## 3 Algorithm Description
### LUT Calculation  
To account for the sensitivity of UV-visible measurements to aerosol properties, the dimensions of the LUT are constructed as listed in Table 4. The entries for each variable are selected assuming a linear variation in reflectance. Because aerosol extinction changes slowly with wavelength, five wavelengths (354, 388, 443, 477 and 490 nm) are selected here. These channels are selected to avoid absorption by gases other than O\({}_{2}\)-O\({}_{2}\), which has a high sensitivity to ALH. The LUTs were calculated assuming a fixed vertical distribution of ozone and O\({}_{2}\)-O\({}_{2}\). The AOD and SSA are based on values at 443 nm. In the RTM simulation, the SSA is obtained based on the refractive index and volume size distribution using Mie theory ([PERSON], 1993). The ranges of AOD and SSA were chosen to cover the range of variation. An analysis using the integrated AERONET inversion dataset shows that 99.9% of AOD at 440 nm is lower than 3.0 and that most SSA values are higher than 0.84. The real part of the refractive index for each aerosol type is assumed to be 1.46, 1.48 and 1.41 for HAF, dust and NA, respectively, as shown in Table 3. Seven values for the imaginary part of the refractive index are used to account for the SSA variation from 0.82 to 1.0 at \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable Name** & **No. of Entries** & **Entries** \\ \hline Wavelength (nm) & 5 & 354, 388, 443, 477, 490 \\ SZA (°) & 12 & 0.01, 5, 10, 15, 20, 27, 34, 41, 48, 55, 62, 69 \\ VZA (°) & 12 & 0.01, 5, 10, 15, 20, 27, 34, 41, 48, 55, 62, 69 \\ RAA (°) & 11 & 0.01, 15, 30, 45, 60, 80, 100, 120, 140, 160, 180 \\ SUR & 4 & 0.0, 0.05, 0.1, 0.2 \\ AOD (443 nm) & 8 & 0.0, 0.1, 0.4, 0.8, 1.2, 2.0, 2.8, 3.6 \\ SSA (443 nm) & 7 & 0.82, 0.85, 0.88, 0.91, 0.94, 0.97, 1.0 \\ Aerosol height (km) & 5 & 0.5, 1.5, 3, 4.5, 6 \\ Surface elevation (km) & 3 & 0, 3, 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dimensions of the LUT for the UV-visible algorithm (SZA: solar zenith angle; VZA: viewing zenith angle; RAA: relative azimuth angle; and SUR: surface reflectance). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Type** & **r\({}_{\text{m1}}\)** & **r\({}_{\text{m2}}\)** & **\(\sigma_{\text{m1}}\)** & **\(\sigma_{\text{m2}}\)** & **M1 Fraction** & **Re(RI) (440 nm)** & **SSA** & **AAE** & **AE** \\  & & & & & & & **(440 nm)** & **440–675 nm** & **440–675 nm** \\ \hline HAF & 0.0854 & 1.4115 & 1.5421 & 1.7630 & 0.99994 & 1.46 & 0.88 & 1.34 & 1.49 \\ Dust & 0.0644 & 1.0392 & 1.4420 & 1.6436 & 0.99823 & 1.48 & 0.91 & 2.11 & 0.25 \\ NA & 0.1013 & 0.8176 & 1.5870 & 1.9371 & 0.99980 & 1.41 & 0.97 & 1.17 & 1.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Integrated optical properties for HAF, dust and NA aerosol types. Optical properties were obtained by averaging inversion data categorized for the three aerosol types. The entire global AERONET inversion dataset was used for the calculation. The mean radius (r) and standard deviation of r (\(\sigma\)) represent a bimodal number size distribution and the M1 fraction indicates the fraction of the total number concentration corresponding to fine particles (mode 1). Re(RI) is the real part of the refractive index; this value is fixed in LUT simulations for each aerosol type. The imaginary part of the refractive index is adjusted to account for SSA variations in the LUT simulations. The single scattering albedo (SSA), absorbing Ångstrom exponent (AAE) and Ångstrom exponent (AE) are the nominal value for each aerosol type obtained from the AERONET inversion dataset. 443 nm. To investigate the wavelength dependence of particle absororptivity, the imaginary indices at 354, 388, 477 and 490 nm were estimated from the value at 443 nm using the power formula with the values for \(\omega\) mentioned in the previous section. The LUT is used to retrieve the a priori state of AOD and SSA using an inversion method with assumed ALH.