Tsunami Probability in the Caribbean Region

We calculated tsunami runup probability (in excess of 0.5 m) at coastal sites throughout the Caribbean region. We applied a Poissonian probability model because of the variety of uncorrelated tsunami sources in the region. Coastlines were discretized into 20 km by 20 km cells, and the mean tsunami runup rate was determined for each cell. The remarkable ~500-year empirical record compiled by O’Loughlin and Lander (2003) was used to calculate an empirical tsunami probability map, the first of three constructed for this study. However, it is unclear whether the 500-year record is complete, so we conducted a seismic moment-balance exercise using a finite-element model of the Caribbean-North American plate boundaries and the earthquake catalog, and found that moment could be balanced if the seismic coupling coefficient is c = 0.32. Modeled moment release was therefore used to generate synthetic earthquake sequences to calculate 50 tsunami runup scenarios for 500-year periods. We made a second probability map from numerically-calculated runup rates in each cell. Differences between the first two probability maps based on empirical and numerical-modeled rates suggest that each captured different aspects of tsunami generation; the empirical model may be deficient in primary plate-boundary events, whereas numerical model rates lack backarc fault and landslide sources. We thus prepared a third probability map using Bayesian likelihood functions derived from the empirical and numerical rate models and their attendant uncertainty to weight a range of rates at each 20 km by 20 km coastal cell. Our best-estimate map gives a range of 30-year runup probability from 0–30% regionally.     

Interactive Visualization to Advance Earthquake Simulation

The geological sciences are challenged to manage and interpret increasing volumes of data as observations and simulations increase in size and complexity. For example, simulations of earthquake-related processes typically generate complex, time-varying data sets in two or more dimensions. To facilitate interpretation and analysis of these data sets, evaluate the underlying models, and to drive future calculations, we have developed methods of interactive visualization with a special focus on using immersive virtual reality (VR) environments to interact with models of Earth’s surface and interior. Virtual mapping tools allow virtual “field studies” in inaccessible regions. Interactive tools allow us to manipulate shapes in order to construct models of geological features for geodynamic models, while feature extraction tools support quantitative measurement of structures that emerge from numerical simulation or field observations, thereby enabling us to improve our interpretation of the dynamical processes that drive earthquakes. VR has traditionally been used primarily as a presentation tool, albeit with active navigation through data. Reaping the full intellectual benefits of immersive VR as a tool for scientific analysis requires building on the method’s strengths, that is, using both 3D perception and interaction with observed or simulated data. This approach also takes advantage of the specialized skills of geological scientists who are trained to interpret, the often limited, geological and geophysical data available from field observations.     

Contrasting origins of Cenozoic silicic volcanic rocks from the western Cordillera of the United States

Two fundamentally different types of silicic volcanic rocks formed during the Cenozoic of the western Cordillera of the United States. Large volumes of dacite and rhyolite, mostly ignimbrites, erupted in the Oligocene in what is now the Great Basin and contrast with rhyolites erupted along the Snake River Plain during the Late Cenozoic. The Great Basin dacites and rhyolites are generally calc-alkaline, magnesian, oxidized, wet, cool (<850°C), Sr-and Al-rich, and Fe-poor. These silicic rocks are interpreted to have been derived from mafic parent magmas generated by dehydration of oceanic lithosphere and melting in the mantle wedge above a subduction zone. Plagioclase fractionation was minimized by the high water fugacity and oxide precipitation was enhanced by high oxygen fugacity. This resulted in the formation of Si-, Al-, and Sr-rich differentiates with low Fe/Mg ratios, relatively low temperatures, and declining densities. Magma mixing, large proportions of crustal assimilation, and polybaric crystal fractionation were all important processes in generating this Oligocene suite. In contrast, most of the rhyolites of the Snake River Plain are alkaline to calc-alkaline, ferroan, reduced, dry, hot (830–1,050°C), Sr-and Al-poor, and Nb-and Fe-rich. They are part of a distinctly bimodal sequence with tholeiitic basalt. These characteristics were largely imposed by their derivation from parental basalt (with low fH₂O and low fO₂) which formed by partial melting in or above a mantle plume. The differences in intensive parameters caused early precipitation of plagioclase and retarded crystallization of Fe–Ti oxides. Fractionation led to higher density magmas and mid-crustal entrapment. Renewed intrusion of mafic magma caused partial melting of the intrusive complex. Varying degrees of partial melting, fractionation, and minor assimilation of older crust led to the array of rhyolite compositions. Only very small volumes of distinctive rhyolite were derived by fractional crystallization of Fe-rich intermediate magmas like those of the Craters of the Moon-Cedar Butte trend. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Streamflow scaling properties: investigating characteristic scales from different statistical approaches

