Revisiting the question "Why is the sky blue?"

Lange, Anna; Rozanov, Alexei; von Savigny, Christian

doi:https://doi.org/10.5194/egusphere-2023-1430

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https://doi.org/10.5194/egusphere-2023-1430

Preprints

04 Jul 2023

| 04 Jul 2023

Revisiting the question "Why is the sky blue?"

Anna Lange, Alexei Rozanov, and Christian von Savigny

Abstract. The common answer to the question "Why is the sky blue" is usually Rayleigh scattering. In 1953 Edward Hulburt demonstrated, that the blue colour of the zenith sky at sunset is to 1/3 caused by Rayleigh scattering and to 2/3 caused by ozone absorption. In this study, an approach to quantify the contribution of ozone to the blue colour of the sky for different viewing geometries is implemented using the radiative transfer model SCIATRAN and the CIE (International Commission on Illumination) XYZ 1931 colour system. The influence of ozone on the blue colour of the sky is calculated for solar zenith angles of 10°–90° and a wide range of viewing geometries. For small solar zenith angles, the influence of ozone on the blue colour of the sky is minor, as expected. However, the effect of ozone increases with increasing solar zenith angle. The calculations for the Sun at the horizon confirm Hulburt's estimation with remarkably good agreement. More aerosols reduce the ozone contribution at and near the zenith for the Sun at the horizon. The exact contribution of ozone depends strongly on the assumed total ozone column. The calculations also show that the contribution of ozone increases with increasing viewing zenith angle and total ozone column. Variations in surface albedo as well as full treatment of polarised radiative transfer were found to have only minor effects on the contribution of ozone to the blue colour of the sky. Furthermore, with an observer at 10 km altitude an increase of the ozone influence can be seen.

Received: 28 Jun 2023 – Discussion started: 04 Jul 2023

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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.

Journal article(s) based on this preprint

01 Dec 2023

Revisiting the question “Why is the sky blue?”

Anna Lange, Alexei Rozanov, and Christian von Savigny

Atmos. Chem. Phys., 23, 14829–14839, https://doi.org/10.5194/acp-23-14829-2023,https://doi.org/10.5194/acp-23-14829-2023, 2023

Short summary

Anna Lange, Alexei Rozanov, and Christian von Savigny

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1430', Anonymous Referee #1, 02 Aug 2023

General comments
The manuscript by Lange et al. focuses on the question “Why is the sky blue?”. Using radiative transfer modelling, previous findings published in 1953 are confirmed and the impact of Rayleigh scattering and ozone absorption on the colour of the sky is investigated quantitatively.
The manuscript elucidates the reasons for the common phenomenon of a blue sky and confirms that ozone absorption has a significant contribution. Therefore, I feel that the subject of the manuscript is suitable for publication in ACP, although this work probably does not represent not cutting-edge science.
The metric used in this study, namely the distance of the chromaticity coordinates to the white point, does not seem to be suitable for a quantification of the “blueness” of the sky. It only tells whether the sky is less white, but it could as well be more green or red if the distance to the white point increases. Instead, I suggest to simply use z value to quantify blueness. Furthermore, the usage of relative differences (Equation 6) leads to very large values if the sky colour is close to the white point even if the absolute change is small. I would therefore suggest to use absolute differences, in particular for the polar diagrams shown in Figures 3, 5 and 7. Using absolute values would also avoid that many data points have to be dismissed, as it is currently the case for data near the white point.
Each of the panels in Fig. 3, 5 and 7 have different colour scales, which makes a quantitative comparison very difficult for the reader. All panels should have the same colour scale.
Why has the influence of ozone on the colour of the sky not been investigated for SZA > 90°, as in previous studies?

