Runoff simulation based on granular computing by introducing terrain factors to construct climate characteristic index

High-precision and accurate runoff simulation is crucial for the management and allocation of water resources, the operation of hydraulic engineering, and the prevention of flood and drought disasters. However, there is currently no consensus on how to effectively filter and reshape the impact of numerous external factors influencing runoff, and also there is a lack of sufficient theoretical support. To maximize the metrics accuracy of the result of runoff simulation and better capture the internal hydrological characteristics of runoff, the concept of granular computing from the field of artificial intelligence was drawn on, terrain factors were extracted and their attribute features were optimal-selected based on granulation rules, and a Long Short-Term Memory (LSTM) model incorporating the climate characteristic index (LSTM-new) was developed based on delineated sub-region areas in this study. Finally, a unidirectional feedback framework was proposed, combining process-driven method based on the Variable Infiltration Capacity (VIC) model with a data-driven method using the established LSTM (CopulingVIC-new), to enhance the hydrological process characteristics of the simulated runoff and improve simulation accuracy. The results showed that the average NSE, R2, KGE, and RMSE of CopulingVIC-new during training, validation, and testing periods achieved 0.93, 0.92, 0.91, and 334.86 m3/s, respectively, which increased by 7.29%、2.97%、9.73%、-19.41% and 13.41%, 12.19%, 19.73%, -46.95% compared to uncoupled LSTM and VIC. Additionally, the proposed framework effectively captured the interannual variation trend of runoff in all seasons except late spring and summer, though it also overestimated the risk of the occurrence of annual maximum daily peak flow (AMDPF) and total flood volume of annual continuous maximum 5-day (TFAM5D) and thier joint variables. The overall results indicated that the scheme of introducing climate characteristic index, based on sub-region division, can more accurately capture extreme runoff in the study area, as well as the variation of seasonal runoff on both intra-annual and interannual scales. Although CouplingVIC-new still had limited ability to capture extreme flow, the structure of extreme value of the output runoff became more robust after unidirectional coupling. This research can help to expand the application of machine learning in hydrological modelling and provide a useful reference for related studies.