Table 1 Description of the USM model parameters
From: Retrieval of hourly aerosol single scattering albedo over land using geostationary satellite data
Parameter | Descriptions |
|---|---|
\(\theta\) | Zenith angle of solar and satellite; subscripts s and v represent solar and satellite, respectively |
\(\varphi\) | Relative azimuth angle |
\(\varOmega\) | Solid angle, which is the cosine of zenith angle θ and azimuth angle φ |
\(\varTheta\) | The scattering angle, \(\cos \left(\varTheta \right)={\mu }_{s}{\mu }_{v}+\sqrt{(1-{\mu }_{s}^{2})(1-{\mu }_{v}^{2})}\cos (\varphi )\) |
\(\mu\) | Cosine of zenith angle θ, μ = cos (θ); subscripts s and v represent solar and satellite, respectively |
\(\lambda\) | Wavelength |
\({\rho }^{{TOA}}\left({\theta }_{s},{\theta }_{v},\varphi \right)\) | Top of atmosphere reflectance |
\(\rho \left({\theta }_{s},{\theta }_{v},\varphi \right)\) | Surface bidirectional reflectance |
\({F}_{0}^{{\prime} }\) | Solar radiance (units = W•m-2•μm-1•sr-1) |
G | Air mass factor, \(G=\frac{1}{{\mu }_{s}}+\frac{1}{{\mu }_{v}}\) |
\(\tau\) | Total atmosphere optical depth, \(\tau ={\tau }_{a}+{\tau }_{r}\); subscripts a and r represent aerosol and molecular Rayleigh optical depth, respectively |
\(\omega\) | Single scattering albedo; subscripts a and r represent aerosol and molecular Rayleigh optical depth, respectively |
\(g\) | Asymmetry factor; subscripts a and r represent aerosol and molecular Rayleigh optical depth, respectively |
\(P\,({\varOmega }_{v},{\varOmega }_{s})\) | Scattering phase function; subscripts t, a, and r represent total atmosphere, aerosol, and Rayleigh scattering phase function, respectively |
\({I}_{0}\left(\tau ,{\varOmega }_{v}\right)\) | Unscattered radiance, i.e. sunlight without atmospheric scattering; after reaching the surface, it is reflected by the surface and enters the sensor (Fig. 4a) |
\({I}_{1}\left(\tau ,{\varOmega }_{v}\right)\) | Single scattering radiance, which refers to direct sunlight that does not reach the surface and enters the sensor after being scattered by the atmosphere once (Fig. 4b) |
\({I}_{m}\left(\tau ,{\varOmega }_{v}\right)\) | Multiple scattering radiance, i.e. the sky light generated by multiple scattering of the atmosphere, which is reflected by the atmosphere and ground and then enters the sensor (Fig. 4c) |
