## 2 Materials and Methods
### Data  
#### 2.2.1 MOPITT CO Retrievals  
MOPITT, aboard NASA's Terra satellite, is the first space-borne instrument to provide measurements of CO on a continuous basis since March 2000 [71]. MOPITT operates in a sun-synchronous orbit at an altitude of 705 km with an equator-crossing time at 10:30 a.m. local time. It has a swath width of 640 km, crossing the satellite track with a footprint size of 22 km \(\times\) 22 km at nadir and can complete global measurement coverage every 3 days [71]. MOPITT measures CO in the 4.7-\(\upmu\)m TIR band and 2.3-\(\upmu\)m NIR band simultaneously. TIR radiances are most sensitive to CO in the middle and upper troposphere, whereas NIR observations mainly provide information about the CO total column with uniform sensitivity throughout the troposphere [72]. In the MOPITT CO data products, the retrieved CO profiles are expressed by a floating surface level and nine uniformly spaced levels from 900 hPa to 100 hPa [73]. Since data products Version 5 [72], MOPITT provides multi-spectral TIR/NIR joint retrieval CO products with greater sensitivity to CO in the lower troposphere [74], which can be used to invert surface-CO emissions [15; 28; 38]. In this research, MOPITT version 8 (V8) multi-spectral TIR/NIR CO retrieval data products (MOPV8) [75; 76] were used. Overall biases of MOPV8 [75; 76] vary from about \(-5\%\) at 600 hPa to about 7% at 200 hPa [77], and bias drift has been decreased to statistically negligible values (0.1% yr\({}^{-1}\) or less) at all retrieval levels [77]. A recent study comparing MOPITT V8 CO retrieval products [75; 76] with aircraft profiles (including in the winter) also showed that MOPITT generally agrees reasonably well with in situ profiles over both urban and non-urban regions, with biases ranging from \(-0.7\%\) to \(0.0\%\)[78]. Figure 2 shows the average of the averaging kernel row sums of CO retrievals over the domain (shown by Figure 1) in four consecutive winter seasons (i.e., December-February) from 2017 to 2020 in MOPV8] [75; 76]. The mean averaging kernel row sums of the surface level (1000 hPa in Figure 2) was about 0.25. Table 2 shows the Mean Absolute Error (MAE), RMSE, and percentage of difference relative to a priori between CO retrievals and thecorresponding a priori CO mixing ratios in MOPV8J. The a priori CO mixing ratios are based on climatological values form 2000 to 2009, simulated by the CAM-Chem model [75]. For each level, the greater the deviation of the retrieved value from the a priori ratios, the more information content the MOPITT observation provides [79]. In Table 2, the difference relative to the a priori ratio of the surface-level CO was 14.79%, which was similar to that of the other levels, suggesting that MOPITT's surface-level observations contain roughly the same amount of information as the other levels. In order to compare vertical CO concentration profiles modeled by the CO flux inversion system with MOPITT CO retrievals, the modeled CO concentration profiles need to be converted by an observation operator \(F\) defined as [37]: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Level** & **MAE** & **RMSE** &
\begin{tabular}{c} **Difference Relative** \\ **to a Priori (\%)** \\ \end{tabular} \\ \hline Surface & 12.66 & 23.94 & 14.79 \\
900 hPa & 12.57 & 20.71 & 10.22 \\
800 hPa & 11.14 & 15.65 & 9.87 \\
700 hPa & 10.51 & 13.93 & 9.96 \\
600 hPa & 10.60 & 13.56 & 10.30 \\
500 hPa & 11.20 & 14.74 & 11.33 \\
400 hPa & 13.74 & 20.22 & 14.69 \\
300 hPa & 15.15 & 24.13 & 18.18 \\
200 hPa & 5.83 & 9.69 & 10.80 \\
100 hPa & 0.75 & 1.16 & 3.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analysis of the difference between the CO retrievals and the a priori CO-mixing ratios over the domain in four consecutive winter seasons from 2017 to 2020 in MOPV8J. Figure 2: Average of the averaging kernel row sums of CO retrievals over the domain in four consecutive winter seasons from 2017 to 2020 in MOPV8J. The horizontal bars represent the standard deviation of each level.