The mathematical sciences help to predict the path and strength of a tsunami following an earthquake or other oceanic event (such as a massive landslide or volcano eruption). Mathematical models underpin tsunami warning systems by estimating where a tsunami will make landfall, how high the waves will be, and how fast the waves will be traveling. More fundamentally, the mathematical sciences help to map the topography of the ocean floor and infer large-scale wave behavior from independent ocean tide gauges that are irregularly spaced and can be hundreds of miles apart. This knowledge is behind emergency warnings and evacuations, which help to avoid potentially devastating consequences.
Numerical models are used to simulate the earthquake, transoceanic propagation, and inundation of dry land. To save time in the event of an emergency, these simulations are run for a variety of possible earthquake sizes and locations, and these scenarios are then combined with ocean tide readings as they become available. This figure shows the predicted sea level increase (in cm) resulting from the deadly 9.0 magnitude earthquake off the coast of Japan in March 2011.