For this validation and closure study, the radiance and polarimetric observations come from the CoSSIR (Configurable Scanning Submillimeter-wave Instrument/Radiometer) onboard the NASA IMPACTS (Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms) campaign ER-2 aircraft, which was cruising at >16 km altitude during operational mode (i.e., above winter weather systems). Other payloads on the same aircraft include a W-band radar (CRS), a dual-frequency Ku/Ka band radar (HIWRAP), and a multi-frequency cloud physics lidar (CPL; ). We will use these three active sensor measurements jointly to provide the best estimates of frozen hydrometeor types and their vertical distributions for the subsequent CoSSIR retrieval of ice water path (IWP) and mass-weighted effective diameter (Dme). The retrieved size parameter will then be compared with in-situ cloud probe measurements from the co-flying P-3 aircraft at a lower altitude (∼ 5–7 km) that co-incides with the channel response function peak altitude of 325±11 GHz. More detailed information and datasets about this campaign can be found in and . Due to the sparseness of dropsondes, the NOAA high-resolution rapid refresh analysis (HRRR) temperature and water vapor profiles are used to represent the ambient and in-cloud thermodynamic structures for our combined active-sensor hydrometeor type classification, and the Weather Research Forecast (WRF) simulations generated atmosphere is used for forward radiative transfer simulation, both of which admittedly contain errors and biases that are difficult to identify.

Data collected during 16:00–18:30 UTC on 15 January 2023 is used for this validation work. Please note that all time labels in figures throughout this paper express time in decimal hours (e.g., 16.75 UTC = 16:45 UTC). The flight trajectories during this period sampled multiple times through the shallow warm-core intensitification phase of a Western Atlantic oceanic cyclone, as shown in Fig. . A consolidated surface low first appeared at 00:00 UTC on 15 January off the North Carolina coast (37° N, 70° W). Then between 06:00 UTC and 12:00 UTC the cold core migrated to warm core, and the shallow surface warm core structure intensified afterwards. Because of the warm core and sea surface temperature (∼22 °C), one can see strong melting band and consistent rainfall below from Fig. d, e and f for W-band radar reflectivity curtains. Above the melting band, different frozen hydrometeors are observed in situ by the CPI (cloud particle imager) onboard the P-3 aircraft. At 16:11 UTC, there were mostly ice plates or ice columns. At 17:12–17:18 UTC when the P-3 flew through the cyclone center from southwest to northeast at the same altitude, CPI captured large plate aggregates at the west side but mostly mixed-phase or ice pellets at the east side (Figs. 10 and 12 in ).

Because the 15 January flight is an atypical case for the IMPACTS campaign, which means the hydrometeor types and vertical distributions could be quite different from the rest winter storm cases sampled during this three-year long campaign, we selected a 5 February case and applied the same strategy to obtain the reference hydrometeor types (see next subsection for methodology). This case was then used for the training task later to test the robustness of our hydrometeor classification algorithm. 5 February was a typical winter frontal system. During 15:00–18:00 UTC, both flights sampled through the warm front sector latitudinally. This warm front was fairly shallow with core mostly below 4 km and absence of the melting band. Plates, columns and their aggregates were consistently observed during this 3 h period .

Currently there are two airborne sub-mm polarimeter-radiometers worldwide that are used as satellite simulators for the current and upcoming spaceborne sub-mm radiometers: ISMAR developed by UK Met Office and ESA , and CoSSIR developed by NASA . The latter was deployed during the CRYSTAL-FACE (Cirrus Regional Study of Tropical Anvils and Cirrus Layers, Florida Area Cirrus Experiment) and TC4 (Tropical Composition, Cloud and Climate Coupling) campaigns, both were in deep tropics. It was then reconfigured to add polarization to all frequencies, updated with a new receiver and a stand-alone pedestal . The new CoSSIR channel frequencies and noise levels can be found in Table . During the January–March, 2023 IMPACTS campaign, CoSSIR was operated under three modes: forward conical scan at a fixed scan-angle of 52.8°, cross-track scan, and along-track scan.

For this closure study, we do not perform direct retrieval using CoSSIR multi-channel radiance measurements. Rather, the IWC and LWC retrieved from the triple-frequency radar algorithm are the inputs fed into the forward model to compute simulated radiance and compare with observed ones to check consistency and sensitivity to ice microphysics. Same microphysics assumptions with radar retrieval algorithms are used for the radiometer forward simulation.

