Time Series Of Surface Elevation Research Articles

Tsunami inundation modeling in constructed environments: A physical and numerical comparison of free-surface elevation, velocity, and momentum flux

A laboratory benchmark test for tsunami inundation through an urban waterfront including free surface elevation, velocity, and specific momentum flux is presented and compared with a numerical model (COULWAVE). The physical model was a 1:50 scale idealization of the town Seaside, Oregon, designed to observe the complex tsunami flow around the macro-roughness such as buildings idealized as impermeable, rectangular blocks. Free surface elevation and velocity time series were measured and analyzed at 31 points along 4 transects. Optical measurements of the leading bore front were used in conjunction with the in-situ velocity and free surface measurements to estimate the time-dependent specific momentum flux at each location. The maximum free surface elevation and specific momentum flux sharply decreased from the shoreline to the landward measurement locations, while the cross-shore velocity slowly decreased linearly. The experimental results show that the maximum specific momentum flux is overestimated by 60 to 260%, if it is calculated using the each maximum values of the free surface elevation and cross-shore velocity. Comparisons show that the numerical model is in good agreement with the physical model at most locations when tuned to a friction factor of 0.005. When the friction factor decreased by a factor of 10 (from 0.01 to 0.001), the average maximum free surface elevation increased 15%, and the average cross-shore velocity and specific momentum flux increased 95 and 208%, respectively. This highlights the importance of comparing velocity in the validation and verification process of numerical models of tsunami inundation.

Analytical study of the water surface fluctuations induced by grid-stirred turbulence

The free surface dynamics excited by grid stirred turbulence is analysed with a Lagrangian approach, with the analytical model calibrated by using experimental results. The Lagrangian model for free surface oscillations has been developed by assuming that coherent structures in the water layer close to the free interface have the shape of blobs and are mobilized by a periodic force. The blobs are assumed to behave like nonlinear oscillators with different spring stiffness in upwelling and downwelling and neglecting viscosity as first approximation. In order to calibrate the model, a set of experiments in a grid stirred tank was used where free surface elevation time series were measured and all the necessary variables were computed.Through calibration and with some working assumptions, the radius of the blobs is shown to be of the order of the integral vertical length scale of turbulence. The forced oscillations are analysed by the method of Rauscher (1938) [1] to predict the amplitude of the oscillations, possible resonances and discontinuities in the amplitude–frequency space. If the forcing term has multiple harmonics, in some cases a blow up of the oscillator is forecast. Some tests including a small damping, in order to evaluate the effects of viscosity, show that a jump is expected in the amplitude–frequency diagram and a range of unstable frequency. The presence of a small damping should also prevent the blow up for multiple harmonics in the forcing term.

Sinking of irregular shape blocks into marine seabed under wave-induced liquefaction

The sinking of initially buried irregular blocks into the seabed under wave-induced liquefaction was investigated by experimental methods. Pore-water pressure in the soil, water surface elevation time series and block displacements were measured. Results indicated that initiation of sinking coincides with the instant at which the accumulated pore-water pressure at the bottom level of the block reaches the initial mean normal effective stress. The drag forces and drag coefficients on steadily sinking irregular shaped blocks, as well as spherical and cubical ones, were calculated from the obtained data and compared with the available data in the literature. The results show that the shape of sinking block is of minor importance as far as the kinematics and dynamics of the sinking block is concerned. The conditions at which the sinking terminates are discussed in the light of experiments. Using the approach presented here, the ultimate sinking depths are calculated for the tested cases and compared with the experimental results. The calculated and measured values showed a reasonable agreement when compared. Finally a summary and remarks are presented to calculate the ultimate sinking depth of irregular shaped blocks for practical applications.

