SWASH Model Research Articles

Uncertainty of wave runup prediction on coral reef-fringed coasts using SWASH model

Predicting wave runup on reef-fringed coasts using phase-resolving modelings suffers from uncertainty induced by wave randomness, spectral-width determination, and reef-surface-roughness reproduction. A multi-layer non-hydrostatic model SWASH was first validated against two physical experiments and then applied to simulate runup over coral reefs. Simulations with different wave sequences for the same wave condition indicated that infragravity swash (RIGW) variability was the main contributor to the extreme runup (R2%) uncertainty. RIGW was positively correlated to the off-reef incident-wave groupiness factor and the average number of waves per wave group, suggesting that prior knowledge of incident group structure could help in reducing the uncertainty of runup prediction. In ensembles with 100 simulations of different random wave sequences, the ratio of R2% with 5% exceedance level to R2% with 95% exceedance level decreased with increasing number of spectral components and approached to 1.15–1.3 with over 600 components. Runup uncertainty induced by randomly phasing did not significantly vary with spectral widths and reef-surface roughness. Runup uncertainty due to arbitrarily specifying reef-surface roughness was much more significant than the uncertainty induced by wave randomness and spectral width, suggesting that accurate reproduction of reef surface roughness has a high priority in physical and numerical modelings.

A convolutional neural network based model to predict nearshore waves and hydrodynamics

This study proposes a convolutional neural network (CNN) based model to predict waves and hydrodynamics in the nearshore zone. Specifically, we address the so-called next-frame prediction of wave and hydrodynamic conditions using the previous-step conditions. A laboratory experiment on unsteady rip currents is simulated using the non-hydrostatic model SWASH. The simulated wave and hydrodynamic results are divided into two groups. The first group of data is used to train the CNN model, and the second group of data is used to evaluate the trained model by comparing the simulated water surface elevation, cross-shore velocity, and longshore velocity by SWASH with the corresponding prediction by the trained CNN model. The result shows that the CNN model accurately predicts the wave propagation over the offshore slope, wave breaking over the sandbar, and bore propagation over the shore including detailed wave crest bending and separation. Time-averaged water level comparison further confirms that the CNN model captures the wave setup induced by wave breaking. The CNN model also correctly predicts the cross-shore velocity and longshore velocity driven by wave breaking over sandbars and wave–current interaction. Finally, the low-frequency nearshore circulation pattern predicted by the CNN model is also evaluated by time-averaging the velocity field. The comparison shows that the CNN model correctly predicts the distribution of circulation cells and the number of cells, as simulated by the SWASH model. This work serves as a paradigm to integrate traditional coastal modeling with machine learning to study coastal processes.

A User-Oriented Local Coastal Flooding Early Warning System Using Metamodelling Techniques

Given recent scientific advances, coastal flooding events can be properly modelled. Nevertheless, such models are computationally expensive (requiring many hours), which prevents their use for forecasting and warning. In addition, there is a gap between the model outputs and information actually needed by decision makers. The present work aims to develop and test a method capable of forecasting coastal flood information adapted to users’ needs. The method must be robust and fast and must integrate the complexity of coastal flood processes. The explored solution relies on metamodels, i.e., mathematical functions that precisely and efficiently (within minutes) estimate the results that would provide the numerical model. While the principle of relying on metamodel solutions is not new, the originality of the present work is to tackle and validate the entire process from the identification of user needs to the establishment and validation of the rapid forecast and early warning system (FEWS) while relying on numerical modelling, metamodelling, the development of indicators, and information technologies. The development and validation are performed at the study site of Gâvres (France). This site is subject to wave overtopping, so the numerical phase-resolving SWASH model is used to build the learning dataset required for the metamodel setup. Gaussian process- and random forest classifier-based metamodels are used and post-processed to estimate 14 indicators of interest for FEWS users. These metamodelling and post-processing schemes are implemented in an FEWS prototype, which is employed by local users and exhibits good warning skills during the validation period. Based on this experience, we provide recommendations for the improvement and/or application of this methodology and individual steps to other sites.

