Projected soil carbon loss with warming in constrained Earth system models

The soil carbon-climate feedback is currently the least constrained component of global warming projections, and the major source of uncertainties stems from a poor understanding of soil carbon turnover processes. Here, we assemble data from long-term temperature-controlled soil incubation studies to show that the arctic and boreal region has the shortest intrinsic soil carbon turnover time while tropical forests have the longest one, and current Earth system models overestimate intrinsic turnover time by 30 percent across active, slow and passive carbon pools. Our constraint suggests that the global soils will switch from carbon sink to source, with a loss of 0.22–0.53 petagrams of carbon per year until the end of this century from strong mitigation to worst emission scenarios, suggesting that global soils will provide a strong positive carbon feedback on warming. Such a reversal of global soil carbon balance would lead to a reduction of 66% and 15% in the current estimated remaining carbon budget for limiting global warming well below 1.5 °C and 2 °C, respectively, rendering climate mitigation much more difficult.


REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): Review of "Projected soil carbon loss with warming in constrained Earth system models" (NCOMMS-23-13941-T) for Nature Communicafions

Paper summary
In this paper, the authors present a compilafion of observafional data of soil carbon turnover fimes in different biomes and climate zones.This analysis shows that the intrinsic turnover fime (i.e.turnover if the soil were at opfimum environmental condifions) is highest in cold / high lafitude regions, and lowest at warmer low lafitudes.The seeming discrepancy with observed slow carbon degradafion in high lafitudes soils is because the apparent turnover fime differs from the intrinsic turnover fime due to nonopfimum environmental condifions (so if high-lafitude soil were subjected to more opfimal condifions, the apparent turnover fime would converge with the intrinsic turnover fime).This data is then used to develop a simple model of soil carbon pools to esfimate global pafterns of intrinsic turnover fime, the results of which compare favourably to esfimates derived from a reduced complexity model emulafing the soil carbon dynamics of Earth System Models.However, while the spafial pafterns align the ESMs substanfially over-esfimate the magnitudes of intrinsic turnover fime.To show what impact this has on future soil carbon projecfions, another model is developed by calibrafing the previous reduced complexity model with intrinsic turnover fime observafions and adding addifional processes (mineral protecfion and rhizosphere priming) and then run to 2100 under low/medium/high emissions scenarios.This indicates soil carbon will switch from a carbon sink to source under all scenarios, offsefting some of the carbon sequestered in plant biomass and so reducing the carbon budget for keeping global warming below 2C.

General comments
In this review I am focusing on the analysis logic and Earth system implicafions rather than the methodological details, which I'm not so familiar with for this field but appears to be sound, supports the conclusions made, and is likely reproducible from the data provided (although uploading code to a repository e.g.github/zenodo as well would improve reproducibility further).
In general this is an interesfing and useful paper with clear relevance to Earth system modellers and future climate policy, and should be published with some text revisions to clarify some things.It is well known that soil carbon dynamics is one of the most uncertain aspects of Earth system models, and this study helps to illustrate and quanfify the gap between ESMs and observafions, indicafing where ESMs can improve in future.However, there's quite a lot packed in to this paper (with results from mulfiple data analyses and models included), so there's not a lot of space to explain things fully and put them in context for readers who are less familiar with soil carbon turnover and its implicafions.For example, I think the difference between the intrinsic and apparent turnover fimes should be unpacked and explained more, as it's not necessarily obvious to non-specialist readers and is a crucial point for understanding the results of this paper.Addifional explanafion on model rafionale and why ESMs are over-esfimafing turnover fime and thus carbon sequestrafion would be helpful too, with the lafter also important for outlining the implicafions of where ESMs could focus future improvements (which could be explicitly noted later too).Word count is no doubt a limitafion here, but I think some brief extra sentences providing context where flagged may be sufficient to resolve this (otherwise a longer paper would be befter to do this work jusfice).Finally, calculafing the implicafions for the 1.5C carbon budget as well as 2C would no doubt be of interest to many.Specific details on where these points apply are below.

