General comments
I appreciate the time and effort the authors invested in revising the manuscript. However, despite these efforts, the central methodological concern raised in my initial review has not been addressed. Moreover, a substantial part of my previous comments on this issue appears to have been ignored, with little to no modification of the relevant text. This represents a major methodological flaw that must be either properly justified or, at minimum, thoroughly discussed.
For clarity: in its current form, the manuscript cannot be recommended for publication. Addressing the concerns outlined below is essential and would, in my view, allow this otherwise strong and potentially impactful work to be considered after major revision.
I elaborate below on the primary unresolved issue, which concerns the justification and use of the aspect ratio distribution in the retrievals. The logic used by the authors to motivate this choice is problematic and, as currently presented, insufficient.
1. Lack of justification and documentation of the empirical distribution
The empirically derived aspect ratio distribution (“red curve” in Fig. 5) is not discussed in any of the studies cited in line 343, notably Torres et al. (2018, 2020) and Ahn et al. (2021). The parameters of this distribution are not specified, and the methodology used to derive it remains unclear. In fact, the derivation of such a distribution is a topic of sufficient importance that it would normally warrant a dedicated publication. Without a clear description and justification, its use in the current study is not adequately supported.
2. Inadequate motivation based on median aspect ratio
The argument provided in lines 320–335, based on median aspect ratio values, does not justify the choice of the proposed distribution. Visually (“by eye”) and given that the aspect ratio kernels used are symmetric, the median of the proposed distribution appears to be 1. More importantly, selecting a distribution based solely on its median value is non-unique and does not constrain the distribution shape in any meaningful way.
3. Inconsistent interpretation of prior literature and unsupported claims
In lines 293–305, Torres et al. (2018) is cited as showing that moving from spherical to non-spherical particles improves the OMI asymmetry issue (referred to as an “anomaly”). In contrast, the present manuscript suggests moving back toward more spherical assumptions, claiming (without supporting evidence) that this further improves the asymmetry. At the same time, counterexamples provided in my initial review, where similar instruments are treated with different retrieval methods using unmodified non-spherical shape distributions and do not exhibit such asymmetry issues, were ignored.
This raises the question of whether the observed asymmetry is truly an instrumental issue (e.g., OMI-specific), a limitation of the retrieval methodology, or due to other factors. Within the scope of this paper, it cannot be uniquely attributed to particle shape. While it is possible that the shape distribution proposed by Dubovik et al. (2006) is not optimal in all situations (e.g., its known limitations for the P22 element in backscattering directions), these issues are unrelated to OMI, TROPOMI, or EPIC viewing geometries. Fine-tuning a well-established shape distribution to compensate for a specific instrumental or retrieval artifact is not an appropriate basis for defining a globally applicable dust shape model across different sensors.
4. Internal inconsistency in assessing the impact of shape assumptions
The manuscript presents conflicting statements regarding the impact of the aspect ratio distribution. On the one hand, lines 314–318 state:
“Despite these differences, the corresponding retrieved SSA (black and red) show a close agreement—indicating that the choice of aspect ratio distribution didn’t play a significant role in the inversion at least for these three dust events.”
On the other hand, improved agreement with AERONET SSA at 440 nm is later used to justify the modified shape distribution (line 347):
“Incorporating these empirically derived aspect ratios into the aerosol LUT significantly improved the agreement between the retrieved SSA at 440 nm from the MFRSR and corresponding AERONET inversions.”
If the MFRSR and AERONET retrievals share more similar assumptions, closer agreement in SSA would be expected. Under this logic, adopting the AERONET shape distribution should have yielded the best SSA(440) agreement, which is not demonstrated. Furthermore, shape is not the only inconsistency between the two methods. Differences in gaseous absorption corrections (notably at 440 nm), surface reflectance assumptions (Ross–Li BRDF in AERONET versus Lambertian surface here), and the substantial redevelopment of the MFRSR retrieval core since Krotkov et al. (2005b), including the introduction of LUTs (line 403) instead of the original iterative approach, all may contribute to the observed discrepancies.
These factors must be systematically examined before concluding that the observed SSA(440) bias (with a reported mean difference of ~0.01 over ~180 observations at a single site) is primarily driven by particle shape, let alone before proposing that the Dubovik et al. (2006) shape distribution should be replaced by the empirically derived one.
