Review of Revision to Measurements of Nearshore Waves through Coherent Arrays of Free-Drifting Wave Buoys
Overview & Big Picture:
I appreciate the authors changes made to the manuscript based on my and others reviews comments. I believe the manuscript is improved by zooming out a bit and not attempting to provide a rigorous comparison between microSwifts and current meter wave statistics. The addition of the thought provoking Section 4 also adds to the manuscript. Although, I believe the manuscript is improved, and should be published after addressing a few concerns (outlined below) one could argue that less rigor results in a weaker manuscript. For instance, the most rigorous investigation into the quality of the microSwift data centers around Fig 9 and lines 270-297. At line 297, the authors conclude, "The agreement in significant wave height and scalar energy density spectra supports that the Level 2 data are useful for investigating wave spectra and statistics."
This is the authors main scientific finding: for some journals, this would not be enough to warrant publication, but I leave it to the editor of this journal to decide whether this is enough for this journal (as I'm not that familiar with this journal).
"Bigger Points"
This leads me to bigger point 1 that concerns Fig 9. Note that, "agreement in significant wave height" is based on Fig 9, where Hsig_mS vs Hsig_AWAC is scattered. The best fit line of the data is Hsig_mS = 0.61 Hsig_AWAC. This is quite poor agreement in my opinion, especially as the rms error is .37 m, a large fraction of the average Hsig (approximate 1.75)! The smaller Hsig_mS is attributed to shadowing by the pier. What is the slope if the shadowed values are omitted (gray dots in Fig 9)? The assertion that shadowing gives rise to the <1 slope should be tested. Shadowing can also be tested by investigating whether proximity to the pier matters (by coloring the dots in Fig 9 by distance to the pier?). Also, does it matter whether the waves are from the north or the south and the resulting direction of the mS? This should be explored in more detail and differences between Hsig_AWAC and Hsig_mS explored in more detail. The authors also state that the difference is due to a short time series. I suspect not, as addressed later in this review. Also, the AWAC is in about 4.5 m of water, which according to gamma=0.35 in the manuscripts means that waves bigger than 1.5 m are breaking at this AWAC. I think only Hsig when BOTH instruments are outside the surfzone should be compared. Hsig_mS in a region of breaking waves will not be reliable (as mentioned by the authors) as mS surf broken waves. Thus, the "good" part of the plot, Hsig_AWAC < 2 m, the relationship between mS and 4.5 m AWAC isn't very good. It doesn't make sense to include data when the mS might be surfing. If the mS might be surfing, that data should not be included in this comparison. Unfortunately, the more I stare at Fig 9, the more I'm not so sure that microSwifts can tell me anything accurate about wave heights. If they can't get this statistic really well, what does that mean for other higher order statistics?
"Bigger Points"
Although this doesn't affect the quality of the paper, because the spectra are only used qualitatively, I still contend that the EFD (effective degrees of freedom) isn't correct for the spectra calculated in this MS. And it should be done correctly. First, notice that in Fig 7 c, the variability of each spectral estimate is bigger than the 95% bars. This means that each peak in the spectra is real, which I doubt. I believe that the 95% bar should be longer more consistent with the variability within the spectra. I.e. the EDF used is too large. The authors state that for the microSwift the EDF is given by equation (2) in the MS,
EDF = (8/3) N/M
(from Thomson and Emery, 2014 table 5.5, but this is actually from Priestley 1981) where N is the number of points in the time series, and M is the 1/2 width. They use N=7200 (600 s x 12 Hz) and M=1800. Then 5 frequencies are averaged. So
EDF = (8/3) * (7200/1800) * 5 = 53. I don't think (8/3) N/M is being correctly used. Either that, or the formula itself is incorrect. I'm not sure, because these formula in T&E are not derived so it isn't clear where N and M come from. Regardless, for a spectra with 3 non overlapping blocks of data, the dof=6 and overlapping the blocks of data reduces the number of degrees of freedom. Thus for 3 blocks of data, the MAXIMUM EDF = 6 and then averaging 5 frequencies would yield 30 dof. The authors can not have more than 30 dof. T&E hint at this on page 476... " Spectra are then computed for each of the K segments and the spectral values for each frequency band then block averaged to form the final spectral estimates for each frequency band. If there is no overlap between segments, the resulting DoF for the composite spectrum will be 2K. This assumes that the individual sample spectra have not been windowed and that each spectral estimate is a chi-squared variable with two DoF."
