A new ocean-modeling study suggests that one of the most persistent compromises in coastal science may no longer be necessary. Researchers have developed a high-resolution computer model of the Salish Sea that represents both shallow intertidal flats and deep, strongly stratified fjord-like channels without smoothing the seafloor. The approach could improve predictions of currents, temperature, transport, and ecological conditions across one of the Pacific Northwest’s most complex marine environments. The Salish Sea stretches from the Pacific Ocean through the Strait of Juan de Fuca, Puget Sound, the Strait of Georgia, and connected Canadian waters. Its geography combines tidal marshes, river deltas, narrow channels, underwater sills, steep slopes, and basins more than 400 meters deep. That combination has long challenged ocean models, especially those used to support habitat restoration, pollution control, navigation, emergency response, and water-quality management.
The central problem involves the vertical coordinate systems used by many coastal models. Unlike a map that divides the ocean into horizontal layers of fixed elevation, terrain-following or sigma-coordinate models make their computational layers follow the shape of the seabed. This is highly useful near complicated shorelines because the model grid naturally conforms to the bottom and can represent wetting and drying as tides expose and flood shallow areas. But the same flexibility creates a serious numerical difficulty over steep underwater slopes. When the modeled layers tilt sharply while the real density surfaces remain comparatively horizontal, small errors appear in the calculation of the horizontal pressure-gradient force. These errors, known as pressure-gradient errors, or PGEs, can generate artificial currents and excessive mixing between water layers. In a deep estuary, that false mixing can gradually erode the salinity and temperature stratification that drives real estuarine circulation.
For decades, scientists have commonly managed PGE by smoothing the bathymetry, or altering the digital representation of the seafloor so that abrupt depth changes become gentler. The technique can stabilize a model and preserve a reasonable approximation of stratification, but it also changes the physical geography that controls circulation. In the Salish Sea, a shallow shelf near the shoreline can descend from roughly 5 to 7 meters into channels tens or hundreds of meters deep over only a few hundred meters. Smoothing such a transition may make the numerical calculation easier, but it can widen or flatten channels, deepen shoals, displace shelf edges, and distort the cross-sectional shape of tidal passages. Those changes matter because bathymetry controls tidal currents, exchange flows, residence times, plume pathways, and the delivery of heat and dissolved substances. A model can therefore match observations at a few monitoring stations while still misrepresenting the broader physical processes taking place between them.
The new study, published in Ocean Dynamics, tests whether a different modeling strategy can retain the original bathymetry while suppressing the worst effects of PGE. The researchers upgraded an existing Salish Sea model, originally built with the Finite Volume Community Ocean Model and ten conventional sigma layers, into a new SCHISM-based system called SSM2.0. SCHISM, the Semi-implicit Cross-scale Hydroscience Integrated System Model, is designed for simulations spanning rivers, estuaries, shelves, and the open ocean. Its unstructured grid can use triangular and quadrilateral cells at different scales, while its semi-implicit time-stepping scheme allows stable calculations with relatively large time steps. The new domain also extends about 134 kilometers farther offshore, reaching waters approximately 2,600 meters deep beyond the continental shelf.
The key innovation is the use of Localized Sigma Coordinates with Shaved Cells, abbreviated LSC². Rather than forcing every location to use the same vertical structure, LSC² allows each model node to have its own arrangement of layers. Shallow intertidal cells can therefore contain only one to six layers, while deeper regions can use as many as 25. The grid is organized around transition zones near 7 meters and 30 meters depth, with the upper 30 meters receiving special attention because that is where strong surface freshwater and seasonal temperature gradients develop. Near abrupt shelf edges, “shaved” or degenerate cells reduce the direct numerical exchange between shallow and deep portions of the water column. In effect, the method prevents near-bottom cells on a steep slope from spanning an unrealistically large vertical range, while localized layers remain closer to horizontal in the stratified upper ocean. The design does not eliminate PGE completely, but it reduces the pathways through which numerical errors create spurious diapycnal mixing.
The researchers evaluated the model using a 2017 simulation, selected because extensive observational data were available. The system included freshwater from 26 major gauged rivers, 135 estimated ungauged streams, and 99 wastewater outfalls, as well as flows associated with the Fraser, Columbia, Willamette, Chehalis, and Willapa rivers. At the offshore boundary, daily temperature, salinity, velocity, and sea-level information came from a global HYCOM analysis, while 15 tidal constituents were taken from the FES2014 database. Hourly atmospheric forcing came from the National Oceanic and Atmospheric Administration’s three-kilometer High-Resolution Rapid Refresh weather model. The model used a 40-second time step, a two-equation kappa-epsilon turbulence closure, spatially varying bottom friction, and wetting-and-drying physics for tidal flats. Together, these components allowed the experiment to represent both regional ocean forcing and local nearshore dynamics within one computational framework.
