Version 4 CALIPSO IIR ice and liquid water cloud microphysical properties, Part I: the retrieval algorithms

Following the release of the Version 4 Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data products from the CloudAerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission, a new version 4 (V4) of the CALIPSO Imaging 15 Infrared Radiometer (IIR) Level 2 data products has been developed. The IIR Level 2 data products include cloud effective emissivities and cloud microphysical properties such as effective diameter and ice or liquid water path estimates. Dedicated retrievals for water clouds were added in V4, taking advantage of the high sensitivity of the IIR retrieval technique to small particle sizes. This paper (Part I) describes the improvements in the V4 algorithms compared to those used in the version 3 (V3) release, while results will be presented in a companion (Part II) paper. To reduce biases at very small emissivities that were made evident 20 in V3, the radiative transfer model used to compute clear sky brightness temperatures over oceans has been updated and tuned for the simulations using MERRA-2 data to match IIR observations in clear sky conditions. Furthermore, the clear-sky mask has been refined compared to V3 by taking advantage of additional information now available in the V4 CALIOP 5-km layer products used as an input to the IIR algorithm. After sea surface emissivity adjustments, observed and computed brightness temperatures differ by less than ± 0.2 K at night for the three IIR channels centered at 08.65, 10.6, and 12.05 μm, and inter-channel biases are reduced 25 from several tens of Kelvin in V3 to less than 0.1 K in V4. We have also aimed at improving retrievals in ice clouds having large optical depths by refining the determination of the radiative temperature needed for emissivity computation. The initial V3 estimate, namely the cloud centroid temperature derived from CALIOP, is corrected using a parameterized function of temperature difference between cloud base and top altitudes, cloud absorption optical depth, and the CALIOP multiple scattering correction factor. As shown in Part II, this improvement reduces the low biases at large optical depths that were seen in V3, and increases the 30 number of retrievals in dense ice clouds. As in V3, the IIR microphysical retrievals use the concept of microphysical indices applied to the pairs of IIR channels at 12.05 μm and 10.6 μm and at 12.05 μm and 08.65 μm. The V4 algorithm uses ice look-up tables (LUTs) built using two ice crystal models from the recent “TAMUice 2016” database, namely the single hexagonal column model and the 8-element column aggregate model, from which bulk properties are synthesized using a gamma size distribution. Four sets of effective diameters derived from a second approach are also reported in V4. Here, the LUTs are analytical functions relating 35 microphysical index applied to IIR channels 12.05 μm and 10.6 μm and effective diameter as derived from in situ measurements at tropical and mid-latitudes during the TC4 and SPARTICUS field experiments. https://doi.org/10.5194/amt-2020-387 Preprint. Discussion started: 30 November 2020 c © Author(s) 2020. CC BY 4.0 License.

and indirect effect analysis (Twomey, 1974). Because robust schemes for estimating Ni are still under active development, Ni has not been included in the IIR operational products thus far.
Following the release of the Version 4 (V4) CALIOP data products, a new version of the IIR Level 2 data products has been developed. Input data products are i) Version 2 IIR Level 1b products that integrate corrections of small but systematic seasonal 80 biases that were observed in the northern hemisphere in Version 1 (Garnier et al., 2017, and ii) V4 CALIOP 5-km cloud layer and aerosol layer products. This new IIR version is named V4 after the CALIOP products. As for the V4 CALIOP products, ancillary atmospheric and surface data are from the Global Modeling and Assimilation Office (GMAO) Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) model (Gelaro et al., 2017), and they replace the various versions of the GMAO Goddard Earth Observing System Version 5 (GEOS-5) model which were used in V3. The IIR V4 algorithm itself 85 has been changed to improve both the estimates of effective emissivity derived over all surfaces and the subsequent microphysical indices retrievals. These improvements incorporate lessons learned from the combined analysis of numerous years of co-located V3 IIR and CALIOP level 2 data (G12; G13; G15). Ice clouds LUTs have been updated in V4 using state-of-the-art ice crystal single scattering properties (Bi and Yang, 2017), and V4 also includes independent retrievals using new parameterizations inferred from in situ measurements (M18). In response to the growing importance of better characterization of liquid water clouds for 90 climate studies, V4 further takes advantage of improvements in microphysical indices to include specific retrievals of water cloud droplet size and liquid water path using dedicated LUTs.
This first paper (Part I) presents the main changes implemented in the V4 IIR Level 2 algorithm and describes improvements with respect to V3. All the changes implemented in V4 relate to the track algorithm. The algorithm used to extend the track retrievals to the IIR swath is as reported in G12 and therefore its description is not repeated here. Microphysical retrievals over oceans and 95 comparisons with other A-Train retrievals will be presented in a companion "Part II" paper . V4 retrievals over land, snow or sea ice with a specific emphasis on the changes in the surface emissivity will be presented in a forthcoming publication. The paper is organized as follows. The main updates to the scene classification algorithm are presented in Sect. 2.
Section 3 describes the changes implemented to compute the effective emissivities in each IIR channel. The changes in the microphysical algorithm are detailed in Sect. 4 (effective diameter) and Sect. 5 (ice or liquid water path). Section 6 discusses how 100 to estimate ice crystal and water droplet concentrations from the V4 CALIOP and IIR Level 2 products. The paper ends with a summary and concluding remarks in Sect. 7.

