Tsunami prediction software download

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Networking Software. Trending from CNET. The RMSE yields values that vary from 0. The design and the built emulators were validated using the leave-one-out LOO diagnostics. Following this approach, we build an emulator by excluding each time one simulation from the training inputs and outputs; we then predict the expected outputs for the selected scenario.

We test the results at three locations to illustrate the variations in the outputs: one close to the gauge that was utilized in the design, one farther away from the design point location 02 but with elevation similar to the one of location 01 and one location 03 close to the design location but with a very different elevation locations 01, 02 and 03 in Fig.

The plots in Fig. As the plots demonstrate, in some cases the emulator underpredicts the response, but there is an overall good agreement between the predictions and the response as the majority of the points are captured by the variance around the predictions Fig. As the waves propagate on land, the prediction becomes more challenging due to even the slightest variations caused by the surrounding topography. The sensitivity of the locations to the variance in the scenarios also plays a significant role.

Location 02, for example, does not show large sensitivity to the variation in the parameters; the maximum elevation is close to zero in all of the cases. Location 03 is closer to the source and is experiencing the highest wave run-up, and it is therefore less affected by these slight variations in the topography but more sensitive to the varying scenarios.

The root mean square error RMSE is also relatively small, ranging from 0. The RMSE is computed at these three locations for illustrating the behaviour of the emulator's predictions at certain points; the relative error might increase further inland at inundated locations.

To gain a more comprehensive understanding of the RMSE trend and the efficacy of the design, we fit 4 emulators in location 01 using as training data the first 20, 30, 40 and 50 runs out of the 60 runs, predicting each time for the last 10 runs and calculating the RMSE Fig.

It is noticed that the error reduces to a significant extent when adding more runs to train the emulators and becomes very small for an emulator trained at 50 runs. Following this trend, a smaller error would be also expected for the emulators trained at 60 runs Fig.

GP emulation is well suited for approximating nonlinear simulation behaviours, even when considering continuous outputs of low regularity and when restricted to small-sized experimental designs with space-filling properties. As shown by Owen et al. By small design sizes, we refer to designs with the number of samples being about 10 times the number of input parameters, a widely used rule of thumb for effective computer experiment design Loeppky et al.

Once the emulators are built, the maximum tsunami elevation can be predicted for any input deformation scenario. The prediction involves the utilization of the built emulator with a given set of inputs to calculate the mean predictions and their uncertainty in the outputs.

Uncertainties are fully propagated to display sometimes complex distributions of outputs such as skewed distributions as in the case below : variance would not be enough to describe such uncertainties. Emulation provides a complete description of uncertainties compared to a mean and variance in more basic approaches.

These inputs can be represented by the distributions of the input parameters Fig. The distributions are flexible and can be used to represent different hypothetical cases. A beta distribution is employed for each parameter, from which scenarios are randomly selected. The shape parameters of the distributions can be utilized to express the scientific knowledge on the source. For the most uncertain parameters we use a symmetric distribution. In more detail, the a and b shape parameters of the beta distributions used to produce the seabed displacement scenarios in Figs.

Figure 10 Input parameter distributions for two sets of hypothetical cases. Histograms of buried ruptures H1 are depicted with dark-green colour and of splay-faulting H2 with dark-blue colour.

Figure 11 Predictions for three cell centres of the grid see locations 01, 02 and 03, respectively, in Fig. The MOGP emulation framework allows us to produce the predictions of tsunami hazard in parallel for each emulator.

The mean predictions are represented in the form of the histograms of the predictions at each location as shown in Fig. Locations 01 and 02 display very small elevation values above the ground level due to the tsunami. It appears that the splay-faulting sensitivity is larger at locations 01 and 03 than at location 02 since the histogram of outputs shifts more towards higher values.

Location 03 gives values that most likely range around 1. The minimum values shown in the histograms can become negative since a positive prediction is not imposed by the emulator, but this is very rare, and it does not manifest in the production of the hazard maps.

Figure 12 The percentiles 50th a , 90th b of the mean predictions at the cell centres of the computational grid, for buried ruptures H1 and for splay-faulting H2: 50th percentile c , 90th percentile d. The circles show the locations of the emulators. The hazard maps in the south-eastern part of Vancouver Island are produced based on the 50th and 90th percentiles of the emulator's predictions for the tsunami scenarios.

