Geomorphological modelling of tropical marine landscapes: Optical remote sensing, patches and spatial statistics

Continental Shelf Research 31 (2011) S151–S161

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Geomorphological modelling of tropical marine landscapes: Optical remote sensing, patches and spatial statistics S.M. Hamylton , T. Spencer Cambridge Coastal Research Unit, Department of Geography, University of Cambridge, Downing Place, Cambridge, CB2 3EN, UK

a r t i c l e in fo

abstract

Article history: Received 12 June 2009 Received in revised form 2 February 2010 Accepted 3 February 2010 Available online 19 February 2010

The relation of structural responses to underlying functional processes at the landscape scale helps develop our understanding of geomorphological phenomena at the coastline. This paper demonstrates how a habitat map derived from remotely sensed imagery was used as the basis for the development of an explanatory model to investigate factors influencing the linearity of alternating carbonate sand and seagrass patches on a reef flat in the Seychelles, western Indian Ocean. In combination with techniques established in landscape ecology for interrogating broad scale processes and spatial statistical procedures that bring geography explicitly into the analysis, an emergent framework for the quantification and investigation of geomorphological processes is illustrated. The combined influence of adjacent spur and groove amplitude and incident wave power accounted for 81% of the variation in sand and seagrass patch linearity across the habitat map. A series of steps in model development are examined, including observation, measurement, experimentation and interpretation. These steps both define and permit an empirical approach to geomorphology and the case study highlights how each can be achieved by adopting an interdisciplinary framework. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Landscape ecology metrics Spur and groove Patch dynamics Seagrass beds Wave power modelling Seychelles Amirante Islands

1. Introduction The mutual co-adjustment of process and form, morphodynamics, is of central interest to geomorphology, the scientific study of landforms and earth surface processes. An empirical approach to geomorphology aims to develop relationships between variables corresponding to aspects of process and those reflecting some measure of system response, as represented by the geometrical form of the landscape (Mather, 1979). Through quantification of the result (structural landform) and driving variable (functional process), models can be developed to reconstruct the laws governing the interaction of the two. This provides a framework for generalization, it being impossible to monitor landform change given the space and timescales involved (Richards et al., 1997). Coral reef systems are particularly amenable to this approach, as the form of the reef surface expresses the relations between biological interactions (including competition and grazing pressures) and physical processes, which include wave action, tidal currents, turbidity and sedimentation, irradiance and subaerial exposure (Woodroffe, 2002). Optical remote sensing datasets allow the accurate representation of both structural and functional attributes at the landscape

 Corresponding author.

E-mail address: [email protected] (S.M. Hamylton). 0278-4343/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.csr.2010.02.003

scale and, therefore, provide a valuable basis for the development of morphodynamic models. Within this framework, landscape ecology techniques provide for the measurement of landscape elements, initially through the metrics associated with individual patches discernable in the landscape, and subsequently through the interrogation of patch assemblages across gradients within landscapes (Frohn, 1998). In conjunction with this approach, spatial statistical procedures, those in which a clear association is maintained and manipulated between the quantitative data and the spatial coordinates that locate them, enable an explicit geographical element to be built into the analysis (Chorley, 1972). Whilst there have been considerable recent advances in seafloor and benthic habitat mapping applications (e.g. Wright and Heyman, 2008), and notwithstanding a strong focus on patch dynamics in understanding seagrass landscapes (e.g. Patriquin, 1975; Robbins and Bell, 1994; Fonseca et al., 2006), geomorphologists have been slow to apply landscape ecology methodologies towards a better understanding of coral reef morphodynamics. For the purpose of this study, the landscape can be defined as an intermediate scale region (1–103 km2) comprising landforms and landform assemblages, ecosystems and anthropogenically modified land (Slaymaker et al., 2009). Structure refers to the spatial relationships between distinctive entities of the landscape: the size, shape, number and configuration of components. Function refers to the interactions between the spatial elements, i.e. the flow of energy and materials between the component