Scene classification
Both in V4 and in V3, the first task of the IIR algorithm is to classify the pixels in the scenes being viewed. This scene classification is based on the characteristics of the layers reported in the CALIOP 5-km cloud and aerosol products and is designed to identify 105 suitable scenes containing the required information for effective emissivity retrievals. The primary information provided by CALIOP includes the number of layers detected, their altitudes, types (i.e., cloud or aerosol), and mean volume depolarization ratio, and a determination of the opacity of the lowermost layer. The V4 classification algorithm is for the most part identical to V3 (G12), and only the main changes implemented in V4 are highlighted here.
For scenes that contain at least one cloud layer, the presence of lower semi-transparent aerosol layers is identified in the data 110 products using the 'type of scene' parameter, but these aerosol layers are ignored when computing the emissivity of the (potentially multi-layered) cloud system. The rationale is that unless these low layers are sufficiently dense dust (or volcanic ash) layers, absorption in the IIR channels is negligible. In contrast, semi-transparent aerosol layers located above the cloud layer(s) are not ignored because they are more likely to be absorbing layers. These layers are those classified by CALIOP as smoke, volcanic ash, https://doi.org/10.5194/amt-2020-387 Preprint. Discussion started: 30 November 2020 c Author(s) 2020. CC BY 4.0 License. dust, or polar stratospheric aerosol (Kim et al., 2018). The number of tropospheric dust layers and of stratospheric aerosols layers 115 in the column is reported in the V4 IIR product so that the retrievals can be filtered if necessary.
Of importance for IIR passive observations, cloud layers with top altitudes lower than 4 km that were detected by CALIOP at single-shot resolution are cleared from the 5-km layer product to improve the detection of aerosols at coarser spatial resolutions (Vaughan et al., 2005). In V3, these single-shot "cleared clouds" were not reported in the 5-km layer products and hence were ignored by the IIR algorithm. However, clouds detected at single shot resolution have large signal-to-noise ratios (SNR), indicating 120 that they are dense and actually should not be ignored. This single shot detection frequently occurs when the overlying signal attenuation is small enough to ensure sufficiently large SNR, which favors scenes containing overlying optically thin aerosol or cloud layers. In V4, these single-shot cleared clouds are reported in the CALIOP 5-km products  and the IIR algorithm is able to use this new piece of information. A "Was_Cleared_Flag_1km" SDS is now available in the V4 IIR product, which reports the number of CALIOP single-shot clouds in the atmospheric column seen by the 1-km IIR pixel that were cleared 125 from the 5-km layer products. Furthermore, scenes that were seemingly cloud-free in V3 are split into multiple categories in V4.
Cloud-free scenes in V4 are pristine and have no single shot cleared clouds, while new types of scenes have been introduced when at least one cleared cloud is present in the column.

Retrieval equations and sensitivity analysis 130
Before discussing the flaws that motivated changes in V4, we recall the retrieval equation of the effective emissivity, εeff,k, in each IIR channel, k (Platt and Gambling, 1971;Platt, 1973 ; G12) :   ,  ,  , , , where Rk,m is the calibrated radiance measured in channel k reported in the IIR Level 1b product, Rk,BG is the background radiance in channel k that would be observed at the top of the atmosphere (TOA) in the absence of the studied cloud system, and Rk,BB is 135 the TOA radiance (also noted Bk(T)) that would be observed if the cloud system were a blackbody source of radiative temperature T. The IIR 1-km pixel is assumed to be fully cloudy and the qualifying adjective "effective" refers here to the contribution from scattering. These three radiances can be converted into equivalent brightness temperatures, noted respectively as Tk,m, Tk,BG, and Tk,BB, using the relationships reported in Sect. 2.4 of Garnier et al. (2018).
For each channel k, the effective absorption optical depth, τa,k, is derived from εeff,k as: 140 Finally, the microphysical indices βeff12/10 and βeff12/08 are written: The background and blackbody radiances are computed according to the scene classification introduced in Sect. 2.
The background radiance is determined either from the Earth's surface or, if the lowest of at least two layers is opaque, by assuming 145 that this lowest layer behaves as a blackbody source. In both cases, the background radiance is preferably derived directly from https://doi.org/10.5194/amt-2020-387 Preprint. Discussion started: 30 November 2020 c Author(s) 2020. CC BY 4.0 License. relevant neighboring observations if they can be found. Otherwise, it is derived from computations using the FASt RADiative transfer model (FASRAD) (Dubuisson et al., 2005) and the meteorological and surface data available at global scale from meteorological analyses (MERRA-2 in V4). FASRAD calculations of the background radiance is required for ~75 % of all retrievals. 150 The blackbody radiance is computed using the FASRAD model and the estimated radiative temperature, which, in V3, is the temperature, Tc, at the centroid altitude, Zc, of the 532-nm attenuated backscatter of the cloud system derived using interpolated temperature profiles. For multi-layer cases, the IIR algorithm computes an equivalent centroid altitude, and thereby sees the cloud system as a single layer.
Sensitivity of the retrieved quantities to errors in Tk,m, Tk,BG, and Tk,BB have been discussed in details in G12, G13, and G15, and 155 equations are repeated in Appendix A. Assuming no biases in the Version 2 calibrated radiances , errors in Tk,m and in Tk,BG when the latter is derived from neighboring pixels are random, and equal to 0.15-0.3 K (G12). In contrast, errors in computed Tk,BG and in Tk,BB are composed of both systematic and random errors. Random errors in Tk,BG from ocean surface computations were assigned after examining the distributions of the differences between observations and computations in clear sky conditions. In V4, the assigned random error is ΔTBG ± 1 K for all channels, which will be justified later in the paper. The 160 assigned random error in Tk,BB is ΔTBG ± 2 K for all channels to reflect uncertainties in the temperature profiles.
Random errors can be mitigated by accumulating a sufficient number of individual retrievals. However, systematic biases will remain and need to be reduced to the best of our ability. As a quantitative illustration, Fig. 1 shows the sensitivity of (a) εeff,12, (b) the inter-channel effective emissivity differences, noted Δεeff12-k, and (c) βeff12/k to systematic biases in TBG and TBB simulated using TBG = 285 K and TBB = 225 K. The sensitivities are inversely proportional to the radiative contrast between the surface and 165 the cloud. Thus, they are typically smaller in ice clouds, for which the temperature contrast over oceans is typically 60 K, as chosen in this example, than in water clouds that are closer to the surface. The black curves in Fig. 1 illustrate the impact of an identical bias of dT12,BG = dTk,BG = +1 K in all the channels. This positive bias increases εeff,12 ~ 0 by ~ 0.02 and has an insignificant impact at εeff,12 ~ 1. Even though the temperature bias is the same in all channels, Δεeff12-k and βeff12/k are also impacted: at εeff,12 ~ 0.1, βeff12/10 (dashed line) is decreased by 0.03 and βeff12/08 (dashed dotted line) by 0.06. The red curves illustrate the impact of a 170 channel-dependent bias in TBG, by taking dT12,BG = 0 K and dT10,BG = dT08,BG = +0.1 K. This modest inter-channel bias of dT12,BG -dTk,BG = -0.1 K induces a similar impact for both pairs of channels, with Δεeff12-k ~ -0.002 at εeff,12 ~ 0 and βeff12/k reduced by about 0.025 at εeff,12 ~ 0.1. Finally, the blue curves are obtained by taking an identical bias in all channels of dT12,BB = dTk,BB = +1 K. This increases εeff,12 ~ 1 by ~ 0.01 and has a negligible impact at εeff,12 ~ 0. Again, this identical bias in all the channels changes Δεeff12-k and βeff12/k: at εeff,12 = 0.95, βeff12/10 is increased by 0.02 and βeff12/08 by 0.03. As seen in Fig. 1c, an acceptable bias 175 of for instance 0.02 defines an emissivity domain of analysis ranging from 0.3 to 0.9. This domain is mostly limited in the low emissivity range, and refinements are necessary to extend this domain as much as possible.

