The manuscript “Trivial improvements of predictive skill due to direct reconstruction of global carbon cycle” by Spring et al. describe results from reconstructed simulations nudging a model simulation to itself for atmospheric physics, ocean physics, and carbon cycle as well as perfect predictability experiments with the original model and these reconstructions.  I like this paper very much as a detailed investigation into the limits of injesting "data" into a model.  The text is extremely dense, with many concepts and model limitations all being discussed at once with a focus on biases without any description of the mean state, which made me need to read over sections over and over before I was able to put the pieces together.  For example, the degredation of ITCZ and Southern Ocean winds is only clear after one puts together a mental map of the base state.  It might help to have the base simulation of each parameter in Figure 1 as a new Figure 1 or provided as supplementary material.  The use of language was combersome, however,  with such vague words as "indirect", "direct" and "reconstruction" are used when descriptive terms like "physically nudged" "physically nudged atmosphere" and "physcially and biogeochemically nudged" would have worked.  I am guessing that there is a literature precedent for this redirection of terms, but it made the early parts of the manuscript difficult to maintain in scope.  The discussion of Figure 2 is incomplete and extends out through Figure 5.  The conclusions seem a bit wanting of the opportunities for future investigation.  Rather than being satisfied with “We conclude that the indirect carbon cycle reconstruction serves its purpose.” It would be much more productive to point out what alternatives to nudging might provide superior options for future work.  It should also be noted in the conclusion that the present work does not address the potential role for structural uncertainty, and potential for ecosystems to be more complex than represented in the current model and thus needing external constraint and providing a potential advantage to “direct initialization”.

technical comments:

p1,ln8 – “We nudge variables from this target onto arbitrary initial conditions 150 years later mimicking an assimilation simulation generating initial conditions for hindcast experiments of prediction systems” I don’t understand how this process works from this description.  There is also a comma missing after “later” Instead, it sounds like the authors “nudged variables towards simulations from the same run 150 years earlier” to create a reconstruction of the target dataset.

P1 ln12 -  I don’t quite understand the distinction between “direct reconstruction” and indirect reconstruction”.  It is not defined in the abstract.

Abstract overall – I think this is the longest abstract I have ever seen, yet it only describes concepts vaguely.  I recommend the authors strip out the details of internally defined distinctions and spend more time on the implications of “We 25 find improvements in global carbon cycle predictive skill from direct reconstruction compared to indirect reconstruction. After correcting for mean bias, indirect and direct reconstruction both predict the target similarly well and only moderately worse than perfect initialization after the first lead year.”

Ln41 – “where the forecast is started from” is redundant.

Ln 42 – comma needed after “Therefore”

Ln 44 – does “indirectly” translate to “uninitialized”?

Ln 55 – This sentence is an identity “In this perfect-model target reconstruction framework, we have perfect knowledge about the ground truth and a perfect model”

Ln 58 – “Originally”? A reference should be provided as to the early work that is being invoked.

Ln 60 and 61 – This appears to be describing results and conclusions of the present work.  References should be provided to establish the literature context (as is done on ln 62).

Ln63 – comma needed after “change”

Ln 65 – How do you know about these “severe consequences”? what is the citation?  I know that this problem is discussed in the following, but there must be others:

Park, et al 2018: Modeling Global Ocean Biogeochemistry With Physical Data Assimilation: A Pragmatic Solution to the Equatorial Instability. Journal of Advances in Modeling Earth Systems, 10(3), DOI:10.1002/2017MS001223.

Ln 91 – This is a strange justification.  One could make the same argument for N2 or O2… presumably the reason for focusing on carbon has more to do with relevance to society.  Is the question being answered why land and ocean are being treated together?  If so, perhaps “We focus on the combined ocean and land aspects of the carbon cycle because this allows us to explore the implications of flux predictability for atmospheric CO2 as well-mixed greenhouse gas.”

Ln 123 – “, when also” should be “when”

Ln 221 – I believe “also” should be “and”

Ln 244-245 – “dominated by the bias of pCO2” instead of the bias in temperature?

Ln  248 – The description of this figure suddenly stops without addressing the XCO2 panels.