On the improvements in nearshore wave height predictions using nested SWAN-SWASH modelling in the eastern coastal waters of India

Nearshore wave prediction is an area of research which still demands continuous developments and the accuracy of wave models in the nearshore regions, is known to be limited. In this work we focus on an improved coastal prediction across east coast of India and this is one step forward to achieve accurate nearshore predictions using nested wave models. The study used two modelling setups, SWAN and SWAN-SWASH with boundary conditions from deep water model WAVEWATCH III. The comparison of wave hindcasts over the east coast of India with buoy measurements at four nearshore locations, represents a higher accuracy in simulating significant wave height (Hs) with a high correlation and high index of agreement, using nested SWAN-SWASH in comparison to SWAN only. Further the accuracy of the models was also evaluated during an extreme event such as Hudhud Cyclone, which showed a better match using SWASH than SWAN at the Visakhapatnam coastal location. The sensitivity of the SWASH model with different grid resolutions was also tested to arrive at the best grid resolutions for achieving accurate nearshore predictions. Hence, a nested SWAN-SWASH setup should be adopted to locally advance the wave prediction in the nearshore regions, reducing the underestimation of wave estimates with SWAN only setup.

An efficient method to calculate depth-integrated, phase-averaged momentum balances in non-hydrostatic models

Analysis of the mean (wave-averaged) momentum balance is a common approach used to explain the physical forcing driving wave set-up and mean currents in the nearshore zone. Traditionally this approach has been applied to phase-averaged models but has more recently been applied to phase-resolving models using post-processing, whereby model output is used to calculate each of the momentum terms. While phase-resolving models have the advantage of capturing the nonlinear properties of waves propagating in the nearshore (making them advantageous to enhance understanding of nearshore processes), the post-processing calculation of the momentum terms does not guarantee that the momentum balance closes. We show that this is largely due to the difficulty (or impossibility) of being consistent with the numerical approach. If the residual is of a similar magnitude as any of the relevant momentum terms (which is common with post-processing methods as we show), the analysis is largely compromised. Here we present a new method to internally calculate and extract the depth-integrated, mean momentum terms in the phase-resolving non-hydrostatic wave-flow model SWASH in a manner that is consistent with the numerical implementation. Further, we demonstrate the utility of the new method with two existing physical model studies. By being consistent with the numerical framework, the internal method calculates the momentum terms with a much lower residual at computer precision, combined with greatly reduced calculation time and output storage requirements compared to post-processing techniques. The method developed here allows the accurate evaluation of the depth-integrated, mean momentum terms of wave-driven flows while taking advantage of the more complete representation of the wave dynamics offered by phase-resolving models. Furthermore, it provides an opportunity for advances in the understanding of nearshore processes particularly at more complex sites where wave nonlinearity and energy transfers are important.

An early warning system for wave-driven coastal flooding at Imperial Beach, CA

Waves overtop berms and seawalls along the shoreline of Imperial Beach (IB), CA when energetic winter swell and high tide coincide. These intermittent, few-hour long events flood low-lying areas and pose a growing inundation risk as sea levels rise. To support city flood response and management, an IB flood warning system was developed. Total water level (TWL) forecasts combine predictions of tides and sea-level anomalies with wave runup estimates based on incident wave forecasts and the nonlinear wave model SWASH. In contrast to widely used empirical runup formulas that rely on significant wave height and peak period, and use only a foreshore slope for bathymetry, the SWASH model incorporates spectral incident wave forcing and uses the cross-shore depth profile. TWL forecasts using a SWASH emulator demonstrate skill several days in advance. Observations set TWL thresholds for minor and moderate flooding. The specific wave and water level conditions that lead to flooding, and key contributors to TWL uncertainty, are identified. TWL forecast skill is reduced by errors in the incident wave forecast and the one-dimensional runup model, and lack of information of variable beach morphology (e.g., protective sand berms can erode during storms). Model errors are largest for the most extreme events. Without mitigation, projected sea-level rise will substantially increase the duration and severity of street flooding. Application of the warning system approach to other locations requires incident wave hindcasts and forecasts, numerical simulation of the runup associated with local storms and beach morphology, and model calibration with flood observations.