Specific comments
L10: The statement that the contribution of ozone increases with increasing VZA is already explained in L6 and L7 and can therefore be removed.
L79: Please specify the wavelength grid used for the simulation of the spectra.
Section 2.2: Since not every reader is familiar with the definition of the chromaticity coordinates, I suggest to add a graphical representation of the CIE colour matching functions. For example, Fig. 4 could be moved to section 2.2, and the three colour matching functions could be added to this graph. This would also make it clearer why the sky appears bluer in the presence of ozone, although its absorption maximum is in the green.
Section 2.3: As already mentioned in the general comments, I feel that the z coordinate is a better proxy for the blueness of the sky than the distance to the white point, and absolute values would be more appropriate than relative ones. It is not defined how the distance is actually calculated. Is this the Euclidean distance?
It is stated that the method described here is not applicable in all cases. What exactly are the criteria for the applicability of the method and for dismissing particular data points?
L129: I do not understand the purpose of normalising the aerosol number density to 1 particle/cm^3.
L203: It would be good if you could add a discussion on the reasons for the increase of sensitivity to ozone with higher stratospheric aerosol load. Is this due to an increase in average scattering altitude, yielding a longer stratospheric light path, or due to a reduced fraction of Rayleigh scattering in the presence of stratospheric particles?
Conclusions: In order to give proper credit to previous work, it would be good if you could make clear in the conclusions that this work is a confirmation of previous studies on the influence of ozone on the colour of the sky, although your study provides a better quantitative assessment.

Technical comments
L63: I suggest to replace the term SAA with RAA (relative azimuth angle), since it represents the azimuth angle between the viewing direction and the direction of the Sun, whereas SAA usually describes the position of the Sun relative to the North.
Equation 6: the term “relative difference” is inappropriate for a variable name. According to existing conventions (Cohen et al, 2008), variable names should preferably consist of a single letter, such as “r”. Multiplying with the term “100%” on the left side is redundant since 100/100 = 1.
L139: The sentence starting with “The radius of the polar diagram corresponds to…” should be moved to the caption of Figure 3.
Figures 3, 5 and 7 should all have the same colour scale in all panels (see general comments).
L151: “light path” -> “light paths”
L155: “a SZA” -> “an SZA”
L160: “increase” -> “increases”
L162 and caption of Fig. 6: It doesn’t make sense to specify the SAA for zenith measurements (VZA = 0°)
L204: delete “units”
L204: “aerosols” -> “stratospheric aerosols”

References
E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, "Quantities, Units and Symbols in Physical Chemistry", IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge (2008)

Citation: https://doi.org/10.5194/egusphere-2023-1430-RC1
- AC1: 'Reply on RC1', Anna Lange, 15 Sep 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1430/egusphere-2023-1430-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1430-AC1
RC2:
'Comment on egusphere-2023-1430', Anonymous Referee #2, 10 Aug 2023
The paper presents a radiative transfer modelling study to explain the blueness of the sky. In most cases the color is due to Rayleigh scattering, but during twilight also ozone absorption plays a role. In 1953 E. Hulbert claimed based on a simplified modeling approach that the color during sunset is to 1/3 caused by Rayleigh scattering and to 2/3 caused by ozone absorption. In this work the color of the sky is investigated quantitatively by simulating spectra under various conditions and converting those to the CIE color space. The study basically confirms the result by E. Hulbert. The paper is clearly written, well understandable with appropriate number of figures. Altough the result is not really new because it just confirms what is expected, it provides some new insights. Therefore I recommend to publish the paper after minor revisions.
General comments:
Eq. 6, Quantification of color difference: Wouldn't it be better to use the absolute valud of the difference vector between the vectors in the CIE diagram instead of distances to the white point, e.g.

abs((x,y)_ozone-(x,y)) ?

You explain that if a point is in another direction (e.g. red) you can not evaluate the result. If you take the difference as a vector, couldn't you also evaluate the reddish points during sunset?

Impact of polarization (l. 71): 1% seems relatively small. Is this result in line with Mishchenko et al 1994? Probably the effect would be largest for a scattering angle around 90° and for large AOD, e.g. SZA=90° and VZA=0°. Has this been tested?

l. 124: AOD=0.04 is quite small. Is it a typical value for Greifswald or rather at the low end?

l. 210ff.: "With 37 % the ozone contribution to the blue colour of the sky is comparatively large for this viewing geometry. For a SAA of 0° , the ground-based observer looks in the sun-ward direction, but with VZA = 50° not directly into the Sun. A final explanation for this high value cannot be given at this point."

Have you looked at the scattering phase function of the aerosol particles? This could explain why you get the largest contribution for this particular geometry.

