General comments:

This paper presents an update to a previous study (Steinkamp et al., 2017) that estimated New Zealand's CO₂ uptake from atmospheric CO₂ measurements. This new study provides a significant update, as it extends the original 3-year study to 10 years, it improves the resolution of the atmospheric transport by a factor of about 10 (which was important to test due to New Zealand's complex topography), and used 2 prior terrestrial models that have been calibrated with country-specific data (in contrast to the Steinkamp study that used one model that was not calibrated for New Zealand). It is worthwhile that these improvements have been made to confirm the general conclusion of the Steinkamp study that the observations show strong CO₂ uptake by forests in New Zealand. 

The paper is very well written and worthy of publication. My main comment is that it would be worthwhile putting the key details of the inversion methodology into the main part of the paper (e.g. move Section S1 to the main paper, or if condensed then include that the inversion is solved analytically, for fluxes in 25 regions at weekly resolution, there is a smoothing on week-to-week variations). The paper currently doesn't really describe well enough what are the unknowns that are solved for - are these scale factors for the regional fluxes for 25 regions x number of weeks? And also that the spatial flux pattern within regions is maintained. As part of this, I would recommend moving Fig S1 from the Supplement to the main part of the paper, which will also help with some of the discussion later. Even though all of the details are in Steinkamp, I believe the main details of the inversion should be repeated here in the main paper, as the inversion is so central to the study. 

Specific comments:

Line 139 - I would emphasise that the custom NZCSM was at ~1.5 km (i.e. "... input data for the period 2014-mid 2016 at 1.5 km (herinafter ..."). Also, at line 146, I would put "... so the mid-term switch from NZLAM at ~1.5 km to NZCSM-generated input data at ~12 km spatial resolution was considered ...". Neither of these changes are critical, but I think they would aid clarity.

Line 153 - Perhaps change to "time-disaggregated modelled footprints ..." or add other information to explain the disaggregated footprints a bit more.

Line 188 - there's not much Northwest at Lauder with NZLAM, mainly north.

Fig 5 - I would put the NZLAM to the left of NZCSM, in the order they are used in time, so either (Meas, NZLAM, NZCSM) or (NZLAM, NZCSM, Meas) - the 2nd option is probably better. In the caption, I would put '(top)' after 'Baring Head', and '(bottom)' after 'Lauder'.

Line 197 - I presume this sentence means that the prior fluxes were used "with the observations in the inversion" to estimate the posterior fluxes. It could be misunderstood how it is. 

Line 312 - What does it mean that you "used" the individual flux components? These components were both estimated in the inversion? 

Line 143 - It would help with this text if Fig S1 was in the main paper. In the previous sentence, the region name is mentioned before the number, I like this better than mentioning the number first (you do need to mention both).

Figs 10 and 11 (and perhaps elsewhere) - The captions say 'air-land flux', but a negative value in the figures indicates a positive air-land flux (uptake) and a positive value in the figures indicates negative air-land flux (source, or land-to-air flux). This could be misleading, and worth specifying in the caption what positive and negative values indicate, and possibly using a different term from air-land flux to avoid the implication of a direction of flow for a positive value. Steinkamp's Fig 5 y-axis label is land-to-air flux.

Line 510 - "the overestimated sink is less pronounced" - this could be expressed more clearly.

Fig 17 - Put a thin black zero line over the top of the plots so it is clear how the data compares to zero. Also, adding a scale and tickmarks to the right side of the right plots would help too.

Line 556 What two features does "Both features" refer to? The previous sentence only mentions one feature (supressed autumn/winter respiration). 

Line 572 - "in the prior" - is this supposed to be "compared to the prior"? Or "in the prior" if it was included in the prior model? This part of the sentence is not clear.

Line 751 - 'less sensitive' that what? Than to the other regions?

Section S1 - What are the unknowns that are solved for in the inversion? I.e. what is x? Are they scale factors for the priors in the 25 regions?  As mentioned above, some details of the inversion system should be described in the main paper, and I would put all of Section S1 into the main paper, with a bit of extra detail.

Typographical errors/technical corrections:

Line 57 - It could be useful to add '(boundary conditions)' after 'background values', as some other studies use this terminology.

Line 42 "scalMOLes"

Line 173 - replace '.' with 'see'

Line 229 - Fore New Zealand

Line 324 - move comma "Australian, region"

Line 340 - add "such" - "such as the"

Line 403 - 'report' -> 'reported. Give a reference for the Inventory here.

Line 479 - 'process' -> 'processes'

Line 543 - 'owing' -> 'showing'

Line 643 - add 'on the' after 'depending'

Line 771 - Check the end of the sentence 'and other .'

This reviewer feels this paper is in scope for ACP, presenting atmospheric top-down carbon dioxide estimates across New Zealand, using two in-situ sites (North and South island) across a 10-year period. The key result for the paper is a larger carbon sink than previously reported compared with both bottom-up estimates and from the study this paper builds on. The potential sources for this difference are presented and discussed. This also presents an updated biospheric flux model tailored to the region.

