Summary and general review

In the manuscript ‘An Emulator-Based Modelling Framework for Studying Astronomical Controls on Ocean Anoxia with an Application on the Devonian’, Sablon and co-authors couple an emulator to GEOCLIM to evaluate the role of orbital forcing on climate fields and it influence on weathering and nutrient dynamics. The first part of the manuscript outlines the method to build and test the Devonian climate emulator in detail. Their emulator predicts the temperature and runoff fields under a range of orbital parameters and pCO2 with good accuracy. In the second part, the climate emulator is coupled to GEOCLIM to simulate how orbitally driven climate changes affect regolith build-up and weathering in a Devonian configuration. They find that regolith grows during high eccentricity (wetter conditions increase regolith production more than erosion) but the impact on nutrient fluxes is small.

Overall, the manuscript is well structured with the aims and objectives clearly defined. It makes two significant scientific contributions. First, by creating a Devonian climate emulator capable of emulating climate under different CO2 and orbits that demonstrates the sensitivity of Devonian climate to these input parameters. This in itself is an incredibly valuable outcome. Second, the emulator coupled GEOCLIM is the first model that can test hypotheses for recurring Devonian OAEs in a transient manner on multi-Myr timescales. The authors have succeeded in clearly outlining the multi-step approach to build the emulator and add on to the GEOCLIM framework, making it suitable for publication in GMD. However, a few points outlined in the attached document (primarily asking to clarification) should be addressed.

Soblon et al describe a coupling of the AOGCM climate of HadCM3/HadSM3 to the weathering model GEOCARB, facilitated by gaussian process emulation of dimensionally reduced climate fields, and applied to a 25-million year transient simulation case study in the Devonian. The paper is useful, interesting and clear, and worthy of publication in GMD. My comments are mostly on structure of the paper and clarification of some technical details.

The authors have taken the decision to submit this as a model development paper, but the introduction reads like a science application with a focus on Devonian OAEs. In my view a more useful introduction would be better directed at the modelling problem. Perhaps starting with GEOCLIM, high computational efficiency and how achieved, some applications, limitations, need for spatially resolved climates e.g. for sensitivity to orbital variability, fundamental incompatibility with speed of GCMs, solution via emulation, perhaps some examples emulators/simulator couplings, then finally the choice to focus on the Devonian and the case study. For me, much of the novelty and relevance to GMD is the coupling, and the above would emphasise that.

The abstract has more of the above approach, presenting a model development paper, though this could be developed in similar direction to the above ideas. In the final sentence, and opposite to above, I would close with something more explicit about the science case study and results, however inconclusive, perhaps the emergent relationship between high eccentricity and soil development. It’s a shame to leave this completely vague.

At the end of all this work there is a product, the coupled model. Can this be provided in a useable form? Does the model need a name and a version number as per the GMD convention?

Some comments as I work through

Section 2.1.1 and Appendix. The slab model HadSM3 requires surface ocean heat fluxes, which are derived from fifteen 250-year simulations of the coupled model HadCM3. I have a few questions on this

• I don’t see the need to put this in an appendix. It’s interesting, it’s not especially technical and it is central to the approach - arguably the fundamental driver of the overall approach is to add orbital variability, and it is here where the modelled ocean response is to orbital forcing described.
• As the design spans the full range of orbital forcing and a stationary solution requires 5000+ years, some justification for short 250-year spin-ups would be useful, and explanation what sort of errors might arise. The additive correction adjusts for the integrated imbalance, but what about the spatial distribution?
• These 15 fields are interpolated with distance weighting for application to the 81 HadSM3 experiments. Can the authors make some attempt at validating this approach. I appreciate cross-validation could be challenging given the samples are few and mostly extreme, but perhaps some characterisation of the ensemble of fields would help. For instance, if a PC decomposition were dominated by a single component, this would help support interpolation. Note the ordering of Figs A1 and A2 should probably be reversed to reflect the logical ordering.

Section 2.1.2. The study uses GEOCLIM, which the authors describe as a 10-box atmosphere-ocean model coupled to a continental model that is spatially resolved. Could more detail be on the continental model be provided, as it is here where the coupling with the emulator is most relevant? Is it for instance configured to the same (Fig 1) topography as HadCM3 simulations, at the same resolution? Also, the ocean model – do the nine boxes represent depth and/or spatial resolution? A figure representing the ocean and continental models might help, perhaps in the Appendix.

Line 155 obliquity is varied between 20.75° and 23.75° for the HadSM3 ensemble. Please discuss why this specific range was chosen (where do the limits come from?). Related, in the HadCM3 ensemble, the range is between 21° and 25°, so worth noting the slight extrapolation implied. Was there a motive for this choice in the HadCM3 ensemble, presumably it was designed with more general applicability in mind?

Section 3.1, here I would argue that a shorter summary of GP would be adequate (perhaps just lines 197-203 and 230-238?), and much of this detail would be better in an Appendix. GP has been around a long time and is widely applied. For my own interest I checked and see Rasmussen 2006 has 39,000 citations and Mackay 1998 has 17,000.

Line 241. Should probably cite Holden and Edwards 2010 which first presented dimensionally reduced emulation for climate to advance beyond pattern scaling.

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2010GL045137

260 please quantify “unsatisfactory” – this is subjective, and quantification would enable the reader to evaluate the cost-benefits of your careful kernel choice. OK, I see this quantification is done later – would be clearer to express this differently, perhaps simply point to the analysis coming later. Or maybe just say you considered two approaches and not yet mention which was preferred.

Section 3.4. Can any of this be moved to the appendix, for instance 311-320 describing a more complex objective function which was not used as too computationally expensive. There is no quantification, either of the value added or the computational speed, and including this in the main body of text adds little value I can see.

Line 382 were seven PCs used, or six as plotted in Figs 6 and 7?

Figs 6, 7. You plot Sobol indices. A definition and/or citation would be useful.

Line 440. Can you better explain/justify this. How do you map spatial fields of emulated surface air temperature onto global average SST. Moreover, why do you use a fixed linear regression using outputs from a different model, which presumably loses the spatial relationships between SST and orbit. Why not relate your patterns of emulated SAT directly onto patterns of SST needed by GEOCLIM?

Line 465. You generate a plausible yet hypothetical forcing scenario. I wonder if this explains your apparent reticence with conclusions. The coupled model is presumably very fast, though I missed whether that was quantified anywhere. Could you not e.g. generate an ensemble of forcing input time series to sample plausible scenario space and use this to generate a distribution of outputs that could be summarised into something more robust? (Not necessary in the context of a model development paper, but posing the question.)