On the colour of noctilucent clouds

. The high-latitude phenomenon of noctilucent clouds (NLCs) is characterised by a silvery-blue or pale blue colour. In this study, we employ the radiative transfer model SCIATRAN to simulate spectra of solar radiation scattered by NLCs for a ground-based observer and assuming spherical NLC particles. To determine the resulting colours of NLCs in an objective way, the CIE (International Commission on Illumination) colour matching functions and chromaticity values are used. Different processes and parameters potentially affecting the colour of NLCs are investigated, i.e., the size of the NLC particles, the 5 abundance of middle atmospheric O 3 and the importance of multiply scattered solar radiation. We afﬁrm previous research indicating that solar radiation absorption in the O 3 Chappuis bands can have a signiﬁcant effect on the colour of the NLCs. A new result of this study is that for sufﬁciently large NLC optical depths and for speciﬁc viewing geometries, O 3 plays only a minor role for the blueish colour of NLCs. The simulations also show that the size of the NLC particles affects the colour of the clouds. Cloud particles of unrealistically large sizes can lead to a reddish colour. Furthermore, the simulations show that 10 the contribution of multiple scattering to the total scattering is only of minor importance, providing additional justiﬁcation for the earlier studies on this topic, which were all based on the single scattering approximation. at altitudes between about 80 and 85 km, slightly below the high latitude summer mesopause (e.g. 15 Rapp and Thomas, 2006). The low temperature and a sufﬁcient amount of water vapour at the summer mesopause lead to the formation of optically thin ice clouds (e.g. Gadsden and Schröder, 1989; Thomas et al, 1995; Baumgarten and Fiedler, 2008; von Savigny et al., 2020). NLCs were ﬁrst reported by Backhouse (1885) and Leslie (1885) in 1885, two years after the Krakatoa volcanic eruption in 1883.


Radiative transfer simulations: SCIATRAN with incorporated Mie Code
To model the sunlight scattered by NLC particles and transmitted to the Earth's surface, the Mie Code implemented into the 45 radiative transfer software SCIATRAN was used. This allows the calculation of aerosol optical parameters by SCIATRAN and the simultaneous implementation as an aerosol layer at a certain height. The NLC particle size distribution was assumed to be mono-modal log-normal: where N 0 is the total particle number density, r m the median radius, r the particle radius and S the geometric standard de-50 viation of the distribution (Grainger, 2017). The calculations were carried out for median radii ranging from 10 to 1000 nm and constant values for S = 1.4 and N 0 = 100 cm −3 . Note that the vertical optical depth of the cloud layer is additionally specified, which leads to an adjustment of the value of N 0 . The input values were guided by previous studies and literature on this topic (e.g., Gadsden and Schröder, 1989;Baumgarten and Fiedler, 2008;Baumgarten et al., 2010). In order to simulate the solar radiation scattered by aerosols and air molecules in a spherical atmosphere, considering refraction effects for the direct 55 solar beam and the scattered light, the "spher_scat" mode was used in SCIATRAN (Rozanov et al., 2014). SCIATRAN was developed by the Institute of Environmental Physics (IUP) of the University of Bremen as a forward model for the retrieval of atmospheric parameters from measurements with the SCIAMACHY instrument on ESA's Envisat spacecraft. More information on SCIATRAN can be found at https://www.iup.uni-bremen.de/sciatran/ (last access: March 7, 2022). The model output contains radiance values at different wavelengths. These data were multiplied by the solar spectrum incident on the Earth's at-60 mosphere (SORCE data (Solar Radiation and Climate Experiment)) (LASP, 2003) to obtain the resulting spectral distribution of the solar radiation scattered to an observer at the Earth's surface.

Colour modelling
The colour corresponding to a given scattered solar spectrum was determined and displayed using a standard approach based on the CIE XYZ colour space established in 1931 (e.g., Wyszecki and Stiles, 2000;CIE, 2004;Brainard and Stockman, 2010).
where I(λ) is the given radiance spectrum and the normalizing factor k is defined as k = 100 800 nm

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with I achromatic (λ) as a reference spectrum with the colour impression of white. In the case of self-luminaries, k remains indeterminate. Based on the XYZ tristimulus values the CIE chromaticity values x and y are calculated using These chromaticity values characterize the colour independently of the brightness and are displayed in a 2-D plot, the socalled CIE chromaticity diagram or "Gamut". Furthermore, the XYZ tristimulus values were converted to sRGB (standard 80 RGB), which can be used to display the colours in the programming software IDL (Interactive Data Language). More detailed information can be found in a previous paper by Wullenweber et al. (2021).

