The field of forecasting oceanic variables has traditionally relied on numerical models, which effectively consider the ocean's dynamic evolution and are of physical importance. However, to make the models more realistic, complicated processes need to be considered, which is difficult because their calculations are complex. In fact, information on the internal dynamic mechanisms and external driving forces of the ocean are already embedded in the time series of observations. Therefore, we can determine the patterns of ocean variations through data mining of these series to achieve forecasting. Furthermore, to predict variations in ocean processes more realistically, interactions between variables and spatial correlations should be effectively considered. Thus, inspired by available remote sensing data and advancements in deep learning technologies, we develop a hybrid model based on a statistical method and a deep learning model to predict multiple sea surface variables. A case study in the South China Sea shows that this model is highly promising for short‐term daily forecasts of the sea surface height anomaly (SSHA) and sea surface temperature (SST). When the forecast time is 10 days, the root mean square errors of this model forecasts for SSHA and SST are approximately 0.0276 m and 0.46°C, respectively, which are much smaller than those of persistence, climatology and linear regression predictions. The anomaly correlation coefficients for SSHA and SST are approximately 0.864 and 0.633, respectively. The model performs satisfactorily under both normal and typhoon weather conditions.

Mid- and long-term predictions of Arctic sea ice concentration (SIC) are important for the safety and security of the Arctic waterways. To date, SIC predictions mainly rely on numerical models, which have the disadvantages of a short prediction time and high computational complexity. Another common forecasting approach is based on a data-driven model, which is generally based on traditional statistical analysis or simple machine learning models, and achieves prediction by learning the relationships between data. Although the prediction performance of such methods has been improved in recent years, it is still difficult to find a balance between unstable model structures and complex spatio-temporal data. In this study, a classical statistical method and a deep learning model are combined to construct a data-driven rolling forecast model of SIC in the Arctic, named the EOF–LSTM–DNN (abbreviated as ELD) model. This model uses the empirical orthogonal function (EOF) method to extract the temporal and spatial features of the Arctic SIC, then the long short-term memory (LSTM) network is served as a feature extraction tool to effectively encode the time series, and, finally, the feature decoding is realized by the deep neural network (DNN). Comparisons of the model with climatology results, persistence predictions, other data-driven model results, and the hybrid coordinate ocean model (HYCOM) forecasts show that the ELD model has good prediction performance for the Arctic SIC on mid- and long-term time scales. When the forecast time is 100 days, the forecast root-mean-square error (RMSE), Pearson correlation coefficient (PCC), and anomaly correlation coefficient (ACC) of the ELD model are 0.2, 0.77, and 0.74, respectively.

Marine forecasting techniques based on data-driven method generally treat each variable as independent and analyze the time series of a single and specific variable, while the real marine environment is the result of the interaction of multiple variables. In this letter, a data-driven method combining the empirical orthogonal function of multivariate (MEOF), complete ensemble empirical mode decomposition (CEEMD), and multilayer perceptron (MEOF-CEEMD-MLP in brief) is proposed to perform mid-term prediction of daily sea surface height anomaly (SSHA) and sea surface temperature (SST) simultaneously, considering that there is a correlation between them in the real marine environment. In this model, application of MEOF not only considers the correlation between SSHA and SST but also establishes the temporal and spatial relationship between discrete points, making predictions more accurate. A case study in the South China Sea (SCS) that predicts the daily SSHA and SST 30 days ahead shows that MEOF-CEEMD-MLP model is highly promising for mid-term daily prediction of SSHA and SST simultaneously. Also, the correlation between these two kinds of ocean variables can be simulated very well by this prediction model.

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.

Physics-based dynamical models can successfully predict short-term sea ice trends, but they struggle to provide reliable subseasonal sea ice predictions over shorter time periods and are not flexible enough to provide real-time/quasi-real-time predictions. Therefore, we use deep learning to establish a purely remote sensing data-driven Arctic sea ice prediction system, IceFormer. IceFormer is trained by high-quality Arctic reanalysis data and remote sensing observations. It can provide daily sea ice concentration (SIC) and sea ice thickness (SIT) predictions for the pan-Arctic region with 45 days lead time. We show that IceFormer advances lightweight multivariate forecasting of Arctic sea ice. Driven by remote sensing data, the prediction performance of IceFormer is far superior to traditional baseline models and machine learning models. The root mean square error (RMSE) and spatial anomaly correlation coefficient (SACC) of SIC (averaged within 45 days) are 6.62% and 0.80, respectively. The RMSE and SACC of SIT (averaged within 45 days) are 0.04m and 0.93, respectively. IceFormer can successfully capture the sea ice evolution on a seasonal scale (especially in the melting season) and the monthly average SACC is stable at around 0.70. After comparison, the SIC prediction performance of IceFormer is better than that of a Coupled Ensemble Numerical Forecast Model (SEAS5) from May to November. The information transfer analysis shows that the simultaneous prediction of SIC and SIT can effectively improve the predictability and explainability of sea ice.

The usage of four‐dimensional variational (4DVar) scheme is limited by the static background error covariance and the adjoint model. In a hybrid frame of the four‐dimensional ensemble‐variational data assimilation scheme (4DEnVar), being able to avoid the tangent linear and adjoint models in the 4DVar and nowadays developed into a cutting‐edge research topic of the next‐generation data assimilation methods, an analytical 4DEnVar (A‐4DEnVar) scheme is designed. First, an analytical expression for explicit evolution of the background error covariances is derived. The expression collects the innovation of observations over an assimilation window simultaneously and propagates information to the initial background field by temporal cross covariances. Second, to estimate the adjoint model, the temporal covariances are constructed with ensemble members being centralized with respect to the model states integrated from the initial condition. Third, an iterative linear search process is introduced to minimize the cost function to update the analysis field until convergence. Twin experiments based on the Lorenz chaos model with three variables are conducted for the validation of the A‐4DEnVar scheme. Comparisons to the conventional 4DVar show that the A‐4DEnVar is comparable in accuracy even with a long assimilation window and sparse observations. The assimilation results also show that the A‐4DEnVar scheme can be implemented with a very small ensemble size which means that under circumstances without the tangent linear and adjoint models it can be easily incorporated into data assimilation systems in use.