General comments:

This paper is a study on the potential of the upcoming CLARREO Pathfinder (CPF) mission to provide more detailed retrievals of cloud properties than heritage (MODIS-like) imaging sensors thanks to a combination of decreased radiometric uncertainty and increased spectral sampling. The specific geophysical situation studied is joint retrieval of cloud optical depth (COD) and effective radius at the top and bottom of the cloud, for marine stratocumulus scenes. In contrast, one of the major current large-scale approaches (MODIS-like bispectral) retrieves COD and near-top effective radius using a pair of bands, and makes multiple bispectral retrievals with their differences being semi-informative on cloud structure.

There are two main parts to the analysis. First is use of VOCALS-REX field campaign data to set up some case studies for the proposed retrieval method using MODIS. This has the advantage of being something which can be tested now. The second is a sensitivity study, comparing the capabilities of a MODIS-like sensor with the EMIT instrument as a surrogate for CPF. Together these provide a starting point for moving towards this next level of detail in passive imager cloud retrieval algorithms.

The manuscript is in scope for AMT. There is a lot to like about this paper: it tackles an important problem, is clearly written, and has some nuance to the discussion. I particularly appreciated the discussion of sampling scales in the VOCALS-REX part of the discussion. The quality of writing and presentation are good. It is (mostly) well-referenced. I also appreciate the authors quickly noticing and fixing the incorrect panel of Figure 3. I think it is worth consideration for an AMT science highlight.

That said, there are points where I think clarification and deeper discussion with respect to realistic performance are needed. As the paper does not claim to be a fully operational approach it does not need to be the final word on the matter, but as a case study and example of what can be done, I think there are sections where more caveats should be discussed, and there are a few things I was not certain about. I recommend minor revisions before publication. I would be willing to review the revision, if the Editor would like.

Specific comments:

1. Line 31: I’m not sure I’d seen COD described as mean photon free paths through the cloud before, although I can see this framing makes sense as it is the integral of extinction coefficient which is units e.g. km^-1 (extinction events per unit distance). Normally it is just referred to as vertical integral of extinction coefficient. I’m curious if there’s a reason the authors picked this particular framing for COD.

1. Line 31: not sure I’d describe effective radius retrievals as “extinction-weighted” but maybe “photon-penetration-weighted”? For a really deep convective cloud, for example, the photons seen from space are still mostly coming from near the cloud top even if the water/extinction would be somewhat further down. And this is in line with e.g. the Platnick (2000) reference cited and weighting functions shown in the paper. To me “extinction-weighted” implies an optical center of mass.

1. Introduction, general: I like the historical discussion, but there are a few omissions that I think are quite relevant. One is the ORAC retrieval which came out of the same lab as Clive Rodgers who put down the Optimal Estimation (OE) formalism used here, applied mostly to European sensors (ATSRs and successors). See Sayer et al (2011) and Poulsen et al (2012). This isn’t an explicitly bispectral approach (uses all bands together) but only retrieved a single effective radius (sensitivity from 1.6 and 3.7 micron bands) as opposed to attempting a profile. Another is the VISST algorithm applied to cloud properties from MODIS observations within CERES pixels (as part of the CERES data processing chain), which is also not bispectral but again retrieving a single effective radius from visible and multiple SWIR bands (0.65, 1.6, 2.1, 3.7 micron). The reference I use for this is Minnis et al (2011) – that paper cites some earlier AVHRR work using that algorithm from the late 1990s, but it’s in conference proceedings that don’t seem to be broadly available, so I can’t say for sure what was done. There is also earlier OE work by e.g. Heidinger (2003) applied to the AVHRRs (a lot of later work from that NOAA team focuses on the infrared, but the above algorithm also used solar radiances and is more conceptually similar to bispectral). All of these approaches (ORAC, CERES, AVHRR) have been applied to multi-decadal multi-sensor records and approach the question of effective radius parameterization a bit differently from either the bispectral method or the profiling method, so I think merit some discussion in the manuscript. Also, I think all of these methods were applied somewhat earlier than the publications describing them were written (otherwise mostly documented in proceedings and technical reports) so they are not such newcomers as the paper dates might imply.

