Employing relaxed smoothness constraints on imaginary part of refractive index in AERONET aerosol retrieval algorithm
Authors: Sinyuk Alexander , Holben Brent N. , Eck Thomas F. , Giles David M. , Slutsker Ilya , Dubovik Oleg , Schafer Joel S. , Smirnov Alexander , Sorokin Mikhail 
Published: July 2022

Abstract. In the Aerosol Robotic Network (AERONET) retrieval algorithm,
smoothness constraints on the imaginary part of the refractive index provide control of retrieved spectral dependence of aerosol absorption by preventing the inversion code from fitting the noise in optical measurements and thus avoiding unrealistic oscillations of retrievals with wavelength. The history
of implementation of the smoothness constraints in the AERONET retrieval
algorithm is discussed. It is shown that the latest version of the
smoothness constraints on the imaginary part of refractive index, termed
standard and employed by Version 3 of the retrieval algorithm, should be
modified to account for strong variability of light absorption by brown-carbon-containing aerosols in UV through mid-visible parts of the solar
spectrum. In Version 3 strong spectral constraints were imposed at high
values of the Ångström exponent (440–870 nm) since black carbon was assumed to be the primary absorber, while the constraints became increasingly relaxed as aerosol exponent deceased to allow for wavelength dependence of absorption for dust aerosols. The new version of the smoothness constraints on the imaginary part of the refractive index assigns different weights to different pairs of wavelengths, which are the same for all values of the Ångström exponent. For example, in the case of four-wavelength input, the weights assigned to short-wavelength pairs (440–675, 675–870 nm) are small so that smoothness constraints do not suppress natural spectral variability of the imaginary part of the refractive index. At longer wavelengths (870–1020 nm), however, the weight is 10 times higher to provide additional constraints on the imaginary part of refractive index retrievals of aerosols with a high Ångström exponent due to low sensitivity to aerosol absorption for
longer channels at relatively low aerosol optical depths. The effect of
applying the new version of smoothness constraints, termed relaxed, on
retrievals of single-scattering albedo is analyzed for case studies of
different aerosol types: black- and brown-carbon-containing fine mode
aerosols, mineral dust coarse mode aerosols, and urban industrial fine mode
aerosol. It is shown that for brown-carbon-containing aerosols employing the relaxed smoothness constraints resulted in significant reduction in
retrieved single-scattering albedo and spectral residual errors (compared to standard) at the short wavelengths. For example, biomass burning smoke cases showed a reduction in single-scattering albedo and spectral residual error at 380 nm of ∼ 0.033 and ∼ 17 %, respectively,
for the Rexburg site and ∼ 0.04 and ∼ 12.7 % for the Rimrock site, both AERONET sites in Idaho, USA. For a site with very
high levels of black-carbon-containing aerosols (Mongu, Zambia), the effect
of modification in the smoothness constraints was minor. For mineral dust
aerosols at small Ångström exponent values (Mezaira site, UAE), the spectral
constraint on the imaginary part of the refractive index was already relaxed in
Version 3; therefore the new relaxed constraint results in minimal change. In the case of weakly absorbing urban industrial aerosols at the GSFC site,
there are significant changes in retrieved single-scattering albedo using
relaxed assumption, especially reductions at longer wavelengths:
∼ 0.016 and ∼ 0.02 at 875 and 1020 nm, respectively, for 440 nm aerosol optical depth (AOD) ∼ 0.3. The modification of smoothness constraints on the imaginary part of the refractive index has a minor
effect on retrievals of other aerosol parameters such as the real part of the
refractive index and parameters of the aerosol size distribution. The
implementation of the relaxed smoothness constraints on the imaginary part
of the refractive index in the next version of the AERONET inversion algorithm
will produce significant impacts at some sites in short wavelength channels
(380 and 440 nm) for some biomass burning smoke cases with significant
brown carbon content and possibly in mid-visible channels (500 and 675 nm)
to near-infrared channels (870 to 1020 nm) for some urban industrial
aerosol types. However, most differences in single-scattering albedo
retrievals between those applying the new relaxed constraint and the standard
constraint will be within the uncertainty of the single-scattering albedo
retrievals, depending on the level of aerosol optical depth, Ångström exponent, brown carbon content and wavelength.