A limited-domain numerical model for long-range tsunami propagation over an ocean of variable depth

Abstract

A limited-domain numerical algorithm with radiational boundary conditions is developed with emphasis on the capability of real-time tsunami prediction. Bottom topography representative of the North West Pacific was employed in this study. An accurate rendition of the dispersion characteristics both in the numerical governing equation and in the radiational condition allows faithful reproduction of the characteristics of the leading tsunami waves over a constant depth ocean. Tests with different size domains reveal that topographic features along or outside the lateral boundaries can produce significant contamination of the trailing portion of the wave record due to reflection, refraction and diffraction. However, such contamination remains in the trailing region or is left behind. The modification to leading waves by topography is mainly due to refraction and true reflection from the lateral boundaries. Such contamination can be reduced significantly by choosing the lateral size comparable to the zonal size of the domain. Along the zonal axis of the domain, the one-dimensional models with or without the consideration of geometric spreading produce time series qualitatively and quantitatively different from those of the limited-domain model. This difference as well as the lateral variation of the wave record suggests that a two-dimensional model is necessary in the presence of topography. From the test runs, it is concluded that the shape and the lateral scale of the initial surface displacement (with fixed initial energy), and bottom topography near the source region are extremely important in characterizing the far-field tsunami signal. The shape and the lateral scale of the initial displacement mainly governs the directivity and the spectral content of a tsunami, respectively. Bottom topography near the source region not only determines the initial direction of energy flow but also governs the direction of major reflection. Beyond the source region topography seems to be of secondary importance except for major ridge signatures such as the Emperor Sea Mount Chain. The effects of earth's rotation and nonlinearity can be important for long propagation times or distances, since these effects directly control the phase and the amplitude of the leading waves of a tsunami. Nonlinearity causes the leading waves to retain more energy (steepening effect). Earth's rotation causes waves within a certain wavennumber band to attain the maximum speed.