Calibration and preparation of field measurements of oblique wave run-up and overtopping on dikes using laser scanners

Wave overtopping is typically measured in the field using overtopping tanks. In this paper, an alternative system is developed that uses two laser scanners. The system also measures wave run-up, as well as run-up depths and velocities, both during perpendicular and oblique waves on a dike in the field. The paper considers the first calibration tests with the system in the field, with perpendicular and oblique waves generated by the wave run-up simulator on a grass dike slope. Furthermore, simulations are performed with the numerical wave model SWASH, to gain more insight in the potential performance of the system during actual oblique wave attack during a storm. The run-up is determined from the measured elevation and reflection intensity, which agrees well with the visually observed run-up. Run-up depths and front velocities can be determined accurately as well. The (virtual) wave overtopping discharge can be calculated from the data, which agrees well with the most commonly used overtopping equations for perpendicularly incident waves. Finally, from the simulated run-up data of obliquely incident waves, it is concluded that an estimate can be obtained of the incident wave period and wave angle of incidence at the toe of the structure.

Numerical characterisation and efficient prediction of landslide-tsunami propagation over a wide range of idealised bathymetries

Landslide-tsunamis are generated by masses, such as landslides or icebergs, impacting into water bodies. Such tsunamis resulted in major catastrophes in the recent past. Generic research into landslide-tsunamis has widely been conducted in idealised water body geometries at uniform water depths. However, varying bathymetries can significantly alter landslide-tsunamis. This article investigates this effect in a 2D flume using selected idealised bathymetries to provide methods to predict the transformed wave characteristics downwave of each feature. The selected bathymetries are: (a) linear beach bathymetries, (b) submerged positive and negative Gaussian bathymetric features and (c) submerged positive and negative step bathymetries. The hydrodynamic model SWASH, based on the non-hydrostatic non-linear shallow water equations, was used to simulate 9 idealised landslide-tsunamis (1 approximate linear, 2 Stokes, 2 cnoidal and 4 solitary waves), for a total of 184 tests. The analysed parameters include the free water surface, wave height and amplitude. Shoaling in (a) is represented by either Green's law or the Boussinesq's adiabatic approximation up to wave breaking with an accuracy of −7% to +10% for cnoidal and solitary waves, respectively. The results are then analysed with an (i) Artificial Neural Network and (ii) a regression analysis. (i) shows a smaller Mean Square Error (MSE) of 0.0027 than (ii) (MSE =0.024) and good generalisation in predicting the transformed wave characteristics and, after defining the best dimensionless parameters, (ii) provides empirical equations to predict transformed waves. In addition, simulations were conducted in a 3D basin to investigate the combined effect of the bathymetry and geometry. The efficient use of the developed prediction methods is demonstrated with the 2014 Lake Askja landslide-tsunami where a good accuracy is achieved compared to available numerical simulations.

