Faster Than Real Time Tsunami Warning with Associated Hazard Uncertainties

Tsunamis are unpredictable events and catastrophic in their potential for destruction of human lives and economy. The unpredictability of their occurrence poses a challenge to the tsunami community, as it is difficult to obtain from the tsunamigenic records estimates of recurrence rates and severity. Accurate and efficient mathematical/computational modeling is thus called upon to provide tsunami forecasts and hazard assessments. Compounding this challenge for warning centres is the physical nature of tsunamis, which can travel at extremely high speeds in the open ocean or be generated close to the shoreline. Thus, tsunami forecasts must be not only accurate but also delivered under severe time constraints. In the immediate aftermath of a tsunamigenic earthquake event, there are uncertainties in the source such as location, rupture geometry, depth, magnitude. Ideally, these uncertainties should be represented in a tsunami warning. However in practice, quantifying the uncertainties in the hazard intensity (i.e., maximum tsunami amplitude) due to the uncertainties in the source is not feasible, since it requires a large number of high resolution simulations. We approximate the functionally complex and computationally expensive high resolution tsunami simulations with a simple and cheap statistical emulator. A workflow integrating the entire chain of components from the tsunami source to quantification of hazard uncertainties is developed here - quantification of uncertainties in tsunamigenic earthquake sources, high resolution simulation of tsunami scenarios using the GPU version of Volna-OP2 on a non-uniform mesh for an ensemble of sources, construction of an emulator using the simulations as training data, and prediction of hazard intensities with associated uncertainties using the emulator. Thus, using the massively parallelized finite volume tsunami code Volna-OP2 as the heart of the workflow, we use statistical emulation to compute uncertainties in hazard intensity at locations of interest. Such an integration also balances the trade-off between computationally expensive simulations and desired accuracy of uncertainties, within given time constraints. The developed workflow is fully generic and independent of the source (1945 Makran earthquake) studied here

Probabilistic, high-resolution tsunami predictions in northern Cascadia by exploiting sequential design for efficient emulation

The potential of a full-margin rupture along the Cascadia subduction zone poses a significant threat over a populous region of North America. Previous probabilistic tsunami hazard assessment studies produced hazard curves based on simulated predictions of tsunami waves, either at low resolution or at high resolution for a local area or under limited ranges of scenarios or at a high computational cost to generate hundreds of scenarios at high resolution. We use the graphics processing unit (GPU)-accelerated tsunami simulator VOLNA-OP2 with a detailed representation of topographic and bathymetric features. We replace the simulator by a Gaussian process emulator at each output location to overcome the large computational burden. The emulators are statistical approximations of the simulator's behaviour. We train the emulators on a set of input–output pairs and use them to generate approximate output values over a six-dimensional scenario parameter space, e.g. uplift/subsidence ratio and maximum uplift, that represent the seabed deformation. We implement an advanced sequential design algorithm for the optimal selection of only 60 simulations. The low cost of emulation provides for additional flexibility in the shape of the deformation, which we illustrate here considering two families – buried rupture and splay-faulting – of 2000 potential scenarios. This approach allows for the first emulation-accelerated computation of probabilistic tsunami hazard in the region of the city of Victoria, British Columbia

Multilevel Bayesian Quadrature

Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We propose to further enhance multilevel Monte Carlo through Bayesian surrogate models of the integrand, focusing on Gaussian process models and the associated Bayesian quadrature estimators. We show, using both theory and numerical experiments, that our approach can lead to significant improvements in accuracy when the integrand is expensive and smooth, and when the dimensionality is small or moderate. We conclude the paper with a case study illustrating the potential impact of our method in landslide-generated tsunami modelling, where the cost of each integrand evaluation is typically too large for operational settings

Probabilistic quantification of tsunami current hazard using statistical emulation