Recommendations
To address the issues above, I strongly recommend the following:
1. Quantitative assessment of aspect ratio impact
Add an explicit estimate of the impact of the aspect ratio distribution to Table 3, analogous to how the effects of other assumptions are evaluated. Given that the primary novelty of this work lies in the treatment of non-spherical particles, a rigorous and isolated assessment of the shape distribution impact is essential. Numerical tests are particularly important, as real datasets may contain confounding factors.
2. Validation using synthetic datasets
Demonstrate the ability of the retrieval to reproduce known inputs using synthetic datasets. This should first be done for spherical particles to avoid ambiguity introduced by aspect ratio assumptions. There is a non-negligible possibility that the retrieval itself introduces bias, which is then partially compensated by tuning the shape distribution.
Specifically, please perform forward simulations using AERONET-consistent inputs (including the imaginary refractive index) and retrieve k and SSA under identical and systematically varied assumptions: spheres, AERONET aspect ratio distribution, and the proposed empirical distribution, across different aerosol loadings. The results should be discussed in detail. If all assumptions are identical, the retrieval should reproduce the input SSA exactly.
Minor comments
• Throughout the manuscript, the term “retrieved” is used for SSA obtained from the MFRSR technique. Strictly speaking, only the imaginary part of the refractive index is retrieved, while SSA is subsequently estimated based on additional microphysical assumptions. Please consider rephrasing accordingly. The same applies, to some extent, to AERONET. Given that much of the analysis focuses on SSA, it would be more consistent to also compare the retrieved imaginary refractive index k (as was done with SSA in Figs. 11 and 12).
• Line 355: “derived aspect ratio distribution was simulated using a modified, substantially faster version of the Light Scattering…” Faster compared to what? The original DLS implementation? As already noted in my previous review, the description in the Appendix indicates that the DLS package was not used in an optimal configuration. Under these circumstances, performance comparisons are not meaningful, especially since computational efficiency is not the focus of this study. An analogy would be outperforming a high-performance system that is improperly configured, this does not constitute a meaningful benchmark. Please revise this wording.
• Lines 742–743: “Next, DLS relies on a computationally expensive cubic spline for interpolating the fixed kernels k…” This statement is incorrect. Spline interpolation is an optional setting in the DLS software. Linear interpolation is also available and is the most straightforward option. It is unlikely that AERONET would rely on an unnecessarily inefficient DLS configuration. Moreover, spline interpolation may have been introduced to mitigate interpolation errors for coarse spherical particles, which could be particularly relevant given the proposed empirical shape distribution includes substantial amount of spheres.
I recommend providing a comparison of SDLS outputs against independent Mie calculations for spherical particles to rule out interpolation-induced biases as a possible contributor to the observed SSA discrepancies.
Finally, I emphasize that it is entirely acceptable to fork and adapt scientific software to suit specific retrieval needs, provided appropriate references and acknowledgments are given, and the authors have clearly invested significant effort in this regard. However, the justification for such developments should not rely on mischaracterizing or implicitly discrediting the original implementation, particularly when it may not have been used under optimal or representative settings. I strongly encourage the authors to revise the SDLS discussion, especially lines 740–750, to ensure factual accuracy and a balanced presentation. |
General comments
Article presents a multi-instrument L2 synergy to estimate absorption of desert dust particles from ground-based observation in the UV spectrum, providing data on dust that are of high demand by the scientific community. Article is well structured, with good English, however some methodology description parts could be improved. I also have several concerns about some statements, notably related to the assumptions of shape distribution used on the dust particles, and its impact on the retrievals not fully justified. Below I address these issues in details, and would recommend a major revision to streamline the work presentation, and make the teams’ impressive results really shine.
Major comments
Section 3.2:
I found the whole approach of particle shape justification rather questionable.
First of all, authors suggest different shape distribution, that is quite badly justified, instead of one that was explicitly designed for the observations they use in their synergetic retrievals. Satellites and ground-based observations work in different scattering angle ranges.
Dubovik et al., 2006 and AERONET uses spheroidal model ONLY in a combination with spheres, where spheroidal particles represent an extreme case of non-spherical particles, and the fraction of spheres is the parameter that is fitted from sky observations and it is never 0. Why not use that one observed by AERONET, instead of basically turning shape distribution inside out and creating inconsistency between different parts of synergy?