1. Line 106: I see there is a paper reference there but for ease it would be good to detail the expected pixel size, orbital geometry, swath width, and spectral sampling/bandwidth of the CPF mission as well. This should be recapped in the conclusion as well, where relevant (e.g. in the discussion of scales of variability in marine stratocumulus clouds).

1. Section 2.1: I would suggest renaming this “the bispectral method” instead of “the standard method”. What does “standard” mean? From a polar-orbiting viewpoint, yes, this method has been applied routinely to MODIS and VIIRS. But that in my view implies it’s the only way things are done, despite e.g. the ATSR, AVHRR, CERES references I provided which have similar (or longer) time series of data.

1. Line 233: In practical terms S_ε tends to be used not just for measurement uncertainty but the combination of measurement plus forward model uncertainty covariance. This may be worth noting. Mathematically, it doesn’t make a difference whether one puts only measurement error in S_ε (in which forward model parameterization uncertainty is normally put in another matrix often called S_b in Rodgers notation), or combines both measurement and forward model uncertainty. This is omitted from the equations and discussions here. See also my comment 11, which is my main issue with the paper as written.

1. Line 260 and elsewhere: the paper often refers to the “constrained” OE approach, kind of making it seem like the constraints are unusual or an innovation. In reality though every algorithm (including OE ones) are putting in constraints similar to this (state bounds). I’m not sure that the word “constrained” needs to be emphasized in the paper very much as it makes the reader focus more on that while in my view the novel aspect is getting at radius profiles in adiabatic clouds.

1. Line 276 and elsewhere: the residual/left side of L² norm is most commonly referred to as the “cost function” and often denoted capital italic J in the Rodgers formalism. For ease of readers comparing different references, I think it would be good to note these notation/terminology differences somewhere around here.

1. Line 286: for completeness, I’d add the equation for uncertainty estimate on the retrieved state here. Unless I missed it, it seems to not be included, and as part of the paper is talking about expected improvements from CPF I think it is worth including explicitly how this is calculated.

1. Line 335: the MODIS retrieval uncertainties used as the a priori uncertainty should be stated here, and a citation to where they came from added.

1. Sections 3 onwards: my main technical issue with the MODIS retrievals and simulated CPF uncertainties it that they are a realistic “best case” performance and this is kind of skirted over. The discussion more or less takes the only relevant uncertainty source as radiometric (sensor absolute calibration uncertainty and shot noise). Even if that were true, from my reading the calibration uncertainty is taken as spectrally independent. In reality it may be spectrally correlated (based on experiences with various space-based sensors) which affects downstream uncertainty characterization. But really, the main issue is the implicit assumption that the forward model (including its numerical implementation) is perfect which is inherently false (and semi-acknowledged by the fact the section 3 title includes “forward model assumptions”). These assumptions, as well as e.g. factors like lookup table interpolation precision, uncertainties in ancillary data (surface reflectance/albedo, gas columns), and non-calibration image artefacts (e.g. 3D radiative transfer effects, image ghosts, delayed impulse response after bright pixels), are often similar to or larger than absolute calibration uncertainty. And these can all have e.g. angular dependence and spectral covariation as well. So this is a big reason why retrievals are never as good as idealized sensitivity studies (as they rarely can take into account these factors). I understand this paper is a proof of concept and not a full operational algorithm. But I think it is necessary to acknowledge these issues seriously (I really doubt we can make our forward models good enough to take advantage of CPF’s radiometric calibration quality). Otherwise it feels like it is misleadingly over-hyping the CPF mission as folks who don’t work in algorithm development may well not be aware that radiometric quality is only one of the determining factors in retrieval quality. I wonder if somehow this discussion could be tied into the existing sensitivity studies (or new sensitivity studies). Maybe this could involve comparing MODIS retrieval uncertainties with the width of contours in figures 7 and 8 – I will leave this to the authors to decide how best to respond.

References:

• Heidinger, A. K., 2003: Rapid Daytime Estimation of Cloud Properties over a Large Area from Radiance Distributions. J. Atmos. Oceanic Technol., 20, 1237–1250, https://doi.org/10.1175/1520-0426(2003)020<1237:RDEOCP>2.0.CO;2.
  