Specific comments
Line 23-27: Does "after observafional constraints" mean from now, or later on?I suggest rephrasing this sentence a bit to make this clearer (could also consider splifting the sentence after "worst emission scenarios").
Line 29-29: As per the more detailed comment on this below, what about implicafions for the carbon budget for 1.5C?Line 32: A minor point, but might be clearer language to say something like "may act as a posifive feedback on climate change" rather than "would act…" Line 33: I found "in the real Earth system" to be oddly phrased on first reading (as those experiments in the previous sentence were done on real parts of the Earth system too, albeit placed under arfificial incubafion condifions), though I do know that you mean across the whole Earth system in pracfice rather than in a few experiments here.
Line 35: I think it'd be useful either here or somewhere early on to briefly define and explain soil carbon turnover for less familiar readers, especially as this is not a disciplinary journal.
Line 47: what do you mean by a "compact" model?Either brief explanafion of that later on, or if you mean reduced complexity, or simple, or stylised model then that that would be more familiar phrasing (at least to me).
Line 53: while the dataset gathered is prefty comprehensive across different biomes, there are some limitafions (e.g.not so many datasets for non-forests, and not many sites in Africa or Central/South/Southeast Asia).I'm sure this reflects data availability and so is somewhat inevitable, but it could bear menfioning as a limitafion in at least the methods secfion (as somefimes ecosystems behave a bit differently on different confinents despite being in the same global biome).Also, in the map there are a few North European sites in e.g. the UK & North Germany that appear to be labelled as Boreal Forest when by most classificafions they'd be in the Temperate biome (unless they're labelled as Boreal because they're from conifer plantafions, but that would lead to different limitafions) so this might need checking, especially as this would reduce Palearcfic Boreal representafion.Lastly on Fig. 1, at first glance it'd be easy to assume the colours in panels b-d are meant to match the biome colours above, so for clarity might be preferable to make as different shades of a new colour if possible, or to maintain confinuity with Fig. 2 re-do the 1a dots as different symbols instead (the red wetland dots in panel a may also clash with green for colour-blind readers).Line 73-77: the opfimal environmental condifions caveat is key here, as a non-familiar reader might be otherwise surprised that colder regions are associated with faster soil carbon turnover given long-term C storage of say permafrost.I feel like this could be made clearer upfront to avoid confusion.
Line 100-103: again, I think this could do with highlighfing / a bit more explanafion to make it clear to less-familiar readers that intrinsic turnover fime is what's expected in theory given otherwise opfimal condifions, but in pracfice condifions make turnover a lot longer parficularly in high lafitudes.
Line 114: "verifying" is perhaps an overly strong word here given inherent uncertainfies on your diagnosed τi, perhaps "supporfing" instead.
Line 118-121: presumably this isn't because the ESM results are showing the enviro-constrained rather than intrinsic turnover fimes?And any thoughts as to why this is the case, both the general offset and the places where it's greatest?(Limitafions to ESM treatment of soil carbon dynamics is outlined in introductory paragraph, but a liftle bit here on key drivers of this specific tendency would be useful for understanding ESM limitafions and improvements in them could be focused in future.) Line 128: as per line 47, does "compact" here also mean reduced complexity?It's not a term for models I'm so familiar with.Also, while it's clear that this is a new model being introduced, it would help to briefly highlight within the main text why a new model is needed to make this projecfion and how it relates to and builds on the previous model (given the previous RC model is also capable of making soil carbon stock projecfions in Fig S6, but presumably is limited to simplisfic ESM soil carbon dynamics so needs extra aspects re.turnover fimes you've idenfified as important added).Fine to leave details to methods/SI some context would improve the logical flow here.
Line 152: there are more than three emission scenarios, so can just say "under three different emissions scenarios" (removing "the" for clarity) Line 156-157: as phrased "will become a large carbon source under SSP1-2.6 (-19.1 PgC) and lose 24 and 45.2 Pg of carbon under SSP2-4.5 and SSP5-8.5..." makes it sound like source and loss are different things.
Line 157-159: bit of a confusing sentence -is the first sentence half reiterafing the previous sentence that the constrained simulafions show a switch to source?Consider rephrasing / merging second half with above sentence if so, because as phrased it sounds "the constraint" is some kind of within-model event triggering the switch.
Line 160: I think why this is expected needs a bit of brief clarificafion -presumably because faster intrinsic turnover means soil carbon stocks react and degrade faster with warming (but possibly with caveat of the apparent/intrinsic turnover fime mismatch reducing this a bit in pracfice?)Line 162-163: "largely weakening the role of ecosystems in carbon sequestrafion potenfial in the future" reads a bit unclear to me -could rephrase as e.g."reducing the potenfial capacity of land biosphere carbon sequestrafion in future".Also, which scenario does the 59 PgC increase plant biomass come from in the previous sentence (so that it can be more directly compared to your scenario-dependent soil loss esfimates)?
Line 181-182: whenever a "we" is invoked in climate mifigafion it should be clear who the we is referring to -e.g. is this humanity as a whole, high emifting countries/demographics, policymakers... Line 187-188: it would also be interesfing to see this done for 1.5C, given that's a goal much discussed in climate policy -would that be possible in your analysis as well?
Line 195: maybe "indicates" instead of "showed", as the model is only an esfimate of course.

