Abstract
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.
Highlights
In the study of weather and climate predictability, it is crucial to determine the fastest growing perturbation
The final solution of Conditional nonlinear optimal perturbation (CNOP) is the pattern of initial SST anomaly (SSTA) and thermocline height anomalies (THA) that will cause the largest evolution at prediction time in the tropical Pacific, named as SSTA-CNOP and THA-CNOP, which are so-called optimal precursor
We proposed an efficient approach based on the gradient definition to solve CNOP around the whole solution space and some parallel strategies were designed to improve gradient calculation efficiency
Summary
In the study of weather and climate predictability, it is crucial to determine the fastest growing perturbation. A localization technique was introduced to ameliorate the spurious correlation between the two ensembles, in which the localization radius was achieved from artificial experience This method calculated the gradient information only once during the whole optimization; it can obtain an approximate CNOP easier and more efficiently than adjoint-based method, but it depends on artificial experience. The dimensions of the numerical models for climate and weather are relatively high, which results in the fact that gradient definition method has rarely been applied in solving CNOP. The gradient calculated was formally the same as the definition of the gradient, but the small amount in the gradient definition equation is the increment of the coefficient, not the increment of the initial perturbations This method can obtain an approximate CNOP, and time efficiency depends on the number of base vectors chosen.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
