The role of large-scale spatial patterns in the chaotic amplification of perturbations in a Lorenz’96 model

Abstract

The preparation of perturbed initial conditions to initialize an ensemble of numerical weather forecasts is a crucial task in current ensemble prediction systems (EPSs). Perturbations are added in the places where they are expected to grow faster, in order to provide an envelope of uncertainty along with the deterministic forecast. This work analyses the influence of large-scale spatial patterns on the growth of small perturbations. Therefore, we compare Lyapunov vector (LV) definitions, used in the initialization of state-of-the-art EPSs, with the so-called characteristic LVs. We test the dynamical behaviour of these LVs in the two-scale Lorenz’96 system. We find that the commonly used definitions of LVs include non-intrinsic and spurious effects due to their mutual orthogonality. We also find that the spatial locations where the small-scale perturbations are growing are ‘quantized’ by the large-scale pattern. This ‘quantization’ enhances the artificial disposition of the LVs, which is only avoided using the characteristic LVs, an unambiguous basis which may also be of great use in realistic models for assessing or initializing EPSs.