I believe T&E can be confusing, especially table 5.5. EDF are considered in a variety of places. EDFs are derived in
http://pordlabs.ucsd.edu/sgille/sioc221a/lecture11_notes.pdf
and I highly suggest looking at this doc. Here, it is clearly shown that the EDF only depends on the number of blocks (aka segments or chunks ==Nb, "K" in T&E) averaged to make the spectra (which does not depend on N the number of samples within the block). With no overlap, EDF = 2*Nb (as outlined above), but since there is overlap, and a Hanning window is used, 2 becomes 1.9 and
EDF = 1.9 * Nb = 1.9 * 3 = 5.7
but 5 frequencies are averaged so EDF = 5.7 * 5 ~= 29.
The 53 stated in the MS is not the number of degrees of freedom for this spectra. Note, if N/M = 2, i.e. the window is 1/2 the length of the entire time series, which it is, then 8/3 *2 = 5.33 which is similar to the 5.7 above. Also note that in the above linked pdf it is stated that, "So what of the other texts? The 2014 edition of Thomson and Emery is as misleading as the earlier editions."
I believe this is in reference specifically to Table 5.5 of T&E, so according to Gille, who I trust, maybe table 5.5, where the 8/3 N/M comes from, isn't the best reference regarding spectra dof?
However, T&E state, "Nuttall and Carter (1980) report that 92% of the maximum number of equivalent degrees of freedom (EDoF) can be achieved for a Hanning window, which uses 50% overlap." I.e. 6 becomes 6*.92 = 5.52, and 5.52*5 = 28 dof. One less than the Gille formula.
For the AWAC, assuming a Hanning window,
EDF = 1.9 * 13 ~= 25 dof
not 42. Again, the larges EDF for the AWAC is 2*13 = 26. but the overlapping blocks result in slightly less.
"Smaller Points"
Line 290: "We also expect that the microSWIFT arrays may under-predict some significant wave heights as the sampling windows are shorter than the AWAC, potentially not measuring the largest and least likely waves in the distribution and times that the microSWIFTs are within the ‘shadow’ of the pier."
This seems a bit misleading. The shortness of the time series doesn't bias the difference between mS and AWAC Hsig, it just creates more variability. The authors could have also said, "We also expect that the microSWIFT arrays may over-predict some significant wave heights as the sampling windows are shorter than the AWAC, potentially over representing the largest and least likely waves in the distribution and not measuring enough of the smaller waves."
Line 323: Fig 11a. Is this GPS u? Or the Kalman filtered u? Hopefully the Kalman filtered u. If GPS velocities, are they de-spiked? Fig 11b. Is the acceleration in the vertical reference frame? If not it should be as the "body frame of reference" is not as obviously useful. The Kalman filtered velocities and accelerations should be used in this figure.
Line 273. 1.416 should be 1.414 as it is 2^{1/2}. Also, does your boot strapping method yield
Hs [1 - 0.41 / N^(1/2) ] < Hs < Hs [1 + 0.41/N^(1/2)]
for the 95% confidence limits? where N is the number of waves in the estimate. I believe these are the 95% confidence limits of Hs based on a Rayleigh distribution and should be confirmed by bootstapping. In my opinion, it is better to use a derivable formula than just say, "we got this number by bootstrapping" as there is no way for a reader to determine if that number is correct. |