Results
For the radiative transfer simulations carried out in this work, SCIATRAN version 4.1.3 (Rozanov et al., 2014)  for high mid-latitudes taken from a climatological database obtained from a 3-D CTM (chemical transport model) developed at the University of Bremen (Sinnhuber et al., 2003) are used. In addition, the "DOM_S" (scalar computation) setting is used, which means that the radiative transfer equation is solved with a scalar discrete ordinate approach (Rozanov et al., 2014) and with "the number of iterations" = 1, an approximate treatment of multiple scattering is performed. This mode is referred to as the approximate spherical solution. The errors resulting from this simplified treatment are small, as further discussed in Sect.   3.1 Impact of the NLC optical depth   scattered and since the density in the atmosphere increases exponentially with decreasing altitude, the scattered radiation comes from lower altitudes and is more affected by the stratospheric ozone. Accordingly, the O 3 Chappuis bands are more clearly visible. Therefore, with a sufficiently large NLC optical depth and a certain viewing geometry, the NLC signal dominate over 130 the background signal and the Chappuis absorption is no longer visible. However, the NLCs still appear blueish. The finding that absorption in the Chappuis bands of O 3 is not required to explain the blue colour of NLCs in some situations is a new result compared to earlier works (e.g. Gadsden, 1975).

Impact of ozone absorption
As evident from the spectra in Fig. 3, ozone absorption may also affect the colour of noctilucent clouds. The effect of ozone 135 was already investigated by Gadsden (1975), who made measurements of the spectral radiance of NLCs with a photoelectric spectropolarimeter. Figure 7 shows a CIE chromaticity diagram including NLCs and different ozone column densities. occurs. This can be explained by the effect of ozone absorption in the Chappuis bands. Due to the long light path through the atmosphere, green, yellow, orange and short-wave red light is effectively absorbed by ozone, so that blue light predominates.
With more ozone, this effect is intensified and leads to a more saturated blue colour (compare 600 DU). However, a noticeable colour change only occurs at a low ozone column density (100 DU). This is due to the lower attenuation of the long-wave light by ozone absorption, resulting in a shift to the reddish region of the Gamut (see VZA = 85 • ). In addition, the effect of ozone 3.3 The role of particle size 150 The typical particle radii of visible NLCs are in the range of 10 -80 nm (see Sect. 1). In order to test the effect of the NLC particle size on the colour of the clouds, we performed SCIATRAN simulations for different median radii of the assumed mono-modal log-normal particle size distribution, i.e. 10 nm, 50 nm, 200 nm, 600 nm and 1000 nm. The width parameter is kept constant at S = 1.4 and the optical depth was assumed to be τ NLC = 10 −4 in all cases. Figure 8 shows a chromaticity diagram with simulated colours for increasing particle sizes. As expected, solar radiation scattered by particles with typical radii (10 to 50 nm) is perceived as blue by a ground-based observer. In addition, these radii also show the colour change from dark blue to white blue / light blue with the VZAs (45 • , 65 • and 85 • ). Assuming significantly larger particles, the scattered light becomes more reddish (compare 600 and 1000 nm).
That means, when the particles become larger and scatter spectrally more neutral, the reddish colouring is also visible from the are in agreement with our results, only in one case their calculations show smaller particles in the yellowish/orange region of the CIE chromaticity diagram. The simulations displayed in Fig. 8 show that the typical colour of NLCs is only present for certain particle sizes. Furthermore, it can be shown that the light scattered by NLCs in the visible spectral range contains important information on the size of NLC particles.

Influence near the horizon 165
During sunset, a reddening appears on the horizon (see Fig. 9), which accompanies most NLC observations (depending on the SZA). Figures 10 and 11 show simulated solar scattering spectra (left column) with the resulting colour impression (right column) for a ground-based observer and SZA = 98 • , VZA = 84 • , 87 • , 90 • (from top to bottom) and SAA = 0 • . Figure 10 shows the calculated results for NLCs with the following parameters: r m = 50 nm, S = 1.4, vertical optical depth of τ NLC = 10 −4 , and an altitude of z NLC = 82 km. In comparison, Fig. 11 illustrates the background without NLCs.

