## 1 Introduction  
Accurate runoff prediction plays a critical role in the efficient and optimal allocation of water resources. Effective runoff prediction can be used for flood control, drought resistance, power generation, and irrigation [1; 2; 3; 4]. In recent years, runoff prediction has received much attention. These studies focus on the exploration and application of neural network models, and the development and performance improvement of physical models. [PERSON] et al. [5] proposed two multi-timescale Long Short-Term Memory architectures that jointly predict multiple timescales within one mode, which can process different input variables at different timescales. An Adaptive Neural Fuzzy Inference System (ANFIS) model was developed to determine the discharge coefficient of the labyrinth spillway and thus predict runoff [6]. A Bayesian geostatistical method was used to interpolate hydrological data with different spatial support, and the model was evaluated by predicting the annual runoff in the watershed around Vos, Norway [7]. It was found that combining the point and surface data produced a higher prediction accuracy compared to using only one data type. In addition, to describe the nonhomogeneous characteristics of runoff series, a novel prediction model was established based on a nonhomogeneous Markovchain (NHMC-RPM) [8]. Furthermore, Excel solver was a promising way to reduce the problems of the parameter estimation of the nonlinear Muskingum routing models [9]. A reverse flood routing approach was developed based on the Muskingum model, and results indicated that the proposed methodology could substantially (up to almost 82%) improve the comparison with the observed inflows [10]. It has been shown that the Bayesian network-cluster model provides a suitable approach for predicting pollutant transport in natural rivers [11]. With the continuous development of machine learning, machine learning methods have been widely used in runoff predictions because of their excellent performance and relatively high applicability. For instance, the Artificial Neural network model and Long Short-Term Memory network model were applied to simulate the rainfall-runoff process according to flood events from 1971 to 2013 in the Fen River basin, monitored by 14 rainfall stations and one hydrologic station [12]. The results show that the two networks are both suitable for rainfall-runoff models and are better than conceptual and physical-based models. [PERSON] et al. [13] proposed a support vector regression hydrologic uncertainty processor (SVR-HUP) model to predict the monthly, flood season, and annual runoff volumes. It was demonstrated that an SVR-HUP can predict the long-term runoff accurately and quantify the prediction uncertainty reasonably. A study of the daily runoff simulation was carried out based on the SVM-Copula model [14], and the results showed that the model can maintain the statistical characteristics of the original daily runoff series well, which means it could be a new way of random simulation in the case of insufficient data. In 2020, a Support Vector Machine-Artificial Flora (SVM-AF) hybrid model was used for the prediction of the daily streamflow [15]. The results showed that the proposed hybrid SVM-AF model outperformed the wavelet support vector machine model and the Bayesian support vector machine model in effectively predicting the flow and daily discharge. In the arid watershed, [PERSON] and [PERSON] [16] applied the Back Propagation Neural Network (BPNN), the Feed Forward Back Propagation Neural Network (FFBPNN), and the Cascade Forward Back Propagation Neural Network CFBPNN) algorithms for the prediction of the runoff. The results showed that the BPNN model is more suitable for predicting the connection between rainfall and runoff. As different evaluation criteria were chosen, it is evident that the best model identified by each criterion is different. Due to the model-dependence, a scientific method is a key issue in runoff prediction.