  
  
  
• Minnis et al., "CERES Edition-2 Cloud Property Retrievals Using TRMM VIRS and Terra and Aqua MODIS Data—Part I: Algorithms," in IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 11, pp. 4374-4400, Nov. 2011, doi: 10.1109/TGRS.2011.2144601.

• Poulsen, C. A., Siddans, R., Thomas, G. E., Sayer, A. M., Grainger, R. G., Campmany, E., Dean, S. M., Arnold, C., and Watts, P. D.: Cloud retrievals from satellite data using optimal estimation: evaluation and application to ATSR, Atmos. Meas. Tech., 5, 1889–1910, https://doi.org/10.5194/amt-5-1889-2012, 2012.

• Sayer, A. M., Poulsen, C. A., Arnold, C., Campmany, E., Dean, S., Ewen, G. B. L., Grainger, R. G., Lawrence, B. N., Siddans, R., Thomas, G. E., and Watts, P. D.: Global retrieval of ATSR cloud parameters and evaluation (GRAPE): dataset assessment, Atmos. Chem. Phys., 11, 3913–3936, https://doi.org/10.5194/acp-11-3913-2011, 2011.

The other reviewer has provided an excellent summary of this study. Overall, I find this to be a meaningful contribution that explores the potential of CLARREO Pathfinder (PF) observations for advanced cloud remote sensing. However, in addition to the concerns raised by other reviewers, this study has a critical issue that must be addressed before publication: the failure to consider compounding factors—particularly sub-pixel inhomogeneity and three-dimensional (3D) radiative effects—that can significantly impact the retrieval of cloud effective radius (Re) profiles.

As outlined below, the influence of 3D radiative transfer effects and sub-pixel inhomogeneity on bi-spectral retrievals, and their implications for effective radius retrievals at different spectral bands (e.g., Re 2.1 µm vs. Re 3.7 µm), have been extensively studied and documented in the literature. Given these well-established issues, I do not believe the paper should be published unless they are thoroughly addressed.

Major Concern: Compounding Factors Affecting Retrievals

The fundamental principle underlying the retrieval algorithm in this study is that different spectral bands are sensitive to different vertical portions of a cloud layer due to their distinct vertical weighting functions, which arise from spectral-dependent absorption. However, spectral differences in retrieved Re values can also be attributed to other factors, such as sub-pixel cloud inhomogeneity and 3D radiative effects, which have not been adequately considered in this paper.

For example, Zhang and Platnick (2011) systematically examined the discrepancies in Re retrievals across different spectral bands. A key finding was that Re values retrieved using the 2.1 µm band tend to be significantly larger than those retrieved using the 3.7 µm band. This contradicts expectations based on vertical weighting arguments alone, as the 3.7 µm band, being more absorptive, should produce a larger Re value than the 2.1 µm band. However, actual MODIS retrievals show the opposite pattern. While CLARREO PF does not include the 3.7 µm band, the same biases due to sub-pixel inhomogeneity and 3D effects can still affect retrievals using the 2.1 µm and other bands.

Further, Zhang et al. (2012, 2016) demonstrated the impact of sub-pixel inhomogeneity on spectral Re differences (Re 3.7 µm vs. Re 2.1 µm). As shown in Figure 1 of Zhang et al. (2012), the retrieval look-up table (LUT) for Re 3.7 µm is more orthogonal and, therefore, less susceptible to sub-pixel inhomogeneity compared to the Re 2.1 µm retrieval. These findings highlight the need for this study to account for similar effects when evaluating CLARREO PF retrievals.

To strengthen the study, I recommend the following:

1. Use more realistic cloud fields in radiative transfer simulations.

   • The study currently focuses only on single vertical profiles of Re without considering horizontal cloud variations within and beyond a given pixel. This approach oversimplifies real-world cloud structures.
   • Ideally, large eddy simulation (LES)-generated cloud fields should be used as input for radiative transfer simulations.
   • At a minimum, simple "toy models," such as step clouds or randomly varying cloud fields, should be employed for sensitivity studies. For example, using a step-cloud case and applying a moving average with a 0.5 km resolution pixel would help emulate CLARREO PF observations and test whether the Re profile retrieval algorithm remains robust under spatially averaged radiances.

