the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Apr 2026
A new method to estimate the characteristic raindrop size from space-borne Doppler radars: Validation with the Monte Carlo model
Abstract. A method to retrieve the mass-weighted mean raindrop diameter (Dm) from a space-borne Doppler radar is presented for Ku, Ka and W-band radars. The contribution of the air motion to the measured Doppler velocities which are the sum of the raindrop fall velocity and the vertical velocity of the atmosphere (Vair), was removed by a physically-based algorithm. The attenuation corrected reflectivity factors, the specific attenuation and the Doppler velocity are used as input in the algorithm to estimate Dm from the theoretical relationships among those values. For Ku-band, the effects of air motion were well removed, whereas the effects of DSD were difficult to remove due to the Rayleigh scattering regime. The latter effects were reduced by using a technique to determine an appropriate DSD by using the dependence of Z-R relationship on Dm. For W-band, modified algorithm were developed to estimate Dm. The validations of the retrieval method were made using simulated rain drop size distributions. A Monte Carlo model was used to evolves DSD by coalescence and breakup in a convective rain. Uncertainties in the retrieved Dm arising from the measurement errors were examined. The validation results show good agreement between the estimated Dm and the model values calculated from the simulated raindrop size distributions.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-1167', Anonymous Referee #1, 10 Jun 2026
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RC2: 'Comment on egusphere-2026-1167', Anonymous Referee #2, 15 Jun 2026
The paper proposes a physically-based retrieval of Dm from single-frequency nadir Doppler radars (PMM KuDPR, EarthCARE CPR, plus a hypothetical Ka), using specific attenuation k from PIA as a third constraint alongside Ze and Vp to remove air motion and constrain DSD shape, validated against a Monte Carlo coalescence/breakup model (MonDrop). The idea of using k as an independent constraint is worthwhile and the gap it addresses is real, since DFR is unavailable on these instruments. However, the validation does not stress the method's headline claims, several of the load-bearing assumptions are either unstated or not operationally realisable, and a few physical statements need correcting.
The motivation is timely and tied to real missions; the k-constraint is a genuine conceptual contribution distinct from the statistical EarthCARE approach; and using a Monte Carlo model is a defensible response to the scarcity of suitable observations. The error analysis, while incomplete (below), is a good-faith attempt to characterise sensitivity.
Major concerns:
1. The validation rests on a single, highly idealized warm-rain simulation. Despite "two settings" (W0 = 5 and 10 m/s), effectively one configuration drives the results. The simulation includes coalescence and breakup only and the cloud is initialised from a single gamma PSD at an unusually high liquid water content (2 g/m3). Because the entire retrieval error budget is dominated by the mismatch between the simulated DSD shapes and the gamma LUT, the realism of those shapes is doing most of the work, yet it is supported only by a qualitative resemblance of the Dm–R scatter to Bringi et al. (2003). A far stronger validation would (a) run the retrieval on disdrometer-measured PSDs (covering Rayleigh Ze > 10 dBZ) with added random vertical wind at, say, 0.5, 1, and 2 m/s standard deviation, and/or (b) compare against a vertically-pointing multi-frequency Doppler-spectra product that includes a W- or G-band channel for a reliable independent wind estimate. Either would test the method on realistic DSD variability and realistic air motion simultaneously.
2. The k constraint carries much less DSD-shape information than the paper claims. You have three unknowns (Vair plus DSD concentration and shape) and three observables (Ze, Vp, k), but they do not span three independent dimensions. In the Rayleigh regime k and Ze are both essentially LWC-weighted and nearly collinear, leaving shape poorly determined. Crucially, even in the Mie regime the dependence of k on the shape parameter is weak: from Fig. 7 the spread between μ=1 and μ=6 is roughly 1 dB/km at a peak near 16 dB/km, under 10%. So the statement that "k depends on the DSD as well as LWC for the Mie regime" overstates the shape sensitivity. k is mostly a function of LWC and Dm, not μ. This directly undercuts the premise that k disambiguates DSD shape, and it is the real reason the Ku correction stays weak and the separate Ze/R technique (4.3) is needed. I'd recommend framing the whole method as an ill-conditioned inverse problem and quantifying the actual information content of k (e.g., via the k/Z ratio — see point 7).
3. The Rayleigh-equivalent Z substitution at W/Ka (Section 4.2) is not operationally realizable and creates a logical circularity. Z is not measured; obtaining it requires estimating the PSD parameters, but once those are known, the retrieval is unnecessary. As written, the method assumes the answer to produce the input. The LUT-based Z(Ze, Vp) conversion partially hides this but does not resolve it, and the additional error it injects is not cleanly separated in the budget. This needs either an operationally defensible route to Z or an explicit acknowledgment that the W/Ka results are a theoretical upper bound.
