Numerical modeling of the impact of sea-level rise on fringing coral reef hydrodynamics and sediment transport
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Most climate projections suggest that sea level may rise on the order of 0.5–1.0 m by 2100; it is not clear, however, how fluid flow and sediment dynamics on exposed fringing reefs might change in response to this rapid sea-level rise. Coupled hydrodynamic and sediment-transport numerical modeling is consistent with recent published results that suggest that an increase in water depth on the order of 0.5–1.0 m on a 1–2 m deep exposed fringing reef flat would result in larger significant wave heights and setup, further elevating water depths on the reef flat. Larger waves would generate higher near-bed shear stresses, which, in turn, would result in an increase in both the size and the quantity of sediment that can be resuspended from the seabed or eroded from adjacent coastal plain deposits. Greater wave- and wind-driven currents would develop with increasing water depth, increasing the alongshore and offshore flux of water and sediment from the inner reef flat to the outer reef flat and fore reef where coral growth is typically greatest. Sediment residence time on the fringing reef flat was modeled to decrease exponentially with increasing sea-level rise as the magnitude of sea-level rise approached the mean water depth over the reef flat. The model results presented here suggest that a 0.5–1.0 m rise in sea level will likely increase coastal erosion, mixing and circulation, the amount of sediment resuspended, and the duration of high turbidity on exposed reef flats, resulting in decreased light availability for photosynthesis, increased sediment-induced stress on the reef ecosystem, and potentially affecting a number of other ecological processes.
KeywordsSea level Fringing reef Waves Currents Sediment Erosion
While rising sea-surface temperatures and ocean acidification have received most of the attention regarding the impacts of climate change on coral reefs, the impact to coral reefs from predicted future rising sea level has only been addressed by a few researchers (Graus and Macintyre 1998; Ogston and Field 2010). 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. 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 to three times the average IPCC (2007) projection of approximately 60 cm above 2000 levels. Since corals’ upward growth is constrained by exposure to air at low tides, Buddemeier and Smith (1988) and Edwards (1995) suggested that coral reef flats may benefit from the additional accommodation space, as detrimental exposure to air would decrease with sea-level rise. Buddemeier and Smith (1988), however, qualify this conclusion as long as “… [coral] communities are protected from destructive waves and not subjected to heavy sedimentation…”.
Increased turbidity over coral reefs due to suspended sediment can decrease light available for photosynthesis (Marszalek 1981; Phillip and Fabricius 2003; Piniak and Storlazzi 2008) and modify coral reef zonation by affecting coral fertilization and recruitment, which, in turn, can result in stress to or mortality of corals (e.g., Rogers 1990; Phillip and Fabricius 2003; Fabricius 2005). Recently, a number of studies have addressed the growing problem of coral reefs impacted by anthropogenic modification of coastal watersheds (e.g., Wolanski et al. 2003; Field et al. 2008), acknowledging that climate change may alter the quantity and timing of sediment delivery to coral reefs.
Despite the widespread discussion of climate change impacts on reefs, there has been little discussion of how sea-level rise may affect fringing coral reefs, in terms of both hydrodynamics and sediment dynamics. A number of studies of bio-physical coupling on reefs (e.g., Sebens and Johnson 1991; Edwards 1995; Falter et al. 2004; Storlazzi et al. 2005) have shown that hydrodynamics control many ecological aspects of reef systems, including photosynthesis, nutrient uptake, prey capture, coral bleaching, and species distribution. Ogston and Field (2010) presented one-dimensional model results from Molokai, Hawaii, USA, demonstrating that twenty-first-century sea-level rise will increase wave heights and suspended-sediment concentrations and cause longer periods of elevated turbidity on the coral reef flat.
In this paper, a two-dimensional numerical profile model of hydrodynamics and sediment transport over the Molokai fringing reef was calibrated with in situ data and was driven by meteorologic and oceanographic forcing conditions that characterize most exposed (not sheltered) tropical coral reefs. The goal of this effort is to better understand the relative importance of different processes (e.g., winds and waves) to hydrodynamics and sediment transport, and the contribution of these different characteristic sets of forcing conditions to annual sediment fluxes. Model results for various projections of sea-level rise are presented to identify the relative importance of these different forcing conditions to hydrodynamics and sediment transport in different sea-level rise scenarios. Reef accretion or changes in roughness were not modeled in these sea-level rise scenarios because published vertical reef flat accretion rates for exposed fringing reefs (1–4 mm year−1 per Buddemeier and Smith 1988; Montaggioni 2005) are up to an order of magnitude smaller than the rates of sea-level rise projected for the years 2000–2100 (8–16 mm year−1 per Grinsted et al. 2009; Nicholls and Cazenave 2010). These data suggest that projected sea-level rise will outstrip potential new reef flat accretion, resulting in a net increase in water depth over exposed fringing reef flats on the order of 0.4–1.5 m during the twenty-first century. Lastly, the implications of these results in the health and sustainability for fringing coral reefs under projected sea-level rise are discussed.
