Marine Pollution Bulletin xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

Marine Pollution Bulletin journal homepage: www.elsevier.com/locate/marpolbul

Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs T.E. Baldock a,⇑, A. Golshani a, D.P Callaghan a, M.I. Saunders b,c, P.J. Mumby b a

School of Civil Engineering, University of Queensland, St Lucia, Qld 4072, Australia Marine Spatial Ecology Lab, School of Biological Sciences, University of Queensland, St Lucia, Qld 4072, Australia c Global Change Institute, University of Queensland, St Lucia, Qld 4072, Australia b

a r t i c l e

i n f o

Keywords: Reef top wave dynamics Sea level rise Wave forces Reef bathymetry Coral health

a b s t r a c t A one-dimensional wave model was used to investigate the reef top wave dynamics across a large suite of idealized reef-lagoon profiles, representing barrier coral reef systems under different sea-level rise (SLR) scenarios. The modeling shows that the impacts of SLR vary spatially and are strongly influenced by the bathymetry of the reef and coral type. A complex response occurs for the wave orbital velocity and forces on corals, such that the changes in the wave dynamics vary reef by reef. Different wave loading regimes on massive and branching corals also leads to contrasting impacts from SLR. For many reef bathymetries, wave orbital velocities increase with SLR and cyclonic wave forces are reduced for certain coral species. These changes may be beneficial to coral health and colony resilience and imply that predicting SLR impacts on coral reefs requires careful consideration of the reef bathymetry and the mix of coral species. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Reefs protect the shore of many tropical islands and beaches from waves, and also provide valuable ecosystem services and economic benefits (Moberg and Folke, 1999). Many of the physical and biological processes on coral reefs are strongly dependent on the reef top hydrodynamics, which control flushing, mixing processes and nutrient supply, and govern destructive forces under extreme conditions. The effective assessment and management of reefs as ecological, social and economic resources requires the ability to assess how these physical and biological processes will be impacted by climate change. The potential impacts of climate change, including sea-level rise (SLR) and the mortality of coral during warm conditions (Hoegh-Guldberg et al., 2011), may reduce the effectiveness of fringing and barrier reefs as protection for islands, and directly change the hydrodynamics, nutrient supply and forces on reefs and corals (Sheppard et al., 2005; Webb and Kench, 2010; Perry et al., 2011; Storlazzi et al., 2011; Grady et al., 2013). This paper investigates the effects of SLR on the physical hydrodynamic processes occurring on barrier coral reefs. We ask how current reef environments may change as water depths change over reefs, and which reef bathymetries and zones are likely ⇑ Corresponding author. Tel.: +61 7 33469432; fax: +61 7 33654599. E-mail addresses: [email protected] (T.E. Baldock), [email protected] (A. Golshani), [email protected] (D.P Callaghan), [email protected] (M.I. Saunders), [email protected] (P.J. Mumby).

to experience the greatest changes. Modifications to the present environment by SLR could have significant impacts on the functioning of coral reefs. Firstly, wave-orbital velocities underpin the rate at which essential dissolved gases (e.g., oxygen, carbon dioxide) and nutrients are both delivered to and removed from benthic organisms (Monismith, 2007). Such fluxes play an important role in driving primary production in corals (Jokiel, 1978; Tribble et al., 1994), algal turfs (Carpenter and Williams, 1993, 2007), and fleshy algae (Renken et al.. 2010). Flow can also influence the response of corals to thermal stress either by influencing the rate of temperature rise directly, through increased mixing between surface and cooler, deeper waters (Skirving et al., 2006), or potentially by reducing the risk of local anoxia that can cause coral mortality (Wangpraseurt et al., 2012). Wave action also plays a key role in damaging or dislodging corals, particularly during storm conditions (Massel and Done, 1993; Storlazzi et al., 2005; Madin and Connolly, 2006). SLR also potentially slows growth as reef flats become subject to erosion by larger waves (Buddemeier and Smith, 1988). Wave action additionally plays a role in overall reef surface geomorphology, with reef width and depth controlling changes in geomorphology (Kench and Brander, 2006). The interaction of these multiple processes suggests the potential for feedback between the biological and physical processes. A number of recent studies (Grinsted et al., 2009; Merrifield et al., 2009) point out that not only is global sea level rising, but the rate is increasing in response to global climate change.

http://dx.doi.org/10.1016/j.marpolbul.2014.03.058 0025-326X/Ó 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058

2

T.E. Baldock et al. / Marine Pollution Bulletin xxx (2014) xxx–xxx

Syntheses by Grinsted et al. (2009) and Nicholls and Cazenave (2010) suggest that global mean sea level in 2100 may exceed the 2000 level by two times the average IPCC (2007) projection of approximately 60 cm above 2000 levels (Storlazzi et al., 2011). The impact on coral reefs from predicted sea level rise has been addressed by number of studies (e.g. Graus and Macintyre, 1998; Sheppard et al., 2005; Ogston and Field, 2010; Storlazzi et al., 2011; Grady et al., 2013). SLR creates deeper water over reefs and lagoons, potentially allowing larger waves, with possibly a different wave period to that of the locally generated wind waves, to reach the leeward reef edge, reef lagoons and reef island shorelines. This may induce beach erosion, turbidity (Storlazzi et al., 2011) and greater damage to reefs under storm or cyclonic conditions as the forces exerted on the coral structure change, potentially leading to greater rates of breakage (Massel and Done, 1993) and an increase in the average depletion of coral populations (Mumby et al., 2011), increasing the vulnerability of reef islands and atolls (Roy and Connell, 1991; Khan et al., 2002). Buddemeier and Smith (1988) note that predicted rates of SLR are significantly greater than the maximum vertical accretion rates of coral reefs and therefore reefs are unlikely to keep up with SLR. Typical wave induced flows, in addition to currents, are governed by the particular morphology of the reef-lagoon itself, and subject to changes in wave climate (Lowe et al., 2009). However, in the absence of detailed knowledge of changes in wave climate, if any, we limit the modeling to investigate the impact of SLR only and therefore the results are not region specific. For deep and/or open lagoon systems, the wave dynamics are largely controlled by the morphology and physical roughness properties of the fore-reef and reef flat, and the morphology of the lagoon plays a minor role in the overall momentum dynamics (Gourlay and Colleter, 2005). In this case, the water depth over the reef flat determines the wave energy dissipation and is a controlling parameter for the wave dynamics (Sheppard et al., 2005, Madin and Connolly, 2006, Storlazzi et al., 2011). Further, wave conditions vary across the reef (e.g. Brander et al., 2004), with reef width and surface roughness also influencing wave dissipation, and therefore different reefs and their ecological process have varying – and context dependent – sensitivity to SLR. This paper studies the effects of SLR on the flow environment on coral reefs under both average and cyclonic climates (defined in Section 2). We use a wide range of barrier reef profiles and a 3rd generation wind-wave model to investigate and obtain insight into the sensitivity of the wave induced velocity and forces on branching and massive corals to SLR for different reef geomorphology and surface roughness. The changes in wave height, wave-orbital velocity and wave induced forces are presented and discussed in terms of their potential impacts on coral health. The paper is organized as follows. Section 2 presents an overview of the numerical model, together with the selected environmental conditions adopted for the model input. Results are given in Section 3, which provides a summary of the model predictions, with a focus on the changes in key parameters (wave height, wave-orbital velocity, wave forces) under SLR. The implications of the results for predicting ecosystem health and for future modeling of reef colonies under SLR are discussed in Section 4. Final conclusions follow in Section 5.

