Run-up Model Research Articles

Assessment of runup predictions by empirical models on non-truncated beaches on the south-east Australian coast

This paper assesses the accuracy of 11 existing runup models against field data collected under moderate wave conditions from 11 non-truncated beaches in New South Wales and Queensland, Australia. Beach types spanned the full range of intermediate beach types from low tide terrace to longshore bar and trough. Model predictions for both the 2% runup exceedance (R2%) and maximum runup (Rmax) were highly variable between models, with predictions shown to vary by a factor of 1.5 for the same incident wave conditions. No single model provided the best predictions on all beaches in the dataset. Overall, model root mean square errors are of the order of 25% of the R2% value. Models for R2% derived from field data were shown to be more accurate for predicting runup in the field than those developed from laboratory data, which overestimate the field data significantly. The most accurate existing models for predicting R2% were those developed by Holman [12] and Vousdoukas et al. [40], with mean RMSE errors of 0.30m or 25%. A new model-of-models for R2% was developed from a best fit to the predictions from six existing field and one large scale laboratory R2% data-derived models. It uses the Hunt [17] scaling parameter tanβHoLo and incorporates a setup parameterisation. This model is shown to be as accurate as the Holman and Vousdoukas et al. models across all tidal stages. It also yielded the smallest maximum error across the dataset. The most accurate predictions for Rmax were given by Hunt [17] but this tended to under predict the observed maximum runup obtained for 15-min records. Mase's [22] model has larger errors but yielded more conservative estimates. Greater observed values of Rmax are expected with increased record length, leading to greater differences in predicted values. Given the large variation in predictions across all models, however, it is clear that predictions by uncalibrated runup models on a given beach may be prone to significant error and this should be considered when using such models for coastal management purposes. It should be noted that in extreme events, which are lacking in the dataset, runup may be truncated by beach scarps, cliffs, and dunes, or may overtop, and as a result, the probability density functions will have different tail shapes. The uncertainty already present in current models is likely to increase in such conditions.

Fully nonlinear Boussinesq equations for long wave propagation and run-up in sloping channels with parabolic cross sections

A general framework for derivation of long wave equations in narrow channels, and their transformation to Lagrangian coordinates is briefly established. Then, fully nonlinear Boussinesq equations are derived for channels of parabolic cross sections. The simplified version with normal nonlinearity is compared with corresponding models from the literature, and propagation properties are discussed. A Lagrangian run-up model is adapted to the fully nonlinear set. This model is tested by means of controlled residues and by a well-controlled comparison to exact analytic solutions from the literature. Then, run-up of solitary waves in simple geometries is simulated and compared to a semi-analytic solution that is derived for propagation and run-up in a composite channel. The dispersive model retains the higher run-up height in a parabolic channels, as reported in the recent literature for NLSW solutions, as compared to a rectangular channel.

Validated coastal flood modeling at Imperial Beach, California: Comparing total water level, empirical and numerical overtopping methodologies

Flood extent field observations collected during a winter storm (Hs∼1.8m, Tp∼14s) coinciding with a spring high tide are used to evaluate the accuracy of static (‘bathtub’) and hydrodynamic coastal flood modeling methodologies. Static models rely on empirically calculated wave setup or runup and simply compare total water level (TWL) to land elevation. The dynamic model resolves temporally variable overtopping rates, overland flow, urban features and storm system drainage. SWAN, a numerical wave model, transformed deep water buoy spectra to the nearshore. Static TWLs were calculated using SWAN output and an empirical runup model. Numerical (XBeach) and Empirical (EurOtop) overtopping models parameterized with survey data and SWAN bulk wave statistics estimated temporally variable overflow rates along representative transects for overland flow model input. XBeach model mode (hydrostatic, nonhydrostatic), boundary depth and random realizations significantly affected overtopping rates. Nonhydrostatic mode estimated order of magnitude larger overflow volumes suggesting the importance of incident waves, particularly in near threshold conditions. Boundary depth and random realizations varied overflow rates approximately fourfold. Field observations showed static TWL models performed poorly, maximum runup substantially overestimated flood extent and setup predicted no flooding. All dynamic models reasonably predicted flood extent despite significant overflow volume differences. Backshore topography and flow dynamics are important flood extent controls. Accurate near threshold coastal flood predictions require dynamic overland flow modeling parameterized with temporally variable overtopping estimates and site specific beach and backshore topography.

