Dear André Düsterhus,

I agree with the positive reports of the three reviewers. In light of the reviewer's comments and the revised version of the manuscript, I would like to suggest a few additional minor revisions.

- page 2, line 35: I suggest to change "climate science" to "atmospheric science", "weather prediction" or similar as all references are from the NWP literature.
- page 2, line 50: Is the model resolutions of 40 km over the ocean correct? I would have expected a lower resolution compared to the T63 model.
- page 3, line 64-65: The revised version of this sentence is more clear (see comments by Anonymous Referee #3), however, I suggest to replace "shown" by "indicated" or similar to clarify further.
- Section 3.3: Personally, I was very happy to see proper divergence measures used for evaluation. However, as evident from all review reports, this concept seems to be not very well known in the community. Therefore, I suggest to make the difference between IQD and CRPS more clear, for example by extending the discussion in lines 111-112 on page 4 by stating more explicitly that the IQD extends the CRPS towards observations that are not deterministic, but "distributions".
- page 5, line 119-121: The sentence starting with "EMD is a metric..." will be very hard to understand for readers not familiar with Thorarinsdottir et al. (2013). Perhaps it can be rephrased in a more generic way without referring to the concepts of "k-proper" or "asymptotically proper"? Further, I am not sure that I understand the reasoning behind the statement in the subsequent sentence claiming that EMD specifically prefers underdispersed model simulations. Why does this follow from being only asymptotically proper, but not a k-proper divergence measure? In my view, this only implies that EMD may prefer incorrect models over the correct one, but may those incorrect models not as well be overdispersed?
- page 9, line 237-238: For evaluating point forecasts the RMSE can be used without an (implicit or explicit) assumption of Gaussianity, see, for example Gneiting (2011, https://doi.org/10.1198/jasa.2011.r10138). The statement in the sentence starting with "An important advantage ..." thus seems a bit misleading and I suggest to rephrase accordingly.
- page 17: The caption of Figure 5 mentions a "dark green" color which is not present. Should this read "red" instead?

Best regards,
Sebastian Lerch

Thank you for the clairifications and the swift response.

I only have two very minor remaining comments regarding the newly added sentence starting on page 5, line 121 ("While EMD is a metric measuring..."): "pdf" should probably read "pdfs" instead. Further, I would like to suggest to replace the term "proper score" by "proper metric", "proper divergence measure" or similar to further clarify the difference in application of proper scores (such as the CRPS) and proper divergence measures (such as IQD).