the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Drop Size Distribution Retrieval Using Dual Frequency Polarimetric Weather Radars
Abstract. Having knowledge of the drop size distribution (DSD) is of particular interest to researchers as it is widely applied to quantitative precipitation estimation (QPE) methods. Polarimetric radar measurements have previously been utilized to derive DSD curve characteristics frequently modeled as a gamma distribution. Likewise, approaches using dual frequency measurements have shown positive results. Both cases have relied on the need to constrain the relationship between the DSD parameters based on prior knowledge or assumptions of the collected data. This paper presents a methodology for retrieving the DSD parameters using the dual frequency and polarimetric nature of measurements from a unique data set taken at colocated Sband and Cband dual polarization radars. Using the reflectivity and differential phase measurements from each radar, an optimization routine employing particle swarm optimization (PSO) and TMatrix computation of radar parameters is able to accurately retrieve the gamma distribution parameters without the constraints required in previous methods. Retrieved results are compared to known truth data collected using a network of OTT PARSIVEL disdrometers in Taiwan in order to assess the success of this procedure.
 Preprint
(5302 KB)  Metadata XML
 BibTeX
 EndNote
Status: final response (author comments only)

CC1: 'Comment on egusphere20232220', Vagner Castro, 11 Dec 2023
Dear Author,
I found your paper on "The Z and ΦDP fields from both C and Sband radars for DSD retrieval" to be very interesting and informative. While I understand the overall methodology, I have a question about the specific details of the quality control procedures used for the reflectivity field.In your paper, you mention that the obtained reflectivity is smoothed with a 4 km smoothing window along each radial direction. I was curious to learn more about how this specific window size was chosen. Were there any specific criteria used to determine this length, or is it a standard practice for this type of analysis"
Sincerely,
Vagner Castro
Citation: https://doi.org/10.5194/egusphere20232220CC1  AC1: 'Reply on CC1', Daniel Durbin, 13 Dec 2023

RC1: 'Comment on egusphere20232220', Anonymous Referee #1, 14 Dec 2023
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 sidebyside scanning radars operating at S and Cband. 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 mulambda 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 mulambda constraints, then will this proposed method be an improvement to QPE? The mulambda 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 mulambda constraint. But, as written, the manuscript does not show the evidence needed to verify the statements made in the manuscript.
Citation: https://doi.org/10.5194/egusphere20232220RC1  AC2: 'Reply on RC1', Daniel Durbin, 02 Feb 2024

