Dear authors,

before I accept you paper finally, I would like you to clarify the first part of your reply to Reviewer #2. As I see it, the question whether the fields to be evaluated are orthogonal or not is irrelevant, both for your old method and for the new one. Non-orthogonality would be fatal if your "vectors" would be used as components of a vector space with linear transformations involving matrix operations. This is not the case, hence orthogonality is not a requirement for your method. In this sense, it seems that the first paragraph of your reply to reviewer #2 is incorrect. You write "The definitions of the statistical quantities ... do request an orthogonal coordinate". I think, it does not!

To my opinion, the use of the word "vector" for something that is merely a "neutral" collection of quantities (a M-tupel), contributes to the puzzling. A "vector" in the physical and mathematical sense is much richer a structure than just a M-tupel.

Please comment to this and include a short paragraph in your manuscript so that the issue is clear to readers without referring to the discussions. The needed paragraph can appear either in the beginning of section 2 or 3.

Dear authors,

thanks for the new revision. With the new clarifications I accept your paper for publication in GMD.

Congratulations!