Sequence of sunset spectral irradiances

This plot shows the changes in brightness and colour of the Sun as it approaches the horizon at sunset. The labels on the sequence of observations in the plot show the colour temperature of the sunlight through the sequence (eg 4150K for the first one). This can be compared with the CT value of the LED lamps you buy to illuminate your home.

The individual spectra can be mathematically modelled to give some information about the state and and content of the atmosphere.

Some more technical details are given in what follows.

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These measurements were made in Bath, UK on the evening of 22 March 2020. The conditions were clear with little haze but with some very light patches of high cloud.

The instrument used was a Sekonic C-7000 SpectroMaster fitted with a tubular shade over the cosine corrector that restricted the field-of-view to a diameter of 10.8° (full illumination) ramping down to zero at 21.2°.

The spectral irradiance was measured at the following apparent (refraction-corrected) solar altitudes calculated from the "NOAA_Solar Calculations_day" spreadsheet ( www.esrl.noaa.gov/gmd/grad/solcalc/calcdetails.html ) using the UTC time and the Latitude and Longitude of the location in Bath.

Observation sequence number__Apparent Solar Altitude (deg)
086_______________________10.3
087_______________________5.2
088 ______________________3.9
089_______________________2.6
090_______________________2.2
091_______________________1.8

They covered a range of Air Masses (AM) of 5.4 to 20.6 (calculated from the formula given in: Kasten, F., and A. T. Young. 1989. "Revised optical air mass tables and approximation formula" Applied Optics 28:4735–4738.

The graphic shows the measurements (thick coloured lines) on a logarithmic scale of spectral irradiance. The thin grey line show the Solar spectrum outside the atmosphere (peaking at 2 W/m^2/nm) and two extinction models with air masses corresponding to the apparent solar altitudes of observations 086 (pale green) and 089 (violet).

The extinction model incorporates Rayleigh scattering, aerosol scattering (with a default power-law slope (spectral index) of -1.3) and ozone absorption in the Hartley, Huggins and Chappuis bands. The fits are made using modest adjustments to the default values of the aerosol spectral index, the aerosol column density wrt to a 'standard atmosphere' (Allen, Astrophysical Quantities, 3rd edition, 1973) and the Ozone STP atmospheric depth of 3mm.

Note that other significant telluric (Earth atmosphere) absorptions are not included in this model, notably water vapour, molecular oxygen, the O2*O2 dimer (or Collisionally Induced Absorption, CIA) and nitrogen dioxide absorption in the blue part of the spectrum. The water and oxygen account for the three strong absorption bands longward of 670nm.

An interesting feature of the sequence is the increasing strength of the absorption band at ~570nm in the yellow part of the spectrum. This is due to the oxygen dimer (CIA) absorption which is dependent on both the oxygen column density AND the pressure — since two oxygens need to interact. Most of these absorptions therefore occur in the low atmosphere where the pressure is highest. There is also a weaker CIA band close to 630nm associated with, but broader than, the molecular oxygen absorption at that wavelength. (See the comment below).

The extinction model spectrum (thin violet line) starts to fall well below the observed spectrum (#089) below 450nm. This indicates the presence of significant multiple scattering in long paths through the low atmosphere, especially from aerosols. My simple model assumes single scattering.

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