A separate idealized experiment examined how much artificial motion remained after the model was initialized with horizontally uniform stratification and all external forcing was removed. This “still-lake” test is designed to expose currents generated solely by numerical pressure-gradient errors. In most of the inner Salish Sea, the resulting currents were less than 0.03 meters per second, and they declined substantially during the year-long simulation. Larger errors appeared near the deep continental shelf slope, where the water depth reached more than 350 meters, but that region lies far from the inner estuaries and did not significantly affect the reported Salish Sea results. The authors acknowledge that the shelf-slope problem will require additional layers and revised LSC² transition zones in future versions. Nevertheless, the stable temperature and salinity structure reproduced during the realistic simulation indicated that PGE had been reduced to an acceptable level where the model was most urgently needed.
The model’s performance was then compared with water levels, temperature, salinity, and current observations. Across six NOAA water-level stations, the average bias was approximately 0.02 meters and the average root-mean-square error was 0.16 meters. Errors remained within 10 percent of the annual tidal range for 99 percent of the modeled period. At 21 Washington State Department of Ecology monitoring stations, temperature and salinity predictions met the study’s target criteria, with temperature root-mean-square error below 0.82 degrees Celsius and salinity error below 0.77 practical salinity units. The model reproduced the seasonal separation between fresher, warmer surface water and saltier, cooler deep water in Hood Canal, Saratoga Passage, East Passage, and the Strait of Georgia. That result is especially important because excessive artificial mixing would normally weaken or destroy these patterns in a steep fjord environment.
Current predictions showed the clearest improvement over the earlier smoothed-bathymetry model. At four NOAA acoustic Doppler current-profiler stations in the San Juan Islands, the new simulation captured the timing and magnitude of spring-neap variations, including dominant current components approaching 2 meters per second. Correlations exceeded 0.95 for the principal flow direction, while most root-mean-square errors remained below 0.2 meters per second. The authors report average reductions of roughly 17 percent in current bias and 14 percent in root-mean-square error compared with the previous model, with some locations showing improvements of 0.1 meters per second in bias and 0.2 meters per second in error. At shallow Sequim Bay, the unsmoothed model also better represented strong channel currents, ebb-flood asymmetry, and differences between surface outflow and near-bottom flow. Temperature predictions improved in several nearshore locations as well, partly because the model retained more accurate water-column depths and used a nearly uniform surface layer about 1.16 meters thick.
The study also reproduced the characteristic exchange circulation of the Salish Sea: fresher water moving seaward near the surface while denser ocean water flows landward below, with sills and narrow channels modifying the pattern from basin to basin. In Saratoga Passage, the depth of zero tidally averaged flow appeared within roughly the upper 10 to 15 percent of the water column, a signature associated with fjord-like circulation. The Strait of Juan de Fuca and Puget Sound showed profiles closer to partially mixed or coastal-plain estuaries, with strongest inflow deeper in the water column. The modeled landward transport through the Strait of Juan de Fuca was approximately 124,000 cubic meters per second, consistent with earlier estimates. Because the model can now resolve tidal flats, steep nearshore shelves, and deep channels without changing the underlying seafloor, the researchers argue that a single regional system could support applications previously requiring separate nested models. Potential uses include habitat restoration, eelgrass and marsh management, shellfish protection, contaminant tracking, emergency response, navigation, and future ecosystem simulations. The authors caution that further testing, calibration, and improvements to sediment heat exchange and deep-slope grid design are still needed, but they describe the Salish Sea application as evidence that cross-scale modeling in a strongly stratified fjord is feasible without sacrificing bathymetric realism.
Subject of Research: Three-dimensional hydrodynamic modeling of estuarine circulation, pressure-gradient error, intertidal dynamics, stratification, and exchange flows in the Salish Sea.
Article Title: Simultaneous resolution of near-shore intertidal and deep estuarine circulation by eliminating bathymetric smoothing in modeling – the Salish Sea
Article References: Khangaonkar, T., Wang, T., Yun, S.K. et al. Ocean Dynamics 76, 42 (2026).
Image Credits: AI Generated
DOI: 10.1007/s10236-026-01794-8
Keywords: Salish Sea, estuarine circulation, pressure-gradient error, nearshore habitats, three-dimensional hydrodynamic modeling, model skill, cross-scale simulation, deep fjord, SCHISM, LSC², bathymetry, intertidal dynamics