2. Methodology 2.1. Wave dynamics model selection The SWAN (Delft University of Technology) and MIKE 21 SW (Danish Hydraulic Institute) third-generation wave models were considered for use in this study. Comparison of SWAN with MIKE

21 SW shows that both models give very similar results. However, as MIKE21 SW is designed for wider application and not specifically for application as a 1D model, it is more computationally expensive than SWAN. Similarly, SWAN 1D provides wave setup as an output based on an explicit solution; therefore there is no need to run a hydrodynamic model to calculate wave setup, again reducing computation time. Consequently, the SWAN 1D model was selected due to the extensive number of simulations required to cover the range of bathymetric conditions. The SWAN model has been used for prediction of waves over coral reefs in a range of locations (Vitousek et al., 2007; Storlazzi et al., 2011), and extensively tested for wave propagation in a wide variety of coastal environments (Ris et al., 1999). The inputs required for the model are bathymetry, water level, surface roughness and wind and wave conditions at the offshore model boundary. 2.2. Bathymetry The idealized cross section of a barrier reef adopted for the modeling includes a sloping fore-reef, a horizontal reef flat, a sloping back-reef, a deeper lagoon, and the shoreface (Fig. 1). It is assumed that the fore-reef and back-reef have slope of 1:2 (26°), the beach has slope of 1:10 (6°), and that the water depth on the outer fore-reef is 50 m. A range of values for the width (50–1200 m) and depth (0.5–3 m) of the reef flat and the width (50–2000 m) and depth (5–20 m) of the lagoon were combined to create 540 different reef profiles. In addition, the roughness of the reef was varied, resulting in a total of 1080 different reef bathymetries (Table 1). A base bathymetry was also chosen for more detailed investigations and model testing or where comparison is required with a particular control case. This profile has a reef flat width of 400 m, a reef flat depth of 1 m, a lagoon width of 1000 m, a lagoon depth of 10 m, and a surface roughness of 0.1 m. This profile is representative of the main reef at Lizard Island, Great Barrier Reef (GBR) Australia (as outlined below), which was selected as a representative location for the selection of appropriate climatic wind, wave and tide data for the model study. The range of the bathymetric parameters (reef flat depth and width, lagoon width and depth, and surface roughness, representing coral cover and dead carbonate) was selected based on typical values for reefs in the GBR and worldwide. In the present study, the reef flat depth is a key parameter; for ease of reference we refer to reefs with reef flat depths in the range 0.5–1 m and 2.5 m–3 m as shallow reefs and deep reefs, respectively. While tides are not included, the range of water levels considered encompasses typical tidal ranges. Hence, results for different water levels are also representative of conditions at different stages of the tide. 2.3. Environmental conditions Met-ocean data was used to identify different climate scenarios. Wind and wave data from the European Centre for Medium Weather Forecast (ECMWF) global atmospheric and oceanic models (C-ERA-40 spanning 1958–2002 and ERA-Int spanning 1989– 2009) with spatial resolution of 1.5° and time resolution of 6 h were extracted. However, because of their coarse resolution, these models do not resolve reef and reef islands very well. Hardy et al. (2001) have run a local wind-wave model for the GBR with temporal resolution of 1hr and spatial resolution of 1500 m covering 1996–2003. With this resolution, Lizard Island is as a whole reasonably well resolved and data are available inside and outside of the lagoon, although detail is limited within the lagoon. However, the duration of this hindcast model is only for 8 years (1996–2003) which is insufficient for predicting statistical extremes, but sufficient to estimate typical conditions for the present modeling. To check the Hardy et al. results, synoptic wind data

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058

3

T.E. Baldock et al. / Marine Pollution Bulletin xxx (2014) xxx–xxx

Fig. 1. Definition sketch of idealized reef bathymetry adopted in the model.

Table 1 Bathymetric parameters. Parameter

Number of cases

Values

Surface roughness (Nikuradse, m) Reef flat depth (m) Reef flat width (m) Lagoon depth (m) Lagoon width (m)

2

0.04 (smooth), 0.1 (rough)

6 6 3 5

0.5, 1, 1.5, 2, 2.5, 3 50, 100, 200, 400, 800, 1200 5, 10, 20 50, 200, 400, 1000, 2000

from the Australian Bureau of Meteorology (BOM), the Australian Institute of Marine Science (AIMS) and the Windfinder website were also obtained, including data for Lizard Island, Cape Flattery and Green Island (1993-present). In addition, wave data for buoys located in the GBR were obtained from the QLD Department of Environment and Resource Management (DERM), including Cairns (depth = 9 m, 1975–2004), Dunk Island (118 km south of Cairns, depth = 20 m, 1998–2002), Lucinda Region (180 km south of Cairns, depth = 9.7 m, 1995–1996) and Townsville (depth = 15 m, 1975–2004). Taking all data sources, the wave and wind climate are clustered into 10 and 3 groups (Tables 2 and 3), broadly representative of the GBR wave and wind climate in this region of the lagoon. An average climate for the area is a wind speed of 10 m/s and a significant wave height, Hs, of 0.5 m. Cyclonic conditions correspond to waves with height of order 3 m. For SLR, four values of 0, 0.25 m, 0.5 m and 1 m were chosen. These values can represent actual SLR, or a pseudo-sea level rise, i.e., changes in relative sea level encompassing coral reef platform accretion or erosion that changes the reef flat elevation. Based on these data clusters, different combinations of boundary conditions (wind, wave height, SLR scenario) were adopted for the forcing conditions in the SWAN model (Table 4). Given the large suite of required model runs and consistent with a 1D model approximation, wind and waves were aligned perpendicular to the reef rim and the wind was held constant over the whole domain. Changes in wave height due to variations in refraction at different SLR are therefore not accounted for. A wide

