| 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.
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.