A theoretical model is developed for wave heights and set-up in a surf zone. In the time averaged equations of energy and momentum the energy flux, radiation stress and energy dissipation are determined by simple approximations which include the surface roller in the breaker. Comparison with measurements shows good agreement. Also the transitions immediately after breaking are analysed and shown to be in accordance with the above mentioned ideas and results.

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Wave Heights and Set-up in a Surf Zone

Sea-level rise (SLR) is predicted to elevate water depths above coral reefs and to increase coastal wave exposure as ecological degradation limits vertical reef growth, but projections lack data on interactions between local rates of reef growth and sea level rise. Here we calculate the vertical growth potential of more than 200 tropical western Atlantic and Indian Ocean reefs, and compare these against recent and projected rates of SLR under different Representative Concentration Pathway (RCP) scenarios. Although many reefs retain accretion rates close to recent SLR trends, few will have the capacity to track SLR projections under RCP4.5 scenarios without sustained ecological recovery, and under RCP8.5 scenarios most reefs are predicted to experience mean water depth increases of more than 0.5 m by 2100. Coral cover strongly predicts reef capacity to track SLR, but threshold cover levels that will be necessary to prevent submergence are well above those observed on most reefs. Urgent action is thus needed to mitigate climate, sea-level and future ecological changes in order to limit the magnitude of future reef submergence.

/pdf/loss-of-coral-reef-growth-capacity-to-track-future-increases-1c0h4ch2tx.pdf

Loss of coral reef growth capacity to track future increases in sea level

/pdf/infragravity-waves-from-driving-mechanisms-to-impacts-3f8467zr8m.pdf

Infragravity waves: From driving mechanisms to impacts

Many low-lying tropical islands are susceptible to sea level rise and often subjected to overwash and flooding during large wave events. To quantify wave dynamics and wave-driven water levels on fringing coral reefs, a 5 month deployment of wave gauges and a current meter was conducted across two shore-normal transects on Roi-Namur Island in the Republic of the Marshall Islands. These observations captured two large wave events that had waves with maximum heights greater than 6 m with peak periods of 16 s over the fore reef. The larger event coincided with a peak spring tide, leading to energetic, highly skewed infragravity (0.04–0.004 Hz) and very low frequency (0.004–0.001 Hz) waves at the shoreline, which reached heights of 1.0 and 0.7 m, respectively. Water surface elevations, combined with wave runup, reached 3.7 m above the reef bed at the innermost reef flat adjacent to the toe of the beach, resulting in flooding of inland areas. This overwash occurred during a 3 h time window that coincided with high tide and maximum low-frequency reef flat wave heights. The relatively low-relief characteristics of this narrow reef flat may further drive shoreline amplification of low-frequency waves due to resonance modes. These results (1) demonstrate how the coupling of high offshore water levels with low-frequency reef flat wave energetics can lead to large impacts along fringing reef-lined shorelines, such as island overwash, and (2) lend support to the hypothesis that predicted higher sea levels will lead to more frequent occurrences of these extreme events, negatively impacting coastal resources and infrastructure.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2015JC011231

Observations of wave transformation over a fringing coral reef and the importance of low‐frequency waves and offshore water levels to runup, overwash, and coastal flooding

https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/1365-2435.13247

Changing geo-ecological functions of coral reefs in the Anthropocene

Infragravity wave (IGW) transformation was quantified from field measurements on two shore platforms on New Zealand's east coast, making this the first study to describe the presence, characteristics and behaviour of IGWs on rock platform coasts. Data was collected using a cross-shore array of pressure transducers during a 22 hour experiment on Oraka shore platform and a 36 hour experiment at Rothesay Bay shore platform. A low pass Fourier filter was used to remove gravity wave frequency oscillations, allowing separate analysis of IGWs and the full wave spectrum. Offshore IGW heights were measured to be 7 cm (Oraka) and 9 cm (Rothesay Bay), which were 21% (Oraka) and 7.5% (Rothesay Bay) the height of incident wave height. At the cliff toe, significant IGW height averaged 15 cm at Oraka and 13 cm at Rothesay Bay. This increase in IGW height over the platform during both experiments is attributed to shoaling of 40 to 55% over the last 50–60 m before the cliff toe, respectively. Shoaling across the platform was quantified as the change in IGW height from the platform edge to cliff toe, resulting in a maximum increase of 1·88 and 2·63 on Rothesay Bay and Oraka platforms. IGW height at the cliff toe showed a strong correlation with incident wave height. The proportional increase in IGW height shows a strong correlation to water level on each platform. The rate of shoaling of long period waves on the shallow, horizontal platforms increased at higher water levels resulting in a super elevation in water level at the cliff toe during high tide. Greater IGW shoaling was also observed on the wider (Oraka) shore platform. Results from this study show the first measurements of IGWs on shore platforms and identify long wave motion a significant process in a morphodynamic understanding of rock coast. Copyright © 2011 John Wiley & Sons, Ltd.

