This manuscript presents inverse model estimates of global and regional CO₂ fluxes over the last two decades. The inverse model is based on a single transport model assimilating observations from 50 sites. A series of 16 model simulations is conducted by varying the prior fluxes and prior and observational errors. Results are evaluated against independent aircraft data. The authors found that the ensemble mean of 16 optimized fluxes outperformed individual model outputs. The spread of flux estimates from these 16 model simulations is considered as the uncertainty of the estimated fluxes.

General comments

The manuscript presents a detailed study focusing on the inverse model estimation (using a single model) of CO₂ fluxes on a global scale for two decades. Therefore, the paper is worthy of publication in ACP after addressing the concerns listed below.

1. Authors should present the novel aspect of this manuscript. This study uses a single inverse model and conducts a series of model simulations by changing model components, keeping the same observational dataset. Many model intercomparison projects (TransCom and GOSAT and OCO-2 inverse model intercomparisons) address the same aspects by including different transport models but by changing individual model components. Calculating the ensemble mean and spread using a single transport model is not the right way of quantifying the mean and uncertainty in CO2 flux estimates (by not accounting for transport errors). 
2. To investigate the impact of different modeling components such as model transport, priors, and specification of uncertainties, there could be other systematic approaches, such as designing a series of simulations and quantitatively assessing the uncertainty components. For example, see Basu et al. (2018) and Philip et al. (2019). More rigorous experiments are required if this manuscript intends to assess the spread from priors and prior/observation uncertainties. Randomly selecting two different terrestrial biosphere models (TBMs) or ocean models is insufficient. Otherwise, reconsider the focus of the manuscript. 
3. This study mainly tests land flux scenarios with and without interannual variability (IAV) (CASA versus VISIT). They should consider using different TBMs as priors (diagnostic/prognostic/with and without IAV etc.) with significant regional differences. That can lead to a reasonable spread in the optimized fluxes. Also, how about conducting a sensitivity test by artificially imposing zero net annual flux in the VISIT model? 
4. The manuscript should be written more carefully, especially the introduction and conclusion sections. There are many empty/loose sentences, no connection between paragraphs, introduction not providing any motivation of the paper (it also discusses unrelated aspects), grammatical mistakes, etc., throughout the manuscript. See some of the corrections in the technical-correction section below. 

Specific comments

Line 17-21: These two sentences are not connected. You state that model errors and insufficient observations lead to uncertainties in regional flux estimates. However, it is unclear how you address these with your simulations using a single model. State clearly what uncertainty component you are addressing here in this article.

Line 26-28: This is just a general statement. Need more clarity here: “Interannual variability and seasonal cycle in CO2 fluxes are more consistently derived for different prior fluxes when a greater degree of freedom is given to the inversion System”.

Line 28-29: In line 261, you mention that fluxes are evaluated with aircraft observations. Are you using surface data as well? “…evaluated the inversion fluxes using independent aircraft and surface measurements not used in the inversion”.

Line 28-29: Good if you can make it more quantitative, i.e., add some summary statistics or so: “which raises our confidence in the ensemble mean flux rather than an individual inversion”

Line 31: It seems like an empty/loose sentence: “Differences between 5-year mean fluxes show promises and capability to track flux changes under ongoing and future CO2 emission mitigation policies.”  

Line 36-38: Cite IPCC report.

Line 44: Be very clear (solutions to …?): “The sinks on the land and ocean constitute a major component of nature-based solutions”.

Line 45-46: Cite proper references to support the statement. 

Line 45-53: In this paragraph, mention global flux uncertainty first, and then note the regional issues, with some additional details. That is, lines 45-46 should come after line 53. 

Line 55-69: It is not clear why you need this paragraph. “However, the impacts of biases in FFC emissions on inversion estimated CO2 fluxes remained relatively unexplored”. Are you exploring this aspect in this paper? Moreover, this paragraph is written poorly. 

Line 70-73: I don’t quite understand this statement! Who provides the metric, what is that metric? What’s the meaning of “metric for evaluation of regional fluxes should be evaluated”? Clarify.

Line 71-73: Is this something new? “…should be evaluated using a new transport model simulation of the predicted fluxes, not using the assimilated CO2 field”. Be clearer with sufficient details. Most evaluations in current published works are based on model simulation of optimized fluxes. For evaluation, using a different transport model than the one used in the inversion (as a forward model) is advantageous (not sure if this is what you mean here). Also, are you exploring this in this manuscript/study? 

Line 73-81: I’m lost here. From re-reading this, I understand that the assessment of the spread of optimized fluxes obtained by conducting multiple simulations using different model inputs is a better way of quantifying the uncertainty than simply evaluating the optimized CO2 concentrations against independent measurement data. Revise the entire paragraph to be more apparent.

Line 82-85: These uncertainty sources have been investigated previously. Cite some of those critical studies here. 

Line 92-95: This statement is not correct: “Such intercomparisons used single inversion from different modeling groups and provided the range in CO2 flux uncertainty due to differences in transport models.”. These intercomparisons assessed uncertainty arising from different model components, not just the transport model differences. For example, see Crowell et al., 2019 and Peiro et al., 2022. 

Line 123-124: This sentence is not clear to me. 

