This study provides useful analysis on Rh within CMIP6 ESMs against observational datasets and provides useful direction in future development of ESMs. It is a study that is well suited for publication in Biogeosciences. Overall, the study is clear and well written, however some improved integration with existing studies and increased detail on the caveats will improve the study.

Major comments

Throughout the study it is referred to as being the ‘first’ to investigate heterotrophic respiration (Rh) in Earth system models (ESMs), though this is not the case. This study is still novel, however wording needs to be addressed here to include how this study fits in with the existing literature.

For example, in the abstract: “capacity of Earth System Models (ESMs) to reproduce this flux has never been evaluated” and “for the first time”. Also, Line 182 in Discussion.

Relevant existing studies include:

1. Shao et al., 2013. This study evaluates Rh in CMIP5 ESMs against observational datasets (Soil microbial respiration from observations and Earth System Models).
2. Varney et al., 2022. This study focuses on soil carbon and has been cited, however spatial evaluation of soil carbon turnover (Cs / Rh) is included, and tables of global Rh values in CMIP6 and CMIP5 ESMs against observational dataset (Tables A1 and A2).

Line 183 – It is unclear to the reader what is meant here and there is no citation to back up this statement or to add clarity. Why is it that previously Rh in ESMs could only be constrained by NEE or ecosystem respiration? If the reason is lack of observational datasets, there are older soil respiration datasets (such as Raich et al., 2002 mentioned)? Plus, existing evaluation study on Rh in CMIP5 ESMs? Please expand on why this is the case or change the motivation behind the sentence.

Line 253 – Similar point here.

Line 36 – This sentence states that Rh has not been well incorporated into ESMs. If this is the case but this is the first study to evaluate this, how do we know? References need to be included here to back up this statement.

Line 189 – The study notes large discrepancies in the observational datasets and is presented as an issue which needs to be addressed in the future. It would be beneficial to see more direct comparisons of the observational datasets. I think a useful addition to either an Appendix or Supplementary material would be comparing the observational datasets, potentially a correlation coefficient between them? I know maps of each are included in Fig. 3, but a quantification or difference map would be useful to see where there is more agreement or less agreement between them.

It has previously been shown that the Hashimoto et al., 2015 dataset has an arbitrary maximum respiration level (see Supplementary Fig. 4 in Varney et al., 2020), which was shown in the same figure to not appear in additional respiration datasets. I think this point found here should be acknowledged and think about whether this could impact your residual results. Potentially the underestimation of Rh at high temperatures (Fig. 4)?

1. Varney, R.M., Chadburn, S.E., Friedlingstein, P. et al., A spatial emergent constraint on the sensitivity of soil carbon turnover to global warming. Nature Communications. 11, 5544 (2020). https://doi.org/10.1038/s41467-020-19208-8.

Line 139 states that the observational data and ESM data Rh means are close in Boreal regions. However, on line 163 it is stated that Rh is underestimated by ESMs for soils rich in carbon (which tend to be boreal regions). Any idea why this is the case?

Paragraph from Line 140 – only tropics and temperate regions mentioned, what about the northern latitudes?

The use of the ESM and observational median is used throughout this study. I was wondering whether as it is not known which dataset or model is ‘better’, a mean value would give equal waiting to each, so could be a fairer metric. Does redoing the analysis with the mean instead affect the results? Especially spatially in regions where the datasets disagree more (Fig. 3)? If it does make a difference, it might be worth thinking about which is better for what you are trying to show or including in the Supplementary Material.

Line 202 – The temperature sensitivity of soil carbon turnover time (Cs / Rh) has been previously investigated in similar ESMs, including discussion on variable Q10s spatially and a constraint on effective Q10 in ESMs (Koven et al., 2017 and Varney et al., 2020). This might link with some of the discussion in this paragraph.

1. Koven, C., Hugelius, G., Lawrence, D. et al., Higher climatological temperature sensitivity of soil carbon in cold than warm climates. Nature Climate Change. 7, 817–822 (2017). https://doi.org/10.1038/nclimate3421.
2. Varney, R.M., Chadburn, S.E., Friedlingstein, P. et al,. A spatial emergent constraint on the sensitivity of soil carbon turnover to global warming. Nature Communications. 11, 5544 (2020). https://doi.org/10.1038/s41467-020-19208-8.