Field observations of infragravity waves and their behaviour on rock shore platforms

The influence of sea swell (SS) waves, infragravity (IG) waves, and wave setup on maximum runup (Rmax) is investigated across different tidal stages on Fatato Island, Funafuti Atoll, Tuvalu. Field results illustrate that SS waves are tidally modulated at the shoreline, with comparatively greater wave attenuation and setup occurring at low tide versus high tide. A shoreward increase in IG wave height is observed across the 100 m wide reef flat at all tidal elevations, with no tidal modulation of IG wave height at the reef flat or island shoreline. A 1-D shock-capturing Green-Naghdi solver is used to replicate the field deployment and analyze Rmax. Model outputs for SS wave height, IG wave height and setup at the shoreline match field results with model skill >0.96. Model outputs for Rmax are used to identify the temporal window when geomorphic activity can occur on the beach face. During periods of moderate swell energy, waves can impact the beach face at spring low tide, due to a combination of wave setup and strong IG wave activity. Under mean wave conditions, the combined influence of setup, IG waves and SS waves results in interaction with island sediment at midtide. At high tide, SS and IG waves directly impact the beach face. Overall, wave activity is present on the beach face for 71% of the study period, a significantly longer duration than is calculated using mean water level and topographic data.

https://hal.archives-ouvertes.fr/hal-01443074/document

Wave transformation and shoreline water level on Funafuti Atoll, Tuvalu

We present new detail on how future SLR will modify nonlinear wave transformation processes, shoreline wave energy and wave driven flooding on atoll islands. Frequent and destructive wave inundation is a primary climate-change hazard that may render atoll islands uninhabitable in the near future. However, limited research has examined the physical vulnerability of atoll islands to future SLR and sparse information is available to implement process based coastal management on coral reef environments. We utilize a field-verified numerical model capable of resolving all nonlinear wave transformation processes to simulate how future SLR will modify wave dissipation and overtopping on Funafuti Atoll, Tuvalu, accounting for static and accretionary reef adjustment morphologies. Results show that future SLR coupled with a static reef morphology will not only increase shoreline wave energy and overtopping but will fundamental alter the spectral composition of shoreline energy by decreasing the contemporary influence of low frequency infragravity waves. ‘Business-as-usual' emissions (RCP 8.5) will result in annual wave overtopping on Funafuti Atoll by 2030, with overtopping at high tide under mean wave conditions occurring from 2090. Comparatively, vertical reef accretion in response to SLR will prevent any significant increase in shoreline wave energy and mitigate wave driven flooding volume by 72%. Our results provide the first quantitative assessment of how effective future reef accretion can be at mitigating SLR associated flooding on atoll islands and endorse active reef conservation and restoration for future coastal protection.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2017EF000589

Future Reef Growth Can Mitigate Physical Impacts of Sea-Level Rise on Atoll Islands

Increased flooding due to sea level rise (SLR) is expected to render reef islands, defined as sandy or gravel islands on top of coral reef platforms, uninhabitable within decades. Such projections generally assume that reef islands are geologically inert landforms unable to adjust morphologically. We present numerical modeling results that show reef islands composed of gravel material are morphodynamically resilient landforms that evolve under SLR by accreting to maintain positive freeboard while retreating lagoonward. Such island adjustment is driven by wave overtopping processes transferring sediment from the beachface to the island surface. Our results indicate that such natural adaptation of reef islands may provide an alternative future trajectory that can potentially support near-term habitability on some islands, albeit with additional management challenges. Full characterization of SLR vulnerability at a given reef island should combine morphodynamic models with assessments of climate-related impacts on freshwater supplies, carbonate sediment supply, and future wave regimes.

https://advances.sciencemag.org/content/advances/6/24/eaay3656.full.pdf

Coral reef islands can accrete vertically in response to sea level rise

Wave-driven flooding is a serious hazard on coral reef-fringed coastlines that will be exacerbated by global sea-level rise. Despite the global awareness of atoll island vulnerability, little is known about the physical processes that control wave induced flooding on reef environments. To resolve the primary controls on wave-driven flooding at present and future sea levels, we present a globally applicable method for calculating wave overtopping thresholds on reef coastlines. A unique dataset of 60,000 fully nonlinear wave transformation simulations representing a wide range of wave energy, morphology and sea levels conditions was analysed to develop a tool for exploring the future trajectory of atoll island vulnerability to sea-level rise. The proposed reef-island overtopping threshold (RIOT) provides a widely applicable first-order assessment of reef-coast vulnerability to wave hazards with sea-level. Future overtopping thresholds identified for different atoll islands reveal marked spatial variability and highlight distinct morphological characteristics that enhance coastal resilience.

/pdf/predicting-wave-overtopping-thresholds-on-coral-reef-island-33z7lkmyrk.pdf

Edward Beetham

Papers

Field observations of infragravity waves and their behaviour on rock shore platforms

Wave transformation and shoreline water level on Funafuti Atoll, Tuvalu

Future Reef Growth Can Mitigate Physical Impacts of Sea-Level Rise on Atoll Islands

Coral reef islands can accrete vertically in response to sea level rise

Predicting wave overtopping thresholds on coral reef-island shorelines with future sea-level rise