Solar eclipse sky brightness and color

The sky viewed by an observer at the center of a solar eclipse is not entirely dark but is instead dimly illuminated by light scattered from the atmosphere outside of the eclipse shadow. This process is dominated by second-order scattering, so the zenith totality sky is expected to be approximately four orders of magnitude darker than the daytime sky and bluer in color. Understanding this promotes more meaningful observation of eclipses and of atmospheric optical effects generally. This paper describes a simple method of calculating sky spectral radiance with a second-order scattering model that includes molecular and aerosol scattering, and then uses this model to predict the spectral radiance of the zenith sky during totality. Key results that agree with previous studies include the finding that the totality zenith skylight comes primarily from light scattered downward from the high troposphere from within a radius for which the optical depth is unity or a distance on the order of 66 km for conditions with modest haze. Advancements presented here include the incorporation of an illumination function that quantifies the falloff of solar illumination with distance from the eclipse center and a favorable comparison of the simulations with radiometrically calibrated all-sky images recorded in Rexburg, Idaho, USA, during the August 2017 solar eclipse.