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, −11.14%, and 15.25 m3/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.

Improving the accuracy of runoff simulations is a significant focus of hydrological science for multiple purposes such as water resources management, flood and drought prediction, and water environment protection. However, the simulated runoff has limitations that cannot be eliminated. This paper proposes a method that integrates the hydrological and time series models to improve the reliability and accuracy of simulated runoffs. Specifically, the block-wise use of TOPMODEL (BTOP) is integrated with three time series models to improve the simulated runoff from a hydrological model of the Zhou River Basin, China. Unlike most previous research that has not addressed the influence of runoff patterns while correcting the runoff, this study manually adds the hydrologic cycle to the machine learning-based time series model. This also incorporates scenario-specific knowledge from the researcher’s area of expertise into the prediction model. The results show that the improved Prophet model proposed in this study, that is, by adjusting its holiday function to a flow function, significantly improved the Nash–Sutcliffe efficiency (NSE) of the simulated runoff by 53.47% (highest) and 23.93% (average). The autoregressive integrated moving average (ARIMA) model and long short-term memory (LSTM) improved the runoff but performed less well than the improved Prophet model. This paper presents an effective method to improve the runoff simulation by integrating the hydrological and time series models.

Quantitative analysis of changes in Lhasa River runoff components was significant to local water resources management. This study constructed the spatial processes in hydrology (SPHY) model in the Lhasa River Basin and optimized the model’s parameters using the hydrograph partitioning curves (HPC) method. The Lhasa River Basin’s precipitation and temperature were forecasted for 2020 to 2100 using the statistical downscaling model (SDSM) and two scenarios from the fifth generation of the Canadian earth system model (CanESM5) dataset, shared socioeconomic pathways 1-2.6 (SSP1-2.6) and shared socioeconomic pathways 2-4.5 (SSP2-4.5). This study analyzed the potential changes in Lhasa River runoff and components based on the future climate. The results showed that the Lhasa River runoff from 2010 to 2019 was composed of snowmelt runoff, glacier melt runoff, rainfall runoff, and baseflow, with the proportions of 15.57, 6.19, 49.98, and 28.26%, respectively. From 2020 to 2100, under the SSP1-2.6 scenario, the precipitation and average temperature increased by 0.76mm and 0.08 °C per decade. Under the SSP2-4.5 scenario, the increasing rate was 3.57 mm and 0.25 °C per decade. Due to the temperature increase, snowmelt and glacier melt runoff showed a decreasing trend. The decline rate of total runoff was 0.31 m3/s per year under the SSP1-2.6 scenario due to the decrease in baseflow. Under the SSP2-4.5 scenario, total runoff and rainfall runoff showed a clear increasing trend at an average rate of 1.13 and 1.16 m3/s per year, respectively, related to the significant increase in precipitation. These conclusions suggested that climate change significantly impacted the Lhasa River’s total runoff and runoff components.

Parameter sensitivity analysis is a significant part of quantifying model uncertainty, effectively identifying key parameters, and improving the efficiency of parameter optimization. The Soil and Water Assessment Tool (SWAT) model was applied to the upper Heihe River basin (UHRB) in China to simulate the monthly runoff for 11 years (1990–2000). Four typical sensitivity analyses, namely, the Morris screening, Sobol analysis, Fourier amplitude sensitivity test (FAST), and extended Fourier amplitude sensitivity test (EFAST), were used to determine the critical parameters affecting hydrological processes. The results show that the sensitivity parameters defined by the four methods were significantly different, resulting in a specific difference in the simulation effect of the SWAT model. The reason may be the different sampling process, sensitivity index, and calculation principle of each method. The snow-melt base temperature (SMTMP) and snowfall temperature (SFTMP) related to the snow-melt process, the available water capacity of the soil layer (SOL_AWC), saturated hydraulic conductivity (SOL_K), depth from the soil surface to the bottom of the layer (SOL_Z), moist bulk density (SOL_BD), deep aquifer percolation fraction (RCHRG_DP), and threshold depth of water in the shallow aquifer required for return flow to occur (GWQMN) related to the soil water and groundwater movement, baseflow alpha factor for bank storage (ALPHA_BNK) related to the base flow regression, and average slope steepness (HRU_SLP) are all very sensitive parameters. The 10 key parameters were optimized 100 times with the sequential uncertainty fitting procedure version 2 (SUFI-2). The Nash–Sutcliffe efficiency coefficient (NSE), Kling–Gupta efficiency coefficient (KGE), mean square error (MSE), and percentage bias (PBIAS) were 0.89, 200, 8.60, and 0.90, respectively. The simulation results are better than optimizing the sensitive parameters defined by the single method and all the selected parameters. The differences illustrate the rationality and importance of parameter sensitivity analysis for hydrological models and the synthesis of multiple approaches to define sensitive parameters. These conclusions have reference significance in the parameter optimization of the SWAT model when studying alpine rivers by constructing the SWAT model.