The importance of explicitly modelling sea-swell waves for runup on reef-lined coasts

doi:10.1016/j.coastaleng.2020.103704

Coastal Engineering

Volume 160, September 2020, 103704

https://doi.org/10.1016/j.coastaleng.2020.103704 Get rights and content

Highlights

•
2D XBeach model of Roi-Namur Island was tested against field observations.
•
Both XB-SB and XB-NH modes reproduce key reef hydrodynamics with good skill.
•
XB-NH gives a better prediction of the wave runup because it resolves SS waves.
•
More extreme conditions and SLR increases difference in XB-SB and XB-NH runup.
•
For flooding, XB-SB may suffice and requiring 4–5 times less computational effort.

Abstract

The importance of explicitly modelling sea-swell waves for runup was examined using a 2D XBeach short wave-averaged (surfbeat, “XB-SB”) and a wave-resolving (non-hydrostatic, “XB-NH”) model of Roi-Namur Island on Kwajalein Atoll in the Republic of Marshall Islands. Field observations on water levels, wave heights, and wave runup were used to drive and evaluate both models, which were subsequently used to determine the effect of sea-level rise and extreme wave conditions on wave runup and its components. Results show that specifically modelling the sea-swell component (using XB-NH) provides a better approximation of the observed runup than XB-SB (which only models the time-variation of the sea-swell wave height), despite good model performance of both models on reef flat water levels and wave heights. XB-SB has a bias of −0.108 – 0.057 m and scatter index of 0.083–0.639, whereas XB-NH has bias of −0.132 – 0.055 m and 0.122–0.490, respectively. However, both models under-predict runup peaks. The difference between XB-SB and XB-NH increases for more extreme wave events and higher sea levels, as XB-NH resolves individual waves and therefore captures SS-wave motions in runup. However, for even larger forcing conditions with offshore wave heights of 6 m, the island is flooded in both XB-SB and XB-NH computations, regardless the sea-swell wave energy contribution. In such cases XB-SB would be adequate to model flooding depths and extents on the island while requiring 4–5 times less computational effort.

Introduction

Low-lying coral reef-lined islands are vulnerable to wave-driven overwash and flooding. These flooding events will become more frequent as sea level rises due to climate-change (Vitousek et al., 2017), and will threaten freshwater resources and infrastructure (Shimozono et al., 2015; Albert et al., 2016; Storlazzi et al., 2018). When taking into account the non-linear effects of sea-level rise (SLR) on wave-driven overwash, some low-lying islands may become uninhabitable in a few decades time (Storlazzi et al., 2015; Storlazzi et al., 2018).

Coral reef-lined atoll islands are typically fronted by a wide, shallow reef flat and a steep fore reef that dissipates open-ocean incoming wave energy through wave breaking and bottom friction (Monismith et al., 2013; Lowe et al., 2005). Wave breaking on the steep fore reef induces high radiation stress gradients, which results in significant wave-induced setup on the reef flat (Becker et al., 2014). Some of the dissipated sea-swell frequency-band (‘SS”, >0.04 Hz) wave energy is transferred to infragravity-band (‘IG’, 0.004–0.04 Hz) and very low frequency-band waves (‘VLF’, 0.001–0.004 Hz) through breakpoint forcing (Symonds et al., 1982) on the steep fore reef (Péquignet et al., 2009, 2014; Pomeroy et al., 2012). Resonant amplification of IG and/or VLF waves can occur when their energy is concentrated at the natural frequency of the reef flat, which is most likely to occur on smooth reefs, with increasing water depth, high SS wave periods and specific reef dimensions (Péquignet et al., 2009, 2014; Gawehn et al., 2016).

The complex interaction between tides, surge, wave-induced setup, SS waves, IG waves, and VLF waves drive runup and subsequent island flooding. To date, few runup field observations have been collected on coral reef-lined beaches (Rueda et al., 2019), as opposed to the more frequently documented measurements of water levels and wave transformation across the reef at the toe of the beach. Similarly, wave runup on a reef profile has been measured in relatively few laboratory flume experiments (e.g. Nwogu and Demirbilek, 2010; Buckley et al., 2015, 2018).

