Scientific understanding, prediction, and communication to stakeholders are common objectives of ocean simulations and observing campaigns. Achieving these objectives can be greatly facilitated by advanced tools for exploring dynamic three-dimensional ocean data. Many scientific visualizations of spatiotemporal simulations rely on static two-dimensional representations that omit one or more spatial dimensions, potentially obscuring important features and relationships. A toolkit capable of creating coherent three-dimensional visualizations of ocean processes should move beyond isolated two-dimensional views and support the exploration of increasingly high-resolution simulations and large multidisciplinary observational data sets. In this work, we present 3DSeaVizKit, a visualization toolkit that processes multidisciplinary oceanographic data in a modular and computationally efficient manner to create portable, web-based, interactive 3D visualizations. Built upon the Plotly JavaScript library, the toolkit enables exploratory analysis of complex ocean fields directly within a web browser. We provide a software pipeline tailored to the computational demands of multivariate 3D ocean visualization and demonstrate its utility for revealing transport pathways, coherent structures, circulation features, biogeochemical-acidification interactions, subduction dynamics, and forecast uncertainties in high-resolution ocean simulations. The toolkit supports scalar fields such as temperature, salinity, and biogeochemical tracers; vector fields such as velocity and vorticity; and Lagrangian products including trajectories, flow maps, and coherent structures. Applications include the visualization of the Loop Current system and eddy interactions in the Gulf of Mexico, subduction processes and forecast uncertainties in the Alboran Sea, coupled biogeochemical and ocean-acidification dynamics in Massachusetts Bay, and transport pathways and coherent structures around Nantucket and Martha’s Vineyard.
Offshore windfarms introduce dense arrays of monopile foundations into shallow shelf seas, but their hydrodynamic effects remain difficult to represent in regional ocean models that cannot resolve individual foundations and their wakes. This study investigates the short-term influence of monopile-induced friction on hydrography, stratification, and turbulence in the North Sea, Danish Straits, and Baltic Sea using the HIROMB–BOOS Model (HBM). The underwater-foundation effect is represented through a subgrid parameterization in which frictional work from monopile–current interactions contributes an additional production term to the turbulent kinetic energy equation of the k–ω closure. The formulation is assessed through a process-based comparison at DanTysk, providing observational support for its physical basis under the evaluated conditions. Paired simulations with and without the windfarm parameterization are conducted for summer and winter conditions over 20 days. The response is evaluated using temperature and salinity differences, potential energy anomaly, relative mixed-layer depth, resolved eddy kinetic energy, subgrid turbulent kinetic energy, and tidal spectral diagnostics. Daily ΔPEA% time series are additionally evaluated at regional and individual-cluster scales to distinguish spatially aggregated responses from stronger localized signals.The most directly attributable hydrographic responses occur within and around the windfarm clusters. Far-field differences, particularly in the Skagerrak, become comparable to those generated by a small perturbation of the control simulation, and are therefore interpreted as the redistribution and nonlinear development of initially generated perturbations rather than as independently forced remote windfarm signals. Within the windfarm regions, both positive and negative stratification anomalies occur, and their persistence depends strongly on the background dynamical regime. In the tidally energetic North Sea, partially stratified summer conditions permit a clearer restratifying response, whereas strong tidal stirring, atmospheric cooling, and wind-driven turbulence constrain the response during winter. In the weakly tidal regions of Anholt and Kriegers Flak, partial wintertime stratification allows the windfarm-induced stratification anomalies to persist more effectively than in the strongly tidal winter regime. The daily time series confirm this seasonal reversal: summer responses dominate in Helgoland and the Southern North Sea, whereas winter responses dominate in Kriegers Flak and Anholt. Regional-union responses generally remain below 1% in the North Sea subdomains and below 0.1% in the Danish Straits, while one illustrative Southern North Sea foundation cluster sustains a local summer response of approximately 3%–5%, demonstrating the dependence of the inferred response on spatial aggregation. Positive stratification and resolved eddy kinetic energy anomalies frequently co-occur in tidally energetic windfarm grid cells, particularly during summer, but their broad scatter does not support a proportional or causal relationship. No similarly clear association is found between stratification and subgrid turbulent kinetic energy. The response therefore cannot be interpreted as a simple local amplification of parameterized turbulence; instead, it reflects the interaction of the foundation forcing with the pre-existing circulation, stratification, and tidal regime. Although the precise anomaly magnitudes remain conditional on the idealized foundation geometry, prescribed drag parameters, turbulence closure, and model resolution, the simulations demonstrate robust seasonal, spatial-scale, and regime-dependent contrasts in the short-term response to unresolved monopile forcing.
