A1 Extreme Surface Events

Topic

Extreme ocean-surface events are the highest-energy and most immediately impactful disturbances occurring right at the interface between the ocean and the atmosphere. Three distinct phenomena make up this category: tropical cyclones, which generate extreme waves and storm surges capable of coastal flooding; rogue waves—solitary waves of abnormally large amplitude that emerge from the sea even amidst moderate wave conditions; and coastal flooding, which occurs when high tide, storm surge, and extreme waves coincide—a convergence that causes the water level at the coast to suddenly exceed what any of those three factors would produce in isolation.

Storm surge is the rise in coastal sea level caused by a tropical cyclone through two simultaneous mechanisms: wind forcing, which pushes and piles water up against the coast; and the cyclone's low central pressure, which causes the sea surface to rise due to the "inverted barometer effect"—a phenomenon in which every one-hectopascal drop in atmospheric pressure raises the sea level by one centimeter.

This same storm surge can be further amplified by coastal resonance—a phenomenon known as Proudman resonance—which occurs when the cyclone's forward speed matches the propagation speed of a long tidal wave (a speed determined by water depth and gravity). When this alignment occurs, Proudman resonance multiplies the storm surge by a factor of three to five compared to what the cyclone would produce on its own. Unlike storm surges, rogue waves do not depend on the presence of a cyclone; wave theory describes them as solutions to the nonlinear Schrödinger equation. Among these solutions, "breather" types—such as the Peregrine breather—are solitary waves that emerge from a background of uniform waves. It is this very sudden emergence that allows them to reach an amplitude up to three times greater than that background before fading back into it.

The formation of these rogue waves is explained by two mechanisms that can act in tandem: nonlinear focusing—known as Benjamin-Feir instability—which concentrates the energy of several nearby waves into a single wave of much greater amplitude; and geometric dispersion, which occurs when the seabed features complex underwater topography that causes wave energy to disperse geometrically and ultimately concentrate at specific points along the coast.

Thus, on coasts exposed to the direct path of a tropical cyclone, storm surges can reach heights of one to ten meters. The accompanying wave height distribution typically follows heavy-tailed patterns—such as the Weibull distribution or a modified Rayleigh distribution—meaning that extreme waves occur more frequently than an ordinary distribution would predict. Coastal flooding—the third extreme ocean-surface event that began this entire discussion—occurs precisely when high tide, a storm surge, and one of these extreme waves (whether a rogue wave or simply part of the storm swell) coincide at the same moment on the same stretch of coast.

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