According to the idea of sequence decomposition-parameter optimization-subitem prediction-result superposition,we construct a medium and long-term monthly runoff prediction model integrating singular spectrum analysis (SSA)-gradient-based optimization (GBO) algorithm with correlation vector machine (RVM) and support vector machine (SVM).To start with,SSA is conducted to process the monthly runoff data of the example and thereby extract multiple independent subsequences.Then,the principle of the GBO algorithm is expounded,and the GBO algorithm is simulated and tested with 6 typical functions.The GBO algorithm is applied to optimize the RVM kernel width factor and hyperparameters as well as the SVM penalty factor and kernel function parameters.SSA-GBO-RVM and SSA-GBO-SVM models are built to predict each subsequence,which is subsequently superimposed to serve as the final monthly runoff prediction result. Finally,the monthly runoff forecast for 65 years (780 months in total) at Longtan Station in Yunnan Province is discussed as an example.The first 53 years are selected as the training samples,and the next 10 years (120 months in total) are taken as the forecast samples to verify the SSA-GBO-RVM and SSA-GBO-SVM models.The results show that the GBO algorithm,with high optimization accuracy and great global search ability,is better than the marine predators algorithm (MPA) and the particle swarm optimization (PSO) algorithm in the optimization effect under different dimensional conditions.The SSA-GBO-RVM and SSA-GBO-SVM models have an average absolute percentage error of 6.20% and 7.82%,respectively,in the 120-month monthly runoff prediction for the example,respectively.The average absolute errors of the two models are 0.88 m3/s and 1.00 m3/s respectively,and the Nash coefficients are 0.992 6 and 0.991 3 respectively.This means the two models both have high prediction accuracy and reliability.Comparatively speaking,the SSA-GBO-RVM model is better than the SSA-GBO-SVM model.