A hybrid SWAT-LSTM-transformer model for transferable runoff simulation in ungauged basins

Runoff simulation in ungauged basins remains a fundamental and challenging issue in hydrological science, with far-reaching implications for water resources management, flood control, and agricultural planning. While previous studies have extensively developed physically-based and data-driven models for runoff simulation in ungauged basins, both models are still constrained by limited cross-basin transferability and inadequate physical interpretability. To address these constrains, we propose a hybrid model for runoff simulations in a target ungauged basin through integrating the physically-based Soil and Water Assessment Tool (SWAT) model with the data-driven Long Short-Term Memory (LSTM) and Transformer models as a hybrid SWAT-LSTM-Transformer model. SWAT model with default parameters simulate runoff generation processes to quantify the relationship between meteorological forcing variables and observed runoff variables. And the bias of the relationship is simulated by the LSTM-Transformer model. Three metrics of R 2 , NSE , PBIAS are employed to evaluate the performances of the models. After the proposed SWAT-LSTM-Transformer model has been calibrated in a gauged basin, it is transferred to a target ungauged basin. There are three basins referring to Tao River water diversion project that are taken as case study area. One is the Upper Wei that is taken as the gauged basin for calibrating models while the other two are Tao, and Zuli River basins that are assumed to be target ungauged basins. The means of R 2 , NSE , and absolute PBIAS values are 0.897, 0.841, and 13.37% from transferring the hybrid SWAT-LSTM-Transformer model while they are 0.206, −4.405, and 106.65% from the transferring calibrated SWAT model and 0.257, −1.244, and 81.74% from the transferring LSTM-Transformer model in Tao, and Zuli River two target ungauged basins. The results demonstrate that the hybrid SWAT-LSTM-Transformer model outperforms both the calibrated SWAT model and the trained LSTM-Transformer model when they are transferred to the target ungauged basins. The relationships between the runoff and the runoff generation processes simulated by a physically-based model even with its default parameters can be captured by the data-driven model, which help to transfer the hybrid SWAT-LSTM-Transformer model. And the Transformer model was integrated with the LSTM model to improve the stability of model transfer and alleviate the limitation in high runoff simulations in the target ungauged basins. The sensitive parameters of the SWAT model and the contributions of inputs to the LSTM-Transformer are similar in both gauged and ungauged basins. Therefore, the proposed hybrid SWAT-LSTM-Transformer model is not only an effective approach in the case study area but also can be applied in a ungauged basin.