The combination of numerical models with field or laboratory experiments can improve understanding of the effects of sea level rise and extreme events on coral reef hydrodynamics. Recent research has been mainly focused on modelling one-dimensional (1D) wave and water level transformation along a cross-shore transect (Pomeroy et al., 2012; Van Dongeren et al., 2013; Quataert et al., 2015; Beetham et al., 2016), wave runup (Nwogu and Demirbilek, 2010; Yao et al., 2012;Shimozono et al., 2015; Beetham et al., 2016; Pearson et al., 2017; Lashley et al., 2018) and overtopping (Beetham and Kench, 2018). Application of a two-dimensional horizontal (2DH) model on coral-reef lined coasts has been limited (Van Dongeren et al., 2013; Roeber and Bricker, 2015; Torres-Freyermuth et al., 2012; Beetham et al., 2018), despite the additional information it provides on the alongshore variation of nearshore hydrodynamics, flooding depths and extents in the coastal area. In 1D (cross-shore profile) models, the assumption of alongshore-uniform hydrodynamics limits the ability of the model to describe wave directional spreading, with implications for the transfer of energy to the IG-band (e.g., Guza and Fedderson, 2012). The implication of this is that the generation of IG wave energy is mostly overestimated in 1D models relative to 2D models and needs to be balanced by higher frictional dissipation (Van Dongeren et al., 2013).

The objective of this study is to study the importance of directionally spread SS wave motions on wave runup at reef-lined coasts typically characterized by steep beaches, using a short wave-averaged model (XB-SB, which does not include sea-swell motions) and a wave-resolving model (XB-NH which includes sea-swell motions) in 2D mode. Our study uses field observations of water levels, wave heights, and wave runup to drive and evaluate both models, which are subsequently used to determine the effect SLR and extreme wave conditions on wave runup and its components in coral reef environments.

Section snippets

Site description and observations

The study site is Roi-Namur Island located on the northern side of Kwajalein Atoll in the Republic of Marshall Islands (Fig. 1). Roi Namur has a fringing reef that is characterized by a relatively smooth platform that ranges from 250 to 350 m wide. A narrow, steep, sandy beach (~1:6 slope) borders the island. The reef crest is emergent at spring low tides; offshore of it the steep (~1:20 slope) fore reef extends down to 25 m water depth and is characterized by a rough surface due to high coral

Field data for model calibration and validation

Wave and water-level data came from a series of tide/wave gauges deployed along two shore-normal profiles; see Cheriton et al. (2016) for a description of the sensors, data sampling, and data processing. Observations of maximum wave runup were collected by two shore-based digital time-lapse cameras located on the berm onshore of the NW and NE transects, taking photos every 31 min. On the beach, five rocks at fixed locations were marked (Fig. 2) and surveyed relative to mean sea level (‘MSL’) as

Runup observations

The observed z_max time series for the NW (Fig. 4c) and NE (Fig. 4d) transects include contributions from mean water levels (by tide and wave-induced setup) and contributions from SS, IG and VLF waves. The camera captured an instance of anomalously high runup at the NW transect on 17 November 2013 (Cheriton et al., 2016) at 16:17 GMT (Fig. 4a), during relatively mild offshore wave forcing (H_m0 = 1.9 m and T_p = 14 s). This event coincided with an instance of resonance (Gawehn et al., 2016),

Discussion

The results presented here indicate that explicitly modelling the sea-swell waves (with XB-NH) gives a better prediction of wave runup (Fig. 7) and that the difference between XB-SB and XB-NH increases for more extreme wave events and higher sea levels (Fig. 9). XB-NH captures SS-wave motions by utilizing a grid resolution high enough to completely resolve individual waves, but this comes at greater computational expense. However, the Roi-Namur case study shows that for even more extreme

Conclusions

Two modes of the XBeach model - which either explicitly model the sea-swell waves (XB-NH) or not (XB-SB) - are able to reproduce key reef hydrodynamics on an atoll reef and island with good skill, XB-SB with bias = −0.108 – 0.057 m, SCI = 0.083–0.639 and XB-NH with bias = −0.132 – 0.055 m, SCI = 0.122–0.490, but under-predict runup peaks. XB-NH was found to give a better prediction of the wave runup because it fully resolves SS wave motions. The observed extreme runup event was not reproduced

CRediT authorship contribution statement

Ellen Quataert: Methodology, Investigation, Writing - original draft, Software. Curt Storlazzi: Conceptualization, Methodology, Writing - review & editing. Ap van Dongeren: Methodology, Writing - review & editing. Robert McCall: Methodology, Writing - review & editing, Software.

