Indeed, as described in the preprint that the sea surface wind and waves are important parameters for the marine environment and ocean dynamics. This also implies that the interactions between them involve complex dynamic procedures resulting in the intricacies of coupling between them that make their individual characteristics difficult to resolve. Buoys on one hand though with limited amounts and distributions have been long providing good measurements of both wind and wave parameters respectively and simultaneously, on the other hand making complementary to remotely sensed wind and waves from satellites. The wind-wave interaction can then be modelled from buoy observations, while deep learning provides powerful tools in non-linear modelling and regression. The author thereby applies a deep neural network (DNN) for extracting wind information from wave spectrums provided by buoys for further applications to buoys without wind measuring ability benefitting such buoys with lower costs. The motivation and origin of this research are reasonable and good. 

Unfortunately, the research in this preprint falls into the trap set by that the DNN theory that can fit all models provided wide enough (though which is true mathematically). This may be due to ignoring that the meaning of the DNN model expressed is data and inputs-outputs dependent or self-consistent within such boundary. The model is only physically meaningful than mathematical results when not only the data or inputs are of good quality but also considering underlying physical principles to an extent a DNN can resolve. This can also be expressed with the state for one of the challenges for the application of artificial intelligence in ocean science: moving from purely statistical prediction to process-based models that embody causal relationships (Catalán, I., A. Solana, et al, 2021). 

More specifically for this research, it applies the spectrum parameters all at once as inputs for wind speed and direction ignoring the underlying multi-scale heterogeneity in time and space due to the complex relation of the interface interaction that can be embodied by a spectrum interpreting them in different approximations of the governing equation for energy distributed for different k values. Such approximation cannot only be expressed in another way round by expanding the observed energy distributed for different k values (spectrums are fitting of the observations) for another fitting from DNN. In other words, here DNN makes little extra contribution than the observed spectrum from this research. What is captured by DNN cannot be clarified makes things worse. Around Line 115, from the results, “the wave spectrum might also better reflect wind information a short period before” is contradictory to the fact that wind-wave spectrum ranges from lower frequencies to higher frequencies due to momentum transformation between waves of different lengths. For wind estimation, short wave measurement is relevant while the modulations from longer waves are non-negligible, from tilting effects to the short waves or modification of amplitudes of the short waves by exchange of energy altering atmosphere conditions close to the sea surface.

Moreover, though the training procedure is mathematically accomplishable, as in the preprint, where the results can be validated in error analysis from the testing set. Let alone the comparison of results to remotely sensed winds are not validated ignoring representative features of remote sensing results and buoy observations. Buoys generally provide the spot-based measurement of winds while remote sensing results are averages of a large region. The distributions of samples for each wind (and direction) bin are not discussed, the sample number may be skewed due to distributions of nature winds, while such effects are ignored in this research. 

Although some sensitive analysis for inputs as the selection of frequency discussed in part 4, this was unfortunately misinterpreted as well, due to the little effort taken for understanding the relation between observed inputs and outputs. This is similar to the results part around line 115, longer waves are with wind information that cannot be resolved by the mapping to winds from the DNN established directly fitting the observations.

The discussions following such content are not proper as well. When the model boundary is not clear due to the aspects listed above, there is little chance for these DNN models to apply in QC procedures or other applications. The results are also not likely to be improved including compact wave drifters, as the air-sea interaction in different scales is not likely to be well described in the reasons above.

To wrap up, for such a model without awareness of the causalities between the inputs and outputs, especially under the circumstances such causalities are complex and wraps between even inputs and outputs, the deductions made based on them can easily go wrong. This is exactly the case for wind-wave interactions, such that improper analysis generally appears here and there for this preprint. 

There are also other defects in descriptions:

1) around line 25, the description of the lack of meteorological buoys may be inherited from the reference (Voermans et al, 2020), while this is only partly true. There are such buoys available in India (NIOT, National Institute of Ocean Technology) and China (NOTC, National Ocean Technology Center). There are also publications applications applying such buoys though NOTC is currently not openly accessible. 