Empirical wave run-up formula for wave, storm surge and berm width

An empirical model to predict wave run-up on beaches considering storm wave and surge conditions and berm widths (dry beach) has been derived through a synthetic data set generated from a one-dimensional Boussinesq wave model. The new run-up equation is expressed as a function of a new Iribarren number composed of three regions: the foreshore, the berm or dry beach width, and the dune. The dissipative effect of the berm is included as a reduction factor expressed as a function of the berm width normalized by the offshore wavelength. The equation is relatively simple but is shown to be applicable for a fairly wide variety of berm widths and storm wave conditions associated with extreme events such as hurricanes, and it is shown to be an improvement over existing empirical run-up models that do not consider the berm width explicitly. In addition, the new parameterization of the Iribarren number considering the three regions and the berm width reduction factor are shown to improve other empirical models.

A rapid estimation of near‐field tsunami runup

AbstractMany efforts have been made to quickly estimate the maximum runup height of tsunamis associated with large earthquakes. This is a difficult task because of the time it takes to construct an accurate tsunami model using real‐time data from the source. It is possible to construct a database of potential seismic sources and their corresponding tsunami a priori. However, such models are generally based on uniform slip distributions and thus oversimplify the knowledge of the earthquake source. Here we show how to predict tsunami runup from any seismic source model using an analytic solution that is specifically designed for subduction zones with a well‐defined geometry, i.e., Chile, Japan, Nicaragua, and Alaska. The main idea of this work is to provide a tool for emergency response, trading off accuracy for speed. The solutions we present for large earthquakes appear promising. Here runup models are computed for the following: the 1992 Mw 7.7 Nicaragua earthquake, the 2001 Mw 8.4 Perú earthquake, the 2003 Mw 8.3 Hokkaido earthquake, the 2007 Mw 8.1 Perú earthquake, the 2010 Mw 8.8 Maule earthquake, the 2011 Mw 9.0 Tohoku earthquake, and the recent 2014 Mw 8.2 Iquique earthquake. The maximum runup estimations are consistent with measurements made inland after each event, with a peak of 9 m for Nicaragua, 8 m for Perú (2001), 32 m for Maule, 41 m for Tohoku, and 4.1 m for Iquique. Considering recent advances made in the analysis of real‐time GPS data and the ability to rapidly resolve the finiteness of a large earthquake close to existing GPS networks, it will be possible in the near future to perform these calculations within the first minutes after the occurrence of similar events. Thus, such calculations will provide faster runup information than is available from existing uniform‐slip seismic source databases or past events of premodeled seismic sources.

Numerical Simulation of Tsunami Run-up and Inundation Employing Horizontal Two-dimensional Model Based on CIP Method

A two-dimensional tsunami run-up and inundation model based on a CIP method was developed in this study so as to satisfy the continuity equation with reasonable accuracy. Numerical simulations on tsunami bore were carried out in order to validate the model and discuss the effects of wet-dry condition and overflow condition on the calculation accuracy. As a result, the model was confirmed to be able to represent closely actual water surface profile by using the slip condition on the wet-dry condition. Furthermore, the numerical results without the overflow formula were found to be in good agreement with the experimental ones.

CLASHデータセットに基づく打上げ・越波統合算定モデルの直立護岸への拡張

CLASHデータセットに基づく打上げ・越波統合算定モデルの直立護岸への拡張

Advanced numerical modelling of tsunami wave propagation, transformation and run-up

This paper presents a series of numerical models tests performed to assess the ability of the OpenFOAM® modelling system to represent the physics that stands behind the propagation of tsunami waves in coastal regions and in particular their transformation (by means of shoaling, refraction, reflection) over uneven bathymetries and their interaction with the shoreline (run-up, run-down, breaking). A series of tests is selected from the literature to explore the accuracy, applicability and limitations of this particular computational fluid dynamics model solving the three-dimensional Navier–Stokes equations for incompressible multiphase fluids. The range of scenarios tested includes experimental work on wave propagation over shoals, solitary wave run-up and the Monai valley tsunami physical model test recreating the Hokkaido–Nansei–Oki 1993 tsunami that struck Okushiri Island, Japan. This allowed direct comparison with experimental data from physical model tests as well as with other established two-dimensional – that is, depth integrated – and three-dimensional numerical models.

