Review for: SURFER v3.0: a fast model with ice sheet tipping points and carbon cycle feedbacks for short and long-term climate scenarios

This paper presents the next iteration of the simple climate model SURFER. The previous version, v2.0, lacked some processes critical for long-term (>1-10 kyr) simulations such as volcanic degassing, rock weathering, and ocean alkalinity cycling. V3.0 captures these processes, adds atmospheric methane, and improves or builds on the parameterizations for ice sheet tipping and land use emissions.

The paper is well-written, and I found the model decisions to be reasonable. I appreciated that the authors laid out the specific goals for updating SURFER in the introduction — it offered a clear frame of reference for my review. There’s room to make certain formulations more mechanistic, but these limitations don’t get in the way of SURFER’s ability to capture complex system responses in a simple model. The authors also do a nice job of showing that SURFER v3.0 out-performs v2.0 and captures the basic response of more sophisticated models across a wide range of timescales. On top of that, the code worked out of the box, and it was easy to figure out how to run my own experiments separate from the examples provided. I really commend the authors on how well they’ve communicated their changes and made the model easy to understand and use.

I think the paper can be accepted after some minor revisions.

Two points of general feedback:

• Overall, more citations would be helpful. I mention a few places in my line-by-line comments where I expected a citation and didn’t get one, but that issue persists throughout much of the text (especially when laying the background). I know a lot of these decisions come down to personal / editorial preferences, so my feedback isn’t very specific. I just encourage the authors to double-check places where citations are absent to decide if it’s worth adding any.
• The calibration / tuning steps are a bit scattered in the text. I know that they’re just qualitative (and I have no issue with that), but for others that might want to test different parameter values it would be very helpful to have a clearer map of what knobs were turned, how, and why. The best way to do this might be to add columns to table 2 (and subsequent, similar tables) for the relevant reference(s) used to tune that parameter and how the reference was used — e.g., was the value tuned to match an independent constraint on the same parameter, or to fit some climate response, etc.

Thoughts on C-cycle component

I just wanted to acknowledge that the new carbon cycle component is very simplistic. For example, inorganic and organic C export from the upper ocean is fixed — it doesn’t respond to climate / pCO2 / riverine inputs, etc. Weathering fluxes only scale with temperature and there’s no runoff dependence (this could be highlighted more, especially as the runoff response to GHGs is less certain than the T response). There’s also no ocean organic carbon burial, which is a substantial component of global geologic C sequestration.

I think this highly simplified treatment is okay because it’s consistent with the rest of the model’s complexity, more mechanistic / comprehensive formulations are often still elusive, and a primary goal is to capture the response of more sophisticated models, not the internal dynamics. The simplified treatment limits the questions SURFER v3.0 can be used to answer, but I think the authors reasonably communicate that in the text.

Line by line:

L15-17: Citations needed for warmest year on record and frequency/intensity of extremes.

L112-114: Citation needed for the two SURFER v2.0 problems noted here.

L132: Consider adding (CBW) after “..and water self-ionisation alkalinity” to clarify the subscript in equation 13.

L143: Should “dissolved organic carbon” be changed to “dissolved inorganic carbon”?

L330: Some references for drivers of F_CaCO3 and F_CaSiO3 would be helpful here.

L891: No action needed here. Just wanted to acknowledge the colorful tone of this mini paragraph. It doesn’t work everywhere, but I’m cool with it in a lengthy model description paper like this 

L913-914: Another place where references would help.

L976: change “od” to “of”.

Acknowledgments: These are left incomplete (but probably intentionally so). Flagging just in case.

The SURFER_v3.ipynb file

• First text block under “Setup”: replace [url_link] with a url (I recognize this might be intentionally incomplete, just flagging it).
• At least for me, markdown doesn’t like the equation formatting in the text under “Emission scenarios”. One option is to edit “CO$_2$” to “$\text{CO}_2$” (and repeat for CH$_4$).

Couplet and co-authors develop an update to SURFER v.2, which includes longer-term carbon cycle processes and additional land surface feedbacks that modify CO2 on long timescales as well as atmospheric CH4. They find that these long-term feedbacks generally act to lower long-term atmospheric CO2 and global temperature, reducing ice sheet melting and resulting in lower sea level rise for a given emission scenario.

I found the paper to be well-written, the equations well-described, and the arguments easy to follow. The figures are well-made and support the contentions in the paper. The references are appropriate. I think these simple models that capture overall Earth system dynamics are incredibly important for the field, so I applaud the authors’ efforts to develop this model and make it easy to use. And I hope the field uses these models more often as tools to understand the basics of complex systems. I also think that these model description papers can be rather tedious, but I found this one to be easy to read and I learned quite a bit from it. Overall, I think this paper is ready for publication pending some minor changes, which I detail below.