Table 2 Wave climate and percentage of occurrence based on Cairns buoy records and GBR wave Atlas, where Hs is the significant wave height and Tp is the peak wave period. Case No.

Hs (m)

Tp (s)

1 2 3 4 5 6 7 8 9 10

0.3 (33.89%) 0.5 (29.52%) 0.75 (13.98%) 1 (5.35%) 1.25 (1.1%) 1.5 (0.05%) 1.75 (0.02%) 2 (0.01%) 2.5 3

6 4 4 4 4 6 6 6 6 6

(11.96%) (14.62%) (11.74%) (4.91%) (1.16%) (0.02%) (0.01%) (0.01%)

Table 3 Wind speed and percentage of occurrence based on Green and Lizard Island wind station records and GBR wind Atlas. Case No.

Wind speed (m/s)

Average wind speed (m/s)

1 2 3

Less than 5 (21%) 5–15 (78%) 15–25 (0.005%)

2.5 10 20

Table 4 Model parameters. Parameter

Number of cases

Values

Wind speed (m/s) Significant wave height (Hs, m) Sea level rise (m)

2 2 4

10, 20 0.5, 3.0 0, 0.25, 0.5, 1

distribution of wave direction (spreading) was also adopted, appropriate for this region. Recent model improvements (van der Westhuysen, 2010), relevant for simulating waves in lagoons, were also included.

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058

4

T.E. Baldock et al. / Marine Pollution Bulletin xxx (2014) xxx–xxx

Friction was based on the Madsen et al. (1988) formulation, wave breaking was based on the Battjes and Janssen (1978) model, and quadruplet and triad interaction and wave setup were enabled in all runs (excluding quadruplet interactions for no wind conditions, as per the recommendation of Booij et al., 1999). Sheppard et al. (2005) recommended friction factors (fw) of 0.1 and 0.2 for smooth and rough healthy coral reefs, respectively, based on the measurements performed by Nelson (1996). These values are consistent with the data of Lowe et al. (2005) estimated using the Madsen friction model and physical measurements. These are equivalent to a Nikuradse roughness (kn) of 0.04 m and 0.1 m for a smooth and rough reef, respectively, as adopted within the Madsen friction formulation. For simplicity, the friction coefficient was held constant over the whole domain, but friction is only a significant factor on the shallower reef flat regions in practice. The sensitivity of the model to the chosen spatial resolution was also investigated and a resolution of 5 m was considered as an optimum resolution, which yields the required accuracy while remaining computationally sensible. 2.4. Model outputs Taking the 1080 different bathymetries and 16 different model boundary conditions, 17,280 model realizations were setup and run. The important output parameters describing the reef flat wave dynamics are wave height, wave induced orbital velocity and wave period. Due to the random and time-varying nature of ocean waves, the wave dynamics are conventionally described by statistical parameters that represent the sea conditions. These are the significant wave height, Hs (the average of the highest one-third of waves), the root-mean-square of the peak wave-orbital velocities, Urms, (noting that the peak wave-orbital velocities are dependent on wave heights, which vary in time for a given wind velocity) and the peak wave period, Tp (which is the wave period of the most energetic waves). The SWAN model has been extensively used and verified for a wide range of wave conditions (see Ris et al., 1999 for a general review), including for conditions with wind and bottom drag (Zijlema et al., 2012) and on reefs (Lowe et al., 2009; Storlazzi et al., 2011). Consequently, while absolute model predictions will contain some inaccuracies, here we are interested in changes in the wave dynamics due to perturbations in the water depth. Therefore, absolute model accuracy is not critical. In addition, since it is not possible to calibrate the model for the extensive set of different bathymetries, we adopt the default model parameters for the simulations. 2.5. Wave-induced forces on corals Wave loads on submerged corals arise from three forces; a drag force from flow separation around the coral body (and some skin friction), lift forces from flow over curved surfaces and inertia forces arising from the pressure gradient across the coral induced by the wave motion. The drag force is expected to be dominant for slender coral bodies, i.e. branching type corals, whereas the inertia force is expected to be dominant for large coral bodies, i.e. massive coral species. Lift forces for branching corals are expected to be small given their geometric shape. For massive corals, Massel and Done (1993) suggest the lift force is an order of magnitude smaller than the inertia force. This influence of the coral diameter on wave forces leads to a different impact from SLR for different coral species. Since the lift force is expected to be small for both branching and massive corals and does not contribute significantly to generating bending moments or shear on the coral skeleton (Massel and Done, 1993), the total wave induced forces on different species of coral were estimated by treating coral

sections as simple cylinders (c.f Storlazzi et al., 2005), and estimating the maximum total wave induced force per unit length, FT. In this simplified approach, cylinders represent the whole assemblage of massive corals and the individual branches of branching corals. The lift and inertia forces are 90° out of phase, so the maximum force is not the sum of the two individual forces. A simple analytical expression is adopted for the total maximum force, from Dean and Dalrymple (1991):

FT ¼ FD þ

F 2I 4F D

ð1Þ

where FD is the drag force and FI is the inertia force, each defined as:

