  During a solar eclipse the solar irradiance reaching the top-of-atmosphere
(TOA) is reduced in the Moon shadow. The solar irradiance is commonly measured
by Earth observation satellites before the start of the solar eclipse and is
not corrected for this reduction, which results in a decrease of the computed
TOA reflectances. Consequently, air quality products that are derived from TOA
reflectance spectra, such as the ultraviolet (UV) Absorbing Aerosol Index
(AAI), are distorted or undefined in the shadow of the Moon. The availability
of air quality satellite data in the penumbral and antumbral shadow during
solar eclipses, however, is of particular interest to users studying the
atmospheric response to solar eclipses. Given the time and location of a point
on the Earth's surface, we explain how to compute the obscuration during a
solar eclipse taking into account wavelength-dependent solar limb darkening.
With the calculated obscuration fractions, we restore the TOA reflectances and
the AAI in the penumbral shadow during the annular solar eclipses on 26
December 2019 and 21 June 2020 measured by the TROPOMI/S5P instrument. In the
corrected products, the signature of the Moon shadow disappeared, but only if
wavelength-dependent solar limb darkening is taken into account. We conclude
that the correction method of this paper can be used to detect real AAI rising
phenomena during a solar eclipse and has the potential to restore any other
product that is derived from TOA reflectance spectra. This would resolve the
solar eclipse anomalies in satellite air quality measurements and would allow
for studying the effect of the eclipse obscuration on the composition of the
Earth's atmosphere from space.