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landforms (Summerfield, 1991). Maps derived from remotely sensed imagery can be viewed as representations of both structural responses and functional drivers at the landscape scale. 1.1. Geomorphology and remote sensing of coral reef landscapes From a geomorphic perspective, reefs are three-dimensional accumulations of calcium carbonate that have evolved over centennial to millennial timescales (Perry et al., 2008). Primary controls of these accumulations act over a range of spatial and temporal scales (Table 1). By comparison, contemporary studies of reef structure often emphasise ecological characteristics, such as the spatial coverage of live coral (e.g. Wilkinson, 2008) and temporal phase shifts between ‘hard’ coral assemblages and ‘soft’ macroalgal communities (e.g. Done, 1992). The distinction between the structure of the underlying reef framework and its ecological veneer is important because their characteristics are controlled by processes, which operate over markedly different temporal and spatial scales. On the one hand, reef surface ecology represents a manifestation of contemporary drivers (over timescales of daysdecades and areas o0.1 km2), while reef structure and the reef sedimentary landforms that are intimately related to such structures (Kench et al., 2009) are a fundamental indicator of longer-term system integrity (operating over timescales of decades to centuries and areas 0.1–100 km2). An understanding of modern reef landforms from either an ecological or a geomorphological perspective is gained from an equal appreciation of physical, biological and chemical functional drivers that act on inherited surfaces and frameworks (Hubbard, 1997). Given the great diversity of coral reef surface morphology, it is remarkable that most classification schemes of reef landforms are variants on Darwin’s (1842) simple tripartite division into fringing reef, barrier reef and atoll, with continental shelf reefs being broadly amalgamated under the barrier reef category. The most elaborate classifications devised have been those concerned with the evolution of reef growth forms on the Great Barrier Reef, originally proposed by Fairbridge (1950) and subsequently elaborated by Maxwell (1968), Flood and Orme (1977) and Hopley (1982). Reef mapping based on satellite imagery dates from the 1970s but morphological interpretation has been largely restricted to the division of reef areas into the basic geomorphic units occurring at water depths and spatial scales that are amenable to detection. These include the categories of forereef, reef crest, reef flat, back reef and lagoon (Kuchler, 1986; Mumby and Harborne, 1999). While these schemes provide insight into the shallow marine landforms visible in imagery, the terminology employed does not necessarily aid understanding of their formation (of which

Maxwell’s (1968) ‘resorbed reef’ type is a prime example) and they do little to engage with the functional processes underlying such structures. Rather than simply the geographical extent of land covers (e.g. Hopley et al., 1989), the empirical relation of morphological structure to function calls for a redefinition of the landscape as a physical realisation of the functional context in which geomorphological processes operate. This paper highlights the utility of remote sensing technology for modelling geomorphological relationships between structure and function in marine landscapes. The application of such a model is demonstrated for a reef flat in the Seychelles and the interdisciplinary framework for uniting the different space and time scale perspectives with which studies of coral reef morphodynamics are commonly employed is illustrated.

2. Location Alphonse Atoll, southern Seychelles (7101S; 521440 E) lies at the southern end of the Amirantes Ridge on the southwestern margin of the Seychelles Plateau, western Indian Ocean (Fig. 1). Alphonse is a small symmetrical, triangular atoll (6  4 km; total area 1128 ha). The peripheral reef-flats cover an area of 402 ha and vary in width from 640 m, at the northwest tip of the atoll, to 1900 m on the east-facing atoll margin (Stoddart, 1984). The atoll has a 540 ha (48% of the total area) lagoon with a simple dish-shaped morphology, reaching a maximum central depth of 13 m. Water exchange between the surrounding ocean and lagoon is dominated by a single channel, 180 m in width and 4–10 m deep, connecting the lagoon to the outer fore-reef slope. The forereef topography comprises three distinct sections. Immediately seaward of the reef-flats, in less than 5 m water depth, is a shallow rocky pavement. In water depths of 5–15 m, a 50–150 m wide, gently sloping rock surface, with live corals in a matrix of rubble and sand, extends down to a drop-off at a water depth of 17–20 m (Spencer et al., 2000). The drop-off may either be a sheer vertical reef wall, as observed on both sides of the north-eastern tip of the atoll, or it may be a steep slope, as on the south-west margin of the atoll. The Alphonse reef flat is subject to a semi-diurnal tidal regime of range 1.8 m and a wave field that is dominated by the influence of the SE Tradewinds. In the Northern Hemisphere summer (May–October) atmospheric pressure is low over Arabia and the Indian subcontinent and high over southern Africa, with strong anticyclonic conditions centred at 29–301S. As a result, the SE Trades dominate over the whole of the southern western Indian Ocean (Walsh, 1984). In the Northern Hemisphere winter (December–March) high pressure develops over the landmasses to the north. A pronounced intertropical trough develops at