Figure 4 – it would be helpful for the reader to see the comparative lines for Indirect Atm only to compare with Figure 2 and Figure 3

Ln 299 – I believe “than” is intended after “larger”

Ln  302 – not sure why this sentence has its own paragraph

Ln 347 - It is only here, after Figure 5 is presented, that I get to find why Figure 2o looks so much like Figure 2m.  If I understand correctly, it is a coincidence – Figure 2m is high because the surface temperature is high, while Figure 2o is high because the land releases CO2 over the course of the year do to the climate mismatch.  A statement to this effect near Ln 248 before moving on to Figure 3 would help orient the reader.

Ln 352 – “direction” should be “direct”

Ln 362 – I believe “also” should be “even”

Ln 365 – measuring” should be “measured by”

Ln 407 – “but below the initialized” is unclear, is “but drifts slightly below the initialized value over the course of the simulation” intended?

Ln 422 – “For a real-world application, our direct land carbon reconstruction method cannot be used.” I would disagree with this statement and should change “cannot” to “should not”.  The easiest form of data assimilation for land would be to simply over-write the vegetation biomass periodically from a satellite product, something very similar in principle to what is being done here.  I think the more interesting question that is answered here is why that is a bad idea.  I think this is a point very much worth making as satellite products become more diverse and land initialization approaches are considered.

Ln 424 – This conclusion appears to be the crux of the paper – that the nudging technique introduces such large biases in climate mean state as to make the “direct” approach incompatible with the original model.   I am not an expert on physical data assimilation, but isn’t that the reason that ensemble Kalman filter is used rather than nudging?  Would one expect these other techniques that do not shift the ITCZ or dampen Southern Ocean winds to also find a “trivial” role for BGC initialization?

457 - Rather than being satisfied with “We conclude that the indirect carbon cycle reconstruction serves its purpose.” It would be much more productive to point out what alternatives to nudging might provide superior options for future work.  It should also be noted in the conclusion that the present work does not address the potential role for structural uncertainty to provide an advantage to “direct initialization”

 Review of "Trivial improvements of predictive skill due to direct reconstruction" by Spring et al.

General comments

The authors have performed a set of perfect model experiments to investigate the impact of the nudging various physical (indirect reconstruction) and biogeochemical variables (direct reconstruction) on the reconstruction of the ocean, land and atmospheric carbon cycle. Further, they look into how this reconstruction impacts the predictive skill of the carbon cycle. They found that nudging of physical state variables reconstructs the carbon cycle well, and that an additional nudging of biogeochemical state variables only gives marginal improvement, and sometimes even deteriorates the reconstruction. Also for the predictive skill they do not find any substantial improvements of directly reconstructing the carbon cycle.

This manuscript is an important contribution to the research on carbon reconstruction and prediction. I do not know of any perfect model studies investigating biogeochemical reconstruction and the importance of direct versus indirect reconstruction. Further, their results on the predictability add confidence to the results of another perfect model study that showed that the biogeochemical initial conditions play a minor role for the predictability of t ocean biogeochemistry. 

However, there are some improvements that can be done before a potential publication:

• I have one question mark regarding the presentation of your results. For the carbon reconstruction, why do you present the results from the atmospheric nudging and the atm+ocean+ice nudging for the indirect simulations? I do not know of any prediction systems that nudge atmospheric variables only (I may be wrong). It is rather the opposite. It is standard practice to nudge ocean variables, and then there might be nudging of atmospheric variables as an “add-on”. I therefore do not see what the scientific community gains from your experiment with atmospheric nudging only. It is quite intuitive that you cannot reconstruct the ocean carbon cycle by assimilating only atmospheric data. I think that the manuscript would greatly improve if you presented the simulation where you nudge the ocean only, and then the atm+ocean+ice simulation. If you want to go into details you could even have one ocean simulation, one ocean+ice and one ocean+ice+atmosphere.  In that way you could see what additional skill you could gain when nudging sea ice and atmospheric variables for carbon reconstructions. 
• The discussion of the results needs some work. Specifically,  the manuscript lacks a deeper discussion on advantages/disadvantages with you various nudging schemes, and the reasons behind (i.e. how does it affect the physics/biogeochemistry, regional differences). For example, why does the indirect reconstruction result in higher correlations in the subtropical ocean compared to the extratropical ocean? It is already done to some extent, but it can be improved. Moreover, you need to put your results more in context  to what is currently done in reconstruction/prediction research. For example, at the moment it is not clear from the text what you want to show with the different indirect reconstruction schemes, and what knowledge we can gain from it.  Overall you need to connect your results better to the literature. For example,  you refer to the Servonnat et al., 2015 and  Fransner et al., 2020 papers in the introduction, but you do not put your results into context with them in the discussion. How does your results compare to other studies with biogeochemical reconstructions/predictions? 
• The structure of the paper can be improved, specifically, the number of sections and subsections can be drastically reduced. See suggestions under Specific comments. 
• Work needs to be done on the language/formulations and flow on sentences. I have put some suggestions under "Technical Notes" below.