Motivations for changes in V4
Changes in V4 were motivated by the need to reduce systematic errors in V3 microphysical retrievals that were made evident from statistical analyses of the IIR V3 products. Because the sensitivity of the split-window technique decreases for optically very thin 185 and very thick clouds, Δεeff12-k is supposed to tend towards zero on average when εeff,12 tends towards 0 and towards 1. Examining whether this behavior was observed in our retrievals allowed us to identify errors related to the determination of background radiances when εeff,12 tended towards 0 and of blackbody radiances when εeff,12 tended towards 1 (G13). These tests were paired with comparisons between observed and modeled brightness temperatures, whenever relevant.

V3 biases at small emissivity 190
Emissivity retrievals using Rk,BG observed in neighboring pixels are a priori more robust than when this radiance is computed using a model. As discussed in G13, no biases were detected in V3 in the former case. However, when the ocean surface background radiances were computed using the model, median Δεeff12-k at εeff,12 ~ 0 was clearly negative, down to ~ -0.015 for the 12-08 pair, which translated into significant low biases of the ice clouds microphysical indices at small emissivity (see Fig. 5 of G13 and Fig.   1c). This was due to channel-dependent biases in the computed radiances, which could be assessed independently by comparing 195 observations and computations in clear sky conditions. Consequently, the modeling of Earth surface radiance has been revisited in V4, as presented and evaluated in Sect. 3.3.

V3 biases at large emissivity
Large emissivities are typically found in so-called opaque clouds that fully attenuate the CALIOP signal. Importantly, "opaque" means opaque to CALIOP, that is cloud visible optical depth typically larger than 3 in V4 (Young et al., 2018) or effective 200 emissivity expected to be larger than about 0.8. In opaque ice clouds, V3 εeff,12 was rarely larger than 0.95 (G12) and median Δεeff12-k was minimum around εeff,12 = 0.95 rather than 1. Both suggested that εeff,12 was systematically too small, and therefore that the cloud radiative temperature was underestimated. In other words, observations in opaque ice clouds tended to be warmer than the computed blackbody temperatures, by about 5 K (see Fig. 8 in G12), while this systematic positive bias was not observed for warm opaque water clouds. A similar contrast between ice and water clouds was also reported by Hu et al. (2010) when 205 comparing IIR observations and mid-cloud temperatures. Stubenrauch et al. (2010) reported that for high opaque ice clouds, the radiative height determined by the Atmospheric Infrared Sounder (AIRS) on board the Aqua satellite is on average lower than the altitude of the maximum CALIOP 532 nm attenuated backscatter by about 10 to 20 % of the CALIOP apparent thickness. The warm bias between radiative temperature (Tr) and the centroid temperature Tc used in V3 was explained theoretically in G15. The Tr -Tc difference was found between 0 and + 8 K for semi-transparent single-layered clouds and increased with cloud emissivity 210 and geometric thickness, in agreement with previous studies (Stubenrauch et al., 2013 and references therein). Underestimating Tr (and therefore TOA TBB) yields under-estimates in εeff,12 and the microphysical indices. Note that Heidinger et al. (2010) infer cirrus radiative height from suitable pairs of channels using a range of expected values of eff as a constraint. The problem here is reversed and is instead to estimate Tr in order to infer microphysical indices. The determination of Tr in ice clouds implemented in V4 is presented and discussed in Sect. 3.4. 215

FASRAD model
The background radiance from the Earth Surface is computed using the FASRAD model fed by interpolated atmospheric profiles and skin temperatures reported in the MERRA-2 reanalysis products in V4. In V3, differences between observed and computed brightness temperatures (BTDoc) in clear sky conditions over oceans exhibited latitudinal and seasonal variations for all channels 220 (G12), which appeared to be related to variations in the water vapor profiles near the surface to which the IIR window channels are the most sensitive. The water vapor absorption coefficients were updated in V4, thanks to the advances in atmospheric spectroscopy over the last decade (Rothman et al., 2013). Using MERRA-2 sea surface temperature and atmospheric profiles, the model was tuned to minimize the residual sensitivity of BTDoc to the column-integrated water vapor path (IWVP). This assessment was carried out in V4 pristine clear sky conditions; i.e., when no layers were detected anywhere in the column or if the 225 column included only low semi-transparent non-dust aerosols in which no single-shot cleared clouds were detected within the IIR pixel (Sect. 2). Systematic biases remained for each channel, even at night where the clear sky mask is a priori the most accurate because of the increased CALIOP nighttime signal-to-noise ratio. Nighttime BTDoc was on average equal to -0.5 K at 08.65 µm, -0.35 K at 10.6 µm, and -0.2 K at 12.05 µm. These biases were explained by the combination of possible errors in the model, in the ancillary data, and in the calibration. We chose to reconcile observations and computations by using a new set of surface 230 emissivity values (see Table 1) with no attempt to include surface temperature variations as reported from airborne measurements (Newman et al., 2005). The derived surface emissivity values used in V4 are close to 0.98 on average. It is noted that to save computation time, the contribution of the clear sky downwelling radiance reflected by the surface is not included in the operational FASRAD model. Because the surface emissivity values are close to 1, the subsequent impact on their derived values is not significant. 235 As an illustration, median BTDoc is shown in Fig. 2a vs. IWVP derived from MERRA-2 for each IIR channel, both in V4 (solid lines) and in V3 (dashed lines). Over-plotted in green is the median MERRA-2 sea surface temperature (Ts). The results are shown for 6 months of nighttime data in 2006 (from July through December) between 60° S and 60° N. The number of clear sky IIR 240 pixels used for this analysis is plotted in Fig. 2b. Even though the ancillary data are from GMAO GEOS 5.10 in V3 for this time period and from MERRA-2 in V4, the differences between V3 and V4 are mostly due to the changes in the radiative transfer model. The amplitude of the variations of median BTDoc with IWVP is drastically reduced in V4 compared to V3 and the interchannel differences are significantly smaller. Between IWVP = 1 and 5 g.cm -2 , where most of the samples are found, V4 median BTDoc is between -0.2 and 0.2 K for the 3 channels. Using the V4 surface emissivities compensates for a residual 10-12 inter-245 channel BTDoc bias of -0.15 K and a residual bias of -0.3 K for the 08-12 pair. In contrast, the V3 median 10-12 and 08-12 interchannels biases were up to -0.7 K and -1.8 K, respectively, at IWVP = 5 g.m -2 .

