Dear Dr. Carlos Lozano,
The revised manuscript of our paper entitled “Removing wave bias from ADCP measurements using Harmonic Analysis” by Sangdon So, Arnoldo Valle-Levinson, Armando Laurel, and Chanyoung Park is uploaded through the electronic paper submission facility of Journal of Atmospheric and Oceanic Technology.
We would like to thank the two reviewers for their constructive criticism and comments on the previous version of our manuscript. We have revised our paper accordingly and the major changes have been highlighted in yellow.
We would like to take this opportunity to thank you and the referees for their fruitful comments that have improved the manuscript substantially. We now trust that our paper is acceptable for publication in Journal of Atmospheric and Oceanic Technology and look forward to your response.
Sincerely,
Sangdon So
Please note that, the reviewers’ comments are shown in italic and they have been numbered sequentially.
Reviewer #2
General Comments:
R2.GC1.This paper attempts to develop a new method for making a difficult measurement--turbulent fluxes in the presence of surface gravity waves. I am glad to see a new effort in this area, but, unfortunately, this paper does not make a strong case that this new method is reliable or better than other methods.
I have several concerns with the manuscript.
We appreciate the reviewer’s comments. We considerably strengthened our manuscript by answering these questions through the revision.
Specific Comments and Edits:
R2.SC1.The authors are proposing a statistical, rather than dynamical, approach. This is not inherently wrong, but in this case there are significant weaknesses. The main one is that the approach could remove turbulent velocities in the wave band in addition to removing wave velocities. I would like to see explanation and evidence that the turbulence won't be removed by a flawless implementation of the method.
Thank you for the comments. Aspectral density represents the power of a signal or sort of signal, including noise. We found local peaks of the spectral densities which are larger than their two neighboring samples. Least square analysis in Appendix calculated the amplitude and phase of periodic signals. With the calculated amplitude and phase, the periodic signals (black line in Figure R2.1) were reconstructed and subtracted from the raw data (red line in Figure R2.1).The red line in Figure R2.2 described the spectral densities of raw data and the blue line showed the spectral densities of signals that the periodic signals were removed. We removed the periodic fluctuations from raw velocities. If we removed turbulence as well, we may not see any spectral density in the high frequency band. Therefore, the blue line in Figure R2.2 represents the spectral density of turbulent flow.
Figure R2. 1. Comparison between raw beam velocities and harmonic signals
Figure R2. 2. Comparison of Spectral density before (red line) and after (blue line) removing periodic signals.
R2.SC2.My biggest concern is that, as far as I can tell, the data presented by the author do not support their conclusions. I may have misunderstood something, but the figures and numbers in the paper still have substantial energy in the wave band. Yes, in some cases their results appear better than the VAF method to which they compare their HF method. But it doesn't look good enough to allow estimation of turbulent fluxes.
As the referee pointed out, the figures in Figure 4 looked as if the contours still have substantial energy in the wave band because the contour bar is on log scale and the contour limit is improper. We changed the contour limits from 10-4 to0.5 as shown in Figure R2.3. The spectral densities in Figure R2.4 shows those corresponding with those on the black solid line in Figure R2.3. The HA analysis provide approximately one order of magnitude less than the uncorrected data, particularly in the dominant wave periods at 7.04m and 9.04m. Vertical Adaptive Filtering method removes the wave-bias as correlating signals at two locations. If the distance between two locations are too close, VAF method can remove turbulence. If the distance is two far each other, VAF may not remove waves. In addition, Least squares Adaptive Filters amplify to minimize the sum of squared residuals between two locations as shown in Figure R2.4. The spectral densities of low frequencies <0.2Hz are larger than those of uncorrected data at 7.04m and 9.04m.
Figure R2. 3. PSD (m2/s) of uncorrected Beam1 velocities (m/s) at A) 9.04m, B) 7.04m, C) 4.04m and D) 1.04m; PSD of Beam1 velocities of VAF method at E) 9.04m, F) 7.04m, G) 4.04m and H) 1.04m and PSD of Beam1 velocities of HA method I) 9.04m, J) 7.04m, K) 4.04m and L) 1.04m
Figure R2. 4 Comparison of Spectral densities for Uncorrected in green line, VAF in red line and HA in black line at A) 1.04m, B) at 4.04m, C) at 7.04m and D) at 9.04m.
R2.SC3.This brings me to my last major point. This paper has no test of their method. I would have liked to see them compare their estimates of turbulence quantities to independent estimates. Without this, it is essentially impossible to determine whether the method is useful.
We apricate this referee’s constructive comment. Turbulent Kinetic Energy budgets are included in Figure 7 in the revised manuscript. The Orgive curves in Figure 7 are replaced with TKE budgets because the cospectra didn’t quantify how much wave energies the methods remove. In addition, we discussed how much the results of each method are different with those of uncorrected data.
Figure R2. 5. Turbulent Kinetic Energies estimated by A) Uncorrected data, B) VAF, C) HA 95% waves removed and D) HA 100% waves removed.