CC2: 'Comment on egusphere20232220', Davide Ori, 18 Dec 2023
Dear authors, editors, and readers,
The manuscript uses an optimization method to establish a retrieval technique of the drop size distribution (DSD) based on the assumption of a simple 3parameter gamma functional form and leveraging on the observations of 2 groundbased S and Cband polarimetric weather radars. The paper is interesting as it finds application for a rather peculiar observational setup, however, I found some issues in the study that I would like to present to the authors to contribute to their work.
1) A great emphasis is given to the fact that the proposed method does not require assumptions on the relation between DSD parameters. I would like to point out that this is not very convincing because:
a  assuming a gamma distribution for the DSD is already an assumption by itself. Why not a 4parameter gamma, a lognormal distribution or perhaps a normalized gamma?
b  the parameters of an unnormalized gamma distribution are indeed mathematically codependent. As an example, one can see just the measuring units of N0 (which, by the way, have not been written in line 32), those should be 1/mm**(mu). Just by noticing that the measuring units of N0 depend on mu, one can realize that the parameters cannot be independent. Some of the drawbacks of using such a size distribution are discussed Testud 2001 and Illingworth 2002 among others.2) The rationale for the selection of the used radar parameters is not clear. The term multifrequency radar is usually related to the leveraging of either differential scattering or differential absorption properties of the hydrometeors (see also the cited literature in the introduction), however here reflectivity at Sband is used (because it is considered unaffected by attenuation) and phase shift at S and Cband. I am not sure if a signal difference in Kdp is to be expected at the S and C band at all apart from the expected 1/wavelength scaling for Rayleigh scatterers. Some points:
a  Due to the 1/wavelength scaling Cband Kdp is more sensitive than Sband, but at the same time, it does not contain additional information. This means that the retrieval of 3 parameters DSDs would be again illposed. One might also test dropping the least sensitive Kdp information (Sband) and see what happens to the results
b  it is not clear to me why Kdp at two frequencies is used and not some other polarimetric/multifrequency quantity. ZDR is a straightforward example, LDR if available. If one assumes Sband reflectivity to be unattenuated (which is also a core assumption in this study) then one can estimate differential attenuation at the S and Cband which would also be a nice proxy for the total liquid water content. I would have expected a better explanation of why certain radar variables have been used and not others. Perhaps, one might have conducted a theoretical sensitivity study with Tmatrix to identify the best choice of observations to include in the retrieval technique given a climatology of observed DSDs... just some suggestions.3) The issue of comparing ground measurements with radar volumes aloft is not discussed enough. From what I understood multiple parsivels on the ground are used to compare their simulated radar quantities with radar variables, those parsivels can be up to 70 km away. I did not understand what is the vertical separation between the radar volume and the parsivels. Is this small enough to ensure that the radar and the disdrometers are observing the same DSDs? I assume that different radar elevation angles are used for the comparison with the various disdrometers, is that taken into account in the TMatrix calculations? if yes, isn't this causing the dataset to be inhomogeneous, what is the effect on the optimization method? What is the effect of the 4km averaging window, isn't this causing the radar quantities to be affected by returns that are up to 4 km away? By judging from figure 4 it seems that the averaging window is not applied as a moving average but rather at discrete points every 4km, does this mean that the bin center of the radar range can be up to 2 km away from the disdrometer position?
4) The metric used to test the DSD retrieval is again not clear. It appears that DSDs are compared only qualitatively. If this is the case I strongly recommend plotting DSD in semilog scale, otherwise it would be extremely difficult to evaluate them. In general, it would be nice to first establish what is the goal in terms of retrieval. Alternatively one might report retrieval errors concerning certain moments of the distribution, for example: total number of droplets, total liquid water content, mean size, and distribution width. To do so, one would need a statistically significant sample of retrieved and observed DSDs, I believe that one reviewer already reported on the lack of that.
5) Another implicit assumption (that should, at least be made explicit) is the fact that the Tmatrix calculations are perfect and do not carry uncertainties. This requires at least some more details such as the refractive index model used. A better approach would have been to estimate the uncertainties in Z and Kdp given by the choice of refractive index (I believe that the reference temperature of 10 degrees C might not be correct at different altitudes). Furthermore, the assumption of null canting angle is quite extreme. Also when comparing with the disdrometer one might want to take into account the limited resolution and maximum observable size. While the integrals of equations 3,4, and 5 go from 0 up to infinity, the parsivel do not (nor natural raindrops), are the integrals truncated at a certain minimum and maximum value? What about the size resolution when computing the integrals?
REFERENCES Illingworth, A. J., and T. M. Blackman, 2002: The Need to Represent Raindrop Size Spectra as Normalized Gamma Distributions for the Interpretation of Polarization Radar Observations. J. Appl. Meteor. Climatol., 41, 286–297, https://doi.org/10.1175/15200450(2002)041<0286:TNTRRS>2.0.CO;2.
 Testud, J., S. Oury, R. A. Black, P. Amayenc, and X. Dou, 2001: The Concept of “Normalized” Distribution to Describe Raindrop Spectra: A Tool for Cloud Physics and Cloud Remote Sensing. J. Appl. Meteor. Climatol., 40, 1118–1140, https://doi.org/10.1175/15200450(2001)040<1118:TCONDT>2.0.CO;2.
Citation: https://doi.org/10.5194/egusphere20232220CC2  AC5: 'Reply on CC2', Daniel Durbin, 02 Feb 2024

RC2: 'Comment on egusphere20232220', Anonymous Referee #2, 22 Dec 2023
 AC3: 'Reply on RC2', Daniel Durbin, 02 Feb 2024

RC3: 'Comment on egusphere20232220', Anonymous Referee #3, 03 Jan 2024
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 dualfrequency approach applied to C and S band radar collocated measurements can be of interest and the setup of practically colocated 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 Sband, supposed to be not affected by attenuation due to precipitation.
Usually, algorithms are first investigated in ideal conditions (i.e. through Tmatrix 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 dualpolarization 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 dualpolarization radar observation at C and S band” could be more suited to the content of the study.
b) About DSD parametric forms. The MarshallPalmer is a particular case of a 2parameter 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/10.1175/15200469(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 KuKa 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 Cband are not so different and Kdp is similar as well apart from the frequency scaling. In this case the contribution of the Cband 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.Citation: https://doi.org/10.5194/egusphere20232220RC3  AC4: 'Reply on RC3', Daniel Durbin, 02 Feb 2024
Viewed
HTML  XML  Total  BibTeX  EndNote  

257  78  32  367  14  15 
 HTML: 257
 PDF: 78
 XML: 32
 Total: 367
 BibTeX: 14
 EndNote: 15
Viewed (geographical distribution)
Country  #  Views  % 

Total:  0 
HTML:  0 
PDF:  0 
XML:  0 
 1