Dr. David A. McKay
Reviewer #2 (Remarks to the Author): The authors fit fluxes from soil incubafion data to a simple three-pool decomposifion model to constrain esfimates of carbon turnover fimes.The data are gathered from a large number of independent studies over global range of biomes, soil types and temperatures.The turnover fimes are then upscaled using machine learning methods.They compare the constrained turnover fimes to those in Earth System models (ESMs) in CMIP6 that have a similar three-pool representafion of soil carbon and find that the majority of these models overesfimate C turnover fimes compared to the incubafion-derived esfimates.A compact version of the model, also containing simple representafions of priming and physical-chemical protecfion mechanisms, is constrained with addifional global data sources.By forcing this model with ESM-predicted temperature and producfivity, the authors find that there is a stronger posifive feedback from soil carbon with warming than predicted by current ESMs, potenfially making climate mifigafion efforts more challenging.
I find this study interesfing and very relevant as it synthesizes many datasets together to constrain a crifical feedback in ESMs.but have a few quesfions on methodology.It's an important and robust conclusion that the models overesfimate turnover fimes and that has impacts on carbon cycle responses.But perhaps more important here is that the derived temperature sensifivifies are quite high and this very likely plays a key role in changing the sign of the soil carbon response with warming.This appears in supplementary table 8 -the Q10 values for the slow and passive pools are substanfially larger than used in most ESMs (2.85 and 3.77).However it's harder to judge the robustness of this result given the methods.Can the authors more quanfitafively assess the relafive roles of model bias in base turnover fime compared to bias in temperature sensifivity?

Specific comments:
Lines 98-99: "Our esfimate of the global mean (316 yr) is more than 16 fimes shorter than the radiocarbon-derived esfimate…" -why not compare the esfimated carbon age directly?
Lines 107-108: The ESMs describe pool-specific turnover fimes in their literature (e.g.Koven et al. 2013).However they may not be directly comparable as they in some cases have aggregated more than three pools into the three reported (Cfast, Cslow, Cpassive), and the model structure may be substanfially different than used in this study.
Lines 108-109: What accounts for the spafial differences in esfimated intrinsic turnover fimes in the models?In most of these models the intrinsic turnover fimes (usually at 20 or 25C under ideal moisture) are fixed parameters.The spafial variafion then must be caused by differences in structure or parameters between your model and the decomposifion module in the ESM.For example, the Q10 value in CESM is 1.5, whereas the assumed value here is significantly higher (Fig. S16).Therefore the derived turnover fime in the tropics at the base temperature of 15C is higher, but this could be an arfifact of the difference in temperature funcfions.
Lines 134-135: How sensifive is the result to the priming effect?As menfioned most ESMs don't esfimate priming.By including priming in the compact model, the turnover fimes will decrease because of increasing root respirafion, but a possible feedback in the ESM of increased nutrient availability for plant growth (increased NPP) would be missing.
Lines 378-388: Why not fit Q10, or some funcfion that predicts Q10 as a funcfion of temperature rather than using an assumed relafionship?The large coverage of temperatures in the incubafions (4 to 35C) should allow for a good fit.
Lines 435-6 (equafion 8): Does this mean total NPP is added to the Cf pool each year?If NPP is increasing over fime due to CO2/warming, lifter producfion will lag NPP due to vegetafion turnover fimes (especially for woody vegetafion).Would it be befter to use lifter producfion, or is this variable not available?
Lines 445-6: Here a constant Q10 =2.5 is used, but for consistency should it not be the same relafionship plofted in Fig. S16? Lines 548-562 (sensifivity tests): Please describe these in more detail.In experiment 1, the Arrhenius funcfion is used to scale the turnover fimes to 15C.Were all of the parameters then recalibrated, including the Q10 for the different pools?Would it make sense to add another sensifivity experiment where you use the Q10 values as prescribed in the models to test the impact of temperature sensifivity compared to base turnover rates?

However, while the spatial patterns align the ESMs substantially over-estimate the magnitudes of intrinsic turnover time. To show what impact this has on future soil carbon projections, another model is developed by calibrating the previous reduced complexity model with intrinsic turnover time observations and adding additional
processes (mineral protection and rhizosphere priming) and then run to 2100 under low/medium/high emissions scenarios.This indicates soil carbon will switch from a carbon sink to source under all scenarios, offsetting some of the carbon sequestered in plant biomass and so reducing the carbon budget for keeping global warming below 2C.
[Response] Thank you so much for your meticulous review, and valuable comments and suggestions on our manuscript.The point-by-point responses are listed following each comment/suggestion.

[Comment 2]
In this review I am focusing on the analysis logic and Earth system implications rather than the methodological details, which I'm not so familiar with for this field but appears to be sound, supports the conclusions made, and is likely reproducible from the data provided (although uploading code to a repository e.g.

github/zenodo as well would improve reproducibility further).
[Response] We thank the reviewer for the positive feedback.Following your suggestion, we have uploaded data and code in this study to the Figshare data repository (https://figshare.com/s/0febe56304920b8536f0).

