Please refer the attachment. 

I have enjoyed reading the manuscript entitled "No increase is detected and modeled for the seasonal cycle amplitude of δ13C of atmospheric carbon dioxide" by Joos and co-authors. 

Their study looks into the seasonal cycle at a number of stations across the globe for CO2 and δ13C(CO2). The authors find no trend in the seasonal cycles of atmospheric observations and simulations from their modeling framework. The model also allows them to assess (iso)fluxes and their spatiotemporal patterns.

Overall I feel that this is a thorough study and I expect that it will be a valuable resource for the community. My main concerns are related to missing connections with some other key δ13C studies and the length and structure of the manuscript. I recommend publishing the manuscript after addressing these comments.

MAIN COMMENTS

(1) CONNECTION WITH KEELING ET AL. (2017)

The key paper by Keeling et al. (2017) is not discussed. I believe that it is a relevant reference at various places in this manuscript, in particular the Introduction and Sect. 5.1. A few specific examples (not-exhaustive) are provided below:

-L9: "no long-term temporal changes in the isotopic fractionation by C3 plants." This seems to contradict with Keeling et al. (2017).

-L48-50: "It remains to be assessed whether a scenario with small long-term changes in fractionation of C3 plants is compatible with atmospheric δ13Ca observations representing carbon fluxes over large regions." How does this relate to Keeling et al. (2017), who conclude that there is a long-term change in discrimination?

-L451: "An absent temporal trend in ci/ca translates into an absent trend in εNPP, and vice versa (Eq. 10)." What if the other terms of Eq. 1 in Keeling et al. (2017) are also considered?

(2) LEARNING FROM dC13(CO2)

The authors make various statements about the potential of the seasonal variation of δ13C to constrain biosphere models. I appreciate the big picture that the authors create, but the statements would be more convincing if authors would also provide some more direction on how to achieve this. Also, some reflection on studies that already attempt this would strengthen the arguments.

-L14-16: "We propose to apply seasonally-resolved δ13C(CO2) observations as a novel constraint for land biosphere models and underlying processes for improved projections of the anthropogenic carbon sink." and L525,526: "We recommend to apply seasonally-resolved δ13Ca observations as a novel constraint for land biosphere models used to simulate the terrestrial sink of anthropogenic carbon and land use emissions." How should this constraint be used?

-L69,70 :"... but to our knowledge have not been used as a benchmark for model performance in combination with an atmospheric transport model and for analyzing trends in SA(δ13Ca) globally." I think the study by van der Velde et al. (2018) does this through data assimilation in their model framework. It would be good to reflect on that, and what more could be done. Finally, also Ballantyne et al. (2011) is not mentioned. Those authors reflect on seasonality of δ13C and use δ13C to learn about some leaf parameterisations.

(3) LENGTH AND STRUCTURE

Overall, I found the manuscript quite lengthy especially Sects. 4 (Results) and 5 (Discussion). Based also on the titles of the subsections there appears to be some overlap in the scope of different subsections. I would recommend shortening and potentially integrating the Results and Discussion section such that in one of those subsections a certain aspect can be described more holistically, avoiding some (perceived) overlap.

Also some paragraphs could be moved to other sections or the supplement, e.g.: L505-508: "On a technical note, transporting simulated 13C fluxes is not without challenges. The definition of the δ-notation can pose numerical difficulties when net 12C fluxes are close to zero. We find that transporting signature-weighted total carbon fluxes is the most reliable method for arriving at local δ13Ca. Similarly, seemingly small errors in the model representation of gross fluxes and mass balances, can become critical when considering net surface-to-atmosphere fluxes." This seems to be a valuable comment, but a bit strange to end the Discussion with this point. This can probably be integrated in a more natural way in the Methods section, e.g. somewhere around Eq. 1.

MINOR COMMENTS

L20: For completeness I recommend to include a definition of δ (this is e.g. needed for the derivations in section 3).

L181-182: "In this way, a positive (negative) flux causes a positive (negative) change in δ13Ca". Should "positive (negative)" in the latter part of the sentence be reversed to "negative (positive)", because of the minus in the equation?

Table 1 and 2: The labels "Standard" (and "Std") are a bit confusing when quickly looking at these tables. I recommend using "Simulated" (and "Sim"), or "Modeled" (and "Mod") to be consistent with the in-text equation in L311-312.

Fig. 4: Is "/yr" missing from the unit on the y-axes for panels a and b?

L557: Here you mention why you used NPP and not GPP. I think this should be stated much earlier, for both Eqs. 9 and 10.

SPECIFIC COMMENTS

L31: "earth system models", capitalize?

L32: "C3" is usually written with subscript (throughout manuscript, similar for "C4")

L58: "(e.g. Peylin et al. (2013))" > "(e.g. Peylin et al., 2013)"

L95: "(about 9ox4.5o)", replace letter "o" with degree symbols, as in e.g. L100 (similar for L131,137)

L95: "(about 9ox4.5o)", replace letter "x" with multiplication symbol ("×"), also for other lines

L181: after "instead" insert "of"

L186, Eq. 7: Move "dt" after "Fas,net(t)"?

L188, Eq. 8: Move "dt" after "d13F*as,net(t)"?

L200: "These seasonal fluxes will be presented in section 3.3." Section 3.3 does not exist

L280: Fig 3, title above panel a misses "("

L323,324: "represents well the (...) atmosphere", change to ""represents the (...) atmosphere well"", or alternatively "accurately represents the (...) atmosphere""

L389: "4;see" > "4; see"

L498: "δ13C(CO2)" > "δ13Ca"

L502 (2x): "δ13C(Ca)" > "δ13Ca" 

L510: "δ13C(CO2)" > "δ13Ca"

L514: "δ13C(CO2)" > "δ13Ca"

L515: "δ13C(CO2)" > "δ13Ca"

L519: "δ13C(CO2)" > "δ13Ca"

L519: "tropic" > "tropical"

L536: "(e.g., Mook (1986); Joos and Bruno (1998))" > "(e.g., Mook, 1986; Joos and Bruno, 1998)"

L708: "CO₂" > "CO2"

L731: "Keeling, C. D., B., B. R.," > "Keeling, C. D., Bacastow, R. B.,"

L733: "https://doi.org/10.1029/GM055p0277" > "https://doi.org/10.1029/GM055p0165"

REFERENCES

Ballantyne et al. (2011). Novel applications of carbon isotopes in atmospheric CO2: what can atmospheric measurements teach us about processes in the biosphere? Biogeosciences, 8, 3093–3106. https://doi.org/10.5194/bg-8-3093-2011

Keeling et al. (2017). Atmospheric evidence for a global secular increase in carbon isotopic discrimination of land photosynthesis. Proceedings of the National Academy of Sciences, 114(39), 10361–10366. https://doi.org/10.1073/pnas.1619240114

van der Velde et al. (2018). The CarbonTracker Data Assimilation System for CO2 and δ13C (CTDAS-C13 v1.0): retrieving information on land–atmosphere exchange processes. Geoscientific Model Development, 11, 283–304. https://doi.org/10.5194/gmd-11-283-2018

Thanks for the opportunity to review this work.