Математическое моделирование волнового режима бухты Ай-Тодор

Investigation of wave regime of coastal water areas is practically important for safe shipping, constructing and using of coastal infrastructure objects. At the present paper statistical characteristics and space distribution of parameters of wind waves in the Ay-Todor Bay region placed on the Crimea South Coast of the Black Sea are obtained on the basis of mathematical simulation. Analysis of the wind wave parameters for the year diapason of 1979–2017 has shown that waves running from the east and having 0.5 m heights and 3.0–3.5 s mean periods are the most repeatable. The most durable storms are formed by waves coming from East–South-South-West sector in the period from December to January. The multiannual calm duration is equal to ~11 days. Estimation of extremal characteristics (height, period and length) of wind waves of different probability, which possible one time in a year, 5, 10, 25, 50 and 100 years are made. For the storm probable one time in 25 years the mean wave height near the boundary of the Ay-Todor Bay is equal to 4.5 m. For this storm the wave height of 1% probability reaches 9.6 m. For the directions of winds of 4 % regime probability which causes the most dangerous waves calculations of wave characteristics with high space resolution (~1.5 m) are carried out by using of SWAN model and nested grid technology. Fields of significant wave height, mean wave length, bottom wave orbital velocities and space distribution of wave breaking zones are analyzed. It is found that most intensive waves are generated by wind having south-east, east and south directions. Maximal bottom orbital velocities of wave current reaches of 2.5–3.5 m/s and occurs along the coast till 10 m depth. Model calculation of wave currents by using of SWASH model allowed obtained presence in the coastal zone near beach of local cyclonic eddy, which transport suspended sediments along its south edge from beach towards the sea.

Numerical and small-scale physical modelling of wave transmission by wooden fences

Mangrove forests, that often act as natural coastal defences, enormously suffered due to ongoing climate change and human disturbances. Thus, it is necessary to have a countermeasure to mitigate the loss of mangroves. Wooden fences are becoming a viable nature-based solution to protect vulnerable replanted mangrove forests. However, the wooden fence's hydraulic characteristics are not yet fully understood due to the complication of branches arrangement. In the present study, a small-scale wave flume modelling of wave damping by a wooden fence was constructed using the inner branches as an inhomogeneous arrangement tested in earlier flow-resistance experiments. The physical model results indicate that the wooden fence is highly effective on wave transmission and that the effectiveness in wave reduction depends on the relative fence thickness, B/Hi. To understand the scale effect on wave transmission further, the numerical model SWASH was used with the laboratory wave data. By applying the prior experiments' drag coefficient on steady flow, the uncalibrated numerical model gave a good agreement with the wave model results, with a root-mean-square error for the total transmitted wave heights of 4.7%. After validation, potential scale effects for small scale tests were determined from scaling simulations at both full scales and the applied 1:5 model scale. These simulations were performed for a fence porosity of 0.81, and different fence thicknesses to understand scale effects between model- and full-scale. Both wave reflection and transmission at model-scale are about 5% higher than full-scale results due to the increased drag coefficient and viscous effects. The effects of fence thickness and porosity were the same in large and small scale, and much larger than the error due to scale effects. Hence testing fence efficiency at physical small scale is regarded as a useful tool, together with numerical modelling.

ASSESSING THE EFFECT OF EARTHQUAKE-INDUCED UPLIFT AND ENGINEERING WORKS ON A SURF BREAK OF NATIONAL SIGNIFICANCE

In November 2016 a Mw7.8 earthquake struck the northeast coast of the New Zealand South Island triggering numerous large landslips which severed key infrastructure and caused parts of the coastline to be uplifted by up to 3 m. This affected a notable surf break at Mangamaunu, north of Kaikoura. The uplift of the seabed at this location caused changes in the wave breaking characteristics and, at the same time, infrastructure recovery efforts proposed construction of engineering works along the site shoreline. The potential impacts of these works on the surf break caused significant local, national and international concern. An extensive study was initiated to better understand the characteristics of the surf break, the effects of the earthquake-induced seabed uplift and the potential effects of the engineering works. This included collection of topographic and bathymetric data using a combination of LiDAR, multibeam and an innovative UAV-based collection method within the surf zone. This provided a seamless terrain model which could be adjusted to pre-earthquake levels based on observed uplift rates. Two fixed camera stations were established with ground control information to collect data on wave breaking position and GPS-watches were deployed and utilized by the local surfing community to collect similar data. Image processing algorithms were developed to extract wave breaking on a wave-by-wave basis and aggregate to obtain breaking exceedance contours, an improvement from threshold analysis on time-averaged imagery. Both physical and numerical modelling was undertaken to better understand the effect of the earthquake and of the proposed works on wave characteristics, particularly wave reflection. The non-hydrostatic wave-flow model SWASH (Smit et al., 2013) was used to evaluate changes in the breaking position, the incident and reflected wave energy gradients, and surf zone hydrodynamics during a range of typical and optimal surfing conditions for present day and future water levels. An innovative wave breaking position post-processing routine was developed to allow assessment of the impact of reflected waves on the surfability of incoming wave forms on a wave-by-wave basis. Results found that the breaking mechanics of the surf break is controlled not only by nearshore bathymetry around break point but also offshore features which cause focusing of wave energy. The uplift has caused significant changes to the breaking characteristics, with increased wave focusing, breaking and dissipation. The proposed engineering works were found to potentially cause increased wave reflection at the outer part of the surf break during high water levels, however the spatial and temporal characteristics of this reflection mean that direct impacts on surfability are likely to be limited.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/u6nLAp-gQxw