2. Include a dedicated section discussing compounding factors that introduce retrieval errors.

   • A thorough discussion should be added to explicitly address the effects of sub-pixel inhomogeneity and 3D radiative transfer.
   • The paper should explain how these issues could affect retrieval accuracy and describe potential strategies to mitigate them in the proposed retrieval algorithm.

3. Expand the discussion on key factors influencing even 1D retrievals.

   • The current study does not sufficiently account for several important factors that impact retrieval accuracy, including:
     • Sun-viewing geometry, which affects radiative transfer and retrieval sensitivity.
     • Errors in ancillary data, which are necessary for atmospheric corrections.
     • Surface reflectance effects, particularly over land and sun-glint regions, which can introduce additional uncertainties.
   • These factors should be explicitly discussed, along with their potential impact on retrieval performance.

While this study explores an important topic, its current approach oversimplifies real-world cloud conditions and neglects key retrieval challenges. Addressing sub-pixel inhomogeneity and 3D radiative transfer effects is crucial for ensuring the validity of the retrieval algorithm. Without such considerations, the conclusions drawn from the study may be misleading. I strongly recommend that these issues be thoroughly addressed before the paper is considered for publication.

This is a review on the manuscript entitled “Retrieving Vertical Profiles of Cloud Droplet Effective Radius using Multispectral Measurements from MODIS: Examples and Limitations” which deals with the retrieval of vertical cloud droplet effective radius profiles from multispectral measurements based on an adiabatic assumption. First, MODIS measurements are used and the retrieval results are compared to in-situ measurements from the VOCALS-REx campaign. A theoretical study then discusses the implications of the usage of more spectral measurements and measurements with a lower radiometric uncertainty.

In general, the paper is well written, mostly clear and good to understand. It also fits well into the scope of AMT and shows nicely how a reduced measurement uncertainty could improve the retrieval of cloud effective radii profiles from space. However, as already stated by the other two reviewers, I also think that the limitations of the retrieval method besides the measurement uncertainty should be discussed further before publication, in particular since this is also subject to the title. Hereby, I am missing the discussion on 3-D radiative transfer and partial cloud cover effects as well, which are known to impact spectral retrievals assuming 1-D plane parallel clouds. 

In addition to that, I would ask the authors to discuss the implications of the constraints made for the optimal estimation method in more detail and further that the “validation” of the retrieval using in-situ measurements is only valid in an idealized world in which the cloud conditions match the ones supported by the retrieval. Particularly, constraining the effective radius at cloud top to be larger than the one at the bottom and both to values smaller than 25 µm limits the retrieval to clouds which do not contain any precipitation formation. Precipitation formation occurs throughout the cloud, and is hence specifically relevant for the here presented retrieval of the vertical cloud effective radius profile. Further, even the cloud top radius can be influenced by drizzle formation. For example, Pörtge et al. (2023) found cloud top effective radii larger than 25 µm for a stratocumulus cloud while simultaneous radar measurements showed precipitating droplets. In addition, the here presented method is also based on the assumption of a relatively narrow monomodal droplet size distribution as it is common in the field. However, the presence of drizzle will lead to the formation of a tail in the distribution (e.g. Zinner et al., 2010; Zhang et al., 2012), which might be an additional factor limiting the retrieval and should be discussed and pointed out more clearly in the conclusions. After consideration of those aspects, I would recommend the publication of the paper.

I further want to address some more specific comments:

