the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 May 2026
On the origin of the twilight color index maximum and its application to cloud-height retrieval
Abstract. A number of previous studies have demonstrated the capability of detecting high-altitude clouds during twilight using the color index (CI), defined as the ratio of zenith intensities at two different wavelengths, typically selected in the visible range or near infrared (NIR). When high clouds are present, a maximum or minimum (depending on the wavelengths selection) is observed in the CI signal (Sarkissian et al., 1991; Toledo et al., 2016). These studies also showed that the solar zenith angle (SZA) at which the CI maximum or minimum occurs (SZAmax) strongly depends on cloud altitude, enabling cloud-height retrieval through comparison with radiative transfer (RT) simulations. Twilight conditions require RT simulations in spherical geometry, which are computationally expensive. In this work, we introduce a single-scattering formulation of the CI that provides a physically transparent framework for identifying the mechanisms that determine the SZA of the CI maximum and, consequently, the inferred cloud altitude. The simplified formulation is explicitly compared with Monte Carlo RT simulations in spherical geometry and is shown to accurately reproduce the behavior of SZAmax over a wide range of conditions relevant for high-altitude clouds. In particular, the model provides reliable cloud-height estimates for cloud optical depths up to τC ≲ 0.3. Within this single-scattering formulation, we demonstrate that SZAmax occurs at the SZA for which the relative SZA-variations of the zenith intensity at the two selected wavelengths become equal, thereby explaining the emergence of the extremum in differential terms. However, achieving a well-defined CI extremum requires selecting two wavelengths with sufficient spectral separation, typically spanning distinct regions of the visible--NIR spectrum. To overcome this spectral dependence, we introduce a Rayleigh-referenced color index (CIR), defined as the ratio between the measured zenith intensity and the corresponding intensity expected for a purely Rayleigh-scattering atmosphere at the same wavelength. This index reproduces the characteristic extrema associated with high-altitude clouds while requiring simulations and observations at only a single wavelength. The proposed formulation facilitates extensive sensitivity studies and provides greater flexibility in spectral selection, particularly in regions affected by gas absorption.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(5435 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(5435 KB) - Metadata XML
- BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2026-2295', Bernhard Mayer, 10 Jul 2026
- AC1: 'Reply on RC1', Daniel Toledo, 29 Jul 2026
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RC2: 'Comment on egusphere-2026-2295', Anonymous Referee #2, 23 Jul 2026
The manuscript presents a simplified formulation to reproduce and understand the behavior of the color index (CI) at high solar zenith angles (SZA) in the presence of optically thin high-altitude clouds, such as polar stratospheric clouds, without the need to solve the full radiative transfer problem. Based on the improved mechanistic understanding, a new so-called Rayleigh-referenced CI is introduced, defined as the ratio between the measured zenith intensity at a single wavelength and the corresponding intensity expected from a purely Rayleigh-scattering atmosphere. The method is verified and tested across a range of relevant parameters using comprehensive spherical radiative transfer simulations.
The work aligns well with the scope of AMT, and I recommend publication after addressing the following minor points.
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General comments
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The manuscript is submitted by a single author, yet the text consistently uses the first-person plural ("we"). To enhance clarity and conform to standard academic conventions, I recommend adopting a more neutral tone throughout. For example, in line 7:
“In this work, we introduce ….” -> “In this work, .… is introduced.”The definition of z_dark (ll. 117–119 and 180–187) is not entirely clear. As I understand it, z_dark refers to the lowest altitude illuminated by the Sun. However, the text describes it as an upper threshold. Please clarify the exact meaning of z_dark and its usage in the formalism. If possible, include z_dark in Fig. 1 to improve illustration and interpretation.
Given that high-altitude clouds have primarily been studied in remote regions using the color index method, how strongly does the absorption by NO2 (and also O3, H2O) affect the cloud height retrieval if the chosen wavelength pair is suboptimal? Please comment on the expected magnitude of such effects (Sect. 3.4 / Fig. 7).
