Review of “Presentation, Calibration and Testing of the DCESS II Earth System Model of Intermediate Complexity (version 1.0)” by Fernandez and Shaffer

This paper describes a new version of the DCESS Earth system model, DCESS II. The main improvements of this model over previous versions include the establishment of twelve ocean basins for regional characterization, the implementation of dynamic schemes for large-scale meridional overturning circulation, and the integration of dynamic vegetation zones. Collectively, these improvements make the model suitable for examining carbon cycle variations across timescales ranging from years to millions of years, while effectively resolving ocean transport and sediment diagenesis. Model performances are validated against the observed modern Earth steady state. The authors also provide illustrative examples of time-evolution calculations, demonstrating the model’s ability to simulate ocean circulation to changes in Southern Hemisphere westerly winds and freshwater pulses from Antarctic ice sheet melting. The authors argue that DCESS II is a useful tool for both future projections and reconstructing Earth system dynamics in the geological past.

I commend the authors for their efforts in developing a comprehensive Earth system model that encompasses a wide range of Earth system processes. I have no doubt that this manuscript and open-source model will be valuable to the biogeochemistry community and beyond, and I am confident that the model has great potential for many fascinating applications well beyond the scope of this paper.

That said, I have several minor suggestions that could further enhance the manuscript. Most of my comments focus on opportunities for the authors to communicate their assumptions and limitations of the model more clearly to readers and should not prevent the publication of this manuscript.

Major comments:

I agree that increasing model complexity is one direction for development; however, it may also introduce indefinite parameters and uncertainties and undermines the generality of the model. In the current manuscript, the motivation for making models more complex is lacking. It would be better to add a discussion on what the limitations of the original model were, why the model needs to be made more complex, and in what ways the new model has yielded better results than the original model.

This paper ought to do more to acknowledge the general caveat that this type of model generally contains many tunable parameters, and that model assumptions (the appropriateness of the chosen functions, parameterizations, and simplifications) are difficult to validate. Given this caveat, clear discussions about the model assumptions and primary limitations are essential. For example, the implementation of a dynamic scheme of ocean circulation is one of the key improvements of this study, but because of “regional tunings”, this scheme cannot be used as is for the deep past, where the continental configuration is largely different from the present.  Additionally, the ignorance of ocean biogeochemical processes under anoxic conditions (e.g., denitrification and sulfate reduction) is not discussed in the paper. This simplification means that this model cannot evaluate the biogeochemistry in anoxic oceans. More discussion of model limitations would be helpful in preventing misunderstanding and misapplications of the model.

It is impressive that the distribution of ocean circulation tracers and biogeochemistry is in very good agreement with modern observations, but this is a separate issue from the question of whether correct projections can be made when the system deviates from the steady state. The dynamic behavior of the model is also examined in section 3.2, but it remains unclear why the results were concluded to be “reasonable” (Line 30), since there is no explicit comparison with the results of more complicated models.

Detailed comments:

Line 18 and Figure 1 caption: “ocean boxes” –ocean regions (or sectors)?

Line 30: “Changes in ocean circulation and in the global carbon cycles found in these experiments are reasonable and agree with results for much more complex models.” –It is unclear, at least for this reviewer, how the validity of the results obtained was assessed, because no explicit comparison with the behavior of more complex models was given.

Line 49—55: Perhaps a comment could be added here about the motivation for further model development. I feel it is unclear what the limitations of the original model were and what problems will be approached by improving the geometry and physical/biogeochemical processes in this study.

Line 96: It might be nice to explain why three vegetation types need to be considered.

Line 480: Estimating decomposition/dissolution rates based on e-folding length is a simple and useful approach, but in practice, the decomposition/dissolution rate at each water depth is influenced by several environmental factors, such as sinking velocity and the degree of saturation of seawater with respect to carbonates.

Eq. (43): The vegetation type would affect the rate of chemical weathering. The rationale behind this simplification is left unstated/unjustified in the current manuscript.

Line 705: "0.2095 μatm" --0.2095 atm?

I hope these comments are useful for the authors.