2) Around line 30, as mentioned before, short gravity-capillary waves are modulated by longer waves, though in the case of scatterometry, the orbital velocity of longer waves cannot be observed, and the tilting effect may not be obvious for them modulated to gather on the crests, by modulating the surface wind stress that changes the amplitudes of the short waves, which cannot be ignored, the long wave information does exist in scatterometer observations.

3) Around line 30, the measuring in the nadir of altimeters does not result in low spatial resolution cross-track, maybe the coverage cross-track is low was meant to express.

4) Around line 35, low temporal resolutions do not cause low performance near shore. There are near-shore products from scatterometers for example. Besides, inter-constellation will solve the coverage problems to an extent. 

5) Around line 45, again, direct comparisons of buoy results are remote sensing products are not validated. 

6) After all listed above, It is difficult to believe this research is included in the projects listed around line 255.

In all, I suggest a rejection of this manuscript for publishing.

Catalán, I., A. Solana, et al. “OCEANS OF BIG DATA AND ARTIFICIAL INTELLIGENCE.” OCEAN SCIENCE CHALLENGES FOR 2030. 2021

The author assume that the referenced power law adequately describes the impact of boundary-layer stability, whereas the authors of the power law point out that it applies only to near neutral conditions.  Such an assumption will often be valid for strong winds (U10 > 15 ms^-1), however for wind speeds <7 ms^-1 the departures from neutral conditions are likely to be substantial. Furthermore, buoys measure winds relative to the fixed Earth where as stress, which drives waves, is dependent on surface relative currents. For lower wind speed cases the impact of currents could be substantial. While this is mentioned later in the manuscript, it would be wiser to address it earlier and perhaps in the quality control of the input data.

What (if any) quality control was applied to the data? Frankly, a paper should not be submitted without this information. If any quality control was applied, why was it applied and why is it likely to be sufficient?  If it was not applied, then why is it not needed?

The Fourier characteristics of waves are poorly described and need to be much more clearly explained.

Does the lack of approximately uniform distribution over the parameter space impact the quality of the results, particularly for conditions that are poorly sampled? Normally there is a very large impact, with the results only applying to the conditions near the peak of the probability distribution.

Are the different Fourier components combined to produce a better result? I assume so, but the math suggests otherwise.

Can the one hour delay be better demonstrated with statistics and an appropriate graphic? It should be possible to show this result in a manner than much more clearly illustrates the width of the peak correlation or a time offset in the DNN.

Errors in the results are attributed to strong currents, but these errors are far larger than expected due to currents (at least in Figure 3a, and unlikely in 3b). Buoys don’t survive long in such strong currents.  Please consider alternative explanations or find evidence that the currents do exist.

In summary, the methodology needs to be greatly improved. The accuracy assessment should not be presented as an overall single value for the dataset, but rather as a function of wind speed. The explanation for the cause of large errors is highly unlikely to be correct, although I appreciate the authors efforts to provide an explanation. The lack of check the quality of the input data, the physics of the adjustment to a 10m wind, and poor assessment of the quality of data should be addressed.

This study is clearly presented and well written. The objective is to improve upon the recent work of Voerman et al. (2020) that attempted to invert near-surface wind speed and wind direction from ocean wave buoy datasets provided by the NDBC network of coastal and offshore buoys.  That previous study provided a thorough review of wind-wave interaction as it pertains to buoy measurements and this inversion.  The present study bypasses the geophysical basis and instead focuses on a sort of brute force neural network (DNN) approach to the wind estimation task using the NDBC data archive of five freq. dependent Fourier coefficients that are used to approximate the directional gravity wave spectrum from long to intermediate scale surface waves (both swell and wind sea).  The study appears to use data from the entire buoy station network to develop separate wind speed and direction algorithms, provides detail on the network training and several relevant DNN adjustments during the training process, and then results that show some promising capability to provide wave-buoy derived wind estimate that agree better with the buoys' anemometer measurements.  They also find that the winds derived in this manner appear to lag behind the actual surface winds in time by 30-60 minutes - and thus their final algorithm estimates not the wind at the present time, but actually the wind that occurred one hour before.   They also find, as did the recent Voermans et al. study, that their best algorithms still have limitations at lower and higher wind speeds where the wave information does not unambiguously relate to the wind.