Extreme wave events in the central Mediterranean: Geomorphic evidence of tsunami on the Maltese Islands

Field evidence from the Maltese Islands is presented of extreme wave activity in the central Mediterranean Sea. An extensive range of extreme wave signatures, both erosional and depositional, is here presented for the first time and indicates a wave attack from the NE. Existing models of runup and boulder detachment imply that the extreme wave signatures lie beyond the capabilities of storm waves. These considerations, taken together with the range of evidence available, point toward tsunami as the agency responsible, which is consistent with the evidence from Mediterranean marginal coasts opposed to the Maltese Islands. Evidence from existing boulder detachment, tsunami runup and wave velocity models suggests that tsunami with shoreline wave height of up to ∼4 m, and with local velocities of >10 ms–1 would have been required in order to form the signatures observed.

Modelling of tsunami-like wave run-up, breaking and impact on a vertical wall by SPH method

Abstract. Accurate predictions of wave run-up and run-down are important for coastal impact assessment of relatively long waves such as tsunami or storm waves. Wave run-up is, however, a complex process involving nonlinear build-up of the wave front, intensive wave breaking and strong turbulent flow, making the numerical approximation challenging. Recent advanced modelling methodologies could help to overcome these numerical challenges. For a demonstration, we study run-up of non-breaking and breaking solitary waves on a vertical wall using two methods, an enhanced smoothed particle hydrodynamics (SPH) method and the traditional non-breaking nonlinear model Tunami-N2. The Tunami-N2 model fails to capture the evolution of steep waves at the proximity of breaking that was observed in the experiments. Whereas the SPH method successfully simulates the wave propagation, breaking, impact on structure and the reform and breaking processes of wave run-down. The study also indicates that inadequate approximation of the wave breaking could lead to significant under-predictions of wave height and impact pressure on structures. The SPH model shows potential applications for accurate impact assessments of wave run-up on to coastal structures.

Boussinesq modelling of solitary wave and N-wave runup on coast

A total variation diminishing Lax–Wendroff scheme has been applied to numerically solve the Boussinesq-type equations. The runup processes on a vertical wall and on a uniform slope by various waves, including solitary waves, leading-depression N-waves and leading-elevation N-waves, have been investigated using the developed numerical model. The results agree well with the runup laws derived analytically by other researchers for non-breaking waves. The predictions with respect to breaking solitary waves generally follow the empirical runup relationship established from laboratory experiments, although some degree of over-prediction on the runup heights has been manifested. Such an over-prediction can be attributed to the exaggeration of the short waves in the front of the breaking waves. The study revealed that the leading-depression N-wave produced a higher runup than the solitary wave of the same amplitude, whereas the leading-elevation N-wave produced a slightly lower runup than the solitary wave of the same amplitude. For the runup on a vertical wall, this trend becomes prominent when the wave height-to-depth ratio exceeds 0.01. For the runup on a slope, this trend is prominent before the strong wave breaking occurs.

SIMULATION THE RUNUP OF NONLINEAR SURFACE GRAVITY WAVES A STEEP COASTAL SLOPE

The paper considers two-dimensional numerical simulation of non- linear gravity wave run-up to a steep coastal slope. The problem is formu- lated, boundary and initial conditions are described, the numerical model is based on Navier-Stokes equations. The discrete model is constructed using the method of splitting with respect to physical processes. A discrete finite-element model of this problem is developed taking into account the cell fill factor. Two- dimensional run-up model of a surface wave to a steep coastal slope, generation of reflected run back and their superposition are presented.

