Offshore Significant Wave Height Research Articles

Field Observations Of The Influence Of Infragravity Waves On Wave Overtopping At A Dike On A Shallow Foreshore

Infragravity (IG) waves are low-frequency waves (0.0033 Hz < f < 0.05 Hz) that exist: (i) being bound to the wave groups of high-frequency sea-swell (SS) waves (0.05 Hz < f < 1 Hz), (ii) generated by the moving breakpoint due to the groupiness of the SS waves (Bertin et al., 2018), and (iii) as free IG waves released from the SS wave groups and reflected from neighbouring coasts (Rijnsdorp et al., 2021). Offshore in deeper water (h/Hm0,o > 4, with h the water depth and Hm0,o the offshore significant wave height), IG waves become most apparent during storm conditions, but are still rather limited in wave height (order of a couple of cm). However, at the toe of coastal structures with a shallow foreshore depth (1 < ht/Hm0,o < 4, with ht the water depth at the toe), the energy of IG waves becomes more significant relative to the SS wave frequency band of the wave spectrum (Hofland et al., 2017), becomes equally important for very shallow foreshores (0.3 < ht/Hm0,o < 1), and even dominates SS wave energy for extremely shallow foreshore depths (ht/Hm0,o < 0.3). IG wave growth on mildly sloped shallow foreshores is a result of IG wave shoaling and SS wave energy transfer to IG waves via nonlinear wave-wave interactions (Bertin et al., 2018), and the relative growth of IG to SS wave energy is further aided by SS wave breaking. Coastal urban areas along the Belgian coast (and in other low-lying countries worldwide) rely on a hybrid beach-dike coastal defense system for protection against flooding. During design storm conditions, the nourished beach erodes to a very to extremely shallow foreshore in front of a low-crested impermeable sea dike. Wave overtopping at this type of structure has been shown to be affected by IG waves, based on physical (Altomare et al., 2016) and numerical modelling (Lashley et al., 2021) for shallow to extremely shallow foreshores. However, field observations of the influence of IG waves on wave overtopping have been scarce (van Gent and Giarusso, 2003) and the influence of free IG waves has not been investigated yet. Indeed, the amount of IG wave energy that is expected to arrive at the coastline, not only depends on IG waves naturally bound to the SS wave groups, but also on free IG waves generated offshore or locally reflected from the coast (edge waves). The Belgian continental shelf is characterized by the prevalence of offshore sandbanks (see Figure 1a), which might be an additional source of free IG waves, due to ss wave breaking on the shallow crest of those banks. These free IG waves are location specific and their existence can only be determined by field observations. Knowledge of the offshore boundary conditions with detailed IG wave information is indispensable for the correct prediction and modelling of surf zone hydrodynamics and beach morphodynamics (Fiedler et al., 2019), and the consequent wave overtopping on the dike. Simultaneous measurements of IG waves, offshore and on the beach-dike system during storm conditions together with wave overtopping has not been done before, as it is complex and needs a specific setup with high precision measurement equipment. In-situ measurements provide an invaluable dataset (i.e., no model nor scale effects) and are essential for validating safety assessment and design methodologies of coastal defense systems.

Joint stochastic simulation of extreme coastal and offshore significant wave heights

Joint stochastic simulation of extreme coastal and offshore significant wave heights

Comparison of wave overtopping estimation models for urban beaches. Towards an early warning system on the Basque coast

This study compares the performance of different wave overtopping estimation models at urban beaches. The models selected for comparison are the Mase et al. (2013) and EurOtop parametric models and the XBeach process-based model in surfbeat and non-hydrostatic mode. Seven energetic storms are selected between 2015 and 2022 with offshore significant wave height ranging between 3 m and 8 m and peak period between 12 s and 20 s to perform the model comparison. The information required to run and validate the models (beach slope, shoreface shape, absence/presence of overtopping) was collected for each storm from coastal videometry. To account for the uncertainties derived from the incident waves randomness and the bathymetry shape when using the process-based model, a series of simulations with random seed boundary conditions were run over two different realistic profile shapes for each storm. The present study is a pilot study on the beach of Zarautz; however, it can be extended to other beaches of the Basque coast. Results indicate that while Mase et al. (2013) and EurOtop tend to reasonably predict the absence or presence of overtopping events, they tend to underestimate the hazard level at the beach of Zarautz. Additionally, the beach underwater profile shape can affect the process-based model performance at intermediate intensity storms and to a lesser extend during moderate storms. Finally, the hazard level at the beach of Zarautz varies significantly alongshore due to the configuration of the seawall, highlighting the need for local adaptation measures. Considering that there is no model that systematically performs better than others, it might be reasonable to use model assemble techniques to draw conclusions from a probabilistic perspective.