Specific comments

• I suggest you merge sections 2.2, 2.3 and 2.5 to one. You could use subsubsections for the different kinds of simulations.
• Similarly, I would suggest you to merge sections 2.4 and 2.6
• Furthermore, I would suggest you to make sections 3 and 4 to subsections in a section “Results” or “Results and DIscussion”. 

(It is difficult for me to understand whether sections 3 and 4 are supposed to be only Results or Results and Discussion)

• You can furthermore reduce the number of subsections in section 3. I would simply merge 3.2.1 and 3.2.2 under 3.2,  3.3.1 and 3.3.2 under 3.3 and 3.4.1 and 3.4.2 under 3.4.
• Why don’t you do any indirect reconstruction of the land physics? You should explain this.
• Under section 3.4 you write that you will start by examining figure 4, but then you only mention it briefly in the end of the section.
• Why are you looking into seasonal timescales when it comes to atmospheric CO2 (figure 5), while you are looking into 10 year chunks for the land and the ocean? I would focus on one time-scale to be consistent, but maybe I’m missing something.
• The manuscript would gain a lot of you would discuss the regional patterns in our results in more detail. For example, for the ocean we see large differences in the reconstruction skill in the tropics compared to the extra-tropics, why is this?
• In your ACC plots, the ACC that is significantly different than internal variability, is found in areas of lower correlation. Why is this? Shouldn’t the significant result be related to higher correlation?
• Why have you chosen RMSE as a measure of skill for your predictions, while you use RMSE and ACC for your reconstructions? Did you try also ACC for your predictions? 
• Section 4.2: if the cVeg is not predictable, what is it then that yields the predictability in the air-land CO2 flux? If you cannot give an answer to this you should at least discuss it. (for the ocean you are looking into the oceanic pCO2 that is an important driver for the air-sea co2 flux.)

Technical Notes

Abstract: The abstract is long and heavy to read. Try to shorten it down and make the text more fluent. Some suggestions:

• The first sentences are not capturing the reader., and need reformulation. Maybe you could start by saying that state-of-the art climate prediction systems now include a carbon component. Then you shortly explain that while there is assimilation of physical state variables, this is not the case for the biogeochemistry.
• line 8 : Why have you chosen the word "target"? It is quite abstract, could you choose another word? If you want to keep it, maybe just a reformulation of the text would help.
• lines 10-15: This is very much into technical detail, and I suggest to remove most of this from the abstract.
• I would suggest not to go into ACC's and RMSE's in the abstract, and instead give your interpretations of your results in words. If you want to keep it, only mention it for the most important results.

Introduction:

• Move lines 47-56 to the end of the introduction
• line 55: the word perfect- model target reconstruction framework is very long. Can you make this shorter? Can't you just write "perfect model framework", and then you describe it in more detail in your methodology?
• Lines 74-77: This part, which is on ocean physics, comes in the middle of your discussion on initialization of the carbon cycle (in between the references to Li et al., 2016, 2019 , Seferian et al., 2018, Lovenduski, et al., 2019 and Fransner et al., 2020). I suggest moving it to the end of the introduction where you discuss your approach. If I understood it right you got inspired from this study?
• lines 74-75: You should make it clear already in this first sentence that Servonnat et al is a perfect model study.
• lines 75-77: This sentence is difficult to understand. There are several reasons behind; i) "target reconstruction approach" is quite abstract, and needs clarification, i.e. why is the method of Servonnat et al., 2015 called like this? Why does it allow to directly assess the quality of reconstructed initial conditions? The last part "which is useful and practical to know for forecaster issuing a forecast" also need a reformulation, or can be removed completely .
• lines 84-85: in which way is this more theoretical?