First, having read the first reviewer’s comments, I agree with their thoughts. I also found it somewhat surprising that the alkalinity flux from carbonate and silicate weathering should be split 50/50, when I think there is good evidence that it is more like a 66/34 split (Gaillardet et al., 1999; Moon et al., 2014). Also, the activation energy used in the paper for silicate weathering (74 ± 29 kJ/mol) is on the high side. Later work by West (West, 2012) found a lower number, and more recent work (Brantley et al., 2023) finds an even lower number (ie, 22 kJ/mol).

I don’t expect incorporating these values into the paper is likely to make a large difference in the results, and I don’t think re-running the simulations to account for this is worthwhile prior to publication. Further, it could be that using a high number in a sense compensates for the lack of a simulated hydrological cycle in the model (a reasonable trade-off to reduce complexity!), which is key to representing the silicate and carbonate weathering fluxes (Kukla et al., 2023; Maher and Chamberlain, 2014). Nevertheless, these exact numbers are going to change the CO2 emissions scenario that will cause more or less sea-level rise via melting of Greenland or Antarctica and some acknowledgment of these limitations in the discussion would be helpful.

Second, I’m curious why CaCO3 accumulation on shelves is ignored (line 279). Is the dissolution flux on shelves likely to be minimal, even with high and rapid emissions? A reference here on why this is a reasonable assumption would be helpful or at least an explanation about how incorporating it would be an unreasonable trade-off in terms of model complexity.

Lastly, while the authors are clear that their goal is to explore sea-level/ice sheet tipping points, their discussion of missing processes that might impact this is short. For example, land surface-vegetation-albedo feedbacks are known to be important in just the recent past (ie, Green Sahara) and might impact temperatures and certainly high-latitude hydroclimate (Feng et al., 2022; Swann et al., 2014). Another potentially critical feedback involves the role of marine anoxia in changing atmospheric CO2. While the authors point out that changes in marine ecosystem production are neglected, organic carbon burial is also neglected and the geologic record at least has multiple examples of tipping points involving organic carbon burial (ie, ocean anoxic events) that could modify atmospheric CO2. Indeed, the geologic record holds many examples of tipping points on these timescales that have been difficult to simulate except in the simplest of models and yet these tipping points would impact the temperature and therefore sea-level over 10^4 timescales. Clearly incorporating these processes would be another paper (and a lot more work), but discussing these missing tipping points more in-depth would be worthwhile, along with how they might be incorporated in to future versions of SURFER. This might help the wider community see the value of these simpler models.

Jeremy K. C. Rugenstein, Colorado State University

References cited in review

Brantley, S. L., Shaughnessy, A., Lebedeva, M. I., and Balashov, V. N.: How temperature-dependent silicate weathering acts as Earth’s geological thermostat, Science, 379, 382–389, 2023.

Feng, R., Bhattacharya, T., Otto-Bliesner, B. L., Brady, E. C., Haywood, A. M., Tindall, J. C., Hunter, S. J., Abe-Ouchi, A., Chan, W.-L., Kageyama, M., Contoux, C., Guo, C., Li, X., Lohmann, G., Stepanek, C., Tan, N., Zhang, Q., Zhang, Z., Han, Z., Williams, C. J. R., Lunt, D. J., Dowsett, H. J., Chandan, D., and Peltier, W. R.: Past terrestrial hydroclimate sensitivity controlled by Earth system feedbacks, Nature Communications, 13, 1–11, https://doi.org/10.1038/s41467-022-28814-7, 2022.

Gaillardet, J., Dupré, B., Louvat, P., and Allegre, C. J.: Global silicate weathering and CO2 consumption rates deduced from the chemistry of large rivers, Chemical Geology, 159, 3–30, 1999.

Kukla, T., Ibarra, D. E., Lau, K. V., and Rugenstein, J. K. C.: All aboard! Earth system investigations with the CH2O-CHOO TRAIN v1.0, Geoscientific Model Development, 16, 5515–5538, https://doi.org/10.5194/gmd-16-5515-2023, 2023.

Maher, K. and Chamberlain, C. P.: Hydrologic regulation of chemical weathering and the geologic carbon cycle, Science, 343, 1502–1504, https://doi.org/10.1126/science.1250770, 2014.

Moon, S., Chamberlain, C. P., and Hilley, G. E.: New estimates of silicate weathering rates and their uncertainties in global rivers, Geochimica et Cosmochimica Acta, 134, 257–274, https://doi.org/10.1016/j.gca.2014.02.033, 2014.

Swann, A. L. S., Fung, I. Y., Liu, Y., and Chiang, J. C. H.: Remote vegetation feedbacks and the mid-Holocene green Sahara, Journal of Climate, 27, 4857–4870, https://doi.org/10.1175/JCLI-D-13-00690.1, 2014.

West, A. J.: Thickness of the chemical weathering zone and implications for erosional and climatic drivers of weathering and for carbon-cycle feedbacks, Geology, 40, 811–814, https://doi.org/10.1130/G33041.1, 2012.