Three independent global observations of nonlinear mesoscale eddy datasets derived from satellite altimeter are analysed to investigate the statistical characteristics of mesoscale eddies. Histograms of amplitude, radius, rotation speed, and Rossby number of mesoscale eddy in the global ocean were fitted by four probability density functions called normal, Rayleigh, gamma, and lognormal distribution. The histograms of these characteristics were best approximated by the lognormal distribution, regardless of the choice of eddy datasets. Further comparison studies between eddies of several large ocean basins and eddy-active regions showed that the lognormal distribution performed better in eddy-active regions. This study improves the understanding of eddy characteristics distributions, and may provide a basis for eddy parameterization in the numerical model.

Storm-surge residuals represent one of the most destructive marine-coastal hazards, and reliable short-term surge residual prediction is critical for coastal disaster preparedness. Conventional empirical forecasting approaches suffer from limited cross-regional generalization, while high-fidelity physics-based hydrodynamic models such as ADCIRC-SWAN can reproduce complete storm-surge physical processes but demand substantial computational resources. In this study, a three-layer back-propagation neural network (BPNN) for storm-surge residual forecasting is constructed, which is driven by output datasets from the validated ADCIRC-SWAN coupled hydrodynamic model. Wind speed, significant wave height, sea-surface atmospheric pressure, and the simulated current-time storm-surge residual are selected as input predictors. Simulation-derived samples are pre-processed via data cleaning and Min-Max normalization, and two different dataset partitioning strategies (random mesh-point-based partition and time-sequential partition) are implemented for comparative experiments. After hyperparameter sensitivity tests, the optimal network configuration with 30 hidden-layer neurons is determined. Model predictive performance is quantitatively evaluated via multi-station time-series comparison and universal statistical metrics including R, NSE, and RMSE. The results show that the BPNN achieves satisfactory performance under random mesh-point-oriented partitioning, yet obvious performance degradation occurs under time-sequential temporal extrapolation, with prominent underestimation of surge peaks. On the basis of BPNN-predicted spatial surge residual fields, storm-surge intensity grading is carried out following the Chinese national standard GB/T 39418-2020. Statistical comparisons between the full computational domain and the Pearl River Estuary sub-region reveal strong spatial aggregation of high-intensity storm-surge grids within the estuary driven by funnel-shaped topographic amplification. This work demonstrates the feasibility of using a BPNN as a surrogate emulator for hydrodynamic outputs under a given typhoon condition; however, limitations in temporal extrapolation performance still need to be addressed before this approach can be practically used in operational early-warning applications.