Trapping of fine-grained sediment on a supply-limited intertidal shore platform at Kaikōura, New Zealand

Shore platforms are generally supply-limited environments and few studies have attempted to measure sediment transport within this rock coast setting. This paper summarises a field-based pilot study that successfully collected fine-grain sediment moving across a sub-horizontal platform at Mudstone Bay, Kaikōura, New Zealand. Two large-aperture and two small-aperture Time-Integrated Mass-sediment Samplers (TIMS) were deployed for 9-days, encompassing 2 days of storm conditions (offshore significant wave heights between 2.0 and 3.6 m, with sediment trapped in both landward and seaward facing directions. The net flux of sediment captured in large aperture samplers was greatest in a seaward-direction (15.2 g), whereas the narrow-mouth samplers, that principally collected suspended sediment had a net onshore flux (5.4 g). The sediment traps yielded sufficient sample to undertake geochemical and textural analysis. Interpretation of these data suggests that the origin of transported material was autochthonous to the platform, being >80 % silt-sized and compositionally consistent with material derived from the shore platform and/or cliff colluvium. This pilot experiment demonstrates that mass-sediment samplers can be used in supply-limited intertidal shore platform settings. Further research involving greater sampling frequency and duration and concomitant detailed hydrodynamic measurements are likely to reveal important insights into the erosion environment.

Numerical modelling of the physical response of coral reef Sandy island to sea level rise by considering seasonal patterns

Sea level rise (SLR) can increase the bathymetry of coral reef platforms, thereby increasing the potential for island erosion and flooding to damage coastal buildings. However, SLR is a threat to the coastal buildings of islands not only in this way, but also in the destruction of coastal buildings due to island morphology changes caused by SLR. Based on sediment, offshore wave, and tidal data from Yongxing Island (sandy island), Xuande Atoll, South China Sea, a process-based morphodynamic model, XBeach-G, was used to predict the morphological evolution of coral reef sandy island under future SLR based on the RCP8.5 scenario. As waves and tides in the South China Sea are distinctly seasonal, the influence of seasonal patterns was considered in the model. Sensitivity analysis of the effects of water level on the reef, offshore significant wave height, sediment porosity and sediment size on the morphological evolution of the islands was conducted. Numerical simulations indicate that under SLR and extreme wave action, the sandy islands eventually retreat landward and the foreshore height increases and the slope steepens and as the SLR rate increases, the island retreats more towards land and the foreshore height rise decreases. While this natural adjustment of the coral reef island increases the island's potential to offset future flood events and support future physical persistence, there is a negative impact on the safety of coastal buildings. This paper highlights the need to develop reasonable conservation policies based on the island's specific environment and conditions. Excessive use of artificial shorelines to protect islands can damage their natural adjustment to resist disasters such as flooding, while artificial defenses are necessary in the case of threats to coastal buildings or the disappearance of certain islands.

Comparison of deep-water-parameter-based wave overtopping with wirewall field measurements and social media reports at Crosby (UK)

Wave overtopping formulae, which often underlie coastal hazard early warning systems, are typically parameterised using wave conditions at the toe of the structure. For very shallow conditions where significant wave breaking occurs over the foreshore, this usually requires computationally-demanding numerical models—and practitioners skilled in their application—to accurately transform offshore waves to the structure toe. An additional concern is that overtopping formulae are scarcely validated in the field due to the very limited availability of in-situ overtopping data obtained at actual structures. Here, we validate a set of deep-water-parameter-based formulae for mean overtopping discharge (q) at smooth slopes, which remove the need for nearshore measurements or additional numerical modelling but require that a single representative foreshore slope angle (m) be defined. The validation is carried out against field data gathered at Crosby (UK) using two novel approaches: i) a new overtopping measurement system called “WireWall”; and ii) crowd-sourced data in the form of overtopping images obtained from a community Facebook page (social media). A method is introduced to define m for irregular bathymetries, based on the location where the local water depth is equal to the offshore significant wave height. The overtopping formulae proved accurate—with estimates of q being within a factor of 4 of observations—when compared to both 1-h averaged and 15-min averaged overtopping data, suggesting that the approach can be used for both design and assessment and now-casting hazard information. Finally, hindcasts made using the newly validated formulae for the events reported by the community indicate that q can exceed 10 l/s/m under yearly winter conditions, posing a serious hazard to pedestrians. This highlights the pressing need to update the current hazard warning system at Crosby, which estimates q to be a factor of 3 lower than the deep-water-parameter-based approach, on average.

