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 often occur many hours after arrival, and hazardous waves may persist for more than a day. To simulate tsunamis at far-field coasts it is common to combine high-resolution nonlinear shallow water models (covering sites of interest) with low-resolution reduced-physics global-scale models (to efficiently simulate propagation). The global propagation 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 issue we compare modelled and observed tsunamis at sixteen nearshore tide-gauges in Australia, which were generated by the following earthquakes: Mw 9.5 Chile 1960; Mw 9.2 Sumatra 2004; Mw 8.8 Chile 2010; Mw 9.1 Tohoku 2011; and Mw 8.3 Chile 2015. Each historic tsunami is represented with multiple earthquake source models from the literature, to prevent bias in any single source from dominating the results. The tsunami is simulated for 60 hours with a nested global-to-local model. On the 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. In comparison with data, the frictionless global model works well for simulating nearshore tsunami maxima for ~ 8 hours after tsunami arrival, and Manning-friction gives similar predictions in this period. Constant linear-friction is found to under-predict the size of early arriving waves. As the simulation duration is increased from 36 to 60 hours, the frictionless global model increasingly over-estimates the observed tsunami maxima; whereas both models with global-scale friction perform 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 the systematic underestimation of early nearshore wave heights. While nonlinear Manning-friction offers comparably good performance, a practical advantage of the linear-friction models in this study is that their solutions can be computed, to high accuracy, with a simple transformation of frictionless solutions. This offers a pragmatic approach to improving unit-source based global tsunami simulations at late times.