The data presented here are from Molokai, Hawaii, in the north-central Pacific Ocean (~21°N, 157°W) between the islands of Oahu and Maui. The physical environment in the Hawaiian Islands during the summer is dominated by 5–10 m s−1 northeasterly trade winds that generate wave heights of 1–3 m with periods of 5–8 s and small (1–2 m), long-period (14–25 s) south swells (Moberly and Chamberlain 1964). Winter conditions, typically beginning in October and extending through March, are characterized by storms and North Pacific swell that produce wave heights of 3–6 m with periods of 10–18 s that approach from the northwest. Due to shadowing by the surrounding islands and the island of Molokai itself, however, most of south Molokai’s fringing reef is sheltered from large North Pacific swell but is exposed to the other wave climates. Hawaii has a mixed, semidiurnal microtidal regime, with the mean daily tidal range of approximately 0.6 m and the minimum and maximum daily tidal ranges are 0.4 and 0.9 m, respectively (Ogston et al. 2004; Storlazzi et al. 2004).
The in situ observations used for model calibration and validation were presented by Storlazzi et al. (2004) and Presto et al. (2006) and are summarized here. Current velocity data were collected via acoustic Doppler current profilers, acoustic Doppler velocimeters, or single-point electromagnetic current meters. Data loggers collected and stored data from these instruments as well as pressure to provide information on tides and waves. Optical backscatter sensors and the acoustic backscatter from acoustic Doppler current profilers and acoustic Doppler velocimeters provided information on turbidity and suspended-sediment concentrations. These instruments were mounted on tripods or deployed from a mobile “backpack” in water depths ranging from 0.5 to 11.0 m.
The Delft3D Online Morphology system (Lesser et al. 2004; Delft User Manual 2010) was used to model hydrodynamics and sediment transport over the south Molokai fringing coral reef. The main components are the two-way coupled Delft3D SWAN and FLOW modules modeling waves and currents, respectively. FLOW forms the core of the model system, simulating water motion due to tidal and meteorological forcing by solving the unsteady shallow-water equations that consist of the continuity equation, the horizontal momentum equations, and the transport equation under the shallow water and Boussinesq assumptions. Wave effects, such as enhanced bed shear stresses and radiation stresses, are included in the flow simulation by coupling the FLOW module with stationary runs of the third-generation SWAN wave model (Walstra et al. 2000). SWAN is based on discrete spectral action balance equations, computing the evolution of random, short-crested waves (Holthuijsen et al. 1993; Booij et al. 1999; Ris et al. 1999). Physical processes included are the generation of waves by wind, nonlinear quadruplet and triad wave–wave interactions, and dissipation due to whitecapping, bottom friction, and depth-induced breaking.
The Delft3D Online Morphology model was used to resolve the sediment resuspension and transport dynamically. At each computational time-step, Online Morphology supplements the FLOW module results with sediment transport using the Van Rijn (1993) formulation, wherein a distinction is made between bed-load and suspended-load transport. Bed-load transport represents the transport of sand particles in the wave boundary layer close to the seabed. Suspended-sediment transport is computed by the advection–diffusion solver. To describe sediment characteristics, additional formulations are included to account for density effects of sediment in suspension, settling velocity, vertical diffusion coefficient for sediment, suspended-sediment correction vector, and sediment exchange with the bed. The elevation of the bed is dynamically updated at each computational time-step by calculating the change in mass of the bottom sediment resulting from the gradients in sediment transport.
