the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Producing aerosol size distributions consistent with optical particle counters measurements using spacebased measurements of aerosol extinction coefficient
Abstract. Stratospheric aerosol has been observed by several longlived observational systems. These include the University of Wyoming series of balloonborne optical particle counters (OPCs) (1971–2020) and the Stratospheric Aerosol and Gas Experiment (SAGE) series of instruments and particularly SAGE II (1984–2005). Inferences of aerosol surface area density (SAD) and volume density are straightforward using data from OPCs. Conversely, many numerical methods to infer size distributions and SAD have been applied to SAGE II observations but all are limited by the low information content of the SAGE optical measurements. We have developed a new method that uses OPC observations to constrain SAGE II inferences of aerosol properties. We start by noting that whatever the details of the underlying size distribution, the SAGE II measured aerosol extinction coefficient ratio (525 to 1020 nm) must reflect the shape of the underlying aerosol size distribution for particles that dominate the extinction coefficient values (roughly radii from 0.1 to 0.5 μm). Since this extinction ratio can be easily calculated from OPC measurements, we use the OPC size distribution measurements, across a broad range of aerosol levels from background to highly volcanic, to compute the associated 525 to 1020 nm extinction coefficient ratios for each measurement. We then sort the OPC measurements by these ratios (across a range of roughly 1 to 6) into discrete ratio bins and derive mean bimodal lognormal size distributions for each bin using a particle swarm optimization. These fits can be applied to SAGE II observations without the need for further retrieval calculations effectively producing an OPClike product consisting of the six bimodal parameters for all SAGE II observations. This method successfully captures the median behavior of the OPC inferences of bulk parameters like aerosol surface area and volume density, although we also observe a significant altitude dependence particularly in the lower stratosphere. In addition, there are occasional deviations of surface area density from the fit behavior by as large as a factor of 10 for individual OPC measurements of SAD, almost exclusively due to a broad range in particles below 0.15 μm. The presence of such particles is effectively invisible to extinction coefficient measurements such as those by SAGE II.
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RC1: 'Comment on amt202462', Anonymous Referee #1, 29 May 2024
This paper uses WOPC measurements to parameterize bimodal lognormal parameters from 525 and 1020nm extinction measurements. The dependence and variability of surface area and volume with extinction ratio is explored. This has applications for extending climatologies such as GloSSAC or more generally deriving microphysical parameters from limited remote sensing measurements. The generalizability is somewhat limited by the use of measurements in the Northern midlatitudes only, but presumably this work can be extended or validated with additional measurements at other latitudes in the future. The limitations and possible solutions to the lack of aerosol particle size information is an important topic and this work is a contribution to that effort. It is clearly written and after minor corrections/additions I would recommend publication.
General Comments
 The section on information content seems somewhat underdeveloped. I appreciate the authors intent on clarifying why only two pieces of information are available, but this was shown in a more mathematical formulation by Thomason and Poole (1993). I would recommend clarifying what this analysis adds, or at least referencing that paper.
 As noted by the authors a limitation of the SAGE II data is the reliance on a single mode lognormal assumption to determine SAD/VD. However, the WOPC SAD/VD retrieval also makes a lognormal assumption. Is the insensitivity of SAGE to small particles the important consideration, or is the difference between a single vs bimodal fit the important distinction? See comment about Line 220 for more details.
 I don’t understand the choice of a particle swarm algorithm to determine the bestfit parameters in Figure 5. I’m left wondering why the authors didn’t take the mean counts in each WOPC bin and fit a bimodal distribution to that using the standard WOPC algorithm.
Specific Comments
Line 19: “…almost exclusively due to a broad range in particles below 0.15 µm…” This cutoff of 0.15µm is not well substantiated in the paper. The WOPC have limited information below this value as well except for the condensation nuclei measurements (which are not always flown?).
Figure 2: Is the dotted line the relative or absolute uncertainty?
Line 101: If I understand correctly, it is the variance between the predicted and measured 452nm signal that is important (as the absolute difference depends on the extrapolation model). However, I don’t see this variance plotted in Figure 2, only the difference so I’m not sure how to interpret this figure.
Line 143: I think reference to Boone et al. (2023) is appropriate here.
Eq. 7: Should “particle value” be “parameter value”?
Line 220: While small scatterers do not directly contribute to SAGE measurements, if the lognormal assumption is correct, it seems they should be reflected in a change to the lognormal parameters. Is there a way to add small scatterers that changes the shape of the lognormal in a way that SAGE is insensitive to? Otherwise, if the small scatterers are present in a way that does not follow the lognormal distribution, what impact does this have on the WOPC retrievals, and the SAD/VD parameters derived here? (Also "poor scatters" > "poor scatterers")
Line 236237: Does neglecting unimodal conditions have an impact on potential SAGE II conversions? E.g. are unimodal fits more prevalent in background conditions biasing these SAD/VD conversions to more elevated aerosol levels, etc?
Figure 6: What parameters drive the SAD/VD dependence on extinction ratio? Perhaps it is just the plotting, but there seems to be little dependence on the lognormal parameters and mode fraction above extinction ratio values of 23 while the SAD/VD relationship remains clear.
Citation: https://doi.org/10.5194/amt202462RC1 
RC2: 'Comment on amt202462, additional figure to support conclusions?', Anonymous Referee #2, 12 Jun 2024
General comments:
The paper introduces a method to derive aerosol surface area and volume densities with a bimodal distribution parameterized on the basis of OPCdata from SAGE II extinctions.
The 2 modes presented in Figure 3 derived from the WOPC are shifted to smaller radii compared to the classical accumulation and coarse modes. A remark on and why that, and on the quantities listed in the legend, should be added. The values differ considerably from the swarm and median values in Figure 5. How many data points went into the optimization procedure?