Declaration of competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

Funding for this research was provided by the U.S. Department of Defense’s Strategic Environmental Research and Development Program under Project RC-2334 (“The Impact of Sea-Level Rise and Climate Change on Department of Defense Installations on Atolls in the Pacific Ocean”), the U.S. Geological Survey’s Pacific Coastal and Marine Science Center, and through Deltares Strategic Research in the “Quantifying Flood Hazards and Impacts” program (11203750). Any use of trade, firm, or product names is

References (41)

R.K. Hoeke et al.
Widespread inundation of Pacific islands triggered by distant-source wind-waves
Global Planet. Change
(2013)
C. Lashley et al.
Nonhydrostatic and surfbeat model predictions of extreme wave run-up in fringing reef environments
Coast Eng.
(2018)
R. McCall et al.
Modelling storm hydrodynamics on gravel beaches with XBeach-G
Coast. Eng.
(2014)
D. Roelvink et al.
Improving predictions of swash dynamics in XBeach: the role of groupiness and incident-band runup
Coast Eng.
(2018)
A. Rueda et al.
HyCReWW: a hybrid coral reef wave and water level metamodel
Comput. Geosci.
(2019)
A.R. Van Dongeren et al.
Numerical modeling of low-frequency wave dynamics over a fringing coral reef
Coast Eng.
(2013)
Y. Yao et al.
1DH Boussinesq modeling of wave transformation over fringing reefs
Ocean Eng.
(2012)
S. Albert et al.
Interactions between sea-level rise and wave exposure on reef island dynamics in the Solomon Islands
Environ. Res. Lett.
(2016)
J.M. Becker et al.
Water level effects on breaking wave setup for Pacific Island fringing reefs
J. Geophys. Res. Oceans
(2014)
E. Beetham et al.
Predicting wave overtopping thresholds on coral reef-island shorelines with future sea-level rise
Nature Communications
(2018)

E. Beetham et al.

Wave transformation and shoreline water level on Funafuti Atoll

Tuvalu. J. Geophys. Res. Oceans

(2016)

E. Beetham et al.

Model skill and sensitivity for simulating wave processes on coral reefs using a shock-capturing Green-Naghdi solver

J. Coast Res.

(2018)

M.L. Buckley et al.

Dynamics of wave setup over a steeply sloping fringing reef

J. Phys. Oceanogr.

(2015)

M.L. Buckley et al.

Mechanisms of wave-driven water level variability on reef-fringed coastlines

J. Geophys. Res.: Oceans

(2018)

O.M. Cheriton et al.

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

J. Geophys. Res.: Oceans

(2016)

De Beer, A.F., R.T. McCall, J.W. Long, M.F.S. Tissier and A.J.H.M. Reniers (in press). Simulating Wave Runup on an...

Z. Demirbilek et al.

Laboratory study of wind effect on runup over fringing reefs

Report 1. Data Report

(2007)

M. Gawehn et al.

Identification and classification of very low frequency waves on a coral reef flat

J. Geophys. Res. Oceans

(2016)

R. Guza et al.

Effect of wave frequency and directional spread on shoreline runup

Geophys. Res. Lett.

(2012)

R.J. Lowe et al.

Spectral wave dissipation over a barrier reef

J. Geophys. Res.

(2005)

Cited by (26)

