Improving tsunami warning with a rapid linear model

When a shallow, undersea earthquake with a magnitude larger than 7.8 occurs, the Pacific Tsunami Warning Center (PTWC) initially places all areas that a tsunami might reach within three hours into a warning. Basing the warning area purely on travel-time is fast, so PTWC can issue a warning within seconds of locating an earthquake and establishing its magnitude. The center now issues warnings within 15 minutes of origin time for almost anywhere on Earth. Basing a warning area purely on travel time, however, ignores the directionality of the tsunami. Off the main lobe of the radiation pattern, warnings may well be unnecessary even though the theoretical arrival time is in less than three hours. Ideally the warning area should be determined by amplitude modeling, but full solution of the nonlinear shallow water equations takes too long. One solution, used by the SIFT package developed by NOAA's Center for Tsunami Research, is to assemble a tsunami from precomputed unit sources. While useful for modeling tsunamis in the far field from large subduction earthquakes, this technique cannot be used for earthquakes smaller than the stored unit sources. Further, the SIFT database contains only thrust on the décollement in subduction zones, so tsunamis from earthquakes at other locations or with other mechanisms cannot be modeled. PTWC is therefore investigating another solution to the problem of rapid modeling: solving only the linearized (and therefore faster, though more approximate) form of the shallow-water equations. The linear modeling code RIFT forecasts offshore wave heights, then projects these to shore using Green's Law. Computation is so rapid, a few tens of seconds, that predicted runups can be used to define the initial warning region. Before the method is incorporated into routine operations, however, its performance must be quantified and evaluated. Using RIFT, we computed coastal runup for nine tsunamis from 1992 to 2010 for which there are abundant field measurements as well as CMTs for the initiating earthquake. A warning should be issued whenever runup exceeds one meter. Using the one-meter criterion, RIFT correctly identified whether points should be warned or not warned 95% of the time, at 2% of the points a warning was missed (i.e., runup less than one meter was predicted, but over one meter was observed), and at 3% of the points there was a false alarm. Missing 2% of the warnings is unacceptable, so we dropped the threshold to 0.5 m. Now the missed warnings fell to 0.5%, which may be acceptable, but the number of false alarms grew to 10%. A 10% false-alarm rate, however, would represent a great improvement; the current false-alarm rate for Hawaii is probably about 50%, but it is significantly larger, as high as 75%, for some countries in the southwest Pacific. We continue to test RIFT and the limitations of Green's Law and many questions need to be addressed (e.g., tsunami heights from slow events tend to be underestimated; if our tests show an earthquake is slow how should we adjust the warning criteria?). Nevertheless, we expect the procedure slowly to be incorporated into our normal operations. RIFT promises to increase the reliability of PTWC's messages dramatically.