What if an island experienced more erosion?

Waves roll onto the beach again and again. Each one takes a tiny bit of sand.

What if the waves got much, much bigger?

Sandy islands are always changing. Waves pick up sand from one place and drop it in another, and wind blows it into dunes. Wearing land away like this is called erosion.

Ordinary waves wear an island slowly. But what if the waves were storm-sized every day? Would the island wear away a little faster, or a lot faster? In this lab you can make the waves bigger around a sandy island and watch what the model shows.

NOAA describes barrier islands as constantly changing deposits of sand that move, erode and grow with wind and waves, and can even disappear.

This lab uses a rule-based model: the only physically calculated number is the waves' power; erosion is a rule proportional to that power, to the softness of the coast and to how much of it is unprotected by plants. What happens to erosion when wave height rises from 1.5 m to 5 m?

On an ordinary day, the waves are small. The island wears away very slowly.

Grass on the sand dunes holds the sand with its roots.

On an ordinary day in the model, waves 1.5 meters high arrive every 8 seconds. Each meter of wave front carries about 8.8 kilowatts of power, all of it rolling in toward the shore.

The island is sand, which washes away easily, but 60 percent of it is covered with plants like dune grass. In the model, those roots cut the wear by 42 percent. After 50 model years, the island still has about 83 percent of its land.

With H = 1.5 m, T = 8 s and ρ = 1,025 kg/m³, P = ρg²H²T/(64π) = 8.8 kW/m. The model's erosion index is 100 for these waves on bare sand; 60 percent plant cover multiplies it by 1 − 0.7 × 0.6 = 0.58, giving 58.

After 50 model years the island keeps 83 percent of its area. Model years and percentages show the pattern only; the model does not predict real meters or dates.

In our pretend lab, Olly makes big storm waves every day.

Now the island wears away much faster! The side facing the waves shrinks the most.

Choose 'big storm': waves 5 meters high. That is only about three times taller, but each meter of wave now carries about 98 kilowatts, roughly 11 times the power.

In the model, the island wears away about 11 times faster. After 10 model years it is down to about two thirds, and after 50 it has only about a quarter left. The side facing the waves shrinks fastest. In real life, storm waves come and go; the model keeps them going all the time.

At H = 5 m, P = 98.1 kW/m, (5/1.5)² = 11.1 times the ordinary value, and the erosion index rises from 58 to 644. The island falls to 66 percent at 10 model years and 23 percent at 50; with no plants it would fall to 8 percent, and with full cover to 41.

The waves are held constant, so this is not a storm: it is a permanently stormier sea. The weather-side wear rate is set to be about eight times the sheltered side's (12 percent).

Big waves carry much more power than small waves.

A wave twice as tall carries four times as much power. So storm waves move lots of sand.

A wave carries energy. Physicists have found that, for waves like these, the power goes up with the square of the wave's height. Make a wave twice as tall and it carries four times the power; three times as tall, about nine times.

More power means more sand stirred up and carried off. Plant roots fight back like a net, holding sand together. That is why in the model, planted coasts wear away more slowly even under big waves.

For mechanical waves, transmitted power is proportional to the square of the amplitude and the square of the frequency (OpenStax); for deep-water ocean waves, the U.S. wave-resource assessment (EPRI 2011, Appendix A) gives P = ρg²H²T/(64π), about 0.49 kW/m × H²T, so longer-period waves also carry more.

The model's limits: the softness values (sand 1, clay 0.35, rock 0.03) and the 0.7 plant factor are rules that order the cases, not measurements. Real waves change in shallow water, and real islands also gain sand from rivers and currents and respond to tides, sea level and people.

People help islands by planting dune grass and repairing islands and marshes.

Marsh plants and oyster reefs calm the waves too.

Barrier islands, long strips of sand along coasts like North Carolina's Outer Banks, help protect the mainland. NOAA explains that their dunes and grasses soak up wave energy before waves reach the coast, which means less flooding.

These islands are shrinking in many places. Causes include rising seas and strong storms, and also dams and dredging that reduce the sand available to build them up. Restoration helps: NOAA reports that thousands of acres of barrier islands and marshes have been restored along the Gulf coast.

NOAA notes barrier islands are disappearing in many areas, with causes including ship traffic, hard levees, damming and dredging that reduce sediment supply, and climate-driven sea-level rise and extreme weather. NOAA supports natural and nature-based restoration; thousands of acres were restored or enhanced in Gulf spill-restoration projects.

USGS's National Assessment of Coastal Change Hazards studies storm-driven beach and dune erosion and long-term shoreline change, so that communities can plan with better forecasts.