General comments:

Authors presented results of a numerical study aimed at understanding the impact of including the diurnal variation in prior surface CO₂ fluxes, as opposed to using flat daily mean fluxes without diurnal variation. The resulting flux changes in the global and regional models at the level of annual mean fluxes for large regions have been found to be substantial. The study results may point to a useful direction to revising the inverse modeling setups. The results will be useful to CO₂ inverse modeling community, as those help understanding the differences between models resolving the diurnal variation in prior fluxes, and those that don’t. The manuscript is well written and can be accepted after minor revisions.

Detailed comments:

Lines 60-75 Some model related uncertainties in simulating diurnal cycle have been studied by Patra et al. 2008, Law et al. 2008. Could be worth mentioning.

Line 192 Suggest adding short description of the diurnal flux dataset (from Bodesheim et al) constructed from FLUXCOM), citing time resolution, meteorological field used to drive diurnal cycle of GPP, net annual flux difference between diurnal and daily versions.

Line 275-284 Data in Figure 5 are interesting specifically to CO₂ inverse modelers and are worthy of more comments. For example, do corrected budgets increase or reduce mean regional flux dipoles? In addition to temperate North America, emissions grow in tropical South America, and North African sink increased, and 2 later regions are not strongly constrained. Maybe those changes are correlating with differences between models in model ensembles like Friedlingstein et al 2023, Byrne et al. 2023?

Technical corrections:

Line 26 correct: FLUXCOM

Line 132 hyperlink covers only part of the path.

References

Byrne, B. et al.: National CO2 budgets (2015–2020) inferred from atmospheric CO2 observations in support of the global stocktake, Earth Syst. Sci. Data, 15, 963–1004, https://doi.org/10.5194/essd-15-963-2023, 2023.

Friedlingstein, P., et al.: Global Carbon Budget 2023, Earth Syst. Sci. Data, 15, 5301–5369, https://doi.org/10.5194/essd-15-5301-2023, 2023.

Law, R. M., et al. (2008), TransCom model simulations of hourly atmospheric CO2: Experimental overview and diurnal cycle results for 2002, Global Biogeochem. Cycles, 22, GB3009, doi:10.1029/2007GB003050.

Patra, P. K., et al. (2008), TransCom model simulations of hourly atmospheric CO2: Analysis of synoptic-scale variations for the period 2002–2003, Global Biogeochem. Cycles, 22, GB4013, doi:10.1029/2007GB003081.

The manuscript "To what extent does CO2 diurnal cycle impact carbon flux estimates in CarboScope?" by Munassar et al. documents a study which relates to the general topic of the impact of the uncertainties in the diurnal cycle of CO2 biogenic fluxes in global and regional atmospheric CO2 inversions. 

Here, I insert and resume my access review and maintain my opinion regarding this manuscript, i.e., that it should be withdrawn, and resubmitted with a major revision of its scope. However, the discussion phase gives the opportunity to the authors to answer my concerns and potentially to propose some major revisions to address them.

My main concern is that although the general topic of this study is relevant for the inverse modelling community, and although the authors provide a clear analysis, this study focuses on a specific question which can hardly provide general insights for this community.

As underlined by "in Carboscope" in the title of the manuscript, the specific type of errors examined by this study is inherent to the specific configuration of the CarboScope global inversion system, which:

- uses prior estimates of the Net Ecosystem Exchange (NEE) with flat diurnal cycles 

- does not control the diurnal cycle of the NEE 

whereas, in general, global and regional inversions (including the CSR system) use prior estimates of the NEE with diurnal cycles and/or control this diurnal cycle. 

Consequently, the manuscript assesses the impact of using and keeping in the global inversions flat diurnal cycles for NEE, and misses broader questions for the inverse modelling community: 

- what is the impact of the current level of uncertainties in the diurnal cycles from "bottom-up" products such as simulations from state-of-the-art vegetation models ?

- what is the capacity of inverse modelling systems to control the NEE diurnal cycle at global and regional scales when only the daytime data are assimilated at most of the measurement stations

And indeed, the conclusion states (l 464-465) : "Hence, an assessment on the uncertainty of the diurnal cycle effect among atmospheric inversions will be presented in a follow-up study." I think that the two studies should be merged, or at least that the first study should take further steps in the direction of the second. In my opinion, this initial step of assessing the impact of flat diurnal cycles in inversions that do not control this cycle can hardly be the stand-alone subject of a publication in ACP.

This general concern is strengthened by other issues:

- The limitations of the scope in this study are exacerbated when analyzing the results from regional scale inversions by the focus on coupling a global inversion without flux diurnal cycle and a regional inversion with a flux diurnal cycle. This specific configuration corresponds to existing systems and brings insights on the impact of biases in the boundary conditions on regional inversions, but in the spirit of the study and of the introduction of this manuscript (also of the abstract, which is misleading regarding this), one would have also expected the coupling between a global inversion and a regional inversion both without flux diurnal cycle.

- I do not really understand the discussions on the rectifier effets here. Is it useful to have such discussions when dealing with atmospheric inversions relying on dynamical models which account for the variations in the vertical mixing (even if with some limited accuracy) ? In a more general way, is not the introduction going back too far ? Several parts of these discussions are quite difficult to follow (in the introduction and in the conclusion) and sometimes misleading, with lines 71-72 stating that "CO2 concentrations are lower near the surface than in the free atmosphere due to strong daytime vertical mixing" while the daytime vertical mixing attenuates the decrease of CO2 near the surface due to the photosynthesis.

- The manuscript assumes that the linearity of the impact of ignoring the diurnal cycle in both the prior estimate of the fluxes and the inversion control vector is obvious. However, it is due to the configuration of the CS system (which would add its correction for the daily fluxes to the prior hourly fluxes as a constant value over the day rather than scale the prior hourly fluxes) and in practice, the variational inverse modelling scheme loses part of this linearity. Therefore, this topic deserves some explanations.

- The manuscript could have expanded the discussions on the signal from the fluxes at the observation sites (depending on the type of observation site and on the periods of the day when their observations are assimilated) that is exploited by the inversions: an integration in time and space of signal or a time-lagged signal from remote fluxes vs. the differences between stations informing about the fluxes in between vs. instant signal from local fluxes; this may help better understand the positive and negative biases in the observations and flux estimates depending on the stations and regions. Why would some of the sites "affected by large-scale ocean background" correspond to large negative biases in the TM3 usual simulations if they bear little terrestrial influences as currently stated by the first paragraph of section 3.1 (the following paragraphs provide a quite different picture, but ignore the large negative biases) ? This section forgets to discriminate results depending on whether the observations are assimilated during nighttime or daytime only.

That said, as indicated earlier, I think that the authors conduct a clear and sensible analysis. Pieces of information are missing in the presentation of the inversion configuration (e.g., regarding the prior error covariances of CSR). Furthermore section 3 is sometimes a bit confusing regarding the sign of the biases since it discusses both the differences inversion with diurnal cycle minus inversion without diurnal cycle and the biases, which correspond to the inversion without diurnal cycle minus the inversion with diurnal cycle. This culminates at lines 307-308 where the underestimation (which should correspond to the bias in the usual CS-CSR inversions) of the CO2 uptake if found during the growing season. The discussions on the IAV may also be led a bit too fast. However, overall, the paper reads well.