the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Jan 2026
MErSiM v1.0: Resolving Biases in Global Silicate Weathering Model with A Data-Driven Surface Erosion Module
Abstract. The silicate weathering feedback is a key planetary thermostat regulating Earth's long-term climate, yet process-based models of this mechanism suffer from biases. The widely-used weathering model, when driven by stream power erosion laws, systematically overestimates weathering fluxes in the tropics and predicts a global total flux nearly double the observation-based estimates. This study demonstrates that this discrepancy partially originates from a poorly constrained erosion submodule. To resolve this, we developed a new global erosion model using a Random Forest algorithm trained on ~4,000 10Be-derived, basin-averaged erosion rates. Our data-driven model explains 90 % of the variance in the observational erosion data, far exceeding the performance of the traditional Stream Power Incision Model (SPIM) and other existing approaches. By integrating this newly developed erosion module into a commonly used framework, we created a revised silicate weathering model, named MErSiM v1.0 (Machine-learning derived Erosion and Silicate-weathering Model). This new model successfully eliminates the systematic tropical overestimation, and its predicted global total flux (~3.1 × 1012 mol C yr-1) is now in better agreement with observations. More fundamentally, MErSiM resolves a critical trade-off in the original framework, now able to simultaneously match both the global total flux and the watershed-scale spatial pattern of weathering. Sensitivity experiments reveal that while MErSiM's response to glacial-interglacial climate change is comparable to previous work, its feedback to intense warming (4×CO2) is profoundly attenuated (a 42 % increase vs. 149 % in the original model). This dampened sensitivity stems from a structural shift to a more supply-limited weathering regime, a finding supported by a newly calibrated set of "sluggish" chemical kinetic parameters. This work delivers a comprehensively evaluated and observationally constrained model, which suggests that the silicate weathering feedback may be a weaker climate stabilizer under extreme greenhouse conditions than previously thought.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-5624', Aaron Bufe, 30 Mar 2026
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RC2: 'Comment on egusphere-2025-5624', Jeremy Caves Rugenstein, 01 Apr 2026
Zhao and co-authors develop a new data-driven model of erosion and weathering and compare this model to similar output presented in Park et al. (2020), which uses a stream-power model coupled to Gabet and Mudd (2009; GM09). They find that their new model does a better job capturing global erosion rates, lowers estimated silicate weathering fluxes, and makes silicate weathering much less sensitive to changes in climate.
I found this an interesting paper to read and the figures are well-done. I especially appreciated the explanations of how the model achieved certain results, and the random-forest technique is especially well-suited to understand the controls on erosion. I also liked the sensitivity test of weathering to changes in CO2, since this is an important parameter in Earth system science that is poorly constrained. However, I have a number of concerns that should be addressed, so that readers understand the foundation on which this model was built.
First, the paper refers repeatedly to the “original GM09” model as including a stream-power component. GM09 does not include anything remotely related to stream-power and is perhaps better described as a reactive-transport-inspired model that attempts to predict weathering on hillslopes. I don’t know which version of GEOCLIM included a stream-power model piggy-backed on to GM09 (perhaps an earlier paper by Pierre Maffre? (Maffre et al., 2018)), but this is used in Park et al. (2020), though I would definitely not characterize this as the original GM09 model.
Second, the authors confuse the meaning of chemostatis (Godsey et al., 2009). Chemostasis refers to constant concentrations as runoff changes. This, in turn, means the silicate weathering fluxes scale linearly with runoff. I believe the authors mean some sort of kinetic-limit, such that, as runoff increases, concentrations decline, and silicate weathering fluxes are—as a consequence—flat.
More critically, the authors motivate much of the paper by arguing that Park et al. (2020) overestimate the silicate weathering flux. Maybe they do, maybe they don’t, but the model presented herein (MErSiM) produces a very low silicate weathering flux. It may match data from Müller et al. (2022), but the uncertainty on the volcanic flux is enormous (over an order of magnitude) (Coogan and Rugenstein, 2025) (see their Figure 13). To the extent that basically the silicate weathering flux must match the volcanic flux, I don’t think optimizing a model to the low-end of this estimate is particularly useful. What would happen if the model was optimized for a higher-end estimate? A higher-end estimate is, anyway, what Moon et al. (2014) estimate; the authors state that their model matches Moon’s estimates, though Moon estimates a global silicate weathering carbon flux nearly an order of magnitude higher than MErSiM. Either way, the authors need to address what would happen if the model was optimized to a different global silicate weathering flux.
