Torrey Pines edge waves were substantial, but a simpler shoreline model still performed reasonably well

At Torrey Pines State Beach in Southern California, researchers found that waves traveling along the shore made up a substantial part of measured nearshore motion. Yet a simpler model that excludes those waves still approximately reproduced important wave patterns. The result, highlighted by the University of Washington on September 28, helps coastal engineers judge what a streamlined model can describe at this beach. It does not establish how well the model would forecast flooding elsewhere.

The researchers analyzed 60 days of pressure and water-velocity observations gathered between October 2021 and February 2022. Their sensors extended from the shoreline to roughly 30 metres of water depth. An eight-element array stretched about 1.5 kilometres along the coast at approximately 7 metres depth, giving the team measurements across the beach as well as along it.

A sizeable component at one depth

The study examined infragravity waves: long-period motions, nominally lasting 25 to 250 seconds, generated through interactions among shorter sea and swell waves in shallow water. Edge waves are one form. They are trapped near the coast, standing across the shore while traveling along it. That direction of travel distinguishes them from the shore-normal waves represented by the one-dimensional model tested in the study.

Using a Bayesian analysis of the sensor measurements, the researchers estimated that edge waves accounted for 28% ± 5% of infragravity sea-surface elevation variance at 7 metres depth. At that depth, their estimated shares were 43% ± 5% of alongshore velocity variance and 14% ± 5% of cross-shore velocity variance. Those percentages describe different measured quantities at one depth; the 28% figure is not a percentage of coastal flooding or a value established for other beaches.

What the simpler model captured

The one-dimensional SWASH model assumes waves approach normally to the shore and leaves out edge waves. Even so, it approximately reproduced infragravity pressure, cross-shore velocity and their pattern across the beach in this experiment. The authors say refraction turns waves closer to shore-normal as they enter shallow water, which helps explain why those modeled properties could agree reasonably well with observations despite the missing alongshore component.

The agreement has a precise limit. The authors conclude that edge waves were unnecessary for a first-order description of infragravity pressure and cross-shore velocity at this open-coast site, but should be considered when estimating alongshore velocity. A substantial measured edge-wave share and a useful simplified model can therefore coexist: they concern different aspects of the water's motion.

The model also tended to overpredict shallow-water and runup infragravity wave height, as well as the infragravity reflection coefficient. The paper discusses possible causes without settling on one. Runup observations were limited, so the comparison cannot establish a demonstrated operational flood-forecast result. It is more accurately a test of how well the model represented selected measured wave properties under the conditions observed.

Why the site matters

Other coastal modeling work shows why the distinction matters. A U.S. Geological Survey record of a Georgia coast study describes wave runup as relevant to total water levels, sediment movement and coastal design. That study used local seabed and beach profiles in its forecasting method and compared estimates with historical hurricane high-water marks. Its reported differences from observed marks ranged from 3 to 32 centimetres for Hurricane Irma and 9 to 70 centimetres for Hurricane Matthew. Those figures concern a different coast and model; they do not validate the Torrey Pines finding.

A separate USGS-associated study comparing two versions of the XBeach model found that the version resolving individual waves predicted runup better at the sandy beach it examined. Its authors describe runup prediction as relevant to assessments of dune erosion, overwash and flooding from wave overtopping. Together, these studies show why engineers test a model against the particular measurements and shoreline conditions that matter for its intended use.

The Torrey Pines authors also identify limits in their edge-wave estimation method: it represents edge waves and one fully reflected shore-normal mode, while omitting progressive waves, wave setup and setdown, and changes in seabed shape along the coast. They call for observations in more settings and say edge waves may matter more at pocket beaches, estuaries or other special sites. Whether the same simplified approach performs as well there, or during stronger storms, remains untested by this experiment.