Review of “The wave-age dependent stress parameterization (WASP) for momentum and heat turbulent fluxes at sea in SURFEX v8.1.”

Very interesting paper, giving a comprehensive summary of the work done to developed WASP parameterisation.

Here are my main comments:

Line 67: “the dependence of the drag coefficient on the wave growth is not relevant for wind speeds higher than 30 m/s”. Whereas I agree that for very strong wind conditions, other physical processes might become relevant than for calmer condition, I would not state that “the dependence of the drag coefficient on the wave growth is not relevant for wind speeds higher than 30 m/s”. Recent work by Janssen and Bidlot (2023) showed that aspect of the wind-wave interaction for strong winds become a bit more subtle, with direct nonlinear feedback on the waves on the growth by winds, therefore a direct impact on the momentum exchange at the surface.

Peter A.E.M. Janssen and Jean-Raymond Bidlot, 2023. Wind–Wave Interaction for Strong Winds" (10.1175/JPO-D-21-0293.1). Journal of Physical Oceanography, vol. 53, no. 3.

https://journals.ametsoc.org/view/journals/phoc/53/3/JPO-D-21-0293.1.xml

Line 69: I agree for the need to reproduce the saturation/decrease of the drag coefficient for strong winds. As a motivation for the extension of the wave generation theory of Janssen (Janssen and Bidlot 2023) (to be implemented in 2024), a simple empirical adjustment of his original work was implemented a few years ago (2020) in the coupled system at ECMWF. The impact of which was essential in obtaining decent forecast results in global simulations of tropical cyclones at high resolution (for a global system, 4.4 km) (Majumdar et al. 2023)

Majumdar, S. J., L. Magnusson, P. Bechtold, J. Bidlot, and J. D. Doyle, 2023:

Advanced tropical cyclone prediction using the experimental global ECMWF and operational regional COAMPS-TC systems.

Mon. Wea. Rev., https://doi.org/10.1175/MWR-D-22-0236.1, in press.

Line 70: the statement that the heat exchange coefficient shows no clear dependence on the wind speed, nor the sea state is a bit misleading as later with equation (7), a dependence on z0 is used, which has been shown to have such dependence. I know this results in a weak dependence and (7) comes about from scaling arguments and the experimental results have large scatter.

Line 105: Note that Janssen (2004) makes the point that the wave age parameter should be defined with the friction velocity (u*) rather than U10 since u* will vary even when U10 is constant. Since (6) is a bulk parameterisation fitted to a cloud of experimental data, it is probably a fair assumption.

Line 130: Cp in (6) is for the peak of the windsea spectrum. Do you make sure to only consider the windsea spectrum when determining the wave peak period (Tp) from which Cp will be determined, otherwise Tp might correspond to the swell part of the spectrum that has nothing to do with the local wind generation?

Line 190: Please refer to Janssen and Bidlot (2023) for a novel modelling of the high frequency gravity-capillary spectrum.

Line 194: why would the coupling via the Charnock coefficient prevent the comparison of wave parameters with observations?

Line 195, (ii): I disagree, this is just parameter fitting to observed data sets.

Line 309: which version of WW3?

Minor corrections:

Line 49: ratio of the wave peak period to the near-surface wind -> ratio of the wave phase speed for the peak of the wave spectrum to the near-surface wind

Line 292: in link -> in line

Lines 315-327 are repeated.

Line 399 and 401: IFS -> operational ECMWF forecasts

Line 445: whatever the wind speed below -> wherever the wind speed is below

This paper describes a package of air-sea flux parameterizations called WASP as executed in  SURFEX v8.1.  The idea is to update to parameterizations of momentum, sensible, and latent heat based on a collection of direct and indirect observations taken from the literature.  Because the transfer coefficients are considered well-constrained by tens of thousands of direct observations for wind speeds 0-25 m/s, the authors emphasize the wind speed regime greater than 25 m/s.  So, WASP is a good fit to existing parameterizations such as COARE in the 0-25 m/s range.  The authors attempt to reach a crude consensus representation of the data for U>25 m/s.  The approach is to throw everything they can find (uncritically) into wind speed bins and produce a mean fit, sort of. The new package is then run in several different models for mesoscale weather and global climate model implementations.  The results from WASP and other competing models are compared. 