• l. 122f./Sec. 4.2: I was wondering why the authors did not simulate CPF spectra directly instead of the EMIT spectra? Since this part is a purely theoretical study, I think one could have used the CPF specifications directly to demonstrate how the smaller radiometric uncertainty and the usage of more spectral channels influences the solution space.
• l. 106f.: In agreement to the first referee, I also think that it would be valuable to introduce the CPF instrument in more detail. In particular, if I have not overseen anything, I am missing the number of spectral channels and the horizontal resolution, please add if possible. And is there a spectral dependence of the measurement uncertainty? If so, the implications for the retrieval should also be addressed in the discussion.
• l. 253: Are the partial derivative fractions presented only valid for the MODIS measurement uncertainty? And are they valid for all wavelengths? Please clarify in the manuscript.
• Table 1: In my opinion, it would be very valuable to add the resolution of each MODIS channel and the respective measurement uncertainty here.
• l. 323f.: Where do you see the shapes of the distributions from?
• l. 336f.: Perhaps there might be something which I did not understand correctly, but why are you using the 2.13 µm weighting function for the cloud bottom here? To my understanding of Fig. 1, the effective radius derived from that one corresponds to the smallest optical thickness of all channels considered?
• l. 375: Are the optical depths stated here derived from the retrieval? Please clarify, where those are derived from.
• Fig. 3: In my opinion, it would be nice to have the corresponding MODIS pictures and an indication where the measurements took place in addition to the profiles. This would give the reader an overall impression of the cloud situation and scenery. Moreover, the measurement times would be interesting to know for the solar geometry for which the comparisons have been made. And how long did it take for the aircraft to sample the profiles, what was the flight distance/spatial coverage of the in-situ measurements?
• l. 400f.: One common issue of the bispectral retrieval is the overestimation of the effective radius due to 3-D cloud radiative effects and broken cloudiness. Could this be a reason for the effective radius profile showing larger values than the in-situ measurements? Here, it would also help to have a visualization of the cloud scenery.
• Fig. 5: Please make a comment on the two spikes which are very pronounced in the blue line. Where do they come from? I suspect that they also influence the derived standard deviation and calculated range quite a lot.
• l. 484: What is the exact definition of “time difference” here? I guess the vertical profiles were sampled over some time as well, so when did MODIS pass over the scene and between which times were the profiles measured? Please clarify in the manuscript.

Technical corrections:

• l. 39: “and has been used to verify …”
• l. 270: “scalar”
• l. 357: “shown”

References:

• Pörtge, V., Kölling, T., Weber, A., Volkmer, L., Emde, C., Zinner, T., Forster, L., and Mayer, B.: High-spatial-resolution retrieval of cloud droplet size distribution from polarized observations of the cloudbow, Atmos. Meas. Tech., 16, 645–667, https://doi.org/10.5194/amt-16-645-2023, 2023.
• Zinner, T., Wind, G., Platnick, S., and Ackerman, A. S.: Testing remote sensing on artificial observations: impact of drizzle and 3-D cloud structure on effective radius retrievals, Atmos. Chem. Phys., 10, 9535–9549, https://doi.org/10.5194/acp-10-9535-2010, 2010.
• Zhang, Z., Ackerman, A. S., Feingold, G., Platnick, S., Pincus, R., and Xue, H.: Effects of cloud horizontal inhomogeneity and drizzle on remote sensing of cloud droplet effective radius: Case studies based on large-eddy simulations, J. Geophys. Res.-Atmos., 117, D19208, https://doi.org/10.1029/2012JD017655, 2012.

This manuscript presents a study on the retrieval of vertical profiles of the effective radius for non-precipitating warm clouds using multispectral solar reflectance measurements in the visible to shortwave infrared regions. Specifically, the study aims to retrieve three parameters: cloud optical thickness, the effective radius at the cloud top, and effective radius at the cloud base.

This study presents two key analyses. First, the three parameters are retrieved from the seven MODIS channels using a framework based on the optimal estimation method. The vertical profiles of the effective radius reconstructed from these parameters are then compared with in-situ measurements from the VOCALS-REx campaign. The second key analysis, based on simulations, examines how increasing the number of spectral channels and reducing the radiometric uncertainties can improve the retrieval accuracy of the three parameters. This analysis is particularly relevant to the upcoming CPF instrument, which will provide hyper-spectral imaging measurements.

This manuscript is generally well written and falls within the scope of AMT. While several previous studies have addressed similar issues, the results presented in this manuscript, particularly those in Figures 3, 7 and 8, provide valuable contributions to the scientific community、enhancing the understanding of this topic.

My major concern, as with other reviewers, is the retrieval bias introduced by subpixel-scale horizontal inhomogeneity and three-dimensional radiative transfer effects. These issues should be addressed in a dedicated section. The relevant previous studies have already been sufficiently cited in other reviewers’ comments. Even if the potential retrieval bias caused by these factors is significant, discussing it should not diminish the value of this study.

