Statistical methods constitute a useful approach to understand and quantify the uncertainty that governs complex tsunami mechanisms. Numerical experiments may often have a high computational cost. This forms a limiting factor for performing uncertainty and sensitivity analyses, where numerous simulations are required. Statistical emulators, as surrogates of these simulators, can provide predictions of the physical process in a much faster and computationally inexpensive way. They can form a prominent solution to explore thousands of scenarios that would be otherwise numerically expensive and difficult to achieve. In this work, we build a statistical emulator of the deterministic codes used to simulate submarine sliding and tsunami generation at the Rockall Bank, NE Atlantic Ocean, in two stages. First we calibrate, against observations of the landslide deposits, the parameters used in the landslide simulations. This calibration is performed under a Bayesian framework using Gaussian Process (GP) emulators to approximate the landslide model, and the discrepancy function between model and observations. Distributions of the calibrated input parameters are obtained as a result of the calibration. In a second step, a GP emulator is built to mimic the coupled landslide-tsunami numerical process. The emulator propagates the uncertainties in the distributions of the calibrated input parameters inferred from the first step to the outputs. As a result, a quantification of the uncertainty of the maximum free surface elevation at specified locations is obtained.
The Indus Canyon in the northwestern Indian Ocean has been reported to be the site of numerous submarine mass failures in the past. This study is the first to investigate potential tsunami hazards associated with such mass failures in this region. We employed statistical emulation, i.e. surrogate modelling, to efficiently quantify uncertainties associated with slump-generated tsunamis at the slopes of the canyon. We simulated 60 slump scenarios with thickness of 100-300 m, width of 6-10.5 km, travel distances of 500-2000 m and submergence depth of 250-450 m. These scenarios were then used to train the emulator and predict 500,000 trial scenarios in order to study probabilistically the tsunami hazard over the near field. Due to narrow-deep canyon walls and the shallow continental shelf in the adjacent regions (\100 m water depth), the tsunami propagation has a unique pattern as an ellipse stretched in the NE-SW direction. The results show that the most likely tsunami amplitudes and velocities are approximately 0.2-1.0 m and 2.5-13 m/s, respectively, which can potentially impact vessels and maritime facilities. We demonstrate that the emulator-based approach is an important tool for probabilistic hazard analysis since it can generate thousands of tsunami scenarios in few seconds, compared to days of computations on High Performance Computing facilities for a single run of the dispersive tsunami solver that we use here.
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