Hydraulic gradient and wave height control the success of estuary artificial entrance openings

Intermittently Open/Closed Estuaries (IOCEs) are dynamic, sensitive estuaries that periodically close as a function of competing marine and fluvial energies. Once closed, IOCEs are often artificially opened to relieve localised flooding. Artificial openings are generally effective as a short-term flood mitigation strategy, however, sometimes IOCEs can close immediately after excavation without draining the lagoon. In this situation, the opening does not achieve its management purpose and reimplementation is required – costing many thousands of dollars at a time and leading to adverse impacts on estuary biota. Using a dataset of 137 openings at 37 IOCEs globally, we show that the hydraulic gradient (or grade) at opening and offshore significant wave height determine whether an estuary will remain open and drain its lagoon. The hydraulic gradient represents the energy slope between the estuary and the ocean, and wave height determines the capacity of waves to infill the channel with sediment to counter offshore erosion. Artificial openings are only successful when IOCEs are opened with a hydraulic gradient steeper than 0.017 m/m (equivalent to a grade of 1:60) and when significant wave height is below 4.30 m. These findings highlight that the estuary water level alone is not a good predictor of opening success, despite it being widely used to decide when to implement artificial openings. Using near-continuous monitoring of geomorphic change at 28 artificial openings, we show that the hydraulic gradient (and grade) at the time of opening controls the rate of channel expansion, outflow velocity at the mouth, lagoon drainage rate, and the time to reach peak channel width and outflow velocities. The tidal stage at opening can be used to either speed up or slow down the rates of change, potentially reducing the occurrence of fish kills associated with rapid drainage. Although the decision to open an estuary is a complex balance between environmental, cultural, socio-economic, and practical factors, we present a simple and cost-effective way to predict if artificial openings will be successful. The thresholds of our study can be used to complement existing decision support tools, but as a standalone method, are best suited for emergency openings where draining the lagoon to reduce flooding is the main management priority.

Supratidal inundation on an incipient marine terrace

Co-seismic uplift of the Kaikōura Peninsula emerged the shore platform at Mudstone Bay upwards by 0.96 m, transforming the formerly intertidal platform. The post-uplift morphology now contains ~90 m of a supratidal zone that represents an incipient marine terrace that has the potential to be preserved in the geological record. This paper investigates wave conditions that drive supratidal inundation, thereby influencing post-uplift terrace development processes. Wave hydrodynamics during austral summer and winter under moderately energetic offshore conditions showed that only 24 % of swell energy propagated to the inner platform compared to 84 % during fair weather swell. Infragravity energy increased inland during storms and dominated the energy spectra (70 %) on the incipient marine terrace. Wave attenuation increased under storm conditions as the effective intertidal width elongated and merged with the incipient marine terrace. Wave propagation under higher energy conditions (offshore significant wave heights of 3.5 m) were sufficient to partially inundate the supratidal terrace up to 9 cm in water depth but only for 2 h. Storm waves when congruent with high tide were used to develop a frequency model of inundation, which suggests that for the post-uplift period 13 % of tides could inundate portions of the supratidal terrace, but full inundation to the cliff toe occurs for <0.05 % of tides. Hence, the new supratidal marine terrace is vulnerable to inundation from annual storm events but protects the cliff toe from wave action.