The manuscript contains a number of valuable contents, but the main achievements – namely, the mechanistic explanation of the CI maximum and the derivation of a new single-wavelength formalism for detecting high-altitude clouds – get a little bit lost in the overall length and technical depth. I recommend overthinking the paper’s structure to better highlight these novel findings. Consider shortening the more mathematical sections in the first half of the manuscript or moving the detailed derivations to an appendix.
Finally, the conclusions would benefit from a broader outlook. How does the proposed Rayleigh-referenced CI advance our understanding of high-altitude cirrus and polar stratospheric clouds compared to previous approaches?
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Specific comment and technical corrections
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l. 22: “Clouds play a major role in Earth climate system” -> “Clouds play a major role in the Earth’s climate system”
l. 35: “heterogeneous reaction that provide” -> “heterogeneous reaction providing”
l. 119: Please rephrase the sentence to avoid misunderstandings regarding “the transition above (?) which the atmosphere no longer receives direct illumination.”
l. 165: Remove parentheses around the citation: (Toledo, 2016) -> Toledo (2016)
l. 171: It appears that P (not P_total) is shown in the figures. Please revise the corresponding text accordingly.
l. 259: Remove parentheses: (see, e.g., (Gomez-Martin et al., 2021)) -> (see, e.g., Gomez-Martin et al., 2021)
l. 325: “at lower SZA<95°” -> “at SZA below 95°”
l. 366/367: For improved readability, move the phrase “as will be discussed in the following sections” to the end of the sentence.
l. 422: Briefly define “droxtals”.
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Fig. 1: Please specfy the resulting optical thickness of the cloud layer considered.
Fig. 2: The small inset in the top-left corner of panel (a) is not referenced in the caption or main text. Consider removing it for clarity, or integrate the zenith angle directly into the Sun’s ray depiction.
Fig. 5: Use a consistent color scheme for the 450 nm and 950 nm results in both panels. Consider using black or a third color for CI* in the right panel.
Fig. 6: The wavelengths listed in the caption do not match those shown in the left panel. Additionally, no results are displayed for the transition region between 550 and 700 nm. Please either include data for these wavelengths or justify the exclusion of 600 and 650 nm.
Fig. 7: The study by Lauster et al. (2022) has been referenced earlier. For completeness, consider including the corresponding CI ratios from that work.
Fig. 10 + 11: It may be helpful to add the value of SZA_max for better visual orientation, similar to Fig. 9.
Citation: https://doi.org/10.5194/egusphere-2026-2295-RC2 - AC2: 'Reply on RC2', Daniel Toledo, 29 Jul 2026
Peer review completion
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2026-2295', Bernhard Mayer, 10 Jul 2026
The author introduces a new method to detect optically thin high clouds from twilight observations at a single wavelength. The method is based on previous work by the same author where they used the color index calculated from the ratio at two wavelengths. It can often be confirmed by visual experience after sunset, when optically thin cirrus clouds light up in bright red and become visible, and the reason for this coloring is nicely explained in the manuscript. The new method which uses only one wavelength rather than the ratio of two, is clearly explained. Sensitivities to all relevant parameters are tested. The method is based on a fast single scattering model which is verified by an accurate Monte Carlo model. I recommend publication of the manuscript after considering the following minor points:
- The description is quite long, and the main points of the manuscript are sometimes hidden by the wealth of equations and information. One way to improve that would be to shorten the first section which deals with the two-wavelengths method and focus on the new part, the single wavelength method
- line 85: it is argued that cloud layers extending over hundreds of km are unrealistic. This is relevant because of the long path of the radiation through the atmosphere. While it is certainly correct that the same cloud extending over hundreds of km is unrealistic, but the long pathlength in fact implies that the detection at one place can be affected by high clouds several hundred kilometres away. This would have an effect on the detection efficiency of the method because the absence of an observation of a cloud above the observer could either be caused by (1) actually no cloud being there, or (2) a distant cloud blocking the path of the radiation on it's long way to the observer
- Figure 1: The normalisation of the CI curves helps to better plot them on the same axis? In principle I would prefer the non-normalised curves because they would illustrate the "red-ness" of the sky. Also the sharp drop is puzzling. It is explained later in the text but it would help to have a brief explanation of the reason for the sharp drop towards larger SZA.