F D ¼ 0:5qC D DU 2rms

ð2Þ

F I ¼ qC m xD2 U rms

ð3Þ

and where CD is the drag coefficient, Cm is the inertia coefficient, q is water density, D is diameter and x ¼ 2Tp, where T is the wave period. For FI > 2FD, Eq. (1) is no longer valid and the maximum total force is the maximum inertia force. Different wave periods are available from the SWAN model; the mean wave period (Tmm10 in SWAN) is considered here, which represents the period of the waves across the full energy spectrum, rather than just the peak frequency. Cm and CD were taken to be equal to 1 and assumed invariant with SLR. Different choices for the drag an inertia coefficient will not significantly change the results presented since we consider the ratio of the different forces under different SLR scenario. Estimates of the change in wave forces under each SLR scenario were calculated for three different values of coral diameter, 0.02 m, 0.5 m and 2 m, representative of coral sections for a range of coral species across the spectrum from branching to massive. 3. Results 3.1. Global impacts of SLR on wave height and wave induced velocities Figs. 2a and 2b illustrate a typical model prediction for the variation of wave height (Hs) and wave induced velocity (Urms) across the reef-lagoon transect. The conditions shown are for the base bathymetry, average wind and wave conditions and both smooth and rough reefs. Wave height and velocity decrease across the reef flat due to wave breaking and friction, with wave heights subsequently increasing across the lagoon due to the wind. Velocities off the reef and in the deep lagoon are generally small compared to reef flat velocities. The sensitivity of the reef flat wave height (Hs) and wave orbital motion on the top reef (Urms) to reef bathymetry and surface roughness is illustrated in Figs. 3 and 4. The conditions correspond to the average off-reef wind-wave climate (i.e. Hs = 0.5 m, Tp = 4s and wind speed = 10 m/s). Results shown are for conditions at centre of the reef flat (midway between the reef rim and lagoon) unless stated otherwise. Clearly, wave height and orbital velocity decrease as the reef becomes wider (Figs. 3 and 4), i.e., as the wave propagation distance over the reef increases. These patterns are altered under SLR but in a non-linear manner and change depending on the bathymetry. Not surprisingly, shallower reef flats act to reduce the average height of waves (Fig. 3) and this effect is weakened under SLR, which increases effective depth, such that wave heights increase under SLR on all bathymetries and in all zones across the reef profile. The pattern is more complex for wave-orbital velocity. SLR reduces orbital velocity on narrow reef flats but increases the velocity once the reef flat width exceeds around 500 m (Fig. 4). The depth of the reef flat has a non-linear impact on orbital velocity such that velocities typically increase to a maximum at a depth of around 1–1.5 m, and then decline as depth increases. However,

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058

T.E. Baldock et al. / Marine Pollution Bulletin xxx (2014) xxx–xxx

5

Fig. 2a. Typical variation in wave height (Hs) across the reef-lagoon profile for different reef roughness. Dashed line – smooth reef; dotted line – rough reef; solid line – bathymetry (right hand scale). Results shown are for the baseline reef flat width and depth of 400 m and 1 m, respectively.

Fig. 2b. Typical variation in wave-orbital velocity (Urms) across the reef-lagoon profile for different reef roughness. Dashed line – smooth reef; dotted line – rough reef; solid line – bathymetry (right hand scale). Results shown are for the baseline reef flat width and depth of 400 m and 1 m, respectively.

under the highest SLR scenario considered (SLR = 1 m), orbital velocity follows a monotonic decline as reef flat depth increases. The influence of SLR is significant, leading to increases in wave height of order 10–15% for SLR = 0.25 m and to increases of order 50–75% for SLR at the upper bound of current projections for 2100 (Fig. 3). These changes in wave height are similar to those found by Storlazzi et al. (2011) and Grady et al. (2013) for fringing reefs. Changes in the orbital velocity are likewise similar or even greater. This is discussed further in the next sub-section. SLR also appears to provide the potential for significant shifts in wave period (not shown) which also influence the changes in orbital velocities and have a significant effect on wave forces on corals, as discussed later. The wave period plays an important role in the generation of wave forces on corals and on sediment transport on

reef flats and at the shore. The wave period is relatively constant on the fore-reef under SLR, but increases at nearly all other locations for nearly all reef bathymetries under both average and cyclonic conditions. The greatest increases in wave period occur on the shallower top reefs. Increased lagoon width clearly increases nearshore wave height because of a greater fetch length, and again significant changes occur with SLR due to the increased water depth over the reef (Fig. 5), consistent with previous modeling (e.g. Sheppard et al., 2005). Changes in lagoon width also induce subtle variations in wave period over and above those induced directly by SLR (not shown). SLR enables longer period waves to propagate over the reef; however, the peak wave period may then decreases as the lagoon fetch increases and new shorter wind waves are generated.

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058

6

T.E. Baldock et al. / Marine Pollution Bulletin xxx (2014) xxx–xxx

Fig. 3. Variation of wave height (Hs) with reef flat width and depth for smooth (top) and rough (bottom) reefs. Color bar and contours indicate wave height (m). SLR varies from left to right as SLR = 0, 0.25 m, 0.5 m, 1 m. Results shown are for a location at the centre of the reef flat. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Variation of near bed wave-orbital velocity (Urms) with reef flat width and depth for smooth (top) and rough (bottom) reefs. Color bar and contours indicate velocity (m/s). SLR varies from left to right as SLR = 0, 0.25 m, 0.5 m, 1 m. Results shown are for a location at the centre of the reef flat. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Underlying this change is a gradual increase in the period of locally generated waves in the lagoon as lagoon width increases. The impact of these changes in wave conditions for the stability of reef island beaches will be considered in a later paper. 3.2. Local impacts and cyclonic versus non-cyclonic conditions Water displacement, or velocity, plays an important role in reef habitats to deliver resources, remove waste, and disperse reproductive propagules (Denny and Shibata, 1989; Madin and Connolly, 2006; Monismith, 2007). In addition, Sebens et al. (1998) show that wave motion can lead to enhanced particle and zooplankton capture, such that periods of higher waves may benefit coral growth. Conversely, if wave-orbital velocity or wave

forces exceed a certain value in any SLR scenario, coral may experience breakage, for example during cyclonic conditions. To investigate potential SLR impacts further, the change in wave-orbital velocity defined by the ratio Urms/Urms0 is adopted as an initial indicator of the impact of SLR on water displacements as a proxy for coral health. Here, Urms and Urms0 are the representative Urms velocities for the SLR condition and the baseline (SLR = 0) condition, respectively. Values of Urms/Urms0 greater or less than 1 indicate increases or decreases in wave-orbital velocity, respectively. Spatial variations in the impact of SLR in terms of this indicator were assessed for all bathymetries at different locations across the reeflagoon transect; results presented here are for the fore-reef at a depth of 2 m below the elevation of the reef flat and at the centre of the reef flat. The ratios Urms/Urms0 on the fore-reef and reef flat