Lines 300-315: I would also insist that aspect ratio distributions of a spheroidal model doesn’t necessarily (actually quite definitely not) have something to do with the aspect ratios of actual particles, it is an extra dimension in the model, that allows modelling scattering with something that is compatible with spheres but at the same time is not spherical, the only connection to the reality it has are the observations it fits. And these were scrumptiously selected and precisely in-situ measured scattering matrices (all six elements of them). Not like OMI that possibly has some sensitivity to P11 elements in forward and backward direction. I would also like to emphasise that the model of dust described in Lopatin et al., 2021, uses same shape distribution of spheroids as suggested in Dubovik et al., 2006 and was successfully used in a large variety of satellite retrievals, including multi-angular polarimeters (e.g. Chen et al., 2020), and S5p/TROPOMI (which shouldn’t be that far from OMI) (Chen et al., 2024; Litvinov et al., 2024) and ground-based observations as well their synergetic combinations (Litvinov et al., 2025) without any modifications, and no biases over dust dominated areas were observed so far. No matter what referenced studies claim, applicability of dust samples shape analysis to an idealisation developed to be applicable to a large bulk of non-spherical dust particles, in general, has little to no support.
Additionally, I found usage of OMI as justification of dust shape distribution rather confusing, above it is indicated that OMI is used only for trace gases’ corrections. The impact of AERONET using one shape distribution, OMI using another, retrieving gas correction using these assumptions, and then SSA retrieved from another observation should be better studied, there are possible biases that propagate from one instrument to another due to the differences in such assumptions, please discuss.
Authors did compare retrievals with AERONET shape distribution (under 0% spheres assumption in the mixture), and frankly, statistically the observed differences are not very convincing, it is a rather small dataset with validation changes not very significantly different from the retrieval accuracy. More on that below.
Lines 366-370: “A total of 21 bins of aspect ratio distribution ranging from about 0.4 (oblate) to about 2.5 (prolate) are prescribed with associated weighting factors shown as the red curve in Figure 5. The 22-bin volume size distribution of AERONET was used as direct input to the SDLS package. Using these parameters as input, the phase matrix elements were simulated at a total of 181 scattering angles at a 1-degree resolution.”
Did authors compared at 440 nm with AERONET provided phase matrices? These will include a “proper” mix of spheres and spheroids that fits the almucantar observations. Also, it would be a nice exercise to see the AERONET provided phase functions for several cases and ones calculated using same refractive index, PSD but using the suggested shape distribution. Ideally simulate almucantar observations to compare the fits. If fitting difference are not that substantial, it also can provide additional justification of the proposed method. Possibly fits of the shorter WL will be even better with updated shape distribution.
In general, it would be also nice to see validations of AODs estimated using the retrieved absorption, and assumed size/shape distribution and real refractive index in UV with AERONET observations (e.g. 340 and 380), I believe Izana should had several CIMELs capable of providing such data.
Also, I got completely lost how LUT’s are generated/used. Are they dynamic and depend on AERONET due to the multiplication factors? Are they static and calculated to a specific grid? Please, provide more details.
Minor comments
Line 246: “inversion parameters of PSD and the real part of the refractive index” it is not clear how the real refractive index is extrapolated to UV, please clarify
Line 373: “The vertical profile of aerosols is assumed to follow the Gaussian distribution with the peak concentration at 3 km.” Any particular reason to use this profile? And 3km is above sea level or Izana station? And what half width was assumed?
Line 380: “The entire inversion procedure was applied to each of the five wavelengths of the MFRSR independently.”
Was spectral dependence controlled in any way? Are there any examples how spectral behaviour of such retrievals looks like? Is it reasonable? Has it spikes, does it have a trend? Would be nice to see plots of examples of full spectrum imaginary refractive index, combined with AERONET data just to have a glimpse what could be expected from dust using this technique.
Line 390: what retrieval is considered a “success”? Please, clarify. Are they treated case-wise or wavelenth-wise, for e.g.? If one channel “failed” is all retrieval discarted?