Table 1 The spatial and temporal scales of key structural responses to functional drivers in coral reef landscapes (after Hubbard, 1997). Dimensions (km)

Temporal duration (yrs)

Landform examples

Major controlling factors

Micro 0.001-1

o 10

Reef-wide Shelf Platform Coral

Light Nutrients Sedimentation Antecedent topography

Meso 1–103

10–103

Ocean basin Reef system Island

Temperature Salinity Wave energy Antecedent topography

Macro 103

104–107

Ocean Trench/ ridge

Tectonics Sea level Seawater chemistry Antecedent topography

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Fig. 1. Regional bathymetry of the Amirante Ridge and Trough, Seychelles Plateau and Mascarene Plateau (D= Desroches; P= Platte; Ct =Constant Bank; C= Coetivy; F = Fortune Bank) (left) and Amirantes Archipelago and Alphonse Atoll, western Indian Ocean (right) (adapted from Spencer et al., 2009).

10–151S and anticyclonic conditions weaken and move to 33–351S. The NE Trades characterise the northern Indian Ocean, becoming the rainy season NW Monsoon south of the Equator in the Amirantes. In the transition periods (April and November) winds tend to be light and variable and intertropical troughs lie close to the Equator. Spencer et al. (2009) document seasonal variations in average wind direction at Mahe´, 415 km north west of Alphonse, which has a typical mean windspeed of 4.7 m s  1 at the height of the SE Trades. By comparison, mean windspeeds associated with the NW Monsoon peak at 2.1 m s  1 in January. Windspeeds in the calm, inter-monsoon months of April and November are 1.7 and 1.9 m s  1, respectively. Tropical cyclones are rarely this close to the equator in the western Indian Ocean; typical frequencies are 2.1 storms per decade (Walsh, 1984). The shallow rocky pavement on the fore-reef at Alphonse exhibits distinct coral spur and groove formations. These extend around the entire atoll perimeter but are particularly well developed on the shallow south-eastern and north-western fore-reef. Alternating linear tongues of seagrass and well-sorted carbonate sediments (D50 = 0.51 mm) are a distinctive feature of the adjacent reef flat. Such patterns have been noted in several shallow water reef environments, both in the Indian Ocean and Caribbean Sea (Guilcher, 1958; Den Hartog, 1971; Cambridge, 1975; Marba and Duarte, 1994; Fonseca and Bell, 1998). The models developed in this case study investigate the functional roles of the magnitude of incident wave power and the frictional attenuation resulting from the seaward spur and groove morphology as drivers of these linear seagrass and sediment patches (structural responses) on the reef flat. Modelling was carried out

in a two stage process, with initial bivariate regressions that investigated the influence of each potential explanatory variable independently, followed by a multivariate regression to investigate their combined effect.