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058

T.E. Baldock et al. / Marine Pollution Bulletin xxx (2014) xxx–xxx

7

implications for potential feedback between the reef ecology and the wave dynamics (see discussion). Further, there is interplay between the influence of depth, width and roughness in terms of the impact of SLR, such that rough reefs show virtually no change in the hydrodynamic conditions for certain bathymetry, while smooth reefs show no change on different bathymetry. Changes to the hydrodynamic environment can be very significant, with increases in wave-orbital velocities from the baseline condition of up to 50–200% for average wave conditions. During cyclonic conditions the pattern of change in the velocities for different bathymetry is very similar to that for average wave conditions (not shown) but the changes are magnified, with increases of up to 400% in wave-orbital velocity on shallow narrow reef flats at SLR = 1 m. 3.3. Effect of reef morphology on cyclonic wave-induced forces for different SLR scenarios Fig. 5. Variation of nearshore wave height (Hs) with lagoon width and SLR. Results shown are for the baseline reef flat width of 400 m, depth of 1 m and a rough reef.

for average wave conditions are plotted for varying reef flat depth (Fig. 6) and as contours against reef width and reef depth (Fig. 7). On the fore-reef (Fig. 6), typically, this ratio is always less than 1, with reductions in wave-orbital velocities of order 20–30% at these locations for SLR = 1 m. Conversely, on the reef flat, the ratio is strongly dependent on the global reef bathymetry, and the magnitude of the change varies according to the depth and width of the reef flat, i.e. changes in the wave dynamics vary reef by reef (Fig. 7). The largest changes in the wave dynamics tend to occur on shallower and narrower reefs, but changes are not monotonic, with the velocity switching between being greater or less than the baseline condition as width and depth vary. Changes are subtle and differ reef by reef. For example, for reefs at the same depth, SLR decreases wave-orbital velocities (Urms/Urms0 < 1) on narrow reefs, but increases wave-orbital velocities (Urms/Urms0 > 1) on wide reefs. However, a maximum in the ratio Urms/Urms0 is observed on shallower reefs, so on very wide reefs velocities reduce back toward the baseline. There are also significant differences in the response to SLR on rough and smooth reefs, with smooth reefs being influenced by SLR to a greater extent than rough reefs. This has

The ratio of the maximum total force under SLR, F, to the maximum total force for SLR = 0, F0, is taken again as a representative indicator of the changes in wave forces. We only consider cyclonic conditions for these calculations. On the fore-reef (not shown), wave forces decrease with SLR for all bathymetries and all coral types, but with little variation for different reefs since reef width does not change conditions on the fore reef. The greatest reduction in force occurs for elements of branching corals, with forces generally reduced to 90% and 75% of the baseline condition for SLR = 0.25 m and SLR = 1 m, respectively. Negligible reduction in wave forces occurs on the fore-reef for massive corals. On the reef flat, consistent with the complex pattern of change observed for the velocity, complex changes occur in the expected wave induced loads, with further variation occurring for different coral diameters, plotted as contours of F/F0 in Fig. 8. Note that the color bar and contours in Fig. 8 indicate the magnitude of log (F/F0), such that magnitudes 1, 0, 1 represent F = 10F0, F = F0 and F = 0.1F0, respectively. Positive values therefore correspond to increases in wave forces and negative values correspond to reductions in wave forces. For elements of branching corals (upper panels), wave forces on the reef flat increase very considerably, with the magnitude of change being dependent on depth. On shallow reefs, forces increase by a factor of 5–10 (500–1000%). On deeper reefs (depths greater than 2.5 m) the increases in wave forces

Fig. 6. Variation of the ratio Urms/Urms0 with reef flat depth on the fore-reef. Results shown are for an elevation 2 m below the reef flat, a rough reef and average wave conditions.

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058

8

T.E. Baldock et al. / Marine Pollution Bulletin xxx (2014) xxx–xxx

Fig. 7. Variation of the ratio Urms/Urms0 with bathymetry and SLR (left, 0.25 m; centre, 0.5 m; right 1 m) at the centre of the reef flat for average wave conditions and smooth (top) and rough (bottom) reefs. Color bar and contours indicate magnitude of Urms/Urms0. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. Variation of the ratio F/F0 with bathymetry and SLR (left, 0.25 m; centre, 0.5 m; right 1 m) at the centre of the reef flat for cyclonic wave conditions and rough reefs. Coral diameter varies from 0.2 m (top), 0.5 m (middle) to 2 m (bottom). Color bar and contours indicate magnitude of log (F/F0), such that magnitudes 1, 0, 1 represent F = 10F0, F = F0 and F = 0.1F0, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

are smaller, but still very significant, of order 100%. Conversely, for corals of intermediate size, D = 0.5 m, SLR leads to a reduction in wave forces in most zones across the reef and for the majority of reef bathymetries. Again, the changes are significant, with reductions in wave forces down to 20–30% of those for the baseline SLR condition on the reef flat on the shallowest reefs. For massive corals, forces decrease with SLR in all zones and for all reef bathymetries. The reductions in wave forces on shallow reef flats are again very significant, up to a factor 5 smaller (or 20% of the forces at the baseline SLR condition). Thus, the changes in wave forces due to SLR are strongly dependent on both coral diameter and reef bathymetry, with branching corals most exposed to increases in wave loads for SLR scenario.

4. Discussion 4.1. Impact of SLR on reef top wave dynamics The large magnitude of the hydrodynamic changes observed from the present modeling are likely to have considerable impacts on biogeochemical fluxes in a wide range of processes acting upon corals and algae. These changes to the reef wave dynamics can clearly impact on coral and algal health through changes in production (Jokiel, 1978; Tribble et al., 1994), (Carpenter and Williams, 1993, 2007), through increased mixing (Skirving et al., 2006; Wangpraseurt et al., 2012) and by imposing damaging wave forces (Massel and Done, 1993; Madin and Connolly, 2006).