Figure R2. 6. Total sum of TKE budgetsof each method shown in Figure R2.5.
R2.SC4.I also had concerns with the introduction. It surveyed many of the important contributions to this field in the past two decades. However, in places it seemed to misattribute contributions by previous researchers, and in other places some of the assumptions made by other authors could have been more thoroughly explained and examined.
R2.SC5.Finally, the method is not clearly explained. I do not feel that I would be able to use this paper to apply this method to my own data set. In particular, I don't understand how the authors identified peaks in their spectra. I also would have liked to see objectively determined limits on the wave band, particularly at low frequencies.
All peaks are the data that are higher than their neighboring points. Most wind-induced waves are distributed in the frequency >0.09 Hz as shown in Figure 1. The lowest frequency is 1/600 because we assumed turbulence is stationary in 10 minutes. If user think the waves at lower frequencies than wind-induced wave frequencies significantly affect the turbulent estimation, they may extend the frequency range. In this study, the waves were distributed in the frequency range >0.09 Hz. This is why we chose the band. We have rewritten the method accordingly.
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Reviewer #3
General Comments:
R3.GC1.This paper introduces a new method to minimise contamination of turbulent velocity fluctuations by waves. It describes the limitations of some existing methods and then introduces a spectral harmonic analysis (HA) method. The HA method does appear to reduce wave contamination, but overall there are significant weaknesses in the description and justification of the methods. My recommendation is that this manuscript requires significant revision before being suitable for publication.
We would like to send our special thanks to the referee for his or her insightful comments.
Specific Comments and Edits:
R3.SC1.The introduction of the method in this manuscript is based on field data collected at a single site for 8 days. Throughout, the authors state that there are periods of energetic waves, but by my reckoning the surface waves are much less than 1 m in height with periods of less than ~10 s. I'm not really sure that these count as energetic waves — it would be highly beneficial to actually demonstrate that the method works for genuinely energetic waves and perhaps compare a shallow nearshore site dominated by short period wind waves with a deep(er) water site dominated by long period swell waves.
We agree with this comment. We removed the term, energetic waves and used surface gravity waves, instead. We deeply believe that the reviewer’s suggestion is certainly a very interesting line of future research. However, we don’t have a shallow nearshore data so the scope of this study has not been extended to cover the suggestion.
R3.SC2.L. 199: How are spectral peaks identified? Surely there must be some criteria of how much energy they contain? Peaks have a magnitude (height) and a bandwidth, so how are these factors addressed here in the "find peaks" routine? It would be highly advantageous to demonstrate the peak identification using the data in Fig. 1 or 2.
R3.SC3.L.200: So, the method relies on being able to clearly identify the range of wave frequencies at the outset. This will become problematic in short-wave dominated wind-sea environments, particularly those close to the coast in shallow waters where locals winds cause rapid changes in sea state. Additional justification is required here.
R3.SC4.L.207: It is unclear to me why you would want to remove the same amount of wave energy from each ensemble. The amount of energy within the wave frequency band will vary with each ensemble as the sea state naturally varies through time — therefore the amount of wave energy that must be removed from each ensemble also changes? This seems like a critical flaw: either I'm missing something here or the authors have not explained something fully.
R3.SC5.L. 211: Why 95%? Is this being used as a critical cutoff? If so it suggests that 5% of wave energy remains in the filtered signal.
R3.SC6.L. 240: It would be beneficial to show a time series of the actual wave statistics so that the reader can visualise what the authors mean by energetic waves — looking at Fig.1, these waves appears to be < 1 m Hs, so the term energetic may be used somewhat erroneously. Please add a figure with time series of Hs, Tz and Tp.
We added the Hs, Tz and Tp in Figure 1 and described the wave statistics.
R3.SC7.L. 263 & Fig. 5: It would be far easier to interpret this figure if panels B and C were presented as deviations from A — i.e. difference plots. This would clearly demonstrate where energy is being filtered and amplified by the different methods.
R3.SC8.L. 279: this is a throwaway comment about internal waves. To include this statement it must be justified by either reference to literature or by data.
R3.SC9.L. 287 & Fig. 7: How significant are the differences between the curves of the VAF and HA methods? They are very similar in all of the panels, so it is essential to actually quantify the difference if the authors want to make the statement on L. 294 that the HA method successfully removes the wave bias.
Thank you for the comment. We agree that the results of VAF and HA are look very similar. We found that it is better to show the results of turbulence properties than the cumulative cospectra. The cumulative cospectra don’t quantify how much wave energies the methods remove. We replaced Figure 7 with TKE budgets and discussed how significant are the differences between the methods.
R3.SC10.L.321 & Fig. 10: There is a problem with the descriptions of the colours in this figure. The text states contour values greater >1, whereas the colorbar in the figure does not exceed 1. Also, being picky — this is not a contour plot — there are no contours plotted, just colour shading.
R3.SC11.L. 335: The conclusion is weak. The first paragraph mostly repeats information from the introduction about previous methods, it does not focus on the HA method, nor justify why we actually need to account for the wave contamination.
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