In the preprint entitled “Presentation, Calibration and Testing of the DCESS II Earth System Model of Intermediate Complexity (version 1.0)” by Fernández and Shaffer, the authors present a newly-developed Earth system model of intermediate complexity, DCESS II. The main improvement of the model is the horizontal resolution, which allows the model to simulate the change in the meridional overturning circulations in the ocean despite the simplicity of the model. They tested the performance of the model by reproducing the present/preindustrial conditions and also by conducting sensitivity tests against the northward Ekman transport in the Southern Ocean and against the freshwater forcing supplied by the melting of Antarctica. Specifically, the reproducibility of the present oceanic circulation is surprisingly good.

I think the model is constructed well and the manuscript is written comprehensively. My primary suggestion is to improve the validity of the model’s performance when simulating conditions that differ from the present/preindustrial condition. I concern the configuration of the lithosphere module and atmospheric oxygen budget of the model, but it is not a critical part of the DCESS II model, and I think it can be resolved in the course of revision. Overall, the reproducibility of the present/preindustrial condition in the model should be appreciated, and I think the model has a great potential to be applied to many phenomena that occurred in the geologic pasts and future anthropogenic climate change.

Major comments:

1. Validation of the model under conditions that differ from the present/preindustrial condition

In the manuscript, the authors tested the performance of their model by comparing their results with observations and other sophisticated models under present/preindustrial conditions. The reproducibility of the temperature, salinity, oxygen isotope, carbon isotopes, phosphate, DIC, alkalinity, and oxygen distributions is surprisingly good considering the simplicity of the model. On the other hand, the validation of the reproducibility of the model when the climate and/or oceanic circulation differ from the preindustrial/present conditions seems not to be sufficient. They conducted sensitivity tests against different Ekman transport out of the Southern Ocean as shown in Section 3.2.1. The results seem to be broadly consistent with previous studies using sophisticated ocean models (Rahmstorf and England, 1997; Jochum and Eden, 2015), but the way the sensitivity test is conducted is different from these previous studies. They have also conducted sensitivity tests against different Antarctic ice sheet melt freshwater forcing as shown in Section 3.2.2. However, this result has not been compared with the previous modeling studies. These would limit the reliability of the performance of the simplified model under different climatic conditions. The authors should, at least, enrich their explanation about these sensitivity tests when compared with the previous modeling studies that used sophisticated models, to support the reliability of the model.

In the previous version of their model DCESS described in Shaffer et al. (2008), the performance of the model was compared with the historical change of the temperature, atmospheric pCO2, pCH4, and pN2O, and atmospheric carbon isotopes. I think this kind of validation should be repeated if the configurations of the ocean and land modules are updated greatly considering that the model may be used for projecting future changes in the Earth system. Changes in the oceanic circulation in the historical time and the near future have been projected using recent CMIP models (e.g., Cheng et al., 2013 Journal of Climate; Weijer et al., 2020 GRL; Baker et al., 2023 GRL). Ideally, conducting a similar sensitivity experiment as done in the previous DCESS model and comparing the response of the atmospheric compositions and response of the oceanic circulations with observations and/or CMIP models would increase the reliability of the performance of their model under different climatic condition, while I think it is not necessarily required if a comparison of the sensitivity tests that have already done in the manuscript with the results of previous studies conducted using sophisticated ocean models is enriched sufficiently in the course of revision.

2. Configuration of the lithosphere module and the treatment of the budgets of atmospheric species

Reading through the manuscript, the configurations of the lithosphere module and the budget of the atmospheric species, especially oxygen, in the model seem to be odd to me, partly because the performance of this module has not been compared with the global biogeochemical cycle models. First, I think that a consideration of the global sulfur cycle would be required for reproducing the steady state of the atmospheric oxygen level in a proper way, as done in many previous global carbon-sulfur-oxygen models. Second, the formulation of the weathering rates seems to be different from the formulation that has been widely used using the conventional global carbon cycle, which makes it unclear whether their formulation can be applied to various conditions in the geologic time. Third, I concern the treatment of the atmospheric budget of oxygen, methane, and CO2. When considering both the fast and slow processes of the atmospheric (photo)chemical reactions, one should pay careful attention to the budget of atmospheric species in the atmosphere and should explain them comprehensively in the manuscript. The details of these concerns are found in the following line-by-line comments.

