On the trade-off between accuracy and efficiency in Probabilistic Tsunami Hazard Assessment

According to historical catalogs, large earthquakes occurring in subduction zones or on other large faults are the principal contributors to tsunami hazard worldwide. Seismotectonic tsunamis are generated by the deformation of the sea-floor during an earthquake. The sea surface is deformed accordingly and propagates outward due to gravity. The rarity of large tsunamis and the limited distribution of monitoring instruments result in scarce real-time observations and incomplete historical records, leading to uncertain real-time forecasts and long-term hazard assessments. Nowadays, computational-based probabilistic methods are powerful tools to describe both the intrinsic variability of the phenomenon (aleatory uncertainty) and the lack of knowledge of the natural phenomenon in absence of evidence (epistemic uncertainty). However, the computational cost associated with Probabilistic Tsunami Hazard Assessment (PTHA) can often be prohibitive, necessitating efficient High-Performance Computing (HPC) systems to partially overcome these practical limitations. Unfortunately, such resources are not always accessible. In the first part of this thesis, the objective is to adjust the complexity of the physical approximations adopted for modeling the generation of a seismotectonic tsunami, based on the desired level of accuracy in hazard assessments. With this aim, an efficient numerical solution for the integral describing tsunami generation under the assumption of static, instantaneous, and piecewise-constant sea-floor deformation on a variable bathymetry was developed. This work, published in Natural Hazards and Earth System Sciences, includes a prototype code that enables the construction of a local database of unit sources, each solved using this integral solution with varying bathymetry and sea floor displacement. These unit sources can be linearly combined to approximate the tsunami's initial condition in realistic scenarios. The computational time required for this numerical evaluation has been greatly reduced compared to previous studies, although it is still not feasible for real-time forecasting, for which further work on GPU architectures, leveraging vectorization and parallelization techniques, is likely required to enhance performance. Another work, recently published in Journal of Geophysical Research: Oceans, explores how different 1D tsunami generation models (considering dynamic or static, instantaneous ruptures) and propagation solvers (employing shallow water or non-hydrostatic multilayer approximations) affect 1D inundation modeling. The experimental results suggested that factors such as source duration, horizontal extent of the source and geometric characteristic of coastal topo/bathymetry significantly condition the choice of model for accurately representing tsunami generation and inundation. In the second part, the aim was to identify a subset of scenarios that optimally represent inundation in PTHA while quantifying the associated uncertainties. The outcomes suggested that only a few thousand scenarios are required to adequately represent inundation PTHA, which is an order of magnitude fewer than the typical number of high-resolution simulations conducted for this purpose. For practical applications, a satisfactory balance between feasibility and accuracy can be achieved by comparing the confidence intervals of estimates after sampling with the range of epistemic uncertainty. After conducting inundation simulations for the source sample, the uncertainty in onshore hazard estimation can be assumed to be comparable to that observed offshore, which can be analytically calculated prior to conduct expensive inundation simulations. By assigning greater weight to near-field scenarios, accuracy can be improved compared to situations where this factor is not considered. This work has been recently submitted to Geophysical Journal International.