Multiple scattering vs. single scattering
In earlier studies on simulations of the spectral distribution of solar radiation scattered by NLC particles, the contribution of multiply-scattered radiation has been neglected (e.g. Gadsden, 1975;Ostdiek and Thomas, 1993). Using SCIATRAN, the 180 contribution of multiple scattering to the NLC spectra as seen by a ground-based observer can be easily simulated. For calculations with a more accurate consideration of multiple scattering, which is referred to as the fully spherical solution, i.e. "number of iterations" > 1 (see Sect. 3), SCIATRAN version 4.5.5 is now used. Figure 12 shows the difference of both methods for scattered solar spectra with VZA = 65 • (left panel) and the ratio for different VZAs (right panel). The differences are mainly in the short-wave blue spectral range (maximum factor of 1.34). Overall they are not crucial in 185 the context of the current study. This is especially the case for the NLC viewing geometry relevant VZAs here (45 • , 65 • and 85 • ). Furthermore, Fig. 13 shows that the more accurate consideration of multiple scattering has no visible effect on the CIE chromaticity values and the resulting colour, which is due to the blue CIE colour matching function z(λ) having its maximum at 450 nm. Therefore, the approximate multiple scattering treatment method is sufficient for the simulations performed here. The scattered solar spectra show that for the single scattering, the simulated values are smaller than for the multiple scattering (the maximum relative difference between the two spectra is 19%). Especially in the short-wave range the influence of multiple scattering is significant. Overall, the differences for the VZAs of the NLC viewing geometry used here are not significant with respect to the focus of this study and confirm the results of Fig. 14. As above, the weak influence of the large differences 200 at shorter wavelengths (compare Fig. 14) is due to the blue CIE colour matching function z(λ) with a maximum at 450 nm.
However, the differences depend highly on the VZA. Near the zenith, multiple scattering has a large influence and results in a maximum factor of about 3.
Single scattering is a valid approximation for the NLC viewing geometry used here, but it should be noted that depending on the relevant VZA range, the effect of multiple scattering may dominate and lead to different conclusions.

Discussion
We begin with a discussion of the limitations of the approach and results presented in this study, followed by a summary of how our results compare to the few earlier studies on the colour of NLCs.
Currently the study is limited to Solar elevation > -8 • , which covers about 40% of all NLCs (Baumgarten et al., 2009, Fig. 3) due to the SZA limitation in SCIATRAN version 4.1.3. In the future we want to study non-spherical particles (Baumgarten It also should be kept in mind that only the position of a given spectrum in the CIE chromaticity diagram provides objective information on the associated colour. The colours of the symbols displayed in the chromaticity diagrams depend on the details of the calculation of the RGB values and will vary to a certain extent between different output devides. In their work, Ostdiek and Thomas (1993) investigated the effect of two different NLC particle size distributions on the chromaticity values of NLC scattering spectra. The distributions were (1) a mono-modal log-normal distribution with an effective radius of 42.6 nm and (2) a power law distribution with an effective radius of about 700 nm. In good qualitative agreement with our results, the population of small particles leads to positions in the blue part of the chromaticity diagram, whereas the population of large particles leads to yellowish colours. Ostdiek and Thomas (1993) neglect refraction, Gadsden (1975) con-220 siders it, but argues that its effect is very small. Ostdiek and Thomas (1993) mention that a test was carried out that showed that refraction does affect the radiance values, but has a minor impact on the spectral shape of the scattering spectra and in subsequence also on the chromaticity values. Our simulations confirm the results of Ostdiek and Thomas (1993) (not shown). Gadsden (1975) also emphasized Chappuis absorption of ozone as a major factor influencing the colour of NLCs. However, our results show that for certain combinations of observation geometry and optical depth, ozone absorption is no longer visible 225 and plays only a minor role for these cases.

Conclusions
In this work, various parameters that influence the colour of NLCs were investigated. The Mie theory was used for the calculations and therefore the assumption of spherical particles was made. To be able to make concrete conclusions about colour changes, the CIE chromaticity diagram was used.

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First, an unrealistically small amount of ozone is required to observe a deviation from the typical blue colour of NLCs. A new result in this work is that for sufficiently large NLC optical depths and for specific viewing geometries, ozone plays only a minor role for the blueish colour of NLCs. Second, the particle size decisively determines the perceived colour of NLCs. From this it follows that the typical colour is only observable for certain particle sizes. Therefore, some information about the size