The bed was schematized in three non-cohesive sediment classes (Fig. 1c) to represent the sediment observed on the reef flat off south Molokai (Field et al. 2008). For the fine terrigenous sediment (fine silt), a mean grain size (d50) of 0.008 mm and a density of 2,700 kg m−3 was prescribed, medium-sized carbonate sediment (fine sand) was characterized by d50 = 0.2 mm and density of 1,850 kg m−3, and coarse carbonate sediment (medium sand) with d50 = 0.4 mm and density of 1,850 kg m−3. In the model, sediment was initially present only in a narrow band extending 400 m from the shoreline while the remainder of the model was initially a non-erodible layer that represented the coral pavement of the fringing reef flat (thin, discontinuous sediment deposits were discounted) based on field observations. The total amount of sediment available in the profile was 56.7 m3 of fine sediment, 18.2 m3 of which is contained in the mud belt (“B”), 27.9 m3 of medium sediment, and 784 m3 of coarse sediment contained in the coastal plain deposit (“A”). The volumes in the coastal plain deposit were somewhat arbitrary, as these depended on the landward extent of the model. The model did allow for sediment accumulation and subsequent erosion of accumulated sediment on the coral pavement during the sediment-transport simulations. Sediment fractions are solved individually in the transport and bed-update modules and therefore were tracked separately. Hydraulic roughness length scales were varied between approximately 0.01 and 0.10 m, with the higher value used for coral surfaces based on previous observations on Hawaiian reefs and numerical modeling results (e.g., Hearn 1999; Lowe et al. 2005), and the lower range (~0.01 m) set by the seabed grain size. Complete overviews of the formulations, testing, and validation of Delft3D Online Morphology have been reported in Lesser et al. (2004). See Walstra and Van Rijn (2003), and Van Rijn (1993, 2007a, b, c) for the specific transport formulations.
Because most fringing reefs are relatively uniform alongshore in water depth and hydrodynamic roughness at larger scales (order ~100 s of m) but heterogeneous at smaller scales (order ~m) due to ridge-and-runnel structures on the reef flat and spur-and-groove structures on the fore reef, a fully realistic three-dimensional model at the spatial scales necessary to resolve the heterogeneity would be too computationally intensive. For this reason, a schematized two-dimensional profile model was used to acquire insight into the dominant sediment-transport processes across a fringing coral reef. Since the model is only one grid cell in the alongshore direction, high vertical and cross-shore resolution could be obtained while minimizing computational time. An underlying assumption in this approach is the dominance of wind- and wave-driven processes. This assumption is justified based on the small tidal velocities observed in the study area (Ogston et al. 2004; Storlazzi et al. 2004; Presto et al. 2006). Model validation therefore was focused on accurate representation of the wave-breaking processes. Sensitivity analyses were performed on variations in the forcing by varying the seasonally schematized input conditions, profile dimensions, and the mean water level, including sea-level rise scenarios. The model bathymetry was based on averaging a number of cross-shore profiles from the high-resolution SHOALS lidar data presented by Storlazzi et al. (2003). The model grid had a 10-m cross-shore resolution, resulting in a total of 350 grid cells in the cross-shore direction for each vertical layer (Fig. 1b). The model was schematized in the vertical by 8 sigma layers with a thickness of 2, 3, 5, 8, 12, 20, 25, and 25% of the total water depth from the seabed up to the surface.
Tidal constituents of the simplified tide used to force the open ocean model boundary based on the application of the Lesser et al. (2004) methodology
Model schematization of wind and wave conditions. In the model, the coast trends north–south (0–180°), with eastward (90°) being oriented onshore
Percent of days year−1
Model calibration and validation
Contributions of waves and currents to sediment transport
The model results show distinctively different transport rates during the different forcing conditions. Storm conditions dominated the hydrodynamics and resulting sediment dynamics despite their low frequency of occurrence. Storm conditions generated the greatest setup on the reef flat (Fig. 3b) due to the strong winds and highest wave energy on the fore reef (Fig. 3c). The winds and waves drove strong (~5–15 cm s−1) currents across the fore reef and reef flat (Fig. 3d) and, together, generated high shear stresses that resuspended large quantities of sediment across the inner reef flat (Fig. 3e). Even though the Swell conditions did not generate strong currents, the long period of the waves generated substantial long-wave energy that caused almost 5 cm of setup. These long-wave motions during the Swell conditions resulted in higher peak suspended-sediment concentrations right at the shoreline than modeled during the Storm conditions, but this zone of elevated suspended-sediment concentrations was confined closer to shore and thus a lower total mass of sediment in suspension over the reef flat than in the Storm conditions. The Trade Wind conditions generated relatively strong wind-driven currents with little wave forcing and resulted in elevated suspended-sediment concentrations close to the shoreline, but these concentrations were on the order of a third to a quarter of those modeled during Storm and Swell conditions. Lastly, Variable conditions generated relative weak currents across the reef flat that resulted in suspended-sediment concentrations on the order of a third to a quarter of those modeled during Trade Wind conditions and almost an order of magnitude lower than during Storm and Swell conditions. Importantly, the waves, current speeds, and resulting suspended-sediment concentrations during the modeled forcing conditions match well with the in situ data collected under similar atmospheric and oceanographic forcing (Ogston et al. 2004; Storlazzi et al. 2004; Presto et al. 2006).
