## 4 Discussion and Conclusions  
On the daily-scale runoff simulation surface, the simulation effect of the FTOP model was not very prominent throughout the simulation period. However, when the runoff was divided into different levels, it can be seen that the advantages of the FTOP model gradually showed. Especially in the low-flow section, the benefits were more pronounced. Comparing the three TOPMODEL models, when other parts were consistent, the differences in the confluence method led to the above differences. Therefore, we can find that the fractional instantaneous unit hydrograph system had apparent advantages in simulating low flow.  
The FTOP model had the most obvious advantage in the hour-scale flood simulation in NSE. NSE focused on the entire flood process and can intuitively reflect the fit between the simulated and measured flow. Although the FTOP model has fewer advantages in simulating the peak flow, peak time, and flood water volume, the FTOP model can simulate the entire flood process well. It also proves that the fractional instantaneous unit hydrograph confluence system can better simulate the whole process of a flood.  
In this study, a fractional instantaneous unit hydrograph confluence system was introduced on the original framework of the TOPMODEL model. The daily runoff and 22 floods in the Chengcun Basin from 1989 to 1996 were simulated using the improved TOPMODEL (FTOP) model. The following are the main conclusions from comparing the simulation results with the original two TOPMODEL models: the NTOP model (the integer instantaneous unit hydrograph method as the confluence method) and the ITOP model (isochrones method as the confluence method).  
(1) In the daily-scale runoff simulation, the NSE, RE, and RMSE of the FTOP model were 0.82, \(-\)11.14%, and 15.25 m\({}^{3}\)/s, respectively, throughout the simulation period, indicating that the simulation results were acceptable. The flow during the simulation period was divided into the high flow section, the medium flow section, and the low flow section. The FTOP model had no apparent advantage in the simulation effect of the high flow part. However, in the middle and low flow sections, the simulation effect of the FTOP model was better than that of the NTOP model and the ITOP model.  
Figure 8: Box plots of four statistical values of the FTOP, NTOP, and ITOP models. The figure’s dotted line represents each statistic’s relative optimal value. (**a–d**) respectively describe the box plots of RDRE, PDRE, POTE, and NSE of the three models.  
(2) In terms of hourly scale flood simulation, the average RDRE, PDRE, POTE, and NSE of the FTOP model in the 22 floods were 1.99%, 14.06%, \(-\)1.27, and 0.88, respectively. Compared with the NTOP and ITOP models, the simulation effect was improved to a certain extent. Especially in terms of NSE, the improvement was more prominent, which shows that the FTOP model can better simulate the flow process of the entire flood.  
Conceptualization, X.X.; formal analysis, X.X.; funding acquisition, T.A. and X.L.; methodology, X.X.; software, X.X.; supervision, X.X. and X.L.; visualization, X.X.; writing--original draft, X.X.; writing--review and editing, X.X. and X.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Regional Innovation Cooperation Program (2020 YFQ0013) and Key R&D Project (2021 YFS0285) from the Science and Technology Department of Sichuan Province, as well as the Key R&D Project (XZ202101 ZY0007G) from the Science and Technology Department of Tibet.  
Not applicable.  
The study did not report any data.  
The authors thank the anonymous referees for their valuable comments and suggestions.  
The authors declare no conflict of interest.