Water Level Modulation of Wave Transformation, Setup and Runup Over La Saline Fringing Reef

AbstractCoral reefs represent an efficient natural mechanical coastal defense against ocean waves. The focus of this study is La Saline fringing coral reef, located in the microtidal West of La Réunion Island in the Indian Ocean, frequently exposed to Southern Ocean swell and cyclonic events. The aim is to provide a better understanding of the reef's coastal defense characteristics for several Southern Ocean swell events. Pressure sensors were placed across the reef to measure water level fluctuations and to study wave transformation. A numerical model (XBeach surfbeat), validated using field observations, was used to deepen understanding of wave transformation, wave setup and runup. Field measurements and model outputs show that as gravity waves dissipate over the reef, and frequency‐dependent dissipation of infragravity waves by bottom‐friction occurs, the reef acts as a low‐pass filter. Wave‐induced setup is found to be the dominant hydrodynamic component. Setup and runup are each 98% and 79% driven by the offshore significant wave height, and 2% and 21% driven by the tide. The modulation of the water level by setup is the main contributor to runup in the fringing reef. At semidiurnal timescales, setup and runup are in antiphase with tidal variations as lower water levels result in higher gravity wave energy dissipation, setup and runup. Simple‐to‐use transfer functions relating incident wave characteristics to these hydrodynamic components are proposed. The effects of bottom friction and water level on the defensive capacity of the coral reef highlight future implications of structural damage and sea level rise.

Interplay Between Coastal Elevation and Wave Height Controls the Occurrence of Coastal Boulder Deposits in the Aran Islands, Ireland

Coastal boulder deposits (CBD) are wave-emplaced supratidal accumulations that record extreme inundation on rocky coasts. They are poorly understood but are of growing importance as we seek to better understand the extremes of wave power on coastlines. The Aran Islands, Ireland, host CBD in varying settings ranging from sheer cliff tops to wide shore platforms, and at elevations to about 40 m above sea level. Deposits are known to be active during strong storm events and provide a unique opportunity to examine relationships between wave energy, setting, and CBD occurrence. We use topographic elevation (Z) and offshore 100-years significant wave height (Hs,100) to calculate a dimensionless elevation Z* = Z/Hs,100 at 25 m intervals all along the Atlantic-facing coasts of the Aran Islands, and record whether CBD were present or absent at each location. The data reveal universal CBD presence at locations with low dimensionless elevations and near-monotonic decreasing frequency of CBD occurrence as Z* increases. On the Aran Islands, CBD are restricted to locations with Z*&amp;lt;3.13. For high elevation deposits it appears that unresolved local factors may be the major determinants in whether CBD will form. This approach can be applied at any CBD-bearing coastline and has the potential to change the way that we think about these deposits. Evaluation of dimensionless elevations at CBD locations around the world will help build broader understanding of the impact local shoreline conditions have on CBD formation. Determining these relationships contributes to the ongoing need to better understand interactions between extreme waves and rocky coasts.

Field Measurements of a High-Energy Headland Deflection Rip Current: Tidal Modulation, Very Low Frequency Pulsation and Vertical Structure

Headland rips, sometimes referred to as boundary rips, are rip currents flowing against natural or artificial obstructions extending seaward from the beach, such as headland or groynes. They can be driven either by the deflection of the longshore current against the obstacle or by alongshore variation in breaking wave height due to wave shadowing in the lee of the obstacle. The driving mechanism therefore essentially depends on the angle of wave incidence with respect to the natural or artificial obstruction. We analyze 42 days of velocity profile measurements against a natural headland at the high-energy meso-macrotidal beach of Anglet, southwest France. Measurements were collected in 6.5–10.5-m depth as tide elevation varied, during the autumn–winter period with offshore significant wave height and period ranging 0.9–6 m and 8–16 s, respectively, and the angle of wave incidence ranging from −20 ∘ to 20 ∘ . Here we analyze deflection rip configurations, corresponding to approximately 24 days of measurements, for which the current meter was alternatively located in the rip neck, rip head or away from the rip as wave and tide conditions changed. Deflection rips were associated with large offshore-directed velocities (up to 0.6 m/s depth-averaged velocities) and tide modulation for low- to moderate-energy waves. The vertical profile of deflection rips was found to vary from depth-uniform in the rip neck to strongly depth-varying further offshore in the rip head with maximum velocities near the surface. Very low frequency motions of the rip were dramatic, ranging 10–60 min with a dominant peak period of approximately 40 min, i.e., with longer periods than commonly reported. The strong offshore-directed velocities measured well beyond the surf zone edge provide new insight into deflection rips as a dominant mechanism for water and sediment exchanges between embayed (or structurally-controlled) beaches and the inner-shelf and/or the adjacent embayments.

