## 1 Introduction  
As one of the most important greenhouse gases, column-averaged CO\({}_{2}\) concentrations can be monitored by several space-based instruments, including the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY) [1, 2] on the European Environmental Satellite (ENVISAT) and the Atmospheric Infrared Sounder (AIRS) [3, 4] on the National Aeronautics and Space Administration (NASA) Aqua platform. However, to characterize CO\({}_{2}\) surface flux and the distribution of CO\({}_{2}\) sources and sinks, the uncertainty of column-averaged CO\({}_{2}\) dry air mole fractions (XCO\({}_{2}\)) retrieval should be less than 1 ppm. This requirement can only be fulfilled by the dedicated CO\({}_{2}\) monitoring sensors, such as the Greenhouse gases Observing Satellite (GOSAT) launched in 2009 [5] and the Orbiting Carbon Observatory-2 (OCO-2) launched in July 2014 [6]. In this context, the Chinese Carbon Dioxide Observation Satellite (TanSat) will have been launched in the end of 2016 [7; 8]. GOSAT, OCO-2 and TanSat measure in three near-infrared (NIR) bands around 0.76, 1.6 and 2.06 \(\upmu\)m, which are more sensitive to CO\({}_{2}\) variations in the lower troposphere to meet the requirement of CO\({}_{2}\) surface flux retrieval [9]. The retrieval of column-averaged CO\({}_{2}\) dry air mole fractions (XCO\({}_{2}\)) is biased due to uncertainties arising from atmospheric particle scattering [10], mainly caused by aerosols. As part of air pollution, aerosols are dramatically affected by human activities, especially for big cities developing quickly in China. Depending on the chemical components and particle size, aerosols with different absorbing and scattering properties could change the light path and have an impact on the radiation. While algorithm dependent, aerosols are shown to produce different patterns of bias in retrieved XCO\({}_{2}\)[11; 12]. The instruments in NASA's Afternoon Constellation (A-Train) can provide near-simultaneous (same Equator-crossing time, i.e., 1:30 p.m.) observations of clouds and aerosols. As the newest member of the A-Train, OCO-2 retrievals will utilize the synergy with other missions in the A-Train, such as Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and MODIS (Moderate Resolution Imaging Spectroradiometer), to correct CO\({}_{2}\) retrieval bias [6]. Unlike OCO-2, however, GOSAT has two subunits: a Fourier-transform spectrometer (the main sensor) and the Cloud and Aerosol Imager (CAI). As an auxiliary sensor, CAI is essential for screening areas contaminated by clouds and correcting for the effects of scattering and absorption by aerosols, so reducing the retrieval errors of XCO\({}_{2}\)[13]. For TanSat, a similar concept for a synergistic observation instrument is the Cloud and Aerosol Polarimetric Imager (CAPI), which is designed to observe radiance in five bands from the ultraviolet to NIR (0.38, 0.67, 0.87, 1.375 and 1.64 \(\upmu\)m), with additional measurements of the Stokes vector polarization quantities at 0.67 and 1.64 \(\upmu\)m [14]. In addition to aerosol detection, CAPI also performs cloud screening, and the 1.375-\(\upmu\)m channel is mainly used to detect cirrus. As with CAI, the additional aerosol information from simultaneous CAPI measurements is expected to deliver improvements in CO\({}_{2}\) retrieval accuracy. The wavelengths and signal-to-noise ratio (SNR) for each channel and some other important instrumental characteristics of CAPI are shown in Table 1.  
The backscattered radiation varies substantially due to scattering by aerosols in the atmosphere. Aerosol optical depth (AOD), expressed in terms of integration of aerosol extinction coefficient over height, and the Angstrom exponent, a dependency of aerosol optical depth on wavelength, are often used to describe aerosol optical properties depending on the chemical composition, microphysical parameters and the vertical distribution [15; 16].