## 4 Development of an Iterative Algorithm for Retrieval of Optically Thick Cloud Properties
Subsequently, by introducing the MWR measured value of LWP (_i.e._, \(\mathrm{LWP_{meas}}\)), Equation (10) is used to obtain better estimation of effective radius (\(\mathrm{R_{eff}}\)), which will again obtain a better estimate of COD using the LUT. This iteration procedure continues until stable values of COD and \(\mathrm{R_{eff}}\) (_i.e._, convergence of \(\mathrm{LWP_{theory}}\) to \(\mathrm{LWP_{meas}}\) occurs) are obtained for each of the atmospheric transmittance measurement (as shown in Figure 5). The schematic of our LUT based iterative approach for cloud optical properties of thick cloud is illustrated in Figure 6. To implement efficiently, initial 2D LUT's are developed for the LWP and diffuse transmittance and interpolation is used when readjusting \(\mathrm{R_{eff}}\) during the retrieval. By  
Figure 5: Convergence of iterative retrieval algorithm for (**a**) COD and (**b**) \(\mathrm{R_{eff}}\). comparing with the results of the MIN approach obtained from the SGP database, we can assess our local algorithm. As discussed earlier, we require real-time measurements of atmospheric transmittance (for 415 nm wavelength) as a function of cosine of solar zenith angle (\(\mu_{0}\)) from the MFRSR, the LWP from the MWR as well an estimate of aerosol loading and surface albedo. The Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART, version 2.4) [44] model, which is based on the DISORT algorithm (Discrete Ordinate Radiative Transfer) to account for multiple scattering within layered media [46] is used for computing the radiation fluxes at the surface and at the TOA. Within SBDART, atmospheric transmittance is defined as the ratio of downwelling irradiance at the surface to that at the TOA for a narrow wavelength band corresponding to the MFRSR 415 nm channel. In a preliminary analysis, we define a site-specific (average) aerosol model based on the long-term climatological record of AERONET Level 2 datasets. The aerosol climatology parameters include aerosol optical  
Figure 6: Schematic illustration of the algorithm flow for the LUT based iterative approach for retrieving cloud optical properties of thick water clouds. Here cloud liquid water path (LWP\({}_{meas}\)) represents the real-time instantaneous liquid water path measurement from MWR and the order (or number) of iteration is denoted by “n” as subscript to the variable terms. depth (AOD), single scattering albedo (SSA) and asymmetry parameter (g) spectrally covering the shortwave region. Also, the climatological surface albedo value is chosen from the ASRVN (AERONET Surface Reflectance Validation Network) data record. SBDART treats atmosphere as a plane parallel system, so vertical inhomogenities of the atmosphere and the aerosol distribution can be taken into account. Given the fixed aerosol model, surface albedo, atmospheric model (US62 Standard Atmosphere), a LUT for the inverse of the atmospheric transmittance (T\({}^{-1}\)) can be computed by varying the COD, R\({}_{\textrm{eff}}\) and \(\mu_{0}\) together in the radiative transfer code. From the LUT, as expected, the linearity of the relationship between COD and T\({}^{-1}\) is observed and their slope is dependent on \(\mu_{0}\), while the intercept is almost independent.