Hello,
I’ve been playing quite a bit with global hindcast using Snl computed with the Gaussian Quadrature Method (GQM) using the great piece of code from Michel Benoit to do so. Since everything has to be retuned now that we do not have Snl errors anymore, I did play quite a bit with the magnitude of the different source terms… but then a thought from the same 2001 paper by Lavrenov keeps haunting me: “The results of numerical simulation shows that wind wave parameter fluctuation produces a significant increase effect of the nonlinear wave spectrum evolution. The present study results in a parameterization, which is made possible taking into account this effect in spectral wind wave models.” Effect of Wind Wave Parameter Fluctuation on the Nonlinear Spectrum Evolution in: Journal of Physical Oceanography Volume 31 Issue 4 (2001)
In other words, how well do we know the magnitude and shape of Snl in real conditions? … and I’m particularly looking at storm conditions with mature wind seas (dominant waves with wave age 0.5-1).
My naive view (backed up by the analysis of lots of data) is that fluctuations are primarily driven by the random phases of the linear waves, which very well explains wave group statistics and fits the data (there are always doubts due to the limited knowledge of the full 2D spectrum … so probably I should test it again with stereo video data … but I’m not expecting big surprises).
In that context I do not see why we should change the Snl because the amplitudes of the linear components are constant - when using a super finely resolved spectrum - but if we coarsen the spectrum, there will be fluctuations. In a way, I’m wondering what is the proper level of coarsening that should be applied to a spectrum to compute Snl from it … if that makes any sense.
Caveat emptor: My thoughts are not fully formed. And I did not read Lavrenof.
I think this hits at the heart of what we mean by scale separation, the spectrum, which parts are stochastic and which parts are deterministic. The wavenumber spectrum is always hand-wavily defined as a quasi-stationary and quasi-homogeneous representation, allowing for a phase-space representation in a position / momentum space.
The price you pay for this is that you must accept a certain fuzziness in your spectral description, as you cannot precisely pin down the wave in location and spectral position at the same time. The more precise we want to capture the mean energy variation in space `deterministically’ (e.g. on the “wave group scale”) - the more we have to accept fuzziness in the spectral description (we cannot pin it down well in wavenumber space anymore). Note that once you start to calculate on a group scale you have to let go of the assumption that components are uncorrelated to a certain extent as well. At this level of detail I suspect you cannot get away with some of the closure assumptions we have on large space/time scales anymore and would formally have to evolve higher order moments.
However - if we calculate variations on the “storm scale” - all these fluctuations are no longer resolved deterministically, and are absorbed into Snl just fine. However, we have to accept that it is a prediction of the mean; and that means that actual transfers may differ.