A general RT modelling question: How is refraction modelled in combination with polarization. For scalar RT the ray is bended according to Snell's law, is this valid when polarization is considered? Or do you need to use the Fresnel equation when the ray crosses a layer boundary? Could you provide a reference describing how this is treated?

Reference:

Mishchenko, M.I., A.A. Lacis, and L.D. Travis, 1994: Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres. J. Quant. Spectrosc. Radiat. Transfer, 51, 491-510, doi:10.1016/0022-4073(94)90149-X.
Citation: https://doi.org/10.5194/egusphere-2023-1430-RC2
- AC2: 'Reply on RC2', Anna Lange, 15 Sep 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1430/egusphere-2023-1430-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1430-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1430', Anonymous Referee #1, 02 Aug 2023

General comments
The manuscript by Lange et al. focuses on the question “Why is the sky blue?”. Using radiative transfer modelling, previous findings published in 1953 are confirmed and the impact of Rayleigh scattering and ozone absorption on the colour of the sky is investigated quantitatively.
The manuscript elucidates the reasons for the common phenomenon of a blue sky and confirms that ozone absorption has a significant contribution. Therefore, I feel that the subject of the manuscript is suitable for publication in ACP, although this work probably does not represent not cutting-edge science.
The metric used in this study, namely the distance of the chromaticity coordinates to the white point, does not seem to be suitable for a quantification of the “blueness” of the sky. It only tells whether the sky is less white, but it could as well be more green or red if the distance to the white point increases. Instead, I suggest to simply use z value to quantify blueness. Furthermore, the usage of relative differences (Equation 6) leads to very large values if the sky colour is close to the white point even if the absolute change is small. I would therefore suggest to use absolute differences, in particular for the polar diagrams shown in Figures 3, 5 and 7. Using absolute values would also avoid that many data points have to be dismissed, as it is currently the case for data near the white point.
Each of the panels in Fig. 3, 5 and 7 have different colour scales, which makes a quantitative comparison very difficult for the reader. All panels should have the same colour scale.
Why has the influence of ozone on the colour of the sky not been investigated for SZA > 90°, as in previous studies?

Specific comments
L10: The statement that the contribution of ozone increases with increasing VZA is already explained in L6 and L7 and can therefore be removed.
L79: Please specify the wavelength grid used for the simulation of the spectra.
Section 2.2: Since not every reader is familiar with the definition of the chromaticity coordinates, I suggest to add a graphical representation of the CIE colour matching functions. For example, Fig. 4 could be moved to section 2.2, and the three colour matching functions could be added to this graph. This would also make it clearer why the sky appears bluer in the presence of ozone, although its absorption maximum is in the green.
Section 2.3: As already mentioned in the general comments, I feel that the z coordinate is a better proxy for the blueness of the sky than the distance to the white point, and absolute values would be more appropriate than relative ones. It is not defined how the distance is actually calculated. Is this the Euclidean distance?
It is stated that the method described here is not applicable in all cases. What exactly are the criteria for the applicability of the method and for dismissing particular data points?
L129: I do not understand the purpose of normalising the aerosol number density to 1 particle/cm^3.
L203: It would be good if you could add a discussion on the reasons for the increase of sensitivity to ozone with higher stratospheric aerosol load. Is this due to an increase in average scattering altitude, yielding a longer stratospheric light path, or due to a reduced fraction of Rayleigh scattering in the presence of stratospheric particles?
Conclusions: In order to give proper credit to previous work, it would be good if you could make clear in the conclusions that this work is a confirmation of previous studies on the influence of ozone on the colour of the sky, although your study provides a better quantitative assessment.

Technical comments
L63: I suggest to replace the term SAA with RAA (relative azimuth angle), since it represents the azimuth angle between the viewing direction and the direction of the Sun, whereas SAA usually describes the position of the Sun relative to the North.
Equation 6: the term “relative difference” is inappropriate for a variable name. According to existing conventions (Cohen et al, 2008), variable names should preferably consist of a single letter, such as “r”. Multiplying with the term “100%” on the left side is redundant since 100/100 = 1.
L139: The sentence starting with “The radius of the polar diagram corresponds to…” should be moved to the caption of Figure 3.
Figures 3, 5 and 7 should all have the same colour scale in all panels (see general comments).
L151: “light path” -> “light paths”
L155: “a SZA” -> “an SZA”
L160: “increase” -> “increases”
L162 and caption of Fig. 6: It doesn’t make sense to specify the SAA for zenith measurements (VZA = 0°)
L204: delete “units”
L204: “aerosols” -> “stratospheric aerosols”