2.1. Methodology 2.1.1. Generation of the habitat map A habitat map for Alphonse Atoll was generated from remotely sensed data collected with an aircraft-mounted Compact Airborne Spectrographic Imager (CASI) in January 2005. Nineteen spectral bands of data were acquired (between wavelengths 434–900 nm, bandwidth 7 nm) at a spatial resolution of 1 m2, yielding synoptic coverage of the area of interest. Corrections for the effects of scattering and absorption in the atmosphere were performed using the Atmospheric Correction Now (ACORN) algorithm to retrieve radiance values at the water surface (ACORN, 2001). Raw data were geocorrected using ground reference points and a first order polynomial model was applied to correct for the linear offset, with nearest neighbour resampling (Erdas inc., 1997). Following geocorrection, flight strips were mosaiced using a band-wise linear colour balancing model to minimise across-track variance, with histogram matching to adjust for radiance offsets. Water column correction was performed to address the effects of light absorption and scattering in the water using an amended version of formulas derived by Bierwirth et al. (1993). These were adjusted to account for the refractive influence of the water

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surface at the air/water boundary and rearranged to solve for substrate reflectance, Rb (Eq. (1)). This method was chosen because it does not rely on band ratios (which reduce the number of bands for subsequent use in classification) and it accounts for refraction Rb ¼

1=0:54Rrs ðz ¼ aÞð1e e2kz

2kz

ÞRw

ð1Þ

where the radiance just above the water surface Rrs (z= a) was provided by atmospherically corrected imagery, the water column reflectance of optically deep water (Rw) was estimated from image statistics and the depth (z) of each pixel was extracted from a bathymetric map. For each band, the diffuse attenuation coefficient (k) was estimated through regression of digital data taken from a series of white targets deployed at known depths, across the range 5–10 m. The gradient of the regression line of log transformed data plotted against water depth yielded an estimation of k. Radiance measures (W sr  1 m  3) over a number of spectral subclasses were extracted to build up training areas, i.e. statistical populations of habitat classes apparent in the image feature space. A maximum likelihood classification was performed on depth invariant bands, assigning each pixel of the image to the most likely habitat (Mather, 2004). Map accuracy was assessed by exporting 283 polygon centroid coordinates to a hand-held GPS (with an x, y accuracy of 710 m) and comparing the corresponding location in the field to the habitat type recorded on the map. 2.1.2. Measurement of the response variable: seagrass patch linearity Gustafson and Parker (1992) developed a unitless metric for assessing patch linearity based on the medial axis transformation (MAT). The MAT skeleton is defined by a depth map of the patch, where each pixel represents the distance (in pixels) to the nearest edge. The MAT skeleton is then produced by removing all pixels from the depth map except local maxima (pixels with no neighbours having greater values). The linearity metric, L, is based on the premise that elongated patches of a given area have MAT skeletons closer to their edges than square patches of the same area (see Fig. 2 for an illustrative example). A depth map was created, where each pixel value represented the distance (in pixels) to the nearest edge; the MAT skeleton was derived by extracting local maxima, i.e. pixels with no neighbours possessing greater values. The linearity metric was calculated

Fig. 2. Example of linearity calculation for two different rasterised patch shapes.