As and have demonstrated that the PD–TB relationship (PD stands for polarization difference, which is defined as TBV-TBH from the same frequency channel pair) for a specific frequency is a function of both IWP and Dme using fully polarized radiative transfer simulations, we can use the look-up-table (LUT) approach to identify the best Dme and IWP pairs in the solution space that minimizes the Eucledian distance to the observed TB and PD from single frequency measurements. and have demonstrated previously that PD is insensitive to the degree of ice particle orientation at scan angle of 52.8°. Hence, using data from this special view-angle can help eliminate the assumption of 100 % horizontal orientation when constructing the LUT, which is an unrealistic assumption in most realworld cases. Avoiding making this assumption is a critical step in assuring robustness of the retrieval results. In this study we therefore only employ CoSSIR measurements from the conical scan mode or cross-track mode with scan angle between 50 and 55° whenever the aircraft is above 16 km (i.e., well above the highest cloud top in this case). Data collected during large yaw, pitch or roll angles are also excluded to avoid cross-polarization information leaking. Strictly speaking, the LUT is also a dependent of ice habit . In our work, we assume two types of representative ice habit when generating the LUT: 6-bullet Rosette to represent the snowflakes, and column ice to represent small ice crystals. The RT4 solver is used for this fully polarized RT simulation . To make sure the uniform habit assumption is not severely violated, we also exclude convective zones by checking the existence of a melting layer. Filtering out convective scenes help mitigate the inhomogeneity issue mentioned above when we compare CoSSIR retrievals against in-situ cloud probe reference.

This study consists of three main objectives, covering two subjects, and the corresponding approach is shown in the flow chart in Fig. . The first objective is a closure study, as enclosed by the pink patched area in Fig. . We will be using the same set of hydromteor type profiles for CRS plus HIWRAP radars to retrieve the IWC and LWC profiles, which will be checked against radar reflectivity measurements using the ARTS radar simulator. The retrieved IWC profiles will be validated against independent 2D-S IWC retrievals at P-3 aircraft cruising level. The retrieved hydrometeor mass and particle size profiles will then be fed into the forward model with the same set of hydrometeor type profiles to generate simulated brightness temperature (TB), which will be compared against CoSSIR observations. Uniform habit assumption throughout the scene will be employed as the sensitivity test to understand how sensitive the cross-instrument consistency is to ice particle shape. However, PD measurements are not considered in this entire closure study task.

The other two objectives explore the subject about how the additional information from PD can constrain microphysics. For the 2nd objective (green dotted area), we will conduct a machine learning task to train CoSSIR to predict the vertical hydrometeor type distribution. PD will first be excluded in the baseline model and then added to evaluate the improvement. For the last objective (blue cross-hatched area), PD will be used together with TB to retrieve ice particle size, which will then be validated against independent 2D-S Dme retrievals. Because both tasks rely on retrieval products generated from the first task, and both include an independent validation step (for Objective #2, the validation follows standard ML protocol), these two objectives fit under the closure-study umbrella in a broader sense.

The radar retrieved IWC and LWC profiles between 16:00–18:30 UTC are shown in Fig. . During this 2.5 h period, the two aircrafts passed the cyclone center 4 times. However, if we only have IWC retrieval without breaking it down into more detailed hydrometeor types, as shown in Fig. a, it is almost impossible to tell how the cyclone changed over this period. When we have more detailed vertical information (Fig. b), we can see this cyclone center was still developing at ∼ 16:12 UTC given a core occupied by graupel and large graupel IWC values. Scattered single convective towers in the vicinity also suggested developing phase. At ∼ 18:00 UTC, the storm center was filled with snow aggregates and decreased IWC values. Stratiform mixed-phase low-level clouds at ∼3 km started to be captured when the aircrafts passed the storm the second time (∼ 17:00–17:12 UTC). Such a layer also indicates saturation and decaying of this cyclone, accompanied by periodic rainfall. After 18:00 UTC when the aircrafts passed the center the 4th times, the stratiform rain layer became quite evident. It is also quite interesting to see positive LWC (i.e., mixed-phase clouds) consistently appearing at the convective cloud top throughout this 2.5 h period, which is certainly SCLW, and they are mostly unambiguously determined by the CPL depolarization ratio. Although there was unfortunately no in-situ cloud probe observations at ∼10 km to validate these SCLW cloud, they were repeatedly reported in cold cloud systems by previous aircraft measurements. attributed this unique SCLW scenario to the imbalance between the large condensate supply rate by strong updraft and the relatively slow ice crystal growth rate because they are small there as well as radiative cooling at cloud top, while provided a similar explanation, but attributing the latter to the lack of ice nuclei there. Moreover, found 19 % of of IMPACTS campaign cloud scenes appeared to have SCLW on the cloud top, again demonstrating the ubiqutous existence of SCLWs. Our work seems to lean toward supporting the explanation by more, because the updraft evidently became weaker at later stage of this studying period, yet the SCLW layer at the cloud top still sustained. As both CRS and HIWRAP are Doppler radars, the vertical velocity measurements should be explored in the future to understand better of these SCLW clouds.

