Tsunami forecasting using proper orthogonal decomposition method

Abstract

Tsunami early warning requires a quick and accurate prediction of the occurrence, arrival time and characteristics of the tsunami waves. The solution of a full set of governing partial differential equations can provide a sufficiently accurate prediction, but it is often computationally intensive and time consuming at high spatial resolution. This paper proposes a new data-driven/reduced-order approach for quick and accurate predictions of tsunami wave propagation and incident wave characteristics. The Proper Orthogonal Decomposition (POD) technique is used for the reduced-order model, with the basis functions determined from an ensemble of offline high-resolution simulations. A nonlinear shallow water model TUNAMI-N2 is utilized to compute the most sensible tsunami scenarios represented by a pair of spatially distributed scalars: the maximum wave amplitude and the arrival time. Initial conditions (sea surface displacement) for the computations are defined by instantaneous movement of sea bottom discrete fault segments characterizing the tsunamigenic earthquakes in a given domain. Tests using hypothetical earthquake-generated tsunamis show that the POD methodology can provide very accurate results for scenarios generated with linear and nonlinear models, and is able to predict the maximum tsunami amplitude and traveltime over the entire computational domain within a few seconds. The presented method can be used in operational tsunami warning systems. Copyright 2008 by the American Geophysical Union.