Line 128 and 129: Just “used” not “simulated” (?): “… is simulated using …”

Line 135: “…downscaled to 3-hourly time intervals…”: Mention how you downscaled; which variable used; and cite proper literature. 

Line 136: Double-check if it is version 4.1? “…fire emissions are used from GFEDv4s (van der Werf et al., 2017…”.

Line 145: Complex notations: gc3t and gvjf. What is “3” and “t” in gc3t? 

Line 149-150: Revise: “to evaluate the strength of MIROC4-ACTM simulations to derive fluxes consistently”. How do you evaluate the strength of simulation? Why did you mention “consistently” here? Fluxes will be derived using the inverse model, so how can you “evaluate the strength of forward simulation”? 

Line 159: Cite proper references: “WDCGG websites as appropriate”

Line 162: Is this the grid cell with the observation location? “…nearest grid of observation location at hourly intervals…”.

Line 164: “These temporal data gaps (1-6 months) are filled using the curve fitting method based on the digital filtering technique”. Have you conducted simulations without using curve-fitted data? Why was this data filling necessary? 

Line 200-210: How about conducting a simulation with “gpp_v4” along with “ocean PFU = 0.5”? Explain the rationale for selecting different prior error scenarios you considered in this study. 

Line 234: “High values (FUR towards 100)”: If FUR is in percentage, then revise the equation in line 233.

Line 244: Not clear: “… indicative of the observational constraint regional fluxes…”

Line 245: “…we recommend that the spread of ensemble inversions provide more representative estimation of the regional CO2 sources and sinks.”. “Spread” represents “a measure of uncertainty”, not a “representative estimation of…”. Why do you add “recommend” here? 

Line 309 and 311: Revise this sentence: “Hence, the magnitude of biases and RMSE indicates predominantly the accuracy of the predicted fluxes.”. Model transport is one of the sources leading to uncertainties in the predicted fluxes. 

Line 649: “CO2 simulations are derived from three sets of prescribed fluxes: “gc3t”, “gvjf”, and “ensm”.”: I’m assuming that the evaluation is conducted for all 16 inversions (?).

Lines 709-720: I’m not sure if these details (+ Figure S10) are required in this paper.  

Line 775-782: Empty/loose sentences. 

Technical corrections

Line 14: Better add “atmospheric” here: “chemistry-transport model (ACTM)”.

Line 16: Better avoid text in parenthesis: “regional flux (+ve: source to the atmosphere; -ve: sink on land/ocean)”.

Line 21: Move the number of the sites (50) from here to the appropriate part of the sentences: “data uncertainties (50 sites)”.

Line 24: Is this “22-33% and 16-18%” for land vs ocean? Not sure this is clear enough here. 

Line 25: Not clear what this approximate means here: “best estimations for (approx. 2000-2009)”.

Line 52: Revise and add more clarity: “partitioning exists greatly in the … release”.

Line 55-56: Revise this sentence: “…because inversion calculations do not optimize…”.

Line 90-91: You can write these in a better way: “inversions from … for inversions using … or for inversions”. 

Line 99: Revise: “observed and model data processing”.

Line 100: Avoid capital letter: “the Results and discussion”.

Line 155-156: Avoid repetition of “from”.

Line 1120: Correct this: “lower panel (b)”.

Line 242: Correct: “…West Asia, Northern Africa. The Tropical Indian Ocean…”.

Line 252: Correct: “as per analysis”.

Line 302-307: Use simple notations. For example, avoid “aircraft” from “x”. 

Line 308: Correct: “CO2 mixing ratios”.

Line 317: Use the term “grid cells”. 

Line 336: Avoid “.”: “3.2. Global totals.”

Line 346: Use “mean”: “Ensemble means land”.

Line 563: Revise: “It is not easy for us to explain”.

Line 763: Avoid “Please”.

Line 766: Correct: “is unanimously located”.

Figure 4: Choose a different font that is clearer.

Figure S2: Correct to CO2: “monthly-mean CO fluxes”

References

Basu, S., Baker, D. F., Chevallier, F., Patra, P. K., Liu, J., and Miller, J. B.: The impact of transport model differences on CO2 surface flux estimates from OCO-2 retrievals of column average CO2, Atmos. Chem. Phys., 18, 7189–7215, https://doi.org/10.5194/acp-18-7189-2018, 2018.

Crowell, S., Baker, D., Schuh, A., Basu, S., Jacobson, A. R., Chevallier, F., Liu, J., Deng, F., Feng, L., McKain, K., Chatterjee, A., Miller, J. B., Stephens, B. B., Eldering, A., Crisp, D., Schimel, D., Nassar, R., O'Dell, C. W., Oda, T., Sweeney, C., Palmer, P. I., and Jones, D. B. A.: The 2015–2016 carbon cycle as seen from OCO-2 and the global in situ network, Atmos. Chem. Phys., 19, 9797–9831, https://doi.org/10.5194/acp-19-9797-2019, 2019.

Peiro, H., Crowell, S., Schuh, A., Baker, D. F., O'Dell, C., Jacobson, A. R., Chevallier, F., Liu, J., Eldering, A., Crisp, D., Deng, F., Weir, B., Basu, S., Johnson, M. S., Philip, S., and Baker, I.: Four years of global carbon cycle observed from the Orbiting Carbon Observatory 2 (OCO-2) version 9 and in situ data and comparison to OCO-2 version 7, Atmos. Chem. Phys., 22, 1097–1130, https://doi.org/10.5194/acp-22-1097-2022, 2022.