Next we check the quality of hydromteor profile retrievals against real CRS and HIWRAP observations by using the ARTS radar forward simulator to convert the hydrometeor profiles to radar reflectivities. 17:00–17:48 UTC is the period picked for scrutinization. During this period, ER-2 flew from southwest toward northeast direction, hovered around the convective center for about 5 min, and returned along roughly the same trajectory. Therefore, it sampled both the southwest sector of this cyclone as well as the center. P-3 was arranged to consistently fly underneath the ER-2 with flight height from 5.4 km at 17:00 UTC to 3.5 km at 17:48 UTC. During this period, P-3 released 9 dropsondes, separated apart by ∼6 min.

The hydrometeor classification results are detailed in Fig. f. Reflectivity differences ΔZ (defined as Zsimu-Zobs) are shown in Fig. a, b and c for Ku-band, Ka-band and W-band, respectively. Such an experiment is also carried out by assuming all frozen hydrometeors are graupel (Fig. d, e, and f) or LCA (Fig. g, h, and i). Note that when we conduct the latter two sensitivity experiments, the uniform ice habit assumptions were made during both the retrieval and forward simulation steps so that the microphysics assumption is maintained across-board and no additional ΔZ is introduced to bias our comparison. The bottom row displays the mean difference as a function of height, where segment below melting layer and above cloud top is excluded. Due to the expected challenge in simulating the melting layer, our LWC retrievals below is also likely biased, so we neglect discussing discrepancies within and below the melting layer and only focus on the frozen hydrometeors above. This is justified as our focus is CoSSIR essentially which is primarily sensitive to frozen hydrometeors.

As one can clearly see, detailed hydrometeor information including mass and habit can effectively help close the gap between observations and simulations. Above the melting layer, |ΔZ|<=2 dBZ mostly when detailed hydrometeor type is considered, although the simulated Z still tends to be on the smaller side within the graupel layer for Ku-band (Fig. j), and snow aggregates generated Z is low-biased as well for W-band (Fig. l). Assuming graupel everywhere produces slightly larger (smaller) negative biases in the convective core for Ku-band (W-band) compared to the results using detailed habits (Fig. j and l). The overall performance across three frequency bands are comparable, but we know graupel in anvil cloud deck is a rather irrational assumption. Assuming LCA everywhere introduces large positive biases (ΔZ>4 dBZ) in anvils for Ku-band large negative biases (ΔZ<-4 dBZ) everywhere for the W-band except for the anvil cloud deck. This means ice particles in the assumption is too strong in scattering, which strongly suggests that LCA should not be the dominant habit within the convective cloud.

Thirdly, now we can also check whether the retrieved IWC with the detailed vertical hydrometeor types can reproduce the CoSSIR observed TBs. ARTS is again employed as the forward simulator to convert between physical variables and measured TBs. Auxillary inputs including temperature and water vapor profiles came from the WRF simulations. For sensitivity tests, whole-column LCA and whole-column graupel are again assumed for all frozen hydrometeors. We can clearly see that both 170.05 and 325.15±11.5 GHz are sensitive to ice particle habit (Fig. a and b). Using LCA assumption can only generate 1/3 or even less TB depression magnitudes (TB depression defined as TBcloudy-TBclear) within the convection tower (∼ 17:00 UTC and 17:24–17:30 UTC). While uniform graupel assumption mitigate the warm bias by more than 20 K within the convective centers, they are still too warm. Only using the detailed hydrometeor types can we reproduce cold enough TB depressions that can produce the closest resemblence of the observations, although they are still 10–20 K too warm compared to the observations for the two wing bands at the deep convective cores (Fig. a and b). Such a warm bias might be caused by the excessive LWC retrieved at and below the melting layer, which also causes the low bias of simulated W-band radar reflectivity there (Fig. c). It may also be explained by ignoring the horizontally oriented snow aggregates between 5–7.5 km (Fig. f) that would introduce a colder TBH signal due to the enhanced scattering. For 325.15±3.4 GHz channel (Fig. c), the same conclusion holds with smaller contrast. That is because this channel is much closer to the water vapor absorption line at 325.15 GHz, and therefore the environmental humidity largely saturates this channel and hence it is less sensitive to hydrometeor types. 684 GHz with channel response function in the upper troposphere is not sensitive to hydrometeor types at all (Fig. d) for this case.