[Comment 3] In general this is an interesting and useful paper with clear relevance to Earth system modellers and future climate policy, and should be published with some text revisions to clarify some things. It is well known that soil carbon dynamics is one of the most uncertain aspects of Earth system models, and this study helps to illustrate and quantify the gap between ESMs and observations, indicating where
ESMs can improve in future.However, there's quite a lot packed in to this paper (with results from multiple data analyses and models included), so there's not a lot of space to explain things fully and put them in context for readers who are less familiar with soil carbon turnover and its implications.For example, I think the difference between the intrinsic and apparent turnover times should be unpacked and explained more, as it's not necessarily obvious to non-specialist readers and is a crucial point for understanding the results of this paper.Additional explanation on model rationale and why ESMs are over-estimating turnover time and thus carbon sequestration would be helpful too, with the latter also important for outlining the implications of where ESMs could focus future improvements (which could be explicitly noted later too).Word count is no doubt a limitation here, but I think some brief extra sentences providing context where flagged may be sufficient to resolve this (otherwise a longer paper would be better to do this work justice).Finally, calculating the implications for the 1.5C carbon budget as well as 2C would no doubt be of interest to many.Specific details on where these points apply are below.
[Response] Thank you for your positive feedback and valuable suggestions.
Following your kind suggestions and comments, we have conducted a throughout revision of the manuscript.First, we have provided a detailed explanation of the difference between intrinsic and apparent carbon turnover times in both the Method

Specific Comments
[Comment 4] Line 23-27: Does "after observational constraints" mean from now, or later on?I suggest rephrasing this sentence a bit to make this clearer (could also consider splitting the sentence after "worst emission scenarios").
[Response] Thanks for your suggestion.In revised manuscript, we have rephrased this sentence to make it clearer as follows: "Our constraint showed that the global soils will switch from carbon sink to source, with a loss of 0.22-0.53petagrams of carbon per year until the end of this century from strong mitigation to worst emission scenarios, suggesting that global soils will provide a strong positive carbon feedback on warming."(Lines 21-25 on Page 2)

