###### Abstract  
The movement of water flow usually has history and path dependence. Fractional calculus is very suitable for describing the process with memory and hereditary properties. In this study, the order of the differential equation in the Nash confluence system was extended from integer order to fractional order. On the basis of the Laplace transform, the fractional instantaneous unit hydrograph was obtained, which was used to describe the long-term memory of the basin confluence system. Furthermore, the enhanced TOPMODEL (FTOP) model was obtained by applying the fractional instantaneous unit hydrograph as the surface runoff calculation. Taking Chengcun Basin in China as an example, the FTOP model was used to simulate the daily runoff and 22 floods from 1989 to 1996. The simulation results were compared with two original TOPMODEL models (the NTOP and ITOP models). The results show that in the daily runoff simulation, the Nash-Sutcliffe efficiency (NSE), relative error (RE), and root mean square error (RMSE) of the FTOP model were 0.82, \(-\)11.4%, and 15.25 m\({}^{3}\)/s, respectively, being slightly better than the other two TOPMODEL models. According to the hydrologic frequency curve, the measured daily runoff was divided into different flow levels. It was found that the FTOP model can improve the simulation effect of the medium-flow (frequency between 10% and 50%) and low-flow (frequency more than 50%) sections to a certain extent. In the flood simulation, the average runoff depth relative error (RDRE), peak discharge relative error (PDRE), peak occurrence time error (POTE), and NSE of 22 floods were 1.99%, 14.06%, \(-\)1.27, and 0.88, respectively, indicating that the simulation effect had been improved. Especially in NSE, the improvement was more prominent, meaning that the FTOP model can better simulate the flooding process. However, the flood peak and runoff depth simulation effect were not significantly improved. These conclusions indicate that the confluence method using the fractional instantaneous unit hydrograph as the TOPMODEL model can improve the simulation effect. T 2023 20  
with the improvement of computing power and the development of the Geographic Information System (GIS), increasingly more distributed hydrological models have been widely used, such as the Soil and Water Assessment Tool (SWAT) model [13], the Hydrologic Simulation Program-Fortran (HSPF) model [14], the Topographic Kinematic Approximation and Integration (TOPKAPI) model [15], and the Variable Infiltration Capacity (VIC) model [16]. However, the input data are complicated, being challenging to meet in some areas lacking data. As a typical semi-distributed hydrological model, the TOPMODEL was proposed in 1979 [17] by [PERSON] and [PERSON]. The TOPMODEL is a link between lumped and distributed hydrological models and has been widely concerned due to its clear physical concept, simple structure, and few optimal parameters [18]. Given the advantages of the TOPMODEL model, many researchers have applied it to many fields. For example, the TOPMODEL model is used to analyze the impact of climate change on runoff [19; 20; 21], as well as to calculate soil moisture content [22; 23], water resources management [24; 25], the impact of urbanization on hydrology [26; 27], and the impact of land use on runoff [28; 29]. To improve the simulation effect of the TOPMODEL model, many researchers have also studied the influencing factors of simulation results. Many studies have analyzed the influence of the resolution and the creation method of the Digital Elevation Model (DEM) on the TOPMODEL model output [30; 31; 32; 33; 34; 35; 36; 37; 38; 39]. Some studies also analyzed the influence of the catchment runoff coefficient [40], topographic index calculation method [41; 42; 43], model parameters [44; 45; 46; 47; 48], and rainfall input conditions [49; 50; 51] on the results of TOPMODEL. Meanwhile, many improvements to the TOPMODEL model have been proposed. These improvements mainly include the following aspects.