This manuscript introduces a method using particle swarm optimization (PSO) to estimate the three parameters of a gamma shaped raindrop size distribution (DSD) along a radial beam using two side-by-side scanning radars operating at S- and C-band. There are several concerns in the manuscript that need to be addressed before this manuscript can be considered for publication.

1.  While the abstract states that the retrieval method “is able to accurately retrieve the gamma distribution parameters without the constraints required in previous methods” (line 9), the manuscript does not present any retrieved parameters, nor does it estimate the accuracy of any retrieved parameters. Thus, it is not possible to evaluate the accuracy of the proposed method because the necessary results are not presented in this manuscript. 

2.  As presented in this manuscript, the PSO method is essentially a random walk through the three DSD parameter space, and not an “optimization” method. A random walk (line 218) through the parameter space is a valid parameter estimation procedure if the neighborhood of solutions around the global solution are used to estimate an uncertainty of the retrieved parameters. 

3.  It appears that the study is based on four radial samples made over two different disdrometers. The manuscript text states that nine (line 245) or ten (line 294) days of data were “used in the performance validation” (line 245), but only four reconstructed raindrop distributions are shown in Figure 9. Since no more retrieved parameters are shown in the manuscript, it must be assumed that those four radials were the only radials that were processed. 

4.  It is major limitation of this work that retrieved DSD parameters are not presented in the manuscript. The four reconstructed raindrop distributions shown in Figure 9 do not show the retrieved slope parameter (lambda) nor the shape parameter (mu). Since three of the four constructed distributions (Fig. 8 a, b, and d) do not have the number concentration approaching zero at zero diameter, this suggests that the retrieved mu value is less than zero. It is unusual for the shape parameter to be negative in scanning radar retrievals due to the large scanning radar sample volume. Which raises concern about the validity of the retrievals. The manuscript must show retrieved parameter statistics to evaluate the performance of the retrieval method.

5.  How much improvement in rainfall estimation does the proposed method provide compared to using one of the mu-lambda relationships proposed by Zhang et al. (2001), Brandes et al. (2002), or Cao et al. (2010)? If the new method does not produce comparable or better rainfall estimates than the mu-lambda constraints, then will this proposed method be an improvement to QPE? The mu-lambda constraints should be the baseline that the new method should aim to beat.

In summary, without the manuscript showing results of the retrieved DSD parameters, it is not possible to evaluate the proposed retrieval method. The proposed method may produce results that are superior to results from imposing a mu-lambda constraint. But, as written, the manuscript does not show the evidence needed to verify the statements made in the manuscript. 

See attachment.

The discussion paper by Durbin et al. looks quite attractive. There are several countries in the world with weather networks composed of C- and S- band with possible overlapping. A dual-frequency approach applied to C- and S- band radar collocated measurements can be of interest and the set-up of practically co-located radars used for the study is quite uncommon.

However, the manuscript lacks of and adequate description of the development of the technique and a thorough validation.

There are many examples in the literature of techniques aiming at estimating DSD with assumptions on gamma DSD and its parameters. The one proposed is based on Kdp at the two frequencies and the equivalent reflectivity factor at S-band, supposed to be not affected by attenuation due to precipitation.

Usually, algorithms are first investigated in ideal conditions (i.e. through T-matrix simulated measurements) and then the performance is investigated in the presence of different error sources (i.e. calibration, attenuation, spatial gradient, difference in volume sampling, etc.) and finally validated with real measurement and comparison with real data.

In the first steps of the development missing is a thorough analysis of the impact of the error sources on the retrieval technique. Only a very limited comparison with a Parsivel is shown that could be influenced by many sources of errors, including the limitation of the Parsivel itself (authors honestly use “qualitatively” word). However, even for this case, the error associated with the retrieval is not provided, and the range of variability of retrieved data is not provided as well.

Moreover, the technique is not checked against techniques based on single frequency dual-polarization radar that can be found in the literature so that a reader can understand the advantage of having two radars insted of a cheaper single radar.

The text should be revised, since is not very clear on several parts. 

 

Some specific issues are listed below:

a)    A title like “Drop Size Distribution Retrieval using joint dual-polarization radar observation at C- and S- band” could be more suited to the content of the study.

b)    About DSD parametric forms. The Marshall-Palmer is a particular case of a 2-parameter exponential DSD. The exponential was used before the Gamma become successful. It should be noticed that gamma is a model that has its own limitations in describing some natural DSD. 

c)    In the introduction, authors are right on the need of assumptions on gamma parameters, although the early technique for Gamma DSD retrieval by Gorgucci et al. 2001 (https://doi.org/10.1175/1520-0469(2002)059%3C2373:EORSDP%3E2.0.CO;2) assumes independent gamma parameters. Also it should be pointed out that the dual frequency techniques described apply to applied to Ku-Ka frequencies for quasi vertical observation while dual polarization radar retrieval operates at quasi horizontal elevation angles based on oblateness of drops which is not seen at vertical incidence.

d)    At line 132, authors say that the dataset include light to moderate precipitation. Actually there should be an influence of rain intensity on performance of the retrieval. In fact, in light rain reflectivites at S- and C-band are not so different and Kdp is similar as well apart from the frequency scaling. In this case the contribution of the C-band freqeuncy should be negligible.

e)    At line 146, authors say that “This range effect is a predictable issue in radar data processing” What is the meaning of this statement ? 

f)    Fig 4. The bias in reflectivity profile is a calibration error or is due to difference in elevation, time and so on ?

g)    Fig 8. This is just visual inspection hampered by the linear scale for N. A meaningful comparison should be done in terms of DSD parameters for a meaningful dataset.