In the paragraph beginning in line 294 a crossreference to Figure 4 with some text might be useful. An additional frame in Figure 7 showing the surface area (SAD) provided in SAGE II data on NASAEOSDIS in the same latitude region would demonstrate the improvements achieved by the new method. This can be also a line plot at some altitude (e.g. 18km) including the time series of the WOPC derived SAD and the one from SAGE II using old and new methods.
Specific comments:
Line 37: Already here and maybe also in the abstract SAGE III should be mentioned since the presented approach is applied to GloSSAC later in the text.
Fig.2 and lines 101ff: The discussed variance is not shown or is there a language problem?
Eqns. 3 and 4 both refer to channels. Why is there a different notation for 'N'? In Eqn.4 a 'j' is missing under the summation sign. It might be also not necessary to use 'a' instead of 'r' in the definite integrals.
Lines 241 and 279: Here 5 parameters are mentioned, in the abstract 6. Please add a clear remark why there is a difference.
Figure 7: Why is the plot not to the end of the SAGE II observations where clear volcanic signals are visible?
Line 306f: I suppose that here extinction data using SAGE II, CLAES, HALOE and groundbased instruments (Lidar) are used. It might be useful to include these details.
Technical corrections:
Line 87: 'λ' missing? Inconsistent to Figure.
Line 94: What is the correct wavelength? Inconsistent to Figure.
Line 221: Typo.
Eqn. 7: Typo?
Labels in figures often too small.
Figure 7: Please include the color steps in the figure in the color bar. Less steps would be better for identification of events.
Lines 398, 400: Use upper and lower case for journal name.Citation: https://doi.org/10.5194/amt202462RC2 
RC3: 'Comment on amt202462', Anonymous Referee #3, 13 Jun 2024
In the paper “Producing aerosol size distributions consistent with optical particle counters measurements using spacebased measurement of aerosol extinction coefficient”, the authors N. Ernest, L. W. Thomason, and T. Deshler describe a method for deriving bimodal lognormal aerosol size distributions (ASD), aerosol surface area densitys (SAD), and volume density (VD) from SAGE II measured aerosol extinction coefficient ratios (R) using Wyoming balloonborne otical particle counter (WOPC) measurements. Due to the lack of data availability, the method is limited to latitudes around 45 °. This limitation is clearly mentioned by the authors, as well as the altitude dependence of the method and the fact that the approach cannot capture the full variability of the derived parameters as measured by WOPC. Despite these limitations, this work contributes to the acquisition of information on the properties of stratospheric aerosols. I recommend this work for publication after a minor revision.
This work is clearly written. In some cases, longer sentences could be shortened to improve reading comprehension. Nevertheless, I have some basic questions that should be answered more clearly in the manuscript:
1) Why is a particle swarm optimization algorithm used to infer ASD from R and not – what would be simpler – an empirical relationship between the median ASD and R?
2) There is only a marginal dependency between ASD and R. It is therefore questionable to derive a relationship from this. In contrast, the dependency between SAD/VD and R is strong. So, why is the ASD infered from R and then used to calculate SAD and VD? Why are SAD and VD not derived directly from R?
3) Why is there a strong dependency between SAD/VD and R (Fig. 6), but a weak dependency between ASD and R (Fig. 5)?
4) On what basis was the intermediate altitude level (19 km19.5km) chosen?
Specific comments:
Line 5: “by the low information content”  please specify.
Line 37: Please indicate the name of the data record.
Line 57: “While both modes do not necessarily contribute significantly to a computed aerosol extinction coefficient at SAGE II wavelength…”
Both modes contribute to the aerosol extinction coefficients. However, do the authors wanted to point out that the calculated aerosol extinction coefficient assuming a bimodal size distribution does not differ significantly from the aerosol extinction coefficient assuming a single size distribution?
Line 61: Please specify “things”.
Line 86: Please indicate the refractive index, temperature, and (?) water wapour content, at least in the figure caption.
Line 109, Figure 1: Was only one Angstrom coefficient calculated and used to calculate all extinction coefficients at 452 nm? Or was individual Angstrom coefficients determined from each measurement and used to calculate the extinction coefficients? If the latter, why does the Angstrom extrapolation work better in some altitude ranges than in others? Can reasons be given for this?
Line 130: limb measurements → occultation measurements?
Equ. 3, 4: Description of parameter “a” is missing.
Equ. 5: “r” should be “a”?
Fig. 3: Numbers and parameters in the legend need appropriate descriptions.
Line 216: “infer SAD from SAGE II measurements”. Should rather be “infer SAD from R” because “SAGE II measurements” could mislead the reader since Fig. 4 shows WOPC data.
Line 229: “under some conditions total volume estimates can be inferred”. Which conditions?
Line 243: Can the authors briefly describe what a particle swarm optimization algorithm does in physical terms?
Equ. 6, Line 249:
 Are r_..., s_..., f_err, and R*w absolute, i.e., positive values?
 I think r, s, f, and R are not the two mode radii, widths of modes, ratio, and the center of an extinction ratio bin, respectively, but the ERRORS of these values.
 r, s, and f have different values depending on the numerical range of the corresponding parameters. Shouldn't a weighting factor be built in that weights the parameter errors accordingly? Can they be weighted equally? Or should errors in r, for example, be weighted more heavily than errors in s?
Line 278: Typo: Figure 5
Line 299: “SAGE measurement”. Should be WOPC measurement, since only WOPC data are shown.  Or do the red lines in Figs. 5 and 6 show the results using SAGE II aerosol extinction ratios?
Citation: https://doi.org/10.5194/amt202462RC3
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