Improved efficient physics-based computational modeling of regional wave-driven coastal flooding for reef-lined coastlines
2024, Ocean Modelling
Coastal flooding affects low-lying communities worldwide and is expected to increase with climate change, especially along reef-lined coasts, where wave-driven flooding is particularly prevalent. However, current regional modeling approaches are either insufficient or too computationally expensive to accurately assess risks in these complex environments. This study introduces and validates an improved computationally efficient and physics-based approach to compute dynamic wave-driven regional flooding on reef-lined coasts. We coupled a simplified-physics flood model (SFINCS) with a one-dimensional wave transformation model (XBeach-1D). To assess the performance of the proposed approach, we compared its results with results from a fully resolving two-dimensional wave transformation model (XBeach-2D). We applied this approach for a range of storms and sea-level rise scenarios for two contrasting reef-lined coastal geomorphologies: one low relief area and one high relief area. Our findings reveal that SFINCS coupled with XBeach-1D generates flood extents comparable to those produced by XBeach-2D, with a hit rate of 92%. However, this method tends to underpredict the flood extent of weaker, high-frequency storms and overpredict stronger, low-frequency storms. Across scenarios, our approach overpredicted the mean flood water depth, with a positive bias of 7 cm and root mean square difference of 15 cm. Offering approximately 100 times greater computational efficiency than its two-dimensional XBeach counterpart, this flood modeling technique is recommended for wave-driven flood modeling in scenarios with high computational demands, such as modeling numerous scenarios or undertaking detailed regional-scale modeling.
An efficient metamodel to downscale total water level in open beaches
2024, Estuarine, Coastal and Shelf Science
A hybrid methodology is described to obtain the wave set-up and infragravity wave level components for estimating total water level (TWL) in coastal areas, taking into account the surf zone hydrodynamics involved. By combining statistical tools and numerical methods, high-resolution spatial distributions of wave height and water level components are calculated efficiently and seamlessly. The proposed methodology is tested and numerically validated on La Salvé beach (Cantabria, Spain), showing a robust performance for diverse scenarios. The resulting TWL can efficiently evaluate coastal hazards in forecast and hindcast mode, having strong potential as a guideline for coastal engineers, managers and emergency planners in the elaboration of adaptation and mitigation strategies. As an application of the metamodel to these coastal management tasks, significant past storm events have been reconstructed, and their associated TWL-driven coastal flooding hazard has been analyzed using a impact rank scale.
A review of the vulnerability of low-lying reef island landscapes to climate change and ways forward for sustainable management
2024, Ocean and Coastal Management
Low-lying small island states whose existence is a product of sediment production from their surrounding reefs are highly vulnerable landscapes to climate change. This vulnerability derives from their low elevation and their evolutionary reliance on growth on the surrounding reef for the creation of materials from which land can form above the sea. They are also exposed to a range of climatic boundary conditions (e.g. tropical cyclones) which vary in intensity with distance from the equator. The diversity of energy environments, evolutionary history, sea level history and local ecology means reef-islands have unique characteristics (sediments and topography) that vary both within individual atolls as well as along island chains. It is also clear the majority of islands today have continued to accrete in the last century. Such development has led to suggestions that islands may be less vulnerable to sea level rise than suggested by their elevation alone. Vulnerability of an island system, however, does not equate to sustainable human occupation. In addition, projected rates of sea level rise will exceed that experienced in the last century. For understanding the stability of reef-island systems it is therefore imperative for managers to be fully cognisant of the principle drivers of island evolution, their modern dynamics and future sea level trends. In this paper, a review is undertaken of the principle physical elements, and methods to investigate them, that are a priority for quantifying when conducting an integrated assessment of the physical landscape of small island states. Advances in remotely operated vehicles combined with simple sedimentological techniques (e.g. visual grain identification) mean it is now possible for local managers to collect key information necessary for protecting their islands and, if needed, the data can be used for numerical models of island change.
Modeling hurricane wave propagation and attenuation after overtopping sand dunes during storm surge
2024, Ocean Engineering
Sand dunes are natural features providing protection to coastal communities against waves from extreme events such as hurricanes. In this study, the non-hydrostatic XBeach model (XBNH) was validated and applied to investigate wave propagation, breaking, and overtopping sand dunes in the coastal zone during various stages of the storm surge in Mexico Beach, Florida during Hurricane Michael (a Category 5 hurricane). Results indicate that, as storm surge rises and stronger waves propagate towards inland, waves break near the foot of the sand dunes, overtop the dunes, and then substantially attenuate toward the communities established behind the dunes. Sand dunes effectively reduce wave heights with a minimum reduction rate of 35% at peak storm surge and 91% reduction at upper rising surge stage. Maximum wave height and dune erosion rate occur around the peak storm surge stage. Model validations show that the non-hydrostatic model is more accurate than the hydrostatic model (XBSB). For significant wave height, the average error is 2.44% from XBNH in comparison with the 16.92% error from XBSB. The maximum error for the peak water surface elevation is 3.48% for XBNH verse the 5.39% for XBSB.
2DH modelling and mapping of surfbeat-driven flooding in the shadow of a jettied tidal inlet
2023, Coastal Engineering
Near estuaries and harbours, submerged shoals and defence structures impact the exposure to overtopping. These features may be accounted for in two-dimensional horizontal (2DH) numerical models, either based on phase-resolving or phase-average solvers for wave propagation. In between, surfbeat solvers, such as in XBeach, combine an affordable computational cost with the ability to generate and propagate the longer infragravity (IG) waves. However, surfzone wave characteristics and the overtopping exposure modelled with XBeach are sensitive to settings such as the shape of the forcing wave spectra and the numerical scheme for wave propagation. The present paper explores this sensitivity and assesses the performance of different inundation models built with the 2DH surfbeat solver of XBeach. These models were forced with downscaled water levels and directional wave spectra and the results fuelled a discussion bounded by data collected downdrift of the entrance to the harbour of Figueira da Foz (Portugal). The original second-order upwind scheme, which propagates short-waves with a lower numerical diffusion improved the model performance in terms of long-wave height, and an unconventional breaking criterion better represented the cross-shore distribution of short-wave height near the shore. A calibrated model was validated through the hindcast of an overtopping event observed under moderate swell forcing, and was used to map the overtopping exposure during a hypothetical combination of an energetic swell with a water level having a return period of ∼70 years. Compared to the default wave spectra shape and model settings, using an appropriate representation of the short-wave directional spectrum at the open boundary was necessary to reproduce the observed overtopping extent. Refining the cross-shore resolution of the model helped to better represent the observed inundation extents, as also did the reduction of the friction coefficient. Additional phase-resolving simulations in 1DH overestimated IG wave energy and produced higher and more frequent overtopping discharges. The differences with the calibrated 2DH surfbeat model increased with the proximity of the inlet and with short-wave height and angle of incidence. Overall, required calibration steps were provided. They aim at making 2DH XBeach surfbeat a credible tool for 1) predicting short and IG wave characteristics up to the shoreline, as well as for 2) providing first estimates of exposure to overtopping in areas with shallow and alongshore-irregular morphologies.
Explicit wave-runup formula for beaches fronted by coral reefs using tree-based models
2023, Coastal Engineering
Fast and accurate estimation of wave runup is needed for coral-reef islands, but most of the existing formulae are not applicable in this context. Tree-based models were applied to the comprehensive numerical database of Pearson et al. (J. Geophys. Res. Oceans. 122, 10099–10117) to identify the essential predictor parameters for runup in coral-reef environments and classify different runup regimes on which a set of runup formulae was developed. It was found that, wave conditions, reef roughness, and reef-flat length are generally crucial for predicting runup, while the importance of forereef and beach slopes depends on the relative reef submergence (reef submergence normalized by off-reef wave height). The forereef slope is more important than the beach slope when waves mainly break over the forereef at low relative reef submergences but less important when waves mainly break over the reef flat and the beach at middle and high relative reef submergences. The proposed formula set was validated against data from laboratory and field coral reefs, which implies that the formula set has the potential for fast prediction of runup along coral-reef islands at broad scales for flooding assessment.

