Global Dissipation Models for Simulating Tsunamis at Far-Field Coasts up to 60 hours Post-Earthquake: Multi-Site Tests in Australia - Davies, Gareth; Romano, Fabrizio; Lorito, Stefano (Frontiers in Earth Science, 2020)
At far-field coasts the largest tsunami waves may occur many hours post-arrival, and hazardous waves may persist for more than one day. Such tsunamis are often simulated by nesting high-resolution nonlinear shallow water models (covering sites of interest) within low-resolution reduced-physics global-scale models (to efficiently simulate propagation). These global models often ignore friction and are mathematically energy conservative, so in theory the modelled tsunami will persist indefinitely. In contrast, real tsunamis exhibit slow dissipation at the global-scale with an energy e-folding time of approximately one day. How strongly do these global-scale approximations affect nearshore tsunamis simulated at far-field coasts? To investigate this we compare modelled and observed tsunamis at sixteen nearshore tide-gauges in Australia, generated by the following earthquakes: $M_{w}9.5$ Chile 1960; $M_{w}9.2$ Sumatra 2004; $M_{w}8.8$ Chile 2010; $M_{w}9.1$ Tohoku 2011; and $M_{w}8.3$ Chile 2015. Each tsunami is represented using multiple published source models, to prevent bias in any single source from dominating the results. Each tsunami is simulated for 60 hours with a nested global-to-local model. On nearshore grids we solve the nonlinear shallow water equations with Manning-friction, while on the global grid we test three reduced-physics propagation models which combine the linear shallow water equations with alternative treatments of friction: 1) frictionless; 2) nonlinear Manning-friction; and 3) constant linear-friction. Compared with data, the frictionless global model well simulates nearshore tsunami maxima for $\simeq$ 8 hours after tsunami arrival, and Manning-friction gives similar predictions in this period. Constant linear-friction underestimates the size of early arriving waves. As the simulation duration is increased from 36 to 60 hours, the frictionless model increasingly overestimates observed wave heights, whereas models with global-scale friction work relatively well. The constant linear-friction model can be improved using delayed-linear-friction, where propagation is simulated with an initial frictionless period (12 hours herein). This prevents systematic underestimation of early wave heights. While nonlinear Manning-friction offers comparably good performance, a practical advantage of the linear-friction models herein is that solutions can be computed, to high accuracy, via a simple transformation of frictionless solutions. This offers a pragmatic approach to improving unit-source based global tsunami simulations at late times.