© 2021 The Authors. In this paper, statistical emulation is shown to be an essential tool for the end-to-end physical and numerical modelling of local tsunami impact, i.e. from the earthquake source to tsunami velocities and heights. In order to surmount the prohibitive computational cost of running a large number of simulations, the emulator, constructed using 300 training simulations from a validated tsunami code, yields 1 million predictions. This constitutes a record for any realistic tsunami code to date, and is a leap in tsunami science since high risk but low probability hazard thresholds can be quantified. For illustrating the efficacy of emulation, we map probabilistic representations of maximum tsunami velocities and heights at around 200 locations about Karachi port. The 1 million predictions comprehensively sweep through a range of possible future tsunamis originating from the Makran Subduction Zone (MSZ). We rigorously model each step in the tsunami life cycle: first use of the three-dimensional subduction geometry Slab2 in MSZ, most refined fault segmentation in MSZ, first sediment enhancements of seabed deformation (up to 60% locally) and bespoke unstructured meshing algorithm. Owing to the synthesis of emulation and meticulous numerical modelling, we also discover substantial local variations of currents and heights.Alan Turing Institute under the EPSRCgrant no. (EP/N510129/1); Royal Society grant no. (CHL/R1/180173); Royal Society-SERB Newton International Fellowship(NF151483); NERC grant no. (NE/P016367/1)

Meteotsunamis and other anomalous “tidal surge” events in Western Europe in Summer 2022

We investigate occurrences of anomalous tidal activity in coastal waters of north-west Europe during Summer 2022. Sightings of an anomalous “tidal surge” occurred on 18 June 2022 in Wales, followed by similar observations in Ireland, France, and Spain. Several anomalous long-wave events were also reported in south England and Wales in the morning of 19 July 2022. We analyzed surface and high-altitude air pressure fields, and sea level oscillations for both days. Our detailed analysis reveals that the 18 June events were a series of meteotsunamis, propagating over several countries in Western Europe and triggered by localized pressure perturbations, originating within a low-pressure area over the North Atlantic Ocean. A local analysis of the southern coast of Ireland suggests that Proudman resonance was the determinant mechanism that amplified the meteotsunami traveling eastward in the afternoon of 18 June. A similar analysis of the 19 July events suggests that the tidal surge reported in the UK and anomalous signals recorded in Ireland and France were episodes of seiching triggered by infragravity waves, resonated subharmonically by wind waves. Numerical simulations of the 18 June event were performed with Volna-OP2, which solves the non-linear shallow water equations using a finite volume discretization. The influence of the atmospheric wave velocity on the amplification of the sea surface elevation is analyzed

Multilayered abstractions for partial differential equations

How do we build maintainable, robust, and performance-portable scientific applications? This thesis argues that the answer to this software engineering question in the context of the finite element method is through the use of layers of Domain-Specific Languages (DSLs) to separate the various concerns in the engineering of such codes. Performance-portable software achieves high performance on multiple diverse hardware platforms without source code changes. We demonstrate that finite element solvers written in a low-level language are not performance-portable, and therefore code must be specialised to the target architecture by a code generation framework. A prototype compiler for finite element variational forms that generates CUDA code is presented, and is used to explore how good performance on many-core platforms in automatically-generated finite element applications can be achieved. The differing code generation requirements for multi- and many-core platforms motivates the design of an additional abstraction, called PyOP2, that enables unstructured mesh applications to be performance-portable. We present a runtime code generation framework comprised of the Unified Form Language (UFL), the FEniCS Form Compiler, and PyOP2. This toolchain separates the succinct expression of a numerical method from the selection and generation of efficient code for local assembly. This is further decoupled from the selection of data formats and algorithms for efficient parallel implementation on a specific target architecture. We establish the successful separation of these concerns by demonstrating the performance-portability of code generated from a single high-level source code written in UFL across sequential C, CUDA, MPI and OpenMP targets. The performance of the generated code exceeds the performance of comparable alternative toolchains on multi-core architectures.Open Acces