Philip, S., Johnson, M. S., Potter, C., Genovesse, V., Baker, D. F., Haynes, K. D., Henze, D. K., Liu, J., and Poulter, B.: Prior biosphere model impact on global terrestrial CO2 fluxes estimated from OCO-2 retrievals, Atmos. Chem. Phys., 19, 13267–13287, https://doi.org/10.5194/acp-19-13267-2019, 2019.

This manuscript explores the sensitivity of a global CO2 flux inversion using CO2 mixing ratio measurements to the choices of prior flux, prior flux uncertainty, and measurement uncertainty assumed in the inversion.  Gap-filled measurements from 50 globally-distributed sites are used and monthly fluxes across 2000-2020 are estimated for 84 emission regions (54 on land, 30 for the oceans).  Given that the fluxes to be estimated are severely under-constrained by the data used here, especially in the tropics and southern hemisphere (SH) were the data are sparse, it is not surprising that the final estimate should depend strongly on the prior estimate assumed going in.  The sensitivity to two different sets of prior fluxes are explored here: 1) annually-balanced CASA land biospheric fluxes paired with Takahashi (1999) ocean fluxes, a combination that results in too large of a trend of CO2 in the atmosphere due to the lack of the realistic global land sink, and 2) land biospheric fluxes from the VISIT model that have too large of an global annual uptake, resulting in a too-small trend of CO2 in the atmosphere, coupled with ocean fluxes from the JMA model.  The bias in the global land+ocean uptake embodied in each of these sets of prior fluxes is reduced in the posterior flux estimates, but remains at a lower level, especially for individual regions instead of the global level.  Since the two priors had errors in the trend of opposite signs, averaging results over the two cases results in lower errors with respect to the truth.

Besides varying the prior fluxes themselves, the authors explore the impact of assuming different values for the uncertainty on these prior fluxes as well as the uncertainty on the measurements (or model-measurement mismatches, to be more precise).  One must assume some value for these uncertainties in the inversions, and these assumed values are always incorrect to some degree, since one never knows precisely what the true uncertainty ought to be: the larger the errors in these assumed values, the larger the error in the a posteriori estimate due to the bad assumptions; these errors tend to be systematic rather than random, so it is quite useful to know how large of an impact they have.  In my view then, this study is worth publishing because it quantifies the impact of these mis-specified statistical assumptions, even if the global CO2 flux inversion underpinning this work is far from being cutting edge.  (Global CO2 inversions of this sort using the in situ CO2 measurement network have been done for over two decades, going back to the 1990s at least.  There are now many more in situ measurement sites than the 50 used here, including tall towers on the continents and the routine aircraft profiles that have been used here for evaluation purposes.  Furthermore, there are column-integrated CO2 measurements from ground-based Fourier spectrometers looking at the sun, as well as the huge volume of column CO2 data from satellites.  These data are now used routinely to estimate fluxes for thousands of regions, instead of just the 84 used here.)

   The authors have done a nice job setting up their ensemble of runs (16 total, permutations of the 2 flux priors, 2 different assumptions for the magnitude of measurement uncertainties assumed, and 4different assumptions for the magnitude of a priori flux uncertainty assumed) and have done a careful job of analyzing the results from a variety of perspectives (global total, land/ocean totals, regional fluxes, annual means, interannual variability, seasonal variability, the estimation uncertainty versus the sensitivity of the estimate to the priors and assumed statistics, and errors evaluated by comparing to independent data).  While the manuscript is quite long and may be daunting to some readers, I realize that there is a lot of ground to cover and am sympathetic that the length is not inappropriate.  However, my main problem with the manuscript is with the writing: in many places, it is difficult to understand the points that are being made.  As a result, I had difficulty understanding precisely what was done in this work, both in terms of the method used for the inversion and the methods used for the analysis, as well as the results obtained and the logic used to interpret those results.  Therefore, before being published in ACP, I would like the authors to do a better job with their writing, making it clearer what was actually done and what the implications of their work really are.  I think that they should also note that their setup here is more under-constrained by the data than most, and therefor the impact of the error sources that they examine is probably larger for this study than for inversions that use more data.  Finally, when quantifying the uncertainty in the flux estimates, the authors need to do a better job explaining what error terms are quantified by their ensemble spread, and what are not (the authors note that transport model error is not quantified, since they only used a single transport model in this study, but they do not do a good job pointing out the difference between the estimation errors usually quantified by the inversion and the errors examined here in their sensitivity study, or the slight overlap between the two (due to the errors or differences in the prior fluxes)).   I have noted below the places where the authors should clarify their text, and I have made numerous editorial corrections and suggestions for better wording that will hopefully make it easier for the reader to understand what is going on.  I apologize for not breaking out the more-editorial comments separately from the more substantive ones: at the moment, they are all mixed together in rough line-number order.

Detailed comments (line number indicated):

24:  "without riverine export correction" -- I take this to mean that these are the actual fluxes inverted, and that if you corrected for 0.6, say, you would get 1.6 +0.6 = 2.2 PgC/yr storage in the ocean.  Please give more detail as to what making this correction would do to the results and how that relates to anthropogenic fluxes/storage.

