Conditional Nonlinear Optimal Perturbation: A New Approach to the Stability and Sensitivity Studies in Geophysical Fluid Dynamics

In the stability, sensitivity and predictability studies in geophysical fluid dynamics, linear singular vector (LSV), which is the fastest growing perturbation of the linearized model, is one of the useful tools. However, the linear approximation has strong limitations on the applicability of LSV, since it ignores the nonlinear processes, such as wave-mean flow interactions. The authors have proposed a new method called CNOPs (Conditional Nonlinear Optimal Perturbations), which generalizes LSV into the fully nonlinear category. CNOP is the initial perturbation whose nonlinear evolution attains the maximum value of the cost function, which is constructed according to the problems of interests with physical constraint conditions. In sensitivity and stability analysis of fluid motions, CNOP describes the most unstable (or most sensitive) initial modes. It can also represent the optimal precursor of certain weather or climate event, or stand for the initial error that has largest effect on the uncertainties at the prediction time. In this review paper, we introduce the concept of CNOPs first. Then we present the results on the stability, sensitivity and predictability obtained by CNOP approach, which includes: the sensitivity and stability of ocean’s thermohaline circulation; predictability of El Nino-Southern Oscillation; nonlinear stability problems of a theoretical grassland ecosystem model. It is shown that CNOPs not only reveal the effect of nonlinearity on the physical problems in which nonlinear process plays an important role, but also demonstrate significant physical characteristics that cannot be shown by LSV. For example, in Zebiak-Cane model, CNOPs, rather than LSVs, act as the initial anomaly patterns that evolve into ENSO events most probably, which shows that nonlinearity enhances the evolution of El Nino. In the theoretical Stommel’s model, a nonlinear asymmetric response of THC to the finite perturbation is revealed by using CNOP approach, which cannot be realized by LSV. Other applications of CNOP, which includes ensemble forecast and target observations, are reviewed too. Prospect and challenge in the future applications of CNOP are also discussed.