# Performance Evaluation for China's Planned CO\({}_{2}\)-Ipda
## 4 Discussion
### Selection of an Appropriate Weighting Function  
As well as the precision and sampling coverage, the issue of the weighting function must be addressed. The direct physical quantity provided by CO\({}_{2}\)-IPDA is the total differential absorption optical depth, not the amount of CO\({}_{2}\). Different on-line wavelength selections yield different weighting functions. Because our goal is to map the distribution of carbon sinks and sources, we need retrievals to be sensitive to CO\({}_{2}\) in the lower troposphere where emission and uptake of carbon occurs. A weighting  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Unit: PPM**} & \multicolumn{6}{c}{**[PERSON] et al. [9]**} & \multicolumn{6}{c}{**[PERSON] et al. [34]**} \\ \cline{2-9}  & \multicolumn{2}{c}{**V7**} & \multicolumn{2}{c}{**V7r**} & \multicolumn{2}{c}{**FP**} & \\ \hline
**Latitude** & **Bias a** ** & **RMS** & **Bias** & **RMS** & **Bias** & **RMS** & **Bias** & **RMS** & **\(N\)** \\ \hline
75 N–85 N & 2.06 & 2.54 & 2.37 & 3.20 & 0.58 & 2.26 & 0.10 & 1.99 & 3 \\
60 N–70 N & 2.30 & 1.58 & 2.02 & 1.48 & 2.80 & 0.79 & 3.15 & 3.21 & 2 \\
45 N–55 N & 0.73 & 2.49 & 0.05 & 2.31 & 0.41 & 1.52 & 0.78 & 1.74 & 180 \\
30 N–40 N & 0.51 & 1.95 & 0.58 & 1.98 & 0.73 & 1.78 & 0.31 & 1.39 & 331 \\
20 S–0 & 0.57 & 1.49 & 0.13 & 1.56 & 0.19 & 1.00 & 0.34 & 0.88 & 299 \\
60 S–30 S & 0.45 & 2.43 & 0.02 & 2.28 & 0.01 & 1.51 & 0.28 & 1.37 & 799 \\ Global & 1.10 & 2.15 & 0.86 & 2.03 & 0.79 & 1.74 & 0.36 & 1.33 & / \\ \hline \hline \end{tabular}
\end{table}
Table 4: Validation of XCO\({}_{2}\) from OCO-2 with TCCON.  
Figure 13: Global atmospheric CO\({}_{2}\) concentrations from 1 January to 11 November 2016, as recorded by National Aeronautics and Space Administration (NASA)’s Orbiting Carbon Observatory-2.  
function is defined in Equation (13). \(p\) and \(T\) are atmospheric pressure and temperature, respectively, \(\sigma\) is the absorption cross-section, \(g\) is the acceleration due to gravity, and \(M_{air}\) is the average mass of a dry air molecule.  
\[\omega(p,T)=\frac{\sigma_{on}(p,T)-\sigma_{off}(p,T)}{gM_{air}} \tag{13}\]  
Using the US standard atmosphere model [36] and HITRAN2012 [37], we simulated a weighting function for several candidate on-line wavelengths belonging to line R18 in the 30012\(\leftarrow\)00001 CO\({}_{2}\) band.  
Figure 14a demonstrates that the central wavenumber is not the best candidate in terms of the WF 6361.195/6361.305 cm\({}^{-1}\) would be very sensitive to the lower troposphere. However, their corresponding differential optical depth would be small according to Figure 14b. As a consequence, the relative error would be enlarged dramatically according to Equation (1). 6361.225 cm\({}^{-1}\) is moderately sensitive to the lower and is evidently better than the central wavelength in terms of the WF. Meanwhile, its corresponding differential optical depth is over 0.8. Consequently, 6361.225 cm\({}^{-1}\) could represent a good compromise for selection of an on-line wavenumber.  
Our previous study showed that selecting an on-line wavenumber in R16 may give lower interference from water vapor [30]. Consequently, a displacement of 0.2 cm\({}^{-1}\) from the line center of R16 (i.e., 1.6 \(\upmu\)m) probably represents the optimum solution for selection of an on-line wavelength.