the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Jul 2026
On the impact of a misestimation of the lidar ratio in the retrieval of the overlap function of an elastic/Raman lidar and a two-step explicit formulation of the overlap function retrieval
Abstract. In a relatively recent paper by the authors, an explicit (i.e. non iterative) formula was provided for recovering the overlap factor in an aerosol lidar equipped with a N2/O2 Raman channel close to an elastic one to retrieve the aerosol extinction coefficient. One of the advantages of that formula is that it allows for the estimation of the impact of an erroneous lidar ratio in the retrieved overlap function. In the cited paper, the equation that relates the retrieved overlap function to the true one and the error on the assumed lidar ratio was given with almost no proof, on the grounds that its derivation was “boring and cumbersome, but otherwise straightforward”. After having discussed that equation with some interested researchers, it turns out that its derivation is not perhaps that straightforward. Therefore, we provide here its derivation. As a subproduct of that derivation, we propose a streamlined, two-step explicit formulation to retrieve the overlap function.
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RC1: 'Comment on egusphere-2026-2703', Anonymous Referee #1, 17 Aug 2026
- AC1: 'Reply on RC1', Adolfo Comeron, 02 Oct 2026
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RC2: 'Comment on egusphere-2026-2703', Anonymous Referee #2, 23 Sep 2026
The previous paper of Comeron et al. 2023 and its extension in this paper are a quite significant contribution for the application of an overlap function for extending the useful range of the lidar towards the near range. The one-step procedure of the "daunting" Eq. (15) of the previous paper (now corrected as Eq. (4) in the present paper), that simplifies the iterative formulation shown in Wandinger and Ansmann (2002), is further simplified here with the two-step procedure in Eq. (5) of the present paper by employing with Eq. (8) the already widely used Raman inversion code introduced by Ansmann et al. (1992). A very important contribution is the formulation of the equation for the error introduced by the unknown aerosol lidar ratio and the extinction related Angström exponent between the elastic and the Raman wavelength.
The manuscript is ready for publication, but the following proposals might be considered:
Although the present improvement of the overlap retrieval is described as "streamlined" in the abstract, chapter 3 mentions an "alternative retrieval" and states: "... we have found a way ... other than the daunting Eq. (4) ...". This gave me the impression that the two papers provide different solutions, which is not true. In fact, to my understanding, the two retrievals are the same, but the calculation of beta_a0, that seems to be additional in Eq. (5), is embedded in Eq. (4) (Eq. (15) in the previous version), while it is done externally with Eq. (8) in the present version.
This equivalence should be made more clear.As already mentioned by reviewer 1, the assumption that the overlap function in the elastic channel is the same as in the Raman channel is critical. It should be mentioned that not only interference filters can have a considerable impact on the overlap function, but also the mechanical misalignments of the detectors and optical elements like lenses and apertures with respect to each other, and that these misalignments, as well as the transmission characteristic of the interference filters, are possibly subject to environmental conditions like temperature changes.
Hence the equality of the two overlap functions should not be blindly assumed, but should be verified with appropriate test setups.
It would be furthermore very helpful if the present error analysis could be extended in a follow-up of these two papers to include the impact of different overlap functions in the elastic and Raman channels.
The figures 3 and 4 of the previous paper give the impression that the differences between the overlap functions retrieved with differently assumed aerosol lidar ratios below about 300 m become small and negligible, but this seems only because the slope of the overlap functions is so steep towards the near range. This wrong impression could be corrected in the present paper.
Typos:In Eq. 4 in the fourth exponential term it should be "beta_m0(x)".
Line 53: probably O'(R) instead of O(R).
Citation: https://doi.org/10.5194/egusphere-2026-2703-RC2 - AC2: 'Reply on RC2', Adolfo Comeron, 02 Oct 2026
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Summary
This is a short and concrete follow-up paper of Comeron et al. 2023 showing how Eq. 7 has been obtained. The paper is almost ready for publication after dealing with some small technical issues.
General comments:
It would be of great value for error simulations and for RR applications to include in the overlap calculation technique the case where the overlap is not exactly the same for both the elastic and Raman channel. In most biaxial lidar systems, the angle of incidence (AoI) on the interference filter of the rays collected by the telescope changes fast with range until the distance of full overlap is reached. The transmission of interference filters used on every lidar channel changes with the AoI. This can introduce a “dichroic” overlap-like effect which, in contrast to the geometric overlap is expected to be different for each channel. Rotational Raman channels are especially sensitive to this effect as small shifts to the transmission spectrum determines which rotational Raman lines are attenuated. The effect can also be significant for elastic and vibrational Raman channels if very narrow interference filters (bandwidth < 0.5 nm) are used.
This comment is rather a recommendation to the authors to improve the scientific importance than a critical missing aspect of the paper. The paper can already be published in its current form.
Specific comments:
Line 14: Is this a rotational or vibrational channel? Single channel or 2 different channels? If single, why both gases are mentioned?
Line 54: The term β_mR / β_m0 can be, in fact, slightly dependent on the temperature because of the temperature dependence of the cross-section of the rotational Raman (RR) lines in combination with the transmission of the interference filter. The interference filter is often not taken into account in the lidar equation. Adam et al. 2009 and 2012 showed that the temperature dependence is generally small enough to be considered negligible for elastic channels. I suggest to refer to those papers here and rephrase the text indicating that the range dependence is negligible. The temperature dependence of β_mR should be also small for vibrational Raman channels. For RR channels temperature effects can be introduced if the filter is not configured properly so that cross-section changes at the transmitted lower J lines are compensated well by the higher J lines.
Eq 5: I have repeated the calculations mentioned by the authors (substituting Eq 3a and 3b in Eq 4) and I can confirm that they result to Eq 5. It might be worth showing how the last exponential term of Eq 4 becomes much simpler after substituting X and X_R (showing that the integrals from 0 to x and from x to R_m add up to an integral from 0 to R_m which is constant and can get out of the double integral). This part requires some “imagination” and might not be straightforward to all readers. The rest of algebraic calculations are straightforward.
Eq. 7: Please mention the equivalent equation from Comeron et al. 2023
Technical comments:
Eq 3a: Please change β_αο to β_α0
Eq 4: Please change β_mο to β_m0 in the second exponential term