Iterative methods for Lyapunov vectors and singular vectors and atmospheric predictability

Abstract

Iterative methods are used to generate Lyapunov vectors (LVs) and singular vectors (SVs). Their roles in describing atmospheric error growth and predictability are studied. LVs are produced by evolving a set of initially random perturbations and using a modified Gram-Schmidt re-orthogonalisation to ensure their orthogonality. The structures of LVs and SVs, and finite-time normal modes (FTNMs), are compared with patterns of 100 errors evolving in a barotropic tangent linear model.