The two formal reviews that have been submitted and the comment by Jessica Loriaux are generally positive about the relevance, novelty, and the quality of the text of the manuscript. However, some issues are raised that need to be addressed. Therefore, major revisions are necessary before the manuscript is ready for publication in HESS.

Particularly important points that have been raised are:
1) The use of hourly rainfall data is likely to bias results, especially the extreme intensities. Referee 1 suggests to redo the analyses using 10-minute data, and I'm happy to see that the authors are willing to do this.

2) Inclusion of figures where the results of the fitting procedure are shown. Again, the authors have indicated that they will include such figures in the revised manuscript.

3) The analyses on other variables than temperature should either be clarified or removed. The authors have indicated that they will refocus this part of the manuscript.

4) Application of the presented methodology to the data set used by Lenderink and van Meijgaard (2009) in order to investigate what causes the apparent difference in scaling. The authors have not replied to this comment.

5) Use of other methods for assessing the scaling coefficients (such as quantile regression). The authors have indicated that they will investigate the effect of using quantile regression.

6) The use of the presence of lightning data to discriminate different storm types may lead to overestimates in scaling coefficients at low precipitation intensities and underestimates at high intensities. These potential biases should be discussed in the revised manuscript.

When you revise the manuscript along these lines, please provide a point-by-point response on how you dealt with the points that were raised by the reviewers.

I am looking forward to the revised manuscript.

I have received two reviews for the revised version of the manuscript. Both reviewers are very pleased with the substantial additional work that has gone into improving the paper. I am also very pleased with the fact that the reviews were taken very seriously, and that the authors have taken maximum advantage of the peer review process by putting so much effort into improving the paper.

Both reviewers have some remaining comments that need to be addressed before the paper is ready for publication. Addressing these comments should not take very long. When you revise the manuscript, please provide a point-by-point response on how you dealt with the points that were raised by the reviewers.

I am looking forward to the revised manuscript.

The comments made by the two reviewers on the revised manuscript have been adequately dealt with. However, the supplementary materials file seems to be corrupt, and the figures in it are not visible. The paper is ready for publication once this file has been fixed.