An information-based model of target stock price runup in the market for corporate control

The stock price runup of target firms in the market for corporate control has been anecdotally attributed to inside trading. Moreover, the empirical merger and acquisitions literature documents a time-varying level and duration of the stock price runup of target firms. Using a market microstructure approach, we model stock price runup as a stochastic process that shifts between a random walk without drift and a predictable process dependent on a parsimonious set of state variables. Consistent with the market microstructure literature, predictability in prices can be exploited only by the informed trader. The model is capable of explaining the complex stylized facts observed in stock price runup. It is also consistent with the merger wave literature, as we find that capital liquidity, economic growth, and market valuations drive the complex dynamics of stock price runup.

Runup and boundary layers on sloping beaches

The present study is devoted to discrepancies between experimental and theoretical runup heights on an inclined plane, which have occasionally been reported in the literature. In a new study on solitary wave-runup on moderately steep slopes, in a wave tank with 20 cm water depth, detailed observations are made for the shoreline motion and velocity profiles during runup. The waves are not breaking during runup, but they do break during the subsequent draw-down. Both capillary effects and viscous boundary layers are detected. In the investigated cases the onshore flow is close to the transitional regime between laminar and turbulent boundary layers. The flow behaviour depends on the amplitude of the incident wave and the location on the beach. Stable laminar flow, fluctuations (Tollmien-Schlichting waves), and formation of vortices are all observed. Comparison with numerical simulations showed that the experimental runup heights were markedly smaller than predictions from inviscid theory. The observed and computed runup heights are discussed in the context of preexisting theory and experiments. Similar deviations are apparent there, but have often been overlooked or given improper physical explanations. Guided by the absence of turbulence and irregular flow features in parts of the experiments we apply laminar boundary layer theory to the inundation flow. Outer flows from potential flow models are inserted in a nonlinear, numerical boundary layer model. Even though the boundary layer model is invalid near the moving the shoreline, the computed velocity profiles are found to compare well with experiments elsewhere, until instabilities are observed in the measurements. Analytical, linear boundary layer solutions are also derived both for an idealized swash zone motion and a polynomial representation of the time dependence of the outer flow. Due to lacking experimental or theoretical descriptions of the contact point dynamics no two-way coupling of the boundary layer model and the inviscid runup models is attempted. Instead, the effect of the boundary layer on the maximum runup is estimated through integrated losses of onshore volume transport and found to be consistent with the differences between inviscid theory and experiments.

A FEMDEM NUMERICAL MODEL STUDY OF RUBBLE-MOUND STRUCTURES ARMOURED WITH CONCRETE ARMOUR UNITS

A new method for the numerical creation of random single-layer systems of concrete armour units is illustrated. The armour layer pack is created by a FEMDEM solver that ensures mechanical equilibrium between all concrete units and rocks of the underlayer. The local and average packing density together with geometric constraints indicative of randomness and interlocking are assessed using analysis tools and shown to be in accordance with unit designer requirements. This solids modelling research is an essential pre-requisite to future simulation of the armour layer response to wave loading and more realistic modelling of wave run-up and overtopping on rubble-mound structures.

Long-Term Modelling of Wave Run-Up and Overtopping during Sea Storms

ABSTRACT Arena, F.; Malara, G.; Barbaro, G.; Romolo, A., and Ghiretti, S., 2013. Long-term modelling of wave run-up and overtopping during sea storms. This paper is concerned with the determination of the return period of a sea storm in which response (run-up or overtopping) of a coastal structure exceeds a fixed threshold. The method is based on long-term statistical analysis of the sea states interacting with the structure and on practical formulas proposed in the past decades for determining response of coastal structures. The proposed methodology accounts for nonstationarity of sea states in time domain by the equivalent triangular storm model, which allows us to determine closed-form solutions of the return period of a storm where maximum significant wave height is larger than a fixed threshold. In this paper the analytical solution is supplemented by a practical application pertaining calculation of the response of a coastal structure. A rubble-mound breakwater is supposed to be placed at a known wa...