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058

T.E. Baldock et al. / Marine Pollution Bulletin xxx (2014) xxx–xxx

Similarly, changes in nearshore wave height in the lagoon due to SLR may strongly influence near shore processes and wave energy reaching nearshore corals, seagrass, mangroves and beaches (Sheppard et al., 2005). The bathymetry of an individual reef has a very strong influence on the wave height over the reef flat, at the leeward reef edge and in the lagoon for present sea level (see Fig. 3). However, this influence weakens for average wave conditions with increasing SLR, i.e. the energy dissipation induced by wide barrier reefs at present SLR is reduced, consistent with Sheppard et al. (2005). Similar effects occur on fringing reefs (e.g. Grady et al., 2013). The greatest influence of SLR occurs on shallow reefs, and these systems may already be under stress because of increases in water temperature and reductions in water quality. SLR induced changes in wave height are very significant. For example, for a reef depth of 1 m, the change in wave height for SLR = 1 m is equivalent to a reef reducing in width from 1200 m to less than 200 m (Fig. 3). For wider reefs, even a modest increase of a SLR = 0.25 m is equivalent to a change in reef width of nearly 1000 m. Conversely, in the reef lagoon, changes in wave height near the shoreline due to SLR are equivalent to the lagoon width increasing from 50 m to 1800 m at the current baseline sea level (Fig. 5). Likewise, for narrow lagoons, a SLR of 25 cm has an impact equivalent to doubling the lagoon width from 200 m to 400 m. Thus, the impact of SLR is equivalent to much greater fetch lengths for the local wind waves within the lagoon. While changes in bathymetry lead to monotonic variations in wave height, the same changes lead to more complex variations in near bed velocity over the reef flat, with a maximum in the near bed wave induced orbital velocity often occurring for particular reef bathymetry. For example, for many bathymetries, maximum velocities occur for reef flats of order 1–1.5 m deep (Fig. 4). Therefore, for narrow and shallow reefs, velocities tend to decrease with SLR; conversely, for wide and deep reefs velocities increase with SLR (Fig. 7). Taking the results for the complete range of bathymetry and wave conditions, the change of response to SLR is a function of the reef zone, both the reef flat width and the depth, and the roughness, illustrated by the contour lines for Urms/Urms0 = 1 in Fig. 7. This change over in response occurs at reef widths of order 200–300 m on shallow reefs but at reef widths of order 1 km on deep reefs with the present model and assumptions. On the forereef, the response is similar for all bathymetries, with a reduction in wave induced velocity with increasing SLR. Conversely, under cyclonic conditions, the velocity increases for all bathymetries and in all reef zones, with no change over in response. Nevertheless, the magnitude of the change in the hydrodynamic conditions continues to vary reef by reef. The changes in wave forces due to SLR are equally complex and specific with regard to location, reef bathymetry and coral species (Fig. 8). While the greatest changes again occur on narrow shallow reefs, the flip over in response now occurs because of different coral species (here represented by a representative diameter), and between different zones on the reef, rather than for different reef bathymetry. The interrelationship between bathymetry, wave height, water depth and wave induced velocity, in conjunction with the dynamics of the wave forcing, results in the complete contrast in the influence of SLR on intermediate and massive corals compared to those on branching corals, particularly on shallower reefs where the impacts of SLR are greatest. Thus, SLR only is detrimental in terms of increased wave forces for branching corals and then primarily only on the reef flat. SLR is generally beneficial, i.e. decreased cyclonic wave forces, for massive corals at all locations. Therefore, different species will be impacted in different ways, and some species may in fact benefit from SLR in terms of reduced risk of cyclone damage. Climate impacts and anthropogenic activities other than SLR may degrade the reef habitat such that a healthy rough reef loses

9

species diversity and becomes more uniform and hence smoother (Kennedy et al., 2013). It should be noted that loss of diversity may result in dominance of a massive coral (Fabricius et al., 2011) and although this might preserve the prior macro-scale roughness, the loss of structural complexity and fine-scale roughness may result in less overall wave damping by friction and drag. Further work is required to resolve this issue. While the impacts of SLR are generally similar on rough reefs and smooth reefs for all parameters discussed above, subtle variations do occur, notably for wave-orbital velocity. Further, the interplay of reef depth, width and roughness in controlling the wave height means that different bathymetries show variations in sensitivity to changes in roughness at different sea levels. For example, for wide reefs, wave height is insensitive to roughness at present sea level, but differences of order 10% are predicted for different roughness at SLR = 1 m (Fig. 3). Similarly, roughness has little impact on wave heights on shallow reefs at present sea level (since energy dissipation is dominated by breaking), but again differences of order 15% emerge at higher sea levels. Therefore, in combination, SLR and changes in reef composition can lead to gradual but significant changes in both reef top and nearshore wave dynamics (Figs. 4– 8). Likewise, in the absence of SLR, changes in water depth over the reef flat may still occur from loss of coral from breakage or erosion which directly reduces reef flat elevations (Sheppard et al., 2005; Grady et al., 2013). Similarly, reef accretion rates may or may not keep up with SLR (Buddemeier and Smith, 1988). Such variations in the reef elevation relative to sea level can be immediately assessed from the present model results by considering them as a pseudo-sea level rise. 4.2. Implications for ecosystem health Paradoxically, the changes in reef wave dynamics from SLR may be both beneficial and detrimental. For example, it is well recognized that greater damage to coral is likely from higher wave induced loads (see Section 3.3). However, coral growth rates increase with increasing flow (Jokiel, 1978) and increasing wave induced velocity enhances particle capture (Sebens et al., 1998), such that larger waves may benefit coral growth, albeit up to a limit, and consequently, SLR (and pseudo sea level rise) may be beneficial for coral production on certain reefs and in certain zones of a range of reefs, even without considering increased accommodation space. This modeling commences the process of identifying such reefs and such zones, and conversely, those ecosystems potentially at greatest risk. Further, the nature of the ecological processes will determine if positive or negative feedback occurs between the ecological and hydrodynamic processes as a result of SLR. For example, taking roughness as a proxy for coral health, a smoother reef results in greater wave induced velocities. Therefore, if increased average wave-orbital velocity is beneficial (up to a limit) to coral health (Figs. 4 and 7), SLR will be beneficial, and there is negative feedback and stability. If however, increased wave-orbital velocity is detrimental to a coral population as a whole, SLR will be detrimental and positive feedback occurs as the roughness continually reduces, leading to greater velocities and further reduction in coral health. Consequently, in this scenario, a tipping point could exist, beyond which SLR induced velocities become very detrimental. These impacts will also influence the distribution of coral species on the reef. Likewise, the varied response of different species in terms of likely changes in breakage rates under cyclonic conditions will influence future species distribution. Consequently, there is a pressing need to investigate geographic trends in colony strength further in order to get realistic models for the future of colony fragmentation and loss during cyclonic conditions with added SLR. Similarly, not all species necessarily benefit from increased waveorbital velocity, e.g. seagrasses, and so the response to SLR would

