An adjoint-free method to determine conditional nonlinear optimal perturbations

The analysis of the growth of initial perturbations in dynamical systems is an important aspect of predictability theory because it informs on error growth. The Conditional Nonlinear Optimal Perturbation (CNOP) method is an approach where the nonlinear growth of perturbations is determined over a certain lead time. The CNOPs can be found by a nonlinear constrained optimisation problem, which is typically solved using sequential quadratic programming (SQP), a routine that requires an adjoint model. Such adjoint models are not always available and hence we here study the performance of an adjoint-free optimisation method (COBYLA), in combination with a dimension reduction technique, to determine CNOPs. The new technique is applied to a quasi-geostrophic model of the wind-driven ocean circulation. We find that COBYLA is able to find good approximations of CNOPs, albeit at a higher computational cost than conventional adjoint-based methods.