Evaluation vs. latitude and season
BTDoc (12) is overall less latitude-dependent in V4 than in V3, owing to the reduced sensitivity to IWVP, and the width of the 260 distributions is reduced. The V4 global standard deviations are similar for nighttime (0.8 K) and daytime (0.9 K) data. Mean V4 BTDoc(12) is larger for daytime than nighttime data at any latitude, by 0.2 K on average. As mentioned earlier, the V4 clear sky mask is expected to be more accurate at night than during the day. Undetected absorbing clouds would decrease the brightness temperature of the observations and therefore BTDoc(12), and a larger fraction of undetected clouds for daytime data would yield smaller daytime BTDoc(12) and not larger values as observed here. A similar finding was reported in Garnier et al. (2017) for both 265 IIR and MODIS, suggesting that these differences are not due to calibration issues. The computations used a different model, namely the 4A-OP radiative transfer model (Scott and Chédin, 1981), and ancillary data were from the ERA-Interim re-analyses (Dee et al., 2011). It is unclear whether the small but systematic day vs. night differences are due to the V4 clear sky mask or other reasons.
Again, the inter-channel differences are drastically reduced in V4 compared to V3, especially for the 08-12 pair of channels. In 270 V4, the mean absolute inter-channel differences are smaller than 0.1 K globally. The worst cases are in July 2006 at 30-60° N (Fig.   4), where mean BTDoc(10-12) and BTDoc(08-12) are equal to -0.15 K and -0.26 K, respectively. The global standard deviations are around 0.31-0.35 K, notably smaller than 0.8-0.9 K found for BTDoc(12), because common biases due to errors in sea surface temperature cancel out. Keeping in mind that the random noise at warm temperature is 0.15-0.2 K (G12) in each channel, the standard deviations around 0.31-0.35 K can be largely explained by the random noise in the observed temperatures, which is 275 https://doi.org/10.5194/amt-2020-387 Preprint. Discussion started: 30 November 2020 c Author(s) 2020. CC BY 4.0 License. estimated to be 0.2 -0.3 K. In conclusion, the uncertainty in computed Tk,BG is taken identical in all channels and equal to the conservative value ± 1 K based on the standard deviations in BTDoc(12).   Again, the presence of clouds that were detected at single-shot resolution and later cleared from the 5-km layer product is forbidden in the V4 clear sky mask. The impact of this refinement in V4 is illustrated in Fig.5, which compares the BTDoc histograms in V4, in which single-shot clouds are specifically excluded, and in pseudo-clear sky conditions (i.e., which contain at least one singleshot cloud) over oceans between 60° S and 60° N in January 2008. When cleared clouds are present (light blue and orange), median and mean BTDoc(12) are smaller by 1.3 K and 2.2 K, respectively, and a marked negative tail down to about -8 K is observed, 295 because these dense cleared clouds are often colder than the surface. In this example, the fraction of IIR pixels that see at least one cleared cloud in the column is 35 % at night and 22 % for daytime data. The larger nighttime fraction is likely related to the fact that the probability for CALIOP to detect a cloud at single-shot resolution is larger at night due to the larger daytime background noise, so that the probability that these clouds are cleared from the product is larger at night. The mean and median values of the inter-channel BTDoc are barely impacted, showing that the cleared clouds induce a similar bias in the three IIR channels. 300

Centroid altitude and temperature
Both in V3 and in V4, the first step into the computation of the radiative temperature is to determine the centroid altitude, Zc, of the cloud system. The centroid altitude of each layer is reported in the CALIOP 5-km layer product, together with the 532-nm integrated attenuated backscatter (hereafter IAB) of each layer. IAB is corrected for the molecular contribution and for the attenuation resulting from the overlying layers, noted T 2 overlying. Following the rationale presented in Appendix B, the centroid 310 altitude of a multi-layer cloud system composed of N layers is computed as: For single-layer cases (N = 1), Zc is obviously the centroid altitude reported in the CALIOP data product. For multi-layer cases, the cloud system is seen as an equivalent single layer characterized by Zc given in Eq. (4), whose top and base altitudes are the top of the uppermost layer and the base of the lowermost layer, respectively. The approach is the same as in V3, except that, because 315 of an error in the computation of T 2 overlying in the V3 IIR algorithm, estimates of Zc could be too low by up to several kilometers in V3 multi-layer cases.
In V3, the radiative temperature (Tr) was set to the centroid temperature (Tc) for any cloud system. The approach is the same in V4, except when all the layers are classified as ice by the V4 ice/water phase algorithm (Avery et al., 2020). In the latter case, Tr is derived from Tc and parameterized functions, as presented and illustrated in the next section. 320

