An EOF-Based Emulator of Means and Covariances of Monthly Climate Fields

Geogdzhayev, Gosha; Souza, Andre N.; Flierl, Glenn R.; Ferrari, Raffaele

doi:https://doi.org/10.5194/egusphere-2025-3768

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https://doi.org/10.5194/egusphere-2025-3768

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18 Aug 2025

| 18 Aug 2025

An EOF-Based Emulator of Means and Covariances of Monthly Climate Fields

Gosha Geogdzhayev, Andre N. Souza, Glenn R. Flierl, and Raffaele Ferrari

Abstract. Fast emulators of comprehensive climate models are often used to explore the impact of anthropogenic emissions on future climate. A new approach to emulators is introduced that predicts means and covariances of monthly averaged climate variables. The emulator is trained with output from a state-of-the-art climate model and serves as a good first-order representation for the evolution of spatially resolved climate variables and their variability. For illustrative purposes, the emulator is applied to predict changes in the mean and variability of monthly values of both temperature and relative humidity as a function of global mean temperature changes. However, the approach can be applied to any other variable of interest.

Received: 03 Aug 2025 – Discussion started: 18 Aug 2025

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Gosha Geogdzhayev, Andre N. Souza, Glenn R. Flierl, and Raffaele Ferrari

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-3768', Anonymous Referee #1, 19 Aug 2025
This manuscript proposes a change of basis method to project spatially explicit means and covariances of monthly climate variables as a function of global average temperature change. There’s nothing wrong I can see in the method and it is an approach to emulation I have not seen before. But it almost reads as not having been developed in close collaboration with a user group and I think suffers some serious shortcomings because of that. Ultimately, I am left asking ‘who is this actually for, specifically? Who is going to pick this up, generate values, and use them? How specifically will they be used?’ I'm confident the authors have something in mind for this, but I think the manuscript would benefit for a more explicit treatment of this question.
Major issues
What is the use case for spatially resolved means and covariances of monthly variables? I’m not trying to be glib, I’m coming at this from the perspective of an impact modeler where I need time series of daily or monthly values of variables. I can’t use the statistics you highlight reconstructing in section 4.2 and Section 5 + appendices. Am I missing something? Do you generate the time series and just demonstrate on statistics (Fig 6-8. E1) because those are more critical for validation? If so, I think having at least an example plot in Appendix E showing an actual time series generated with this method is key, You may also want to consider extending Appendix E and moving it explicitly into the main body of the manuscript.
If I have to plug into another emulator like DiffESM to get daily values, why do I need this? A skim of the DiffESM paper shows they only need monthly averages and not covariances and other, simpler methods can give monthly averages. The STITCHES approach can generate a decent sized ensemble of time series of multiple variables jointly just from global temperature.

The method seems to apply well to any individual gridded variables (demonstrated in the manuscript with surface temperature and surface relative humidity) but, unless I read it wrong, this doesn’t extend to coherent joint emulation of multiple variables, right? There are certainly some impact models that only need temperature or relative humidity or precipitation, but many need all of those variables coherently together. I’m thinking of hydrology models especially. Can this method handle that? If not, what could be downsides of using independently generated time series of temperature, relative humidity, and precipitation together?

The authors are clear an ESM needs to have provided a sufficiently large collection of runs to train from, but how large is large?
You touch on the implications of this in your final paragraph but I think this needs to be expanded. Like most emulation techniques, this approach targets a single ESM. But many studies using outputs from emulation, say to study projections of a novel scenario, are also concerned with multi-model uncertainty, i.e. they would want multiple emulators each trained on a different ESM. Does the collection of ESMs that provided ‘enough’ training have uncertainty properties at all similar uncertainty characteristics as the full collection of models? I don’t have any way of even roughly guessing because I don’t know what the extent of ESMs providing enough data to be individually emulated is.

Missing relevant citations for exclusively emulators of the class trained to extend ESMs to arbitrary future scenarios:
Bassetti et al was actually published nearly a year ago https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2023MS004194

Tebaldi, C., Snyder, A., and Dorheim, K.: STITCHES: creating new scenarios of climate model output by stitching together pieces of existing simulations, Earth Syst. Dynam., 13, 1557–1609, https://doi.org/10.5194/esd-13-1557-2022, 2022.

Quilcaille et al https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022GL099012

and Quilcaille et al https://esd.copernicus.org/articles/14/1333/2023/
Citation: https://doi.org/10.5194/egusphere-2025-3768-RC1
RC2: 'Comment on egusphere-2025-3768', Anonymous Referee #2, 01 Oct 2025

The authors use large-ensemble historical and scenario simulations of a single climate model to train a regression model that predicts means and covariances of 2-m temperature and relative humidity for each month as a quadratic function of global-mean (and ensemble-mean) temperature. The model trained on one scenario successfully approximates the means and covariances of the fields of interest over other two scenarios.
This is a reasonable strategy and implementation. I do have a relatively minor comment though that I would like to clarify. The authors apply the EOF decomposition to the full historical data, rather than anomalies, as is usually done. This is fine for the purposes of the data compression (the leading EOF would essentially give you mean field and the trailing EOFs would be close to the EOFs of anomalies) . Such choices are convenient sometimes (for example, when you use EOFs as a basis to project dynamical equations on (where you need mean state orthogonal to the basis of anomalies) but I am not sure this choice is super-convenient or most economical for the present purposes. I would compute instead the standard EOFs of the historical period (after subtracting the mean) [better yet - ensemble EOFs - why use the single realization?], use pattern scaling for projecting the mean into the future (quadratic regression on global mean at each grid point), and then linear regression of eof amplitudes (or quadratic regression of EOF variances) on global mean temperature to project the covariance matrices. Since EOFs diagonalize covariance matrices, you would still get the positive-definite covariances as long as your projected EOF amplitudes remain positive. I think it is highly likely that this much simpler training procedure (which assumes a still diagonal future covariance matrix in the basis of historical EOFs) will give essentially the same results as a more complex method used by the authors - but, of course, I'd be willing and happy to hear the authors opinion and discuss further!

Citation: https://doi.org/10.5194/egusphere-2025-3768-RC2

Gosha Geogdzhayev, Andre N. Souza, Glenn R. Flierl, and Raffaele Ferrari

Data sets

GaussianEarth Gosha Geogdzhayev and Andre N. Souza https://github.com/sandreza/GaussianEarth

Gosha Geogdzhayev, Andre N. Souza, Glenn R. Flierl, and Raffaele Ferrari

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Short summary

Climate models serve as good guesses of how humans affect the climate, but they cannot explore all possible future scenarios of interest. We develop a method that can serve as a fast and cheap stand-in to evaluate likely changes in variables like surface temperature and relative humidity at a regional scale in arbitrary future climates. Crucially, our method captures relationships between different geographic areas and predicts both average values and likely ranges using a unified framework.


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