Surface wave generation due to glacier calving

Coastal glaciers reach the ocean in a spectacular process called ‘calving’. Immediately after calving, the impulsive surface waves are generated, sometimes of large height. These waves are particularly dangerous for vessels sailing close to the glacier fronts. The paper presents a theoretical model of surface wave generation due to glacier calving. To explain the wave generation process, four case studies of ice blocks falling into water are discussed: a cylindrical ice block of small thickness impacting on water, an ice column sliding into water without impact, a large ice block falling on to water with a pressure impulse, and an ice column becoming detached from the glacier wall and falling on to the sea surface. These case studies encompass simplified, selected modes of the glacier calving, which can be treated in a theoretical way. Example calculations illustrate the predicted time series of surface elevations for each mode of glacier calving.

Potential impacts of the mean sea level rise on the hydrodynamics of the Douro river estuary

Numerous studies based on tide gauge records demonstrated the sea level rise on the Portuguese coast during the last century. Different climatic models predict a mean sea level rise for this coast ranging between 0.28 m and 0.42 m, for the period 2091–2100 relative to 1980–1999. Thus, the potential evaluation of the sea level rise impact on the Portuguese coast becomes critical, especially in sensitive areas as estuaries. The main aim of this work is to evaluate hydrodynamic changes in the Douro estuary induced by the sea level rise. A baroclinic finite volume numerical model was implemented to the Douro estuary in a 2D mode. The model calibration was performed comparing predicted and observed sea surface elevation time series for several stations. The tidal input at the ocean open boundary forces the 2D hydrodynamic model considering actual and future mean sea levels. At the landward boundary the model is forced with the freshwater discharge. The research explores changes in current velocity and amplitude and phase differences of the main diurnal and semi-diurnal tidal constituents along the estuary. The results suggest local significant changes in the Douro hydrodynamics in response to the sea level rise. Nevertheless, the differences don't affect the general estuary’s circulation. Concerning the main tidal constituents, the amplitude increases and the phase decreases, revealing that the tide tends to propagate faster upstream and with higher tidal ranges. Owing to the increasing of the amplitude and the water level, the current velocity values tend to decrease in the estuary, mainly near the low-lying areas.

Frequency Domain Response at Pacific Coast Harbors to Major Tsunamis of 2005–2011

Tsunamis waves caused by submarine earthquake or landslide might contain large wave energy, which could cause significant human loss and property damage locally as well as in distant region. The response of three harbors located at the Pacific coast (i.e. Crescent City Harbor, Los Angeles/Long Beach Port, and San Diego Harbor) to six well-known tsunamis events generated (both near-field and far-field) between 2005 and 2011 are examined and simulated using a hybrid finite element numerical model in frequency domain. The model incorporated the effects of wave refraction, wave diffraction, partial wave reflection from boundaries, entrance and bottom energy dissipation. It can be applied to harbor regions with arbitrary shapes and variable water depth. The computed resonant periods or modes of oscillation for three harbors are in good agreement with the energy spectral analysis of the time series of water surface elevations recorded at tide gauge stations inside three harbors during the six tsunamis events. The computed wave induced currents based on the present model are also in qualitative agreement with some of the reported eye-witness accounts absence of reliable current data. The simulated results show that each harbor responded differently and significantly amplified certain wave period(s) of incident wave trains according to the shape, topography, characteristic dimensions and water depth of the harbor basins.

Ice-sheet surface elevation change from crossover of ENVISAT data

Understanding the current state of the polar ice sheets is critical for determining their contribution to sea-level rise and predicting their response to climate change. Surface elevation time series especially can be used to study ice-sheet dynamics and the mass or volume balance of the ice sheets, which are relevant to global climate change and sea-level rise. During the last two decades, satellite radar altimetry or airborne laser altimetry could obtain accuracy by an order of magnitude greater than the traditional airborne barometric altimetry, which has a precision of typically several tens of meters at best and only a limited coverage. The widest coverage comes from satellites, especially from the ERS1/2 and ENVISAT, which extends to 81.5° of latitude, covering almost all of Greenland and most of Antarctica. In this paper, an algorithm for time series analysis based on crossover was used to obtain 4-year (September 2002–March 2007) ice-sheet elevation changes from ENVISAT data. The height of the whole Antarctic ice sheet has a decline of about 0.4 ± 0.43 cm from September 2002 to March 2007. The time series data present clearly a seasonal and annual signal feature; that the ice sheet thickens in March. From the time series data, the seasonal and annual signal can be observed clearly.