Line 203 – Could the underestimation in these regions be due to little or no soil carbon in these regions within ESMs (Varney et al. 2022)?

Line 209 – I would also include a more recent reference, for example, Todd-Brown et al., 2018 (Field-warmed soil carbon changes imply high 21st-century modeling uncertainty). In this study Q10 values are derived and the sensitivity of ESMs to this parameter is investigated.

Minor Comments

Abstract – I would include that you are looking at CMIP6 ESMs here as I had to skim to the end of the introduction to check this, and it is useful to know upfront.

Line 31 / Line 188 – Update Friedlingstein et al., 2020 reference to Friedlingstein et al., 2022. As this is the most up to date Global Carbon Budget paper.

Line 66 – I don’t think this sentence makes sense “, which were used to derived two observation products we used.” I think it should be “dervive the”, rather than "derived”.

Line 114 – The acronym AIC is used in this study, but it is not defined. I would at least add a sentence in the Methods to describe what this term measures.

Line 155 – Ito et al., 2020 is cited here, however the first order kinetics of decomposition is not discussed in this study that I can see. Todd-Brown et al. 2013 and Varney et al. 2022 include information and discussion about ESM decomposition dependencies to temperature and precipitation.

Line 160 – “Since the drivers are ...” might be worth changing to “Since the main drivers are ...” as many factors affecting respiration, as stated in your conclusions (Schmidt et al., 2011).

1. Schmidt, M., Torn, M., Abiven, S. et al., Persistence of soil organic matter as an ecosystem property. Nature. 478, 49–56 (2011). https://doi.org/10.1038/nature10386.

Line 178 – Maybe better to present temperatures in degrees C rather than K in European journal, and better relates to how 1.5C / 2C targets are often presented.

Line 183 – This sentence might change due to an above comment, but there is a typo. “by constrtaint” should read “be constrained”.

Line 210 – Do you mean Figure 4c here? I would include this in brackets so reader can be reminded where this result came from.

## Main comments

This article presents an evaluation of global-scale heterotrophic respiration (Rh) from CMIP6 output in comparison to three different observation-based data products.

The main conclusion presented by the authors is that even though the global aggregated Rh agrees well between models and the data products, the models 'fail' at reproducing spatial patterns. The authors also provide a list of well-known mechanisms that influence soil respiration and advocate for their inclusion in new versions of the models. 

Although in general I agree with the importance of model evaluation studies, I find little incremental value in this analysis. Despite the author's claim of priority, other studies have already made comparisons between ESM output and Rh data products, pointing out disagreements (see comments and references from other reviewers). The list of potential mechanisms to be included in a new generation of models, presented in the Discussion, are well-known mechanisms that influence soil carbon dynamics and Rh, and this discussion is relatively shallow regarding more relevant modeling topics such as the type of functions that should be implemented and how to obtain parameters for those new functions at the global scale. The analysis of residuals and their relation to other variables is helpful in providing some clues about the importance of these different processes, but without a more clear and systematic analysis of different mathematical functions to be implemented in ESMs, there are no elements for modeling teams to make decisions about what new functions to implement and how to obtain their parameters. For instance, this analysis identified a major discrepancy between residuals of Rh and precipitation, and the authors advocate the inclusion of hump-shaped functions in models, which is something that has been previously said (e.g., Moyano et al. 2013, Davidson et al. 2014). There are a number of such functions proposed in the literature (Sierra et al. 2015), and a more relevant discussion would be which of those functions are more relevant at the grid-size level of an ESM, and what type of observations should be used to obtain parameter values for these functions, or whether one single set of parameters should be used at the global scale or whether they should change spatially and temporally. Although I am not trying to convince the authors that they should add this discussion here, I feel that without a more in depth analysis, there is little new value in the present study. 