This paper studies the links between scaling properties of river flow time series by comparing the results of three techniques applied to an extended data set of 34 French discharge gauging stations. The three approaches used are based on different mathematical tools and hypotheses: (1) shape analysis of flood hydrographs; (2) a multifractal framework through spectral and moment analyses, and (3) flood frequency analysis through the fitting of flood duration frequency curves (QdF). The general aim is to test the hypothesis of scaling invariance of river flow and the shape invariance of the hydrographs, in order to investigate the link between scaling properties and flow dynamics. In particular, the coherence between different approaches widely used in the literature to describe these characteristics is evaluated through the estimation of parameters defining the range of time‐scales on which the scaling properties are valid. The results show that most of these timescale parameters are linked to the flow dynamics and suggest that the approaches applied are interrelated. Copyright © 2008 John Wiley & Sons, Ltd.     

On the mathematical stability of stratified flow models with local turbulence closure schemes

Occasionally, numerical simulations using local turbulence closure schemes to estimate vertical turbulent fluxes exhibit small-scale oscillations in space, causing the eddy coefficients to vary over several orders of magnitude on short distances. Theoretical developments suggest that these spurious oscillations are essentially due to the way the eddy coefficients depend on the vertical gradient of the model’s variables. An instability criterion is derived based on the assumptions that the artefacts under study are due to the development of small-amplitude, small time- and space-scale perturbations of a smooth solution. The relevance of this criterion is demonstrated by applying it to a series a closure schemes, ranging from the Pacanowski–Philander formulas to the Mellor–Yamada level 2.5 model.     

Turbulent kinetic energy budget in a gravel-bed channel flow

The present experimental investigation focuses on the characteristics of near bed turbulence in a fully rough, uniform open-channel flow over a gravel-type bed. Due to bed topography small scale heterogeneity, the flow is not uniform locally in the near bed region and a double averaging methodology is applied over a length scale much larger than the gravel size. The double-averaged Turbulent Kinetic Energy (TKE) budget derived in the context of the present flow over a gravel bed differs from the TKE budget written for flow over a vegetation canopy. The non-constant shape of the roughness function measured in our gravel bed leads to an additional bed-induced production term which is null for vertical roughness elements, such as simplified vegetation elements. The experimental estimation of the terms of the TKE budget reveals that the maximum turbulent activity takes place away from the reference plane, near the roughness crests. However, within the interface sublayer the work of the bed induced velocity fluctuations against the Reynolds stress is of the same magnitude as the main turbulence production term. Consequently, the characteristics of the TKE budget have similarities with uniform flows over canopies and strongly differ from uniform flows over smooth and transitionally rough flows over sedimentlike beds.     

Storm surge computations in estuarine and near-coastal regions: the Mersey estuary and Irish Sea area

An unstructured grid storm surge model of the west coast of Britain, incorporating a high-resolution representation of the Mersey estuary is used to examine storm surge dynamics in the region. The focus of the study is the major surge that occurred during the period 11–14 November 1977, which has been investigated previously using uniform grid finite difference models and a finite element model of the west coast of Britain. However, none of these models included the Mersey estuary. Comparison of solutions in the eastern Irish Sea with those computed with these earlier models showed that, away from the Liverpool Bay region, the inclusion of the Mersey estuary had little effect. However, at the entrance to the Mersey, its inclusion did influence the solution. By including a detailed representation of the Mersey estuary within the model, it was possible to conduct a detailed study of storm surge propagation in the Mersey, which had never previously been performed. This detailed study showed for the first time that the surge’s temporal variability within the estuary is influenced by surge elevation at its entrance. This varies with time as a function of spatial and temporal variations of wind stress over the west coast of Britain. Within the Mersey, calculations show that the spatial variability is mainly determined by changes in bottom topography, which had not been included in earlier finite difference models. However, since water depth is influenced by variations in tidal elevation, this, together with tide surge interaction through bottom friction and momentum advection, influences the surge. The ability of the finite element model to vary the mesh in near-shore regions to such an extent that it can resolve the Mersey and hence the impact of the Mersey estuary upon the Liverpool Bay circulation shows that it has distinct advantages over earlier finite difference models. In the absence of detailed measurements within the Mersey at the time of the surge, it was not possible to validate predicted surge elevations within the Mersey. However, significant insight into physical processes influencing the surge propagation down the estuary, its reflection and spatial/temporal variability could be gained.     

