Nonlinear Local Lyapunov Vectors and Their Potential Application in Ensemble Prediction

This study developed the nonlinear local Lyapunov vectors (NLLVs) to indicate orthogonal perturbations in phase space with different growth rates. In particular, the top ranking NLLVs are considered to be an appropriate orthogonal basis spanning the fast-growing subspace. The relationship between the NLLVs and the baroclinic structure is investigated and the physical and dynamical natures of the NLLVs are revealed. Using the quasi-geostrophic (QG) T21L3 model, we attempt to use the linear combination of the first few NLLVs to acquire the unstable perturbation mode. The results showed that the unstable mode can well represent the spatial structure of initial error growth. The maximum value regions over mid-high latitudes of the unstable mode are closely related to the baroclinic instabilities. Compared to the unstable modes constructed by the BVs, the ones derived by the NLLVs have higher spatial correlation with the spatial structure of initial error growth and better indentify the relative strength of error amplification. Since the initial perturbations of ensemble forecasting are generated to grasp the fast-growing directions, the NLLV method is expected to be further employed to produce initial ensemble perturbations.