The IWMO workshops are managed by an international steering committee of scientists drawn from ten different countries, with local volunteers from the hosting institute handling organization and support. A defining tradition of the series is the publication of a special issue, or Topical Collection, of peer-reviewed papers in the journal Ocean Dynamics after each meeting. More than 200 papers have now appeared in these collections, making the workshop series one of the most consistently productive venues for ocean modeling research. To promote international collaboration and diverse participation, organizers deliberately rotate the meeting across continents: IWMO-2023 was held in Hamburg, Germany, and IWMO-2024 took place in Sapporo, Japan. Since the organization’s inauguration in Taiwan in 2009, six meetings have been held in Asia, four in Europe, four in North America, one in South America and one in Australia. Only two previous meetings were held in the United States, in Virginia in 2010 and in Ann Arbor, Michigan in 2022. Following the Stanford meeting, IWMO-2026 was held in Palma de Mallorca, Spain, and IWMO-2027 is planned for June 2027 in Hangzhou, China.

The scientific program at Stanford featured 32 oral presentations, including four keynote invited presentations by prominent scientists, along with 10 posters. Sessions spanned the breadth of modern ocean modeling: internal and surface waves, coupled physical-biological interactions, global and basin-scale circulation, mixing and sub-mesoscale processes, coastal and estuarine modeling, and numerical methods. Continuing the IWMO tradition of encouraging early-career participation, 13 graduate students and postdoctoral researchers presented their work as part of the Outstanding Young Scientist Award competition, with the top winners hailing from the United States, Japan and Germany. The accompanying Topical Collection in Ocean Dynamics includes eight peer-reviewed papers from workshop participants, each subjected to rigorous review by IWMO members and external experts under the stewardship of a team of guest editors. Together the papers showcase a variety of numerical ocean and wave models, diverse analysis methods, and study sites ranging from the German Bight and the coasts of the United States and Canada to seas along the Asian Pacific coasts.

Among the collection’s contributions, Zhang and colleagues developed an idealized coupled Computational Fluid Dynamics and Discrete Element Method model, known as CFD-DEM, to study how cross-flow velocities affect particle transport near a subsea pipeline. The simulations identified distinct critical velocity thresholds for different particle sizes, offering a practical engineering tool for subsea pipeline design and backfilling projects, where the loss of backfill material is a persistent operational concern. The work illustrates how idealized numerical experiments can distill complex sediment-structure interactions into design guidance that engineers can apply directly to offshore infrastructure.

Wave dynamics featured prominently in the collection as well. Imamura and Yoshikawa tackled the long-standing challenge of parameterizing surface-wave breaking in wave-resolving simulations using a nonhydrostatic numerical model. Rather than relying on the empirical criteria that many existing models employ, they introduced a fourth-order diffusivity into the surface elevation equation to explicitly represent wave breaking. The approach was validated successfully against laboratory experiments and theory, demonstrating a physically grounded alternative to heuristic breaking schemes. In a related vein of coastal prediction, Ezer used the Princeton Ocean Model to explore how high-frequency oscillations in the Gulf Stream, with periods ranging from one week to two months, can induce coastal sea level variability. Comparisons with observations revealed a statistically significant anticorrelation between Gulf Stream strength and coastal sea level, but the relationship depends nonlinearly on location along the coast and on the frequency of the current’s variability, complicating the prediction of coastal flooding.

Nature-based coastal protection emerged as another theme. Jacob, Pein and Staneva used the unstructured-grid SCHISM hydrodynamic model, extended with sediment dynamics and vegetation, to evaluate seagrass as a nature-based solution for coastal protection in the German Wadden Sea. Their simulations, which incorporated end-of-the-century sea level rise projections, showed that despite rising seas, seagrass meadows retain their damping capacity and can reduce wave heights by as much as 30 percent in shallow areas. This finding carries significant implications for coastal management, suggesting that restored ecosystems could complement or even substitute for hard engineering defenses in some settings. In the Pacific Northwest, Khangaonkar and colleagues tested a sigma-coordinates formulation with shaved cells in the SCHISM model to simulate the Salish Sea, a fjord-like deep estuary. The refined grid and higher resolution compared with a past FVCOM configuration of the region eliminated the need for bathymetric smoothing and improved predictions of currents and temperatures, resolving near-shore intertidal and deep estuarine circulation simultaneously.

Aquaculture’s footprint on coastal hydrodynamics was examined by Fu and colleagues, who applied the FVCOM numerical model with an enhanced dual-drag parameterization to simulate the impact of large-scale floating-raft aquaculture structures in the open waters near Zhangzi Island in the northern Yellow Sea of China. The simulations showed that floating rafts can significantly reduce tidal current velocities, especially near the surface, with consequences for regional circulation and the transport of material. On the neighboring Pacific coast of North America, Lin and Dunphy deployed the NEMO model with AGRIF two-way nesting to resolve a fjord tidal jet in Quatsino Sound, British Columbia, Canada. The nested model reproduced tidal mixing in good agreement with observations and generated internal waves during each flood phase, with barotropic-to-baroclinic energy conversion for the M2 tide identified along the tidal-jet slope and in shallow waters.