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058

10

T.E. Baldock et al. / Marine Pollution Bulletin xxx (2014) xxx–xxx

be reversed in those cases. Overall, the modeling clearly demonstrates that predicting SLR impacts arising from changing wave dynamics on coral reefs requires careful consideration of the reef bathymetry, the reef zone and the mix of coral species. 5. Conclusions A one-dimensional wave model has been used to investigate changes in reef top wave dynamics and wave forces under different sea-level rise (SLR) scenarios for a large suite of idealized reef profiles. The model results predict that the impacts of SLR vary spatially and are also strongly influenced by the bathymetry of the reef and coral type. While wave heights increase under SLR, changes in the wave induced velocity are more complex, such that the changes vary reef by reef. For many reef bathymetries, wave orbital velocities increase with SLR during average wave conditions and cyclonic wave forces are reduced for certain coral species. Both these changes suggest sea level rise may be beneficial to coral health and colony resilience because of the potential for increased wave induced orbital motion under average wave conditions or less breakage under cyclonic conditions. However, predicting the impact of SLR on individual reefs requires consideration of the reef bathymetry, the reef zone and the type of coral species. The model and results presented here provides a basis for an initial broadscale assessment of the impacts of SLR on the ecosystem services provided by reefs. References Battjes, J.A., Janssen, J.P.F.M., 1978. Energy loss and set-up due to breaking of random waves. In: Proc. 16th Int. Conf. Coastal Engineering, ASCE, pp. 569–587. Booij, N., Ris, R., Holthuijsen, L.H., 1999. A third generation wave model for coastal regions 1. Model description and validation. J. Geophys. Res. 104, 7649–7666. Brander, R.W., Kench, P.S., Hart, D., 2004. Spatial and temporal variations in wave characteristics across a reef platform, Warraber Island, Torres Strait, Australia. Mar. Geol. 207, 169–184. Buddemeier, R.W., Smith, S.V., 1988. Coral reef growth in an era of rapidly rising sea level: predictions and suggestions for long-term research. Coral Reefs 7, 51–56. Carpenter, R.C., Williams, S.L., 1993. Effects of algal turf canopy height and microscale substratum topography on profiles of flow speed in a coral fore-reef environment. Limnol. Oceanogr. 38, 687–694. Carpenter, R.C., Williams, S.L., 2007. Mass transfer limitation of photosynthesis of coral reef algal turfs. Mar. Biol. 151, 435–450. Dean, R.G., Dalrymple, R.A., 1991. Water Wave Mechanics for Engineers and Scientists. Advanced Series on Ocean Engineering. World Scientific. Denny, M.W., Shibata, M.F., 1989. Consequences of surf-zone turbulence for settlement and external fertilization. Am. Nat., 859–889. Fabricius, K.E., Langdon, C., Uthicke, S., Humphrey, C., Noonan, S., De’ath, G., Okazaki, R., Muehllehner, N., Glas, M.S., Lough, J.M., 2011. Losers and winners in coral reefs acclimatized to elevated carbon dioxide concentrations. Nat. Clim. Change 1 (3), 165–169. Gourlay, M.R., Colleter, G., 2005. Wave-generated flow on coral reefs – an analysis for two dimensional horizontal reef tops with steep faces. Coast. Eng. 52, 353– 387. Grady, A.E., Moore, L.J., Storlazzi, C.D., Elias, E., Reidenbach, M.A., 2013. The influence of sea level rise and changes in fringing reef morphology on gradients in alongshore sediment transport. Geophys. Res. Lett. 40 (12), 3096–3101. Graus, R.R., Macintyre, I.G., 1998. Global warming and future of Caribbean reefs. Carbonates Evaporites 13, 43–47. Grinsted, A., Moore, J.C., Jevrejeva, S., 2009. Reconstructing sea level from paleo and projected temperatures 200–2100 AD. Clim. Dyn. 34 (4), 461–472. Hardy, T.A., Mason, L.B., McConochie, J.D., 2001. A wave model for the Great Barrier Reef. Ocean Eng. 28, 45–70. Hoegh-Guldberg, O., Mumby, P.J., Hooten, A.J., Steneck, R.S., Greenfield, P., Gomez, E., Harvell, C.D., Sale, P.F., Edwards, A.J., Caldeira, K., Knowlton, N., Eakin, C.M., Iglesias-Prieto, R., Muthiga, N., Hoeke, R.K., Storlazzi, C.D., Ridd, P.V., 2011. Hydrodynamics of a bathymetrically complex fringing coral reef embayment; wave climate, in situ observations and wave prediction. Journal of Geophysical Research, Oceans, 116, pp. C04018, http://dx.doi.org/10.1029/2010JC006170. Jokiel, P.L., 1978. Effects of water motion on reef corals. J. Exp. Mar. Biol. Ecol. 35, 87–97. Kench, P.S., Brander, R.W., 2006. Wave processes on coral reef flats: Implications for reef geomorphology using Australian case studies. J. Coastal Res. 22, 209–223.

