see attached review

Review of "Measurements of Nearshore Waves through Coherent Arrays of Free-Drifting Wave Buoys"

This article compares surface gravity wave statistics as measured by GPS and IMU equipped "microSWIFTs", or "mSs" for short (essentially a drifter), to an AWAC (an ADCP). Although this article is informative and should be published, I believe it should only be published after minor to major revision. 

I will first comment on a couple "bigger" concerns that I have. 

1) The main point of this article is to compare the significant wave height from small drifters equipped with an IMU and GPS to a nearby AWAC. I think the main difficulty with this analysis is that the mS's drift past the depth of the AWAC quite quickly, such that there is relatively few mS observations at the same water depth as the AWAC. The authors are aware of this (eg. line 40) and this is discussed at line 201, 212, 234 etc. 

As such only mSs close to the AWAC depth are used in the comparison and there is few mS observations used in the comparison. I believe that the authors might be able to get more mS data to compare as long as the mSs are not within the inner surfzone with active wave breaking. I believe this as Hs should be similar offshore to the break point as it only increases slightly (~10%) as waves shoal to the break point. The critical spot is the break point and not so much the exact same depths. Perhaps the authors could get more data this way?

If they can, I would like a more detailed comparison between the spectra of the mSs and AWAC and not just the mSs that have similar depths as the AWAC. Currently the only comparison in the MS is between the AWAC and mS Hs and a_0(f), the SSH spectra. This is a limited comparison. I think the analysis should be extended to compared mean periods, mean directions, and directional spreads. The analysis needs to be expanded to include aspects of the wave field in addition to the significant wave height. I also believe that the authors should calculate Hs as the integral of the spectra over sea-swell frequencies and not from the distribution of wave heights as they should be the same. If possible Hs from AWAC and mSs should be calculated in the exact same manner. Also, getting the significant wave height as the mean of the top 1/3 wave heights (line 235) isn't as straight forward as 

Hs = <H^2>^{1/2) 

or 

Hs = (8/pi)^(1/2) <H>   (1.6 times the mean of all wave heights)

where H is the random wave heights. Recall, Hs = 4<eta^2>^{1/2} and eta=H/2. As, the distribution of H is Rayleigh distributed, there is only 1 free parameter (Hs). see 

https://en.wikipedia.org/wiki/Rayleigh_distribution

it would be more straight forward to calculate Hs this way and it should be more robust than the mean of the top 1/3 waves (which limit the number of waves you use by 1/3!). The mean of top 1/3 merely a consequence of a Rayleigh distribution with only 1 free parameter (and gets rid of the 1.6 factor for all waves). And it would be easier to derive error bars (see link above). 

2) This article purports to compare wave statistics from mS's and an AWAC. And the article does compare Hs (significant wave height) between the two instruments. The article also compares the SSH (see surface height) frequency spectra between the instruments. I believe this article would be greatly improved if additional statistics  were compared such as mean direction and directional spread (like in Ragkukumar et al 2019). See also comment above.

3) I believe that a more detailed exploration of the uncertainty in Hs (for instance) should be explored. What is the 95% CL of the AWAC Hs? What is the 95% CL on the mS estimate. The authors should look at Gemmrich et al 2016 regarding this calculation. Are the differences in Hs between mS and AWAC real or statistical? The article would be greatly improved if the authors can state whether the differences in Hs between the instruments are within expectations. If there are real differences in Hs, reasons for the differences should be explained. 

4) Only wave statistics are compared in this article but I think the currents could be compared as well. How do mean currents compare? How much of the mean on-off shore velocity can be attributed to Stokes drift? Do the mS's surf broken wave bores? 

