# Optimal Estimation Retrieval of Aerosol Fine-Mode Fraction from Ground-Based Sky Light Measurements
However, the accuracy of retrieved FMF was not sufficient for estimating PM\({}_{2.5}\) mass concentration near the ground. [15]. There are also some related algorithms that try to retrieve FMF from measurements of the multi-viewing polarized satellite sensor, such as the Polarization and Directionality of the Earth's Reflectances (POLDER) onboard the Polarization and Anisotropy of Reflectances for Atmospheric Science coupled with Observations from a Lidar (PARASOL), whereas most of the algorithms are limited to the research phase and cannot obtain stable and reliable products [16; 17; 18]. On the other hand, the optical and microphysical properties of aerosol can be derived from ground-based remote sensing measurements. The active Raman and elastic lidar techniques provide the vertical structure of cloud and aerosol properties. However, studies of aerosol optical FMF parameters resolved from multi-spectral lidar still need to be further developed [19]. With regard to the passive measurements of direct and diffused radiation, there are currently two approaches to obtain the FMF. One is using the semi-empirical method, called spectral discrimination, to calculate FMF, which is based on the high-precision spectral aerosol optical depth (AOD) from the direct measurements of a Sun Photometer [20]. The method is also the operational algorithm to get FMF products of the AErosol RObotic NETwork (AERONET) [21]. The other is obtaining physical volume concentrations of fine and coarse particles, first by scattering light measurements from the atmosphere [22], and then by calculating FMF from the results of particle size distribution (PSD). However, there are still some limitations in the latter approach, such as a lack of constraint of coarse aerosol particles without obtaining measurements of longer wavebands. For passive instruments that detect reflected or scattered solar radiation, shortcomings are generally due to the limited information available in the measurements [23]. Consequently, both ground-based and satellite sensors, such as CE318-DP, POLDER, and DPC (Directional Polarimetric Camera), are currently focused on multi-band, multi-angle, and polarization observations to increase effective information [24; 25; 26; 27]. However, as the instruments become more and more complex, it becomes increasingly difficult to link the aerosol parameter retrieval capability to measurement characteristics intuitively, especially for polarimetric observations. In this paper, we try to explore the possibility of spectral AOD and FMF inversion using ground-based, single-viewing, multi-spectral intensity measurements of the sky light. For this purpose, the measurement of the near-infrared (NIR) band centered on 1610 nm was introduced to improve the retrieval capability for coarse-mode aerosols [28]. At the same time, a multi-parameter inversion framework based on the optimal estimation (OE) theory [29] was adopted to make full use of the observation information. The paper is organized as follows. Following an overview of the model and algorithm in Section 2, we introduce the ground-based field experiment data acquired by the Synchronization Monitoring Atmospheric Corrector (SMAC) sensor in Section 3. Subsequently, the retrieval algorithm is tested using the synthetic data and the real data in Section 4. A brief discussion is given in Section 5. Finally, the summary and conclusion are presented in Section 6.