View all citing articles on Scopus

View full text

The importance of explicitly modelling sea-swell waves for runup on reef-lined coasts

Highlights

Abstract

Introduction

Section snippets

Site description and observations

Field data for model calibration and validation

Runup observations

Discussion

Conclusions

CRediT authorship contribution statement

Declaration of competing Interest

Acknowledgements

Global Planet. Change

Coast Eng.

Coast. Eng.

Coast Eng.

Comput. Geosci.

Coast Eng.

Ocean Eng.

Interactions between sea-level rise and wave exposure on reef island dynamics in the Solomon Islands

Environ. Res. Lett.

Water level effects on breaking wave setup for Pacific Island fringing reefs

J. Geophys. Res. Oceans

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

Nature Communications

Wave transformation and shoreline water level on Funafuti Atoll

Tuvalu. J. Geophys. Res. Oceans

Model skill and sensitivity for simulating wave processes on coral reefs using a shock-capturing Green-Naghdi solver

J. Coast Res.

Dynamics of wave setup over a steeply sloping fringing reef

J. Phys. Oceanogr.

Mechanisms of wave-driven water level variability on reef-fringed coastlines

J. Geophys. Res.: Oceans

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

J. Geophys. Res.: Oceans

Laboratory study of wind effect on runup over fringing reefs

Report 1. Data Report

Identification and classification of very low frequency waves on a coral reef flat

J. Geophys. Res. Oceans

Effect of wave frequency and directional spread on shoreline runup

Geophys. Res. Lett.

Spectral wave dissipation over a barrier reef

J. Geophys. Res.