Please see the attached PDF file.

The study makes use of hail pad and drone imagery to estimate hail size distributions. Then, using double moment normalisation a functional fit is found and the errors are assessed. Discrepancies (biases) are seen at the large and small end of the fits relative to the test data. Application of the statistical functions for use with radar retrieval is suggested.

I think that the general approach of double moment normalisation, the segregation of the data into training and test datasets and the quantification of bias and root mean square error is all good. I am particularly excited by the use of drone observations. This drone imagery approach could vastly improve the statistics of hail observations from the ground and the comparison to traditional hail pads supports this. Perhaps more could be made of this in the conclusions?

The data is all fine - i think that all that is needed is to revisit the fitting again, perhaps taking into account the missing or truncated data. Maybe consider different models and it would be good to look at emphasizing results for moment choices that would allow this work to be used more easily by modelers (e.g. moments, 0,3) and people doing retrievals (e.g. radar:6). I think this would be major revision.

Main points:

1. The choice of moments. Moments 2 and 4 are difficult to relate to physical quantities. Perhaps number (0), mass (~3), radar reflectivity (~6) would be more useful for others to use for radar retrievals (as mentioned in the conclusion) or  in models that predict mass and potentially number. The fits are given for those pairs of moments but they look to have not converged.

2. The fit values for  c, mu. The fits are done in log space using the normalized bin value and bin centers so that data with widely varying sample times can be used (i think). What is done for the bins where N(x)dx =0? Are these bins ignored for the fitting? Or is some large negative value in log space assumed? Some of the fit values for the exponent on x are large (c=0.37, mu=46 for moments 2,4, giving an exponent of 16). Are these large exponents a function of trying to fit the unobserved values at the small end that are assigned a small value? Should a simpler model for the size distribution be used instead that will converge for all moment choices?

3. The c and mu values that have not converged (i.e. where the fit values are at one end (e.g. 500) or the other of the allowed range) should probably not be considered useful and there will be no need to report on their bias and rmse. I'm slightly worried that some non-converged fits (e.g. 0,1, 0,5) have less bias and rmse than those that have (e.g. 2,4). The very large mu values are unconstrained because of the lack of observations. Again maybe a different model would be better?