Radiance and color of the sky at twilight: Perturbations caused by stratospheric haze

Abstract

Layers of stratospheric aerosol with optical thicknesses as small as 10⁻⁴ cause noticeable perturbations in the monochromatic logarithmic brightness gradient,G, and the color ratio,C, of the twilight sky. Modeling of the twilight's radiant properties shows that definite single-valued relationships exist between maxima inC or minima inG and optical thickness, τ, physical thickness Δh, and mean altitude,$\overline h$, of stratospheric layers. It is therefore possible to determine τ, Δh and$\overline h$ and monitor their variations by performing either single wavelength measurements ofG or two-wavelength spectrophotometric measurements ofC. The presence of haze in the lower troposphere and the occurrence of multiple scattering both have relatively minor influences on the recovery of the stratospheric dust properties, provided that 10<$\overline h$<30 km.

Formal mathematical inversions of the single-scattering twilight equations are possible in principle, but difficult in practice because of non-linearities. Inversions incorporating an iterative linearization process with constrained smoothing, successfully recovered the features of the haze layer, but tended to oversmooth the vertical profile and underestimate the mean altitude of the haze layer.