Radiative temperature in ice clouds
As demonstrated in G15, Tr is the brightness temperature associated with the centroid radiance of the attenuated infrared emissivity profile within the cloud, whereas Tc is the temperature associated with the centroid altitude of the attenuated 532 nm extinction coefficient profile. For CALIOP, the in-cloud attenuation profile is the overlying two-way transmittance, , where τa(z) is the in-cloud overlying infrared absorption optical depth, which is about half of τvis(z) (G15). Using V3 CALIOP extinction profiles in semi-transparent ice clouds, the Tr-Tc difference was found to increase with both cloud optical depth and geometric thickness (G15).
Because the CALIOP extinction profiles are not used in the IIR operational algorithm, the approach in V4 was to establish 330 parameterized correction functions, Tr (k) -Tc, for each channel k, and to correct the initial estimate Tc that was used in V3 as Tr (k) = Tc + [Tr (k)-Tc]. These correction functions were derived off-line from the statistical analysis of a series of simulated extinction and attenuated backscatter profiles. In order to reproduce the variability associated to the various possible shapes of the extinction profiles, we chose to use actual V4 CALIOP profiles (8,000 profiles were used) rather than synthetic profiles. These initial CALIOP profiles were derived from single-layered semi-transparent clouds classified with high confidence as randomly 335 oriented ice (ROI) by the V4 ice/water phase algorithm (Avery et al., 2020). Each CALIOP extinction (and backscatter) profile was scaled to simulate several pre-defined optical depths and the attenuated backscatter profile was simulated by applying the required attenuation to the simulated total (molecular and particulate) backscatter profile. The simulations were carried out for eff,k ranging between 0.1 (or τa,k = 0.1, see Eq. (2)) and 0.99 (or τa,k = 4.6). Variations of Tr (k) -Tc with η between 0.5 and 0.8 were also analyzed in order to cover the range of temperature-dependent values used in V4 (G15; Young et al., 2018). Variations with 340 η were not discussed in G15 because η was taken constant and equal to 0.6 in V3.
The Tr(k) -Tc differences were examined against the "thermal thickness" of the simulated clouds; that is, the difference between the temperatures at cloud base (Tbase) and at cloud top (Ttop). The median relative difference (Tr -Tc)/(Tbase -Ttop) was found to vary linearly with Tbase -Ttop, as illustrated in Fig. 6a for channel 12.05 µm using η = 0.6. Figures 6b and 6c show that the intercepts (a0) and the slopes (a1) of the regression lines vary with cloud absorption optical depth τa,12. Furthermore, the Tr -Tc differences increase 345 with η because the CALIOP signal is attenuated more quickly when less multiple scattering (i. e., larger η) contributes to the backscattered signal. As a result, both a0 (Fig. 6b) and a1 (Fig. 6c) increase as η is increased from 0.5 to 0.8. Finally, the mathematical expression for the correction implemented in V4 is: where the letter k refers to the IIR channel. The corrections derived from Fig. 6a are shown in Fig. 6d. For a given value of Tbase -350 Ttop, Tr -Tc increases with eff,12 until eff,12 = 0.7-0.8 and is maximum for eff,12 = 0.8-0.99 (or τa,12 between 1.6 and 4.6), where it represents 10 to 25 % of the cloud thermal thickness. We find that Tr(k) is slightly larger at 10.6 μm than at 12.05 μm, by less than 0.3 K in the worst case, and somewhat larger at 08.65 μm than at 12.05 μm, but always by less than 1 K (not shown). Because at https://doi.org/10.5194/amt-2020-387 Preprint. Discussion started: 30 November 2020 c Author(s) 2020. CC BY 4.0 License. this stage of the algorithm, the final value of τa,k is still unknown, τa,k in Eq. (5) is the initial V3 value derived by taking Tr = Tc.
No correction is applied when the initial emissivity is found larger than 1. 355

360
Again, the maximum corrections are for clouds having initial effective emissivities in the 0.8-0.99 range and are similar for emissivities larger than 0.9. This range of initial emissivities is found for clouds that are opaque to CALIOP. It is noted that the corrections are a priori underestimated for opaque clouds. Because the CALIOP signal does not penetrate to the true base of opaque layers, the reported base is instead an apparent one, and so Tbase -Ttop is a priori too small. Figure 7 illustrates the impact of the correction applied to V4 opaque ice clouds classified as high confidence ROIs for IIR channel 12.05. The apparent thermal 365 thickness (Fig. 7a) is larger at night (blue) compared to day (red), as already mentioned in Young et al. (2018). In this example, nighttime and daytime mean ± standard deviation of Tbase -Ttop are 28 ± 13 K and 21 ± 9 K, respectively. Similarly, the Tr -Tc corrections shown in Fig. 7b are larger at night. The discontinuities around Tr -Tc = 0 in Fig. 7b are due to pixels with initial emissivity larger than 1 for which no correction is applied, which occurs more often at night. The smaller daytime apparent thickness is explained by the larger background noise in CALIOP daytime measurements, which increases the difficulty in 370 accurately locating cloud boundaries. Consequently, both Tc and Tr are a priori more accurate at night. Figure 7c shows the Tr -Ttop (solid lines) and Tc -Ttop (dashed lines) differences relative to the apparent Tbase -Ttop. After correction, the nighttime mean ± standard deviation of (Tr -Ttop)/(Tbase -Ttop) is 0.48 ± 0.15. This result is fully consistent with Stubenrauch et al. (2017), who report that the radiative cloud height derived from AIRS is, on average, at mid-distance between the CALIOP cloud top and cloud apparent base in high opaque clouds at night. Because the IR absorption above ice clouds is usually weak, Tr is close to TOA TBB. 375 For reference, the dotted lines in Fig. 7c represent (Tm -Ttop)/(Tbase -Ttop), where Tm is the measured brightness temperature (here T12,m). Tm represents the warmest possible value for TBB ~ Tr if all clouds had effective emissivity equal to unity. At night, Tm is always located within the apparent cloud, at 61 % from the top as compared to 48 % for Tr. The Tm -Tr difference represents the maximum possible bias in the estimation of Tr and is equal to 1.5 K on average. For daytime data, both Tr and Tm are lower in the apparent cloud than at night, and even below (Tm > Tbase), which is at least in part due to the smaller daytime apparent thickness. 380 Further evaluation will be carried out in the future using extinction profiles and true cloud base altitudes derived from the CloudSat radar.
With the introduction of corrections to the cloud radiative temperatures for ice clouds, V4 emissivities and microphysical indices now depend on the CALIOP ice/water phase classification. However, for optically very thin ice clouds, the corrections are typically smaller than 1 K, and, furthermore, these small corrections induce little changes in the final effective emissivity and microphysical indices (see Fig. 1). Thus, microphysical indices can be considered independent of the CALIOP ice/water phase at small 390 emissivities, typically smaller than 0.3.

Radiative temperature in liquid water clouds
In case of opaque liquid water clouds, the observed brightness temperature (Tm) is, on average, close to the TOA TBB inferred from Tc. This indicates that the temperature at the centroid altitude is a good proxy for Tr, which is why no change was implemented in the V4 algorithm for liquid water clouds. Nevertheless, significant differences between V4 and V3 can arise from differences in 395 the meteorological data. This is illustrated in Fig. 8, which shows PDFs of Tm -TBB at 12.05 µm in V4 (solid lines) and in V3 (dashed lines) for opaque water clouds having identical centroid altitudes in V3 and in V4. These clouds are classified as water with high confidence by the V4 ice/water phase algorithm and they are the only layer detected in the column. The V3-V4 differences are due mainly to the different temperature profiles (GMAO GEOS 5.10 in V3 and MERRA-2 in V4), yielding different values of Tc for an identical centroid altitude, and to a smaller extent to the changes in the water vapor profiles and in the FASRAD 400 model. The V4 median differences are -0.6 ± 2.2 K at night and 0.12 ± 2.7 during the day. The larger fraction of negative Tm -TBB differences in V3, from -2 K down to -10 K, has been traced back to cases with strong temperature inversions near the top of the opaque cloud, which seem to be better reproduced in MERRA-2.

