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RC1: 'Review of Wolfensberger et al. "Multifractal evaluation of simulated precipitation intensities from the COSMO NWP model"', Anonymous Referee #1, 14 Mar 2017
RC2: 'Review', Anonymous Referee #2, 11 Apr 2017
AC1: 'Answer to reviewers', Daniel Wolfensberger, 30 Jul 2017

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Daniel Wolfensberger on behalf of the Authors (14 Aug 2017) Author's response Manuscript

ED: Referee Nomination & Report Request started (15 Aug 2017) by Graham Feingold

RR by Anonymous Referee #2 (11 Sep 2017)

Suggestions for revision or reasons for rejection

General comments

I appreciate the effort put forth by the authors in revising the manuscript. I believe it has vastly improved. The addition of Tables 1 and 3 made the paper much easier to understand. I do have a few very minor additional comments.

Minor comments
1) There are still issues with grammar, especially comma usage, that make the text hard to follow in places. For example, on Pg. 13, “…two-dimensional geophysical process and in time, we consider…” is confusing without a comma before “and”. Moreover, when introducing a sentence with “For x”, a comma is needed after “x”. Another example is on Pg. 14, Line 4, where a comma is needed before “follows”.
2) Throughout the paper, there are many erroneous subsection numbers that should be removed.
3) Throughout the paper, there are many erroneous line breaks within sentences that need to be removed.
4) Periods are missing at the end of several figure captions.
5) The added figures in Appendix A and Appendix B are nice; however, I would suggest just included them in the main text unless you add text surrounding them in the corresponding appendix.
6) Please review the reference – there are formatting inconsistencies.
7) Pg. 1, Line 1: Reword – “allows to characterize” is awkward.
8) Pg. 2 Line 34: Change “simulations of” to “simulated”.
9) Table 1: Use “Wind speed”; add a space between units to avoid confusion.
10) Pg. 5, Line 2: Should be “These data are”.
11) Pg. 5, Line 3: Need to add “the” before “beginning”.
12) Pg. 6, Line 17: QPE already defined.
13) Fig. 2: Enlarge to make it easier to read.
14) Pg. 11, Line 11: Move to end of prior paragraph.
15) Pg. 13, Line 24: Change to “second-order”.
16) Fig. 3: The caption is incorrect – there is no left and right panel.
17) Pg. 15, Line 15: Consider replacing “spectacular” with a more descriptive term.
18) Pg. 16, Line 1: Define ANOVA and use capital letters.
19) Pg. 16, Line 2: Change to “tests”.
20) Pg. 18, Line 25: Change “that” to “which”.
21) Pg. 18, Lines 28-30: The wording is awkward; reword.
22) Pg. 20, Line 20: Change to “large-scale”.
23) Pg. 20, Line 25: Use the variables from the table instead of just H.
24) Pg. 20, Line 32: Use “one-moment scheme”.
25) Pg. 20, Line 33: You are comparing QPE between the radar and model, not the radar QPE with the scheme itself; reword.
26) Pg. 24: Line 2: Use “south”.
27) Section 5.4: The section is a bit confusing because you start off saying that you will focus on the third event; however, there are two paragraphs on the first and second. Either omit the discussion of the first and second events or reword/reorganize the beginning of the section.
28) Pg. 24, Line 29: This should not be a paragraph on its own.
29) Pg. 25, Lines 1-2: The sentence is awkward; reword.
30) Figure B3: Place figure title below color bar so that it is clear to the reader what the colors represent. For potential vorticity, use units of 10-5 K m2 kg-1 s-1 to remove the large number of zeroes in the colorbar.

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RR by Anonymous Referee #1 (19 Sep 2017)

Suggestions for revision or reasons for rejection

General comments

Wolfensberger et al. characterize the spatio-temporal variability of precipitation intensity using universal multifractals. Their analysis consists of two parts. In a first part, they relate multifractal parameters and climatology in a correlation analysis that is based on geographical and meteorological descriptors. In a second part, Wolfensberger et al. apply multifractal parameters to evaluate the NWP model COSMO with 1- and 2-moment cloud microphysics against a radar composite. While the second part has been addressed in the previous review of this paper, the first part is a new analysis that replaces the previous first part. The new approach is very promising, especially in terms of providing physical interpretations, but could in my opinion be improved in terms of the chosen parameters (see specific comments). Also, the connection between the two parts of the paper, i.e. how the insights from the climatological analysis can help the model evaluation, could be motivated more clearly.

Specific comments

- In my opinion, the climatological analysis could be greatly simplified and streamlined by directly using the Köppen classification as descriptor instead of the meteorological and geographical parameters. As shown in Figs. 3 and B3, the meteorological and geographical parameters used in the climatological analysis are not independent: Potential vorticity is highly correlated to altitude and temperature to latitude. It would therefore be enough to use either the meteorological or the geographical set of parameters - or, as suggested, the Köppen classification, which both parameters sets are also related to.

- The above suggestions would exclude the characteristics of the precipitation distribution (total amount, variance, wet fraction) as descriptors. Especially the wet fraction is currently used to explain the relationship between climatological classification as determined by latitude and altitude to the multifractal parameters. I am not fully convinced by the corresponding argument because the precipitation characteristics seem to be already ``half-way'' to the multifractal parameters. I would instead try to explain the multifractal parameters based on the typical precipitation types that correspond to the Köppen classification (e.g. frontal). Also the case studies from the second part might be useful here.

- The TM coefficient is not included on p. 16, l 3 because it is not a real parameter. Why is it shown and discussed in Figs. 3, 5 and 6?
The paper does not seem consistent in terms of the multifractal parameters investigated: The fractal dimension D_l is only used in the first part (without introduction) and Fig. 10 does not discuss $\gamma_s$. Is there a specific motivation for these choices?

- Why is the new analysis in part 1 performed on the direct fields - despite H > 0.5 for the spatial analysis - but on the fluctuation fields in the second part?

- Why are both, Fig. 7 and Fig. 8, needed? Are they not redundant, both providing the same scaling insights?

- p. 21, l 2: In general, the error of the parameters is not necessarily the same as the significance of the model. In how far can the discrepancies between the spatial and temporal analysis be used to estimate the systematic error of the parameters?

Technical corrections

- p13, l 31 + p 15, l 12, 13: The qualifier ``much'' does not seem appropriate and could be left out.

- Fig. 3: This is a very busy figure with lots of information. I think a different color scale, which only shows blue and red for high correlation coefficients and lighter/whiter colors in between would make the figure easier to grasp. Also, it could be helpful not to show (or hatch or replace by gray squares) correlations that disagree in sign between the spatial and temporal analysis, thus only showing robust correlations. Also, it would be helpful to visually separate the blocks with descriptors and multifractal parameters.

- Fig. 7: It would be helpful to add fit lines for the COSMO data as well - it is hard to follow the qualitative discussion about whether the 1- or 2-moment schemes scales more like the radar by having to guess where the lines might lie.

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ED: Reconsider after minor revisions (Editor review) (03 Oct 2017) by Graham Feingold

AR by Daniel Wolfensberger on behalf of the Authors (20 Oct 2017) Author's response Manuscript

ED: Publish subject to technical corrections (24 Oct 2017) by Graham Feingold

AR by Daniel Wolfensberger on behalf of the Authors (25 Oct 2017) Manuscript