Numerical Simulation of Sloshing Phenomena in Cubic Tank with Multiple Baffles

A two‐phase fluid flow model solving Navier‐Stokes equations was employed in this paper to investigate liquid sloshing phenomena in cubic tank with horizontal baffle, perforated vertical baffle, and their combinatorial configurations under the harmonic motion excitation. Laboratory experiment of liquid sloshing in cubic tank with perforated vertical baffle was carried out to validate the present numerical model. Fairly good agreements were obtained from the comparisons between the present numerical results and the present experimental data, available numerical data. Liquid sloshing in cubic tank with multiple baffles was investigated numerically in detail under different external excitation frequencies. Power spectrum of the time series of free surface elevation was presented with the aid of fast Fourier transform technique. The dynamic impact pressures acting on the normal and parallel sidewalls were discussed in detail.

Predicting surface scattering from surface elevation time series

Surface reverberation in mid-frequency bands (we are considering 3–15 kHz) can be an important determinant for the performance of underwater communications systems operating in surface scattering environments. At these frequencies and at relatively short ranges (order 10 water depths), gravity waves focus sound energy incident on the surface, creating intensifications, Doppler shifts and phase shifts in the reflected field, all of which impact the performance of underwater acoustic communications systems. Observations of the time-varying arrival intensity structure from an experiment conducted in the Martha's Vineyard Coastal Observatory will be presented along with model calculations made using the Kirchhoff approximation. The sensitivity of the reflected field to the distribution of energy in the surface wave field and short wavelength gravity waves will will be discussed. [Work supported by the ONR Ocean Acoustics Program.]

Observations and simulation of winds, surge, and currents on Florida's east coast during hurricane Jeanne (2004)

A novel set of measurements of winds, water levels, and currents recorded in September of 2004 captured the landfall of Hurricane Jeanne. The dataset provides a full picture of the meteorology and hydrodynamics associated with Hurricane Jeanne and are used to test the state-of-the-art in numerical modeling of storm surge. A shallow water equations model (ADCIRC) is driven by rigorously modeled winds and astronomic tides to replicate continuous hydrodynamic records at two stations, one in Melbourne Beach (Spessard) and the other inside Port Canaveral (Trident Pier), where instrumentation was located by happenstance. Simulation results represent the time-series of water surface elevations measured in the open coast off Melbourne Beach (Spessard) within 0.05m root mean square error and within 12% of observed maximum surge elevation (1.35m simulated vs. 1.52m measured) and exhibit details induced by a ‘loop’ performed by the hurricane before it made landfall. Prediction of water levels inside Port Canaveral (Trident Pier) is to within 0.06m root mean square error and includes the observed forerunner and peak surge of the hurricane. In regard to nearshore currents off Melbourne Beach (Spessard), the timing of a sudden switch in the direction of the measured (longshore) current is replicated well with the magnitude of the peak current simulated to within 14% of observation (0.96m/s modeled vs. 1.11m/s measured). The capability to accurately simulate the tidal and storm surge hydrodynamics during Hurricane Jeanne provides confidence in using this class of shallow water equations models in coastal engineering practice.

Coupled wave action and shallow-water modelling for random wave runup on a slope

Wave runup statistics on beaches, dunes and coastal structures are needed for coastal management and engineering designs. Spectral wave energy–action models are widely used to predict wave propagation in deep and shallow water, incorporating the effects of refraction, bed friction, breaking and wave–wave interactions. To calculate nearshore runup or overtopping, wave-by-wave or phase-resolving modelling is necessary as spectral, phase-averaged models only give the spectral evolution and wave-induced setup. Herein, unidirectional wave propagation up a uniform slope predicted by the Simulating WAves Nearshore (SWAN) model is compared with experimental data. The surface elevation time series near the breaking position is then created from the predicted nearshore spectra and input to a non-linear shallow-water equation solver to give statistical runup predictions which are also compared with experimental data. Sensitivity to the offshore position for wave input is investigated. Runup statistics are shown to be reasonably well predicted.