Lines 433 – 439, Line 550: I’m not sure such comparison is rather fair. First of all as mentioned above there should be certain persentage of spherical particles retrieved by AERONET, so the distribution won’t be exactly as in Dubovik 2006, and maybe be somewhat closer in resulting phase function to what authors suggest. Also it is not clear do they compare sucessed cases of their retrievals only or all of them, maybe choise of shape affect success rates? Also I’m confused how method using the same refractive index, same psd and as claimed same shape distribution as in AERONET (case a) shows bias with AERONET retrieval itself, I mean these SSA values retrieved under exactly the same assumptions, it is clear that the shape distribution can’t be the not only reason in that case.
Figure 12-13: Why wishers are so much bigger for July-August? Please discuss
Line 482-485: “the imaginary part of the refractive index and AAOD both exhibit a weak spectral trend in the visible to near-IR region (AERONET) but a distinct increasing trend towards shorter UV wavelengths—a typical and expected spectral absorption behavior of coarse-mode dust aerosols” if I understood correctly “multipication factors” in table 2 there’s little to no chance that method will retrieve imaginary part of refractive index below the one of AERONET, and it seems that a trend for decreasing absorption with wavelengths is kinda “bult-in” through these factors.
Table 2: It is not clear how “multiplying factor” are used actually these are iportant and not mentioned anywhere else. It is a significant flaw in method description. Also if imaginary part of refractive index is retrieved a a factor to AERONET it is not completely clear how LUTs are generated, are they individual for every case? Or it is the factos that are retrieved, please, provide a more comprehensive description of this part of the method. And why such specific selection of factors? They are quite different for the UV and blue for e.g.
Line 657: “The original FORTRAN code was translated to C/C++, as this work was initiated as part of translation of MAIAC’s (Lyapustin et al., 2021) polarized radiative transfer solver IPOL (Korkin and Lyapustin, 2023) from FORTRAN into C.”
It is not clear which translation is mentioned, was code manully re-written in C? FORTRAN and C share compliler and their translator makes same pseudocode for further compilation, this doesn’t affect the speed of execution.
Generally the whole Appendix part of the DLS package modifications looks a bit weird to me. Especially for a user of DLS package. It looks like the package wasn’t used in the optimal way, and instead of changing several parameters in the it was re-written… I presume the explicit permissions for such code use were provided.
Majority of statements are either not directly related to the DLS package performance, but rather to the use case that was not optimal, FORTRAN and C binds naturally so the whole C translation for the performance looks a bit superficial.
Lines 639-644: it is not clear why loading kernes was such an issue, since they can be loaded once and then every-minute retrieval be performed with all the matrices already loaded. I do understand that binary format is more practical and faster, but after all reading could be done only once per large retrieval sample. And if compared to radiative transfer computational efforts, kernel reading and even interpolations shouldn’t be such a performance issue… Besides authors keep saying that LUTs containing imag parts were used for the retrievals, i.e. multiple running and reading of phase functions kernels as well as RT calculations for different imaginary parts supposedly was done only once, and then LUTs were re-used, or I’m missing something, please provide more details on this.
I’m no expert in this, but I believe a clear statement that original DLS package re-use was done with explicit permission of its authors is required in this appendix or proper authorship affiliations should be provided in the linked repository. Otherwise it gives a rather weird feeling to say the least. For e.g. git repository contains binary kernels that contain transformed information from the text files of the original DLS package without any authorship affiliation nor licence mentioned, and due to this transformation (which to my understanding is not completely justified, see above) these can’t be automatically compared. To be frank, these are the essence of the package, non-spherical part being the important improvement in this study, and making these from scratch is not as easy as loading and interpolating between the already calculated nodes. And the only “link” with the kernels authors in repository with its authors is an image, representing a screen shot of the original article in the doc section… I encourage authors to make the coding contributions more transparent and suitable for automatic affiliation research. Ideally, publish the code that converted kernels to binaries with proper link to the original kernel repository.
Technical comments
Line 117: “multiple” I’d suggest replacing with “five”
Line 121: “these wavelengths”, are these 6 or 5?
Line 392: “higher AERONET SSA”, please provide wavelength, is it 440?
Figure 8: Consider making it double Y plot with AOD on the right, it is bit messy, too many fine text in color around points, quite hard to analyse.
Line 431: “440 nm to 325 nm” I would suggest “325 to 440” this way it will be clearer where trend increases.
Figure 11: Consider making text bigger, and what are these tiny numbers below?
Figure 12-13: Generally hard to follow spectral and temporal dependencies and the font is rather small and hard to read, is there a better way to present these data?