frequency – direction coordinates.
  • and was developed for large (i.e. global scale, North Atlantic, Pacific) and medium scale (Mediterranean, North Sea, Baltic, Great Lakes) deep or shallow water applications and is able to consider stationary currents and ice coverage. Multiple nesting is possible.
  • The model is forced by time series of
  • wind fields at 10 m above sea surface,
  • wave spectra at open boundaries ,
  • currents and water level fields.

Example 1

Example 2 (animation 1.9 MB) Example 2 (animation 1.9 MB)



  • deep or shallow water propagation,
  • depth and/or current refraction,
  • cartesian or spherical propagation.

Source functions:

  • wind input term ,
  • nonlinear wave interaction ,
  • dissipation by white capping ,
  • dissipation by bottom friction,
  • and optional wave breaking .

Example 2

Output Options

Wave information of total sea, wind waves and swell:

  • significant wave height,
  • wave periods (Peak, Mean, Tm1, Tm2),
  • wave direction,
  • directional spread,
  • wave spectra (frequency-direction).
  • forcing fields,
  • boundary spectra for nested grids.




  • first order explicit forward flux scheme,

Source functions:

  • fully implicit scheme

Different time steps for propagation and source function .


Model Equation





F: represents the spectral density with respect

             to (σ, q , j , l )

j: denotes frequencies

q: directions

l: latitudes

j: longitudes

rate of change of the position of wave packets in geographical and physical space.

Source function S:



Sin                           wind input

Sdis                         dissipation

Snl                           nonlinear transfer

Sbot                         bottom friction

Sbr                           wave breaking 



WAMDI Group (S. Hasselmann, K. Hasselmann, E. Bauer, P.A.E.M. Janssen, G.J. Komen, L. Bertotti, P. Lionello, A. Guillaume, V.C. Cardone, J.A. Greenwood, M. Reistad, L. Zambresky, J.A. Ewing), 1988: The WAM model – A third generation wave prediction model, J. Phys. Oceanography., 18, 1775-1810.

Komen, G.J., L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann, and P.A.E.M. Janssen, 1994: Dynamics and Modelling of Ocean Waves. Cambridge University Press, 532pp.