[Comment 5] Line 29-29: As per the more detailed comment on this below, what about implications for the carbon budget for 1.5C?
[Response] Following your kind suggestion, we have also calculated the remaining carbon budget for limiting global warming well below 1.5 °C.Our results showed that global soils will sequester 45 (33-58) PgC less than the estimate based on the original Earth system model projections by 2100 for the 1.5 °C warming target (Figure R1).
Based on this result, the remaining carbon budget, which is currently estimated at 110 PgC, should be further reduced by 41% over the course of this century to achieve the 1.5 °C warming target.This information has been added in the revised manuscript  [Comment 6] Line 32: A minor point, but might be clearer language to say something like "may act as a positive feedback on climate change" rather than "would act…" [Response] Done as suggested.
[Comment 7] Line 33: I found "in the real Earth system" to be oddly phrased on first reading (as those experiments in the previous sentence were done on real parts of the Earth system too, albeit placed under artificial incubation conditions), though I do know that you mean across the whole Earth system in practice rather than in a few experiments here.
[Response] In revised manuscript, we have deleted this odd expression.
[Comment 8] Line 35: I think it'd be useful either here or somewhere early on to briefly define and explain soil carbon turnover for less familiar readers, especially as this is not a disciplinary journal.
[Response] Thanks for your suggestion.We have added a sentence to explain soil carbon turnover time as follows: "One significant, and poorly understood, component of the system is the soil carbon turnover 1,6 , which is defined as the average time it takes for a carbon atom to enter and leave the soil system 7 ."(Lines 33-35 on Page 3) [Comment 9] Line 47: what do you mean by a "compact" model?Either brief explanation of that later on, or if you mean reduced complexity, or simple, or stylised model then that that would be more familiar phrasing (at least to me).
[Response] Following your kind suggestions, we have discarded the use of "a compact model" and used "refined reduced-complexity model" throughout the manuscript.
[Comment 10] Line 53: while the dataset gathered is pretty comprehensive across different biomes, there are some limitations (e.g.not so many datasets for non-forests, and not many sites in Africa or Central/South/Southeast Asia).I'm sure this reflects data availability and so is somewhat inevitable, but it could bear mentioning as a limitation in at least the methods section (as sometimes ecosystems behave a bit differently on different continents despite being in the same global biome).Also, in the map there are a few North European sites in e.g. the UK & North Germany that appear to be labelled as Boreal Forest when by most classifications they'd be in the Temperate biome (unless they're labelled as Boreal because they're from conifer plantations, but that would lead to different limitations) so this might need checking, especially as this would reduce Palearctic Boreal representation.Lastly on Fig. 1, at first glance it'd be easy to assume the colours in panels b-d are meant to match the biome colours above, so for clarity might be preferable to make as different shades of a new colour if possible, or to maintain continuity with Fig. 2 re-do the 1a dots as different symbols instead (the red wetland dots in panel a may also clash with green for colour-blind readers).
[Response] Thanks so much for your understanding and valuable suggestions."Despite this, certain regions (such as Africa, central and southern Asia and some high latitudes) are underrepresented by our samples (Fig. 1).Thus, more long-term soil incubations are urgently needed in these specific regions."(Lines 343-345 on Page 18) In addition, we have also carefully checked the information on forest type for each North European site (Table R1), and found that most of forest types at these sites were correctly categorized based on the tree species in this study.As the reviewer correctly pinpointed, there are two sites from the United Kingdom that are classified as planted forests, while the obtained soil τ i patterns across different biomes are robust even when these two sites were moved into the "temperate forest" category (Figure R2).
We also fine-tuned the color and shape of the biome markers to ensure better differentiation (Figure R3).All this information has been added in the method section of the revised manuscript.to underline this point.
[Response] Thanks for your suggestion.We have rewritten this sentence as follows: "Of the tested predictors, mean annual temperature (MAT) was the most important variable in explaining cross-site variability of soil τ i for all three soil carbon pools, with relative variable importance of 27-42% across the different pools (Supplementary Fig. 1)."(Lines 76-79 on Page 5) [Comment 12] Line 73-77: the optimal environmental conditions caveat is key here, as a non-familiar reader might be otherwise surprised that colder regions are associated with faster soil carbon turnover given long-term C storage of say permafrost.I feel like this could be made clearer upfront to avoid confusion.
[Response] Thanks for your constructive suggestions.In order to clarify the difference between intrinsic and apparent soil carbon turnover times, we have firstly added a brief explanation in the introduction of main text: "Notably, soil τ i is representative of the theoretical carbon turnover time under optimal conditions.While various environmental constraints such as freezing and physical protection could inhibit the achievement of this theoretical value, leading to longer apparent value of τ i in the real-world settings 8 (Methods)."(Lines 47-50 on Pages 3-4) Then, in the Method section, we have added detailed explanations regarding the difference between intrinsic and apparent carbon turnover times.
" what's expected in theory given otherwise optimal conditions, but in practice conditions make turnover a lot longer particularly in high latitudes.
[Response] Thanks for your suggestion.Please see detailed responses to Comment 12.
[Comment 14] Line 114: "verifying" is perhaps an overly strong word here given inherent uncertainties on your diagnosed τi, perhaps "supporting" instead.
[Response] Thanks for your suggestion.[Response] Thanks for your suggestion.Following your constructive suggestion, we have added the following sentences to explain the results: "The model-data bias of soil τ i could be attributed to the omission of critical microbial processes from ESMs, such as thermal adaptation 24 .Specifically, microbial turnover rates have been shown to adjust to temperature changes via biochemical trade-offs in enzyme and cell membrane structure and function 25,26 .Low temperatures typically select for enzymes and/or membranes that are highly flexible to efficiently alter conformation and facilitate interactions 27 .As a result, cold-adapted microbial communities have faster growth and respiration rates than the warm-adapted when compared at common temperatures 5,26 ."(Lines 121-128 on Pages 7) In addition, after carefully examining each ESM parametrization, we realized that intrinsic turnover times in different carbon pools from all ESMs are fixed parameters without any spatial variability.In the revised manuscript, we therefore removed the part related to the spatial diagnosis of intrinsic turnover times from ESMs, and directly compared data-driven intrinsic turnover times to those prescribed in ESMs.