29-30: "which raises our confidence in the ensemble mean flux rather than an individual inversion."  Reword for clarity.

52: what does "greatly" indicate here?  Reword for clarity.

56:  It is not correct to say that inversions do not optimize the FFC emissions.  They solve for corrections to the prior fluxes (including FFC ones), and then this correction must be partitioned between ocean, land biospheric, and FFC fluxes.  Because the uncertainty on the prior FFC fluxes is thought to be much lower than that on the land biospheric fluxes, most of the correction should therefor be attributed to the land biospheric fluxes.  However, a small part of it could also be attributed to the FFC ones.  Usually this small amount is neglected and all of the correction over land is attributed to the land biospheric fluxes.  However, this is a simplification.  Inverse modelers could, without changing their inversions, choose to partition the correction differently between the two.  As it is, they are very aware that some of the correction that they currently attribute to the land biospheric fluxes could also be due, in part, to errors in the initial FFC fluxes.

64: reword "slower or faster" to "more slowly or quickly";  also add "and" before ")3"

66: change "on" to "from" in "on the IEA"

70-81: While interesting, the authors need to do a better job later in the text of explaining why this new metric is needed (i.e. why one should get a different set of simulated measurements when doing a separate forward run than in the inversion itself).

84: add "to" after "leading";  add "and" after "error,"

92: change to "single inversions"

93-95: What you are trying to say here is that none of these studies partition the inversion-group-based uncertainty between these three sources, but just give the total uncertainty.  Try to reword it to bring out that point better.

100: change to "Section 2" and "Discussion"

104: change to "Section 4"

112: remove "(" before "Bisht"

134: change "via" to "due to", for clarity;  correct "on the net a large land sink" -- doesn't make sense now

144: add "fluxes" after "land"

Table 1, line 3: add a degree sign after the first "2.8"

155: change "The 38" to "Of these, 38"

156: "and 3"

162: reword to "sampled at the observation time and the grid box nearest to the observation location at hourly intervals."

163: change "six months" to "six-month"

166: "with six harmonics by a cut-off length of 24 months for the digital filter."

It is not really clear how these six harmonics were chosen, given this wording. Please reword it to be clearer.

169, Section 2.4:  It is unclear what sort of Transcom-like inversion is being performed here.  Is it the so-called "cyclo-stationary" inversion, in which a single, typical seasonal cycle of flux is being solved for, then added onto the prior?  Or is it a fully time-dependent inversion in which the seasonal cycle for each year is optimized?  How many terms are in the state vector solved for?  Is it a matrix-based inversion?  How large is the matrix actually inverted?  How is the prior treated in this framework (i.e. what is the set of equations that is actually solved, and where does the prior fit into that)?  I note below that equations (1)-(3) do not seem to be written correctly, in that S and D ought to be vectors, not matrices.  In Figure S1 it is suggested that the basis functions in the G matrix have only been run out for four months -- how is the impact of a flux represented for times after those four months?  Is the influence just ignored? Perhaps I am missing something here -- please describe what you are doing more completely to make all this clearer.

173: change "lands" to "land"

178: usually, you would give the cost function a symbol, like:   "J = (D-Gs)T ... etc."

Note on equations: These need to be cleaned up a bit to conform with standard notation.  Vectors should be lower case and bold.  Matrices should be upper case and bold.  Change this both in the equations and text.  At the moment, you have the fluxes being put into a 2-degree matrix, S, whereas they are usually put into a 1-degree vector, s.  Why do you have it as a matrix?  Are you putting the vectors for multiple inversion cases all together into one big matrix and doing the inversion all together at the same time across all cases?  (If so, the equations given are not correct.)  If not, the fluxes should be put in vectors s.

187-188: A word about how you order the monthly fluxes into vector s (not matrix S) would be useful: the 84 measurements for month 1, followed by the 84 for month 2, etc...?

191:  Similarly, what you have at the moment as matrices D_obs and D_ACTM should actually be vectors d_obs and d_ACTM, right?

183: change "prior source covariance matrix" to "prior source error covariance matrix"

184: change "data covariance matrix" to "data error covariance matrix"

183-187:  Some more detail needs to be given about how these Green's functions are created.  Apparently, you are solving for monthly fluxes.  Are you also averaging all the measurements together into blocks of one month, as well?  Or are they treated at a finer temporal resolution?  How far out in time are the Green's functions run?  All 23 years, or across a shorter span?  If truncated, how is the effect after that handled?  Are the fluxes inside each emission region divided by the flux uncertainty before being run through the transport model (so that the spatial distribution of the uncertainty inside the region is captured)?  Or after the fact (i.e. uncertainty for the region as a whole)?

193: usually one uses the term "model data error" or "model data mismatch" to indicate that much of the error here is due to the model itself being unable to represent the data, as distinguished from a pure measurement error.  That is not captured by your term "measurement data uncertainty".

Change this to "model-data uncertainty" or something that indicates the model contribution, as well?

Table 2 caption, line 2: change "Every PFU and MDU cases are" to "Each PFU and MDU combination case is"

206-207: if you are multiplying by 3 and 4 in place of 2, shouldn't the ranges then become 0.3-3.0 and 0.4-4.0 PgC/yr?  That is not what you give at the moment.  Why do you change the lower bounds?