A total of coastline locations that correspond to the cell centres of the computational grid are studied Fig. The 50th percentile of the predictions demonstrates that When considering the 90th percentile, however, H max values increase. The results show that It is noted that the fitting of each emulator takes approximately 1. Hence, once the emulators are built, they can be used to explore alternative rupture scenarios in fast times.

Such is the hypothetical case of increased uplift in the northern part of the subduction zone caused by splay-faulting. There is a large uncertainty surrounding the presence of splay-faulting in the northern part of the zone Gao et al.

Although such enhanced vertical displacements are not likely to occur in the southern part of the zone, the tsunami impact from a short-north segment or a long rupture could be similar for British Columbia Cherniawsky et al. To fully assess splay-faulting-related tsunami hazard in south-eastern Vancouver Island, the complexity of the fault geometry needs to be more accurately incorporated at the initial stages of the process. The impact of an enhanced uplift is thus explored in a simplified form for the area here.

Looking at the 50th percentile of the predictions for H2, it is shown that the H max values from these scenarios are increased Fig. In Fig. However, when considering the 90th percentile of the predictions, the outputs become more severe Fig. In this case, only slightly more than one-third of H max Following similar procedures, seismic data in combination with expert knowledge on the rupture characteristics can be translated to probabilistic tsunami hazard outputs.

Tsunami amplification is especially apparent at narrow bays and coves inside the Victoria and Esquimalt harbours and is likely the outcome of wave resonance Fig.

Wave amplification in harbours and small bays has also been observed in other numerical studies in the area Cherniawsky et al.

In their numerical studies of large earthquake-induced tsunamis, Cherniawsky et al. Similar values ca. These higher values are possibly the effect of wave resonance attributed to the regional geomorphology. Wave resonance has been observed in Port Alberni, located at the head of a narrow inlet in the western part of Vancouver Island, during the Alaskan earthquake Fine et al.

The recorded wave heights in the port were 3—4 times larger than in the adjacent areas, often recorded in the third or later waves, and the tsunami oscillations continued for days after the event Fine et al.

It is likely that local topographic features can contribute to tsunami amplification also in other parts of the region. Figure 13 Panel a shows the relationship between earthquake magnitude M w and maximum uplift hmax when using a linear Okada solution for full rupture of the zone.

The sample hazard curves in c show the annual exceedance rates at three locations. The coastal hazard map in d shows the hazard values for the return period of years. Further, we associate the scenarios with annual frequencies to be able to calculate probability of exceedance for predictions of the H2 distribution.

To link seabed deformations to earthquake moment magnitudes, we use a simplified approach by matching maximum seabed uplift, calculated using the Okada solution for idealized planar fault, with rupture dimensions similar to Cascadia subduction interface experiencing linearly decaying slip with depth. Following this approach, the magnitudes of the H2 scenarios range between 8. To associate frequency of events with earthquake magnitudes, a tapered Gutenberg—Richter TGR distribution is utilized, which has been proven to give adequate predictions for the Cascadia subduction zone Rong et al.

The TGR complementary cumulative distribution function for a given earthquake magnitude m is defined as. The discrete number of m j magnitudes can also be computed by. In the same figure, the number of events per magnitude band for the H2 predictions is shown. Because prediction parameters, especially h max , were drawn from independent distributions, the frequencies of the H2 set events need to be rescaled using the ratio between number of events per magnitude band for TGR distribution and the H2 set to assign the appropriate relative frequency of each event within H2.

Having the event frequencies, occurrence exceedance probability for the hazard values can be calculated for each of the sites. The exceedance probability for the largest hazard value h 1 corresponding magnitude is M w 9. The above relations are valid for a set of independent events when their annual occurrence rates are known. They are derived from basic probability theory and used in hazard analysis studies, such as for example in Monte Carlo event-based probabilistic seismic hazard assessment e.

Musson , Accordingly, the mean annual exceedance rate can be computed for the hazard values at each location Fig. The hazard curves for each location can be used to construct the hazard map of Fig. The hazard map shows that when considering an event within this interval, 4. Compared to the hazard values at Seaside, Oregon, as calculated by Park et al. One factor for these discrepancies is the location of the two sites as Seaside is impacted by the tsunami waves from the Cascadia subduction zone directly, whereas Victoria is protected by the Olympic Peninsula and the western side of Vancouver Island; therefore, to reach sites in Victoria, the waves have to travel much farther and are attenuated along their path.