Effective diameter
The eff12/k microphysical indices (Eq. 3) are interpreted in terms of ice crystal or liquid droplet effective diameter using LUTs built with the FASDOM model (Dubuisson et al., 2008) and available optical properties (G13). Following Foot (1988) and Mitchell 410 et al. (2002), the effective diameter is defined as: where V and A are the total volume and the projected area that are integrated over the size distribution, respectively.

V4 Look-Up Tables
The difference between the V4 and the V3 ice LUTs is twofold: the ice crystal models are different and a particle size distribution 415 (PSD) is introduced in V4. Three ice crystal models were used in V3. These were taken from the database described in Yang et al. (2005) and represented three families of relationships between eff12/10 and eff12/08: solid column, aggregate, and plate (G13).
In practice, the plate model was rarely selected by the algorithm. In V4, the LUTs are computed using state-of-the-art ice crystals properties referred to as "TAMUice2016" by Bi and Yang (2017), which were updated with respect to "TAMUice2013" reported in 2013 . These optical properties determined by the Texas A&M University group are now widely used by the 420 scientific community (Yang et al., 2018). Two models are used in V4: severely roughened "8-element column aggregate" (hereafter CO8) and "single hexagonal column" (hereafter SCO), for which the degree of the particle's surface roughness has little impact for the IIR channels. The former is the MODIS Collection 6 ice model for retrievals in the visible/near infrared spectral domain (except that the choice of the MODIS model was based on "TAMUice2013" properties), where the so-called "bulk" optical properties are computed using a gamma PSD with an effective variance of 0.1 (Hansen, 1971;Baum et al., 2011;Platnick et al., 425 2017). The same gamma PSD is chosen to compute the V4 IIR LUTs, whereas no PSD was introduced in V3 (G13).
For retrievals in liquid water clouds, which were added in V4, the LUTs are computed using the Lorenz-Mie theory with refractive indices from Hale and Querry (1973) and using the same PSD as for ice clouds.
As in V3, the LUTs are established for several values of εeff,12 (G13). Shown in Fig. 9 are the V4 (solid lines) and V3 (dashed lines) LUTs computed for εeff,12 = 0.23 (visible optical depth ~ 0.5). This figure highlights that the eff12/k microphysical indices are very 430 sensitive to the presence of small particles in the PSD (Mitchell et al., 2010), with 12/k decreasing rapidly as De increases up to 50 µm, and then tending asymptotically to ~ 1 at the upper limit of the sensitivity range; that is, De = 120 µm for ice crystals and 60 µm for liquid droplets. The retrieval of large particle sizes becomes very sensitive to noise and biases in the microphysical indices.
In V4, the LUTs are extended to De = 200 µm for ice clouds and 100 µm for water clouds. Doing this allows the user to perform dedicated analyses when 12/k is only slightly smaller than the lower sensitivity limit, but De retrievals beyond the sensitivity limit 435 are very uncertain and flagged accordingly.
For ice clouds, the V4 eff12/10-De relationships are relatively insensitive to the crystal model compared to the eff12/08-De ones, owing to the larger single scattering albedo at 08.65 µm. The model dependence of the eff12/10-eff12/08 relationship is used as a piece of information about the ice model and the shape of the ice crystals to ultimately improve the De retrievals. First, the algorithm identifies the model that provides the best agreement with the IIR parameters in terms of relationship between eff12/10 and 440 eff12/08, and then De is retrieved using this selected model. The water model is used for retrievals in liquid water clouds. For any model, De is the mean of the effective diameters De12/10 and De12/08 when these two values can be retrieved from the respective eff12/k; i.e.,

Ice cloud model selection
As stated above, the ice cloud model is selected according to the relationship between eff12/10 and eff12/08. The theoretical relationships derived from the V4 ice models are shown in Fig. 10, where the purple curves with square symbols show the CO8 model and the green curves with diamond symbols represent the SCO model. The colors of the symbols denote the value of De 450 between 20 μm and 120 μm. Because of the channel-dependent sensitivity to scattering, the overall relationship between eff12/10 and eff12/08 varies with effective emissivity, as seen when comparing the dotted (εeff,12 = 0.1) and dashed dotted (εeff,12 = 0.9) curves. Increasing εeff,12 from 0.1 to 0.9 increases eff12/10 by only about 0.03 regardless of De, but tends to decrease eff12/08, by up to 0.12 at De = 20 μm. As a result, the slope of the curves is increased by about 30 % from εeff,12 = 0.1 to 0.9 for both models, while the models themselves (purple and green curves) differ by only 10 % for a given εeff,12 value, thereby showing the importance 455 of properly taking scattering into account. For reference, the thin solid lines show the relationships derived from approximate eff12/k defined by Parol et al. (1991) as: 12 / 1 1 where Qi is the extinction efficiency, ꞷi is the single-scattering albedo, and gi is the asymmetry factor in the IIR channels i=12 or k. For each crystal model, the approximate LUT value happens to be fairly close to the LUT value obtained at εeff,12 = 0.9. 460 https://doi.org/10.5194/amt-2020-387 Preprint. Discussion started: 30 November 2020 c Author(s) 2020. CC BY 4.0 License.

Comparing the V3 and V4 ice models 465
In order to illustrate the impact of the changes introduced in the ice models in V4, Fig. 11 compares i) the V4 LUT values (solid lines and large symbols), ii) the V4 CO8 and SCO models but with no PSD (dashed dotted lines and small symbols), and iii) the V3 solid column and aggregate LUT values (dashed lines and different symbols), which had no PSD. For the three configurations, εeff,12 is arbitrarily taken equal to 0.23. First, we see that the V4 CO8 (purple solid) and the V3 aggregate (purple dashed) models are very similar in terms of relationship between eff12/10 and eff12/08. In contrast, V3 solid column (green dashed) appears to 470 be systematically shifted towards smaller eff12/08 compared to V4 SCO (green solid). As a result, the difference between the V4 models is not as marked as the difference between the V3 models. Secondly, we note that for both V4 models, the solid and dashed dotted lines are very close, showing that the PSD chosen in V4 has a negligible impact on the relationship between eff12/10 and eff12/08, because it is quasi-linear. In other words, the ice model selection by the IIR algorithm is not impacted by the PSD introduced in V4. However, for a given De, eff12/10 and eff12/08 are larger with the V4 PSD (large symbols) than with no PSD 475 (small symbols), because of the large sensitivity of eff12/k to the smallest crystals included in the distribution. In other words, including a PSD in V4 increases retrieved De. https://doi.org/10.5194/amt-2020-387 Preprint. Discussion started: 30 November 2020 c Author(s) 2020. CC BY 4.0 License.

