Comparison of Nonlinear Local Lyapunov Vectors and Bred Vectors In Estimating The Spatial Distribution of Error Growth

Abstract

Instabilities play a critical role in understanding atmospheric predictability and improving weather forecasting. The bred vectors (BVs) are dynamically evolved and flow-dependent nonlinear perturbations, indicating the most unstable modes of the underlying flow. Especially over smaller areas, however, BVs with different initial seeds may to some extent be constrained to a small subspace, missing potential forecast error growth along other unstable perturbation directions. In this paper, the authors study the nonlinear local Lyapunov vectors (NLLVs) that are designed to capture an orthogonal basis spanning the most unstable perturbation subspace, thus potentially ameliorating the limitation of BVs. The NLLVs are theoretically related to the linear Lyapunov vectors (LVs), which also form an orthogonal basis. Like BVs, NLLVs are generated by dynamically evolving perturbations with a full nonlinear model. In simulated forecast experiments, a set of mutually orthogonal NLLVs show an advantage in predicting the structure of forecast error growth when compared to using a set of BVs that are not fully independent. NLLVs are also found to have a higher local dimension, enabling them to better capture localized instabilities, leading to increased ensemble spread.