This paper is thorough and well written, includes interesting and well-justified conclusions, has appropriate references to current literature throughout and some novel work which could prove useful for the community. The scientific methods are well discussed, with details given on the sets of inputs to the inversion model. Some details for the inversion model itself are included in the Supplementary Information but as this is the focus for the paper these methods should be included and discussed in the main text (as also noted and expanded upon by Reviewer 1).

Specific comments below:

L153: "Our inversion used 4-day integrated air concentration (i.e., footprints, units g s m-3, Fig. 3), averaged throughout the Planetary Boundary Layer (PBL)". What is meant by averaged throughout the Planetary Boundary Layer (PBL) here?  Was this taken at various heights above the surface based on the PBL values in NAME meaning this was variable for each footprint?

L159: "By the end of the 4 days, most of the particles had left the model domain." Has this been tested for the footprints involved in this study as well as Steinkamp et al., 2017? A 4-day period seems short but is this due to small domain and large wind speeds?

Section 2.2.1 Atmopsheric model transport validation: Why are wind speed and wind direction the most important meteorlogical parameters to investigate here? Were there other parameters which may be significant as well?

Section 2.4 Prior and posterior uncertainties: Would be good to see justification for the uncertainty terms chosen including:

 - "we fixed (i.e. summed) 50% of the uncertainty term"

 - "The uncertainity for pine fluxes from CenW were assumed to be 30%, 30%, 60% of the NEE, GPP and ER flux magnitudes"

 - what was the justification for these choices for uncertainties? Do we know they are representative (or that the extremes included within the sensitvity tests are justified)?

Table 2: Exclusion of Test 9 and 10 from the table itself (and details included in the caption) is a little confusing when comparing to Figure 14. Would be good to see the details of these tests included within the table.

Supplementary Info

SL54: "NAME III vn6.5 dispersion model for the years 2014-2020 while for the period 2011-2013, we retained the original NAME III vn6.1 simulations" - was any comparison made between the outputs between the two NAME versions? Did this make any difference to the sensitivity profiles?

SL68: "00Z" - does this mean UTC at midnight?

Figure S6: Consider updating the red-green in this plot to something colour-blind friendly (this could include changing one of the maker styles to be distinctive).

Table S3: For the "Area (m2)" column is the area itself known to this level of precision?

Figure S17: "Diurnal cycle test results for the land inversion regions." Caption is not too descriptive and requires other details to understand the context for this. Please add a few more details here to this caption more standalone.

Typos and grammer:

- L42    scalMOLes --> scales

- L123-124 (Terao et al., 2011; Yamagishi et al., 2012; Müller et al., 2021)) - Bracket within a bracket here, this should be typeset to remove this.

- L229: Fore --> For

- L256: Front quote around 'other forests' is a back rather than a front quote

- L726: "the inverse model detect" --> grammer issue here

Supplementary Info

- SL68: creata --> create

- Figure S16: Tabel 3. --> Table

- Figure S19: Timseries --> Timeseries

Review of “Inverse modelling of New Zealand's carbon dioxide balance estimates a larger than expected carbon sink” by Beata Bukosa et al.

I read this interesting manuscript submitted for publication in ACP. The paper uses observations of CO2 from two sites in New Zealand, an inverse model that uses for transport modelling and land fluxes from two terrestrial ecosystem models plus oceanic exchange fluxes. The paper is very detailed and well written. However, as it appears from the writing, the authors are finding it difficult to reconcile the inversion estimated flux of CO2 with the country level estimations by bottom-up methods or those predicted by the land models. I have one concern that is the handling of the boundary condition which is most tricky in original model when simulating the long-lived atmospheric constituents. I am fairly convinced that this paper should be published, but a follow-up study with a variety of boundary conditions would be of interests for the research community.

Specific comments:

Line 42:  typo - scalMOLes

Line 51-53: a bit of overstatement here, given that you are still struggling with reconcillation of bottom up and top down estimations. Of course, it is possible to get good comparison for a specific set of results which may not be universally applicable.

Figure 2: this is one of the most important plots in my view because the clear offset with background, as seen from panel b at Lauder, will produce more pronounced sinks around Lauder, that is, the South Island of New Zealand.

Line 121-124: i think this is likely a wrong construct of the inversion, when the zonal winds are very strong over NZ! You probably need to use a global model providing 3D concentrations of CO2 for use as a background, possibly after adjusting to BHD & TF5 measurements.

Line 144: how do you define the planetary boundary layer-does it change with hour of the day? What data and method is used to determine the PBL height?

Figure 8: as expected from Figure 2b, the inversion results for South Island, in particular south of Lauder, show strong negative values or CO2 sink.

Figure 9: the issue of strong sink south of Lauder is further clear from this plots. The green bars are bigger compare to the black ones for the regions 13 to 15.

Figure 17: are these a priori or a poste? in any case they can clearly see the observed concentrations were lower than the model in the case of Lauder . And then as expected you would need more sink in the south ern part of the South Island (Fig. 9)

Figure 17: caption can start with “Model – measured …”