Our response to Anonymous Referee #1 has been uploaded as a pdf file.

Dear Anonymous Referee #2,

We are grateful for your insightful review that will help us to improve the manuscript. Your verbatim comments are below (in bold), each followed by our response.

General comments: The authors aimed to measure the physical similarity between several phenomenological dynamical paleoclimate models and the real world. They proposed that a model should have a link with known physical assumptions, rather than a statistical description of proxy data. Overall, the manuscript is interesting and may have important implications for the future development/evaluation of phenomenological models.

Response: We are grateful for your vision that “the manuscript is interesting and may have important implications for the future development/evaluation of phenomenological models.”

Specific comments: As I am not an expert on this issue, I fully agree with the comments from Reviewer#1. However, I still have some comments that may be considered to improve the quality of the manuscript.

1. Figure 2 shows a specific case of the models used here. I am wondering how you choose the values of each parameter (e.g., why obliquity-period doubling is used?). Please clarify.

Response: We do not prescribe the obliquity-period doubling. Instead we calculate VCV18 and G23 models responses (with the reference values of parameters published in VCV18 and G23) to the external sinusoidal forcing of the obliquity period and find that in both cases the period of response is twice the forcing period. Most importantly, it happens with similarity parameters, both the ratio of astronomical forcing amplitude to the terrestrial growth rate and the positive-to-negative feedback ratio, having reasonably close values in both models. Therefore we conclude that there is physical similarity between VCV18 and G23 models in terms of the above similarity parameters.

Action: We will further clarify this in the text.

1. The physical similarity is measured in the ε/â -V space. I am just wondering what are the limitations of the proposed method? For example, G23 model clearly differs from the VDP model in the ε/â -V space. Are there possibilities that G23 model shares similarities with VDP model in some aspects?

Response: Fig. 3 is just an attempt to present most important results visually in one diagram. Since it is 2-dimensional, it may demonstrate similarity (or its absence) in terms of only 2 similarity parameters. It was sufficient for us, since we found similarity between phenomenological and physical models in terms of two similarity parameters, the ratio of astronomical forcing amplitude to the terrestrial growth rate and the positive-to-negative feedback ratio. This space wouldn’t be sufficient if more similarity parameters needed to be visually presented. For example, equation (21) shows that G23 model depends on the similarity parameter that is the ratio of the orbital period  T to the internal timescale 1/a. This similarity parameter is absent in VCV18 model. This absence of similarity is not apparent from Fig. 3, but it is discussed in lines 240-254.

Action: We will further clarify this in the text.

1. The positive-vs-negative feedback loops are important to understand the periodicity of glacial-interglacial cycles. Could you add additional discussions on the differences in the loops between each model?

Response: We agree with your observation. Indeed, “The positive-vs-negative feedback loops are important to understand the periodicity of glacial-interglacial cycles”. While, these loops is the central part of VCV18-1 and LP22 models comparison (lines 407-415), in other cases such discussions, we admit, may be too brief.

Action: We will add additional discussions of the feedback-loops diagrams.

Respectfully,

Mikhail Verbitsky and Michel Crucifix