- line 215, eq 16: true, but a hint that this directly follows from the evaluation of the derivative of the ratio in eq (4) would be helpful
Figure 7: I was a bit surprised that water vapor was not included. Water vapor has strong absorption bands in particular in the right red block which is nearly free of absorption by NO2 and O3. Most of the water vapor is located in the atmospheric boundary layer between 0 and 2km but the zenith radiance has to pass through it in any case.
Figure 12: It wasn't very clear to me here that you look for the crossing between the Rayleigh and the total curve to identify cloud height. Maybe it is mentioned in the text and I missed it but you may mention it directly when you describe Figure 12 in the text.
In the Conclusions I was wondering if you could give a lower threshold for the optical thickness of the clouds to define a detection limit? You study a number of optical thicknesses up to 0.3 but I'm not sure about the lower end.
Citation: https://doi.org/10.5194/egusphere-2026-2295-RC1 - AC1: 'Reply on RC1', Daniel Toledo, 29 Jul 2026
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RC2: 'Comment on egusphere-2026-2295', Anonymous Referee #2, 23 Jul 2026
The manuscript presents a simplified formulation to reproduce and understand the behavior of the color index (CI) at high solar zenith angles (SZA) in the presence of optically thin high-altitude clouds, such as polar stratospheric clouds, without the need to solve the full radiative transfer problem. Based on the improved mechanistic understanding, a new so-called Rayleigh-referenced CI is introduced, defined as the ratio between the measured zenith intensity at a single wavelength and the corresponding intensity expected from a purely Rayleigh-scattering atmosphere. The method is verified and tested across a range of relevant parameters using comprehensive spherical radiative transfer simulations.
The work aligns well with the scope of AMT, and I recommend publication after addressing the following minor points.
---
General comments
---
The manuscript is submitted by a single author, yet the text consistently uses the first-person plural ("we"). To enhance clarity and conform to standard academic conventions, I recommend adopting a more neutral tone throughout. For example, in line 7:
“In this work, we introduce ….” -> “In this work, .… is introduced.”The definition of z_dark (ll. 117–119 and 180–187) is not entirely clear. As I understand it, z_dark refers to the lowest altitude illuminated by the Sun. However, the text describes it as an upper threshold. Please clarify the exact meaning of z_dark and its usage in the formalism. If possible, include z_dark in Fig. 1 to improve illustration and interpretation.
Given that high-altitude clouds have primarily been studied in remote regions using the color index method, how strongly does the absorption by NO2 (and also O3, H2O) affect the cloud height retrieval if the chosen wavelength pair is suboptimal? Please comment on the expected magnitude of such effects (Sect. 3.4 / Fig. 7).
The manuscript contains a number of valuable contents, but the main achievements – namely, the mechanistic explanation of the CI maximum and the derivation of a new single-wavelength formalism for detecting high-altitude clouds – get a little bit lost in the overall length and technical depth. I recommend overthinking the paper’s structure to better highlight these novel findings. Consider shortening the more mathematical sections in the first half of the manuscript or moving the detailed derivations to an appendix.
Finally, the conclusions would benefit from a broader outlook. How does the proposed Rayleigh-referenced CI advance our understanding of high-altitude cirrus and polar stratospheric clouds compared to previous approaches?
---
Specific comment and technical corrections
---
l. 22: “Clouds play a major role in Earth climate system” -> “Clouds play a major role in the Earth’s climate system”
l. 35: “heterogeneous reaction that provide” -> “heterogeneous reaction providing”
l. 119: Please rephrase the sentence to avoid misunderstandings regarding “the transition above (?) which the atmosphere no longer receives direct illumination.”
l. 165: Remove parentheses around the citation: (Toledo, 2016) -> Toledo (2016)
l. 171: It appears that P (not P_total) is shown in the figures. Please revise the corresponding text accordingly.
l. 259: Remove parentheses: (see, e.g., (Gomez-Martin et al., 2021)) -> (see, e.g., Gomez-Martin et al., 2021)
l. 325: “at lower SZA<95°” -> “at SZA below 95°”
l. 366/367: For improved readability, move the phrase “as will be discussed in the following sections” to the end of the sentence.
l. 422: Briefly define “droxtals”.
