The uncertainty in the initial condition seriously affects the forecasting skill of numerical models. Targeted observations play an important role in reducing uncertainty in numerical prediction. The conditional nonlinear optimal perturbation (CNOP) method is a useful tool for studying adaptive observation. However, the traditional CNOP method highly relies on the adjoint model, and it is difficult to find the global optimal solution. In this paper, a pre-screening and ensemble CNOP hybrid method called PECNOP is proposed to identify optimal sensitive areas in targeted observations. PECNOP is an adjoint-free method that captures global CNOP with high probability, which can effectively solve the two major problems faced by traditional CNOP methods. We evaluated the performance of PECNOP by building an observation simulation system consisting of an ocean model and data assimilation. One of the assimilation experiments was dedicated to evaluating the stability and effectiveness of PECNOP in extreme events. The results show that, compared with traditional methods, PECNOP can stably capture the global CNOP. Extra observations and assimilation in the optimal sensitive areas identified by PECNOP can effectively improve forecasting by about 20% within 30 days. Therefore, PECNOP has potential to reduce the initial error of numerical models, which is important for improving forecasting.

Conditional nonlinear optimal perturbation (CNOP) represents the initial perturbation that satisfies a certain physical constraint condition, and leads to a maximum prediction error at the moment of prediction. The CNOP method is a useful tool in studying atmosphere and ocean predictability problems. Generally, the optimization algorithm based on the gradient of the cost function to compute CNOP requires an initial guess. The traditional scheme randomly chooses the initial guess of CNOP within the constraint range and therefore this scheme is called RIG-CNOP. However, the RIG-CNOP scheme reduces the probability of capturing the global CNOP in many cases, such as the prediction model is strongly nonlinear or long-term prediction is performed, or multiple extreme values existed in the cost function. Considering the limitations of the RIG-CNOP scheme, we propose a new initial guess selection scheme. In this scheme, we first pre-analyze a series of random initial guesses, and then, an optimal initial guess is selected. The above process replaces the initial guess selection scheme in the traditional scheme, which is called PAIG-CNOP. Numerical experiments are conducted utilizing the Lorenz-63 model. Also, to compare the performance of the PAIG-CNOP method with the RIG-CNOP method in capturing global CNOP, the CNOP and the maximum cost function value (MCFV) obtained by the filtering method (FM) are used as benchmarks (this value is called FMMCFV in brief). The experimental results show that even the prediction model is strongly nonlinear or the prediction time is long, or the cost function has multiple extreme values, the PAIG-CNOP method can capture the global CNOP with a high probability. The results show that the PAIG-CNOP method has a higher probability of capturing the global CNOP than the RIG-CNOP method. In addition, we use an ensemble-based technique in the computation of gradients, thus avoiding the use of adjoint techniques in the maximization process. Due to the attractive features of the new method, the PAIG-CNOP method is an efficient and useful method for solving CNOP, it can be more easily applied to obtain the global CNOP of operational prediction models.

Advances in data assimilation (DA) methods have greatly improved the accuracy of Earth system predictions. To fuse multi-source data and reconstruct the nonlinear evolution missing from observations, geoscientists are developing future-oriented DA methods. In this paper, we redesign a purely data-driven latent space DA framework (DeepDA) that employs a generative artificial intelligence model to capture the nonlinear evolution in sea surface temperature. Under variational constraints, DeepDA embedded with nonlinear features can effectively fuse heterogeneous data. The results show that DeepDA remains highly stable in capturing and generating nonlinear evolutions even when a large amount of observational information is missing. It can be found that when only 10% of the observation information is available, the error increase of DeepDA does not exceed 40%. Furthermore, DeepDA has been shown to be robust in the fusion of real observations and ensemble simulations. In particular, this paper provides a mechanism analysis of the nonlinear evolution generated by DeepDA from the perspective of physical patterns, which reveals the inherent explainability of our DL model in capturing multi-scale ocean signals.