Our updated results showed that global soil τ i is still overestimated by models (~30% across carbon pools).We have therefore updated figures and modified the text correspondingly in the revised manuscript (see detailed responses to Comment 5 by Reviewer #2).
[ [Response] Thanks for your suggestion.In this study, we developed a reducedcomplexity three-pool model to approximate soil carbon dynamics in complex ESMs, and then refined this reduced-complexity model by including representations of priming effect and physical protection to constrain soil carbon projections.
To well resolve the reviewer's concern, we added "Although our constructed reduced-complexity model is capable of mimicking ESMs soil carbon dynamics and making projections, it is limited to rudimentary processes without integrating emerging knowledge of controls on soil carbon turnover time."into the revised manuscript (lines 134-137 on Page 8).
In addition, we have also added the following text into the Method section: "Our constructed reduced-complexity model was demonstrated to well mimic soil carbon dynamics in ESMs (Supplementary Fig. 6), but it generally assumes that decomposition rates are only constrained by temperature and moisture availability [9][10][11] .
In [Response] Thanks for your suggestion.We have rephrased this sentence as follows.
Furthermore, we acknowledge that environmental constraints could potentially obscure this effect in practice.However, our sensitivity analysis based on the reduced model confirmed the robustness of this interpretation (Sensitivity Experiment 3; Figure S19)."This finding is generally consistent with the expectation that the intrinsic turnover time was overestimated in complex ESMs (Fig. 2).This is because [Response] In revised manuscript, we have incorporated this point and rewritten the sentence as follows: "However, the magnitude of soil carbon losses from tropical forests under SSP5-8.5 (21.4 PgC)  [Response] Thanks for your constructive suggestions.To resolve your concern regarding the relative importance of soil τ i and Q10 in soil carbon projections, we have added a sensitivity experiment in the revised manuscript (Figure R4).In this sensitivity experiment, we performed the three tests using the reduced-complexity model, in which input variables such as net primary productivity, mean annual temperature and mean annual precipitation were derived from original ESMs.
Specially, in the first test, we replaced soil τ i with our data-driven estimates, and replaced Q10 for each pool with that derived from the refined reduced-complexity model, in which Q10 for each pool was obtained through calibration against observed soil carbon stocks (Table S9).For the second test, we replaced soil τ i with our datadriven estimates and used ESM's own Q10 and associated reference temperatures (Table R2).For the third test, we used ESM's own soil τi, but assigned Q10 for each pool to the calibrated one.
Our results showed that global soils will become a source of carbon to the atmosphere by the end of this century under different emissions scenarios.However, compared to the Q10-constrained model ( 13   [Response] In our study, the global estimates of soil carbon turnover times are intrinsic ones upscaled from the incubation experiments, rather than apparent or realized turnover time that can be approximated by radiocarbon-derived estimate.We have rewritten this sentence to make it clearer as follows: "To explore the extent to which the intrinsic turnover times translate into the realized ones due to environmental constraints 8 , we compared our estimates with the radiocarbon-derived carbon age as a surrogate of realized or apparent turnover times (Supplementary Table 1)."(Lines 103-106 on Page 6) [Comment 4] Lines 107-108: The ESMs describe pool-specific turnover times in their literature (e.g.Koven et al. 2013).However they may not be directly comparable as they in some cases have aggregated more than three pools into the three reported (Cfast, Cslow, Cpassive), and the model structure may be substantially different than used in this study.
[Response] The current state-of-the-art earth system models (ESMs) simulated soil carbon dynamics using conceptual soil pools with spatial-invariant intrinsic turnover rates.In the revised manuscript, we realized that intrinsic turnover times in different carbon pools from all ESMs are fixed parameters without any spatial variability, and therefore directly evaluated these fixed intrinsic turnover times in ESMs using our data-driven ones (see detailed responses to Comment 5 by Reviewer #2).
As the reviewer correctly pinpointed, ESMs differed in structuring of carbon pools.According to outputs of ESMs archived in CMIP6 repository, models differed in the number of soil carbon pools ranging from one (e.g., CanESM5) to at least five (e.g., CESM2-WACCM), and the majority of models lack any depth-related information.Only a few models such as CLM have a vertical discretization of carbon pools at different soil depths (Koven et al., 2013).In this study, we only selected ESMs with at least three carbon pools.Although ESMs differed in the number of carbon pools and their associated parameters (such as Q10 and intrinsic carbon turnover time), parameterizations of climatic constraints on soil carbon turnover times is structurally similar among different ESMs.
Here we have demonstrated that the reduced-complexity model with three carbon pools could well capture soil carbon dynamics of different pools in each ESM.This also holds true for those ESMs with more than three carbon pools, with their litter or woody debris carbon pools (cLitter and cCwd) being integrated with cFast (see also He et al., 2016).This result highlighted that using a reduced-complexity model framework to simulate complex ESMs is robust in capturing soil carbon dynamics, even in the presence of variations in the number of carbon pools.
Last but not the least, the main purpose of this study is to extract the intrinsic soil carbon turnover time from soil incubation experiments to constrain realized soil turnover rates and then project soil carbon dynamics based on the reduced-complexity modeling framework.While, the intrinsic soil carbon turnover times derived from soil incubation experiments did not account for variations across different soil depths and easily-decomposable pools such as litter.When developing a reduced-complexity modeling framework to constrain soil carbon projections, we solely utilized climatic and NPP data from ESMs, without incorporating any model data related to soil carbon.Therefore, different structuring of soil carbon pools in ESMs would have marginal impacts on our constrained soil carbon dynamics.
[Comment 5] Lines 108-109: What accounts for the spatial differences in estimated intrinsic turnover times in the models?In most of these models the intrinsic turnover times (usually at 20 or 25C under ideal moisture) are fixed parameters.The spatial variation then must be caused by differences in structure or parameters between your model and the decomposition module in the ESM.For example, the Q10 value in CESM is 1.5, whereas the assumed value here is significantly higher (Fig. S16).