Line by line comments:

Line 41. When discussing wave statistics, the authors state "Fixed sensors generally have robust statistics since they measure continuously for long periods." This feels misleading to me. Most fixed sensors, such as a wave buoy (or ADCP), measures the variance of SSH over a fixed duration, say 30 min, ie. var(eta). Then Hs = 4 * (var(eta))^(1/2). As this is done every 30 min (or 20 min), there is now a time series of Hs. The robustness of a single estimate of Hs doesn't have anything to do with the instrument being fixed as you could get the same estimate from a drifting instrument (see Herbers et al 2012) as long as it sampled for 30 min straight and it samples a statistically stationary wave field. In this article, the issue is that the mS's don't sample a statistically stationary wave field as they drift through the surfzone (see big comment #1 above). 

Line 131. The authors say, "However, when deployed in large numbers as coherent arrays, the mS's can be processed together to explore the spatial variability of the nearshore waves and currents." Is this done here? This article does not explore the spatial variation of the wave field. I believe that it should and show that Hs decreases shoreward consistent with expectations. 

Line 192. When discussing the AWAC wave statistics, the authors should describe the statistics in much better detail. I suppose that the AWAC gives: a_0(f), the SSH spectra, a_1(f), a_2(f), b_1(f), b_2(f). From these the AWAC estimates: Theta(f), the mean direction at each frequency; and sigma_Theta(f), the directional spread at each frequency. These statistics should be listed in a methods section. In that section, how the AWAC computes these statistics should be stated. ie., How long is the record for which a_0(f) is calculated? The number of degrees of freedom is stated at 48, where does this number come from? Also, the authors state at line 206 that there are 51 degrees of freedom for the mS a_0(f). How does one get an odd number of degrees of freedom for a spectra? I calculate the DOF as 2x3x5=30: 2 for each periodogram, 3 for 3 separate 5 minute chunks of data (these are not completely independent, and 5 for averaging 5 independent frequencies.

Line 216. "... some of the mS's will be measuring the same wave as it propagates ... which improves the robustness of the statistics by sampling many realizations." I don't think this is correct. In order to increase the robustness (ie. get an estimate closer to the true value), it is necessary to sample different regions (or times) of the wave field (eg Gemmrich et al 2016). If two mS's have the exact same 10 min z(t), the 2 estimates of Hs are the same and I would argue less robust. In this case, having mS's far from each other, so they are not coherent, would increase the robustness of the estimate. Fig 9 in Raghukumar et al 2019 suggests that 50 m is the length scale over which waves decorrelate. This suggests a thorough investigation of the errors in estimating Hs.

Fig 1. Add LLW and HHW levels to Fig 1c for reference.

Fig 5a,b. Add a dashed line where wave breaking starts. Do the mSs sample a region of broken waves? Where is the shoreline. How wide is the surfzone?

Fig 7a,b. Add a dashed line where wave breaking starts. Do the mSs sample a region of broken waves? Where is the shoreline. How wide is the surfzone? 

Fig 7c. The lines are very hard to tell apart. Choose better colors, especially for the AWAC (thick black?). Also choose some different thicknesses. Hs for each should also be stated in the caption. Maybe also show the mean of all mSs? Then the individual mSs could be thin gray. 

Fig 8a,b. Add a dashed line where wave breaking starts. Do the mSs sample a region of broken waves? Where is the shoreline. How wide is the surfzone? 

Fig 9. Not sure if this figure needs to be included. It could be improved too. Use contour rather than contourf for the the bathy. 

Fig 10a,b. std bars are on mSs Hs in 10a but on AWAC Hs in 10b. Shouldn't the error bars in 10b be on mSs as they are the same as in 10a? In 10b, error bars on should be on the AWAC and mS estimates. Also, these should be 95% confidence limits, not stds as the reader will be interested in how good your estimate is and not how much scatter there is in the estimate. Please calculate correct 95% confidence limits based on the number of wave heights used.

Fig 10b. Although overall the scatter is OK (R^2 = .67), for AWAC Hs>2, there is little to no relationship between AWAC and mS Hs. This should be commented on in the Ms. Perhaps including all mSs that are not in the surfzone will make the relationship better? Perhaps, correct 95% confidence limits will help to explain when the relationship isn't so great?