Thank you very much for your review. We address each of your points below.

In general, the manuscript is well written and comprehensible. The purpose of the study is met. Nevertheless, it would be beneficial for modelers and other people dealing with climate model data but not proficient in Bayesian statistics, to give a brief introduction regarding the most important Bayesian concepts used inside the manuscript (prior, posterior, MCMC, Dirichlet distributions, ...).

Thank you. We will clarify key concepts in the Introduction and otherwise add a brief section in the appendix to give an overview of the Bayesian concepts we use in the paper.



I recommend to publish the article on condition of adding the aforementioned explications as well as implementation of the following minor revisions:

Line 67, 88, Box 1, 95, 100, 101, 110, 117, 184, ... [general]: I would recommend to refrain from the term "prediction" when talking about climate models

Yes, we will update this and use ‘model output’ or ‘simulated data’ instead of ‘model predictions’. 



Box 1: it would be good, to include something like i=[1,N] or i=1,..,N in Box 1; in Equation 4 N is used but not defined, the first explanation of N is in line 136 (although it is quite intuitive what N should mean)

We agree that, even though it is quite intuitive, it’s better to explicitly define it in Box 1, which we will do in the revised manuscript.



equation 5: superscript v missing for y in P(y|...)

Right, we will add it.



Lines 114–120: please add reference(s) for this paragraph

We will add a reference to a classical textbook on Bayesian data analysis here.

L140: please add more information and reference regarding Dirichlet distribution (if not done in the general explanations regarding Bayesian statistics)

As suggested, we will add a new section in the appendix with a short introduction to the statistical concepts used in the paper. In this section we will also add information about the Dirichlet distribution and a reference to the classical textbook on Bayesian Data analysis from Andrew Gelman et al.



Figure 1: a) although clear from the text, please add information that model 1 and 2 are hidden below model 1 in the two lower rows

We agree and will add this information to the caption.



Line 194: please inform the reader that i.i.d. = independent and identically distributed

We will do so.



Lines 217/218: please include reference for "common pri distribution ... Invserse-gamma"

We will add a reference to the Gelman textbook.



Line 266: Reference for ERA5 missing (question mark in brackets)

Thank you, this will be fixed.



Line 278: This (always same weight for M1 irrespective of number of M2 copies) only holds true for ensemble performance weighting (not for individual performance weighting) [as also can be seen in Figure 6]

That’s right, we will rewrite this sentence to make that clear.



Figure 7: is each point in Fig. 7a a different location and Fig. 7b the spatial variance? From equation 8 and the discussion I deduce that this is not the case. So I don't understand the single points. In Figure 6 there is just one weight for each model and now we have plenty of them? Or is this the probability distribution of the weights again?

That’s right. Here we show the sampled individual weights, i.e. the entries of the sampled weight vectors, while in Fig.6 we only show their mean values. We will rewrite the caption of Fig. 7 to make this clearer.



Line 332: please write out in full SSP5-8.5

We will do so.



Line 333: please use (en) dash instead of hyphen for time span

We will do so.



Figure 8: Please add unit to x-axis. Is this K per W/m² or K per doubling of CO2?

We will do so.



Figure 9: "Projected" instead of "Predicted" please, please write out in full SSP5-8.5

We will do so.



Line 351: I cannot find any "thin dashed green lines in Fig. 9"

We will fix this and will refer to the shaded regions, which we actually meant. We had previously used thin dashed green lines but overlooked this in the text.



Line 368: "ECS as performance metric" this is no metric but a variable considered for weighting (which is then applied to temperature data) -> a basis for assessing model performance

Right, we will rephrase this formulation.

Lines 393–396: This is a good point. The other way round, also holds true: models with very similar model structures can lead to different projections, e.g. if they are based on the same ocean model but the atmosphere is different, …

That’s right. Two models with similar structure that yield different outputs (as in your example), are independent enough to generate such different outputs and are thus upweighted. However, two models that are structurally more different, but generate more similar outputs, are downweighted even though this should give us more confidence in the output. The worst case, however, in terms of the resulting uncertainties, is to not downweight models with similar outputs and similar structures as this would make the uncertainty range overly narrow. 

Please check: sometimes, blank spaces between commas ("e.g.,see") or dots ("vs.0.5820") and the following words/numbers are missing

We will do so.

Thank you very much for your review. We will address the points you raised one by one below.

I consider this paper a successful attempt to put clarity in the field of ensemble weighting.

What is probably reducing the value of this manuscript is the fact that what starts as a nice and well-presented and exhaustive theoretical framework, appears tailor made for the mere application to climate modelling.

In my view that remains a mere application, an important one but yet an application, whereas all the treatment presented applies to any kind of ensemble treatment for any kind of data.

In this respect I would change the title to reflect this aspect thus distinguishing between the general character of the topic and the application to climate models.

Thank you for raising this point. We agree that the theoretical framework is general and could be applied to other kinds of data beyond climate data. However, we deliberately frame and motivate the paper around climate model ensembles, since this is the application context that shapes our choices throughout; in particular the model interdependencies, as well as the choice of ECS as an example. We believe that not mentioning climate models in the title might make interested readers expect a paper that goes beyond our contribution of a focused application to climate model data, that we believe, and as you also mention, is important in itself. To address your broader point, we will add text to the abstract and the conclusion and also add a short paragraph in the discussion, noting that the framework is not specific to climate data and may be relevant for ensemble weighting problems more generally.

In ACP, other examples exist of publications that intended to put clarity on the topic of ensemble modelling regardless of the fields of application:

ACP - Est modus in rebus: analytical properties of multi-model ensembles (https://acp.copernicus.org/articles/9/9471/2009/)

ACP - Pauci ex tanto numero: reduce redundancy in multi-model ensembles (https://acp.copernicus.org/articles/13/8315/2013/)

ACP - Seeking for the rational basis of the Median Model: the optimal combination of multi-model ensemble results (https://acp.copernicus.org/articles/7/6085/2007/)

Many aspects of this paper are common with these publications although their fields of applications are different.

Thank you very much for pointing us at this interesting research that we had not been aware of. We will cite these papers in the discussion paragraph on the broader applicability of the framework that we will add.

Distinguishing the theoretical treatment from the application case would increase the value and breath of your research. Making the case that your approach as a vaster field of applications will increase that value and breath even further.

As stated in our response further up, we will add a paragraph in the discussion about the broader applicability of the framework and further reference the ACP papers you highlighted as examples. 

More technical aspects were exhaustively covered by the fellow reviewer, and I have nothing more to add as the paper is very well written. Attending to his comments will further improve the manuscript, its readability and accessibility by non-experts in Bayesian statistics.

Thank you very much. Please see our comments to Reviewer 1.