Interactive comment on “ Determination of Ice Water Content ( IWC ) in tropical convective clouds from X-band dual-polarization airborne radar

This is a very important study demonstrating a potential of a polarimetric radar for accurate estimation of ice water content in clouds by using a unique experimental setup combining X-band polarimetric radar measurements and in situ microphysical observations on the same airborne platform. It is shown in a number of flights that the polarimetric method grossly outperforms existing IWC-Z relations and that the combination of KDP and ZDR yields better accuracy of the IWC estimate than a use of sole KDP. I am particularly pleased to find out that empirically derived relations IWC(KDP) and IWC(KDP,ZDR) are very close to the theoretical relations derived by Ryzhkov et

General Comments: 1. Combining KDP and ZDR in IWC retrieval is not new concept. For example, Eq. (13) in the current manuscript is very similar to Eq. (29) in Ryzhkov et al. (1998). In my opinion, the authors should discuss more on the relationships and differences between the current study and the other more theoretical studies.
2. Section 2 lacks detailed derivation and/or reference to existing literatures and is very difficult to follow. This section needs to be heavily rewritten. The author should provide detailed derivations or clearly refer to existing literatures for the equations. When doing so, the authors should make sure that the conventions of the equations are consistent.
3. The parameters (a, b) used in the Kdp only and Kdp-ZDR combined algorithm are obtained from linear fittings of data from 7 cases. By looking at Figure 12, it seems different values of (a, b) could be obtained if data from only one, or some of, the 7 cases are used in the fitting. What is the variability of the parameters (a, b)? How large the retrieval uncertainty will be due to the uncertainty in (a, b)?
Specific comments: P2, L14: What is the conclusion of Ryzhkov et al. (1998)? P3, L11 and L14: Which convention is used for the back-scattering matrices and forward scattering amplitudes? P3, L10 and L13: The radar observables, Zdr and Kdp, are usually integrated over a particle size distribution. Although Eq. (1) and Eq. (2) are OK if all the particles are of the same size and aspect ratio, this situation rarely happens. I think these equations can be removed since Eq. (5) and Eq. (6) are more general. Instead, the authors can discuss scattering properties in single particle level here.
P3, L15-17: This sentence is confusing. I guess the authors mean that Zdr does not change with increasing number of small particles while Kdp increases with increasing number of particles. The authors may want to rephrase this sentence. P3, L20: Is the permittivity of particle based on solid ice? C2 P5, Eq. (9-11): By using symbol for "approximately equal", do the authors really mean "proportional"? P5, Eq. (11): Derivation for this equation is needed. Also, Eq. (9) and Eq. (10) use integration over a PSD, why Eq. (11) only use one mass?
P5, L7-9: Again, detailed derivation is needed. How to derive a closed form of IWC as a function of Kdp and ZDR? What does "particle mass variation is small within the radar volume" mean?
P5, L19-20: What are the physical meanings of the constants b1 and b2?
P10, L7: What does "initial observations" mean? Should the "include" be replaced with "indicate"? P10, L8: "latter" is confusing. Better to clearly state which observations are weighted and biased towards Zdr.
P10, L7-12: Are the polarimetric variables Kdp, Zdr, Zh, and rho_hv shown in Fiugre (4) measured at a specific distance from the airplane or averaged over a range? How about those shown in Figure (5) and (6) P20, L12: I think the word "significantly" is too subjective and optimistic. For example, when Kdp=1, in panel (a), IWC varies by 50% of the maximum value (range 1∼2 with maximum 2), and in panel (b), modified IWC also varies by 50% (range 0.15∼0.3 with maximum 0.3). I would suggest remove the word "significantly".
Technical corrections: P1, L9: Is the differential reflectivity here in linear scale or log scale? C3