Abstract:
Motivated by the long-standing limitation of traditional perturbation methods in jointly accounting for initial and model errors, which has constrained further improvements in ensemble forecasting performance, this study systematically introduces a new optimal perturbation theory—the nonlinear forcing singular vector (NFSV)—to address this challenge. Innovatively, this theory quantifies the combined effects of multiple sources of model error through model “tendency perturbations” and, based on the intrinsic linkage between the growth of initial errors and model errors, proposes a new framework in which the coordinated growth of initial and model perturbations is represented by a “full tendency perturbation.” It further develops a novel approach in which the optimal full tendency perturbation, namely the combined nonlinear forcing singular vector (C-NFSV), is solved to characterize the synergistic effects of initial errors and model errors. In this way, the theory breaks, at the dynamical-mechanism level, with the conventional separation of these two types of errors and overcomes the limitations of traditional methods.C-NFSV, when applied to ensemble forecasting, effectively quantifies the synergistic influence of these two types of errors and shows clear advantages over mainstream international methods in improving forecast skill for high-impact events. In tropical cyclone forecasting, it more accurately captures sharp turning points in cyclone tracks and reproduces rapid intensification processes with higher probability, thereby substantially reducing forecast biases for extreme tropical cyclones. In El Niño prediction, it effectively distinguishes the air–sea coupling characteristics of different El Niño types and significantly enhances ensemble prediction capability for event diversity. This theory and methodology provide a fundamentally new framework for forecasting high-impact weather and climate events. In the future, if deeply integrated with artificial intelligence technologies, it is expected to help overcome key bottlenecks in ensemble forecasting, including the high computational cost and the fragmented treatment of uncertainties across different components of the Earth system, thereby providing more efficient and reliable scientific support for meteorological disaster warnings and climate-related decision-making.