Changes in the dynamics of marine terminating outlet glaciers in west Greenland (2000–2009)

Recent changes in the dynamics of Greenland's marine terminating outlet glaciers indicate a rapid and complex response to external forcing. Despite observed ice front retreat and recent geophysical evidence for accelerated mass loss along Greenland's northwestern margin, it is unclear whether west Greenland glaciers have undergone the synchronous speed‐up and subsequent slow‐down as observed in southeastern glaciers earlier in the decade. To investigate changes in west Greenland outlet glacier dynamics and the potential controls behind their behavior, we derive time series of front position, surface elevation, and surface slope for 59 marine terminating outlet glaciers and surface speeds for select glaciers in west Greenland from 2000 to 2009. Using these data, we look for relationships between retreat, thinning, acceleration, and geometric parameters to determine the first‐order controls on glacier behavior. Our data indicate that changes in front positions and surface elevations were asynchronous on annual time scales, though nearly all glaciers retreated and thinned over the decade. We found no direct relationship between retreat, acceleration, and external forcing applicable to the entire region. In regard to geometry, we found that, following retreat, (1) glaciers with grounded termini experienced more pronounced changes in dynamics than those with floating termini and (2) thinning rates declined more quickly for glaciers with steeper slopes. Overall, glacier geometry should influence outlet glacier dynamics via stress redistribution following perturbations at the front, but our data indicate that the relative importance of geometry as a control of glacier behavior is highly variable throughout west Greenland.

Identification of breaking events from the responses of a data buoy

Conventional data buoys record wave spectral parameters such as the significant height, peak period, and mean direction. Information about the existence of wave groups and breaking waves is also important for the design of ocean structures. To derive such information from data buoy measurements, understanding of the motion characteristics of data buoys under a variety of wave conditions is essential. In the present study, the motion characteristics of a scale-modelled discus data buoy were tested under the action of deep-water breaking waves of different intensities, covering spilling to steep plunging types. The laboratory generation of breaking waves was based on the constructive wave—wave interaction method. The buoy heave and pitch motions were measured using potentiometers and non-contact motion-capturing cameras. The measured time series of the breaking-wave surface elevation and the resulting buoy motions were analysed by continuous wavelet transformation and phase—time methods. A closer insight into the wavelet phases reveals that the breaking events leave a constant phase variation over a wider range of higher frequencies. Through appropriate filtering of the localized frequencies, the phase—time method could also be adopted to detect breaking events in the time histories of the measured wave elevation and motion response. The details of the model, instrumentation, testing conditions, and analysis are presented and discussed in this paper.

Laboratory Study of Low-Frequency Waves Induced by Random Gravity Waves on Sloping Beaches

Low-frequency waves induced by the shoaling of random gravity waves (the primary waves) on sloping beaches were studied experimentally. Incident primary waves with a Pierson-Moskowitz (PM) spectrum were mechanically generated at a water depth of 0.7 m and propagated toward beaches with three different slopes (1/20, 1/30, and 1/40) in separate experiments. Four wave conditions with significant wave heights ranging from 0.078 to 0.125 m were used. The time series of surface elevations were simultaneously recorded at various water depths along the beach. Low-frequency waves were obtained from the data with a low-pass filter. Our results show that the spectra of low-frequency waves on beaches are dramatically changed by the beach slope and the wave height of incident primary waves. The cross-correlation of low-frequency waves with the surface-elevation envelope of the primary waves shows that the incident bound long waves are dominant. Free low-frequency waves propagate in the offshore direction with very low...