using Eq. (2) L¼

½aij =ð2brÞ2 1 aij

ð2Þ

where aij* is the area of patch ij in terms of number of cells, and b the average cell value of the pixels comprising the patch, r =0 if the patch contains side-by-side pixel rows; 1 if not. Six analysis windows were established in the centre of the reef flat to investigate patch structure around the atoll. Linearity was calculated for each sand and seagrass patch by calculating Euclidean distance from patch boundaries and averaging pixel values across patch spatial extents. A focal rank operator (3  3 pixels) was used to record the number of pixels in the immediate neighbourhood with a value less than the centre pixel. For each pixel, local maxima were returned as zero values in an output thematic layer. An optimal sample size for the analysis windows was defined using an experimental semivariogram. This was calculated by sequentially comparing the linearity of each individual patch to the rest of the patches in the map via the Moran statistic and plotting these values against the distance between patches. The lag distance at which the maximum semivariance was reached for linearity of all seagrass patches within the landscape was found to be 300 m; hence, this was adopted as the sample window dimensions. To derive information on potential drivers of reef flat patch structure as a response variable, i. field data were collected on spur and groove amplitudes, and; ii. wave power was empirically modelled. 2.1.3. Measurement of independent variables: spur and groove amplitude Field measurements of groove depths were made using a Norcross DF2200PX handheld bathymetric sounder. A 50 m transect was established along a defined bearing, along which a diver swam at a constant depth above the spur and groove morphology, perpendicular to the direction of groove alignment. Hand-held GPS locations were recorded at both ends of the transect and depth measurements were recorded at 1 m intervals. The independent variable of spur and groove amplitude, Sg, was expressed as the average amplitude of all spurs and grooves falling inside the analysis window. 2.1.4. Development of a bathymetric model It was necessary to produce a detailed bathymetric model of the study area for input into both the water column correction algorithm and the wave exposure model. The bathymetric model was derived by adapting the approach employed by Jupp (1988) for use with CASI data. Jupp (1988) used the range of depths to which light penetrates in different wavebands to map water depths using Landsat imagery on the Great Barrier Reef. Red light attenuates more rapidly than green or blue light due to the effects of absorption and scattering in the water column. A depth, therefore, exists at which red light is fully attenuated, whereas green and blue light can still be detected. Zones where there is no red signal, but green and blue are apparent, are analogous to depth ranges and, given a certain water quality, can be mapped as depth of penetration zones. Three assumptions underpin this method: (i) that light attenuation is an exponential function of depth, (ii) that water quality, and hence the attenuation coefficient, is constant across the image and (iii) that the albedo of the substrate is constant across depths. All three assumptions were met in this case study. A Type I water quality was assumed. This was selected because it related to open ocean waters, as opposed to coastal or lagoonal

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waters where variation of suspended sediment concentrations within the water column may add further complications. Jerlov (1976) modelled the depth of light penetration in Type I water columns for the visible section of the electromagnetic spectrum. From this model, maximum depths were inferred from the return signal discerned from successively shorter wavelengths. This was done by constructing a logic table to relate maximum reflectance values in each band to depth ranges. Converting the data from pixels assigned a depth of penetration to a continuous surface was necessary for input into the wave power model. An inverse distance weighting interpolation method was used for this conversion as the available set of points, i.e. assigned pixels, produced was dense enough to capture the extent of local bathymetric variation needed for analysis (i.e. 475% of pixels were assigned a depth) (Childs, 2004). The resulting bathymetric map for Alphonse Atoll had a spatial resolution of 1 m2. 2.1.5. Calculation of wave power Wave power was calculated using the approach described by Roberts (1974). Transects of 5 km length were established at 101 intervals around the atoll, running from deep water towards the lagoon centre, using the radiating lines extension tool to ArcView (Jenness, 2006). Wave height and period were hindcast for the outer limit of each transect using mean wind data from an 8 year period. Wind distributions and strengths were obtained from the Indian Ocean volume of the Marine Climatic Atlas of the World (US Navy, 1976). These were recorded as mean monthly wind strength and frequency from the southern Seychelles cell at 51S and 451E and represented the best available data on wind speeds for the region. There have been no significant changes in the characteristics of the wind regime since the acquisition of these measurements (Liu et al., 2008). Fetch lines were created of length 22 km, spaced 451 apart, originating from each end point (Fig. 3). All fetch-limited lines (i.e. those intersecting an overlaid coastline shapefile) were exported and trimmed to the point of intersection with the coastline, using a land mask. Polyline

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lengths were then calculated and input as fetch distances into the wave transformation model. Significant wave height was estimated at the deep-water end of each transect from the fetch distances and wind data 1:1 0:45 F Hj0 ¼ 0:00082U10

ð3Þ

4:6 0:27 Tj0 ¼ 0:087U10 F

ð4Þ

where Hj0 is the significant wave height, Tm the wave period at the peak of the spectrum, U10 the wind speed at an elevation of 10 m, F the fetch in m. For fully developed seas, Hj0 and Tj0 were calculated using Eqs. (5) and (6). 2 Hj0 ¼ 0:034U10

