PCGD: Principal components-based great deluge method for solving CNOP

Abstract

Conditional nonlinear optimal perturbation (CNOP) is an initial perturbation evolving into the largest nonlinear evolution at the prediction time. It has become a useful tool in meteorology and oceanography. The common method for solving the CNOP is the adjoint-based method which is always referred to as the benchmark. Unfortunately, many numerical models have no corresponding adjoint models, and developing a new one is usually a huge engineering, which consequently limits the application of the CNOP. In order to avoid adjoint models, we propose a principal components-based great deluge method to solve the CNOP. Through extracting principal components, the original problem is reduced into a low-dimensional space to hunt the coordinate of the optimal CNOP with the great deluge method. A regeneration strategy is also designed for the great deluge method to break away from local optimal positions. In addition, the proposed method can be parallelized to improve the computing efficiency. To demonstrate the validity, the proposed method has been studied in the Zebiak-Cane model to solve the CNOP. Experimental results show that the proposed method can efficiently obtain a satisfactory CNOP, approximate to the one computed with the adjoint-based method, and the parallelizing version can reach the speedup of 9.7 times with 12 cores.