Most prediction models based on artificial neural networks (ANNs) are site‐specific and do not provide simultaneous spatial information similar to numerical schemes. Such ANNs do not account for the correlations across grid points or the dynamic balance among different variables, which is an obvious physical defect. Moreover, such methods generally perform well on a single scale, while the actual marine environmental variability is multiscale. To cope with these issues, a data‐driven hybrid model based on ocean reanalysis is developed. This model combines empirical orthogonal function (EOF) analysis and complete ensemble empirical mode decomposition (CEEMD) with ANN (referred to as EOF‐CEEMD‐ANN). The results demonstrate that the EOF‐CEEMD‐ANN model is efficient for mid‐term predictions of sea surface multivariate including sea surface height (SSH), temperature (SST), salinity (SSS), and velocity (SSV) in the entire South China Sea (SCS) region. During the 30 days forecast window, the root‐mean‐square errors (RMSEs) of this model forecasts for SSH, SST, SSS, U, and V at the end of the forecast window are about 0.042 m, 0.52°C, 0.08 psu, 0.073 m/s, and 0.064 m/s, respectively, which are much smaller than those with persistence and optimal climatic normal (OCN) prediction. The anomaly correlation coefficients (ACCs) are approximately 0.75, 0.66, 0.73, 0.69, and 0.71, respectively. Case studies show that eddies and their evolutions can be simulated well by this model.

The joint state and parameter estimation problem is an important issue in data assimilation. An adjoint free data assimilation method, namely analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation method, was developed to provide a solution for the joint estimation problem. In the algorithm, to estimate the adjoint model reasonably, the ensemble initial conditions and parameters are generated by Gaussian noise whose covariance is constructed by multiplying a very small factor by their background error covariance. The ensemble perturbations are calculated with respect to background states rather than the ensemble mean. Next, the usage of temporal cross covariances makes it possible to avoid the adjoint model and estimate the gradient in 4DVar. Furthermore, we update the solution iteratively with a linear search process to improve the stability and ensure the convergence of the algorithm. The method is tested using the three-variable Lorenz model (Lorenz-1963) to illustrate its efficiency. It is shown that A-4DEnVar results in similar performance with 4DVar. Sensitivity experiments show that A-4DEnVar is able to assimilate observations successfully with different settings. The proposed method is able to work as well as 4DVar and avoid adjoint models for the joint state and parameter estimation.

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.