In addition, there are other topics of model evaluation that are very relevant for this study that are not discussed at all. One topic is the use of objective metrics to characterize distance between model output and data products. The authors claim that the models 'fail' to reproduce spatial patterns, but a definition of 'failure' is not provided, nor a measure of distance or probability of model output to lay in some rejection zone. A more formal analysis would be required to assess how far the model output is with respect to data-products, which are also uncertain. Throughout the manuscript the authors use the three data products as error free, but it is well-known that these products are also subjected to biases and errors. Despite their growing size, Rh databases still lack comprehensive coverage in some key regions such as the tropics. If all the models would agree well with a biased data-product, we would be very misled in our carbon-climate projections!

Another topic of relevance is the issue of spatial aggregation in soil respiration estimates. Since the 1990s, there has been a discussion on how to deal with aggregation errors in estimates of Rh at ecosystem and global scales (Kicklighter et al. 1994, Rastteter et al. 1992). The authors downscaled the CMIP6 output to a common spatial resolution, but it is not clear how this 'dis-aggregation' would affect uncertainties and biases. 

In summary, although the results presented here are interesting to explore differences between CMIP6 Rh output with respect to observation-based data products, the authors make claims about scientific priority/novelty and 'failure' of the models that are poorly supported.

## Minor comments

- L37-40. What do you mean by that these fluxes are not well characterized? Do you mean 'evaluated' instead of 'characterized'? What has been done with plant and ocean fluxes that has not been done with Rh?

- L94. Please provide more details about 'cdo remapdis (nco module)'. What is this? A software, a package of a programing language? Can you provide a reference?

- Section 2.5. This paragraph is very difficult to understand. I get the general idea of the analysis, but I can’t understand well the specific details. Please consider rewriting this section, adding more details for each step, adding some equations about how the medians and model differences were obtained, and maybe a figure describing the different steps. 

- L114. From what programing language is the gls package? Add a reference. 

- L140-141. The median of the mean across products? or the median of the residuals after fitting a statistical model? Legend of Fig 3 says that each map is a residual. Be more specific.

- L142. I’m not sure if 'overestimate' is the right word to use here. The comparison is not directly with measured data, but with the output of a model that was informed by data. The data-products may also include biases.

- L158-159. I still don’t understand how the use of first-order rates in models is connected to the need to use the median of the residuals in this comparison. Can you explain this better?

- L160-161. This set of drivers of Rh is well-know, even before Swift et al. (1979). I’m not sure why this single recent reference is relevant here.

- L160-163. The entire sentence is difficult to understand. Consider rewriting. 

## References

E. A. Davidson, K. E. Savage, and A. C. Finzi. A big- microsite framework for soil carbon modeling. Global Change Biology, 20(12):3610–3620, 2014. 

D. W. Kicklighter, J. M. Melillo, W. T. Peterjohn, E. B. Rastetter, A. D. McGuire, P. A. Steudler, and J. D. Aber. Aspects of spatial and temporal aggregation in estimating regional carbon dioxide fluxes from temperate forest soils. J. Geophys. Res., 99(D1):1303–1315, 1994.

F. E. Moyano, S. Manzoni, and C. Chenu. Responses of soil heterotrophic respiration to moisture availability: An exploration of processes and models. Soil Biology and Biochemistry, 59(0):72 – 85, 2013. 

Rastetter, King, Cosby, Hornberger, O’Neill, and Hobbie] E. B. Rastetter, A. W. King, B. J. Cosby, G. M. Hornberger, R. V. O’Neill, and J. E. Hobbie. Aggregating fine-scale ecological knowledge to model coarser-scale attributes of ecosystems. Ecological Applications, 2(1):55–70, 1992. 

C. A. Sierra, S. E. Trumbore, E. A. Davidson, S. Vicca, and I. Janssens. Sensitivity of decomposition rates of soil organic matter with respect to simultaneous changes in temperature and moisture. Journal of Advances in Modeling Earth Systems, 7(1):335–356, 2015. 

M. J. Swift, O. W. Heal, and J. M. Anderson. Decomposition in terrestrial ecosystems. University of California Press, Berkeley, 1979.