NUMERICAL SIMULATION OF WAVE-DRIVEN FLOWS ON A MORPHOLOGICALLY EVOLVING BEACH

Wave-driven flows in the nearshore zone are responsible for the erosion and transport of beach sediments, causing a continuous cycle of bathymetric change that is linked with changes to wave transformation and nearshore hydrodynamics. Numerical models have been used to investigate the evolving nearshore wave field corresponding to beach morphology change in field studies (e.g., Ruiz de Alegria-Arzaburu et al., 2013). In the present study, the non-hydrostatic wave-flow SWASH model (Zijlema et al., 2011) is applied to five laboratory cases to investigate the change in wave and flow fields corresponding to evolving beach morphology during a simulated storm event.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/LZQQuuiqsPY

ADVANCED MODELLING OF WAVE PENETRATION IN PORTS

Wave penetration is a challenge for port engineers as it governs vessels' safe sailing and mooring and unequivocally regulates the handling of port operations. A complete way to describe this phenomenon is by a physical scale model. However, this approach can be time consuming and expensive, therefore the use of a numerical model is a valid alternative. In this study, wave penetration is simulated with the non-hydrostatic model SWASH (Zijlema, 2011). To validate the model, the output of an open benchmark dataset of physical scale model tests (Van der Ven, 2018) is used. This study evaluates to what degree SWASH models correctly simulate wave penetration per wave process, separately in simplified models and in combination in the full harbour layout, to identify their role in the model accuracy.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/Y8ds-sW4VIQ

AN INTERNAL WAVE GENERATION METHOD FOR THE NON-HYDROSTATIC MODEL SWASH

Numerical wave propagation models are commonly used as engineering tools for the study of wave transformation in coastal areas. In order to simulate waves in the nearshore zone correctly, the generation and absorption of waves at the boundaries of the models need to be modelled accurately. In numerical models, incident waves are usually generated by prescribing their horizontal velocity component at the boundary of the computational domain over the vertical direction. Additionally, in order to absorb and to prevent re-reflections in front of the numerical wave generator, a weakly reflective wave generation boundary condition is applied in which the total velocity signal is a superposition of the incident velocity signal and a velocity signal of the reflected waves. However, this method is based on the assumption that the reflected waves are small amplitude shallow water waves propagating perpendicular to the boundary of the computational domain and hence this method is weakly reflective for directional and dispersive waves. Within the present study, an internal wave generation method combined with sponge layers is applied in the non-hydrostatic model SWASH, in order to more accurately generate waves and avoid re-reflections at the boundaries.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/5M3aU03XJvI

An Inter-Model Comparison for Wave Interactions with Sea Dikes on Shallow Foreshores