Comparing the V4 ice models and parameterizations from in situ observations
The four sets of analytical functions relating IIR ßeff12/10 and De established in M18 were derived from in situ measurements in ice clouds performed during the SPARTICUS and TC4 field experiments, at mid-latitudes over land and at tropical latitudes over oceans, respectively. Because of uncertainties in the first bin, N(D)1, of the measured size distributions (D < 15 μm), two LUTs 485 were established for each campaign, one with N(D)1 unmodified and the other with N(D)1 set to zero to maximize the impact of a possible overestimate of N(D)1. These four sets of ßeff12/10 -De relationships are shown in Fig. 12, alongside the relationships derived from the V4 CO8 and the SCO models. For this comparison exercise, ßeff12/10 is computed using the approximate formulation given in Eq. 7. For a given De, βeff12/10 is notably larger when N(D)1 is not modified (blue and red solid lines) than when N(D)1 is forced to zero (blue and red dashed lines), because the presence of small particles in the unmodified PSD increases βeff12/10 faster than De. The difference between the six De values associated to a given value of ßeff12/10 is a measure of possible uncertainties resulting from 495 https://doi.org/10.5194/amt-2020-387 Preprint. Discussion started: 30 November 2020 c Author(s) 2020. CC BY 4.0 License.
the LUTs. For instance, βeff12/10 = 1.6 yields De between 10 and 16 µm, and βeff12/10 = 1.1 yields De between 40 and 70 µm. The V4 SCO (green) and CO8 (purple) βeff12/10 -De relationships are fairly close to those derived using N(D)1 = 0 (dashed), likely because the gamma functions with effective variance of 0.1 used in the V4 LUTs tend to fulfill this condition. Even though a PSD is now included for the computation of the V4 LUTs as an attempt to better simulate realistic conditions, the chosen gamma function is undoubtedly not adapted for any ice cloud globally. 500 5 Ice and liquid water path

Ice water path
As in V3, ice water path (IWP) in ice clouds is estimated from the visible extinction optical depth, τvis, and De using (Stephens, 1978 where ρi is the ice bulk density (ρi = 9.17 x 10 2 kg. m -3 ) and Qe,vis is the visible extinction efficiency of the size distribution, typically close to 2. In V3, vis was estimated from τa,12 (Eq. 2) as: where Qa,12 is the effective absorption efficiency at 12.05 µm of the size distribution, which was taken to be close to 1. However, as shown in Fig. 13a, the vis/2τa,12 ratio varies with De, by up to 15 % for the V4 SCO model (green). In V4, vis is estimated from 510 τa,12 and τa,10 as: ,12 ,10 vis a a    + (9b) As seen in Fig. 13b, using (τa,12+ τa,10) instead of 2τa,12 as a proxy for vis notably reduces De-dependent errors when De is larger than 20 μm, as prevailingly found in ice clouds. The vis/(τa,12 + τa,10) ratio slightly decreases as τa,12 increases because of increasing influence of scattering in the effective infrared absorption optical depths, but by less than 5 % for the opaque clouds of τa,12 = 3 or 515 εeff,12 = 0.95. The overall errors in the V4 vis estimates are within ± 6 % at De = 20 μm and ± 3 % at De = 70 μm. The simplified V4 formulation reduces the dependence on De and is a straightforward approach to estimate vis from IIR retrievals. It is convenient for comparisons with other sensors, providing that errors of about 5 % are acceptable.

Liquid water path
For liquid water clouds, liquid water path (LWP) is derived from De and τa,12 (Platt, 1976;Pinnick et al., 1979)  where ρw is the liquid water density. Unlike for ice clouds, the variation of Qa,12 with De is taken into account (Pinnick et al., 1979) and is represented using a fourth-degree polynomial for De ≤ 20 m, so that: De ≤ 20 µm ( )  Because IIR is a passive sensor, IIR Level 2 primary retrievals are vertically integrated quantities such as a,k and IWP or LWP.
Similarly, De represents a layer average. Even though not provided in the V4 products, equivalent layer absorption coefficient and layer ice or water content can be derived for specific studies, and ultimately ice and liquid cloud concentrations can be determined. 540

Equivalent layer absorption coefficient and layer ice or liquid water content
The IIR retrievals are all tied to the retrieved effective emissivities. As demonstrated in G15, εeff,k is the vertical integration of an attenuated effective emissivity profile, which can be determined from the CALIOP extinction profile, vis(z). An IIR weighting function within a cloud of geometric thickness ΔZ can be determined after normalization by εeff,k. This applies to semi-transparent clouds whose true base is detected by CALIOP. This IIR weighting function, WFIIR(z), has been used to compare cloud radiative 545 temperature and cloud centroid temperature and to ultimately establish the correction functions presented in Sect. 3.4.2. This concept has also been used in M18 to compute an equivalent effective thickness seen by IIR, ΔZeq, as:

Ice crystal and water droplets concentration
First characterizations of particle concentrations have been developed for ice clouds. Following M18, the ice crystal concentration 555 (Ni) in semi-transparent ice clouds can be derived as: where the (Ni/IWC) ratio is a function of βeff12/10 that was derived from in situ observations, depending on hypotheses in the measured PSD (see Table 1 in M18). As seen from MI18, the uncertainty in the derivation of Ni/IWC increases rapidly as βeff12/10 decreases below 1.1, e.g. as the effective diameter of ice crystals grows. 560 In the case of liquid water clouds, a similar approach can be used and the droplet concentration, Nd, can be written: https://doi.org/10.5194/amt-2020-387 Preprint. Discussion started: 30 November 2020 c Author(s) 2020. CC BY 4.0 License.
Here, the (Nd/LWC) ratio can be written as a function of the effective radius Re=De/2 as: where k is a factor determined from the ratio of the mean volume radius and the effective radius. Two values k=0.67 and k=0.80 565 (with an uncertainty of 0.05) have been proposed for ocean and land respectively as derived from in situ measurements (Martin et al., 1994).

