The numerical solutions of Shallow Water Equations are useful for applications related to geophysical flows that usually take place in large computational domains and could require real time calculation. Therefore, parallel versions of accurate and efficient numerical solvers for high performance platforms are needed to be able to deal with these simulation scenarios in reasonable times. In this paper we present an efficient CUDA implementation of a first and second order HLL methods and a two-waves TVD-WAF one. We propose to write all these methods under a common framework, the WAF method is slightly slower that the first order HLL method and two times faster than the second order HLL method, but it provides numerical results almost as accurate as the second order HLL scheme.
Abstract. We present a database of pre-calculated tsunami waveforms for the entire Mediterranean Sea, obtained by numerical propagation of uniformly spaced Gaussian-shaped elementary sources for the sea level elevation. Based on any initial sea surface displacement, the database allows the fast calculation of full waveforms at the 50 m isobath offshore of coastal sites of interest by linear superposition. A computationally inexpensive procedure is set to estimate the coefficients for the linear superposition based on the potential energy of the initial elevation field. The elementary sources size and spacing is fine enough to satisfactorily reproduce the effects of M > = 6.0 earthquakes. Tsunami propagation is modelled by using the Tsunami-HySEA code, a GPU finite volume solver for the non-linear shallow water equations. Like other existing methods based on the initial sea level elevation, the database is independent on the faulting geometry and mechanism, which makes it applicable in any tectonic environment. We model a large set of synthetic tsunami test scenarios, selected to explore the uncertainty introduced when approximating tsunami waveforms and their maxima by fast and simplified linear combination. This is the first time to our knowledge that the uncertainty associated to such a procedure is systematically analysed and that relatively small earthquakes are considered, which may be relevant in the near-field of the source in a complex tectonic setting. We find that non-linearity of tsunami evolution affects the reconstruction of the waveforms and of their maxima by introducing an almost unbiased (centred at zero) error distribution of relatively modest extent. The uncertainty introduced by our approximation can be in principle propagated to forecast results. The resulting product then is suitable for different applications such as probabilistic tsunami hazard analysis, tsunami source inversions and tsunami warning systems.
The numerical solution of shallow water systems is useful for several applications related to geophysical flows, but the big dimensions of the domains suggests the use of powerful accelerators to obtain numerical results in reasonable times. This paper addresses how to speed up the numerical solution of a first order wellbalanced finite volume scheme for 2D one-layer shallow water systems by using modern Graphics Processing Units (GPUs) supporting the NVIDIA CUDA programming model. An algorithm which exploits the potential data parallelism of this method is presented and implemented using the CUDA model in single and double floating point precision. Numerical experiments show the high efficiency of this CUDA solver in comparison with a CPU parallel implementation of the solver and with respect to a previously existing GPU solver based on a shading language.
Probabilistic Tsunami Hazard Analysis (PTHA) quantifies the probability of exceeding a specified inundation intensity at a given location within a given time interval. PTHA provides scientific guidance for tsunami risk analysis and risk management, including coastal planning and early warning. Explicit computation of site-specific PTHA, with an adequate discretization of source scenarios combined with high-resolution numerical inundation modelling, has been out of reach with existing models and computing capabilities, with tens to hundreds of thousands of moderately intensive numerical simulations being required for exhaustive uncertainty quantification. In recent years, more efficient GPU-based High-Performance Computing (HPC) facilities, together with efficient GPU-optimized shallow water type models for simulating tsunami inundation, have now made local long-term hazard assessment feasible. A workflow has been developed with three main stages: 1) Site-specific source selection and discretization, 2) Efficient numerical inundation simulation for each scenario using the GPU-based Tsunami-HySEA numerical tsunami propagation and inundation model using a system of nested topo-bathymetric grids, and 3) Hazard aggregation. We apply this site-specific PTHA workflow here to Catania, Sicily, for tsunamigenic earthquake sources in the Mediterranean. We illustrate the workflows of the PTHA as implemented for High-Performance Computing applications, including preliminary simulations carried out on intermediate scale GPU clusters. We show how the local hazard analysis conducted here produces a more fine-grained assessment than is possible with a regional assessment. However, the new local PTHA indicates somewhat lower probabilities of exceedance for higher maximum inundation heights than the available regional PTHA. The local hazard analysis takes into account small-scale tsunami inundation features and non-linearity which the regional-scale assessment does not incorporate. However, the deterministic inundation simulations neglect some uncertainties stemming from the simplified source treatment and tsunami modelling that are embedded in the regional stochastic approach to inundation height estimation. Further research is needed to quantify the uncertainty associated with numerical inundation modelling and to properly propagate it onto the hazard results, to fully exploit the potential of site-specific hazard assessment based on massive simulations.
Inundation maps are a fundamental tool for coastal risk management and in particular for designing evacuation maps and evacuation planning. These in turn are a necessary component of the tsunami warning systems’ last-mile. In Italy inundation maps are informed by a probabilistic tsunami hazard model. Based on a given level of acceptable risk, Italian authorities in charge for this task recommended to consider, as design hazard intensity, the average return period of 2500 years and the 84th percentile of the hazard model uncertainty. An available, regional-scale tsunami hazard model was used that covers the entire Italian coastline. Safety factors based on analysis of run-up variability and an empirical coastal dissipation law on a digital terrain model (DTM) were applied to convert the regional hazard into the design run-up and the corresponding evacuation maps with a GIS-based approach. Since the regional hazard cannot fully capture the local-scale variability, this simplified and conservative approach is considered a viable and feasible practice to inform local coastal risk management in the absence of high-resolution hazard models. The present work is a first attempt to quantify the uncertainty stemming from such procedure. We compare the GIS-based inundation maps informed by a regional model with those obtained from a local high-resolution hazard model. Two locations on the coast of eastern Sicily were considered, and the local hazard was addressed with the same seismic model as the regional one, but using a higher-resolution DTM and massive numerical inundation calculations with the GPU-based Tsunami-HySEA nonlinear shallow water code. This study shows that the GIS-based inundation maps used for planning deal conservatively with potential hazard underestimation at the local scale, stemming from typically unmodeled uncertainties in the numerical source and tsunami evolution models. The GIS-based maps used for planning fall within the estimated “error-bar” due to such uncertainties. The analysis also demonstrates the need to develop local assessments to serve very specific risk mitigation actions to reduce the uncertainty. More in general, the presented case-studies highlight the importance to explore ways of dealing with uncertainty hidden within the high-resolution numerical inundation models, e.g., related to the crude parameterization of the bottom friction, or the inaccuracy of the DTM.
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