211: add a comma before "are used"

215: reword to "added these to an"

Figure 2: what does the subscript "pred" indicate?  Are these the a posteriori results?  Maybe something like "post" would be better...

233-234: Again, "posterior" or "a posteriori" would be more easy to understand in this context than "predicted", which could just as easily be thought to indicate the prior.

In general, "FUR" is not a great statistic, since it depends heavily on the prior uncertainty, which can be made arbitrarily large and not change the final uncertainty much, at least in cases where most of the information is coming from the data rather than the prior.

201:  Here you say that the PFU for the oceans in the control case is 1.0 PgC/yr, the same as it is in the fourth case, gpp_v4.  However, in the left column of Figure 3, they appear to be different colors.  Was the PFU for the oceans in the control case not 1.0 PgC/yr?

240: not the South Pacific -- a 1-5% reduction in uncertainty is not "good", I think.

242: after "Northern", change "Africa. The Tropical" to ""Africa, and The Tropical"

244: add "on the" before "regional fluxes"?  Otherwise, the meaning is not clear, so please clarofy

249: reword "into 1o x 1o spatial resolutions" to "to the 1o x 1o spatial resolution"

253-254: You assert that the ensemble mean of the 16 different cases is the "best estimate", but how do you really know that this is the case?  Maybe one of the looser prior cases is the best, because it allows the estimate to go closer to what the data indicate.  Or maybe one of the tighter prior cases is the best because it damps down the dipoles caused by the generally underconstrained nature of these inversions.  What criterion do you use to make this assertion?

256-257:  You should indicate what portion of the total uncertainty this ensemble-based measure pertains to.  In particular, since you use a matrix inversion-based inverse method, you can presumably get a full-rank covariance matrix pertaining to the flux estimate (for each ensemble member).  The uncertainties derived from this covariance would give you that portion of the total flux uncertainty due to the uncertainty in the measurements (the random error part) plus the uncertainty in the prior fluxes.  The spread across the ensemble quantifies other errors -- say here what you think those are.

260: reword "3-dimensional CO2 observations" to "3-dimensional CO2 mixing ratio fields"?

Because you don't have an observation at each point in the full 3-d field.

262: You need to give a reference to the source of this data.  In the References, you have a Schuldt et al reference pointing to obspack_co2_1_GLOBALVIEWplus_v7.0_2021-08-18. Does that pertain to this?  Which did you use, v6.1 or v7.0?  Please clarify.

271: "latitude intervals"?

279: Please indicate the total number of routine NOAA aircraft profile sites or time series you use.  Table S4 seems to indicate that more than just these three sites were used.  Maybe point to this Table S4 here in the text.

308: subscript "CO2"

309: What errors do you mean to include in the term "uncertainties in the predicted flux"?  Just those due to random errors (since uncertainty usually pertains to those errors)?  If you mean to say "errors" instead of "uncertainties", then wouldn't some of those errors already be due to transport errors?

321: "though" -- is this the word you want?  The sentence, as it is written now, is unclear.  Are you trying to say that the posterior results make reasonable corrections regardless of which prior they start from?  Please reword so that this is clearer.

333: "However, the degree of freedom of our inversions is similar to the gridded inversions when spatial flux correlations of greater than 1000 km are assumed (Peylin et al., 2013)."

A gridded inversion with a correlation length of ~1000 km would have, say, 36x15=480 independent regions being estimated, more or less, compared to 84 in your case.  This is not really comparable.  I would agree, maybe, if you said ~2000 km.  But what gridded inversions are using ~2000 km resolution?  Please reword this to make your meaning clearer.

340:  "two combinations": It appears that all 16 combinations of priors/prior uncertainties are shown in Figure 5 -- who do you say only two?

349-350: If you say that the uncertainties for the global land and ocean fluxes are 1.4 and 0.7 ppm, respectively, it makes me wonder whether you have accounted for the correlations (the off-diagonal terms) in the a posteriori covariance matrix properly in computing the uncertainties for those two regions.  Other global inversions of in situ CO2 data have found the uncertainty for the global land flux to be down around 0.5 PgC/yr.  Do you consider the off-diagonal terms in the a posteriori covariance matrix when calculating these uncertainty values on the global land and ocean regions?

Figure 5 caption, line 150: "brackets"

Figure 5 caption, line 150: "Numbers in the bracket in the legend are budget imbalance between inversions and observed CO2 growth rate."  The description given here and in the text (lines 360-361) does not make it clear how these values were calculated.  Do they measure the difference in _trend_ across the twenty years?  (I.e., the difference in the beginning and ending values, divided by the number of years.)  Or is it not the trend but rather the absolute offset that you are calculating?  Or is it the RMS difference between individual annual values?  Or monthly values?  What are the units?  Please do a better job describing this quantity in both places.

373: "-induced changes": this doesn't work with a long parenthetical expression squeeze in between the original word ("La Nina") and this phrase.  Please put the information inside the parentheses elsewhere (maybe in the caption to Fig. 5).

377: "generally showing an increased ocean sink during strong El Niño events (e.g., during 2015-2016)".  But your Figure 5c does not show this: it has an increased ocean sink at the end of 2016/beginning of 2017 and a reduced ocean sink in 2015.  The 2015/2016 El Nino began in mid-2015 (or earlier) and was well over by mid-2016.  The increased uptake, due to the capping of the thermocline in the East Pacific that occurs during the El Nino, should therefore be seen a full year before it is seen in Figure 5c.  Please remove this or do a better job explaining what you mean.