Away from the deep convective center where low-level stratiform rainfall and scattered congestus clouds prevail, both observed and simulated TB match well at the warm end for both wing channels (Fig. a and b). Interestingly, this is not exactly the case for two water vapor channels (Fig. c and d). Simulated TBs match well during 17:06–17:21 UTC, but then produces about 10 K warm bias during 17:36–17:48 UTC. Shallow congestus with mixed-phase clouds (cloud top below 5 km) were captured by radars and CPL during this period (Fig. ). As the weighting function (WF) for 325±3.4 GHz and 684 GHz are in middle troposphere (∼5 km) and upper troposphere (∼10 km), respectively, the warm TB biases in these two channel simulations indicate a possible dry bias in the middle and upper troposphere in the WRF water vapor field. This hypothesis turns out to be indeed the plausible explanation. As we can see from the water vapor field comparison between WRF simulations and dropsonde observations (Fig. ), a dry tougue is observed thrusting into 4–6 km altitude in the WRF data. The contrast between wing bands and the channels close to the water vapor absorption lines during 17:06–17:08 UTC clearly demonstrates the sensitivity of the latter two to atmospheric water vapor structures especially when clouds are below the weighting function peaking altitudes.

For the last step of the entire closure study, we shall validate the remote sensing retrievals using independent 2D-S cloud probe “observations”. By adding the quotation mark, it is important to stress again that cloud probe “observations” are also “retrievals” with orders of magnitude difference in scales. As mentioned previously, P-3 co-flew with ER-2 only during 16:12–17:30 UTC. Hence we can identify 2D-S retrievals from collocated radar range bins where P-3 was cruising as collocated and coincident in-situ IWC “truths”. It turns out these collocated samples cover more than 3 orders of magnitude of IWC values, and the radar retrievals turns out to agree quite well for all values with a slight over-estimation for IWC<0.1 g m⁻² (Fig. ). Note that the m–D relationship is assumed here to convert 2D-S images to IWC retrievals. If other m–D relationships are used, as will be shown later in Sect. 3.3, they will alter the bias direction. We shall hence focus on the excellent overall agreements, which nicely concludes this closure study.

This section will explore the advantage of polarimetric difference (PD≡TBV-TBH) in helping differentiating the hydrometeor type both vertically and horizontally. Although CoSSIR is a passive sensor that collects the WF-weighted vertically-integrated information, the fact that different channel WFs give preference at different altitudes suggests that CoSSIR has capabilities, although likely limited, at differentiating vertical profiles of hydrometeors. This is also vividly suggested in Figs.  and .