Three open source wave models are applied in 2DV to reproduce a large-scale wave flume experiment of bichromatic wave transformations over a steep-sloped dike with a mildly-sloped and very shallow foreshore: (i) the Reynolds-averaged Navier–Stokes equations solver interFoam of OpenFOAM® (OF), (ii) the weakly compressible smoothed particle hydrodynamics model DualSPHysics (DSPH) and (iii) the non-hydrostatic nonlinear shallow water equations model SWASH. An inter-model comparison is performed to determine the (standalone) applicability of the three models for this specific case, which requires the simulation of many processes simultaneously, including wave transformations over the foreshore and wave-structure interactions with the dike, promenade and vertical wall. A qualitative comparison is done based on the time series of the measured quantities along the wave flume, and snapshots of bore interactions on the promenade and impacts on the vertical wall. In addition, model performance and pattern statistics are employed to quantify the model differences. The results show that overall, OF provides the highest model skill, but has the highest computational cost. DSPH is shown to have a reduced model performance, but still comparable to OF and for a lower computational cost. Even though SWASH is a much more simplified model than both OF and DSPH, it is shown to provide very similar results: SWASH exhibits an equal capability to estimate the maximum quasi-static horizontal impact force with the highest computational efficiency, but does have an important model performance decrease compared to OF and DSPH for the force impulse.

Hydrodynamic Modeling of a Reef-Fringed Pocket Beach Using a Phase-Resolved Non-Hydrostatic Model

The non-hydrostatic wave-flow model SWASH was used to investigate the hydrodynamic processes at a reef fringed pocket beach in southwestern Australia (Gnarabup Beach). Gnarabup Beach is a ~1.5 km long beach with highly variable bathymetry that is bounded by rocky headlands. The site is also exposed to large waves from the Southern Ocean. The model performance was evaluated using observations collected during a field program measuring waves, currents and water levels between June and July 2017. Modeled sea-swell wave heights (periods 5–25 s), infragravity wave heights (periods 25–600 s), and wave-induced setup exhibited moderate to good agreement with the observations throughout the model domain. The mean currents, which were highly-spatially variable across the study site, were less accurately predicted at most sites. Model agreement with the observations tended to be the worst in the areas with the most uncertain bathymetry (i.e., areas where high resolution survey data was not available). The nearshore sea-swell wave heights, infragravity wave heights and setup were strongly modulated by the offshore waves. The headlands and offshore reefs also had a strong impact on the hydrodynamics within the lagoon (bordered by the reefs) by dissipating much of the offshore sea-swell wave energy and modifying the pattern of the nearshore flows (magnitude and direction). Wave breaking on the reef platforms drove strong onshore directed mean currents over the reefs, resulting in off-shore flow through channels between the reefs and headlands where water exchanges from the lagoon to ocean. Our results demonstrate that the SWASH model is able to produce realistic predictions of the hydrodynamic processes within bathymetrically-complex nearshore systems.

Computation of free surface waves in coastal waters with SWASH on unstructured grids

This paper aims to present the extension of the non-hydrostatic wave-flow model SWASH with the covolume method to build discretization schemes on unstructured triangular grids. Central to this method that is free of spurious pressure modes, is the use of dual pairs of meshes that are mutually orthogonal, such as the Delaunay-Voronoi mesh systems. The approximants sought are the components of the flow velocity vector normal to the cell faces of the primal mesh. In addition to the covolume approach, a novel upwind difference scheme for the horizontal advection terms in the momentum equation is proposed. This scheme obeys the Rankine-Hugoniot jump relations and prevents the odd-even decoupling of the velocity field accordingly. Moreover, cases with flow discontinuities, such as steady bores and broken waves, are properly treated. In spite of the low-order accuracy of the proposed method, unstructured meshes easily allow for local refinement in a way that retains the desired accuracy. The unstructured-grid version of SWASH is applicable to a wide range of 2DH wave-flow problems to investigate the nonlinear dynamics of free surface waves over varying bathymetries. Its efficiency and robustness is tested on a number of these problems employing unstructured triangular meshes.