Relatedly, I don’t follow the argument about why erosion is the particular parameter that is most underconstrained and therefore produces a wrong silicate weathering flux. Maybe I just don’t understand the argument, but the fact that we don’t even know what the silicate weathering flux should be means it’s difficult to assign to a specific parameter why a certain model doesn’t match certain estimates of silicate weathering. I like the authors’ approach to building a better erosion model; however, I don’t see this statement as a particularly helpful motivation for building such a model.
A few other caveats on the erosion model would be valuable. For example, I presume that there is no glacial erosion processes, meaning that calculating an LGM erosion flux assumes that glaciers only negligibly modify erosion and weathering processes. This is, of course, a major controversy in the field, and the lack of such a glacial erosion process is a major caveat. Similarly, at high CO2 levels, one robust expectation of a warming climate is a change in the timing and intensity of storms, which is likely to modify erosion. Based upon the parameters in MErSiM, I don’t think such a shift in precipitation timing/intensity and its effect on erosion is captured in MErSiM. Another caveat that should be mentioned.
I found the sensitivity experiment to be particularly interesting, and I appreciated the explanation of why the model responds the way it does. However, it should be noted that in, for example, the 4x CO2 experiment, the rise in silicate weathering flux is best understand as the instantaneous transient adjustment to a change in climate. Given the need to maintain mass balance in the carbon cycle (Berner and Caldeira, 1997; Caves et al., 2016; Zeebe and Caldeira, 2008), the silicate weathering flux will ultimately have to rise by exactly the same amount as whatever input flux of CO2 caused the increase in atmospheric CO2. This would presumably involve changes in erosion beyond what is predicted by MErSiM (or including other components of the Earth system, such as weathering on marine shelves (Trapp-Müller et al., 2025) or in seafloor basalts (Coogan and Gillis, 2018)). However, the authors state that MErSiM is best thought of as a long-term (and not short-term, transient) model. Some acknowledgement that this is still a barrier to be resolved would help to place these sensitivity experiments in context.
Lastly, equation 10 (similar to West (2012)) demonstrates that erosion will be the predominant variable impacting the estimate silicate weathering flux (Equation 10 needs to be derived…it’s not clear to me how the authors reach Equation 10 from the previous equations). This is in contrast to Maher and Chamberlain (2014) who parameterize silicate weathering as being predominantly impacted by runoff and the equilibrium concentration (equation 3 and Fwsil = q*C, where q is runoff and C is concentration). I bring this up to point out that I don’t think this paper demonstrates that their formulation is indeed the best formulation to understand silicate weathering. It simply does a better job than a similar formulation that also places a heavy emphasis on erosion. One would need to do a similar analysis using Maher and Chamberlain (2014) (or another model) to demonstrate which model produces a better estimate of the silicate weathering flux. Even this is difficult, since our constraints on the weathering flux are poor. Thus, MErSiM ends up predicting that catchments are near the kinetic boundary and will be sensitive to changes in erosion, but it’s not clear to me that this is supported by the data, particularly if another model is used to interpret catchment solute data. Perhaps this is beyond the scope of this paper, but it is an overall caveat in how one conceptualizes the modeling presented herein.
Again, thanks for an interesting paper, and I hope these comments are helpful in revising the paper and addressing any outstanding questions.
Jeremy K. C. Rugenstein, CSU Fort Collins
Minor comments:
Line 18: What is the systematic tropical overestimation?
Line 48: I’m not sure the global degassing flux is that well-constrained. Müller et al. (2022) may claim it is, but recent compilations suggest nearly an order of magnitude uncertainty (Coogan and Rugenstein, 2025) (see their Figure 13 and references therein).
Line 67: I would not characterize GM09 as using a simplified stream power incision model. If anything, they use a sort of reactive-transport-inspired model that looks only at hillslopes.
Equation 8: This equation is not in the original GM09 model. I believe it is a modification in GEOCLIM. In the original GM09 model, erosion is simply an independent variable.
Equation 10: Please provide the derivation for this equation.
Lines 185-9: Only 2 purposes are listed, rather than 3.
Line 490: I wouldn’t say that the peak of the yellow curve is strictly within the gray bar…it is still somewhat shifted to the right.
