The application of nonlinear local Lyapunov vectors to the Zebiak–Cane model and their performance in ensemble prediction

Abstract

Nonlinear local Lyapunov vectors (NLLVs) are the nonlinear extension of the Lyapunov vectors (LVs) based on linear error growth theory. As a development of bred vectors (BVs), NLLVs retain the time-saving, simply-applied and flow-dependent advantages of BVs. However, unlike BVs, NLLVs correspond not only to the leading LV but also to other orthogonal LVs. In this paper, NLLVs are applied to the Zebiak–Cane (ZC) coupled model. First, using the analysis data from the ensemble Kalman filter, we explore the effect of the parameters of the breeding process on calculating the NLLVs. It is found that the statistical properties of NLLVs are not very sensitive to the breeding parameters. However, the higher NLLVs (i.e., excluding NLLV1) show temporal randomness. Then, we study the characteristics of the spatial structures and growth rates of different NLLVs. The different NLLVs each have a certain probability of being the fastest error growth direction and together construct the error growth subspace of the ZC model. Compared with BVs, the NLLVs have some advantages in terms of the relationship between the generated error growth subspace and the analysis errors. The NLLVs also have higher local dimensionality than the BVs. NLLVs, as initial ensemble perturbations, are applied to the ensemble prediction of ENSO in a perfect environment. Compared with the results obtained using ensembles employing the random perturbation technique and the BV method, the present results demonstrate the advantages of using the NLLV method in ensemble forecasts.