Artificial intelligence also made its mark on the collection. Hu and colleagues proposed a geospatially encoded dual-channel network with attention mechanisms and physics constraints for reconstructing complex seafloor topography. Bathymetric prediction based on gravity anomalies remains the dominant approach for mapping the seafloor, but the new study integrates traditional physical models with neural networks to enhance the model’s fitting capacity, pointing toward a hybrid future in which machine learning and process-based oceanography reinforce one another rather than compete.

Taken together, the IWMO-2025 proceedings capture a field in vigorous transition, one in which classical process models such as the Princeton Ocean Model and FVCOM share the stage with next-generation frameworks like SCHISM and NEMO, and in which data-driven methods are beginning to reshape how the seafloor and the flows above it are mapped. The breadth of applications, from pipeline engineering and aquaculture siting to flood prediction and ecosystem-based coastal defense, underscores why ocean modeling has become indispensable infrastructure for climate adaptation worldwide. The organizers extended thanks to the local organizing committee at Stanford and to all participants for sustaining the collaborative spirit of the IWMO tradition, and the community now looks ahead to Palma de Mallorca and Hangzhou, where the next chapters of this sixteen-year-old scientific conversation will unfold.

Subject of Research: The 15th International Workshop on Modeling the Ocean (IWMO-2025) and its associated peer-reviewed papers on numerical ocean modeling

Article Title: The 15th international workshop on modeling the ocean (IWMO-2025) in Stanford, California, USA, June 30th – July 1st, 2025

Article References: Fringer, O., de Camargo, R., Chang, Y.-L., Xue, H., & Ezer, T. (2026). The 15th international workshop on modeling the ocean (IWMO-2025) in Stanford, California, USA, June 30th – July 1st, 2025. Ocean Dynamics, 76(9), Article 95. https://doi.org/10.1007/s10236-026-01853-0

Image Credits: AI Generated

DOI: 10.1007/s10236-026-01853-0

Keywords: IWMO-2025, ocean modeling, Ocean Dynamics, Stanford University, coastal sea level, seagrass coastal protection, SCHISM, NEMO, FVCOM, Gulf Stream, wave breaking parameterization, seafloor topography reconstruction

The study, carried out by Jiaqi Guo and Xueen Chen of the Ocean University of China together with Pengyang Song of the Alfred Wegener Institute in Bremerhaven, centers on a seemingly technical but consequential change to a global tidal model: the introduction of an Internal Wave Viscosity, or IWV, parameterization. In ocean modeling, a parameterization is a compact mathematical scheme that stands in for physical processes too small or too complex to resolve directly on the model’s grid. The IWV scheme represents the drag exerted on the tides as energy leaks from surface-expressed barotropic tides into internal waves — slow, hidden undulations of the ocean’s density layers that radiate away from undersea ridges and other rough topography before breaking into turbulence.

Barotropic tides are the familiar kind: the entire water column rises and falls in unison, and their energy is concentrated near the surface where satellites can measure it. Baroclinic tides, by contrast, involve vertical shearing between layers of different density and carry energy into the ocean interior. The conversion between these two modes is the gateway through which mechanical tidal energy ultimately becomes deep-ocean turbulence, and turbulence, in turn, mixes heat, carbon and nutrients through the water column. Without a realistic representation of this conversion, global tidal models systematically overestimate how much barotropic tidal energy survives the deep ocean and crashes onto the continental shelves, where it drives shallow-water dynamics.

To quantify the effect, the team ran a global tidal model forced purely by the solar and lunar tidal potentials — a setup reminiscent of the classic benchmark calculations of the tidal equations performed in the late 1970s — and compared simulations with and without the IWV term. The reference standard was TPXO9, a widely used assimilative tidal solution derived from satellite altimetry by inverse modeling. The comparison focused on four principal tidal constituents: M2, the dominant semidiurnal lunar tide with a period of about 12.42 hours; S2, its solar counterpart at exactly 12 hours; and the diurnal constituents K1 and O1, which complete their cycles in roughly 23.93 and 25.82 hours respectively.

The improvements were striking. Adding IWV reduced the model’s errors in shallow-water regions by roughly 30 percent for M2, 18 percent for S2, 21 percent for K1 and 27 percent for O1. In the deep ocean, the parameterization contributed significantly to tidal dissipation, siphoning energy out of the barotropic tide at exactly the places — mid-ocean ridges, seamounts, and rough abyssal topography — where internal wave generation is known to occur. The authors conclude that IWV supplies a physically sufficient conversion of energy from barotropic to baroclinic tides, curtailing the artificially inflated tidal energy that unmodified models propagate toward the shelves, and yielding a more faithful simulation of how astronomical tides are generated, propagate and die.