ð5Þ

Tj0 ¼ 0:073U10

ð6Þ

A lookup table was separately created for the derivation of a shoaling coefficient in conjunction with a bathymetric map for a given depth to wavelength ratio. A refraction coefficient was calculated from the change in angles between the waves and shoreline and wave velocity (Wiegel, 1964). At each 1 m increment, j, along the transect, the mean wave height, Hj, was computed for the corresponding base map pixel as a function of the wave height at the previous interval, Hj  1, change in shoaling coefficient, Ks, refraction coefficient, Kr, and frictional attenuation (Bretschneider, 1966) Hj ¼ Hmj =ð½f Hmj 2fðDxÞj =Ksj T 4  þ 1Þ

ð7Þ

in which Hmj ¼ Hj1 þ Oj =Z

ð8Þ

where

Oj ¼ Hj1ðKsj=Ksj1 Krj=Krj1Þ

ð9Þ

f is a constant friction factor (%), the value of which depends on bottom roughness, this was aggregated for all the different bottom coverages on the Alphonse fore-reef to a value of 0.03, which accounts for energy dissipation across shallow reef crests; (Dx) is the linear distance along the ray between points j and j  1, and 64p½ksj=sinh2pz=l3 3g 2

f¼

ð10Þ

where g is the acceleration of gravity, z the water depth, and l the wavelength. Wave characteristics were determined at each interval. From these, wave energy was computed. The mean square horizontal and vertical velocities were then calculated for each pixel using Eqs. (11) and (12). v2x ¼

v2z ¼

a2 g 2 k2 2

2o2 cosh ðkhÞ a2 g 2 k2 2

2o2 cosh ðkhÞ

cosh2ðkðz þ hÞÞ

ð11Þ

sinh2ðkðz þhÞÞ

ð12Þ

where h is the water depth and z the depth measured negatively from the surface (since we were calculating benthic wave energy, z=  h and vz =0 always), where o is the rotational frequency, k the wave number and a the mean-to-peak amplitude

Fig. 3. A schematic of the wave energy model applied to Alphonse. Significant wave height was hindcast at the end of each transect. The effects of wave refraction, friction and shoaling were modelled at 1 m increments along each transect.

o¼

2p Tm

ð13Þ

k¼

4p2 2 gTm

ð14Þ

Hj0 a ¼ pffiffiffi 2 2

ð15Þ

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The energy density (J m  3) was then expressed as the kinetic energy according to Eq. (16) Ek ¼

1 pðv2x þ v2Z Þ 2

ð16Þ

where r is the density of seawater (1030 kg m  3). Once wave energy had been calculated in each direction, apparent wave power (Pp) at a given point p was derived using Eq. (17) Pp ¼

n X

ðti Eki Þ

from the sample windows to the patches comprising the rest of the atoll habitat map. Tests were run to ensure the assumptions of multiple regression were met (Fox, 1997).

ð17Þ

i¼1

where ti is the annual probability that the wind blows from direction i, Eki the wave power in the direction of line i and n the number of directions considered (in this case, this was 8). 2.1.6. Two stages of model development: descriptive bivariate and inferential multivariate regression models The influence of water movement was experimentally investigated on patch structure by carrying out regressions of patch linearity against independent variables in two stages. In the first instance, descriptive bivariate regressions were used to explore the separate influence of ‘‘groove amplitude’’ and ‘‘wave power’’ on the linearity of patch assemblages within the analysis windows. The geographical distribution of the residuals from these bivariate models was then reviewed to investigate additional model covariates. In the second instance, multivariate regression was used inferentially to extend statements about the mean patch statistics

2.2. Results The image classification generated clear and accurate representation of the heterogeneity of shallow reef habitats apparent in the raw image (Fig. 4). Overall accuracy of the habitat map, measured in terms of the number of patches correctly identified divided by the total number of patches in the validation assessment (Congalton, 1991), was found to be 77%. For the seagrass and sand classes, average producer and user accuracies were 88% and 81%, respectively. Computed values for the linearity metric ranged between 0.22 and 0.67 for seagrass patches on the reef flat. Shallow rocky pavement spur and groove formations adjacent to the survey windows were well pronounced on the southeastern (site C, Fig. 5), eastern (site B, Fig. 5) and northwestern (site F, Fig. 5) sides of the atoll; at these sites deep (4 2 m) grooves were prevalent. Lower relief spur and groove formations were recorded at sites A, D and E (Fig. 5) where wider, less frequent spurs divided shallower ( o 1 m) grooves. The wave power model indicated that the south-east coastline of the atoll was subject to higher energy levels than the remainder of the atoll, with wave power reaching 300 J m3 in this region, compared to 100–150 J m3 elsewhere (Fig. 6).

