Conditional Nonlinear Optimal Perturbations: Adjoint-Free Calculation Method and Preliminary Test

Abstract

An ensemble-based approach is proposed to obtain conditional nonlinear optimal perturbation (CNOP), which is a natural extension of linear singular vector to a nonlinear regime. The new approach avoids the use of adjoint technique during maximization and is thus more attractive. Comparisons among CNOPs of a simple theoretical model generated by the ensemble-based, adjoint-based, and simplex-search methods, respectively, not only show potential equivalence of the first two approaches in application according to their very similar spatial structures and time evolutions of the CNOPs, but also reveal the limited performance of the third measure, an existing adjoint-free algorithm, due to its inconsistent spatial distribution and weak net growth ratio of norm square of CNOP comparing with the results of the first two methods. Because of its attractive features, the new approach is likely to make it easier to apply CNOP in predictability or sensitivity studies using operational prediction models.