Principal component analysis of tsunami buoy record: Tide prediction and removal

Principal component or Empirical Orthogonal Function (EOF) analysis is applied to tsunameter records by treating them as two-dimensional signals, where the second dimension is created by breaking a single time series into cycles and treating the cycle number as a second dimension. Under certain conditions, principal components calculated from different records are shown to determine the same functional space. Signal decomposition into pre-calculated principal components is used to predict or extract the tidal component of a record. This work shows that EOF processing allows for short-term tidal predictions at tsunami buoy locations with the precision of more advanced methods and with minimal a priori knowledge about tidal dynamics. Also shown is that filtering in EOF domain is sensitive to the non-tidal component of a record and therefore presents a tool for early tsunami detection and quantification.     

The Tjellefonna fault system of Western Norway: Linking late-Caledonian extension, post-Caledonian normal faulting, and Tertiary rock column uplift with the landslide-generated tsunami event of 1756

On February 22, 1756, approximately 15.7 million cubic meters of bedrock were catastrophically released as a giant rockslide into the Langfjorden. Subsequently, three  40 meter high tsunami waves overwhelmed the village of Tjelle and several other local communities. Inherited structures had isolated a compartment in the hanging wall damage zone of the fjord-dwelling Tjellefonna fault. Because the region is seismically active in oblique-normal mode, and in accordance with scant historical sources, we speculate that an earthquake on a nearby fault may have caused the already-weakened Tjelle hillside to fail.From interpretation of structural, geomorphic, and thermo-chronological data we suggest that today's escarpment topography of Møre og Trøndelag is controlled to a first order by post-rift reactivation of faults parallel to the Mesozoic passive margin. In turn, a number of these faults reactivated Late Caledonian or early post-Caledonian fabrics.Normal-sense reactivation of inherited structures along much of coastal Norway suggests that a structural link exists between the processes that destroy today's mountains and those that created them. The Paleozoic Møre–Trøndelag Fault Complex was reactivated as a normal fault during the Mesozoic and, probably, throughout the Cenozoic until the present day. Its NE–SW trending strands crop out between the coast and the base of a c. 1.7 km high NW-facing topographic ‘Great Escarpment.’ Well-preserved kinematic indicators and multiple generations of fault products are exposed along the Tjellefonna fault, a well-defined structural and topographic lineament parallel to both the Langfjorden and the Great Escarpment. The slope instability that was formerly present at Tjelle, and additional instabilities currently present throughout the region, may be viewed as the direct product of past and ongoing development of tectonic topography in Møre og Trøndelag county. In the Langfjorden region in particular, structural geometry suggests additional unreleased rock compartments may be isolated and under normal fault control.Although post-glacial rebound and topographically-derived horizontal spreading stresses might in part help drive present-day oblique normal seismicity, the normal-fault-controlled escarpments of Norway were at least partly erected in pre-glacial times. Cretaceous to Early Tertiary post-rift subsidence was interrupted by normal faulting at the innermost portion of the passive margin, imposing a strong tectonic empreinte on the developing landscape.     

The role of strong earthquakes and tsunami in the Late Holocene evolution of the Fortore River coastal plain (Apulia, Italy): A synthesis

Morphological analysis of the Fortore River coastal plain and the Lesina Lake coastal barrier integrated with radiocarbon age data indicates that the evolution of the coastal landscape has been strongly affected by a number of strong earthquakes and related tsunamis which occurred during the last 3000 years. The first seismic event struck this coastal area in the V century BC. It produced strong erosion of the Fortore River coastal plain and significant emersion of Punta delle Pietre Nere, as well as the large tsunami responsible for the development of the Sant'Andrea washover fan. The second event occurred in 493 AD; it induced severe erosion of the Fortore River coastal plain and triggered the large tsunami that hit the Lesina Lake coastal barrier, producing the Foce Cauto washover fan. Then later in 1627, an earthquake was responsible for the further coseismic uplift of Punta delle Pietre Nere, the subsidence of Lesina village area and the development of a tsunami which produced two washover fans.Morphological analysis points out that seismic events strong enough to control the morphological evolution of local coastal landscapes show a statistical return period of about 1000 years. These major events produced important coseismic vertical movements and large tsunamis. However, the correct identification of the tectonic structure responsible for the generation of these strong earthquakes is still an unsolved problem.     

How does multiscale modelling and inclusion of realistic palaeobathymetry affect numerical simulation of the Storegga Slide tsunami?

The ∼8.15 ka Storegga submarine slide was a large (∼3000 km³), tsunamigenic slide off the coast of Norway. The resulting tsunami had run-up heights of around 10–20 m on the Norwegian coast, over 12 m in Shetland, 3–6 m on the Scottish mainland coast and reached as far as Greenland. Accurate numerical simulations of Storegga require high spatial resolution near the coasts, particularly near tsunami run-up observations, and also in the slide region. However, as the computational domain must span the whole of the Norwegian-Greenland sea, employing uniformly high spatial resolution is computationally prohibitive. To overcome this problem, we present a multiscale numerical model of the Storegga slide-generated tsunami where spatial resolution varies from 500 m to 50 km across the entire Norwegian-Greenland sea domain to optimally resolve the slide region, important coastlines and bathymetric changes. We compare results from our multiscale model to previous results using constant-resolution models and show that accounting for changes in bathymetry since 8.15 ka, neglected in previous numerical studies of the Storegga slide-tsunami, improves the agreement between the model and inferred run-up heights in specific locations, especially in the Shetlands, where maximum run-up height increased from 8 m (modern bathymetry) to 13 m (palaeobathymetry). By tracking the Storegga tsunami as far south as the southern North sea, we also found that wave heights were high enough to inundate Doggerland, an island in the southern North Sea prior to sea level rise over the last 8 ka.     

