## 3 Results
### Further Analysis of New Model  
#### 3.2.1 Model Performance Under Different Conditions  
By considering the superior performance of New Model, more analysis on this model was conducted in terms of its performance under various conditions including time scales, moments, geolocations, and land cover types. Furthermore, the estimated \(R_{nd\text{-}Cd\text{-}NM}\) was used to represent the accuracy of New Model. It is known that the largest difference between New Model and the existing models is that it could estimate \(C_{d}\) at any moment during 9:30-14:30 hours. To illustrate the  
Figure 8: The validation accuracy of the estimated \(R_{nd\text{-}Cd\text{-}NM}\) from New Model against the validation samples corresponding to (**a**) \(S\) model and (**b**) \(R\) model. The red and blue dot dash lines in (**a**) represent Bias and rRMSE, respectively. influence of different time scales on this model, the \(R_{nd\text{-}Cd\text{-}NM}\) estimates at the interval of 1/10/20/30/60 min were validated against the SURFRAD measurements at the central moments of 10:30 hour, 12:00 hour, and 13:30 hour, respectively, and the results are shown in Figure 9. From the results, the performance of New Model represented by \(R_{nd}\) estimation was relatively stable for different time scales at the three specific moments, with the changes in the validated RMSE all being less than 1.5 Wm\({}^{-2}\), but 30 min was the relatively optimal one. Hence, it is suggested to apply New Model at a time scale within 60 min, especially 30 min. Additionally, the \(R_{nd\text{-}Cd\text{-}NM}\) estimation accuracy at different moments during 9:30-14:30 hours (30 min as an interval) was also explored and shown in Figure 10. The results demonstrated the accuracy of the estimated \(R_{nd\text{-}Cd\text{-}NM}\) was basically stable across all moments with a validated rRMSE of 12.10-15.01% (RMSE of 13.98-16.37 Wm\({}^{-2}\)), which indicated the robustness of New Model. Relatively, the model performed the best at 12:30 hour with the smallest rRMSE of 12.96% (RMSE = 13.98 Wm\({}^{-2}\)). Hence, the further it is from noontime (12:30 hour), the worse the estimated \(R_{nd\text{-}Cd\text{-}NM}\) accuracy, especially in the late afternoon. Meanwhile, it was also found that the \(C_{d}\) value is the smallest during noontime, which means that the uncertainty of the estimated \(R_{nd\text{-}Cd\text{-}NM}\) would decrease with decreasing \(C_{d}\). Afterwards, the validation results of the \(R_{nd\text{-}Cd\text{-}NM}\) were examined by their land cover types and shown in Figure 11. It can be seen that the \(R_{nd\text{-}Cd\text{-}NM}\) accuracy was generally stable for different land covers except for WET, with their validated R\({}^{2}\) values ranging from 0.90 to 0.96, RMSE of 12.49 to 18.22 Wm\({}^{-2}\), and Bias of \(-0.67\) to 5.81 Wm\({}^{-2}\). Relatively, the rRMSE of the forest types including DBF, EBF, DNF, and MF were smaller, with their values between 10.80 and 12.66%, whereas for other vegetation types having a small NDVI, such as GRA, OSH, and so on, their \(R_{nd\text{-}Cd\text{-}NM}\)-validated rRMSE was larger, ranging 14.29-15.53%. The results were consistent with our previous findings shown in Figure 6. But the poor accuracy for WET most likely resulted from the small sample size. Figure 9: Validation accuracy of the \(R_{nd\text{-}Cd\text{-}NM}\) estimates (represented by RMSE) for different time scales (1/10/20/30/60 min) against the measurements from SURFRAD at the central moment of 10:30 hour, 12:00 hour, and 13:30 hour, respectively. Finally, the spatial distribution of the \(R_{nl\text{-}Cd\text{-}NM}\) validation accuracy (Figure 12) demonstrated that New Model generally worked well around the globe, with most of the validated R\({}^{2}\) being larger than 0.90 (Figure 12a) and the RMSE (rRMSE) was within 20 Wm\({}^{-2}\) (15%) (Figure 12c,d), but the overestimation tendency was mainly observed over the Eastern hemisphere (red points in Figure 12b), and vice versa over the Western hemisphere (blue points in Figure 12b).