382: reword "caused by increasing pCO2 between the" to "caused by the increasing CO2 difference between the"

384: "and the gradual sink increase...":  Wait, if you remove the strong increase in sink lasting up to 2012, possibly caused by the incorrect reporting of Chinese FFC use, then there is no increase in sink after that, but rather a decrease in sink (after 2012).  Which effect do you want to argue for most -- the FFC effect or the CO2 fertilization effect?  (It does not seem that you can have it both ways...)

Figure 5d:  With your sign convention for land and ocean fluxes, the quantity plotted here should be labeled "FF + (land+ocean)" -- i.e. change the minus sign to a plus sign.

398-402: This is really worded poorly and makes it difficult to understand what point is trying to be made.  Really you are first giving the values the VISIT prior has for certain regions, followed by what the final predicted values are.  However, it reads as if you are first giving the difference between the VISIT and predicted values (actually, it is not clear at all what the values in parentheses refer to).  Please reword it to say: here is what the VISIT prior says the values should be, then here is what the predicted value is, then say where the final uptake is more or less than the prior.  I.e., reword it for clarity.

406: "neighborhood"

408: "less certainly"

409: "groups"

411: since a sink of -0.18 PgC/yr could also be considered "mild", maybe change the wording here from "show a mild carbon sink" to "show almost no carbon sink"

412: Why do you mention that the VISIT prior has strong sinks over all three South American regions?  Are you contrasting it to something?  Not clear why you mention it.

418-419: It is not clear why you tie the trend towards increasing sink in East Asia to the trend in increasing FFC values there.  If you are implying that the prior FFC numbers are overestimated there, please say that, to be clear.

420-422: "Because the atmospheric data constrain the total net surface flux, the rapid increase in fossil fuel emissions is required to be compensated by increasing the natural land uptake of similar magnitude through inversion."  This compensation is only required if the atmospheric CO2 amount is not increasing to take up the fossil fuel added.  There is no requirement for local land uptake in areas of increasing fossil fuel input, since the winds can blow the input around across the globe quickly.  Please reword this to make your argument clearer.

428: "support"

430-431: reword "while the prior flux consisted no" to ", starting from a prior flux that has no"

435: change "due to" to "given by" or "caused by the assumed"?

437: add "in the" before "gvjf inversions"

437-442:  In order for this discussion to be understood better by the reader, you should mention that the incomplete measurement constraint in the inversions permits "dipoles" of flux errors to appear between neighboring regions (compensating errors of opposite sign due to the inability of the measurements to completely localize the source or sink in the right place), and that that is what is likely being seen here.

443: replace "two-fold" with  "a two-fold higher"

444: replace "Inversion largely follows" with "The inversion results largely follow"

446: replace "as" with "is"

447: replace "of" with "off"

448: "is also known to have" -- what, "occurred"?  Please reword so that this makes some sense.

448-449: replace "tighter constrain by" with "a tighter constraint due to the"

450: replace "; while, we have" with ", even though we have"

Figure 8 caption:  it is unclear what "TDI calculation" refers to -- please spell out "TDI" and describe better what is meant by it here.

462-465: This sentence needs to be reworded for clarity.  It is only dimly clear what point is trying to be made, at the moment.

474 and Table S3 caption: subscript "CO2"

Table S3: You need to give some more detail here on what ENSO index you are using when doing this correlation.

470-471: "The CO2 flux anomalies in the tropical regions are strongly correlated with the ENSO index, while temperate and boreal regions are weakly correlated".  This is an overly-generous characterization of the correlations you show in Table S3: there are only a couple regions that might at all be considered to have "strong" correlations with the ENSO index (Southeast Asia at +0.61, Western Pacific at -0.62), and this is only because that correlated variability was present in the prior at a slightly stronger level.  Notably, the other set of priors did not give posterior estimates for these regions with a correlation stronger than 0.3.  You are blithely twisting your narrative well beyond what the data justify.

476: Russia is not one of the regions given in Table S3 -- maybe change to "North Asia"?

483:  Figure 7 refers to ocean fluxes.  Do you mean to point to Figure 6 or 8?

492:  In your discussion of the large IAV seen in Oceania, you do not mention that this is all coming from the gvjf prior and not from the data.  This is because the a priori flux uncertainty for that region is quite tight, according to Figure 3a (except for the control case -- why is the uncertainty in the control case so much higher there than for the other prior cases?  Is this an error in Figure 3a?).  Because the fluxes for the two different prior models (gc3t and gvjf) are so different, it would have been more reasonable to have used a looser prior for this region, reflecting the disagreement between the two actual prior timeseries that you used.  I like your discussion of the variability in the GFED prior, but it is unfortunate that you did not leave the fluxes for this region loose enough to test whether this prior is in fact in agreement with the available CO2 data.

500: You seem to be contrasting the gc3t and gvjf priors here -- please add something like "The gc3t" at the beginning of the sentence to indicate that you are talking about that case first, before switching to talk about the gvjf case.

