Science of Tsunami Hazards (Feb 2015)
AN OCEAN DEPTH-CORRECTION METHOD FOR REDUCING MODEL ERRORS IN TSUNAMI TRAVEL TIME: APPLICATION TO THE 2010 CHILE AND 2011 TOHOKU TSUNAMIS
Abstract
In this paper, we attempt to reduce the discrepancies between the modeled and observed tsunami arrival times. We treat the ocean as a homogenous fluid, ignoring stratification due to compressibility and variations of temperature and salinity. The phase speed of surface gravity waves is reduced for a compressible fluid compared to that of an incompressible fluid. At the shallow water limit, the reduction in speed is about 0.86% at a water depth of 4000 m. We propose a simple ocean depth- correction method to implement the reduction in wave speed in the framework of shallow water equations of an incompressible fluid: 1) we define an effective ocean depth such that the reduction of the phase speed due to compressibility of seawater is exactly matched by the decrease in water depth (about 2.5% reduction at ocean depth of 6000 m and less than 0.1% at 200 m); 2) this effective depth is treated as if it were the real ocean depth. Implementation of the method only requires replacing the ocean bathymetry with the effective bathymetry so there is no need to modify existing tsunami codes and thus there is no additional computational cost. We interpret the depth-correction method as a bulk-parameterization of the combined effects of physical dispersion, compressibility, stratification, and elasticity of the earth on wave speed. We applied this method to the 2010 Chile and 2011 Tohoku basin-crossing tsunamis. For the 2010 Chile tsunami, this approach resulted in very good agreement between the observed and modeled tsunami arrival times. For the 2011 Tohoku tsunami, we found good agreements between the modeled and the observed tsunami arrival times for most of the DARTs except the farthest ones from the source region, where discrepancies as much as 3-4 min. still remain.
