The spectrum of a thundercloud

[Original plots and text replaced 9/8/2014]

The light emerging from the base of thick, probably many-layered, cloud carries the story of the photons that make it through the soup of cloud water droplets of a wide range of sizes. The visible/nir spectrum of this emergent light has three dominant properties:

1. It is remarkably blue compared with direct sunlight.

2. It shows very strong water vapour absorption bands especially at longer wavelengths but extending identifiably right down to the blue/green part of the spectrum.

3. It exhibits absorption bands due to the transient association of oxygen molecules (O2.O2, called O4 CIA). This process, called 'collision induced absorption' is effective only in the low atmosphere where the gas pressure is highest. In this cloud, the CIA bands are considerably stronger than seen in direct sunlight at similar solar altitudes.

While trying to obtain the spectrum of lightning flashes during the daytime with a solar altitude of close to 45 degrees, I collected spectra of the dark grey clouds during the thunderstorm and accompanying rain. The upper plot shows, on a logarithmic intensity scale, the spectra of the cloud and, for comparison, of the Sun seen in a relatively clear (some light cirrus) sky.

orange line: Sun spectrum at zenith distance (zd) = 51.5 deg (altitude = 90 - zd)

grey line: Grey sky spectrum with some lightning emission lines from cloud reflections. Sun at zd ~ 45 deg

[Both of these are in flux/nm normalised at around 770nm.]

green line: The ratio of the thundercloud/sun

red line: A lambda^(-2) power law continuum.

violet line: The O4 CIA transmission of the power law continuum: Ref: GEISA Spectroscopic Database ( ether.ipsl.jussieu.fr/etherTypo/?id=950 )

The lower plot shows a zoom of the visible part of the spectrum to show the CIA lines more clearly. This also marks the 'Rain Band', the observation of which with small visual spectroscopes, allowed the observer - generally unsuccessfully - to predict the onset of rain. This pursuit was popular at the end of the 19th century in Britain (at least). The fortuitous combination of this band at one side (red) and the 578nm O4 band on the other (blue) with the centre of the ozone Chappuis absorption band seen strongly in the orange when the Sun is low in the sky (which it is not in this case) produces a very characteristic feature in the middle of the spectrum when seen with a visual spectroscope.

The ratio of the sky to the solar spectrum is quite blue and fitted well with a power-law in wavelength with an index of minus two. The Rayleigh blue sky has an index of -4 and atmospheric aerosol/haze usually exhibits an index of around -1.3 (Allen, C.W, "Astrophysical Quantities", third edition, The Athlone Press, 1973, p126).

The notable feature in the spectrum of the sky here is the great strength of the absorption bands due to collision induced absorption (CIA) produced by the temporary close proximity of two oxygen molecules. Such absorption is produced predominantly at low atmospheric altitudes since the strength is proportional to the square of the oxygen molecular density (while that of the other telluric absorbers goes with only the first power of their density).

Why is the grey sky so blue and why are the CIA bands so strong - much stronger than in direct sunlight at this zd?

The three spectral characteristics mentioned above are all consistent with the emerging photons being scattered very many times during their passage through the cloud and accumulating a long pathlength through a moist, low altitude atmosphere.

From the fit to the depth of the CIA bands at 476, 578 and 630nm, it is possible to make some estimates of the behaviour of the photons as they traverse the cloud. If we assume that CIA bands are formed in the lower regions of the cloud, say at an altitude of around 2km where the partial pressure of oxygen is 16 kPa - corresponding to a molecular O2 density of 4 x 10^18 cm^-3, then we require that the path traversed by a typical photon around this altitude is 110km. If while being multiply scattered from water droplets the photon remains within a region of 2km in diameter (i.e. within the cloud), it will scatter about 3000 times with a mean free path between scatterings of 30 or 40m. This means that if you were within this part of the cloud, you would be able to see clearly objects that were this distance away from you and much beyond that they would become 'lost in the mist'.

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