4. The air-motion correction (the primary selling point) is barely exercised, and even the calm-air case already needs correction. The clean validations (Figs 9, 11, 17, 18) are stated to be in still air for most data, so they test the secondary DSD effect, not the effect the authors themselves call dominant. Worse, the Ku-band discrepancy that motivates the μ-correction already appears with no air motion; adding realistic up/downdrafts and turbulence broadening should make errors larger, not smaller. The ±0.5 m/s random Vp sweep is too narrow given convective vertical velocities of several m/s unless the retrieval technique is dedicated to stratiform/sedimenting rain but that should be stated.
5. "k and attenuation-corrected Ze are assumed given," and the error analysis is correspondingly optimistic. The PIA -> k inversion is itself hard and error-prone, especially at W-band, and its errors are correlated in range rather than random. Testing +-20% random k error therefore both understates the magnitude and misrepresents the structure of the real error. The error analysis does not span the expected range and should be redone with correlated errors and the wider wind range suggested in point 1; as it stands it shows too-optimistic performance.
6. Several claims are overstated. The assertion that the vertical Ze–Dm correlation sign can identify the precipitation life stage from GPM DPR overstates DPR's capability: the dual-frequency Dm problem is under-constrained (PIA is not always available, the gamma PSD has three free parameters, and k is not measured but inferred from an adjusted k–Z relation), and single-profile Dm is too noisy at DPR's resolution and sensitivity to read stage from the correlation sign. Similarly, "good agreement" in the abstract should be tempered by the still-air and given-k caveats.
Minor points:
7. Ze variability with μ and the k/Z ratio are not discussed. Most attenuation retrievals hinge on the k/Z (α) coefficient, which is itself the DSD indicator the method implicitly exploits. The paper neither shows how Ze varies with μ at fixed Dm nor frames the information content through k/Z. Adding this would clarify exactly what the constraint buys.
8. The Atlas et al. (1973) fall-speed formula is misapplied to the cloud regime. V = 9.65 − 10.3 exp(−0.6D) crosses zero near D ≈ 0.11 mm and is negative (i.e. spurious upward motion) below it. Since the initial cloud is set at D0 = 0.1–0.2 mm, a meaningful fraction of the starting population lies where this raindrop formula is invalid, which contaminates the early coalescence dynamics and the cloud sedimentation. A small-drop (Stokes-regime) terminal velocity should be used below the formula's validity range or at least the issue should be noted.
9. The frequency of the simulated Ze is not consistently stated. Line 170 notes C-band for one figure, but elsewhere (Figs 3, 5, 6) it is ambiguous. If these are Rayleigh values, say so explicitly and uniformly.
10. The W-band "measures only light rain below 20 dBZ" framing is physically misleading. W-band detects the same rain rates as Ku; what differs is that Mie scattering lowers the apparent reflectivity and attenuation lowers it further, so the measured Ze caps around 20 dBZ. The correct statement is that W-band attenuates quickly and drops below sensitivity at higher rain rates, so reliable retrievals are not expected above roughly 5–10 mm/h, not that the instrument is blind to heavier rain.
11. Doppler folding (CPR Nyquist ~5–6 m/s, Fig. 16) is not a minor aside given the method's acute Vp sensitivity; its interaction with the Vp iteration deserves explicit treatment or mentioning that Vp needs to be unfolded before the retrieval is applied.
12. Figure 16 should be a 2-D histogram / density plot. The black crosses obscure the point concentration and fully cover parts of the panel.
13. Citations and language need a careful pass. "Moroz" should be "Mroz" (l. 309); recurring typos include "evolves DSD," "understating," "Martial-Palmer" (Marshall–Palmer), "Gillespi"/"Gillespie," "relializations," "siginicant," "diffes," "DmEs1t."
14. Conclusions should mention that the algorithm is effectively a no-prior limit of the variational/optimal-estimation retrievals it is contrasted against, and the operational error chain is not accounted for. The scheme is a deterministic fixed-point iteration that adjusts Vp until the LUT-predicted k matches the observed k given Ze (and the Rayleigh-equivalent Z at W/Ka).Citation: https://doi.org/10.5194/egusphere-2026-1167-RC2
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The manuscript presents a retrieval method to retrieval mass-weighted mean diameter (Dm) using satellite-based nadir pointing Doppler radar measurements. The retrieval method uses the attenuation-corrected reflectivity, measured Doppler velocity, and a constrained specific attenuation (k in dB/km). The simulated DSDs are produced with a Monte Carlo model to produce convective rain DSDs with extreme rain rates (exceeding 200 mm/hr) using a coalescence and breakup parameters. While I would like to see Dm and vertical air motion retrieved from satellite Doppler radar measurements, I believe the current manuscript is not up to the standards of Atmospheric Measurement Techniques. My specific comments are listed below.
