# Article: From Math to Maps

In communities such as Cannon Beach, Oregon, or Crescent City, California, or the Quinault Indian Nation in Washington, bright blue metal signs with a white, menacing ocean wave dot coastal streets. “Tsunami hazard zone,” they warn, or “evacuation shelter,” or “tsunami evacuation route.” A tsunami hasn’t affected the Pacific Northwest coast since 1964, when an earthquake and submarine landslides at Alaska’s Prince William Sound caused a significant one. Still, scientists are certain that these specific communities are at risk. Exhaustive computer modelingmathematical simulations of where a likely wave will start, travel, and end uptell NOAA, the U.S. government agency responsible for tsunami warning, where to stake the signs.

Communities that participate in NOAA's TsunamiReady program post warning and evacuation signs in low-elevation areas.

Jason Lelchuk for AMNH

###### Lessons from Sumatra

Vasily Titov, a mathematician for NOAA’s Pacific Marine Environmental Lab in Seattle, is one of a handful of researchers worldwide who can craft a computerized tsunami. His expertise was put grimly to the test when NOAA learned that an earthquake had generated an enormous tsunami off the coast of Sumatra, Indonesia, on December 26, 2004. After eight hours of overnight work, Titov generated the first model to describe the wave’s travel speed, direction, and amplitude (height) in the open ocean.

But the tsunami raced faster than could Titov. It was slamming into Somalia and Kenya by the time the model was complete. “I had to start from scratch,” he explains. “If the event were in the Pacific Ocean, the model could have been done minutes after learning the magnitude and location of the quake.”

The delay was due to lack of data. The Indian Ocean has been studied far less than the Pacific, where the vast majority of tsunamis occur. The first piece of information Titov needed, he hadan initial seismic measurement of the earthquake. The quake’s magnitude roughly relates to how much seawater the shifting Earth’s crust could displace. (The first alert about the quake, after about fifteen minutes, described it as magnitude 8.0. The measure was refined four hours later to 8.9. New calculations published in Nature in March 2005, however, put it at 9.3the second-largest earthquake ever recorded on a seismograph.)

Global Reach: the Indian Ocean Tsunami (Watch Video)

NOAA

Titov’s model applied equations incorporating Newton’s laws and wave physics to the data about this initial “bump” of water. The calculations described how the tsunami would likely propagate from its source. “But the nature of the tsunami wave is such that underwater topography, or bathymetry, defines the way it propagates,” explains Titov. The shapes of coastlines further transform a tsunami’s speed and size, as the sloping seafloor slows the wave and increases its amplitude.

For the model to predict where and when the wave would hit, and how hard, Titov desperately needed bathymetric data for coastal regions around the Indian Ocean. This information, regrettably, was both scarce and impossible to access in time. When combined with political hurdles and an infrastructure not suited to handle tsunami warning in the Indian Ocean basin, NOAA’s efforts were unable to help avert some of the disaster’s more than 283,000 deaths.

NOAA computer modeler Vasily Titov and the model he made within hours of the Indian Ocean tsunami.

Jason Lelchuk for AMNH

###### Toward the Future

Still, Titov’s Sumatra model is incredibly useful for mitigating the effects of future tsunamis. Researchers are now comparing its predictions to the wave’s real-life effects on coastlines around the world. “Every tsunami leaves traces on the coast,” says Titov. “So we go to the hardest-hit coasts and measure how high the wave came up the shore, or on trees. That gives us the amplitude data for the tsunami at different coasts.”

Worldwide data on the tsunami is still being collected months after the event. Some of it has been surprising, and illuminating. For example, the tsunami took 30 to 32 hours to reach the most distant coastlines, such as those in Halifax, Nova Scotia, 24,000 km from Sumatra. Curiously, some wide-ranging spots like Halifax and Lima, Peru, recorded waves several times larger than those that hit the Cocos Islands in Australia, only 1,000 km from the source. “Now we realize how a tsunami can import energy into different oceans,” says Titov. It turns out that the energy can be channeled by mid-ocean ridges: long, underwater mountain ranges formed by magma rising up in between plate boundaries. “The mid-Atlantic ridge provided the pathway for the tsunami into the Atlantic,” he explains.

Overall, Titov’s Sumatra computer model closely matches the real event. That means the calculations can be applied to models modified for use in places like the Pacific Northwest, which has a coastal fault line of the same type and length, and with similar bathymetry, as Sumatra. A magnitude 9 earthquake there could produce a tsunami that could affect coasts worldwide. Since local communities would be hit hardest, however, Titov is now working to test dozens of scenarios with his models, trying different combinations of earthquake magnitudes, locations, and local bathymetries in northern California, Oregon, Washington, and British Columbia. If an earthquake occurs at any fault in the Pacific basin, emergency managers could draw from this stockpile of scenarios to predict wave characteristics and time of strike at a particular coastline.

A prototype system for such model forecasting is already in place, and is now being tested by NOAA and by tsunami warning centers responsible for events in the Pacific, Atlantic, and Caribbean. (As for the Indian Ocean, a warning system is still being set up, negotiated, and organized both technically and politically, says Titov.) The hopes are that within a year, NOAA’s system will be able to generate model forecasts in a matter of minutes. “We definitely don't want the Sumatra case to repeat itself,” he says. “We’re hoping to get our system in good enough shape so that the next big tsunami will not catch us by surprise.”

NOAA general tsunami page
http://www.noaa.gov/tsunamis.html

Surviving A Tsunami: Lessons from Chile, Hawaii, and Japan
http://pubs.usgs.gov/circ/c1187/
A USGS publication with incredible images and interview clips from survivors in tsunami-prone areas.

National Tsunami Hazard Mitigation Program: Links for Kids (K-12)
http://www.pmel.noaa.gov/tsunami-hazard/kids.html

December 26, 2004 Indian Ocean Tsunami: Data for Graphing
http://wcatwc.arh.noaa.gov/IndianOSite/IndianO12-26-04.htm
A list of some affected communities with wave height and arrival time data.

National Geophysical Data Center Tsunami Event Database
http://www.ngdc.noaa.gov/seg/hazard/tsevsrch_idb.shtml
Exhaustive, searchable information about most tsunamis on record.