Numerical study of nearshore hydrodynamics and morphology changes behind offshore breakwaters under actions of waves using a sediment transport model coupled with the SWASH model

ABSTRACT This paper presents the results of numerical study on the wave-induced currents and morphology changes due to the complicated interaction between waves and a sandy beach with shore-parallel breakwaters set on. The study was based on the SWASH wave model coupled with a sediment transport model developed in this research. The simulated results of the coupling model were compared with the published laboratory experimental data. The good agreements were obtained for both wave-induced currents and formation of salient and tombolo behind breakwaters. The models were also applied for studying the evolution of wave-induced currents associated with topography changes of a sandy beach. The wave-induced currents and sediment transport processes have a strong relationship and their interaction could reach a quasi-equilibrium state in which the changes of current pattern and bathymetry become very slow. Numerical results of shoreline response mode were also compared with a published empirical formula and confirmed good agreements.

Evolution of Infragravity Waves Over a Shoal Under Nonbreaking Conditions

AbstractThe present paper aims to clarify the mechanism of infragravity wave (IGW) energy amplification over nearshore shoals reported in recent studies. Wave transformation and energy transfer between short waves (SWs) and IGWs were investigated using SWASH model for nonbreaking random waves propagating over trapezoid shoals with different bottom slopes. It was found that the time lag of IGWs relative to SW groups is the major mechanism for energy transfer from SWs to IGWs and the amplification of IGW energy over all segments of the shoal. The time lag is generated on the front slope and enlarged on the plateau of the shoal, decreases on the rear slope with higher decreasing rates on milder slopes. Over the rear slope, the evolution of IGWs depends on the relative importance of deshoaling and nonlinear energy transfer. It was found that nonlinear energy transfer dominates over the rear slope gentler than 1/60, causing the IGW energy to increase over the first half of the deshoaling process and decrease over the second half whereas deshoaling dominates for steeper rear slope and the IGW energy decay over the whole slope. It is demonstrated numerically and theoretically that the shoals with gentler bottom slopes amplify the IGW energy more effectively by providing longer distance for nonlinear energy transfer to build up. The persistent nonlinear energy transfer on the plateau indicates the important role of wave spatial evolution history in the subsequent IGWs evolution. Strong free IGWs were detected on leeward of the shoal, possibly due to release of topography‐induced additional bound IGWs.

Predicting site-specific storm wave run-up

Storm wave run-up causes beach erosion, wave overtopping, and street flooding. Extreme runup estimates may be improved, relative to predictions from general empirical formulae with default parameter values, by using historical storm waves and eroded profiles in numerical runup simulations. A climatology of storm wave run-up at Imperial Beach, California is developed using the numerical model SWASH, and over a decade of hindcast spectral waves and observed depth profiles. For use in a local flood warning system, the relationship between incident wave energy spectra E(f) and SWASH-modeled shoreline water levels is approximated with the numerically simple integrated power law approximation (IPA). Broad and multi-peaked E(f) are accommodated by characterizing wave forcing with frequency-weighted integrals of E(f). This integral approach improves runup estimates compared to the more commonly used bulk parameterization using deep water wave height H_0 and deep water wavelength L_0 Hunt (Trans Am Soc Civ Eng 126(4):542–570, 1961) and Stockdon et al. (Coast Eng 53(7):573–588, 2006. https://doi.org/10.1016/j.coastaleng.2005.12.005). Scaling of energy and frequency contributions in IPA, determined by searching parameter space for the best fit to SWASH, show an H_0L_0 scaling is near optimal. IPA performance is tested with LiDAR observations of storm run-up, which reached 2.5 m above the offshore water level, overtopped backshore riprap, and eroded the foreshore beach slope. Driven with estimates from a regional wave model and observed beta _f, the IPA reproduced observed run-up with <30% error. However, errors in model physics, depth profile, and incoming wave predictions partially cancelled. IPA (or alternative empirical forms) can be calibrated (using SWASH or similar) for sites where historical waves and eroded bathymetry are available.