Dear authors,

Thank you for your thoughtful consideration of the reviewers' comments and the additional analysis performed in response. I do believe that your responses are very promising, however due to the doubts expressed by the reviewers about advancement of hydrological science by this paper, I am likely to send the revised paper out for a second round of reviews. If possible, please include a brief summary of the current use of the B-N analysis and where you see it be used in the future, considering your analysis and the discussion raised by Reviewer 2. Thank you!

Best regards,
Stan

Dear authors,

The reviewers have not found any more technical issues with your manuscript, but in a seperate exchange of emails I found out that Reviewer 2 is still not convinced of the usefulness of the work presented here. One of the reviewer's points is:

"But since its publication in 1977 people have been pointing to several shortcomings, the most fundamental ones raised by Harman in a series of papers from his Msc. There is also a recent paper by Rupp and Bogaart that points out other shortcomings. In summary, the method is not reliable in the presence of heterogeneity and/or topography. Therefore the observed slopes in the dQ/dt vs Q plots are arbitrary and not necessarily the result of Boussinesq dynamics."

While a general discussion of the applicability and limitations of the BN method is outside the scope of this technical note, I believe that the reader should be pointed to the importance of spatial heterogeneity in addition to the limitations already mentioned (Harman et al. WRR 45, W09404). Perhaps the authors would also like to highlight potential use of their improved formula for purposes other than deduction of catchment-scale effective parameters from flow recession, such as simulations of drainage and water table dynamics from hypothetical hillslopes and improved understanding of hillslope processes.

In addition, I would like the authors to address a couple of points I have myself:

L. 75: "applied with (i) and (iii)" is not very clear. The meaning of (i) and (iii) is mentioned right at the beginning of the introduction but no equations are given. Could you actually provide equations that represent these solutions and write "BN77 method based on Solutions (i, Eq. x) and (iii, Eq. y) of the Boussinesq equation"

L. 180: "investigate" instead of "invetigate"

L. 184-187: I had trouble to follow here. What do you mean by "deviates considerably from the true value when H0 is 40% or greater of H" and by "while this deviation occurs when H0..."? What does "deviates considerably" mean and what is "this deviation"? I think what you mean is that the BN77 estimates of k_0 and n_e under-estimate the numerical ("true") values more and more as phi_0 increases, starting with phi_0 > 0.3 and phi_0>0 for k_0 and n_e respectively. Did I understand correctly? For better clarity, you should also explain k_0, n_e, and phi_0 in the figure captions.

Dear authors,
Thank you very much for embracing the various comments and further improving the paper. I hope that the paper will facilitate analysis of hillslope processes and contribute to the generation of new scientific insights.