Modelling the green flash spectrum: the green band

Note The original image and the text of this post have been replaced by a more complete description of the modelling of the green flash spectrum (15 April 2018).

The only observation I have been able to find of the spectrum of the green flash appears in a paper published by T. S. Jakobsen in the Royal Astronomical Society of Canada Journal in 1952 ( adsabs.harvard.edu/full/1952JRASC..46...93J ). The measurements were obtained with a movie camera from a beach in Hawaii using colour film and vertically dispersed with a Roland replica transmission grating. The film was carefully scanned and calibrated to produce the green flash spectrum that is discussed here (see Jakobsen's Fig. 3 and Table 1).

I have explored this observation using the spectral extinction model described in: www.flickr.com/photos/bob_81667/40402297274/in/photostream/

Note that this spectral model starts with the spectral energy distribution of the sun above the atmosphere and computes the wavelength-dependent extinction of the sunlight as it passes through the atmosphere from different altitudes above the horizon. The model includes molecular (Rayleigh) scattering and also scattering by aersols using a prescription given in "Astrophysical Quantities" (C. W. Allen, Third Edition, The Athlone Press, 1973, p126). The only molecular absorption included is that of ozone with the standard absorption due to 0.3 atmo-cm or 300 Dobson units. The only other significant absorbers in this spectral range are water and the O2*O2 dimer, often known as tetraoxygen or the O4 Collisionally Induced Absorber (CIA): these have a relatively minor effect on the green flash and are neglected.

The essential ingredient in the model turns out to be the ozone molecular absorption since the instrinsically rather weak Chappuis band — a broad structured vibronic band centred close to 590nm — becomes very strong when sunlight is travelling through around 40 airmasses (an airmass is the amount of atmosphere vertically above your head) to reach the observer as the sun sets or rises. At this strength, the Chappuis band esentially divides the solar spectrum into a wavelength-separated green-blue and deep red section with a wide, dark gap between. This same absorption results in the deep blue of twilight and the period after sunset that artists know as "The Blue Hour". It is this bifurcated spectrum, along with the often complex, mirage-related refraction produced by the atmosphere at very low elevations that generates the green flash. I emphasise, because it is not well-represented in the green flash literature, that the ozone absorption is an essential ingredient in the formation of the phenomenon. It would not be seen, other that perhaps as a thin purely refracted green rim above the sun, if there were no ozone.

The two important parameters that determine the intensity, the width and the position (colour) of the green band are the aerosol and the ozone densities. The two plots here show the dependence of the spectrum on each of these quantities in turn. The left panel shows the variation of the spectrum with the ozone content increasing from one to five times the standard value of 0.3cm (at an aerosol content of 10%). The Jakobsen green flash observed spectrum is shown as the black dashed line: the vertical scale of this measurement is arbitrary but I have kept it constant across both the left and the right panels. The variation with aerosol content is shown in the right panel with an ozone content of 4 and the aerosol variation ranging from 0% (no aerosols at all) to 70% of what is considered a normal atmosphere (see the Allen reference above). We would not expect to see a green flash in an atmosphere with a normal aerosol content.

Considering first the ozone variation, we have to note that my model assumes a homgenous atmosphere with all the constituents fully mixed. For a high sun this is a good approximation for computing solar extinction. With the sun on the horizon and the light taking a tangential path through the atmosphere however, the altitude through which the majority of the sunlight passes becomes important. The low altitudes tend to become masked by high density and aerosols. This implies that the light reaching us as the green flash may have travelled mostly through higher altitudes where most of the ozone resides (between about 15 and 40km). Within these regions the relative ozone content can become much higher than the homogeneous atmosphere model would imply. The ability of ozone to produce the spectral gap in the orange part of the spectrum only happens with an ozone content of >3 times the homogeneous approximation, a finding that is not unexpected. As the ozone increases, the intensity of the green band decreases and it also shifts significantly towards the blue.

Regarding the aerosols, the dominant effect on the spectrum of increasing aerosol content is to decrease the intensity of the green band: it is essentially a filtering of the sunlight. While not immediately obvious from the plot however, increasing the aerosol content moves the band to the red. Such an effect can be seen very clearly when watching a sunset through fine haze or smoke — the blood-red sun. The effect here is more subtle but the ratio of 450nm (blue) to 550nm (green-yellow) light changes from 0.54 for 0% aersols to 0.33 for 70%.

The best fit of this model to the Jakobsen spectrum yields an aerosol content of 10% and an ozone factor of 3.1. To see a blue flash requires a very low aerosol concentration and a high effective ozone density, likely to be achieved by an optimum refractive guidance of the sunlight through the ozone layer.

Note again that this model does not include either water or O_4 (tetraoxygen) absorption which, if added would absorb light at ~600nm and 578nm, darkening further the 'saddle' between the green band and the far red emission.

What do we learn from this exercise? In summary:

1. The passage of sunlight through a long pathlength of ozone gas in the ozone layer is essential for enabling a clear separation of the blue-green light from the remaining redder light. Separation by refraction on its own is not enough. The ozone shapes the spectrum of the green band.

2. Variations in the ozone and aerosol content of the traversed atmosphere can explain the observed variations in the brightness and the colour of the green/blue flash.

3. the various mirage-like refractive effects choreograph the shape, visibility and temporal behaviour of these phenomena.

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