We note that as a first demonstration on how the emulators' predictions can be linked with the probability of exceeding a tsunami intensity measure over time, this is a simplified case. To better capture the probabilistic tsunami hazard in the region, the seabed deformation parameter distributions used for generation of the predictions need to be more precisely associated with Cascadia rupture characteristics.

In future research, the Okada solution for a realistic slip distribution on the precisely modelled Cascadia subduction interface will be employed to generate more physically driven seabed uplifts. To these uplifts, perturbations can be applied to gather a distribution of deformation parameters.

Also, alternative, more realistic magnitude—frequency relationships than the selected tapered Gutenberg—Richter distribution can be considered, for example the distribution used by the Geological Survey of Canada for the new 6th Generation seismic hazard model for Canada or for the National Seismic Hazard Model for the United States.

In this work, a sequential design algorithm was employed for the conduction of the computational experiments for earthquake-generated tsunami hazard in the Cascadia subduction zone. This approach aided an informative, innovative selection of the sets of numerical experiments in order to train the statistical emulators.

It forms the first of its kind, to the authors' knowledge, which involves the application of a sequential design algorithm towards realistic tsunami hazard predictions through emulation. Focusing the high-resolution computations in the south-eastern part of Vancouver Island, H max was predicted at coastal locations with the utilization of the emulators. Once the emulators are built, expert knowledge can be facilitated to swiftly assess hazard in the region.

The flexibility of the method allowed here the prediction of thousands of scenarios in a few moments of time under different parameter set-ups.

The emulators' predictions were linked to their occurrence exceedance probability, which allowed us to produce probabilistic hazard maps that assess the hazard intensity of such events in the area Fig. This forms one way of representing the mean predictions under a probabilistic framework. Alternatively one could present other probabilistic statements, for instance assessing the probability of exceeding some given threshold of maximum tsunami run-up.

This methodology could prove useful for assessing the hazard at the first stages of mitigation planning in order to take preventive measures such as built structures or natural hazard solutions. The predictions showed a high dependence of the maximum wave heights or flow depths on the maximum uplift during the rupture.

However, wave amplification is observed inside the harbours and especially in narrow bays and coves, possibly as an effect of wave resonance. In rare cases at 1. These percentages are expected to increase when looking at larger return periods, and the hazard values have to be further assessed to produce a probabilistic risk assessment for the area.

This study expands on the methodology and the development of the workflow to build the emulators under a sequential design approach. As such, there are some aspects that need to be considered in future work to further refine the probabilistic outputs. These span from the tsunami generation to the inundation. In this case, an idealized geometry was used for the source, and the current results agree with the numerical studies of more incorporating fault geometries.

However, to fully explore the complexity of the rupture, future work would benefit from the integration of compound rupture characteristics, especially when it comes to splay-faulting consideration. Furthermore, gaps and mismatches in the digital elevation data should be accounted for and incorporated in the modelling for a more finely resolved representation. Model bias is also not addressed in this study but could be explored in future investigations, for example by correcting the bias by adding a discrepancy estimated by comparing against past observations.

Finally, to produce a complete hazard assessment in the region, probabilistic tsunami inundation should be carried out. This is enabled by highly nonlinear features in the emulators' predictions and even benefits from recent advances in emulation Ming et al.

DMS carried out the analysis and writing. SG also supervised the analysis. The contact author has declared that neither they nor their co-authors have any competing interests. Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We gratefully acknowledge the support, advice and fruitful discussions with Simon Day. His help was important in the first stages of the study for the conceptualization of the seabed deformation and the parameterization. We are also thankful to Devaraj Gopinathan for his support with the meshing techniques for the numerical simulations. We also thank the two anonymous reviewers for their thorough comments, which greatly helped us to improve and clarify the manuscript.

Finally, we would like to thank the research software engineering team at the Alan Turing Institute and especially Eric Daub and Oliver Strickson for their help with MOGP and the automation of the workflows. Atwater, B. Beck, J. Behrens, J. Bilek, S. Cherniawsky, J.