Why should a viscosity term aimed at internal waves matter so much for the surface tide? The answer lies in the energetics. The nonlinear tidal energy equation used in the analysis shows that the global energy budget of astronomical tides depends closely on the distribution of water depth. Over deep basins, tidal flows interact with topographic roughness through stratification, spawning internal waves that act as an effective drag on the barotropic mode. If that drag is absent from a model, the residual energy must go somewhere — and in practice it spills into the shallow seas, producing tides that are too energetic and phases that drift away from observations. The IWV scheme closes this gap by routing the energy to its physical destination in the ocean interior.

Beyond correcting the deep-ocean energy ledger, the study produced a genuinely novel result. By evaluating the full nonlinear tidal energy equation globally, the researchers isolated, for the first time, a global dissipation of approximately 0.24 terawatts attributable to the nonlinear advection effect — the quadratic interactions of tidal currents with themselves and with spatially varying sea surface elevation in shallow water. Nonlinear advection matters because in shallow seas, where tidal currents are swift and water depths are small, different tidal constituents no longer behave independently. The M2 tide can interact with S2, K1 or O1, transferring energy among them and generating compound frequencies — the so-called shallow-water tides that appear as overtides and compound tides in coastal tidal records.

This discovery carries a double significance. Scientifically, it confirms that astronomical tidal constituents interact nonlinearly as they propagate through shallow regions, and it quantifies the energy fuelling the generation of shallow-water tides that classical linear theory cannot produce. Practically, it gives modelers a new budget term to respect: roughly a quarter of a terawatt — a nontrivial fraction of the approximately 3.7 terawatts that tidal dissipation estimates generally assign to the oceans — is consumed not by bottom friction or internal wave drag, but by the mathematics of nonlinearity itself. Any global model aspiring to accurate coastal tides, and any application relying on them, from storm surge forecasting to tidal energy siting, must account for this pathway.

The broader implications reach into some of the deepest questions in oceanography and Earth science. Since the landmark “Abyssal Recipes” work of Walter Munk and Carl Wunsch in 1998, oceanographers have known that maintaining the ocean’s stratified overturning circulation requires roughly two terawatts of mechanical mixing power, with tides supplying a substantial share. Satellite measurements of the M2 tide from the TOPEX/Poseidon mission, analyzed in detail in the early 2000s, confirmed that about a terawatt of that tide’s energy dissipates in the deep ocean rather than on the shelves. Simultaneously, lunar laser ranging and satellite tracking reveal that tidal friction is slowly braking Earth’s rotation, lengthening the day by milliseconds per century — a budget that must balance to within observational error. Every refinement of where tidal energy goes therefore tightens constraints on both the ocean’s mixing engine and the Earth-Moon system’s long-term evolution.

The methodology behind the new results combines several established tools in a fresh configuration. Bathymetry for the model was drawn from the ETOPO Global Relief Model maintained by NOAA, while the bottom buoyancy frequency — a measure of stratification that governs how readily internal waves can be generated — was computed from the World Ocean Atlas 2013 climatology. Harmonic analysis of the model output followed standard practice for tidal work, and validation against TPXO9 allowed the team to compute error reductions basin by basin and constituent by constituent. The use of a forward model forced only by the tidal potential, rather than one nudged toward observations, makes the energetics diagnostics particularly meaningful: the energy budget emerges from the dynamics rather than being imposed by data assimilation.

Support for the work came from the National Natural Science Foundation of China, under grants directed at the mechanisms of internal tide generation and evolution in the Luzon Strait and at interactions between internal waves and multi-scale ocean processes in the South China Sea — regions where some of the world’s most intense internal tides are found. The authors also acknowledged computing resources from the National Supercomputing Center in Jinan and the Marine Big Data Center at the Ocean University of China. That regional expertise feeding a global calculation is fitting: the physics validated here at planetary scale is the same physics that sculpts the turbulent underwater weather observed above the Luzon Strait ridges.

For the wider community, the message of the study is that the global tidal energy budget is not a fixed inheritance from twentieth-century calculations but an evolving account that sharpens as parameterizations improve. With IWV in place, the model describes a more reasonable cycle in which the astronomical tides born of celestial mechanics lose a proper share of their energy to the deep-ocean interior, arrive at the continental shelves with realistic amplitudes, and there surrender part of their remaining energy to the nonlinear interactions that breed shallow-water tides. The newly quantified 0.24-terawatt advection sink completes a picture in which generation, propagation and dissipation are, for the first time, balanced end to end on a global scale. As high-resolution global models increasingly simulate tides, eddies and the general circulation together, schemes like IWV — and budgets honest about nonlinearity — will be essential ingredients.