The authors have certainly addressed all the specific criticisms and by that improved the manuscript. Also, I do not have the impression that there are any differences between authors and reviewers on the mathematics.
That said, I would still encourage the authors to make stronger recommendations for change to "established" or "widespread" eddy flux processing procedures. I will elaborate more in the paragraphs below. I believe such strengthening of the messages would increase the impact of the paper and would be fruitful for the "flux community".
There seems to be some remaining disagreement between me and the authors on the relative merits of the cross-covariance maximisation method. While I would call it "dubious" and "flawed", the authors still describe it as a "practical solution". I do not doubt that the authors have understood my line of reasoning, so it comes down to a matter of opinion what degree of known imperfection is still considered acceptable. Ultimately it is the authors' call how to put this. I can only appeal to them to consider a more strongly critical wording, on the following grounds.
I have many years of experience with EC measurements with closed-path analysers near the ground, i.e. 2 m above agricultural surfaces. There, lag times are typically of order 0.3 to 3 s, and I have always found the cross-covariance maximisation method causing more trouble than a fixed lag time, even a somewhat inaccurate one, ever would. For all gases I've looked at (H2O, CO2, CH4, N2O, NH3), covariance maximisation introduces frequent unrealistic, widely oscillating, lag time estimates that have nothing to do with instabilities in the sampling system. The reason for that is that correlation coefficients of w with a scalar variable are not huge to begin with (typically 0.2 to 0.4) and when one of the variables is attenuated, the peak of the correlation function becomes rather flat and thus hard to detect. Worse, because it is a "maximisation" procedure, the method selects against near-zero fluxes even when these are true. For example, measuring N2O fluxes after a long period without any nitrogen inputs to the soil should yield a single-peak flux histogram with a near-zero median. However, with the maximisation method, the histogram becomes double-peaked (one positive, one negative) because zero flux is actively avoided by the method. But this is not a reflection of separate source and sink processes, it is simply due to bias in the individual flux estimates (because random non-zero correlations, of either sign, get "detected" and locked on by the method). Gas fluxes that change sign twice daily, such as that of CO2, are equally affected by this bias around the sign-change periods.
I would concede that cross-covariance maximisation can be useful as a diagnostic tool, because it allows early detection of clear trends (such as two clocks drifting apart). But still, actual flux values should be calculated with a lag time that is based on the technical flow parameters of the system and not automatically varying from run to run (apart from corrections for known clock drifts).
Hence, my opinion remains that the use of the cross-covariance maximisation method (in its present widespread form) should be discouraged, and if the present authors do not include a recommendation to this effect, they are missing a chance to influence the thinking of the "flux community" in this regard.
The following remarks are deliberately provocative. Please do not take them as personal criticism!
Can the authors perhaps ask themselves why they are reluctant to recommend abandoning the cross-covariance maximisation method? The fact that it is "widespread" is no good reason. If a method is known to be poor, it should be replaced with better ones. In this case, do the authors consider such change too laborious for users? Do they not wish to make this recommendation because, if followed widely, it would remove the need to use their here-presented correction procedure in the future? Do they fear conflict in the scientist networks they are involved in (in particular ICOS with its drive to standardise procedures)? Do they worry about changes in the FLUXNET databases that could ensue from revised processing?
I do not expect answers to these questions. They are merely intended to encourage the authors to be bolder in the paper's Discussion and Conclusions sections.
Specific comments (line numbers refer to the tracked-changes version)
P 5 L 23 and P 17 L 1
The authors have added information on flow and tube dimensions for Hyytiälä. The tube volume is so small that the total physical lag time is affected at a comparable rate by the time it takes to exchange the air in the volume of the Li-Cor measurement cell. In addition, there is a known processing lag if the LI-7550 Interface Unit is used. The three effects (tube, cell, processing) need to be added to estimate physical lag time.
P 21 L 20-21
I believe the reader should be warned more clearly that the "approximation" is limited to the cases of relatively minor attenuation presented in this study. In particular, it should be noted that in cases where the phase effects cause sign reversals in the cospectrum, the sqrt(H) approach must fail.
P 21 L 32
In line with my General Comments, I find the inserted "Hence, investigating..." too weak. Why not say something like "Hence, other means for estimating the physical lag time should be used whenever possible." (Please do not use "signal travel time", that sounds like an electromagnetic phenomenon.)