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.

We explore to what extent data-driven prediction models have skills in forecasting daily sea-surface temperature (SST), which are comparable to or perform better than current physics-based operational systems over long-range forecast horizons. Three hybrid deep learning-based models are developed within the South China Sea (SCS) basin by integrating deep neural networks (back propagation, long short-term memory, and gated recurrent unit) with traditional empirical orthogonal function analysis and empirical mode decomposition. Utilizing a 40-year (1982–2021) satellite-based daily SST time series on a 0.25° grid, we train these models on the first 32 years (1982–2013) of detrended SST anomaly (SSTA) data. Their predictive accuracies are then validated using data from 2014 and tested over the subsequent seven years (2015–2021). The models’ forecast skills are assessed using spatial anomaly correlation coefficient (ACC) and root-mean-square error (RMSE), with ACC proving to be a stricter metric. A forecast skill horizon, defined as the lead time before ACC drops below 0.6, is determined to be 50 days. The models are equally capable of achieving a basin-wide average ACC of ~0.62 and an RMSE of ~0.48 °C at this horizon, indicating a 36% improvement in RMSE over climatology. This implies that on average the forecast skill horizon for these models is beyond the available forecast length. Analysis of one model, the BP neural network, reveals a variable forecast skill horizon (5 to 50 days) for each individual day, showing that it can adapt to different time scales. This adaptability seems to be influenced by a number of mechanisms arising from the evident regional and global atmosphere–ocean coupling variations on time scales ranging from intraseasonal to decadal in the SSTA of the SCS basin.

Numerical modeling is one of the popular means to simulate and forecast the state of oceanographic systems. However, it still suffers from some limitations, e.g., parameter uncertainties, simplification of model assumptions, and absence of data for proper boundary and initial conditions. This paper proposes a hybrid data assimilation scheme, which combines the Kalman filter (KF) with a data-driven model (local linear model (LM)), to directly correct numerical model outputs at locations without measurements. Two different types of KF (unscented Kalman filter and two-sample Kalman filter) are tested and compared. A local LM is utilized to describe the evolution of the model state and then assimilated into the KF. This in turns simplifies the application of KF for highly complex nonlinear systems such as the dynamic motion of Singapore regional water. The proposed scheme is first examined using a simple hypothetical bay experiment followed by an operational model of the Singapore Regional Model (SRM), in which both are set up in the Delft3D modeling environment. This combination of KF and data-driven model provides insights into the influence of different error covariance estimations on the model updating accuracy. This research also provides guidance to offline utilization of KF in updating of numerical model output.

Accurately and timely estimating three-dimensional ocean states is crucial for improving operational ocean forecasting capabilities. Although satellite observations provide valuable evolutionary information, they are confined to surface-level variables. While in situ observations can offer subsurface information, their spatiotemporal distribution is highly uneven, making it difficult to obtain complete three-dimensional ocean structures. This study developed an operational-oriented lightweight framework for three-dimensional ocean state reconstruction by integrating multi-source observations through a computationally efficient multivariate empirical orthogonal function (MEOF) method. The MEOF method can extract physically consistent multivariate ocean evolution modes from high-resolution reanalysis data. We utilized these modes to further integrate satellite remote sensing and buoy observation data, thereby establishing physical connections between the sea surface and subsurface. The framework was tested in the South China Sea, with optimal data integration schemes determined for different reconstruction variables. The experimental results demonstrate that the sea surface height (SSH) and sea surface temperature (SST) are the key factors determining the subsurface temperature reconstruction, while the sea surface salinity (SSS) plays a primary role in enhancing salinity estimation. Meanwhile, current fields are most effectively reconstructed using SSH alone. The evaluations show that the reconstruction results exhibited high consistency with independent Argo observations, outperforming traditional baseline methods and effectively capturing the vertical structure of ocean eddies. Additionally, the framework can easily integrate sparse in situ observations to further improve the reconstruction performance. The high computational efficiency and reasonable reconstruction results confirm the feasibility and reliability of this framework for operational applications.

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.