Figure a and b showcase an example of triple-frequency radar retrieved hydrometeor types (a for 5-class, and b for finer 8-class categorization) for a contiguous 32-footprints (∼32 km) nadir-looking curtain. The originally 240 m vertical resolution is coarsened to 500 m, partially because the image size (16 km × 32 km =32×32 pixels) is more suitable for machine learning (ML) training, and more importantly, due to the concern that CoSSIR is at its best able to tell apart 7-layers of vertical information indepedently according to our previous information content analysis . This translates into about 1 km vertical resolution for a 7 km thick ice clouds, or 500 m vertical resolution for a shallow 3 km thick ice clouds. In practice, the actual vertical resolution is about 2 km in most scenarios , so we should bear in mind that our ML exercise here tends to be on the optimistic side. Figure c stacks from bottom to top normalized CoSSIR observed TB, PD and σTB2 along the horizontal axis for the 32 observations, where rich information can be clearly seen from the polarimetric measurements (i.e., rectangle enclosed regions). The pink, light blue and black rectangles in Fig.  highlight three regions where the vertical cloud structures are distinctively different, namely anvil clouds (A), middle-layer ice core (B) and stratiform precipitating layers (C). This is the first time that PDs are compared amongst different channels laterally for a weather system, where we see greater channel-by-channel variations compared to the constrasts among TBs measurements from different channels. Typically speaking, for the same channel frequency, a larger PD accompanied by cold TB usually suggests dominantly horizontally oriented large ice particles (e.g., rosette), a smaller PD with warm TB indicates small cloud ice with no preferred orientation, but a smaller PD with cold TB implies possible turbulence inside convective cores . Combining PD and TB from different channels therefore unveils more details. For example, PD at 180 and 325.15±3 GHz both enhance significantly in Zone A. Because both of these channels are close to the water vapor absorption line, their enhancements indicate a significant anvil layer dominated by horizontally oriented ice. Meanwhile, as TB across all CoSSIR bands remain the coldest among this scene for Zone A with PD enhancement at 170 GHz, we can infer a large IWC layer in the lower troposphere with small vertical velocity, i.e., a dying convective core. This is also clearly indicated in the radar hydrometeor classification figure by the heavily riming aggregates and graupel near 3.25 km in Zone A. As a contrast, 325±11 GHz with WF peaking at around 6–7 km, shows a PD enhancement in Zone C, which indicates an alofted stratiform layer at 6–7 km. In Zone B, TBs are relatively warm, PDs are small, which could correspond to a shallow congestus or developing shallow convection with fresh unrimed ice and larger internal vertical velocity.

The ML segmentation task employs the full set of CoSSIR channel TB, PD and σTB2 observations except 182.3 V and 325±0.9 V as we experienced some calibration issues with these two bands and data quality was not satisfying (data quality backed to normal after 31 January for these two channels). This yields a total of 36 input features and the target is 9-class hydrometeor type (clear-sky is included as the 9th class) at 500 m vertical resolution between 0–16 km. The radar curtain is randomly cropped into images with 32×32 pixels in size as the example shown in Fig. b. To avoid data leaking, we employed a total of 1575 training images from the 5 February 2023 winter storm case, and target at predicting 479 independent testing samples from this 15 January 2023 case. In the 1575 training samples, training/validation was split at 80 % / 20 % ratio. A standard fully-connected Unet segmentation model is employed in this ML task with 5-layer model depth and a standard binary cross entropy (BCE) loss function. Since this paper is by no means intended as a ML-oriented effort, we didn't a run a full grid search of optimal hyperparameters. Rather, with a satisfactory performance after several trials, we apply exactly the same set of hyperparameter values and identical model to another sensitivity test that excludes all 6-channel PDs. The baseline model is called “full-set”, and the sensitivity test is called “No-PD”. Although BCE loss function was employed for training and testing, the mIoU (Mean Intersection over Union) score is also used as the evaluation metric. mIoU is defined as: 2mIoU≡19Σi=19TPiTPi+FPi+FNi where TP, FP and FN stand for true positive, false positive and false negative, respectively. mIoU score ranges from 0 to 1, where 0 means every pixel is segmented into a wrong class while 1 means every pixel is segmented correctly (i.e., a perfect match between predicted image and reference truth). Typically a mIoU score of 0.5 is considered a good result for 9-class segmentation tasks, and a value of 0.7 or higher usually indicates a very high-quality result.

The mIoU score for the baseline full-set model and no-PD sensitivity run is 0.642 and 0.4024, respectively. Both of the scores indicate descent retrieval potential of CoSSIR in distinguishing vertical hydrometeor structures. Figures  and  give two example scenes, one for the deep convective cloud with three cloud layers at the outskirt, and the other with boundary layer broken mixed-phase clouds and liquid precipitation layer beneath. For the former complicated multi-layer thick cloud scene, we can see excluding PDs is really limited in reproducing the true vertical cloud structure (Fig. a vs. b), although it does reasonably well in capturing the location of convective core, the rough vertical separations of frozen and liquid hydrometeors and the overall geometric thickness. Once PD measurements are included, the prediction quality improves dramatically. When the cloud layer is thin and low, both ML models perform relatively poorly, but including PDs help in general. For example, both ML models predict a wrong cirrus cloud layer in the upper troposphere for the multi-layer boundary layer cloud scene shown in Fig. , including PDs seems to be not critical, although the no-PD prediction gives a false cirrus cloud for this case (not for many other similar scenes). Yet, including PDs effectively predict the mixed-phase layer above the liquid layer correctly while the No-PD model missed in predicting the existence of the mixed-phase layer completely.