Line-by-line specific comments (The capital L represents line number):

L65: It is unclear what “seasonal cycles” means. Is it a seasonal cycle of climate and/or atmospheric pCO2?

L100: Why does air-sea exchange affect the energy balance of the atmosphere? If the intended meaning is that the atmospheric pCO2 changes owing to the air-sea exchange, it should be specified clearly.

L110: … and the ocean surface, respectively, …

L115: Does this Ta(Φ) correspond to the temperature at any given latitude, different from the temperature of each atmospheric box? It would be helpful if more comprehensive explanation is given.

L166–167: The application limit of the formulations of Byrne and Goldblatt should be specified (i.e., 200–10000 ppmv for CO2, 0.1–100 ppmv for CH4 and N2O if I understand correctly). Also, it is worth noting that the formulation considers the overlap of the absorption by N2O with CH4 and CO2.

L168–169: Could these preindustrial values be justified by comparing with the observation values from ice cores or else?

L226: Please specify how much the climate should be warm for “extremely warm climates” that requires the Schmidt number formulation.

L275–295: These sentences would correspond to the explanation of the terms Ψ_I(χ), but I think it is clearer to formulate these terms in equations as done for Ψ_S(χ) and Ψ_T(χ).

L275: Should “(see Sect. 2.5)” be “(see Sect. 2.6)”?

L277: Is λ_CH4 pCH₄ in the sentence an equation? If so, isn’t this equation necessary to be normalized by the preindustrial pCH4 value?

L289: The budget of oxygen in the atmosphere should be explained in more detail using equations. I have several concerns regarding the treatment of oxygen in the model. My first concern regarding this is the representation of the atmospheric pO2 budget by the oxidation of methane and reactions with OH radicals. I agree that the net (photo)chemical reactions would work as a net sink of oxygen during the oxidation of methane in the atmosphere because part of OH radicals originate from oxygen via many chemical reactions. As a result, the net reaction is represented as follows:

CH4 + 2O2 –> CO2 + 2H2O

A similar approach can be seen in a previous study (Goldblatt et al., 2006 Nature). The produced CO2 in the above net chemical reaction compensates the net consumption of CO2 when producing methane. Is this treated in the source and sink terms of O2 and CO2 properly? In addition, I’m not sure why a reaction of oxygen with OH radicals can be a net sink of oxygen. Obviously, oxygen is consumed and produced by many fast (photo)chemical reactions. An example is the Chapman mechanism that forms ozone in the stratosphere. However, the key for understanding the net budget of oxygen in the atmosphere is the net reaction as in the case of the methane oxidation mentioned above. For the case of the reaction with OH radicals, however, I do not come up with the mechanism that works as the net sink of oxygen in the atmosphere. The authors should explain the configurations and assumptions regarding the budgets of atmospheric chemical species in the model clearly.

Second, the long-term steady state of the atmospheric pO2 should also be affected critically by the oxidation of continental sulfide minerals (i.e., pyrite) and the deposition of pyrite from the ocean. Many previous studies of the oxygen biogeochemical cycle in geologic time consider the global sulfur cycle (Berner et al., 2000 Science; Berner, 2001 GCA; 2006 GCA; Bergman et al., 2004 Am. J. Sci.; Lenton et al., 2018 Earth-Sci. Rev.; Krause et al., 2018 Nature Commun.; Ozaki and Reinhard, 2021 Nature Geosci.; Ozaki et al., 2022 GMD). I think the consideration of the global sulfur cycle is required to reproduce the long-term steady state of the present-day atmospheric pO2 (~0.21 atm). I think it can be treated easily in the framework of DCESS II model by considering the global sulfur budget in the model as in the above previous studies. Alternatively, I think that not treating the atmospheric oxygen in the model would also be okay because it is not the primary focus of the model.