The ocean’s surface mixed layer is an important interface between the ocean and atmosphere, and it is where most of the ocean's primary productivity takes place. Accurately reproducing the mixed layer depth (MLD) in ocean models is crucial. In this study, we use a multi-scale data assimilation system to investigate changes in MLD calculated from the model forecast fields of an assimilation experiment using the global ocean model MPI-OM. We compare the MLD results of assimilative model run with those derived from widely used high-resolution reanalysis datasets (GLORYS, HYCOM, and CORA) that exhibit high accuracy along with high spatial and temporal resolution. The performance of the MLD results of assimilative model run agrees closely with the reanalysis datasets. The assimilation experiment shows a reduction in MLD bias using ARMOR as a reference product. We assess the assimilated results according to the latitude and season, observing a significant improvement in regions where a positive MLD bias existed, but limited effect or even an increase in bias in regions where a negative MLD bias existed. We observed that regions with significant positive biases in the MLD were accompanied by notable positive biases in both temperature and salinity. After the temperature-salinity assimilation, the vertical density stability of the upper ocean was enhanced, which further mitigated the issue of excessive vertical mixing in the model. Further evaluation across diverse regions supports this finding: data assimilation effectively reduces bias in the eastern hemisphere segment of the Antarctic Circumpolar Current (ACC) yet shows limited impact in the ACC’s western hemisphere segment and the Pacific Ocean.
In this paper, a hybrid horizontally two-dimensional (2DH) Boussinesq-type model is developed for simulating nearshore wave processes based on the equations of Simarro et al. (2013), which maintain accurate dispersion up to kh = 10. In this model, the convective flux terms are reconstructed with a fifth‑order finite‑volume weighted essentially non‑oscillatory (WENO) scheme, which not only offers improved computational efficiency and lower memory usage but also handles wave breaking through its shock‑capturing capability. The remaining terms are approximated by finite differences. Time stepping is performed by a third-order Strong Stability-Preserving (SSP) Runge–Kutta scheme. The model is validated against linear wave theory and a series of benchmark physical experiments to assess its capability in simulating wave dispersion, shoaling, breaking, runup, refraction, diffraction, and currents, with a specific strength in capturing infragravity waves.
Accurate assimilation of wave fields under sparse and irregular observational coverage remains a central challenge in ocean modelling. Conventional variational methods are often limited by predefined error covariance structures, which restrict their ability to represent and transmit spatial dependencies. To address these challenges, a graph neural network (GNN)–based data assimilation framework is developed to reconstruct geophysical fields from sparse observations. By representing spatial relationships between observation locations and background grid points, the proposed framework enables efficient aggregation and propagation of observational information across the spatial domain. The framework is evaluated through an application to wave data assimilation in the China seas and adjacent coastal regions, using long-term simulations and synthetic sparse observations. The GNN-based assimilation is systematically compared with the conventional three-dimensional variational (3DVar) method across multiple observational coverages and sea-state conditions. The results show that the proposed approach consistently achieves lower mean errors, improved statistical stability, and enhanced spatial coherence. Notably, under extremely sparse observational coverage, the GNN framework maintains effective error reduction over extended spatial ranges away from observation locations, whereas the influence of 3DVar remains largely confined to regions near observations. These findings demonstrate that graph-based data assimilation provides a robust and flexible approach for exploiting sparse and irregular observations in ocean wave modelling.