Methods:

• line 103: merge the two parentheses to one.
• lines 103-107: you repeat the reference Mauritsen et al., 2019 three times. Maybe this is not needed if you talk about the same model all the time
• lines 115-117: here comes the explanation for the "perfect-model target reconstruction framework" that I was looking for in the introduction. I would suggest to move these first lines there. Alternatively, you only use the phrasing "perfect model framework" before this section. Then the exact methodology and details behind are described here. In that case you can keep these lines here. Please consider making two sentences out of this one. it is very long.
• lines 117-118: how can the restart file for year 2005 come from the per-industrial control simulation?
• Line 119: you have already described the model setup in the previous section, and do not have to write about is again here.
•  lines 126-128 + equation: here comes the explanation for the use of the word "target" that I was looking for earlier. I would suggest moving this after the first sentence in section 2.2.
• lines 132-134: The observational data is not needed at each model time step, but at the time scale of relaxation, right?
• line 136: I would suggest to write "a shorter relaxation time scale" instead of a "a stronger nudging strength"
• line 138-139: you need to clarify why you nudge the logarithm of the surface pressure. Is the reference to Pohlmann et al related to this, or to the nudging of all variables?
• line 139: I would suggest you to briefly mention the 63 spherical harmonics in the model description.
• line143: I don’t understand the use of the word “only” here. Should it be nudging the atmosphere only?
• line 144: consider merging the parentheses that are coincident.
• line 156: consider removing this first sentence, the information in it is basically repeated in the next sentence.
• Lines 157-160:To avoid repetition,  I would remove the “over 10 year windows” in the first sentence. In the second sentence you can then explain that you do the calculations over ten year windows, and why you do it. Moreover, I would move the second sentence to be after the explanation of your skill-metrics.

Section 3:

• figure 1: the letters in subplots g-l are barely visible, consider changing the color to white. Check this also for the other figures.
• section 3.1: why are you looking at these physical variables, specifically? A short explanation would be good.
• lines 211-212: The ACC is not significantly better in most grid cells from what it looks like in Figure 1.
• line 238: “the state variable of the ocean carbon sink surface ocean pCO2” needs reformulation 
• Lines 246-248: Here it would be interesting if you discussed the results more in detail and put it into context with the results in 3.1. For example, how come that the atmospheric nudging only improves the reconstruction in the tropics?
• Line 260: the biases in the direct reconstruction does not look larger than the ones in the indirect reconstruction for pCO2 in Figure 2 ?
• section 3.4.1: here you are again describing the effect of the reconstruction on the land and ocean carbon cycle as you did in sections 3.2 and 3.3 . I would remove it from here and only discuss the effect on the atmospheric CO2. The description of the land and the ocean carbon cycles should be done in the previous sections.

Section 4:

• figure 6: Use the same y-label for the two rows in the left hand side, i.e. either RMSE or root mean squared error
• line 389: add flux after “global air-sea CO2” 
• 373: you have to describe how you construct this perfectly initialized ensemble in the methods. You write that it is started from perfect initial conditions. I assumed that you applied some perturbation to these restart files?

Section 5

• Line 435: shouldn’t it be “reconstruction of the physical ocean fields”?
• Line 435-436: It is quite expected that you cannot reconstruct the ocean carbon cycle by nuding the atmosphere only no? You need to discuss this in more detail. Also please put your results into context of what is currently done in state-of-the-art climate prediction models, and other studies showing that the ocean carbon cycle/biogeochemistry can be reconstructed by nudging physics only (i.e Li et al., 2016, Seferian et al., 2014, Park et al., 2018 ...). 
• Lines 451-460: you need to put these results into context with the Fransner et al., 2020 study. 

References:

Séférian et al 2014, Predictability tropical marine productivity, PNAS, DOI: 10.1073/pnas.1315855111

Park et al, 2018,  Modeling Global Ocean Biogeochemistry With Physical Data Assimilation: A Pragmatic Solution to the Equatorial Instability, Journal of Advances in Modeling Earth Systems, https://doi.org/10.1002/2017MS001223,