# Performance Evaluation for China's Planned CO\({}_{2}\)-Ipda
## 3 Results
### Critical Environmental Parameters  
When other conditions remain unchanged, the relationship between each parameter discussed above and the performance of the CO\({}_{2}\)-IDPA load is linear. Nevertheless, the relationship between critical environmental parameters and the performance of the CO\({}_{2}\)-IPDA is nonlinear. Referring to Equation (2), the composition of the errors in a single pulse is very complex. When the reflectance is so large that the dark current noise is a relatively small component of the total error, the relative random error is inversely proportional to \(P\), which is linearly related to the reflectance. However, when the dark current noise dominates the total noise, any slight increase in \(P\) leads to a significant improvement in the SNR. This explains why the relationship between reflectance and relative random error is not linear.  
Regarding reflectance, when the surface reflectance is greater than 0.4, the relative error decreases slowly and almost linearly with increasing reflectance. In contrast, the relative error increases dramatically with decreasing reflectance when the reflectance is lower than 0.15. This relationship could be an obstacle to obtaining accurate and precise measurements with high spatial resolution over seas, where the reflectance is rarely greater than 0.08. Meanwhile, the land surface reflectance varies between 0.1 and 0.6 with respect to different land cover types, implying that the spatial distribution of the performance of the CO\({}_{2}\)-IPDA may be heterogeneous.  
Figure 7 demonstrates accelerating growth in the relative error with increasing AOD. Surprisingly, the increase in the relative error caused by high aerosol loadings overwhelms that caused by low surface reflectance. \(P\) is proportional to \(\tau^{2}\) and \(\tau=e^{- AOD}\). Hence, \(P\) is inversely proportional to the square of AOD. This explains why the effect of AOD is larger than that of reflectance.  
Figure 7 explicitly demonstrates that the relative error could easily exceed the threshold of 1%. When AOD is greater than 2, meaningful measurements cannot be acquired by the CO\({}_{2}\)-IDPA. Taking into account the frequent occurrence of heavy pollution [32] and the high AOD levels [33] in China, it would be a challenging task to retrieve XCO\({}_{2}\) accurately over most urban areas.  
Figure 6: The effect of hardware parameters on the relative random error.  
Figure 8 demonstrates the combined effect of two key environmental parameters on the performance of China's CO\({}_{2}\)-IDPA. The ideal target cannot be reached in regions where the AOD is greater than 1.3. The reflectance of most human settlements where anthropogenic CO\({}_{2}\) is emitted into the atmosphere is lower than 0.35, suggesting that the maximum AOD that allows the ideal performance target to be met may be 0.8, unless further improvements are made to the hardware system or the retrieving algorithm. Ideal results are very likely to be obtained over forests because aerosol loadings are usually low. In desert areas, where the reflectance can reach 0.6, the retrieval threshold will not be exceeded even when AOD > 2, indicating that China's CO\({}_{2}\)-IPDA could yield useful results when these regions experience sandstorms. As shown in Figures 7 and 8, environmental parameters seem to play a much more significant role in determining the performance of the CO\({}_{2}\)-IDPA when the margins for improvement in the hardware and orbital parameters are small. To this end, a detailed simulation will be carried out, supported by real measurements of reflectance and AOD acquired by remote sensing satellites, to explore the performance of China's CO\({}_{2}\)-IDPA in China and surrounding regions, and to facilitate finalization of the prototype design.  
Figure 8: The effect of environmental parameters on the relative random error.  
Figure 7: The independent effects of reflectance and AOD on the performance of the CO\({}_{2}\)-IPDA. (a) shows Reflectance and (b) panel shows AOD.