## 3 EMI NO\({}_{2}\) Retrieval Algorithm
### AMF Calculation  
Tropospheric NO\({}_{2}\) SCD is obtained after the STS procedure. Then, we need to convert the tropospheric SCD to tropospheric VCD, which is the main output of the EMI NO\({}_{2}\) retrieval algorithm, by means of the tropospheric AMF. The method for tropospheric AMF (\(M\)) calculation is adopted from [PERSON] et al. (2004):  
\[M=\frac{\sum\limits_{l}m_{l}\left[x_{a,l}\cdot c_{l}\right.}{\sum\limits_{l}x_{a,l}} \tag{5}\]  
\[c_{l}=1-0.003[T(p)-T_{0}] \tag{6}\]  
where \(m_{l}\) is the scattering weight AMF (box-AMF), \(x_{a,l}\) is the NO\({}_{2}\) sub-column in layer l, \(c_{l}\) is the temperature correction factor applied to correct the absorption cross section spectrum according to the effective temperature \(T(p)\) at a specific layer \(p\), and \(T_{0}\) (220K) is the temperature of the NO\({}_{2}\) absorption cross section used in the DOAS fitting. The independent pixel approximation (IPA) allows the calculation of AMF for a partly cloudy scene as a linear combination of cloudy (\(M_{cl}\)) and clear (\(M_{\sigma}\)) components:  
\[M=\omega M_{cl}+(1-\omega)M_{\sigma} \tag{7}\]  
where \(\omega\) represents the effective cloud fraction, and is obtained from the TROPOMI cloud products. With an assumption of Lambertian equivalent surface reflectance (LER) for both the ground and clouds, the AMF was determined by pre-calculated scattering weight look-up tables (LUTs) and 437.5 nm was selected as an effective wavelength for scattering weight calculation [28]. The Unified Linearized Vector Radiative Transfer Model (UNL-VRTM) was used to calculate the scattering weight in this study. It comprises the Vector-linearized discrete ordinate radiative transfer (VLIDORT [50]) for radiative transfer simulation that meets the requirements for the scattering weight calculation [51]. The LUT is created as a function of the solar zenith angle (SZA), viewing zenith angle (VZA), relative azimuth angle (RAA), surface albedo, and elevation-dependent surface pressure. The mid-latitude summer atmospheric type with 49 fixed layers was used. Table 2 lists the nodes of these parameters in the LUTs. Given the influence of cloud on trace gas retrieval, it is necessary to determine whether the pixel is affected by cloud or not before NO\({}_{2}\) retrieval. As the spectra range of EMI does not cover the absorption characteristics of the O\({}_{2}\)-A band near 760 nm, the cloud retrieval algorithm based on the O\({}_{2}\)-A channel, as used by the TROPOMI algorithm, cannot be used for EMI. Although the cloud retrieval algorithm developed for OMI, for example, OMI/Aura Cloud Pressure and Fraction Raman Scattering [52] and OMI/Aura Cloud Pressure and Fraction O\({}_{2}\)-O\({}_{2}\) Absorption [53], could be adopted for EMI, such a cloud retrieval algorithm for EMI is excluded in this paper. For simplification, other external cloud parameter products, i.e., the cloud fraction, cloud pressure, and cloud radiation fraction information from TROPOMI cloud products, are used for the AMF calculation of cloudy pixels. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Number of Nodes** & **Grid Values** \\ \hline SZA (\({}^{\circ}\)) & 16 & 0, 10, 20, 30, 40, 45, 50, 55, 60, 65, 70, 72, 74, 76, \\  & 9 & 0, 10, 20, 30, 40, 50, 60, 65, 70 \\ RAA (\({}^{\circ}\)) & 5 & 0, 45, 90, 135, 175 \\ Albedo & 14 & 0, 0.01, 0.025, 0.05, 0.75, 0.1, 0.15, 0.2, 0.25, 0.3, \\  & & 0.4, 0.6, 0.8, 1.0 \\  & & 1063.10, 1037.90, 1013.30, 989.28, 965.83, 920.58, \\ Surface/Cloud pressure (hPa) & 17 & 876.98, 834.99, \\  & & 795.01, 701.21, 616.60, 540.48, 411.05, 308.00, \\  & & 226.99, 165.79, 121.11 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters that define the box-air mass factor (AMF) look-up table (LUT). The a priori NO2 profile and surface pressure used in this study for AMF calculations were obtained from TM5-MP CTM [54]. The model provides global coverage information of 34 atmospheric layers with a \(1^{\circ}\times 1^{\circ}\) grid resolution and 30 min temporal frequency.