# Optimal Estimation Retrieval of Aerosol Fine-Mode Fraction from Ground-Based Sky Light Measurements
## 3 Experimental Data  
As one of the most polluted regions affected by anthropogenic aerosol emissions, Beijing, the capital of China, is an area where there is deep concern about particulate pollution [49; 50]. Thus, the field experiment was performed in Beijing from November 2-November 15, 2017. In order to compare and validate with AERONET observations, the experiment location was next to the AERONET Beijing_RADI site. Figure 2 shows the variations of AOD and \(\mathrm{PM}_{2.5}\) (with unit of \(\upmu\)g/m\({}^{3}\)) during the experiment. The AOD and \(\mathrm{PM}_{2.5}\) data were from AERONET and the Beijing Municipal Environmental Protection Monitoring Center (BMEMC), respectively. From Figure 2, we can see that Beijing experienced several haze events. The mean AOD on November 6 and 9 was about 1.4, representing a high pollution situation, while the mean AOD on November 3 and 10 was about 0.1, which represents clean atmospheric conditions. A good consistency between AOD and \(\mathrm{PM}_{2.5}\) was found when AOD was less than 0.4, while for high pollution conditions, there were relatively larger differences between AOD and \(\mathrm{PM}_{2.5}\). Furthermore, the weather conditions were very suitable for testing the proposed algorithms. With regard to the measuring instrument, we adopted the newly developed Synchronization Monitoring Atmospheric Corrector (SMAC) sensor. SMAC is a satellite instrument designed to provide aerosol and cloud properties for the atmospheric corrections of a high-resolution camera onboard the same satellite. In order to achieve this purpose, the sensor has a total of eight channels from \begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{1}{c}{**Name**} & \multicolumn{1}{c}{**Setting**} \\ \hline Measurement vector & \(\mathbf{y}\ =\ [t_{\text{490}},\,I_{\text{550}},\,I_{\text{670}},\,I_{\text{870}},\,I_{ \text{1610}}]^{\mathrm{T}}\) \\ Observation uncertainties & \(\mathbf{S}_{\text{y}}\ =\ \epsilon_{\text{r1}}^{2}I^{2}(\lambda),\,\epsilon_{ \text{I}}=5\%\) (relative error) \\ \hline State vector & \(\mathbf{x}\ =\ [V_{0},\mathrm{FMF}_{\mathrm{v}}]^{T}\) \\  & \(V_{0}\geq 0.001\)\(\mathrm{\SIUnitSymbolMicro m}^{3}/\mathrm{\SIUnitSymbolMicro m}^{2}\) \\ A priori estimates uncertainties & \(0.01\leq\mathrm{FMF}_{\mathrm{v}}\leq 0.99\) \\  & \(\mathbf{S}_{\text{a}}\ =\ \begin{pmatrix}\epsilon_{V_{0}}^{2}\,\psi_{0}^{2}&0\\ 0&\epsilon_{\mathrm{FMF}_{\mathrm{v}}}^{2}\,\mathrm{FMF}_{\mathrm{v}}^{2}\\ \end{pmatrix}\) \\  & \(\epsilon_{V_{0}}\ =\ 100\%\), \(\epsilon_{\mathrm{FMF}_{\mathrm{v}}}\ =\ 100\%\) (relative error) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Definition of the measurement vector and state vector. blue (490 nm) through to near-infrared (1610 and 2250 nm). The observations included intensity bands centered at 490, 550, 670, 870, 1610, and 2250 nm, and four of these bands had polarimetric measurement capabilities, except for channel 550 nm (the polarization measurements were not used in this paper). There were also two channels centered at 910 and 1380 nm for water vapor remote sensing, where major water vapor absorption bands were located. The bandwidth was between 20 and 60 nm, depending on the spectral bands. Furthermore, the single-viewing sensor had a high time resolution of up to 10 samplings per second. In the experiment, continuous zenith observations were conducted, and all the measurements were carried out under cloudless conditions. Since the detectors in the 2250 nm channel needed to be passively cooled, and were difficult to achieve a stable operating temperature, the data on that wavelength were not available for ground-based measurements. Figure 3 shows the measurements of sky light by SMAC at 490, 550, 670, 870, and 1610 nm on November 6, 2017. The horizontal axis is the UTC time (from 1-8, corresponding to Beijing time 9 a.m.-4 p.m.), and the ordinate axis is the radiance. From Figure 3, the sky light radiance gradually increased with the solar zenith angle, reached the maximum at midday, and then gradually decreased.