## 1 Introduction
Several satellite instruments have been used to monitor aerosols from space by detecting multispectral reflected radiance. The MODIS, AVHRR (Advanced Very High Resolution Radiometer) and SCIAMACHY instruments can provide measurements from the visible to infrared in nadir viewing geometry [17; 18; 19; 20; 21; 22]. Near-UV measurements from the TOMS (Total Ozone Mapping Spectrometer) and OMI (Ozone Monitoring Instrument) are suitable for aerosol detection over bright land surfaces [23; 24]. AOD and the Angstrom exponent can be derived from these observations [25; 26; 27], but the microphysical properties of aerosols, such as the refractive index and particle size distribution, cannot usually be determined exactly [21]. The Multi-angle Imaging SpectroRadiometer (MISR) measures radiance at various viewing angles along the track and combines these measurements in the retrieval to improve aerosol detection [28; 29; 30]. Furthermore, polarization has \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Channels**} & **Band Centre** & **Band Range** & **Signal-to-Noise** & **Radiance** & **Polarization** \\  & **Wavelength (\(\upmu\)m)** & **(\(\upmu\)m)** & **Ratio (SNR)** & **(W/m\({}^{2}\)/\(\upmu\)m/sr)** & **Angle 1** \\ \hline
1 & 0.38 & 0.365–0.408 & 260 & 28.0 & - \\
2 & 0.67 & 0.66–0.685 & 160 & 22 & 0\({}^{\circ}\), 60\({}^{\circ}\), 120\({}^{\circ}\) \\
3 & 0.87 & 0.862–0.877 & 400 & 25 & - \\
4 & 1.375 & 1.36–1.39 & 180 & 6.0 & - \\
5 & 1.64 & 1.628–1.654 & 110 & 7.3 & 0\({}^{\circ}\), 60\({}^{\circ}\), 120\({}^{\circ}\) \\ \hline \hline \end{tabular}  
* Polarization angle represents the angle three polarizers placed in one axial direction.  
\end{table} 
Table 1: Instrument configuration for the Cloud and Aerosol Polarimetric Imager (CAPI). long been shown to be sensitive to the aerosol microphysical properties [31]. Therefore, simultaneous measurements of polarization and radiances, such as those obtained from the Polarization and Directionality of Earth Reflectances (POLDER) instrument [32; 33] at 14 viewing angles, are shown to be valuable for characterizing aerosol microphysical properties [34]. The TOA radiances measured by satellites are affected by both aerosol backscattering and surface reflection. Therefore, the main challenge in improving satellite aerosol retrieval is to separate the contributions from aerosols and surface reflection [35]. Some algorithms use the relationship of surface reflectance between visible bands and the near-infrared band, like MODIS [18; 19]. Others utilize the lower surface reflectance at shorter wavelengths, such as UV or the blue band, like the OMI aerosol algorithm [24; 36; 37]. A simultaneous retrieval approach for retrieving aerosol parameters along with XCO\({}_{2}\) has been proposed [38]. Simulation experiments applicable to measurements of GOSAT or OCO-2 have shown that residual aerosol-induced CO\({}_{2}\) errors can be reduced to some extent by this method [39]. In this study, we focus on analyzing the sensitivity to aerosol parameters and their retrieval errors from the a priori error and instrument noise using simulated CAPI observations. A numerical tool comprising a forward model, an instrument model and an error analysis model is established for CAPI simulation. This tool is similar in concept to the one developed for Geostationary (GEO) satellites [40] and used in simulation of CAPI [41]. The degrees of freedom for the signal (DFS) are used to evaluate the sensitivity of CAPI measurements to aerosol parameters in the state vector (AOD, refractive index and particle size distribution). Based on the optimal estimation inverse model, component retrieval errors are also calculated and analyzed. This theory has been used in estimation of information content from satellite measurements in some studies [38; 42; 43]. The wide field of view (FOV) for CAPI may cause some differences in aerosol retrieval for different viewing zenith angles (VZA); therefore, we check the variation in DFS and retrieval error with viewing angles.