Comments to the authors:

While this paper does show some potential for a neural network algorithm that takes the basic directional wave information provided by NDBC and outputs wind information, it does not appear to move things too far forward from the Voermans study they follow on from and the low and higher wind speed regime limitations that were highlighted in that study.  What it does illustrate is that a DNN can improve on the semi-analytical approach used in the previous investigation.  

The finding that there they is an apparent delay between the wind speed and the wave-inferred wind speed is not physically inconsistent with Voermans et al. (2020) Figure 9g where the wind acceleration is related to model error residuals.  However, there is an additional issue for the authors to consider first.  The wave buoy measurements provided by NDBC have a center time that is 30 min past the top of the hour with data collected +-10 min of that time.   The authors do not clearly provide detail on the NDBC wind products they are using, but if that product is the stdmet product then the center time for that 8 min. avg wind estimate is at minute 46 (measurements made from 42-50).  Thus there is an inherent 15 min offset with the hourly wave data leading the wind.  This factor may also color why the previous wind measurement is more highly correlated with the wave-inferred winds.  Finally, the NDBC network does contain a large number of continuous wind measurement buoys where winds are measured every 10 minutes.  Thus the authors have the opportunity to investigate the actual lagged correlation between DNN wave-derived winds and the anemometer data with 10 min resolution and perhaps at varying wind speeds.    

Regardless, this issue points outs that using a series of DNN models to sort this out is an indirect and poorly-posed reverse engineering approach to infer the growth or dissipation rate of wind waves, as well as an illustration of the fundamental limitation in the use of surface waves to provide accurate wind measurements under a full range of wind forcing and sea states discussed in Voermans et al. (2020.   

A significant concern related to this time delay is the need to explain the potential implications of their DNN-derived estimates for users such as forecasters.   The final DNN models are tuned to give wind speed and direction from the hour before.  Thus I believe the first sentence of the Concluding Remarks should clarify this point.  I believe the authors should consider a revisit of this product.  Perhaps they should provide statistics and models for two wind options, the nearest time wind and the previous hour winds?   

The model sensitivity tests in the discussion section are an ad hoc revisit of the more in-depth work of Voermans et al. (2020) and previous work (e.g. Jusko et al., J. Phys Ocean. 1995).   But simply withholding part of the frequency spectrum from the inputs does not provide new results.  It confirms, as the authors note (lines 205-210), what has already been shown in terms of the importance of the higher frequency portion of the spectrum closer to the wind sea peak frequency and the tail of the spectrum.  The authors appear to perform this test in the same way for all wind speeds and conditions and perform the RMSE assessments similarly for all winds.  This is a course sensitivity test.  Perhaps something more creative could be done to investigate the potential to modify inputs with a goal to improve performance at low and high wind speeds?

General comments:

More detailed information on the specific wind and wave buoy products that they used in training, their data filtering and quality control, and references describing the approach that NDBC uses to extract the directional wave Fourier coefficients should be provided.

Given what is observed in terms of data quality in the section surrounding Figure 3, is there any concern that such corrupt data are present in the training and/or validation datasets?   Moreover, as noted in the next paragraph, it would seem to be obvious that the algorithm training set should not include buoys where there is strong known wave/current interaction such as 46087 and 46088.   This would be a highly unusual case of wind-wave-current interactions that would not be desired in a general-purpose wind algorithm that only uses the 5 Fourier coefficients and no surface current data as inputs.

Similarly, was there any consideration given to differentiating between coastal, offshore, and/or differing wind-wave climate buoys in the model input training sets to improve performance, for example at low or high wind speeds. 

The authors seem to be interested to develop a wind measurement system that competes with a satellite scatterometer or altimeter, but this project is inherently dealing with in an in situ platform.   Is not the goal to develop an in situ system that has precision and accuracy metrics similar to those of the 10 min averaged wind anemometers used at sea?