Line 515: The Moon et al. (2014) estimate is substantially higher when considering all fluxes (ie, ~11 x 10^13 mols C/yr)
Line 567: “Chemostatic” has the opposite meaning; that is, solute concentrations remain the same as runoff changes, which has been used to suggest that the catchment has reached reaction equilibrium. I think you mean to say, “kinetically limited”.
Line 570: Again, I think you mean close to the kinetic boundary
Line 618: Again, wrong use of chemostatic
References cited
Berner, R.A., Caldeira, K., 1997. The need for mass balance and feedback in the geochemical carbon cycle. Geology 25, 955–956. https://doi.org/10.1130/0091-7613(1997)025%3C0955:TNFMBA%3E2.3.CO;2
Caves, J.K., Jost, A.B., Lau, K.V., Maher, K., 2016. Cenozoic carbon cycle imbalances and a variable silicate weathering feedback. Earth and Planetary Science Letters 450, 152–163. https://doi.org/10.1016/j.epsl.2016.06.035
Coogan, L.A., Gillis, K.M., 2018. Low-Temperature Alteration of the Seafloor: Impacts on Ocean Chemistry. Annu. Rev. Earth Planet. Sci 46, 21–45. https://doi.org/10.1146/annurev-earth-082517
Coogan, L.A., Rugenstein, J.K.C., 2025. Regulation of the carbon cycle on geological timescales, in: Reference Module in Earth Systems and Environmental Sciences. Elsevier. https://doi.org/10.1016/B978-0-323-99762-1.00060-7
Godsey, S.E., Kirchner, J.W., Clow, D.W., 2009. Concentration – discharge relationships reflect chemostatic characteristics of US catchments. Hydrological Processes 23, 1844–1864. https://doi.org/10.1002/hyp
Maffre, P., Ladant, J., Moquet, J., Carretier, S., Labat, D., Goddéris, Y., 2018. Mountain ranges, climate and weathering. Do orogens strengthen or weaken the silicate weathering carbon sink? Earth and Planetary Science Letters 493, 174–185. https://doi.org/10.1016/j.epsl.2018.04.034
Trapp-Müller, G., Caves Rugenstein, J., Conley, D.J., Geilert, S., Hagens, M., Hong, W.-L., Jeandel, C., Longman, J., Mason, P.R.D., Middelburg, J.J., Milliken, K.L., Navarre-Sitchler, A., Planavsky, N.J., Reichart, G.-J., Slomp, C.P., Sluijs, A., Van Hinsbergen, D.J.J., Zhang, X.Y., 2025. Earth’s silicate weathering continuum. Nat. Geosci. 18, 691–701. https://doi.org/10.1038/s41561-025-01743-y
West, A.J., 2012. 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
Zeebe, R.E., Caldeira, K., 2008. Close mass balance of long-term carbon fluxes from ice-core CO2 and ocean chemistry records. Nature Geoscience 1, 312–315. https://doi.org/10.1038/ngeo185
Citation: https://doi.org/10.5194/egusphere-2025-5624-RC2
Data sets
MErSiM v1.0: Machine learning derived Erosion and Silicate weathering Model; code and data of Zhao et al. (2025) GMD Jiaxi Zhao et al. https://doi.org/10.5281/zenodo.18015309
Model code and software
MErSiM v1.0: Machine learning derived Erosion and Silicate weathering Model; code and data of Zhao et al. (2025) GMD Jiaxi Zhao et al. https://doi.org/10.5281/zenodo.18015309
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- 1
Review of MErSiM v1.0: Resolving Biases in Global Silicate Weathering Model with A Data-Driven Surface Erosion Module, submitted to Geoscientific Model Development
In this paper, the authors hypothesize that the mismatch between modelled and measured global silicate-weathering rates are due to uncertainties in the underlying erosion models. The authors therefore present a global erosion-rate model trained against cosmogenic-nuclide derived erosion rates using a random forest approach. They show that this model can reproduce erosion rates much better than a basic stream-power-erosion approach. The authors then incorporate their predicted erosion patterns into an existing steady-state silicate-weathering model and demonstrate that the new product can predict both the total global weathering flux and the spatial distribution of weathering rates better than previous models.
I found the study to be very well motivated, well written, and convincingly argued. The analysis is sound and provides a significant contribution for modelling global silicate-weathering fluxes. The figures and text are of a high quality. In particular, I appreciate the explanations of complex terms and approaches (e.g. the SHAP work) for the unfamiliar reader. I only have a few relatively minor comments that may be interesting to consider before publication.
