Role of Compressibility on Tsunami Propagation

In the present paper, we aim to reduce the discrepancies between tsunami arrival times evaluated from tsunami models and real measurements considering the role of ocean compressibility. We perform qualitative studies to reveal the phase speed reduction rate via a modified version of the Mild Slope Equation for Weakly Compressible fluid (MSEWC) proposed by Sammarco et al. (2013). The model is validated against a 3-D computational model. Physical properties of surface gravity waves are studied and compared with those for waves evaluated from an incompressible flow solver over realistic geometry for 2011 Tohoku-oki event, revealing reduction in phase speed. Plain Language Summary Submarine earthquakes and submarine mass failures (SMFs), can generate long gravitational waves (or tsunamis) that propagate at the free surface. Tsunami waves can travel long distances and are known for their dramatic effects on coastal areas. Nowadays, numerical models are used to reconstruct the tsunamigenic events for many scientific and socioeconomic aspects i.e. Tsunami Early Warning Systems, inundation mapping, risk and hazard analysis, etc. A number of typically neglected parameters in these models cause discrepancies between model outputs and observations. Most of the tsunami models predict tsunami arrival times at distant stations slightly early in comparison to observations. In this study, we show how ocean compressibility would affect the tsunami wave propagation speed. In this framework, an efficient two-dimensional model equation for the weakly compressible ocean has been developed, validated and tested for simplified and real cases against three dimensional and incompressible solvers. Taking the effect of compressibility, the phase speed of surface gravity waves is reduced compared to that of an incompressible fluid. Then, we used the model for the case of devastating Tohoku-Oki 2011 tsunami event, improving the model accuracy. This study sheds light for future model development to include ocean compressibility among other typically neglected parameters.