Assessing coastal hazard from extreme storms with a phase resolving wave model: Case study of Narragansett, RI, USA

Coastal hazard at the residential scale, resulting from the combined effects of storm surge and waves including dynamic set-up and wave runup, is assessed for the local 100-year Synthetic Design Storm (SDS) in Narragansett, RI, USA, based on high resolution (2 m) simulations with the nonlinear phase-resolving Boussinesq wave model FUNWAVE. The accuracy of wave-flow-structure interaction modeling is improved using a built-up DEM, defined by adding coastal structures to the bare-earth DEM. In addition, bathymetry and topography are modified to reflect post-storm conditions based on simulating the same storm with the morphodynamic model XBeach. Comparisons of FUNWAVE results with those of the phase-averaged model STWAVE, for the same storm conditions, show that including individual wave effects increases the inundated area by 13% and maximum water levels (TWL) across the shoreline by 11%, in average; however, in high runup areas (such as along exposed structures), the predicted maximum water levels can increase by up to 100%. FUNWAVE predicts maximum runups on the order of ∼1.5Hs (with Hs the offshore significant wave height), which is consistent with empirical formulae for steep seawalls (Van der Meer, 2002), and these occur at the most exposed structures, which historical records show have been periodically damaged by large storms. The maximum momentum forces predicted by FUNWAVE are much larger than those derived from STWAVE simulations (based on linear wave theory and assuming Rayleigh distributed waves), and also occur on the most exposed structures. The study provides a quantitative assessment of the local coastal hazard associated with the selected SDS at the scale of individual structures, and stresses the importance of accurately modeling individual wave effects, runups and associated forces in coastal hazard assessment modeling studies.

Lidar Observations of the Swash Zone of a Low-Tide Terraced Tropical Beach under Variable Wave Conditions: The Nha Trang (Vietnam) COASTVAR Experiment

A field experiment was conducted at a tropical microtidal intermediate sandy beach with a low tide terrace (Nha Trang, Vietnam) to investigate the short-term swash-zone hydrodynamics and morphodynamics under variable wave conditions. Continuous 2D Lidar scanner observations of wave height at the lower foreshore, subsequent run-up and swash-induced topographic changes were obtained. These data were complemented by detailed real-time kinematic GPS topographic surveys. Variable wave and tide conditions were experienced during the field experiment with relatively large swell waves (offshore significant wave height, Hs = 0.9 m to 1.3 m; peak wave period, Tp = 8 to 12 s) concomitant with spring tides at the beginning of the period, followed by mild wind waves (offshore Hs under 0.5 m and Tp 5 s) and neap tides. This resulted in the following morphological sequence: berm erosion followed by rapid neap berm reformation and beach recovery within a few days. New insights into the link between intra-tidal swash dynamics and daily beach profile evolution were found using the Lidar dataset. While waves directly cause morphology changes on a wave-by-wave basis, tidal levels were found to be a key factor in determining the morphological wave-effect (accretive or erosive) due to modulated interaction between surf and swash hydro-morphodynamics.

Runups of Unusual Size: Rogueness and Variability of Swash

AbstractThe occurrence of swash larger than those predicted by the Rayleigh distribution is examined using a phase‐resolved numerical model. Multiple realizations of spectral boundary conditions and beach configurations are considered in the analysis. Planar beaches characterized by surf similarity parameters between 0.3 and 0.6 are found to be more likely to produce unusually large swash. Maximum runup is found to correlate with the maximum infragravity (IG) wave height at the location of swash initiation, the landwardmost continuously wet point. The analysis is extended to beaches with bilinear profiles, where the foreshore slope is steeper than the shoaling slope. It is found that the still water level plays a controlling role in the magnitude of large swash. For these beaches it is found that the still water level with respect to the beach toe influences both the IG and shortwave height at swash initiation. Similar to the planar beach case, swash is found to be maximized when the sum of both IG and shortwave height is maximum; this occurs at toe depths 2–3 times the offshore significant wave height.

