Articles | Volume 18, issue 19
https://doi.org/10.5194/gmd-18-6701-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.An information-theoretic approach to obtain ensemble averages from Earth system models
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- Final revised paper (published on 01 Oct 2025)
- Preprint (discussion started on 19 May 2025)
Interactive discussion
Status: closed
Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor
| : Report abuse
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RC1: 'Comment on egusphere-2025-1640', Anonymous Referee #1, 04 Jun 2025
- AC1: 'Reply on RC1', Carlos Sierra, 10 Aug 2025
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RC2: 'Comment on egusphere-2025-1640', Uwe Ehret, 19 Jun 2025
- AC2: 'Reply on RC2', Carlos Sierra, 10 Aug 2025
Peer review completion
AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload
AR by Carlos Sierra on behalf of the Authors (10 Aug 2025)
Author's response
Author's tracked changes
Manuscript
ED: Publish as is (27 Aug 2025) by Olivier Marti
AR by Carlos Sierra on behalf of the Authors (27 Aug 2025)
Manuscript
This is a nice study that proposes an information-theoretic rationale for weighting ESM outputs when computing multi-model average projections. The approach constructs weights from the divergence between each ESM’s output distribution and the observed-climate distribution, thereby rewarding models that align more closely with an observational product. The method is demonstrated on an ensemble of eight CMIP6 models to project net ecosystem exchange of CO₂ and net biome production, with weighting schemes calibrated against observational datasets.
I found the study well written, with a clear and intuitive presentation of the information-theoretic background. These concepts are often missing from discussions of climate-model post-processing, and it is refreshing to see them used here. I also enjoyed learning about the connection between cross-entropy and AIC. I have a small quibble with calling the KL divergence a distance, but I will not press the point because the term likely helps build intuition.
Although I am not deeply familiar with all work on combining ESM outputs, my understanding is that another common strategy is to reward models that (i) simulate today’s climate well and (ii) remain close to the ensemble consensus for future change. The manuscript cites earlier work (e.g. Tebaldi & Knutti) at several points, but a fuller discussion of how existing methods compare would be valuable. Readers will want guidance on when this weighting scheme should be preferred and why.
L95-100 : could the authors expand on why the approximation dismissing K is appropriate? I know this is discussed later in the manuscript as a limitation of the proposed method, but I think it would be useful to also have an argument at this point on why that's a reasonable approximation to start with.
L105-110 : "but given the absence of any other method for obtaining a log-likelihood function of a parameterized ESM with respect to data" I would recommend nuancing this statement. There exists methods out there that allow to model loglikelihood functions (e.g. variational approaches). This doesn't diminish the proposed approach, since it might be the simplest first step to take, and in the Occam's razor philosophy, it makes sense being explored and worthy of a publication.
Eq 13 : Am I correct in saying that the weights end up being wi = 1/σ̂i / Σ1/σ̂i ? I think it would be useful to explicitly include this in the manuscript. The current presentation aims for a greater level of generality in its formalism, which is commendable, and could apply to any choice of distance metric A. However, for the particular choice made by the authors here, the expression of wi simplifies a lot and becomes very interpretable : we simply give more weight to model that have better least square agreement with the observational product.