Modeling of Hydrodynamics and Cohesive Sediment Processes in an Estuarine System: Study Case in Danshui River

The Danshui River estuarine system is the largest estuarine system in northern Taiwan and is formed by the confluence of Tahan Stream, Hsintien Stream, and Keelung River. A comprehensive one-dimensional (1-D) model was used to model the hydrodynamics and cohesive sediment transport in this branched river estuarine system. The applied unsteady model uses advection/dispersion equation to model the cohesive sediment transport. The erosion and deposition processes are modeled as source/sink terms. The equations are solved numerically using an implicit finite difference scheme. Water surface elevation and longitudinal velocity time series were used to calibrate and verify the hydrodynamics of the system. To calibrate and verify the mixing process, the salinity time series was used and the dispersion coefficient of the advection/dispersion equation was determined. The cohesive sediment module was calibrated by comparing the simulated and field measured sediment concentration data and the erosion coefficient of the system was determined. A minimum mean absolute error of 4.22 mg/L was obtained and the snapshots of model results and field measurements showed a reasonable agreement. Our modeling showed that a 1-D model is capable of simulating the hydrodynamics and sediment processes in this estuary and the sediment concentration has a local maximum at the limit of salinity intrusion. Furthermore, it was indicated that for Q 50 (the flow which is equaled or exceeded 50% times), the turbidity maximum location during neap tide is about 1 km closer to the mouth compared to that during spring tide. It was found that deposition is the dominant sediment transport process in the river during spring–neap periods. It was shown that, while sediment concentration at the upstream depends on the river discharge, the concentration in the downstream is not a function of river discharge.

Physical modeling of intermediate cross‐shore beach morphology: Transients and equilibrium states

Laboratory experiments on cross‐shore beach morphodynamics are presented. A lightweight sediment (density ρs = 1.19 g cm−3) model is used in order to fulfill a Shields number and Rouse number scaling. This choice aims at correctly reproducing bed load transport as well as suspension dynamics. Terraces and barred beach profiles obtained in the experiments also present close similarities with profiles observed in the field. In order to question the concept of equilibrium beach profile, wave forcings conforming to a JONSWAP spectrum were imposed over long periods (up to more than a hundred hours). An average bottom evolution velocity is defined and used to determine when the profile reaches equilibrium. Usually, beach profiles are characterized according to the Wright and Short (1984) classification based on the Dean number Ω. This well‐known classification is investigated and refined in the intermediate range, that is, for 1 ≤ Ω < 5. For Ω close to 1, a typical reflective profile is obtained. Terraces are obtained for the Ω = 2.5 cases. For Ω ≈ 3.7, the profiles exhibit two parts: a mild dissipative offshore slope producing low reflection and a steeper beach face with slightly higher reflection. The wave dissipation, velocity skewness, and acceleration skewness are computed from the free surface elevation time series. The dissipation and wave nonlinearities patterns are similar for similar equilibrium beach profiles, that is, with the same Dean number. Dissipation peaks coincide with bottom slope transitions as higher energy dissipation occurs with milder bottom slope sections. Besides, the uniformity of volumetric wave energy dissipation seems to concern only a limited zone of beaches with a widely developed surf zone.

The 2004 December 26 Indian Ocean tsunami impact on Sri Lanka: cascade modelling from ocean to city scales

