Dear Prof Mingguo Zheng.

I had a close look at your manuscript, the two reviews and your corresponding responses. In line with reviewer 2 I see that the proposed approach to assess and discriminate model sensitivities to climate and catchment characteristics is more general than what you call the total differential. The latter corresponds to the derivative of a multivariate function if and only if the variables are orthogonal. This must not be the case for hydrological state variables as you correctly stated.
Acceptance of a new method for publication of requires however, a) a convincing demonstration of its relevance and b) a clear and broadly understandable explanation of the underlying math, particularly in comparison to other existing methods. The present manuscript should be considerably improved respect to both issues. This requires major revisions, which should address the reviewers’ recommendations.

Moreover I recommend you should consider the following issues during the revision process:
- As I am not sure, whether all partial derivatives of R are correct, I recommend that you provide a supplement which details the important steps to facilitate the evaluation/understanding of the math.

- How strong is the actual dependence of precipitation and potential evaporation? This is of key importance to evaluate, whether the new methods needs to be used or not.

- With all the respect I have for the Budyko framework, for me n is nothing else like a fitting factor. Of course we expect that offsets from the Budyko curves are explainable with catchment characteristics, but this should much be more precise- is it landuse, total soil storage volume, field capacity and retention properties or what are we talking about. The latter can be investigated in a straightforward manner with a conceptual hydrological model. The current way how this issue is addressed is way too unspecific.

- I agree that changes have different impacts on non-linear dynamics when they occur during different systems state and thus on different points in time. However, I doubt that the Budyko framework is suitable for working this out, because it refers to the steady state water balance. A dynamic system catchment under change will develop from old to a new steady state behavior. Why should this new steady state functioning depend on the time where the change occurred?

- Last but not least you should make sure that you manuscript is in line with the common guidelines for equations and variables published on the HESS webpage.

Best regards,

Erwin Zehe

Dear Prof. Zheng,

I am sorry my delayed assessment of your manuscript. From the manuscript history I noted that you uploaded your revisions and response 4 days after my decision that this work needs major revisions. A close look at the current manuscript reveals that you implemented minor changes, which neither address the reviewers nor my comments in a satisfactory manner.
I thus return the manuscript to you again and advise you to carefully address the reviewers and my recommendations from the previous round.
Best regards,

Erwin Zehe
Chief Executive Editor

Dear Prof. Zheng,

I am pleased to inform you that the reviewer recommended to publish your study after minor revisions. I kindly ask to to check the reviewer comments and particularly to consider streamlining the paper.

Best regards,

Erwin Zehe

Dear Prof. Zheng,

I am delighted to accept this manuscript for final publication in HESS.

Best regards,

Erwin Zehe