Fig. 4. Habitat map of Alphonse Atoll.

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Fig. 5. Profiles of spur and groove amplitudes adjacent to the analysis sites around the atoll, taken from six transects of length 50 m.

Descriptive bivariate regressions revealed moderate positive correlations for groove amplitude and wave power against patch linearity (r2 = 0.58 and r2 = 0.62 for groove amplitude and wave power, respectively). These findings suggested that the better ‘‘developed’’ the spur and groove morphology, and the greater the wave power, the more linear the adjacent seagrass patches. The groove depth and linearity bilinear regression gave rise to positive residuals on the west side of the atoll and negative residuals on the east side, approaching unity in the southeast. Overall values ranged from –0.004 to 0.13 (Fig. 7). Comparison of the groove depth and wave power model revealed both variables to be at a maximum on the southeast region of the atoll. The east side was subject to high energy levels relative to shallow groove depth, whereas the west side had deeper grooves and lower energy in relative terms. This suggested that the two variables might have more explanatory power combined in a multivariate model. The combined influence of adjacent groove depths and incident wave power explained 81% of the variation in seagrass patch linearity across the overall habitat map (Fig. 8). The multivariate regression yielded a function that read L ¼ 0:23 þ2:58  103 Pp þ 3:93  103 Sg where L is the patch linearity, Pp the modelled wave power and Sg the measured spur and groove amplitude. T-test values were 9.337 and 12.429 for the mean wind force and groove depth,

respectively (5611 of freedom; po0.001; T critical 3.92), suggesting that the estimated coefficients were significantly different from zero. All diagnostics indicated compliance with the assumptions of multiple regression (Fox, 1997).

3. Discussion Overall, it was found that spur and groove morphology (as measured by groove and groove amplitude) and incident wave power had a moderate influence on reef flat seagrass patch linearity when treated independently, with greater explanatory power in a combined model. The spatial pattern of linearity among sand and seagrass patches can be linked to the absolute amount of energy reaching the coastline as a result of wind-driven surface waves, as confirmed by the bivariate regression (r2 = 0.62). The plan-view pattern is one of the abundant alternating linear patches of seagrass and sand in the south-east and north-west of the atoll, with lower values in the north-east. This corresponds to the surface wave energy field, driven by the prevailing monsoons. The amount of energy reaching a shore is influenced by water depth, which is controlled by wave-setup and tides on the Alphonse reef flat. Setup, the rise in mean water level above the still-water elevation of the sea due to waves breaking, is a

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Fig. 6. Wave power as modelled using linear wave theory around the atoll (units J m3).

significant determinant of reef-top sediment transport (Komar, 1998). Experimental results have found wave setup and flow to increase with increasing off-reef wave height and period, and with decreasing reef top water depth (Gourlay, 1996). On Alphonse reef flat, determine the geomorphic work that can be carried out in two ways: through unidirectional currents flowing into and out of the lagoon with a diurnal tide frequency and by modulating reef flat wave energy through water depth. At low tide, waves break on the reef edge and no significant energy is propagated across the reef top. However, at high tides, depthlimited waves are able to propagate across the reef-top. Such a distinction is important at Alphonse, where the 1.8 m tidal range coincides with the height of the reef crest. Collectively, setup and tides separate out the influence of (i) wind-driven surface waves, and (ii) subsurface currents. This separation, along with the absence of multicollinearity between the explanatory variables of wave power and groove depth, justifies the inclusion of two functional drivers that operate at different depths of the water column, and a corresponding multivariate analysis. The geographical distribution of residuals from the spur and groove amplitude versus linearity bilinear regression revealed spatial structure that suggested additional independent variables to have been omitted from the model. This spatial structure consisted of elevated values relative to spur and groove amplitude on the east side of the atoll and lower relative values in the west, as was the case with wave power. The multivariate regression encompassed processes that differed in the nature of their influence on the independent variable, as evidenced by the greater level of explanatory power of the multivariate model.