Modeled cumulative total annual sediment transport and residence times under present and predicted future sea-level rise scenarios
Cumulative transport (m3)
Effects of sea-level rise on waves and currents
Effects of sea-level rise on sediment dynamics
Similar to the study of hydrodynamics, the effect of sea-level rise on sediment-transport rates was investigated by elevating mean sea level (+0.10 m, +0.25 m, +0.50 m, and +1.00 m). The remainder of the model schematizations and parameter settings were unchanged compared to the base case simulation (sea level = 0.00 m). Sediment transport in the sea-level rise scenario model runs was governed by the fine sediment fractions, similar to the present-day (sea level = 0.00 m) model runs. Current speeds in the “mud belt” were relatively small (~5 cm s−1; Fig. 6c) and did not exceed the critical threshold of motion for the larger (sand-sized) grain-size fractions. As sea level was increased, current speeds increased and the relative minima in alongshore current speeds and maxima in cross-shore current speeds at the reef crest due to wave breaking migrated onshore, similar to the maxima in wave height and energy dissipation (Fig. 5).
The higher wave-induced high peak-bed shear stresses (Fig. 5d) and current speeds (Fig. 6c) close to shore resulted in a narrow band of suspended-sediment concentrations and transport along the shoreline (Fig. 6d). Transport rates due to Storm conditions were an order of magnitude larger than the Swell conditions, which were an order higher than Trade Wind conditions. While suspended-sediment concentrations increased in magnitude close to the shoreline and elevated suspended-sediment concentrations extend further across the inner half of the reef flat with increasing sea level between +0.10 m and +0.50 m, there is a distinct change in this pattern when sea level reached +1.00 m. When sea level was set at +1.00 m (almost doubling water depth over much of the reef flat), enough deep-water wave energy was able to propagate onto the reef flat such that larger waves impacted the shoreline, causing significant (>0.30 m) setup along the shoreline. These waves eroded approximately 350 m horizontally into the coastal plain deposit, resulting in wave heights (Fig. 5b), water levels (Fig. 6b), currents (Fig. 6c), and suspended-sediment concentrations (Fig. 6d) shoreward of the original shoreline location in the model at a cross-shore distance of 3,000 m. The erosion of the coastal plain deposit resulted in a lower maximum suspended-sediment concentrations but a greater overall volume of material in suspension over the profile (Table 3) as the elevated suspended-sediment concentrations extended seaward out to the reef crest (cross-shore distance of 2,000 m) and shoreward to the new shoreline (cross-shore distance of ~3,350 m). The lower maximum suspended-sediment concentrations at +1.00 m of sea-level rise resulted from the erosion of the primarily coarse-grained coastal plain deposit, which provided only 5% fine-grained material by volume to the reef flat that could easily be resuspended by the waves and currents.
The numerical modeling of hydrodynamics and sediment transport over fringing coral reefs presented here suggest the following changes are expected to occur under future sea-level rise scenarios:
Greater water depths over a fringing reef would reduce bottom friction and increase water depth relative to the wave height, resulting in larger and more energetic waves that could propagate over the reef crest and reef flat without breaking and larger wind-waves develop in situ on the reef flat, similar to the model results presented by Hearn (1999) and Hearn and Atkinson (2000). These findings are supported by data from Storlazzi et al. (2004), who showed that while wave heights offshore of the reef crest on the fore reef (depth ~10 m) are independent of sea level (r2 = 0.003, n = 961, P not significant), both wave height and wave period on the reef flat (depth ~1 m) are significantly correlated with sea level (r2 = 0.791 and 0.797, respectively; both n = 961 and P < 0.001), suggesting that waves on the reef flat are depth-limited. As sea-level rise increases, the larger waves over the reef and the landward migration of the zone of primary incident wave breaking will also modify the zone of high turbulence, primarily moving it shorewards.
Increased water depth would result in stronger currents all across the reef due to greater wave-driven flows from larger waves and the reduced height of hydrodynamic roughness relative to water depth that would allow for faster wind-driven currents to develop. The greatest increases in current velocity would be in shallow water on the inner reef flat where the water depth is on order of the hydrodynamic roughness of the seabed. This finding is supported by data from Presto et al. (2006), who showed the current speed at a given location on the reef flat was statistically greater (mean difference = 2 cm s−2, n = 27, P < 0.05) during periods with higher sea level than during periods of lower sea level. This would result in greater water exchange across and lower residence time of water on the reef flat, potentially altering the physical and chemical properties of the water column. The increased mixing and flushing of the reef flat with sea-level rise may help to dilute material delivered to the inner reef flat from the adjacent land, but it might also result in greater transport of terrestrial sediment onto the fore reef. The model results presented here, along with the observations made by Ogston et al. (2004), Storlazzi and Jaffe (2008), and Lowe et al. (2009) and modeled by Gourlay (1996), Hearn (1999), and Hearn and Atkinson (2000), show the effect of sea level on the magnitude of currents, driven both by wind and by wave-breaking, on coral reef flats.
