A Novel ML–NWP Coupled Optimization Approach on a Reconstructed WRF Model

Optimizing numerical weather prediction (NWP) or correcting its errors using data-driven machine learning (ML) methods is a highly challenging task. To tackle this problem, we propose a coupled ML–NWP optimization framework that incorporates data-driven model bias calibration directly into NWP integration loops. By reimplementing the dynamic solver and physical parameterizations of the Weather Research and Forecasting (WRF) model in Python, we develop a tensor-based PyWRF model that fully supports automatic differentiation in PyTorch. A single-column neural network (NN) is coupled with PyWRF to enable observation-guided backward gradient propagation, facilitating feedback between observations and integration steps to modulate specific model variables. During numerical integration, online coupled training of the NN with PyWRF is achieved through local gradient masking, truncated backpropagation over a finite number of steps, and skip-connection-based variable transfer. Eight mesoscale precipitation events over East China were selected to train and evaluate the coupled model. The results demonstrate that the model trained on limited observational data within this framework exhibits robust generalization capability. Comparative experiments indicate that the proposed framework outperforms standalone NWP and conventional single-step artificial intelligence (AI) correction methods in forecast accuracy. This study provides a pathway for next-generation physics–data–intelligence weather forecasting systems.