502-504:  "The oceanographic observations indicate that sea surface temperature and pCO2 in the equatorial warm pool areas (5°N–5°S, west of the dateline) are not sensitive to El Niño conditions (Takahashi et al., 2003)."  If that is the case, how do you explain the "strong" correlation in the West Pacific in the gvjf case, both in the prior and final estimate?  What about the JMA model is correlated with ENSO if not SST and pCO2?

521-522: reword this first sentence so it is clear that the CASA model is the one with the July peak.

524: reword this to make it clear that it is the a posteriori, or predicted, estimates for the gc3t case that you are comparing to the prior.

527: It appears that you are still discussing the total land flux at this point, which is not shown in Fig 9a, but rather the figure to the left of that one -- please fix this reference here.

534: change to "Northern land fluxes drive"

539: change "are" to "is"

539-542:  You have described why the prior fluxes agree or disagree here, but not why the posterior fluxes do so.  For the posterior fluxes, they do not converge well in the tropics mainly because of the general sparseness of data there, or rather data that constrain the fluxes there.  Perhaps noting that, as well, would be useful.

547: add "adjoining" before "neighborhoods'" to indicate that it is observations in the surrounding area that are providing the constraint.

552: add "and" before "East Asia"

560: add a comma before "caused"

563: "It is not easy for us to explain the mechanism for the Northern Ocean to be a weaker sink in summer than in winter."  One possibility is simply the reduced solubility of CO2 in warmer waters leading to an outgassing of CO2 then.

568: add a comma after "Overall"

Figure 10 caption, 2nd line: replace "Each inversion cases" with "The different inversion cases"

Table S4 caption: change "is" to "are";  Also you need to say how you calculate the differences that are being plotted: is it model-observation?  Is it the average of the a posteriori fluxes for all 16 cases that make up the modeled value?

590-593:  It is not clear what distinction you are making between the 25 and 75 percent error bounds.  Aren't these just the two sides of the mean (i.e. 25% on either side of the mean, given by the bounds of the boxes in Figure 10)?  When talking about the 25% results, do you really mean the 5%/95% bounds (given by the whiskers)?  Not clear as currently written...

595: This lack of reduction for the larger regions makes me wonder again whether you have properly accounted for the off-diagonal terms in the a posteriori covariance matrix when grouping regions.

615: "hosts" and "and hence is"

624: it is not clear what you mean by "at a higher magnitude" -- please reword for clarity.

626: put the wiggle on the n in "El Nino"

633: "unanimously" doesn't seem to be used correctly here -- remove it?

636: subscript "CO2"

640: "is in the North Pacific,"

641: instead of "CO2 uptake rate", say "change in CO2 uptake", since it is not very clear that by "uptake rate" you mean the time derivative of uptake.

644: the Long et al reference is missing from the Reference list -- add it

646. This new section should presumably be numbered "6.", not "4.", since it follows "5.", and the Conclusion section later as "7.", not "5."

649: You need to define how you came up with these three sets of fluxes: 'gc3t', 'gvjf', and 'ensm' -- are they created from the average of the 8 gc3t and 8 gvjf ones, and the average of all 16?  If so, say so.

651, 653: "ATom"

Fig 11 caption, line 1: "meridional"

Fig 11 caption: you should indicate which quantity is subtracted from which when computing the biases -- it is not clear from the figure.

664: "Most of the aircraft data over these latitude bands are available over the continental regions, and this comparison suggests a higher sink than the estimated sink by inversion."  

It is not clear whether the aircraft data that you refer to here are the ATom and HIPPO data that you were discussing in the previous sentence, or other data.  Since the sign of the observation-model difference has changed, this implies that you are discussion some other set of data.  Please clarify this.  If the data is still the HIPPO and ATom data, then the two sentences seem to contradict each other.  Please reword these sentences so that your meaning is clear.   Also, in the final sentence in this paragraph, why do you say that the models seem to do a good job in terms of the mean CO2 level when in the previous two sentences you have just pointed out that they do not do a good job (i.e. they are biased), at least in the north?

673: "The inversions underestimate"

693: It is not clear what the broken lines are meant to indicate in Fig 12d-f.  Are these what you get using the prior fluxes, and the solid lines what you get using the predicted fluxes?  Please reword this both in the text and in the caption to Fig 12, so that this is clear.

694-697:  "In the case of predicted data, the inversion fits the observation well due to minimisation of prior model-observation differences, but when the simulations are run using predicted fluxes, the (small) systematic biases produce a (large) cumulative effect over the model integration period."  

This is NOT a general feature of flux inversion models, but rather a peculiarity of your inversion setup.  In most inversion models, when you do a forward run with the optimized fluxes, you get the same modeled measurements as the inversion would give (unless for some reason you choose to run the model at a different resolution than what was used in the inversion).  What is it about your inversion setup that causes this not to be the case?  One possibility that comes to mind is that you have not extended your Green's functions runs out in time long enough: how long do you run them for?  How do you handle the influence of a Green's function after this (i.e. after the end of your run)?  You must provide more discussion on why you get different modeled measurements from what you assume in the inversion when you run the optimized fluxes forward through the model.

Fig 12 caption and legend:  it is not clear what the dashed lines labeled 'gc3t' and 'gvjf' indicate -- are these the modeled measurements given by these two priors?  Please say in the caption what they are.  If they are the modeled measurements given by the priors, why do you not also plot these lines for the top panels?

