Global Dissipation Models for Simulating Tsunamis at Far-Field Coasts up to 60 hours Post-Earthquake: Multi-Site Tests in Australia

At far-field coasts the largest tsunami waves may occur many hours post-arrival, and
hazardous waves may persist for more than 1 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 modeled tsunami will persist indefinitely. In contrast, real tsunamis exhibit slow
dissipation at the global-scale with an energy e-folding time of approximately 1 day. How
strongly do these global-scale approximations affect nearshore tsunamis simulated at farfield
coasts? To investigate this we compare modeled and observed tsunamis at sixteen
nearshore tide-gauges in Australia, generated by the following earthquakes: Mw9.5 Chile
1960; Mw9.2 Sumatra 2004; Mw8.8 Chile 2010; Mw9.1 Tohoku 2011; and Mw8.3 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 h
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 reducedphysics
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 x8 h after tsunami arrival, and Manningfriction
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 h, 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 h 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.