References
E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, "Quantities, Units and Symbols in Physical Chemistry", IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge (2008)

Citation: https://doi.org/10.5194/egusphere-2023-1430-RC1
- AC1: 'Reply on RC1', Anna Lange, 15 Sep 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1430/egusphere-2023-1430-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1430-AC1
RC2:
'Comment on egusphere-2023-1430', Anonymous Referee #2, 10 Aug 2023
The paper presents a radiative transfer modelling study to explain the blueness of the sky. In most cases the color is due to Rayleigh scattering, but during twilight also ozone absorption plays a role. In 1953 E. Hulbert claimed based on a simplified modeling approach that the color during sunset is to 1/3 caused by Rayleigh scattering and to 2/3 caused by ozone absorption. In this work the color of the sky is investigated quantitatively by simulating spectra under various conditions and converting those to the CIE color space. The study basically confirms the result by E. Hulbert. The paper is clearly written, well understandable with appropriate number of figures. Altough the result is not really new because it just confirms what is expected, it provides some new insights. Therefore I recommend to publish the paper after minor revisions.
General comments:
Eq. 6, Quantification of color difference: Wouldn't it be better to use the absolute valud of the difference vector between the vectors in the CIE diagram instead of distances to the white point, e.g.

abs((x,y)_ozone-(x,y)) ?

You explain that if a point is in another direction (e.g. red) you can not evaluate the result. If you take the difference as a vector, couldn't you also evaluate the reddish points during sunset?

Impact of polarization (l. 71): 1% seems relatively small. Is this result in line with Mishchenko et al 1994? Probably the effect would be largest for a scattering angle around 90° and for large AOD, e.g. SZA=90° and VZA=0°. Has this been tested?

l. 124: AOD=0.04 is quite small. Is it a typical value for Greifswald or rather at the low end?

l. 210ff.: "With 37 % the ozone contribution to the blue colour of the sky is comparatively large for this viewing geometry. For a SAA of 0° , the ground-based observer looks in the sun-ward direction, but with VZA = 50° not directly into the Sun. A final explanation for this high value cannot be given at this point."

Have you looked at the scattering phase function of the aerosol particles? This could explain why you get the largest contribution for this particular geometry.

A general RT modelling question: How is refraction modelled in combination with polarization. For scalar RT the ray is bended according to Snell's law, is this valid when polarization is considered? Or do you need to use the Fresnel equation when the ray crosses a layer boundary? Could you provide a reference describing how this is treated?

Reference:

Mishchenko, M.I., A.A. Lacis, and L.D. Travis, 1994: Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres. J. Quant. Spectrosc. Radiat. Transfer, 51, 491-510, doi:10.1016/0022-4073(94)90149-X.
Citation: https://doi.org/10.5194/egusphere-2023-1430-RC2
- AC2: 'Reply on RC2', Anna Lange, 15 Sep 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1430/egusphere-2023-1430-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1430-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Anna Lange on behalf of the Authors (15 Sep 2023) Author's response Author's tracked changes Manuscript

ED: Publish as is (20 Oct 2023) by Mathias Palm

AR by Anna Lange on behalf of the Authors (23 Oct 2023) Author's response Manuscript

Journal article(s) based on this preprint

01 Dec 2023

Revisiting the question “Why is the sky blue?”

Anna Lange, Alexei Rozanov, and Christian von Savigny

Atmos. Chem. Phys., 23, 14829–14839, https://doi.org/10.5194/acp-23-14829-2023,https://doi.org/10.5194/acp-23-14829-2023, 2023

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Anna Lange, Alexei Rozanov, and Christian von Savigny

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We were able to demonstrate quantitatively that the blue colour of the sky cannot be solely attributed to Rayleigh scattering. The influence of ozone on the blue colour of the sky is calculated for different viewing geometries, total ozone columns and an enhanced stratospheric aerosol scenario. Furthermore, the effects of polarisation, surface albedo and observer height are investigated.


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