The Pacific Decadal Oscillation (PDO), as the dominant mode of decadal sea surface temperature variability in the North Pacific, exhibits both interannual and decadal fluctuations that significantly influence global climate. The complexity associated with PDO changes poses challenges for accurate predictions. This study develops a BiLSTM-WOA-MMD (BWM) model, which integrates a bidirectional long short-term memory network with a whale optimization algorithm (WOA) and multiple modal decomposition (MMD), to forecast PDO at both interannual and decadal time scales. The model successfully predicts monthly/annual average PDO index of up to 15 months/5 years in advance, achieving a correlation coefficient of 0.56/0.55. By utilizing the WOA to effectively optimize hyperparameters, the model enhances the PDO prediction skill compared to existing deep learning PDO prediction models, improving the correlation coefficient from 0.47 to 0.68 at a 6-month lead time. The combination of MMD and WOA further minimizes prediction errors and extends the forecasting effective time to 15 months by capturing essential modes. The BWM model can be employed for future PDO prediction and the predicted PDO will remain in its cool phase in the next year both using the PDO index from NECI and derived from near-time satellite data. This proposed model offers an effective way to advance the prediction skill of climate variability on multiple time scales by utilizing all kinds of data available including satellite data, and provides a large-scale background to monitor marine heatwaves.

A mesoscopic lattice Boltzmann method based on the BGK model is proposed to solve a class of two-dimensional second-order nonlinear partial differential equations by incorporating an amending function. The model provides an efficient and stable framework for simulating initial value problems of second-order nonlinear partial differential equations and is adaptable to various nonlinear systems, including strongly nonlinear cases. The numerical characteristics and evolution patterns of these nonlinear equations are systematically investigated. A D2Q4 lattice model is employed, and the kinetic moment constraints for both local equilibrium and correction distribution functions are derived in the four velocity directions. Explicit analytical expressions for these distribution functions are presented. The model is verified to recover the target macroscopic equations in the continuous limit via Chapman–Enskog analysis. Numerical experiments using exact solutions are performed to assess the model’s accuracy and stability. The results show excellent agreement with exact solutions and demonstrate the model’s robustness in capturing nonlinear dynamics.