---
Fig. 1: Please specfy the resulting optical thickness of the cloud layer considered.
Fig. 2: The small inset in the top-left corner of panel (a) is not referenced in the caption or main text. Consider removing it for clarity, or integrate the zenith angle directly into the Sun’s ray depiction.
Fig. 5: Use a consistent color scheme for the 450 nm and 950 nm results in both panels. Consider using black or a third color for CI* in the right panel.
Fig. 6: The wavelengths listed in the caption do not match those shown in the left panel. Additionally, no results are displayed for the transition region between 550 and 700 nm. Please either include data for these wavelengths or justify the exclusion of 600 and 650 nm.
Fig. 7: The study by Lauster et al. (2022) has been referenced earlier. For completeness, consider including the corresponding CI ratios from that work.
Fig. 10 + 11: It may be helpful to add the value of SZA_max for better visual orientation, similar to Fig. 9.
Citation: https://doi.org/10.5194/egusphere-2026-2295-RC2 - AC2: 'Reply on RC2', Daniel Toledo, 29 Jul 2026
Peer review completion
Journal article(s) based on this preprint
Model code and software
Code for: On the origin of the twilight color index maximum and its application to cloud-height retrieval Daniel Toledo https://doi.org/10.5281/zenodo.19682745
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(5435 KB) - Metadata XML
The author introduces a new method to detect optically thin high clouds from twilight observations at a single wavelength. The method is based on previous work by the same author where they used the color index calculated from the ratio at two wavelengths. It can often be confirmed by visual experience after sunset, when optically thin cirrus clouds light up in bright red and become visible, and the reason for this coloring is nicely explained in the manuscript. The new method which uses only one wavelength rather than the ratio of two, is clearly explained. Sensitivities to all relevant parameters are tested. The method is based on a fast single scattering model which is verified by an accurate Monte Carlo model. I recommend publication of the manuscript after considering the following minor points:
- The description is quite long, and the main points of the manuscript are sometimes hidden by the wealth of equations and information. One way to improve that would be to shorten the first section which deals with the two-wavelengths method and focus on the new part, the single wavelength method
- line 85: it is argued that cloud layers extending over hundreds of km are unrealistic. This is relevant because of the long path of the radiation through the atmosphere. While it is certainly correct that the same cloud extending over hundreds of km is unrealistic, but the long pathlength in fact implies that the detection at one place can be affected by high clouds several hundred kilometres away. This would have an effect on the detection efficiency of the method because the absence of an observation of a cloud above the observer could either be caused by (1) actually no cloud being there, or (2) a distant cloud blocking the path of the radiation on it's long way to the observer
- Figure 1: The normalisation of the CI curves helps to better plot them on the same axis? In principle I would prefer the non-normalised curves because they would illustrate the "red-ness" of the sky. Also the sharp drop is puzzling. It is explained later in the text but it would help to have a brief explanation of the reason for the sharp drop towards larger SZA.
- line 215, eq 16: true, but a hint that this directly follows from the evaluation of the derivative of the ratio in eq (4) would be helpful
Figure 7: I was a bit surprised that water vapor was not included. Water vapor has strong absorption bands in particular in the right red block which is nearly free of absorption by NO2 and O3. Most of the water vapor is located in the atmospheric boundary layer between 0 and 2km but the zenith radiance has to pass through it in any case.
Figure 12: It wasn't very clear to me here that you look for the crossing between the Rayleigh and the total curve to identify cloud height. Maybe it is mentioned in the text and I missed it but you may mention it directly when you describe Figure 12 in the text.
In the Conclusions I was wondering if you could give a lower threshold for the optical thickness of the clouds to define a detection limit? You study a number of optical thicknesses up to 0.3 but I'm not sure about the lower end.