Below are my minor comments.

Minor comments:

• Abstract: The abstract should explicitly state that this study focuses on “non-precipitating warm clouds”.
• L15, “near-infrared”: This study utilizes the MODIS 1.6 μm and 2.1 μm channels. While these channels are generally considered part of the near-infrared spectrum, they are often referred to as "shortwave infrared" in research involving MODIS cloud retrievals. Since “MODIS” is mentioned in the title, it would be helpful to clearly specify the wavelength range included in “near-infrared” to avoid potential confusion.
• L150-152, Sect 2.1: Is aerosol scattering and absorption being ignored, or is it excluded from the retrieval variables but still accounted for in the radiative transfer calculations?
• “adiabatic assumption” for Eqs. (3) and (4), Sect 2.2: My understanding might be incorrect, but in the case of a well-known adiabatic cloud model (e.g., Bennartz, 2007; Merk et al., 2016), all supersaturated water vapor is assumed to condense, meaning the number of free parameters is imitated to two. Allowing three degrees of freedom, as in Eqs. (3) and (4), would correspond to a sub-adiabatic model, which assumes that the condensation rate is less than 100%. What is important is not the name, but the cloud microphysical reason why three independent parameters are allowed.
• L294: Is “the distribution width parameter, α” a parameter of the gamma distribution?”
• L296, “Cloud geometric thickness was set to 0.5 km”: The setting is acceptable in radiative calculations. However, in the (sub)adiabatic cloud models, the cloud geometric thickness H should be determined uniquely from the set of τ_c, r_top, and r_bot.
• L331, “the first seven spectral channels of MODIS”: Are the response functions of these channels taken into account in the forward calculation?
• L332, “because they deliberately avoid water vapor absorption, simplifying the forward model”: Are water vapor absorption and and Rayleigh scattering taken into account in the forward calculation?
• L376: Is it correct that 0.55 µm is being used?
• Figure 3: To verify horizontal inhomogeneity, it would be preferable to include the corresponding RGB images for these MODIS retrievals. At the very least, the latitude and longitude of the MODIS retrievals should be provided, allowing readers to check the images themselves.
• Figure 3: I recommend also showing the other effective radius (r_e,1.6) retrieved using 1.6 µm instead of 2.1 µm (r_e,2.1), which is included in MOD06, in Figure 3. r_e,1.6 may be able to sense the cloud particle size in a deeper depth than r_e,2.1.
• L401-405: To investigate why the case in Figure 3b performs worse than the other two, have you considered conducting a remote sensing simulation using the VOCALS-REx in-situ measurements?  That is, simulating MODIS reflectance measurements using the droplet size distribution obtained from the VOCALS-REx as input, and then retrieving τ_c, r_top, and r_bot using your algorithm.
• Section 4.2: Why are the EMIT specifications and wavelengths used in the simulation instead of CPF?
• Figure 7: Has it been discussed why this contour pattern appears, particularly why the uncertainties of τ_c and r_top - r_bot exhibit a negatively correlated pattern?
• L509: Please list the wavelengths of the 35 spectral channels used. It would be even better if they were presented along with the transmittance of atmospheric gases.
• L529-531, Sect. 4.2: Is assuming a radiometric uncertainty of 0.3% still reasonable, even when considering potential uncertainty in forward calculation, including uncertainties in given parameters such as gas absorption, surface albedo, and aerosols? Additionally, is this 0.3% uncertainty fairly defined in comparison to the 2% uncertainty of MODIS L1B?

[References]

• Bennartz, R., 2007: Global assessment of marine boundary layer cloud droplet number concentration from satellite. Journal of Geophysical Research: Atmospheres, 112, 32141, https://doi.org/10.1029/2006jd007547.
• Merk, D., H. Deneke, B. Pospichal, and P. Seifert, 2016: Investigation of the adiabatic assumption for estimating cloud micro- and macrophysical properties from satellite and ground observations. Atmospheric Chemistry and Physics, 16, 933–952, https://doi.org/10.5194/acp-16-933-2016.