Improved parameterization of swell dissipation

A threshold effect in the TEST441 parameterization of wave dissipation (Ardhuin et al. JPO 2010) has been corrected. The new parameterization, named TEST451, gives an average reduction of 4.2% in the error on the wave heights, and a much more realistic distribution of wave heights. This was done by smoothing the transition from a laminar to a turbulent atmospheric boundary layer. The change has been included in the Ifremer code repository (trunk, revision 513) and will be transferred shortly to NOAA/NCEP as part of the NOPP-supported project on the improvement of numerical wave models. The new parameterization should be used shortly by the Previmer system. Tests are under way to further optimize the results. This is the largest single improvement to the model parameterizations since the definition of the TEST350 parameterization, back in 2007.
All the IOWAGA and Previmer products that have a NetCDF attribute "software_version=4.05-Ifremer_revXXX", with XXX > 512, will include these changes.

Wave model results from the IOWAGA & Previmer projects have been used in the processing of Aquarius-SAC/D data by NASA, in particular the surface roughness estimates (or "mean square slope"). Before the launch of the satellite, about 1 year ago, Doug Vandemark (UNH) noted that our distribution of the wave heights was very different from the observations: the IOWAGA model was giving too many wave heights around 1.7 meters. That was likely due to a "threshold effect" in the way we represented the dissipation of swells: the dissipation of waves with Hs > 2 m was too large, and that of waves with Hs < 1.5 m was too small, so that all these waves ended up with a value around 1.7 m.

Looking up at the problem, graduate student Fabien Leckler found a trick to correct this: using a simple smoothing of the dissipation rate as a function of the Reynolds number which defined the laminar to turbulent transition and ... voilà !

Well, we would like to know why the swell dissipation behaves like this and get more direct data to measure this dissipation. Numerical experiments planned in the framework of the "Changing Ocean laboratory", may be one way to go.

So this works, but we are not sure why! If there is any lesson from the "model tuning" exercise, it is that it is always good to look at data and model results in many different ways. We had never looked at our results in the way that was most natural for Doug, making a histogram of the model values to see if they occur with the right frequency. We had made other kinds of plots that also showed the problem but never as clearly as the histogram plot.

As an aside, we may also wonder "What is the limit to the model accuracy?". A lot of that depends on the accuracy of the wind fields. In the stable trade wind areas the model accuracy reaches 5%. Maybe that is the limit. At any rate, to do better than what we have today, we will need to improve not only the wave heights, but also the energies of the different components that make up the sea state. This is the whole purpose of the IOWAGA project: combining very diverse observations, from seismic noise to stereo video data of breaking waves, and providing wave information for various kinds of users, from seismologists who study the solid Earth, all the way to space agencies that are trying to measure salinity or other things at the ocean surface.

In the plots below, the regions of the ocean that appear in purple are the areas where the model error is less than 7.5% of the mean observed value. These figures are for the year 2008. The largest improvements are throughout the tropics (except for the East Pacific) with local error reductions exceeding 30% (see bottom plot).



And here is a map of the relative difference in error: