Numerical Methods in Support of Advanced Tsunami Early Warning

After the 2004 Great Sumatra-Andaman tsunami that devastated vast areas bordering the Indian Ocean and claimed over 230,000 lives many research activities began to improve tsunami early warning capacities. Development efforts were further promoted after the occurrence of several major events thereafter – Samoa 2009, Chile 2010, and Japan 2011, to name just the most severe ones. Among these efforts was a large scientific and development project, the German-Indonesian Tsunami Early Warning System (GITEWS) endeavor as described by Rudloff et al. (2009). Advanced numerical methods for simulating the tsunami propagation and inundation, as well as for evaluating the measurement data and providing a forecast for precise warning bulletins, have been developed in that context. We will take the developments of the GITEWS modeling as a guideline for introducing concepts and existing approaches in tsunami modeling and early warning.For tsunami propagation and inundation modeling, numerical methods for solving hyperbolic or parabolic partial differential equations play the predominant role. The behavior of tsunami waves is usually modeled by simplifications of the Navier-Stokes equations.In tsunami early warning approaches, an inverse problem needs to be solved, which can be formulated as follows: given a number of measurements of the tsunami event, what was the source; and when knowing the source, how do future states look like? This problem has to be solved within a few minutes in order to be of any use, and the number of available measurements is very small within the first few minutes after the rupture causing a tsunami.