SUMMARY The 2004 December 26 Indian Ocean tsunami severely hit Sri Lanka. Although it was not in the direct path of the initial tsunami waves, the western coast was struck by diffracted waves that caused much damage. The numerical model GEOWAVE is used to compute tsunami generation, propagation and inundation from the earthquake source to the Sri Lankan coast. A nested grid system is constructed to increase the resolution until Galle Bay, on the southwestern coast, where a 20 m-grid is used. The six nested topobathymetric grids are interpolated from ETOPO2 and high resolution data, at sea as onshore. Simulation results are compared with tsunami height data from National Oceanic and Atmospheric Administration (NOAA; US) and Geological Survey & Mines Bureau (GSMB; Sri Lanka). When the grid resolution increases, the discrepancy between the model and the data remains, on average, good, whereas its spread increases. We then conclude that the order of magnitude of the tsunami height is consistent from the 180 m-resolution grid, but the spatial imprecision is too high to locally predict reliable water heights. Nevertheless, the comparison between computed time-series of sea surface elevation at the Colombo tide station and tide-gauge data shows a very good agreement as both amplitude, and arrival time of the first wave are well reproduced. When focusing onshore, the modelled inundation limit is compared with the limit measured in the field. With its a priori setup, computed inundation spreads much farther behind the field limit. We then integrate more accurate nearshore conditions into the model. Non-linear shallow water equations are chosen instead of fully non-linear Boussinesq equations; the bottom friction on land is increased to a much higher value than at sea; the buildings cover and the low tide conditions are taken into account in the DEM. The resulting high resolution simulation agrees better with field data, even if discrepancies are still locally observed in places of DEM imprecision and in a river valley. This simulation, however, demonstrates that taking into account nearshore and onshore features may significantly improve tsunami impact assessment.

Influence of Spectral Width on Wave Height Parameter Estimates in Coastal Environments

In this study, we present comparisons of wave height estimates using data from acoustic Doppler wave gauges in ten coastal and estuarine environments. The results confirm that the agreement between significant wave height estimates based on spectral moments (Hm0) versus zero-crossing analysis (H1∕3) is linked to the underlying narrow band assumption, and that a divergence from theory occurs as spectral width increases with changes in the wave field. Long-term measurements of the maximum to significant wave height ratio, Hmax∕H1∕3, show a predictable dependence on the site-specific wave climate and sampling scheme. As an engineering tool for other investigators, we present empirically derived equations relating Hm0∕H1∕3 and H1∕3∕m0 to the spectral bandwidth parameter, ν, and evaluate two procedures to predict Hmax from the spectrum when the surface elevation time series is unavailable. Comparisons with observations at each site demonstrate the utility of the methods to predict Hmax within 10% on average.

Asymptotic behavior of frequency and wave number spectra of nearshore shoaling and breaking waves

Wave number spectra from shoaling and breaking waves in five laboratory tests are compared to a recently published parameterization describing the evolutionary characteristics of surf zone wave spectra. This parameterization proposes two regions in which different wave number spectral shapes are present; the Zakharov range (2.5 kp ≤ k ≤ 1/h) has a k−4/3 dependence, while the Toba range (k > 1/h) has a k−5/2 shape. Comparison to laboratory data reveals that the spectral slopes from the Zakharov range of the data trend toward increased agreement with the parameterization in the range of incipient breaking. In contrast, the spectral slopes from the Toba range evolve slowly, likely owing to nonlinear interactions with lower, more energetic wave numbers. However, in the inner surf zone the spectral shape for both parameterized ranges tend toward k−2 (or equivalently, f−2 in shallow water). The dissipation coefficient α(f) is extracted from time series of free surface elevations; it is found that α(f) has a reciprocal frequency dependence with that of the frequency spectra S(f) of the data, and that this correspondence increases as the waves enter the surf zone. Additionally α(f) ∼ 1/S(f) ∼ f2 in the inner surf zone. It is concluded that the wave number spectrum parameterization, particularly in the Zakharov range, reasonably describes the spectral shape while the surf zone is still only partially saturated. However, continued breaking moves the spectral shape away from the parameterized slope toward a f−2 (or k−2) spectral shape, representative of the sawtooth‐like shape of surf zone waves. This spectral shape is a clear inner surf zone asymptote.

Correlation between Wave Pressures and Water Surface Elevations for Irregular Waves

This study aims to develop efficient methods for an estimation of wave pressures under irregular waves by using time series of water surface elevations. Two methods are presented in this study. One is a linear filter approximation method which is extended from an original way to calculate water particle velocities from the water surface elevations. The other one is a local approximation method which is also extended from an original way to obtain non linear water surface elevations by using time series of subsurface pressures. The validity of each method is verified comparing with experimental results for simultaneous measurements of water surface elevations and subsurface pressures under progressive and standing irregular waves in 2-D wave flume.