## 5 Results
### Evaluation Using Daily Observations from 2000 to 2020
#### 5.1.2 Monthly Time Scale  
In this subsection, the daily observations (i.e., target and reference precipitations) are compared on monthly time scales. In other words, the continuous and categorical metrics were computed for each month, including dry and wet months, using the daily observations to investigate the performance of the GPPs. In addition to providing the temporal accuracy characteristics of GPPs, the findings might benefit researchers working in individual months. In this regard, the computed metrics are presented using the Taylor Diagram [86] and Performance Diagram [87], through which the performance of the GPPs in multi-metric methods can be compared. The Taylor Diagram [86] focuses on precipitation intensity assessment metrics, i.e., RMSE, CC, and Standard Deviation (SD), for performance comparison, and the associated results are illustrated in Figure 7. In these diagrams, the points (i.e., representing target precipitations for GPPs) closer to the \"Reference\" (i.e., representing reference precipitations from synoptic stations) point, illustrated on the horizontal axis, show better performances. In other words, closer points to the \"Reference\" had lower RMSE values, higher CC values, and similar SD values to the reference precipitations. In general, Figure 7 illustrates that in drier months in Iran (i.e., June, July, August, and September), in which lower precipitations occur, all GPPs are relatively closer to the \"Reference\" point, indicating their better performances. This was because, in drier months, the obtained RMSE and SD values  
Figure 6: Obtained CSI values for (**a**) TMPA, (**b**) CHIRPS, (**c**) PERSIANN, (**d**) GSMaP, (**e**) IMERG, and (**f**) ERA5 at the station level using daily observations between 2000 and 2020.  
for all GPPs were closer to the ones obtained from reference precipitations. However, the results indicated that all GPPs had their lowest CC values in drier months. Figure 7 shows that TMPA and GSMaP always had lower SD values than reference precipitations, and the exact reverse for IMERG, while the other GPPs did not have identical characteristics. According to Figure 7, IMERG had the highest distance from the \"Reference\" point, mainly due to its higher RMSE and SD values compared to other GPPs. The IMERG CC values were mostly between 0.4 and 0.6 in wet months and lower than 0.4 in drier months, making it the third most accurate GPP. The two other GPPs, namely GSMaP and ERA5, had comparable performances since, in some months, GSMaP performed better and in the remnant, ERA5 had the highest accuracies, and no exact monthly pattern was seen. For these GPPs, the CC values were between 0.4 and 0.7, both had relatively lower RMSE values, and their SD values, especially ERA5, were much closer to the reference precipitations. The other GPPs, i.e., TMPA, CHIRPS, and PERISANN, had the weakest performance in nearly all months, where low CC, relatively higher RMSE, and disparate SD values were obtained. Figure 7: Taylor diagrams for comparing six GPPs using daily observations between 2000 and 2020 in the monthly time scale from (**a**–**l**) January to December, respectively. The Performance Diagram [87] focuses on precipitation occurrence assessment metrics, i.e., POD, success ratio (\(1-\text{FAR}\)), CSI, and biases, to compare GPPs performances, and related results are presented in Figure 8. In these diagrams, the points (i.e., representing target precipitation for GPPs) closer to the right top corner had better precipitations occurrence detectability. In other words, closer points to the right top corner had high POD and CSI values and low FAR and bias values. Figure 8 demonstrates that in nearly all months, PERSIANN obtained higher biases, except for two months, in which ERA5 and IMERG had higher values. Conversely, TMPA and CHIRPS, respectively, had the lowest biases in all months. Additionally, ERA5 achieved the highest POD values monthly time scale, which was most often followed by GSMaP.