Kennedy, E.V., Perry, C.T., Halloran, P.R., Iglesias-Prieto, R., Schonberg, C.H., Wisshak, M., Form, A.U., Carricart-Ganivet, J.P., Fine, M., Eakin, C.M., Mumby, P.J., 2013. Avoiding coral reef functional collapse requires local and global action. Curr. Biol. 23, 912–918. Khan, T.M.A., Quadir, D.A., Murty, T.S., Kabir, A., Aktar, F., Sarker, M.A., 2002. Relative sea level changes in Maldives and vulnerability of land due to abnormal coastal inundation. Mar. Geodesy 25 (1–2), 133–143. Lowe, R.J., Falter, J.L., Bandet, M.D., Pawlak, G., Atkinson, M.J., Monismith, S.G., Koseff, J.R., 2005. Spectral wave dissipation over a barrier coral reef. J. Geophys. Res.-Oceans 110, C04001. http://dx.doi.org/10.1029/2004JC002711. Lowe, R.J., Falter, J.L., Monismith, S.G., Atkinson, M.J., 2009. Wave-driven circulation of a coastal reef-lagoon system. J. Phys. Oceanogr. 39, 869–889. Madin, J.S., Connolly, S.R., 2006. Ecological consequences of major hydrodynamic disturbances on coral reefs. Nature 444, 477–480. Madsen, O.S., Poon, Y.K., Graber, H.C., 1988. Spectral wave attenuation by bottom friction: Theory. In: Proc. 21th Int. Conf. Coastal Engineering, ASCE, pp. 492– 504. Massel, S.R., Done, T.J., 1993. Effects of cyclone waves on massive coral assemblages on the Great Barrier Reef: meteorology, hydrodynamics and demography. Coral Reefs 12, 153–166. Merrifield, M.A., Merrifield, S.T., Mitchum, G.T., 2009. An anomalous recent acceleration of global sea-level rise. J. Clim. 22, 5772–5781. Moberg, F., Folke, C., 1999. Ecological goods and services of coral reef ecosystems. Ecol. Econ. 29, 215–233. Monismith, S.G., 2007. Hydrodynamics of coral reefs. Annu. Rev. Fluid Mech. 39, 37– 55. Mumby, P.J., Vitolo, R., Stephenson, D.B., 2011. Temporal clustering of tropical cyclones and its ecosystem impacts. Proc. Nat. Acad. Sci. U.S.A. 108, 17626– 17630. Nelson, R.C., 1996. Hydraulic roughness of coral reef platforms. Appl. Ocean Res. 18, 265–274. Nicholls, R.J., Cazenave, A., 2010. Sea-level rise and its impact on coastal zones. Science 328, 1517–1520. Ogston, A.S., Field, M.E., 2010. Prediction of turbidity due to enhanced sediment resuspension resulting from sea-level rise on a fringing coral reef: evidence from Molaki, Hawaii. J. Coastal Res. 26, 1027–1037. Perry, C.T., Kench, P.S., Smithers, G., Riegl, B., Yamano, H., O’Leary, M.J., 2011. Implications of reef ecosystem change for the stability and maintenance of coral reef islands. Glob. Change Biol. 17, 3679–3696. Renken, H., Mumby, P.J., Matsikis, I., Edwards, H.J., 2010. Effects of physical environmental conditions on the patch dynamics of Dictyota pulchella and Lobophora variegata on Caribbean coral reefs. Mar. Ecol.-Progr. Series 403, 63– 74. Ris, R.C., Booij, N., Holthuijsen, L.H., 1999. A third-generation wave model for coastal regions, Part II, Verification. J. Geophys. Res. (Oceans) 104, 7667–7681. Roy, P., Connell, J., 1991. Climatic change and the future of atoll states. J. Coastal Res. 7 (4), 1057–1075. Sebens, K.S Grace., Helmuth, B., Maney Jr., E., Miles, J., 1998. Water flow and prey capture by three scleractinian corals, Madracis mirabilis, Montastrea cavernosa and Porites porites, in a field enclosure. Mar. Biol. 131 (2), 347–360. Sheppard, C., Dixon, D.J., Gourlay, M., Sheppard, A., Payet, R., 2005. Coral mortality increases wave energy reaching shores protected by reef flats: examples from the Seychelles. Estuar. Coast. Shelf Sci. 64, 223–234. Skirving, W., Heron, M.L., Heron, S.F., 2006. The hydrodynamics of a bleaching event: implications for management and monitoring. In: Hoegh-Guldberg, O., Kleypas, J., Phinney, J.T., Skirving, W., Strong, A. (Eds.), Corals and climate change. American Geophysical Union, Coastal and Estuarine Series, Washington, DC, pp. 145–161. Storlazzi, C.D., Brown, E.K., Field, M.E., Rodgers, K., Jokiel, P.L., 2005. A model for wave control on coral breakage and species distribution in the Hawaiian Islands. Coral Reefs 24 (1), 43–55. Storlazzi, C.D., Elias, E., Field, M.E., 2011. Numerical modeling of the impact of sealevel rise on fringing coral reef hydrodynamics and sediment transport. Coral Reefs 30, 83–96. Tribble, G.W., Atkinson, M.J., Sansone, F.J., Smith, S.V., 1994. Reef metabolism and endo-upwelling in perspective. Coral Reefs 13, 199–201. Van der Westhuysen, A.J., 2010. Modeling of depth-induced wave breaking under finite depth wave growth conditions. J. Geophys. Res. 115 (C1), C01008. Vitousek, S., Fletcher, C.H., Merrifield, M.A., Pawlak, G., Storlazzi, C.D., 2007. Model scenarios of shoreline change at Kaanapali Beach, Maui, Hawaii; seasonal and extreme events: coastal Sediments 2007. In: American Society of Civil Engineers International Symposium on Coastal Engineering and Science of Coastal Sediment Processes, 6th, New Orleans, La., May 13–17, 2007, Proceedings, vol. 2, pp. 1227–1240. Wangpraseurt, D., Weber, M., Roy, H., Polerecky, L., de Beer, D., Suharsono, N., Nugues, M.M., 2012. In Situ Oxygen Dynamics in Coral-Algal Interactions. Plos One, 7. Webb, A.P., Kench, P.S., 2010. The dynamic response of reef islands to sea-level rise: evidence from multi-decadal analysis of island change in the Central Pacific. Global Planet. Change 72, 234–246. Zijlema, M., van Vledder, G., Holthuijsen, L.H., 2012. Bottom friction and wind drag for wave models. Coast. Eng. 65, 19–26.

Please cite this article in press as: Baldock, T.E., et al. Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull. (2014), http://dx.doi.org/10.1016/j.marpolbul.2014.03.058