An explicit finite difference model for simulating weakly nonlinear and weakly dispersive waves over slowly varying water depth

In this paper, a modified leap-frog finite difference (FD) scheme is developed to solve Non linear Shallow Water Equations (NSWE). By adjusting the FD mesh system and modifying the leap-frog algorithm, numerical dispersion is manipulated to mimic physical frequency dispersion for water wave propagation. The resulting numerical scheme is suitable for weakly nonlinear and weakly dispersive waves propagating over a slowly varying water depth. Numerical studies demonstrate that the results of the new numerical scheme agree well with those obtained by directly solving Boussinesq-type models for both long distance propagation, shoaling and re-fraction over a slowly varying bathymetry. Most importantly, the new algorithm is much more computationally efficient than existing Boussinesq-type models, making it an excellent alternative tool for simulating tsunami waves when the frequency dispersion needs to be considered.     

Optical measurements of tsunami inundation through an urban waterfront modeled in a large-scale laboratory basin

This paper presents optical measurements of tsunami inundation through an urban waterfront in a laboratory wave basin. The physical model was constructed at 1:50 scale and was an idealization of the town of Seaside, Oregon. The fixed-bed model was designed to study the initial inundation zone along an urban waterfront, such that the flow around several large buildings could be observed. This paper presents an analysis of the optical measurements made with two overhead video cameras, focusing on tracking the leading edge of the tsunami inundation through the urban waterfront and quantifies the accuracy of the algorithm used to track the edge. The results show that the methodology provides high-resolution information in both time and space of the leading edge position, and that these data can be used to quantify the influence of large macro-roughness features on the tsunami inundation processes in laboratory settings. The overall effect of the macro-roughness was to decrease the bore propagation speed relative to the control section with no macro-roughness. The bore speed could be reduced by as much as 40% due to the presence of the macro-roughness relative to the control section.     

Wave characteristic and morphologic effects on the onshore hydrodynamic response of tsunamis

While the destruction caused by a tsunami can vary significantly owing to near- and onshore controls, we have only a limited quantitative understanding of how different local parameters influence the onshore response of tsunamis. Here, a numerical model based on the non-linear shallow water equations is first shown to agree well with analytical expressions developed for periodic long waves inundating over planar slopes. More than 13,000 simulations are then conducted to examine the effects variations in the wave characteristics, bed slopes, and bottom roughness have on maximum tsunami run-up and water velocity at the still water shoreline. While deviations from periodic waves and planar slopes affect the onshore dynamics, the details of these effects depend on a combination of factors. In general, the effects differ for breaking and non-breaking waves, and are related to the relative shift of the waves along the breaking–non-breaking wave continuum. Variations that shift waves toward increased breaking, such as steeper wave fronts, tend to increase the onshore impact of non-breaking waves, but decrease the impact of already breaking waves. The onshore impact of a tsunami composed of multiple waves can be different from that of a single wave tsunami, with the largest difference occurring on long, shallow onshore topographies. These results demonstrate that the onshore response of a tsunami is complex, and that using analytical expressions derived from simplified conditions may not always be appropriate.     

Numerical simulation of tsunami waves generated by deformable submarine landslides

This paper presents a new submarine landslide model based on the non-hydrostatic wave model NHWAVE of Ma et al. (2012). The landslide is modeled as a water–sediment mixture. The dense plume is driven by baroclinic pressure forcing introduced by spatial density variations. The model is validated using laboratory measurements of turbidity currents and of water wave generation by a granular landslide. The model is then utilized to study the dependence of landslide motion and associated tsunami wave generation on parameters including sediment settling velocity, initial depth of the landslide and slide density. Model results show that the slide motion and water waves which it generates are both sensitive to these parameters. The relative tsunamigenic response to rigid and deformable landslides of equal initial geometry and density is also examined. It is found that the wave energy is mostly concentrated on a narrow band of the dominant slide direction for the waves generated by rigid landslides, while directional spreading is more significant for waves generated by deformable landslides. The deformable landslide has larger speed and acceleration at the early stage of landslide, resulting in larger surface waves. The numerical results indicate that the model is capable of reasonably simulating tsunami wave generation by submarine landslides.     

Relevance of Bathymetry for Tsunami Run‐up Modeling

Abstract

Marine positioning is relevant for several aspects of tsunami research, observation, and prediction. These include accurate positioning of instruments on the ocean bottom for determining the deep‐water signature of the tsunami, seismic observational setups to measure the earthquake parameters, equipment to determine the tsunami characteristics during the propagation phase, and instruments to map the vertical uplift and subsidence that occurs during a dip‐slip earthquake.

In the accurate calculation of coastal tsunami run‐up through numerical models, accurate bathymetry is needed, not only near the coast (for tsunami run‐up) but also in the deep ocean (for tsunami generation and propagation). If the bathymetry is wrong in the source region, errors will accumulate and will render the numerical calculations inaccurate. Without correct and detailed run‐up values on the various coastlines, tsunami prediction for actual events will lead to false alarms and loss of public confidence.     

Statistical Simulation of Boxing Day Tsunami of The Indian Ocean and a Predictive Equation for Beach Run up Heights Based on Work-Energy Theorem

The tsunami similar to the one that has occurred in December 26, 2004 (Boxing Day Tsunami) in the Indian Ocean is simulated using the expression derived from Modified Weibull Distribution (for maximum wave height simulation) for extreme wave height predictions. The tuning coefficient plays a significant role in estimating the tsunami heights at various stages. It follows well defined mathematical laws at different stages. It is time dependent in the first three stages and depth dependent in the last two stages. The beach run-up heights estimated by the expression derived from the work-energy relation are comparable with observed values with reasonable accuracy.