Both referees agree that there are substantial improvements in the manuscript. Referee # 2 still is asking for some changes, however, and seems a bit dissatisfied with some general issues.

I agree with Referee #2 that the material in Appendix 2 is important, and I agree with the suggested changes. I suggest, in fact, that you move the material in Appendix 2 into the main text, as the comparison at a site level is clearly important to the credibility of your model, and this treatment should be thorough enough to withstand the sort of review expected for the main text.

I also ask that you respond more fully to the last paragraph of the earlier (first) review of Referee #2. The key issue here concerns the relationship between the rate of change of global average CO2 concentration, as derived from the NOAA surface data, and the global averaged surface fluxes. It is simply not appropriate to treat these two quantities as being equivalent on seasonal time scales, because the mixing of the atmosphere is too slow. As the referee points out, there are various previous studies that would help to assess the difference between these two types of averages. Among your options, for example, would be to use averaged fluxes from inverse models that use the NOAA data rather than the NOAA data themselves, thus accounting for atmospheric mixing. Many inverse modeling groups can presumably provide you with global averaged fluxes, or fluxes over more appropriate to set of latitude bands.

I appreciate that your treatment of global fluxes is mainly motivational to your main point about substrate limitation and the fate of short-lived detritus. Still, it is not appropriate to ignore known processes in your motivation. Global atmospheric concentrations and global fluxes are not simply related, except on time scales much longer than the mixing time of the atmosphere.

Thanks for your attention to the questions from earlier. In the interest of efficiency, I have responded directly, rather than sending back to the reviewers.

I can see that there is still a small misconception, and I'm sorry that I was not clear enough in my earlier response. Your "Frankly speaking.. " comment was very helpful for clarifying the main issue, which is this:

We are dealing here with two different notions of "global average". The NOAA product, which you have been using, is an estimate of the average concentration at the sea surface. It is global in the sense that it is an average over the sea surface of the entire Earth (extrapolated from discrete station data). The other type of global average is the volumetric average of the entire atmosphere, i.e. total moles of CO2 in the atmosphere divided by the total moles of dry air. This second quantity is not available directly from observations, although its time derivative (the global flux) is available from inverse model calculations.

I suggest from now on we agree to call the first concept a "surface average" and the second a "volumetric average, and we avoid the term "global average" altogether.

So what needs to be done going forward?

The biggest issue is fixing up the terminology, and avoiding making any implicit assumptions that the volumetric and surface averages are identical. Please consider using the terms "volumetric" and "surface" average, as suggested above. Also, because you have been using the symbol Ca interchangeably for both quantities, the formalism and the presentation will need some changes. If both quantities remain important to your paper going forward, you will need two symbols, not one. For now, instead of Ca, I'll use Cav (volumetric average) and Cas (surface average). And instead of Na, I'll use Nav = dCav/dt and Nas = dCas/dt.

Appendix A2. I agree that the time average of the volumetric average is equal to the global flux, i.e. dCav/dt = Nav = global flux. You don't need to address this, as it follows directly from the conservation of mass. What does need addressing is the difference between the time derivative of the surface average (Nas) and the global flux (Nav), which you seem to have accomplished adequately with the Transcom comparison. All of the equations in Appendix A2 and the surrounding text therefore need to be cut. The only material from Appendix A2 that is relevant is the final paragraph (Page 16, line 16) starting "At the Figure 9...". Instead of putting this now in an appendix, I think this should move to the main text. You need to put the Transcom results in a more central position in the paper because it is appropriate to compare your model only with Nav, not with Nas. This will eliminate the need for Appendix A2.

Please change Figures 3, 4 so that you are comparing your model with dCav/dt = Nav, not with Nas. This will require using the monthly fluxes shown in Figure 8 for Nav. (As a reminder, here Nas is what you were calling Na).

Section 2.1.1 Observations. I suggest you introduce (briefly) the Transcom and eddy flux data here, since these are the key datasets for which you can compare your model. In fact (although I expect you won't agree) you might consider completely cutting the use of the NOAA surface average from the paper, as it not longer assumes the central role for model comparisons. I accept, however, the comparison between Nas and Nav has some interest, even if Nas is not central.

Other minor points I noted on re-reading the paper:

After Eq. 19, I think it would be helpful add a sentence of clarification, stating that the growing season ends at different times in different places, so the time index "n" depends on location. Then please clarify also that Eq. 20 is the same as Eq. 19, after switching to an absolute time coordinate, m. As worded now, one gets the impression (also because you also switch from small s to capital S, which is perhaps not necessary?) that you are introducing a fundamentally new variable here.

Page 10, line 9. It's not clear what you mean by "width". Perhaps change "of the same width as that" to "the same as the amplitude" .

Page 10, line 12, An example of a place needing wording changes, because the NOAA data is a surface average, not volumetric average, as mentioned above.

Figure 5 is not referenced in the text. Please cut?

The manuscript seems much improved. Nice work.