NUMERICAL MODELING OF THE GLOBAL TSUNAMI : Indonesian Tsunami of 26 December 2004

A new model for the global tsunami computation is constructed. It includes a high order of approximation for the spatial derivatives. The boundary condition at the shore line is controlled by the total depth and can be set either to runup or to the zero normal velocity. This model, with spatial resolution of one minute, is applied to the tsunami of 26 December 2004 in the World Ocean from 80◦S to 69◦N. Because the computational domain includes close to 200 million grid points, a parallel version of the code was developed and run on a supercomputer. The high spatial resolution of one minute produces very small numerical dispersion even when tsunamis wave travel over large distances. Model results for the Indonesian tsunami show that the tsunami traveled to every location of the World Ocean. In the Indian Ocean the tsunami properties are related to the source function, i.e., to the magnitude of the bottom displacement and directional properties of the source. In the Southern Ocean surrounding Antarctica, in the Pacific, and especially in the Atlantic, tsunami waves propagate over large distances by energy ducting over oceanic ridges. Tsunami energy is concentrated by long wave trapping over the oceanic ridges. Our computations show the Coriolis force plays a noticeable but secondary role in the trapping. Travel times obtained from computations as arrival of the first significant wave show a clear and consistent pattern only in the region of the high amplitude and in the simply connected domains. The tsunami traveled from Indonesia, around New Zealand, and into the Pacific Ocean. The path through the deep ocean to North America carried miniscule energy, while the stronger signal traveled a much longer distance via South Pacific ridges. The time difference between first signal and later signals strong enough to be recorded at North Pacific locations was several hours. Science of Tsunami Hazards, Vol. 23, No. 1, page 40(2005) 1. Basic equations and tools To study tsunami the equations of motion and continuity are formulated in the spherical polar coordinates. λ, φ and R, are defined as longitude, latitude and distance from the Earth’s center. If the origin of the system is located on the ocean surface, it is more suitable to introduce a vertical coordinate z = R−R0. Here R0 is the radius of Earth and is equal 6370km. Because Earth is not exactly spherical, the equations given below will better describe the large scale motion relative to the geopotential and not to the spherical surfaces. For further discussion of this problem see Gill (1982). The vertically averaged equations of motion and continuity in the spherical system are ∂u ∂t + u R◦ cosφ ∂u ∂λ + v R◦ ∂u ∂φ − (2Ω + u R◦ cosφ )v sinφ = − g R◦ cosφ ∂ζ ∂λ − τ b λ ρoD (1) ∂v ∂t + u R◦ cosφ ∂v ∂λ + v R◦ ∂v ∂φ + (2Ω + u R◦ cosφ )u sinφ = − g R◦ ∂ζ ∂φ − τ b φ