Data-driven predictions of marine environmental variables are typically focused on single variables. However, in real marine environments, there are correlations among different oceanic variables. Additionally, sea–air interactions play a significant role in influencing the evolution of the marine environment. Both internal dynamics and external drivers contribute to these changes. In this study, a data-driven model is proposed using sea surface height anomaly (SSHA), sea surface temperature (SST), and sea surface wind (SSW) in the Bohai Sea. This model combines multivariate empirical orthogonal functions (MEOFs) with long and short-term memory (LSTM). MEOF analysis is used on the multivariate dataset of SSHA and SST, considering the correlation among sea surface variables. SSW is introduced as a predictor to enhance the predictability of the multivariate sea surface model. In the case of the Bohai Sea, the comparative tests of the model without wind field effect, the fully coupled model, and the proposed prediction model were carried out. MEOF analysis is employed in comparative experiments for oceanic variables, atmospheric variables, and combined atmospheric and oceanic variables. The results demonstrate that using wind field as a predictor can improve the forecast accuracy of SSHA and SST in the Bohai Sea. The root mean square errors (RMSE) for SSHA and SST in a 7-day forecast are 0.016 m and 0.3200 °C, respectively.

In this paper, a novel and simple statistical prediction model for sea surface multivariate is developed based on extended empirical orthogonal functions (referred to as the MEEOF model). This simple model embeds the temporal evolution information into the empirical orthogonal function spatial patterns, which effectively captures the spatial distribution of the sea surface variables and their evolution process over time, and can be used to improve the accuracy of intra-seasonal ocean forecasts. At the same time, it considers both the correlation between different spatial and temporal points and the dynamic balance between different sea surface variables. The performance of the MEEOF prediction model has been examined in the South China Sea (SCS) based on remote sensing satellite datasets. Experimental results demonstrate that this model has significant forecasting capability within the forecast window of 15–90 days, compared with the traditional persistence forecasts and optimal climatic normal (OCN) results. Furthermore, this model exhibits good forecast performance throughout the entire forecast window; the final prediction model (referred to as the fusion model) is established by obtaining the weighted average for the MEEOF forecasts and persistence forecast results. Numerical experimental results show that this fusion prediction model consistently outperforms the persistence model, the OCN model, and the linear regression model over the entire forecast window. A case study shows that the propagation of ocean waves and the coordination between different sea surface variables can be well predicted by this simple model, indicating that this fusion model has a potential advantage in intra-seasonal predictions of the ocean.

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.