Therefore the derived turnover time in the tropics at the base temperature of 15C is higher, but this could be an artifact of the difference in temperature functions.
[Response] Thank you for the constructive comment.After carefully examining each ESM parametrization, we realized that intrinsic turnover times in different carbon pools from all ESMs are fixed parameters without any spatial variability.In the revised manuscript, we therefore removed the part related to the spatial diagnosis of intrinsic turnover times from ESMs, and directly evaluated these fixed intrinsic turnover times in ESMs using our data-driven ones (Figure R5).We have updated figures and modified the text correspondingly in the revised manuscript.[Comment 6] Lines 134-135: How sensitive is the result to the priming effect?As mentioned most ESMs don't estimate priming.By including priming in the compact model, the turnover times will decrease because of increasing root respiration, but a possible feedback in the ESM of increased nutrient availability for plant growth (increased NPP) would be missing.
[Response] Thanks for your constructive comment.By comparing paired simulations with and without the rhizosphere priming effect in our reduced-complexity model (Figure R4), the priming effect, without considering the feedbacks between nutrients and soil carbon dynamics, reduced soil carbon stocks by 11-19 PgC across different emissions scenarios.As the reviewer correctly pinpointed, the rhizosphere priming effect could also increase the release of soil nutrients, which would in turn stimulate plant growth (Brzostek et al., 2012; Drake et al., 2013) and thereby create a positive feedback loop that further decreases soil carbon turnover time.This implied that the soil carbon stock would be further reduced because of this possible feedback on soil carbon turnover time.But on the other hand, enhanced plant growth due to the rhizosphere priming effect would partly offset soil carbon losses due to enhanced soil carbon turnover rates.Therefore, the net effect due to this positive feedback on soil carbon stock changes might not be so large.While, fully resolving this question requires next generation of Earth system models that explicitly incorporate the rhizosphere priming effect within the coupled carbon-nitrogen cycle framework.In order to well resolve the reviewer's concern, we have added the following discussion into the Method section of the revised manuscript.
"The rhizosphere priming effect could also increase the release of soil nutrients, which would in turn stimulate plant growth 57  Would it be better to use litter production, or is this variable not available?
[Response] Thanks for your comment.We acknowledge that using litter production as soil carbon input in this equation would be better, but this specific variable is not available in ESMs.While our reduced-complexity model still well captured the soil carbon dynamics simulated in ESMs (Figure R6), tentatively suggesting that NPP can be used as a good proxy for soil carbon inputs.[Comment 9] Lines 445-6: Here a constant Q10 =2.5 is used, but for consistency should it not be the same relationship plotted in Fig. S16? [Response] In the revised version, we have used model-prescribed Q10 in the reduced-estimates of soil τ i in a machine learning algorithm linking these τ i to environmental variables across sites.We then prescribed τ i using these data-driven estimates based on the Arrhenius function in refined reduced-complexity model to constrain soil carbon projections (SE1).Second, the use of laboratory incubation experiments, albeit with the length of the period longer than six months, would still have uncertainties in the quantification of τ i of slow-cycling carbon pool especially Cpassive.
In SE2, we prescribed τ i of Cpassive as the ensemble mean of ESM's own values rather than the data-driven estimates in our default simulation (Fig. 2).budget is shrinking since).
[Response] Following your constructive suggestion, we have updated the remaining carbon budget for 1.5℃ (68 PgC, 50% chance) and 2℃ (327 PgC, 50% chance), and found that a reversal of global soil carbon balance would lead to a reduction of about 66% and 15% in the remaining carbon budget for limiting global warming well below 1.5℃ and 2℃ , respectively.This information has been updated in the revised version (L26-L28 on Page 2; L198-L206 on Page 11).
[Comment 3] Explanation has also been added on why ESMs over-estimate turnover times (bearing in mind the wider revisions in this section in response to reviewer 2, which seems to have been sufficiently resolved).I'm wondering though if as well as latitudinal differences whether anything can be drawn out from inter-pool differences, e.g. the ESM slow pool average being generally a worse fit than the fast/passive pools.Additionally, while this study does implicitly indicate the areas which require improvement in ESMs as stated in the end summary, if there's space a brief explicit mention of key processes to prioritise for inclusion in future ESMs would be a valuable addition.
[Response] Thanks for your constructive suggestion.In the revised manuscript, we have mentioned the inter-pool difference and added a brief and clear description about future modelling efforts as follows.
"Future modelling efforts should seek a spatial representation of soil intrinsic turnover parameters especially for Cslow, e.g. by incorporating microbial metrics (such as thermal adaptation 24 , species composition 28 ) into ESMs to build confidence in predicting soil carbon-climate feedback."(L130-L134 on Page 7).
[Comment 4] The basis of N Europe sites being classified as Boreal has also been clarified as being a latitudinal cut-off of 50oN (and those sites representing coniferous forest and not being consequential to the results).This doesn't quite fit the classic biogeographic definition of boreal, but is a reasonable global approximation (fitting N America better than Eurasia) and is made clear in the Methods.
[Response] We appreciate your positive comment.
To Reviewer #2 [Comment 1] The authors have provided a comprehensive response to both reviews and have addressed nearly all of my concerns with additional analysis and clarification.I appreciate the additional sensitivity analysis to address my concerns about the impact of temperature sensitivity on the analysis.
[Response] Thank you so much for your valuable suggestions, which were very helpful for us to improve the quality of the manuscript. [ Line 70: could briefly menfion a headline quanfificafion of the importance of MAT here from Fig S1 (looks like c. 27-42% across the different pools) to underline this point.
section and the main text (see detailed responses to Comment 12 by Reviewer #1).Second, we have explicitly discussed the possible reasons for the relatively short intrinsic turnover time in ESMs and outlined potential directions for future modelling efforts (see detailed responses to Comment 15 by Reviewer #1).Third, we have added an additional analysis for the 1.5 °C temperature target (see detailed responses to Comment 5 by Reviewer #1).