699: "We speculate that MIROC4-ACTM produces stronger sinks in the high northern latitudes":

stronger than what?  Please reword this to make the meaning clear.

697-707: "It is also interesting to note that the meridional gradients in biases for independent aircraft observations (Fig. 12a,b,c) and sites used in inversion (Fig. 12d,e,f) show opposite phases, i.e., most negative and most positive at 25oN, respectively. We speculate that MIROC4-ACTM produces stronger sinks in the high northern latitudes (negative model-observation bias at surface sites over 75oN or HIPPO/ATOM latitude-altitude plots in Fig. S5, S6), which can arise from the model's inability to simulate the sites over the land because of the coarse horizontal resolution. Thus, resulting in a weaker sink or a stronger source in the northern tropics and subtropical (25oN) regions, respectively. The tropical source is then transported to the mid-high latitudes, which is captured by the aircraft observations, as a positively biased concentration. This experience suggests a need for new forward model simulations using inversion fluxes, not the optimised atmospheric CO2 fields during data assimilation, should be used for evaluating inversion fluxes with the help of independent observations."

This discussion is not clear and makes no sense to me.  Why should 75 deg N be an important inflection point for the surface data (there being very few surface sites that far north, anyway)?  If there is a stronger sink than there should be in the northern extratropics, then yes, there could be a balancing stronger source south of that.  But how could the positive perturbation in atmospheric CO2 then jump over the negative perturbation to the north of it to then somehow cause the positive model-obs differences seen in the far north (Figure 12 and S5)?  And even if this were a plausible explanation, how does this relate to running the optimized fluxes back through the forward model?  An alternate explanation would be too-weak mixing during the summer and too-strong mixing during the winter in the north, causing overestimation of the summer drawdown and underestimation of the winter accumulation of CO2 in the PBL.

710 and Figure S10:  If the same transport model is being used for the forward run as was used in the inversion, and run at the same resolution, then why would you expect that it would give a different simulation of the 3-D CO2 field than was obtained in the inversion?  What is the underlying reason?  (I can think of one possibility: that the Green's functions used in the inversion were not run out far enough in time, driving basis function time truncation errors in the inversion.  Is this the reason?)  Please do a better job describing why you think doing a final forward run would give different modeled CO2 fields, if this is a perfect model situation and the same model is being used for the forward run as in the inversions.

711-720:  This whole discussion also makes no sense to me.  For CO2, a model with weaker interhemispheric transport causes a stronger N/S gradient when forced with NH-dominant fossil fuel emissions.  When compared to the weaker observed N/S CO2 gradient, this then requires a stronger NH CO2 sink than a model that gives a weaker N/S CO2 gradient.  It is not very complicated and "complex interactions" need not be invoked.  I agree that one should not use the assimilated data as a test, but rather comparison against independent data.  But you do compare against independent data here (HIPPO, ATom), so why do you need this whole paragraph in the first place.  Please do a better job with your argument, so that the reader can understand your point.

723: You should be more specific and say that the land and ocean absorb 53% of the FFC fluxes, not of the total anthropogenic fluxes, because if you add in deforestation (which is an anthropogenic flux), it is no longer 53%.

730: add a comma before "and two"

734: replace "resultant" with "result"

735-736: "The spread between the ensemble members provides us a reasonable measure of the inversion estimated flux uncertainty but lacks the quantification of transport model uncertainty."

   It seems to me that the spread in the ensemble results should quantify the variability due to only those things that are varied across the ensemble: prior fluxes, prior flux uncertainty, and characterization of the MDU. It should not be expected to capture the usual estimation uncertainty due to errors in the measurements and errors in the prior flux (why? because the spread across the ensemble only quantifies the effect of mis-characterizing or changing the assumed statistics for those quantities, but does not capture the uncertainty due to those errors themselves).  Therefore, in addition to the errors due to transport, you should also add on these usual estimation uncertainties to get the total errors.  This would be a good place to mention that additional error source.

742: replace "extratropical" with "extratropical southern", since you are focusing only on the south not the north

743: "The ensemble of inversions splits into a “near-neutral” group and a “strong-source” group based on the priors."

It is unclear what feature in the flux results you are referring to here, with this statement.  Please say what flux feature you are discussing -- global total?  global land total? global ocean total?

750 remove the comma before "in less agreement"

752: "ATom"

766: what do you mean by "unanimously"?  That it is true across all 16 cases?

772: "North Pacific"

772: What do you mean by "the most considerable CO₂ uptake"?  The uptake in the Southern Ocean that you discuss here is not as large as the uptake in the land regions you just mentioned.  Do you mean "the most considerable CO₂ uptake in the oceans"?

778-779: "There is no doubt that this set of results is unique because they close the year-to-year budget of decadal CO₂ changes in the atmosphere."

Almost all inversions close the year-to-year budget in decadal CO₂ change, due to the strong observability of the fossil fuel input minus atmospheric increase.  Given that, why is your set of results unique?  I have the little doubt that it is not.  Please reword to make your point clearer.

779-780:  "The bottom-up inventory or other modelling system still has limitations in closing year-to-year budgets."

You have used two sets of priors here that make no attempt to satisfy the long-term CO₂ trend in the atmosphere by trying to model an appropriate global land biospheric uptake.  That does not point to a limitation in the modelling systems but rather a deliberate choice that you have made in the work you present here.