An inter-comparison of tidal solutions computed with a range of unstructured grid models of the Irish and Celtic Sea Regions

Three finite element codes, namely TELEMAC, ADCIRC and QUODDY, are used to compute the spatial distributions of the M₂, M₄ and M₆ components of the tide in the sea region off the west coast of Britain. This region is chosen because there is an accurate topographic dataset in the area and detailed open boundary M₂ tidal forcing for driving the model. In addition, accurate solutions (based upon comparisons with extensive observations) using uniform grid finite difference models forced with these open boundary data exist for comparison purposes. By using boundary forcing, bottom topography and bottom drag coefficients identical to those used in an earlier finite difference model, there is no danger of comparing finite element solutions for “untuned unoptimised solutions” with those from a “tuned optimised solution”. In addition, by placing the open boundary in all finite element calculations at the same location as that used in a previous finite difference model and using the same M₂ tidal boundary forcing and water depths, a like with like comparison of solutions derived with the various finite element models was possible. In addition, this open boundary was well removed from the shallow water region, namely the eastern Irish Sea where the higher harmonics were generated. Since these are not included in the open boundary, forcing their generation was determined by physical processes within the models. Consequently, an inter-comparison of these higher harmonics generated by the various finite element codes gives some indication of the degree of variability in the solution particularly in coastal regions from one finite element model to another. Initial calculations using high-resolution near-shore topography in the eastern Irish Sea and including “wetting and drying” showed that M₂ tidal amplitudes and phases in the region computed with TELEMAC were in good agreement with observations. The ADCIRC code gave amplitudes about 30 cm lower and phases about 8° higher. For the M₄ tide, in the eastern Irish Sea amplitudes computed with TELEMAC were about 4 cm higher than ADCIRC on average, with phase differences of order 5°. For the M₆ component, amplitudes and phases showed significant small-scale variability in the eastern Irish Sea, and no clear bias between the models could be found. Although setting a minimum water depth of 5 m in the near-shore region, hence removing wetting and drying, reduced the small-scale variability in the models, the differences in M₂ and M₄ tide between models remained. For M₆, a significant reduction in variability occurred in the eastern Irish Sea when a minimum 5-m water depth was specified. In this case, TELEMAC gave amplitudes that were 1 cm higher and phases 30° lower than ADCIRC on average. For QUODDY in the eastern Irish Sea, average M₂ tidal amplitudes were about 10 cm higher and phase 8° higher than those computed with TELEMAC. For M₄, amplitudes were approximately 2 cm higher with phases of order 15° higher in the northern part of the region and 15° lower in the southern part. For M₆ in the north of the region, amplitudes were 2 cm higher and about 2 cm lower in the south. Very rapid M₆ tidal-phase changes occurred in the near-shore regions. The lessons learned from this model inter-comparison study are summarised in the final section of the paper. In addition, the problems of performing a detailed model–model inter-comparison are discussed, as are the enormous difficulties of conducting a true model skill assessment that would require detailed measurements of tidal boundary forcing, near-shore topography and precise knowledge of bed types and bed forms. Such data are at present not available.     

Microtopographic evolution of mineral surfaces as a tool to identify and date young fault scarps in bedrock

Faulting that results in surface ruptures through bedrock can be particularly difficult to date. For example, stratigraphic control on the age of faulting, based on the age of the bedrock, often leaves unacceptably large uncertainty on the age of the faulting. From a paleoseismological perspective, there is a clear need to determine if a bedrock fault scarp is actually a young feature. For young fault ruptures that create fresh mineral surfaces, analysis of microtopography developed by weathering of the mineral surface may provide a quantifiable method for determining the fault age. The direct quantitative measurement of mineral surface microtopography using Atomic Force Microscopy affords a novel method to study the rupture ages of active faults. The method for using microtopographic evolution of mineral surfaces depends on three conditions. The first condition is that freshly exposed mineral cleavage surfaces, which can be described geometrically as planes, are formed during a rupture event. The formation of these fresh surfaces is analogous to the initiation of a weathering ‘clock’ that defines time t=0. Following cleavage formation dissolution of the planar mineral surface occurs. The rate of dissolution for a mineral species under given climatic conditions, governs the rate of mineral surface alteration. Thus as dissolution proceeds, the roughness of the mineral surface increases. We suggest that the progression of microtopographic roughness over time, which can be estimated by computing quantitative statistics derived from digital mineral surface topography, will systematically vary until a steady state surface topography is reached. The fractal dimension, D_f, is one such measure of surface roughness where, D_f at time t=0 is 2. The dissolution of the mineral surface increases the fractal dimension as the removal of material proceeds. We posit that somewhere between D_f=2 and D_f=3, the microtopography reaches a steady state. Therefore, in the pre-steady state stage of surface roughness, the quantitative measure of roughness of the mineral may serve as a measure of time elapsed since faulting. The period of time this initial stage of surface roughening represents is dependent on the mineral and as a consequence, its dissolution rate, in a specific set of environmental conditions. The time elapsed since fault rupture and grain cleavage can also be estimated from the measurement of the volume of material removed through dissolution. If part of the original cleavage surface remains and can be identified then AFM measurements of the surface microtopography can be used to calculate the dissolved volume per unit area.