Prediction and Attribution Analysis of Surface Upward Longwave Radiation Based on a Hybrid Neural Network Model

Accurate prediction of surface upward longwave radiation (SULR) is crucial for understanding Earth’s energy balance and climate dynamics. Traditional approaches, such as physical models and empirical regressions, often fail to handle the complexity and variability of environmental data. To overcome these challenges, this study introduces a hybrid neural network model integrating several advanced techniques: the Alpha Evolution (AE) optimizer, a Transformer-LSTM neural network, Adaptive Bandwidth Kernel Density Estimation (ABKDE), and SHAP-based interpretability analysis. The AE optimizer fine-tunes model parameters to enhance convergence and efficiency. The Transformer-LSTM architecture uses self-attention and long short-term memory to capture complex temporal patterns in the data. ABKDE delivers reliable interval predictions for SULR, while SHAP uncovers feature importance and the rationale behind model decisions. Using datasets from two stations in the Taihu region, the hybrid model was compared with LSTM, GRU, Transformer, and theoretical models. Results indicate that the hybrid model notably outperforms traditional methods, as evidenced by improvements in R², RMSE, and MAE. Furthermore, ABKDE shows high accuracy in interval predictions, while SHAP analysis identifies water temperature, air temperature, and downward longwave radiation as the most influential factors affecting SULR. By offering a robust, interpretable SULR prediction model, this study advances Earth’s energy balance research and presents promising applications in climate modeling and environmental monitoring.