The paper „Characterizing the space-time structure of rainfall in the Sahel with a view to estimating IDAF curves“ by Panthou et al. was reviewed by two referees. The authors responded to the reviews and provided a first draft of a revised manuscript. I agree with the referees that despite the fact that methodologically this paper does not produce novelty, new knowledge gained from applications to new datasets in poorly studied and monitored areas, such as western Africa, are indeed valuable.

Based on the HESS Discussion and the assessment of the reviewers I consider the manuscript to be fit for publication in HESS. I do however have some minor technical/editorial requests to improve the final manuscript before accepting it in HESS. I ask that the authors consider these and revise their final manuscript accordingly, providing also a short response to me on how they dealt with each of the questions below.

1) Firstly, I am confused with your response to the referees regarding the definition of the areal reduction factor (ARF) as the ratio between point rainfall and areal rainfall (beginning of section 2.3). Indeed as Referee 1 pointed out the most common definition is that it is the ratio of areal/point rainfall, bounding ARF between 0 and 1. You say the opposite in section 2.3, yet your equations (9) and (10) are indeed showing that ARF is the ratio of areal/point rainfall as it should be. Please correct the text at the beginning of the paragraph or explain where the problem is.

2) In section 3.1 you describe the interpolation method by which you generate gridded precipitation 1x1 km from the point measurements by Vischel et al. (2011). I think this deserves a few more lines to explain the method, e.g. what does dynamic kriging mean, how exactly are the gridded data generated, are station vales replicated exactly, is elevation used, what is the shape of the semi-variogram, etc. This is important in conjunction with the application of your space-average in equation (18). In your revision you explain now that equation (18) is used on the gridded data, this was unclear in the first manuscript.

3) The message in the paper is that the at-a-station estimation of IDAF parameters (Fig 5) is not indicating a systematic geographical variability, so the region is considered homogeneous and the data are pooled for the final estimation of the global IDAF model. The spatial variability is indeed captured by the new Fig 5, but I would consider summarizing these plots also for instance in box plots of the estimates to better show the real variability between stations. An option would be an 8th panel where for each parameter on the x-axis a box plot of the parameter values would be shown. Or an additional line to Table 1, where the (between-station) mean and standard deviation would be listed together with the new estimates for the global IDAF model. This is only a suggestion, the authors can decide if this information has added value to their work.

4) In section 2.2 the authors begin by stating that the simple scaling framework is the right way to go arguing that multi-scaling is not tractable. I think I understand what you mean, but the fact is that the concept of the areal reduction factor has been analytically treated for the multiscaling (multifractal) setup of which simple scaling is one particular case (e.g. Veneziano and Langousis, 2005). It would be advisable to read and cite this work (and perhaps others) to give recognition to where it is due on methodology.

5) In section 2.4 equations (15) and (16) should the term representing lambda not be the ratio D/Dref?

6) I advise to call the last section “Discussion and Conclusions”.

7) Both reviewers wrote to me that the figures need to be improved. The main deficiency is that all figures need to have captions which are fully explaining the figure. In other words, just by reading the caption the message of the figure has to be clear. Please critically revise all your figure captions and consider if they submit to this requirement. Some more detailed comments are:
- Fig 2: In my version the label q=3 is missing
- Fig 3: In panel b the labels for 5 min and 1 hr resolutions must be mixed. The caption is also not sufficiently explanatory.
- Fig 4: Why are there two lines (linear equations) for the simple scaling fit in a)? Is not one, which is mentioned in the text sufficient? Please put units to miu_ref and sigma_ref (this applies to everywhere in the text). In the label of 2) “biais” is misspelled and I suggest putting r^2 instead of r_squared.
- Fig 6: Same question as above, why list two lines for simple scaling in the legend? Is this necessary?
- Figs 7 and 8: In the label “biais” is misspelled.
- Fig 10: In my version the symbols in the legend are missing.

8) Other text editing (in the draft of the revised manuscript with track changes):
- p2 line 20: say “and equally important”
- p3 line 17: the item (i) does not make sense, drop “having produced”?
- p4 line 25: say “for a range of durations”
- p5 line 15: say “analytical formulation”
- p7 line 9: the brackets for the eta term seem wrong
- p9 line 8: would it make sense to stress that these parameters are “computed for the arbitrary reference duration Dref at a point”?
p9 line 13: will allow “to verify” or will allow the “verification of”
p10 line 4: “all years with more than”

References
Veneziano, D., Langousis, A.: The areal reduction factor: a multifractal analysis, Water Resour. Res., 41, W07008, doi:10.1029/2004WR003765, 2005.