The authors face a well-known problem – the existing high-quality data describe the fluxes for U<25 m/s but modeling centers and researchers insist on running their models in hurricanes and other high wind speed events well outside the constraint boundaries.  We have to provide them with our best estimates of the transfer coefficients regardless of the quality of the observations.  Yes, for U>25 m/s we have a collection of bad or uncertain data, but the average of bad = good, right?  It is easy to quibble with details of what the authors have done.  For example, Black et al 2007 and French et al 2007 are the same data.  Or, why include data from 1976?  Or, if a data set’s value for Cd is 25% below COARE at U=23 m/s, why would you trust if for U=28 m/s? Or, if WASP if a good representation of Cd for U>45 m/s, why to do 8 data points fall above WASP and only 3 points fall below in Fig. 2B?  Reasonable quibbles, but a glance at Figs. 2 and 2b suggests it makes no sense for this reviewer to second guess the authors.  Is WASP better than just capping Cd at U=30 m/s?  I have no idea.

So, on balance I recommend publication of this paper but with some substantial changes to address problems with the manuscript.  My more important issues are

1. The presentation of the data and the various figures is a bit chaotic.  I have trouble figuring out exactly which data went into which figures.  Perhaps there are too many such figures? The authors state using a data base of 27,000 values for C3, 21,000 for Ch, and 24,000 for Ce and refer to Table B1.  But, the data in Table B1 are likely less than 1,000 points.  And none of the data in Table B2 (way less than 20,000 observations) were used in COARE fits.  So where do the 72,000 values come from?
2. The authors need to make it clear that the use of the Gulf of Lion buoy data and the case study intercomparisons model outputs in section 3 are not actual validation but are model intercomparisons. There are no actual direct flux observations involved.
3. I have my doubts about the value of the comparisons done in Section 3. Do they provide a basis for deciding WASP is superior to ECUME or ERA5? 
4. The authors make some claims about the change in processes that lead to the saturation and decrease of Cd with increasing wind speed. They state in several places that this is due to the transition to a state with no ‘wave growth’ because of a balance with wave breaking. The is a difference between wave energy and momentum input from the atmospheric (via the pressure-slope correlation) versus increase in the actual wave energy (increasing significant wave height) which you might characterize as ‘growth’.  It is doubtful there is a balance between pressure input and dissipation in hurricanes (which have relatively young waves) but even if there is it does not require Cd to level off or decrease.  If the authors wish to invoke a mechanism, I suggest they spend some time to make a clear and defensible argument.
5. The use of the oceanic momentum budget data sets given in Table B3 might be worth pondering. There is a difference in the momentum removed from the atmosphere (say, inferred from dropsonde on measured with sonic anemometers) vs the momentum realized in ocean currents and/or input to waves.

Here are a few other editorial comments

Eqs. 1 and 2.  The authors have ignored gustiness (distinction between mean wind speed and magnitude of the mean wind vector) in their parameterization.  This leads to Cd, Ch, and Ce becoming singular as wind speed approaches zero.

Fig. 1  Doesn’t it bother the authors that WASP and COARE curves fall well below the average of the data for U<8 m/s?  Is this a consequence of ignoring gustiness?  Why are there more black data than blue data?

Figs. 2 and 3  I don’t see the COARE 3.0 line.

Fig. 5.  That caption is confusing.  I think the dots in 5a are the wave dependent COARE3.5.  The green line is misidentified.  A good figure because it shows the Oost and Taylor wave formulae have problems.

Line 199 Not sure WASP dependence on wave age is shown.

Fig. 7.  This figure is confusing and hard to interpret.  Nice try, but it doesn’t work.  Suggest you find something simpler.

Line 256  What is ‘wave effect dependent on wind speed only’?

Line 310-318  This text is repeated in 318-327.

Table B1.  I doubt these data were used by Edson et al. 2013. 

Perhaps compare WASP to the GFDL parameterization of Cd in

Chen, Xuanyu, Tetsu Hara, and Isaac Ginis. 2020. “Impact of Shoaling Ocean Surface Waves on Wind Stress and Drag Coefficient in Coastal Waters: 1. Uniform Wind.” Journal of Geophysical Research: Oceans 125 (7): e2020JC016222. doi:10.1029/2020JC016222.