An Efficient Approach Based on the Gradient Definition for Solving Conditional Nonlinear Optimal Perturbation

Conditional nonlinear optimal perturbation (CNOP) has been widely applied to study the predictability of weather and climate. The classical method of solving CNOP is adjoint method, in which the gradient is obtained using the adjoint model. But some numerical models have no adjoint models implemented, and it is not realistic to develop from scratch because of the huge amount of work. The gradient can be obtained by the definition in mathematics; however, with the sharp growth of dimensions, its calculation efficiency will decrease dramatically. Therefore, the gradient is rarely obtained by the definition when solving CNOP. In this paper, an efficient approach based on the gradient definition is proposed to solve CNOP around the whole solution space and parallelized. Our approach is applied to solve CNOP in Zebiak-Cane (ZC) model, and, compared with adjoint method, which is the benchmark, our approach can obtain similar results in CNOP value and pattern aspects and higher efficiency in time consumption aspect, only 12.83 s, while adjoint method spends 15.04 s and consumes less time if more CPU cores are provided. All the experimental results show that it is feasible to solve CNOP with our approach based on the gradient definition around the whole solution space.