## 1 Introduction
They obtained AOD and the Angstrom exponent from the VIIRS, UV aerosol index (UVAI) from the OMPS and the backscatter coefficient from the CALIOP measurement and retrieved aerosol height with SSA based on a look-up table (LUT) approach. For passive remote sensing, the OMI measurement of the 477 nm O\({}_{2}\)-O\({}_{2}\) spectral band has been widely used to retrieve aerosol height information. [PERSON] et al. [20] and [PERSON] et al. [21] applied the differential optical absorption spectroscopy technique and the multilayer perceptron neural network approach to the OMI O\({}_{2}\)-O\({}_{2}\) band measurement over northeast Asia, collocated with the MODIS aerosol product and obtained ALH. Previous studies achieved good performance for aerosol height derivation or AOD and SSA retrieval through multi-sensor measurements but there has been limited work on the stand-alone retrieval of AOD, SSA and aerosol height. With regard to the GEMS operation, differences in spatial coverage, temporal and spatial resolution and the lifetime of multiple sensors can cause problems in operation efficiency and stability. Thus, the GEMS aerosol retrieval algorithm uses the optimal estimation (OE) method [22]. The OE method finds the best solution to minimize differences between measured and simulated spectral intensity and has traditionally been used to retrieve vertical profiles of the atmosphere from sounding observations [23]. It has also been used for the retrieval of aerosol vertical profiles [24] and the joint retrieval of surface reflectance and AOD [25; 26]. In this study, the OE method is applied to find optimized values for AOD, SSA and ALH to fit the simulated radiance to observations. To describe the vertical profile of aerosols, [PERSON] et al. [27] used the Gaussian function characterized by a peak height (in km) and a half-width. The peak height and half-width were defined as the ALH and geometrical thickness, respectively. Then, the concept of ALH was introduced to the Total Ozone Mapping Spectrometer (TOMS) and OMI aerosol algorithms [14; 27]. Using the CALIOP-measured attenuated backscatter profiles at 1064 nm, the ALH can be estimated by the attenuated-backscatter-weighted height (\(Z_{\text{aer}}\)) according to the expression  
\[Z_{\text{aer}}=\sum_{i-1}^{n}H(i)\bigg{[}\frac{B_{sc}(i)}{\sum_{i=1}^{n}B_{sc} (i)}\bigg{]}, \tag{1}\]  
where \(B_{sc}(i)\) is the attenuated backscatter at height \(H(i)\) and \(n\) is the number of altitude bins. The assumption of a Gaussian aerosol vertical distribution is adopted in this study. To apply the OE method, a two-channel method [28] is adopted first to estimate an a priori state for AOD and SSA. [PERSON] et al. [26] showed that updating the a priori state clearly improved the performance of the OE to retrieve AOD and surface reflectance. Because of the importance of the a priori state, the GEMS aerosol algorithm retrieves a priori states for AOD and SSA prior to applying the OE method based on the two-channel approach, which has been used in the OMI UV algorithm, instead of using the climatological state. Because the sensitivity of backscattering in the UV-visible spectrum to AOD and SSA varies with aerosol type, three types of aerosol (dust (absorbing coarse particles), highly absorbing fine (HAF) and non-absorbing (NA)) were defined for a radiative transfer model (RTM) simulation using the Vector Linearized Discrete Ordinate Radiative Transfer code (VLIDORT; Spurr [29]). The optical characteristics for each type were calculated from the AERONET inversion product over Asia using the classification method suggested by [PERSON] et al. [30]. Then, the aerosol type was distinguished using the aerosol index (AI) calculated from two pairs of wavelengths in the UV (354 nm and 388 nm) and the blue range (477 nm and 490 nm) before the OE retrieval. The algorithm was tested using OMI measurements, which has specifications similar to those of the GEMS and its retrieval uncertainties were estimated using a synthetic spectrum.