Analysis and comparison of errors in weathering fluxes
When the authors investigate the performance of erosion module within the silicate weathering model, to me the text at times seemed a bit pushed compared to the results. In particular:
L478 – 496: You write that Fig. 9 “clearly illustrates the trade-off”, that the value in Fig. 9a is “far to the right of the observed range” and that its value within the square-band is “low”. To my eyes, the peak is just to the right of the optimum and there are still reasonable values within the grey band. Next, you write that in Fig. 9b, “peaks of all three metric curves are now located squarely within the grey observational band”. For the red and blue curves that is true, but the peak of the yellow curve is clearly not in the square band and actually looks quite close to the location in Fig 9b. Can you revise this text so that the text matches the data more clearly?
Perhaps, you can also explicitly quantify (1) the global weathering fluxes predicted by the two different models (MErSiM versu Park20) including an estimate of uncertainty for both, and (2) the difference between each one of these predictions and the measured total weathering fluxes.
Finally, in the section L478 – 496 you claim that these results speak to the trade-off between matching total weathering fluxes versus the pattern of weathering fluxes. I did not understand how Figure 9 relates to (or informs) the spatial pattern of silicate weathering fluxes.
L497 – 504: Similar to above, the text here seems a bit more pushed than warranted based on Fig 10. I agree that the errors are clearly smaller in the RF model, but there are still quite large errors, in particular in the tropical regions. When you write things like “large” errors and is “much less” severe, can you explain quantitatively what you understand by a large and small error. How much were errors reduced on average etc.?
Sensitivity of the model to CO2 increases
I was confused by the discussion about the effect of CO2 increases. You explain your models small response to the CO2 increase by widespread chemostasis and a resulting runoff insensitivity of the weathering flux. My understanding is exactly the opposite: To me, chemostasis means that concentrations remain constant with changes in runoff – contrary to what is suggested in L568 (e.g. Godsey et al., 2019; Godsey et al., 2009). Under these conditions (common in active mountains (Godsey et al., 2019)) the weathering fluxes should strongly increase with runoff. Hence, the system should have a high sensitivity to increased CO2 and runoff. Something is off here, and maybe it is just about the term chemostasis? I guess your model also has a negative temperature response, does that matter here?
Number of variables
Your paper demonstrates that an erosion model based on 7 input parameters performs equally well to a model based on 14 parameters. That makes me wonder: would a model with even fewer parameters also work? For example, if I understand Fig. 6 correctly, the lithology may play a minor role. Would it be feasible to progressively eliminate parameters from your model (starting with the least important) and see when the model starts breaking down?
Line comments
L10: Which “widely used weathering model”- can you be specific? There are several out there.
L51: became
L60: How can a model “bias [be] supported by […] data”? Wasn’t your point that the bias is a bias because it doesn’t match global fluxes?
L102 – 136: Please systematically define all variables (even if they are obvious); e.g. missing t in equation 1 (definition comes only for equation 2) and many of the parameters in the Arrhenius relationship (equation 6).
L140: I guess you could cite West (2012) here who explores that steady-state expression that you show
L149: You have the variable name R already in the Arrhenius relationship. It would be useful to choose a different name for runoff – for example qw.
L263: By “this compilation” you refer to the Gaillardet et al. (1999) compilation, right? Maybe specify to clarify sentence
Figure 3: Please define the abbreviations in the figure caption
Figure 8: Can you indicate the units of these variables?
I hope these comments are useful and remain with best wishes to authors and editors
Aaron Bufe
References
Gaillardet, J., Dupré, B., Louvat, P., and Allègre, C. J., 1999, Global silicate weathering and CO2 consumption rates deduced from the chemistry of large rivers: Chemical Geology, v. 159, no. 1, p. 3-30.
Godsey, S. E., Hartmann, J., and Kirchner, J. W., 2019, Catchment chemostasis revisited: Water quality responds differently to variations in weather and climate: Hydrological Processes, v. 33, no. 24, p. 3056-3069.
Godsey, S. E., Kirchner, J. W., and Clow, D. W., 2009, Concentration–discharge relationships reflect chemostatic characteristics of US catchments: Hydrological Processes, v. 23, no. 13, p. 1844-1864.
West, A. J., 2012, Thickness of the chemical weathering zone and implications for erosional and climatic drivers of weathering and for carbon-cycle feedbacks: Geology, v. 40, no. 9, p. 811-814.