Flows over crescentic bars under control of wave energy

Crescentic bars with wavelengths of 250–450 m were observed on a micro-tidal, open coast (Anmok Beach, Korea) to unravel the flow patterns over them under various wave conditions. The horn and bay environments of the crescents were distinguished to measure respective near-bottom flow conditions in the nearshore 3–8 m deep. Offshore waves were measured at a station about 18 m deep. The measurement duration spanned approximately one winter month and two stormy spells of several days each in summer and another winter comprising three different field campaigns. In addition, bar morphologies were measured with single- and multi-beam echo-sounders before and after each hydrodynamic measurement. Winter-storm waves yielded discernable bar movements offshore accompanied by a merging of small bays into a larger one. During the field campaigns, the bars moved alongshore by far less than a half of their wavelength. Hydrodynamic measurements show a suite of the flow patterns including onshore and offshore uniform flows and rip cell circulations. The flow patterns depend exclusively on the offshore significant wave height (Hs), or a non-dimensional parameter $$ {\mathrm{H}}_{\mathrm{p}}={H}_s\sqrt{\tan \theta }/{h}_c $$, where hc is the water depth of the bar crest and tanθ the slope gradient. Therefore, the specific ranges of Hp could be given to individual flow patterns measured. These results are used to illustrate a coupled behavior of the bars and flows in a beach-state cycle forced by varying wave energies.

Nonstationary joint probability analysis of extreme marine variables to assess design water levels at the shoreline in a changing climate

In the present study, a recently developed novel approach (Bender et al. in J Hydrol 514:123–130, 2014) has been further extended to investigate the changes in the joint probabilities of extreme offshore and nearshore marine variables with time and to assess design the total water level (TWL) at the shoreline under the effects of climate change. The nonstationary generalised extreme value (GEV) distribution has been utilised to model the marginal distribution functions of marine variables (wave characteristics and sea levels), within a 40-year moving window. All parameters of the GEV were tested for statistically significant linear and polynomial trends over time, and best-fitted trends have been detected. Different copula functions were fitted at the 40-year moving windows, to model the dependence structure of extreme offshore significant wave heights and peak spectral periods, and of wave-induced sea levels on the shoreline and nearshore sea levels due to storm surges. The most appropriate bivariate models were then selected. Statistically significant polynomial trends were detected in the dependence parameters of the selected copulas, and time-dependent most likely bivariate events were extracted to be used in the estimation of the TWL at the shoreline. The methods of the present work were implemented in three selected Greek coastal areas in the Aegean Sea. The analysis revealed different variations in the most likely estimates of the offshore wave characteristics and nearshore storm surges in the three study areas, as well as in the time-dependent estimates of TWL at the shoreline. The approach combines nonstationarity and bivariate analysis, blends coastal and offshore marine features and finally provides non-trivial alterations in the response of coastal sea level dynamics to climate change signals, compared to former work on the subject. The methodology produces reasonable estimates of design quantities for coastal structures and boundary conditions for the assessment of flood hazard and risk in coastal areas.

Physical and Numerical Modeling of Infragravity Wave Generation and Transformation on Coral Reef Platforms

AbstractWave transformation across reef platforms strongly controls sediment transport processes and coral reef island morphodynamics with infragravity (IG) waves playing an important contributing role. A small‐scale (1:50) laboratory experiment and prototype numerical modeling are used to explore the characteristics of IG wave motion on coral reefs. The slope of the fore reef is the key factor controlling the mechanism of IG wave generation. Steep slopes (&gt;1/10) are dominated by landward and seaward propagating breakpoint‐forced long waves, whereas incoming and then released bound long waves become increasingly important for slopes &lt;1/20. The breakpoint‐forced long wave mechanism is the more effective generator of IG energy, and the most energetic IG motion (normalized by incident wave motion) is generated on reef platforms with a fore reef slope &gt; 1/6. The water level relative to the reef platform hreef is also a key factor, and the largest IG waves are generated for a ratio between hreef and offshore significant wave height Hs,o of −0.25 to 0.75, that is, when most waves break across the reef slope and a fully saturated surf zone extends across the reef platform. An island on the reef platform substantially increases the contribution of IG waves to the total wave spectrum, but increased reef surface roughness reduces IG importance. Under the most optimal conditions, the IG wave height averaged across the platform is 20–30% of the incident offshore wave height. The geomorphic influence of IG waves is considered most significant for reef platforms with energetic waves breaking on the steepest fore reefs.

