The problem the team set out to solve is one of scale. Traditional ocean models typically rely on structured grids, in which the computational domain is divided into cells of roughly uniform size. That works well in the open ocean, but coastal zones are a different beast. Complex coastlines, lagoons, estuaries and deltas demand fine resolution precisely where structured grids are least flexible, while offshore areas can tolerate much coarser spacing. Unstructured grids, built from triangles of varying size, allow modellers to concentrate computational effort where it matters most — a philosophy that underpins ShyBFM.

ShyBFM is a marriage of two established components. The physical engine is SHYFEM-MPI, a parallel finite-element ocean circulation model that solves the primitive equations for an incompressible fluid under the hydrostatic and Boussinesq approximations. It runs on a triangular mesh with scalar quantities computed at grid nodes and vector quantities at element centroids, and it uses a semi-implicit algorithm to integrate the free-surface equation, damping the fastest external gravity waves to preserve stability. Vertical turbulent mixing is handled by the General Ocean Turbulence Model, with eddy viscosities and diffusivities treated fully implicitly.

The biological half of the couple is the Biogeochemical Flux Model, version 5.3, a community-developed ecosystem model that resolves the lower trophic levels of marine food webs. BFM tracks the cycles of carbon, nitrogen, phosphorus and silicon separately, representing living functional groups — four phytoplankton groups including diatoms and dinoflagellates, four zooplankton groups, and bacteria — alongside non-living pools of dissolved and particulate organic matter. In this first release, sediments are handled with a benthic return parameterization, in which deposited particulate organic matter is remineralized at constant rates and returned to the water column as dissolved inorganic nutrients.

The mathematical heart of the coupling is the advection-diffusion-reaction equation, which describes how the concentration of any biogeochemical tracer changes in time. The physical terms — horizontal and vertical advection and diffusion — are supplied by SHYFEM-MPI, while BFM computes the reaction rates arising from biological and chemical processes. The team solved the equation using a synchronous source splitting method, applying the same timestep to both the physical and reaction parts to eliminate errors that arise when different processes are stepped at different rates. Vertical diffusion is integrated implicitly and the resulting tridiagonal system is inverted with the classical Thomas algorithm at every node of the domain.

Careful attention was paid to boundary conditions, which are critical for conserving tracer inventories. At the sea surface, the model accounts for wet and dry deposition from the atmosphere, river inputs, and a dilution-concentration term tied to evaporation, precipitation and runoff. At the seabed, particulate matter settles into the benthic compartment while dissolved nutrients are returned upward through the remineralization flux. Lateral open boundaries are flow-dependent: tracer values are prescribed from an external parent model where water flows into the domain, and taken from the nearest interior grid point where water flows out.

To put the system through its paces, the researchers applied ShyBFM to the Emilia-Romagna coast of the northern Adriatic Sea, a shallow, nutrient-impacted region dominated by the Po River. The Po discharges an average of 1,500 cubic metres of water per second and carries more than half of all riverine nutrient loads entering the northern Adriatic, including roughly 116 kilotonnes of dissolved inorganic nitrogen per year. The computational grid comprised 15,392 elements and 8,142 nodes, with resolution stretching from 2 kilometres offshore down to 300 metres at the coast, and 43 vertical levels only 1 metre thick in the upper 30 metres of the water column.

The model was nested within an existing large-scale coupled system, NEMO-BFM, which supplied daily initial and lateral boundary conditions, and was forced with 6-kilometre atmospheric fields from the Weather Research and Forecasting model and hourly river runoff from WRF-Hydro. After a calibration phase of roughly twenty one-year simulations that tuned phytoplankton growth rates, nutrient membrane affinities and bacterial respiration parameters, the team ran a ten-year simulation spanning 2000 to 2009 and compared the results against the parent model and the EMODnet observational climatology.

The verdict was encouraging. ShyBFM successfully reproduced the seasonal cycles of chlorophyll a, dissolved inorganic nitrogen, phosphate and silicate, and in several respects outperformed its coarser parent. Chlorophyll a root-mean-square error was 45 percent lower than in NEMO-BFM, and the nitrogen error fell by 47 percent, with the model’s spatial variability closer to the climatology. Notably, the simulation captured the exceptional phytoplankton blooms of 2001 and 2002, years when unusually high Po discharge delivered nutrient loads well above the decadal mean and triggered notorious mucilage events in the northern Adriatic. The model also proved computationally frugal, requiring about 695 core-hours per simulated year on 36 processors, compared with roughly 1,728 core-hours on 288 processors for the parent model.

Limitations remain, and the authors are candid about them. Oxygen concentrations were systematically overestimated by 10 to 15 percent, a bias the team attributes to the absence of light attenuation by inorganic suspended matter and chromophoric dissolved organic matter, both abundant in Po River waters. The simple benthic return closure likewise cannot resolve the complex early diagenetic processes that govern silicate and oxygen fluxes in shallow coastal sediments, and the first-order upwind advection scheme, though robust and positivity-preserving, introduces numerical diffusion that smooths sharp plume gradients. Future development will target higher-order advection schemes, improved optics and mechanistic sediment modules. Even so, with its combination of mesh flexibility, full baroclinicity and detailed ecosystem dynamics — and its code freely available on Zenodo — ShyBFM offers coastal managers and environmental agencies a powerful new lens for studying eutrophication, hypoxia and the delicate interplay between rivers, currents and marine life.

Subject of Research: Coupled physical–biogeochemical ocean modelling on unstructured grids for coastal seas

Article Title: ShyBFM v1.0: unstructured grid advection-diffusion-reaction modelling for coastal biogeochemical processes

Article References: Alessandri, J., Bonino, G., Lovato, T., Butenschön, M., Mentaschi, L., Verri, G., Federico, I., & Pinardi, N. (2026). ShyBFM v1.0: unstructured grid advection-diffusion-reaction modelling for coastal biogeochemical processes. Geoscientific Model Development, 19(19), 9301-9324. https://doi.org/10.5194/gmd-19-9301-2026

Image Credits: AI Generated

DOI: 10.5194/gmd-19-9301-2026

Keywords: ShyBFM, unstructured grid, biogeochemical modelling, coastal ocean, Adriatic Sea, Po River, eutrophication, chlorophyll a, BFM, SHYFEM-MPI, ocean model, water quality