Figure
Figure R1 (also shown as Figure S11 in revised manuscript).Relationship between the Although our data set encompassed most of environmental conditions on the Earth (Figure S15 in revised manuscript), tropical regions such as Africa, high latitude areas and central and southern Asia are still underrepresented.Following your suggestion, we have discussed this limitation in both main text and Method section of the revised manuscript as follows: "By including more data, particularly from under-sampled regions, such as Africa, central and southern Asia and some high latitudes, similar constrained projection studies are likely to provide further value to this area of research."(Lines 216-219 on Page 12)

Figure R2 .
Figure R2.Boxplots showing the distributions of soil τ i of Cfast (a), Cslow (b) and

Figure
Figure R3 (also shown as Figure 1 in revised manuscript).Distribution of intrinsic soil PgC averaged across scenarios), the magnitude of soil carbon loss in the τ i -constrained model (19.5 PgC) is much closer to that in model constrained by the both (26.3 PgC), suggesting that soil τ i is more important than Q10 in determining projections of soil carbon dynamics.This information has been added in the revised manuscript (see detailed responses to Comment 10 by Reviewer #2).

Figure R4 .
Figure R4.Projected changes in global soil carbon stocks from original ESMs,

Figure R5 (
Figure R5 (also shown as Figure 2 in revised manuscript).Global distributions of

Figure R6 (
Figure R6 (also shown as Figure S6 in revised manuscript).Comparison of different

Table R1 .
Boreal forest site characteristics across the North Europe.
The intrinsic soil carbon turnover time reflects kinetic properties of various soil [Comment 13] Line 100-103: again, I think this could do with highlighting/a bit more explanation to make it clear to less-familiar readers that intrinsic turnover time is
The authors have provided a comprehensive response to both reviews and have addressed nearly all of my concerns with addifional analysis and clarificafion.I appreciate the addifional sensifivity analysis to address my concerns about the impact of temperature sensifivity on the analysis.My only remaining concern upon seeing table R2 is that all 5 ESMS have quite similar turnover rates.All 5 models, I believe, heavily draw from the CENTURY model (the three variants that use variants of CLM fromKoven et al. (2013), IPSL, and ACCESS-ESM that uses CASA-CNP with a similar structure.Other models that have a different number of pools likely derive from models other than CENTURY and so may behave differently.Are these 5 models representafive of the broader CMIP6 ensemble in terms of the responses to the different emissions scenarios?A brief menfion of CENTRY's influence may be useful in the discussion, especially in the context of how biome-specific or otherwise spafially varying turnover rates may improve predicfions.patchiness in Africa, southern Asia, and high latitudes), implemented most of the minor edits requested, and have calculated the implications for the 1.5C carbon budget as suggested, leading to a very topical result.A minor point on the latter is that a recent update to remaining carbon budget (https://www.nature.com/articles/s41558-023-01848-5)indicate an even smaller carbon budget is now available, which if incorporated would make your percentage reductions even bigger (but it may make more sense to keep to 2020 baseline, noting Third, in SE3-SE6, we used the reduced-complexity model (equation 8), which only considered climate controls on soil carbon turnover time and used model inputs such as NPP, MAT and MAP directly from the original ESMs, instead of the refined model (Equation11) to constrain soil carbon projections in ESMs.In order to evaluate the relative importance of soil τ i and Q10 in soil carbon projections, we This reference may be useful: Berardi, D, Brzostek, E, Blanc-Betes, E, et al. 21st-century biogeochemical modeling: Challenges for Century-based models and where do we go from here?GCB Bioenergy.2020; 12: 774-788.hftps://doi.org/10.1111/gcbb.12730 Comment 5] Beyond the above, my only remaining specific comments are: considering changing "showed that" on line 21 to "suggests that" (as models can only over indicate and project, not definitively predict), defining "ESM" on first mention (currently several mentions in on line 112), considering the same magnitude scale on Fig S5a as other panels (to make them visually inter-comparable, with difference in panel a likely noticeably paler), and capitalising Arctic on line 57.
Comment 2] My only remaining concern upon seeing table R2 is that all 5 ESMS have quite similar turnover rates.All 5 models, I believe, heavily draw from the CENTURY model (the three variants that use variants of CLM fromKoven et al.   (2013), IPSL, and ACCESS-ESM that uses CASA-CNP with a similar structure.Other models that have a different number of pools likely derive from models other than CENTURY and so may behave differently.Are these 5 models representative of the broader CMIP6 ensemble in terms of the responses to the different emissions scenarios?A brief mention of CENTRY's influence may be useful in the discussion, especially in the context of how biome-specific or otherwise spatially varying turnover rates may improve predictions.Thanks for your suggestions.We have provided a brief mention of CENTRY's influence as follows."Notably, the five models used in this study may not be representative of the broader CMIP6 ensemble because they draw heavily from the CENTURY model and have then similar structures (e.g., three different soil carbon pools)37.Other CMIP models derived from models other than CENTURY may behave differently and deserve further exploration."(L397-L401 on Page 20).