Honestly speaking, I have conducted research for inverse modeling and eddy covariance observations for more than 10 years, but still feel this MS (egusphere-2023-805) by Upton et al. (2023) is very hard to follow and understand in recent version, including both the logical organizing for different paragraphs and detailed expressions in sentences. This MS is not a bottom-up and top-down based research paper, but a mathematic based way that made use of avalable dataset, and without enough details. Therefore, I do not recommend for publication unless large and significant improvement have been made to improve its reliability and robustness and readability. 

First, although the authors combined “bottom-up” CO2 flux and “top-down” atmospheric inversion CO2 flux data set, from my first feeling when go through the introduction and methods sections, it reads like the authors conducted at least one of above approaches. However, after I read through results for quite a few times, it seems the authors only used some mathematic method (i.e. a region-specific sparse linear model) to make use of both datasets and made some adjustment. Hence, the mathematic method is the main advantage, but it has not been descripted in details how to use this method and its advantage when compared with above “bottom-up” and “top-down” methods.

Lines 15-21, “The inferred global terrestrial carbon flux from land, excluding fires and riverine evasion across 2001-2017 is -3.14±1.75 PgC year -1 (±1 σ). This is a strong improvement over the -20.28±1.75 PgC year -1 from the exact same data-driven flux model trained without the additional regional top-down constraint (i.e., single constraint) when compared to current best estimates of the global carbon flux from land.”, the authors said this result is considerably different with another result, and why the readers can believe your results is robust as you said “is a strong improvement”? there are many previous studies that calculated global NEE, how does your results compared with theirs?

Line 60, please give us the extent of recent studies who calculated global NEE here, including both top-down and bottom-up approaches.

Line 70-85, after reading this part, which aim to describe the method the authors used in this MS, I am still confused why only a few sit-scale based regressions can be used to represent whole regional scale? As the authors said this is based on atmospheric inversion results, and the available global NEE products as Carbon Tracker provide NEE at more than 1^o, how does this coarse spatial resolution be used with FLUXNET and eddy covariance tower at site scale (i.e. 100m*100m)?

The main assumption in this MS is “The central hypothesis of this study is that individually trained regional sparse linear models can serve this function”, how to certify your hypothesis is robust from site to local and regional scales?

Line 92 “At tower locations the meteorological data is derived from the FLUXNET and ERA5 data,”, the highest spatial resolution of ERA5 is 0.25^o (~25 km), and the EC tower site is point scale, so how to evaluate the footprint mismatch between them. And for the section of 2.1, what data is produced by the authors and what is produced by the references? I am still confused here what the authors’ contribution.

Section 2.2, the atmospheric inversion community have found the flux results by different assimilation systems largely varied by both global total NEE, and its magnitude, especially for spatial distributions, which are caused by difference in atmospheric transport models observed concentration, how to choose which is reliable in your research?

Line 111, “These variables are were computed” delete were

Line 113. “and are reconstructed here by the on the percentage of the component PFTs”, it’s hard to follow.

In Figure 2, what’s the reason for the large difference between red, blue lines and green, yellow lines, emissions from rivers as you stated?

Section 5.1, I am very confused why the authors believe atmospheric information (inversion flux) is reasonable at grid scale? Large bias exist even for large regional scales as whole continent or country.

I have not provided coments on the spatial-temporal patterns of NEE, which seems not robust before the authors add more descriptions to verify their method.

Review of “Constraining biospheric carbon dioxide fluxes by combined top-down and bottom-up approaches” by Samuel Upton et al.

The paper addresses the quantification of Net Ecosystem Exchange (NEE) from multiple datasets. The concept is a multi-scale approach to estimate NEE fluxes using an additional atmospheric "top-down" constraint to further extrapolate the bottom-up data-driven flux model, originally derived from eddy covariance sites. Overall, the paper is well written, and mostly need to educate more the readers about the author’s innovative framework.

The proposed method seems to provide a substantial contribution to the field by attempting to reach reliable continental scale carbon dioxide flux estimates. However, in order to reach such conclusions, the authors should outline better and more clearly the steps regarding the EC-ATM optimization constraints. This could be done simply by presenting more illustrations of the technical implementation such as, for example the one shown in the appendix.

Specifically, it looks like the various weights employed in the objective functions and parameters such as the region-specific parameter are playing an important role in the optimization and extrapolation from local NEE to RECCAP regions. The considerable change in the global flux suggests that the top-down inversion’s weights will drive the flux estimation at regional scale. It seems important to quantify such effects to further appreciate the multi-scale flux estimate and its uncertainties at the RECCAP-2 level. This is illustrated in Fig. C1 where the EC-ATM can diverge from both the inversion mean and the EC model.

The results seem to be overconfident in regions such as the tropics where there are much fewer observations to drive both the bottom-up and the top-down datasets. This suggests that the uncertainties in top-down inversions is underestimated. I apologized if I missed something and I did not understand fully the evaluation

There must be a way to propagate uncertainties to estimate the combined errors associated with the EC-ATM.

Minor comments:

Section 3.3: Can you expand about how inversions are used here, is the model is trained using 16 out of the 18 years? Does it mean only the ensemble mean is considered?

The shorten word Fig has to be spelled with a dot as Fig.

P2L43: Gaubert et al., showed improvements at the scale of the latitudinal distribution of fluxes, not at the scale of continental-sized regions.

P4L152: “from the as an independent data to test” There are two article the and an.

P8L198: The accent ^ should be on the m (not on the r).

P9L214: “are are” repeated word

P9L235: “The EC-ATM ensemble mean preserves the correlation with the scaled anomalies, producing very similar results to the FLUXCOM RS+METEO results 3.”

The sentence is not clear, what is result 3?

Maybe it is Table 3, I cannot find mentions of Table 3 in the text.

 P19L384: xCO2, the x is usually upper case. Maybe you could spell out what are XCO2.