The limitation of No-PD retrieval of hydrometeor vertical type for thick ice cloud is as expected because TBs at >183 GHz lacks the channel-by-channel contrast when encountering thick ice cloud layers. This is also suggested by Fig. c and the example channel response function (CRF) shown by Fig.  in the Appendix. Although our current RT capabilities limit us in simulating the correct response function for PDs for thick clouds, the ML experiments clearly demonstrate the merits and potential. For single-layer thin ice clouds, there are enough differentiations among 183.31, 325.15 and 684 GHz wing bands to unveil vertical variations. As for boundary layer warm clouds, CoSSIR lacks the lower-frequency bands that are sensitive to liquid emissions. Yet, Fig.  and many other lower cloud scenes (not shown) demonstrate that PD signals might be very useful in telling apart liquid from mixed-phase clouds in the boundary layer.

Lastly, it is worth emphasizing that we intentionally designed to train on a typical winter storm case (5 February) and to predict on an atypical case (15 January) to test the robustness of our hypothesis that CoSSIR PD signals contain useful information about the vertical hydrometeor phase distribution. As most of the IMPACTS cases are typical winter storm cases, making a good prediction on another winter storm case might be partially explained by the similarity of winter storm vertical structures.

In this last objective, we further explore the merit of using PD in constraining the ice particle habit and size. found a statistically robust upside down “bell-curve” for the PD–TB relationship using the Global Precipitation Measurement Microwave Imager (GPM-GMI) observations at 166 GHz. They also identified a similar curve for 684 GHz using CoSSIR observations collected during the TC4 campaign over deep tropics. They further found the value range of PD is strongly dependent on the ice particle shape assumption, while the curvature of the bell curve is a function of mass-weighted ice particle diameter (Dme). further proposed a look-up-table (LUT) method to retrieve Dme using a single frequency PD–TB measurements. All these conclusions were based on highly idealized RT simulations assuming 100 % horizontal orientation, one single ice habit in the entire column, and a box cloud shape with fixed cloud top and bottom height. Whether such a LUT approach can work in real world cases was never explored.

In this vein, we first inspected the PD–TB scatter plots from three different channels, presumably with WF peaking at different altitudes. The entire period of interest is also separated into three sub-periods: 16:05–16:24, 16:48–17:03 and 17:15–17:30 UTC to exclude contamination of the general statistics from clear-sky or pure-liquid scenes because the LUT method does not apply to these scenes. Such a segmentation also originates from the consideration to separate samples from different stages because the microphysical properties could evolve. The statistical relationship from the first sub-period is shown in Fig. , while all three sub-periods are displayed in Fig. .

Firstly, the upside down bell-curve does not present in 170 and 684 GHz like what was previously discovered using tropical observations. This is because this 15 January warm-core cyclone never introduced cold enough TB nor strong enough turbulence to drive the PD value back to zero at cold TBs. 325.15±11 GHz shows the largest dynamic range of TB for this system, which is as expected and the most suitable for applying the LUT method (see Fig.  in the Appendix for a detailed explanation). Secondly, the largest PD value is ∼15 K, which indicates 6-bullet rosette is likely the most proper ice habit assumption as other particle shapes we tried (plate, column, dendrite) all produce too large PD (40–80 K). Two examples are given in Fig. . As a matter of fact, 6-bullet rosette assumption holds as the best choice for all three sub-periods. Lastly, we apply the LUT method to CoSSIR 325.15±11 GHz as its WF peaking height is the closest to P-3 cruising altitude during this period. The retrieved Dme can then be compared against collocated 2D-S retrieved ones.

The comparison results are shown in Fig. . Three different m–D relationship assumptions are employed to generate Dme retrievals from 2D-S, and we can see the single-channel retrieval results match well to the reference no matter what m–D relationship is chosen, although seems to produce the best matches in this case. Further, we can clearly observe an increase of ice particle size along with time, which agree with our previous observation of the evolvement of hydrometeor vertical structures over time (Fig. ).