|I thank the authors for their work addressing my comments. I believe that the text is clearer now and that the reader will have a better opportunity to understand the work done here and its significance. While the authors have generally done a good job addressing my questions, I still have some worries and questions about the work that I would like addressed before giving the thumbs up for publication.|
In my original comments (at line 595) I questioned the small uncertainty reductions (under 10%) seen in Figure 3 for many regions, especially those in the tropics, and speculated that the uncertainties for the grouped regions might not be being calculated correctly. Similarly, in my comment on lines 349-350, I suggested that the 1.4 PgC/yr uncertainty on the global land flux was a few times higher than it should be. The authors, in their response, gave a list of a posteriori uncertainties at the scale of Transcom regions (lines 113-142 of the response) that, rather than squelching my worries have instead exacerbated them. Along with the uncertainties for the individual Transcom regions, they give uncertainties for the global land and global ocean total, along with the global land+ocean total: those for land and the land+ocean total are up around 8 PgC/year -- those values seem to be in conflict with the 1.4 PgC/year value given in the paper, so which is correct? If these uncertainties are indeed up around 8 PgC/year, that would suggest that the correlations in the a posteriori covariance matrix are not being considered (since taking the sum of the squares of the uncertainties for the individual Transcom regions given in lines 113-142 of the response gives about (8 PgC/year)^2). Another possibility is that there is a problem with the posterior covariance matrix that they are using for the calculation: for example, if the correlations given by the off-diagonal elements were computed incorrectly. In my original comments (lines 183-187), I asked about one point that might lead to that covariance matrix to be calculated incorrectly: if the Green's function relating fluxes at a given time to mixing ratios at later times were to be truncated too soon. The authors responded that they run the Greens' functions for each flux pulse out for four years. This is long enough to capture the spread of the input pulse to the point where it have negligible latitudinal gradients and is typical what has been done in previous inversions. However, what the authors do not address (and what could cause problems that might result in an incorrect covariance matrix) is what is assumed for the influence of those fluxes at times after those four years: is zero influence put in the matrix (bad), is the fully spread-out value of about 0.4 ppm / (PgC/year) put in (better), or some exponential decay to the spread out value (even better)? The authors point to the original Rayner et al code that they have modified for use here, but don't explicitly address this issue. If they put zeroes in matrix J for all years after Year 4 instead of a better spread-out value, I could see how the correlations in the posterior covariance could be too low and the a posteriori uncertainties would be wrong. The original Rayner et al code may have been used for only a short span (four years) such that this point would not have been an issue. As things stand at the moment, I do not have confidence that the posterior covariance, upon which so many of the uncertainties discussed here rest, is being calculated correctly.
Another issue about which I asked for clarification in my original comments (lines 70-81 and 694-967) was why an additional forward run with the optimized fluxes was needed (i.e., why the impact of the fluxes on concentrations through the J matrix did not fully represent the effect). The authors give some vague generalities but do not explicitly say what the answer is. They also delete some text. However, it is possible that the answer (not given) is that there is no influence whatsoever after four years from a given set of fluxes (i.e. zeroes in the J matrix after Year 4). As mentioned above, this would have an impact on the a posteriori covariances calculated.
I would need to have answers to these questions before I will feel confident in the results presented here. Errors in the J matrix would affect not only the uncertainties calculated in this manuscript, but also the flux estimates themselves, and could materially change some conclusions presented.