An increase in wave energy and circulation due to elevated sea level will also affect sediment dynamics across a fringing coral reef. Larger waves resulting from high water levels will generate increased wave-induced stresses, which, in turn, will result in greater resuspension of sediment across the reef for a given grain size or composition (e.g., density) as suggested by Ogston and Field (2010). Statistically greater suspended-sediment concentrations (mean difference = 46 mg l−1, n = 32, P < 0.001) were observed by Presto et al. (2006) during periods with higher sea level; Storlazzi et al. (2004; Fig. 9 therein) showed that suspended-sediment concentrations on both reef flat (r2 = 0.383 for n = 961; P < 0.001) and fore reef (r2 = 0.238 for n = 961; P < 0.02) were significantly greater during periods with higher sea level. These observations, combined with their observations showing that greater offshore flow occurred with higher sea level, resulted in a statistically significant greater flux of sediment off the reef flat (r2 = 0.369 for n = 961; P < 0.05) and over the fore reef (r2 = 0.576 for n = 961; P < 0.001) with higher sea levels. The greater resuspension and transport would result in higher and longer persistence of turbidity as the increased shear stresses and turbulence would inhibit sediment from settling. The increased resuspension and larger wave-orbital velocities with sea-level rise may also alter patterns of abrasion of corals adjacent to sedimentary deposits such as the sediment-filled “grooves” of spur-and-groove structures. Although alongshore current speeds on the reef flat and over the fore reef are generally much greater (~2–8 times) than the cross-shore current speeds (Ogston et al. 2004; Presto et al. 2006), there is strong coupling between offshore flow and high suspended-sediment concentrations on reef flats such that the greatest sediment fluxes generally have an offshore component (Storlazzi et al. 2004). Storlazzi and Jaffe (2008) showed similar reef flat–fore reef coupling off west Maui, especially during periods of large waves and storms when water levels are elevated over the reef flat due to wind- and wave-induced setup.
As pointed out by Graus and Macintyre (1998) and Ogston and Field (2010), the larger waves on the reef flat that would result from sea-level rise will also increase the delivery of energy to the coastline. As these larger, more energetic waves reach the shoreline, which at present is in quasi-equilibrium with the current wave climate, they would exceed the critical shear stresses for resuspension of the beach and coastal plain material, causing coastal erosion and adding additional sedimentary material to the reef flat, similar to the observations by Sheppard et al. (2005). This additional material, resuspended by larger waves and stronger currents, would likely exacerbate turbidity not only on the reef flat but also likely on the fore reef as well (Storlazzi et al. 2004; Storlazzi and Jaffe 2008). Although the stronger currents may reduce the overall residence time of any given sedimentary particle on the reef flat, the increased supply of material by erosion and the increased duration of resuspension for a given set of waves and currents could potentially result in greater exposure of corals to suspended sediment on both reef flat and fore reef.
The one-dimensional modeling by Ogston and Field (2010) on waves and sediment resuspension and the two-dimensional coupled hydrodynamics and sediment-transport modeling presented here provide insight into the potential affects of sea-level rise on flow and sediment dynamics over an exposed fringing coral reef based on current observations of forcing conditions (winds and waves). The hydrodynamic and sediment-transport data presented here suggest that while some protected fringing coral reefs many benefit from the additional accommodation space as suggested by Edwards (1995), all will undergo a number of changes in both chemical and biological processes (e.g., Sebens and Johnson 1991; Edwards 1995; Falter et al. 2004; Storlazzi et al. 2005) due to changes in the hydrodynamics caused by sea-level rise. Many exposed fringing coral reefs may be threatened by additional input and resuspension of terrestrial sediment that will likely negatively affect corals and the ecosystems they support on both reef flat and fore reef, as first postulated by Buddemeier and Smith (1988).
This work was carried out as part of the US Geological Survey’s Coral Reef Project as part of an effort in the United States and its trust territories to better understand the effects of geologic processes on coral reef systems. Andrea Ogston (UW), Joshua Logan, Thomas Reiss, and David Gonzales (USGS) assisted with the fieldwork and instrumentation. We would also like to thank Mark Buckley (USGS), Jeff Hansen (USGS), and the editors at Coral Reefs who contributed numerous excellent suggestions and a timely review of our work. Any use of product, trade, or firm names is for descriptive purposes only and does not imply endorsement by the US Government.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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