Wave Runup Over Steep Rocky Cliffs

AbstractWave runup is known to depend on offshore wave conditions and coastal morphology. While most field studies on wave runup have focused on low‐to‐mild‐sloping sandy beaches, runup measurements on steep and irregular rocky cliff profiles are still very scarce. Here we investigate the physical processes controlling wave runup in such environments and the range of applicability of empirical runup formula. This study focuses on the steep rocky cliffs (0.1 &lt; tanβ &lt; 0.4) of Banneg Island, a small island located in the Molène archipelago, Brittany, France, occasionally flooded during extreme water level events. A statistical parameter for extreme runup is derived from the measurements of pressure sensors deployed in the intertidal zone. Deep water wave parameters are used to force a high‐resolution wave model, and nearshore wave parameters and high‐resolution topographic data are analyzed concurrently with runup time series in order to assess the dependence of the runup on hydrodynamic conditions and morphological parameters. The wave runup is shown to be strongly related to the square root of the offshore significant wave height times the offshore wavelength. The measurements also reveal the depth dependence of the runup, which is mainly attributed to the curvature of the foreshore profile. In comparison to empirical relation obtained for a mild‐sloping beach, the present data show a significant reduction in normalized wave runup, that is attributed to enhanced bottom friction over the rocky bottom.

Tidal Flow Asymmetry Owing to Inertia and Waves on an Unstratified, Shallow Ebb Shoal

AbstractObservations of water levels, waves, currents, and bathymetry collected for a month at an unstratified tidal inlet with a shallow (1 to 2 m deep) ebb shoal are used to evaluate the asymmetry in flows and dynamics owing to inertia and waves. Along‐channel currents ranged from −1.5 to 0.6 m/s (positive inland) inside the main (3 to 5 m deep) channel crossing the ebb shoal. Net discharge is negligible, and ebb dominance of the channel flows is owing to inflow and outflow asymmetries near the inlet mouth. Offshore wave heights ranged from 0.5 to 2.5 m. During moderate to large wave events (offshore significant wave heights &gt;1.2 m), wave forcing enhanced onshore mass flux near the shoal edge and inside the inlet, leading to reduced ebb flow dominance. Momentum balances estimated with the water depths, currents, and waves simulated with a quasi 3‐D numerical model reproduce the momentum balances estimated from the observations reasonably well. Both observations and simulations suggest that ebb‐dominant bottom stresses are balanced by the ebb‐dominant pressure gradient and the tidally asymmetric inertia, which is a sink (source) of momentum on flood (ebb). Simulations with and without waves suggest that waves drive local and nonlocal changes in the water levels and flows. Specifically, breaking waves at the offshore edge of the ebb shoal induce setup and partially block the ebb jet (local effects), which leads to a more onshore‐directed mass flux, changes to the advection across the ebb shoal, and increased water levels inside the inlet mouth (nonlocal effects).

Irregular wave runup statistics on plane beaches: Application of a Boussinesq-type model incorporating a generating–absorbing sponge layer and second-order wave generation

Efficient absorption of reflected waves at the offshore boundary is a prerequisite for the accurate physical or theoretical modelling of long-duration irregular wave runup statistics at uniform, gently sloped beaches. This paper presents an implementation of the method suggested by Zhang et al. (2014) to achieve reflected wave absorption and simultaneous generation and propagation of incident waves in an existing numerical wave flume incorporating a moving boundary wavemaker. A generating–absorbing layer is incorporated within this 1DH hybrid Boussinesq-nonlinear shallow water equation model such that inshore-travelling incident waves, encompassing bound-wave structure approximately correct to second order, propagate unhindered while offshore-travelling reflected waves are absorbed. Once validated, the method is used to compile random wave runup statistics on uniform beach slopes broadly representative of dissipative, intermediate, and reflective beaches. Analyses of the individual runup time series, ensemble statistics and comparison to an empirical formula based on experimental runup data suggest that the main aspects of runup observed in the field are properly represented by the model. Existence of an upper limit on maximum runup is investigated using a simple extreme-value statistical analysis. Spectral saturation is examined by considering ensemble-averaged swash spectra for three representative beach slopes subject to incident waves with two different offshore significant wave heights. All spectra show f−4 roll-off at high frequencies in agreement with many previous field studies. The effect is also investigated of the swash motions preceding one particular extreme runup event on the eventual maximum runup elevation.