L569–575: The configuration of the land ecosystem should be explained in more detail. Specifically, the formulation of the meridional limits for each vegetation zone would be, at most, very rough. For example, the combined grasslands-savanna-desserts zone should, in reality, include the dessert regions, the grassland of C4 plants in tropical and subtropical regions, and the grassland of C3 plants in extratropical regions including the tundra region near the Arctic. Although this rough treatment may be acceptable considering the simplicity of the DCESS II model, it is unclear to me what is the purpose of the consideration of the three vegetation zones in such a simplified model. Given that the relationship between atmospheric pCO2 and the land NPP in equation (36) is common for three vegetation zone (except for the small difference in NPP_PI), I’d rather prefer a uniform distribution of vegetation in such a simplified land model (such as, Lenton and Huntingford, 2003 GCB). I guess that the authors introduced the shift of vegetation zones because it improves the estimation of the reproducibility of the land NPP and/or the carbon distributions in litter and soil reservoirs. If so, this treatment would still be acceptable, but the limitation of the configuration of land vegetation should be clearly explained in the text.

L569: Does the change in surface vegetation feedback to the surface albedo? Regardless, this should be mentioned in this section.

L595: There should be an upper limit of the atmospheric pCO2 for the condition in which the relationship between atmospheric pCO2 and the land NPP holds. It may be worth mentioning this because this model may be applied to a geologic event with extremely high atmospheric pCO2 (for example, > 2,000 ppm), such as the eruption of the Ontong Java Plateau and Caribbean Plateau during the Cretaceous, and/or a distant future of a severe global warming scenario.

L605–614: The explanation about the allocation of carbon to leaves and wood (the numbers in equations 37 and 38) is found only in the previous description paper (Shaffer et al., 2008). It would be helpful if the assumptions regarding this are explained at least briefly in the present study.

L640: Usually, the conventional global carbon cycle models consider both temperature- and CO2- dependency on silicate and carbonate weathering rates (e.g., Berner, 1991 Am. J. Sci.; Tajika, 2003 EPSL; Bergman et al., 2004 Am. J. Sci.; Berner, 2006 GCA; Krissansen-Totton and Catling, 2017 Nature Commun.; Krissansen-Totton et al., 2018 PNAS). I believe that the temperature dependency using Q10 function (Q10 = 2) would also reproduces a similar dependency to the conventional models, but this would limit the applicability of the model when the relationship between the atmospheric pCO2 and surface temperature is different from the present-day condition (e.g., under very high atmospheric pCO2, different solar luminosity, different continental areas, lack of land plants, etc.). I recommend using the conventional dependency on continental weathering rates, but if not, I recommend enriching the explanation about the validation of the formulation of the weathering rates comparing with the previous conventional global carbon cycle models and mentioning the known limitations of this treatment.

L683–690: This section seems to correspond to Model description, not to Model solution, calibration and validation.

L695: References for a climate sensitivity of 3 ˚C may be added (e.g., Meehl et al., 2020 Sci. Adv.; Zelinka et al., 2020 GRL).

L700: Is the function f(I) and the parameters in equation (36) (i.e., f0, a, b, and c) different between atmospheric sectors and/or vegetation zones? This should be clarified near equation (36).

L702: The amplitude of the seasonal variation of the atmospheric pCO2 varies spatially as can be seen in atmospheric pCO2 reanalysis data (e.g., Maki et al., 2010 Tellus B), which is especially large near the boreal forest region. Is the model tuned to reproduce the amplitude in each atmospheric sector or to reproduce the global mean amplitude? I think the detail of the calibration of the atmospheric pCO2 and the reference of the observation should be provided.

L727: “atom m-2 s-1” –> “atom m-2 s-1 respectively”

L795: How does the extensive sea ice increase the deep ocean temperature in the Arctic?

L913: It may be worth noting that the organic carbon burial flux of 0.11 GtC yr–1 (~9 Tmol yr–1) is broadly consistent with the values in conventional global carbon cycle models (e.g., Berner, 1991 Am. J. Sci.; Bergman et al., 2004 Am. J. Sci.).

L955–968: The values in Table 5 seems to be okay to me, but I think they should be compared with observational and/or theoretical estimates following the previous studies using the global carbon cycle models mentioned in the above comments.

L986: It may be worth mentioning here that the strengthened clockwise recirculation cell at 40–55˚S is also consistent with Rahmstorf and England (1997), although it has already been stated briefly at L991–993.

L1003–1004: Should “Exp1 and Exp2” be “Exp1a (Exp1b)”?

Yasuto Watanabe