Summary and perspectives
The IIR Level 2 algorithm has been modified in the V4 data release to improve the accuracy of the microphysical indices in clouds of very small (close to 0) and very large (close to 1) effective emissivities. In addition, a new set of LUTs is used to retrieve ice 570 cloud microphysical properties, and the retrievals have been extended to liquid water clouds.
Improving the microphysical indices at emissivities typically smaller than about 0.2 required improvements in the accuracy of the simulated background radiances. In this first of a pair of papers describing the V4 IIR level 2 updates, we focused on retrievals above the oceans. The changes in the new radiative transfer calculations using sea surface and atmospheric data from MERRA-2 were evaluated through comparisons with IIR measurements in clear sky conditions. These clear air conditions were identified 575 using co-located CALIOP observations and were refined in V4 using additional information now reported in the V4 CALIOP 5 km layer products. Water vapor absorption and sea surface emissivities in each IIR channel were adjusted to reconcile observations and simulations. In V4, clear air observations and simulations agree within ± 0.2 K on average at night. The inter-channel 08-12 and 10-12 differences are drastically reduced from several tens of Kelvins in V3 to less than 0.1 K on average in V4.
The retrieval of cloud properties is increasingly difficult as effective emissivity approaches 1, because the sensitivity of the 580 technique decreases when the measured radiance is close to the cloud equivalent blackbody radiance. Biases in the determined value of the blackbody brightness temperature thus have growing importance. In V3, we used the CALIOP centroid altitude as a proxy for the equivalent radiative altitude, but it was shown later that in case of ice clouds, the corresponding infrared radiative temperature was underestimated. We have aimed at minimizing this bias in V4 by refining the relationship between lidar geometric altitude and infrared radiative temperature. We have implemented a parameterized correction of the V3 estimates which is a 585 function of ice cloud thermal thickness, cloud absorption optical depth, and CALIOP multiple scattering correction factor. This correction is expected to increase the number of valid retrievals of crystal sizes for dense ice clouds as well as to reduce biases at large optical depths.
One of the specific features of the IIR algorithm is accounting for the relationships between the 12/10 and 12/08 microphysical indices in order to retrieve the particle effective diameter. New ice optical properties ("TAMUice 2016") have been used and two 590 crystal shapes have been selected to determine theoretical values of the microphysical indices as a function of effective diameter.
One of these models is the 8-element column aggregate model selected by the MODIS science team for the Collection 6 products, and the other one is the single hexagonal column model. In V4, the bulk properties are computed using the same gamma PSD as selected by the MODIS team. The selection of the crystal model used for the retrievals is not impacted by this assumed size distribution, whereas introducing a size distribution in V4 increases the retrieved diameters. Another independent approach for deriving effective diameters is discussed, which relies on parameterizations based on in situ measurements from the SPARTICUS and TC4 field experiments used to determine the relationship between the 12/10 microphysical index and effective diameter. A simple and fairly accurate formulation of the ice cloud visible optical depth is proposed, which is based on IIR absorption optical depths at both 10.6 and 12.05 µm, and which could be conveniently used for comparisons with other sensors. This formulation is used to provide ice water path estimates. 600 The IIR V4 algorithm now includes a dedicated retrieval for liquid water clouds. These water clouds were not a priority in V3, due to the smaller radiative contrast between water clouds and the surface compared to ice clouds, and the resulting larger uncertainties.
The water cloud retrieval was introduced in V4 because the uncertainties will be smaller than in V3, owing to the reduced biases, and because the IIR retrieval technique is well adapted for the smaller particle sizes found in liquid water clouds. Our primary targets will be supercooled liquid water clouds. 605 The changes and improvements in the V4 IIR Level 2 products resulting from the changes implemented in the V4 algorithm are presented in a companion (Part II) paper. One key feature of the IIR algorithm is the initial scene classification inferred from the co-located CALIOP observations, and specifically from the CALIOP 5-km cloud and aerosol layer products. The synergy with CALIOP could be reinforced by using the CALIOP extinction profiles to infer the in-cloud IIR weighting function and thus better characterize the fraction of the cloud layer to which IIR is sensitive, as was implemented for ice concentration retrievals in MI18. 610 This would improve the equivalent vertical resolution of the geophysical parameters retrieved by IIR and ultimately open the possibility to report vertically resolved parameters such as ice crystals and liquid droplet concentrations in a future version of the operational products.
Finally, the relative sensitivity of βeff12/k to an error dTk,x is uncertainties ΔTk,x, and the overall uncertainty is then estimated by assuming that these three uncertainty terms are not correlated.
Computing ( ) 12 / eff x k   requires establishing whether the two terms of Eq. (A4) are correlated. Assuming no bias in the calibration, the error ΔTk,m represents the overall radiometric random noise for an individual pixel in for each channel k, and the errors in the respective channels are not correlated. Regarding the background radiance, ΔT12,BG and ΔTk,BG depend on the way in which the background radiances are determined. If from neighboring pixels, ΔT12,BG and ΔTk,BG are due to their radiometric random 635 noise and are not correlated. In contrast, when the background radiances are computed using the FASRAD model and the same ancillary data, ΔT12,BG and ΔTk,BG are correlated. Finally, because the blackbody radiances result from the cloud radiative temperature derived from Tc and the Tr -Tc correction functions, ΔT12,BB and ΔTk,BB are also correlated. The IIR Level 2 track products are also available at the AERIS/ICARE Data and Services Center at https://www.icare.univlille.fr/data-access/data-archive-access/?dir=IIR/ (last access 14 September 2020). 665

Author contribution
AG and JP defined the changes implemented in the V4 IIR algorithm and wrote the original draft. AG performed the data analysis and prepared the figures. NP was in charge of software development and provided V4 IIR test data. MV provided assistance for the use of the CALIOP data. PD provided the FASRAD and FASDOM radiative transfer models and bulk scattering properties.
PY provided the ice crystal models from the "TAMUice 2016" database. DM provided the analytical functions derived from in 670 situ measurements. All authors contributed to the review and editing of this paper.

Competing interests
Author Jacques Pelon is a co-guest editor for the "CALIPSO Version 4 Algorithms and Data Products" special issue in Atmospheric Measurements Techniques but will not participate in any aspects of the editorial review of this manuscript. All other authors declare that they have no conflicts of interest. 675