A New Method to Determine Maximum Perturbation Growth in a Quasi-Geostrophic Ocean Model

Abstract

Analysing growth of initial perturbations in dynamical systems is an important aspect of predictability theory because it tells us which perturbations have the strongest influence on the system. For linear systems, these perturbation are the modes with the largest eigenvalues. For nonlinear systems, we consider the conditional nonlinear perturbation (CNOP). These can be found by solving a nonlinear constrained maximization problem, which is typically done using sequential quadratic programming (SQP), a routine that requires an adjoint model. Such adjoint models are not always available. Therefore, we study two adjoint-free methods: PSO and COBYLA. Because such methods typically work best on low-dimensional problems, we apply dimension reduction. We use the proposed methodology to find the CNOPs of a quasi-geostrophic ocean model. We find that COBYLA outperforms PSO and is able to find reasonable CNOPs, although at a higher computational cost than conventional adjoint-based methods.