Le modèle WAVEWATCH III

WAVEWATCH III est un modèle numérique qui calcule l'évolution de l'action des vagues. Il est fondé sur une décomposition spectrale (de Fourier) de l'état de la mer ...

On calcule les propriétés des vagues à différents points qui forment les noeuds d'un maillage de l'océan. L'espacement de ces noeuds est plus ou moins grand et définit la résolution spatiale du modèle (de quelques mètres pour desa pplications littorales à ds dizaines de kilomètres quand on traite tous les océans). 

A chaque noeud de ce maillage, l'état de mer est décomposé en un spectre: le spectre donne la distribution des énergies des différentes "composantes". Chaque composante est une famille de trains d'ondes de périodes et direction proches. S'il n'y avait de l'énergie que dans une seule composante la mer aurait une forme de tôle ondulée. La somme de toutes les composantes de directions θ et fréquences f est l'état de la mer. A droite, un exemple de spectre en fréquence est en noir. Pour chaque fréquence on peut redistribuer les énergies sur les directions de propagation, ce qui donne le diagramme en couleur.

Les énergies des vagues s'additionnent. On les mesures en mètres carrés.Rigoureusement il s'agit de la "variance de l'élévation de surface" E, pour avoir une énergie par unié de surface il faut multiplier E par la densité de l'eau de mer (1026 kg/m3 environ) et la gravité g. Ici, l'aire en noir est E=0.6 m2 , ce qui fait une énergie Et=6 kiloJoules /m2.

This energy changes in time and space as the waves are generated by the wind, propagate, and dissipate.

In order to track the evolution of this energy (for example for weather forecasting), the model WAVEWATCH III computes the evolution of the wave spectrum from one ocean location to another, by solving the Wave Action Equation (WAE),

local evolution in time +[ propagation  + turning of the waves ] = generation  + exchange of energy - dissipation

This equation is written for EACH spectral component (typically 24 direction x 32 frequencies), and all these equations are coupled by the terms:

  • "turning of the waves" (energy from one direction is shifted to energy from another direction)
  • "exchange of energy" : the different wave trains permanently exchange energy between them and with currents
  • dissipation: the dissipation of one wave component is a complex function of the energy of all components
  • generation: the amount of energy given by the wind to one wave train can also depend on the other wave trains

Models such as WAVEWATCH III differ in their method from the old "ray tracing models" that conserved energy due to the last 3 interactions. When the energy of a wave component is nearly conserved ray tracing is a more simple method for tracking the energy ... but this is not the case in general.

It is customary to summarize the sea state by a few numbers. The most common is the significant wave height Hs=4√E  .  The maps shown above with wave heights are computed with WAVEWATCH III: at each point of the ocean the full spectrum E(f,θ) was computed and from that spectrum we computed Hs.

The main reason for using such a rich spectral decomposition, introduced in the 1950s by Gelci and his colleagues, is that the wavesdisperse: each component travels at a different speed and in a different direction.  In very shallow water the waves tend to travel at the same speed and other methods can be much more efficient.

The cost of a wave model can be much larger than that of an ocean circulation model with the same horizontal resolution because the wave model usually carries many more variables (the spectral densities) compared to the velocity, temperature and salinity at different levels.

The accuracy of wave models critically depends on :

- the accuracy of the forcing fields (winds, currents, sea ice, bathymetry, bottom roughness ...)

- the accuracy of the parameterizations that represent the generation, exchange and dissipation  processes

- the quality of the numerical methods used to solve the WAE.

For recent reviews see Rascle and Ardhuin (Ocean Modelling 2013) and Roland and Ardhuin (Ocean Dynamics 2014)