A one-dimensional shock-capturing model for long wave run-up on sloping beaches

This paper presents a one-dimensional finite-volume model to investigate long wave run-up under non-breaking and breaking conditions. A conservative form of the non-linear shallow water equations is solved using a high-resolution Godunov-type scheme coupled with the HLL Riemann solver. The surface gradient method leads to a well-balanced formulation between the flux and the source terms. The explicit time discretisation is first-order accurate, but a piecewise linear reconstruction of numerical data at cell interfaces helps achieve second-order accuracy in space. The computed surface elevation, flow velocity and run-up show very good agreement with available analytical solutions and experimental observations. The model accurately describes propagation of non-breaking and breaking waves on a sloping beach.

A multi-layer non-hydrostatic model for wave breaking and run-up

In this paper, a multi-layer non-hydrostatic model is developed to simulate wave breaking and run-up. The model uses explicit projection method to solve the three dimensional (3D) Navier–Stokes equations (NSE). The nonlinear free surface boundary condition is employed to track the free surface. A momentum conservative scheme is used to discretize the advection terms in momentum equations, which enables the model to efficiently resolve discontinuous flow, involving breaking waves and hydraulic jumps. A new grid arrangement is presented to accurately include the non-hydrostatic pressure effect, which is very important to describe dispersive waves. To capture the moving shoreline, a novel wet–dry algorithm is incorporated in the model. Comparisons between numerical results and analytical or experimental data are presented. It is shown that the proposed model without the use of predefined criteria is capable of accurately simulating both breaking waves and wave run-up in 2D or 3D dimensions.

Examination of three practical run-up models for assessing tsunami impact on highly populated areas

Abstract. This paper describes the examination of three practical tsunami run-up models that can be used to assess the tsunami impact on human beings in densely populated areas. The first of the examined models applies a uniform bottom roughness coefficient throughout the study area. The second uses a very detailed topographic data set that includes the building height information integrated on a Digital Elevation Model (DEM); and the third model utilizes different bottom roughness coefficients, depending on the type of land use and on the percentage of building occupancy on each grid cell. These models were compared with each other by taking the one with the most detailed topographic data (which is the second) as reference. The analysis was performed with the aim of identifying how specific features of high resolution topographic data can influence the tsunami run-up characteristics. Further, we promote a method to be used when very detailed topographic data is unavailable and discuss the related limitations. To this purpose we demonstrate that the effect of buildings on the tsunami flow can be well modeled by using an equivalent roughness coefficient if the topographic data has no information of building height. The results from the models have been utilized to quantify the tsunami impact by using the tsunami casualty algorithm. The models have been applied in Padang city, Indonesia, which is one of the areas with the highest potential of tsunami risk in the world.

Measured and modeled wave overtopping on a natural beach

The rate of wave overtopping of a barrier beach is measured and modeled. Unique rate of wave overtopping field data are obtained from the measure of the Carmel River, California, lagoon filling during a time when the lagoon is closed-off with no river inflow. Volume changes are based on measured lagoon height changes applied to a measured hypsometric curve. Wave heights and periods are obtained from directional wave spectra data in 15 m fronting the beach. Beach morphology was measured by GPS walking surveys. Three empirical overtopping models by Van der Meer and Janssen (1995), Hedges and Reis (1998) and Pullen et al. (2007) with differing parameterizations on wave height, period and beach slope and calibrated using extensive laboratory data obtained over plane, impermeable beaches are applied in a quasi-2D manner and compared with the field observations. Three overtopping events are considered when morphology data were available less than 2 weeks prior to the event. The models are tuned to fit the data using a reduction factor to account for beach permeability, berm characteristics, non-normal wave incidence and surface roughness influence. In addition, the run-up model by Stockdon et al. (2006) based on field data is examined and found to underestimate run-up as the calculated values were too small to predict any of the observed overtopping. The three overtopping models performed similarly well with values of 0.72–0.87 for the two narrow-banded wave cases, with an average reduction factor of 0.78. The European model (Pullen et. al., 2007) performed best overall and in particular for the case of the broad-banded, double peaked wave spectrum.