1. Since the proposed Dm retrieval method uses the measured Doppler velocity and assumes DSD gamma shape parameters, the air motion should also be retrievable. Getting the air motion correct is critical for the Dm retrieval. Why was air motion retrieval not discussed?
2. The manuscript described the retrieval method for observations at Ku-band and at W-band. The retrieval at Ku-band is appropriate because Ku-band radars can observer through convective rain. However, the proposed retrieval method for radar observations in the W-band is not practical. The specific attenuation is greater than 10 dB/km at W-band for Dm between 0.5 and 2 mm (See Fig. 7). For the convective rain simulated in Section 2, with rain rates exceeding 200 mm/hr, the W-band signal will be extinguished before reaching the surface, preventing a retrieved specific attenuation using the surface return. If the manuscript wants to convince the reader that the method is possible at W-band, then the simulation needs to start with attenuated reflectivities (also known as measured reflectivities). The manuscript would need to estimate the attenuation-corrected reflectivities and then perform the retrieval.
3. There are several assumptions that need to be removed, or accounted for, before this retrieval method can be taken seriously. Specific assumptions:
a) Attenuation-corrected reflectivity Ze assumed to be known beforehand. (Line 339)
b) Look-up table (LUT) is based on a fixed mu and a gamma shaped distribution.
c) The Ze vs. Doppler velocity curve with the over-plotting of the k and Dm grid (Fig. 8) are based on fixed mu gamma distribution, and the retrieval accuracy depends on selecting the correct LUT (Line 418).
4. Line 418. “This figure suggests that selection of appropriate LUT is critical for accurate estimation.” How is the appropriate LUT going to be determined? If we knew the DSD shape, then the retrieval would be trivial.
5. Fig. 9 and 11. Both figures show the first and final Dm estimates are underestimated relative to the model Dm. As an example of numbers from Fig. 11, it looks like Dm_est ~ 1.25 mm and Dm_model ~ 1.5 mm for Est 2. We can use Fig. 10 to see the change in Doppler velocity for Dm changing from 1.25 to 1.5 mm is about 1 m/s, for all three models assuming mu = 1, 3, or 12. This is a very large error in vertical air motion. And this is in a rain region assumed to have zero air motion (see the text on Line 396, “The vertical velocities of the atmosphere are zero for most data.”) This suggests that the air motion is not being removed correctly from equation (3) and the error is not only in Dm but for the air motion estimate, also.
6. How does the retrieval work for the profiles with upward vertical air motion of 10 m/s? If the Dm were 1 mm, the zero air motion Doppler velocity would be about 5.5 m/s downward (see Fig. 9), and the measured Doppler velocity (Vp) would be about +4.5 m/s upward, and off the axis of Fig. 9.
7. Can the manuscript provide a scatter plot retrieved air motions vs. modeled air motions?
8. In step 3 of the retrieval algorithm (Line 370), it states “If estimated k differs from the measured value, estimate Dm and k again …” How is the “measured k” determined in this manuscript from the simulated DSDs? How is the method used in this manuscript different than how the satellite algorithm would estimate k from PIA?
9. In Fig. 2 shows that the simulation produces convective rain rates of 200 to 400 mm/hr. What is the specific attenuation at Ku- and W-bands for these extreme rain rates? What are the LWCs for these extreme rain rates? How representative are the specific attenuations shown in Fig. 7 for LWC = 1 g/m^3 when the simulated rain rates are over 200 mm/hr?
10. From the description of the retrieval algorithm (Lines 366 to 374), it appears that the red dots shown in Fig. 8 are not used in the retrieval algorithm. Is that correct? A more appropriate figure would be one without the red dots, because the iterative procedure is moving around the Dm vs. k grid box using Ze, Vp, and an unknown measured k. Please clarify this for the reader because as shown, the reader may think the red dots are used in the retrieval.
11. Line 759. In the summary section, “For Ku-band, the effects of air motion were well removed, …” I do not think the manuscript showed that air motions were well removed. The manuscript did not present any figures showing the accuracy of retrieving air motion.
12. At Ku-band, specific attenuation has been shown to be a good estimate of rain rate. So, can this method be described as a modified Z-R-Vp method?