The distribution of patch linearity in relation to adjacent spur and groove morphology may be explained by particle transport associated with the transformation of energy from the outer to inner sections of the reef system. The particle size of the carbonate sand (D50 = 0.51 mm) on the reef flat and the subsurface current speed ( 20 cm s  1) correspond to a critical force threshold for particle entrainment (Komar, 1998). Spurs contribute to energy dissipation through the action of bottom friction against subsurface currents on the shallow rocky pavement. Frictional attenuation over spurs lowers the energy available for particle entrainment, inducing sediment deposition closer to the reef crest. In areas adjacent to grooves, lower lying topography and a smaller surface may promote extended entrainment, producing sand tongues that extend further onto the reef flat. An energy attenuation profile could, therefore, be established for landwardmoving reef flat water that reflects the spur and groove topography seaward of the reef crest.

4. Conclusions: observation, measurement, experimentation, and theoretical interpretation The transition from descriptive to inferential modelling in this two-stage process of model development highlights the importance of good observation and measurement of both structural and functional phenomena. Although it is not possible to instantaneously see the reef and resolve constituent communities at the landscape scale, the habitat map derived from a remotely sensed image provides a theoretical representation of its structure. Functional drivers of these landforms can be similarly

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Fig. 7. Distribution of the residuals inside each of the analysis windows from the initial bivariate regression of groove depth against seagrass patch linearity.

Fig. 8. Multivariate regression of wave power and spur and groove amplitude against linearity at the patch level.

inferred on the basis of physical reasoning from different domains of the image (Verstappen, 1977; Langrebe, 1998). In geomorphological research, the reliability of measurement requires continual scrutiny and coincidence between the results of several different

measurements predicted by a combination of geomorphological and optical remote sensing theory and those collected directly from the field gives confidence that these closely approximate ‘‘reality’’ (Richards, 2003). In this case, this was sought through

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validation of the habitat map against field data and the representations of both independent and dependent variables appeared to be fit for the purpose of model development. Landscape ecologists commonly employ metrics to quantitatively capture spatial elements of patterning in a single variable for an individual patch, while the statistical properties of ensembles can be interrogated to reveal broader scale trends. Quantification at both the patch and patch assemblage scale has important implications in the model development process. Firstly, decomposition of the Alphonse landscape into patches, the fundamental unit of habitat maps, permitted measurement at a level (interval) for which statistical investigation was possible. Furthermore, the use of the linearity metric enabled a response variable, with both ecological and geomorphological meaning, to be quantified. Effective experimental design can reveal meaningful components of observational data through control, simplification and manipulation of remote sensing datasets as representations of reality. Moving window analysis enabled the linearity statistics of patches on the Alphonse reef flat to be sampled for a specific purpose. These were investigated experimentally using regression, by stating a null hypothesis (that the linearity of sand and seagrass patches across the reef flat is independent of the amplitude of adjacent spur and groove formations and the power from incident waves) and then seeking to disprove this in order to accept the logical alternative that an effect does exist. The bivariate regressions were ‘‘descriptive’’, in that they were carried out on seagrass and sand patch assemblages inside windows, the location and size of which were chosen to sample the apparent variation in a response variable where all covariates were not necessarily present in the model. Interactions between structural forms and functional drivers are rarely bilateral, but encompass a number of components. Such interactions, therefore, call for the use of multivariate models to provide adequate explanation in geomorphology (Summerfield, 1991). Examination of the geographical variation in the residuals from this step added value by providing a useful basis for addition of a covariate that enhanced the explanatory power of the model. In turn, this allowed the descriptive statement to be extended to an inferential statement relating to the whole habitat map. The model revealed a relationship between the combined influence of wave exposure and depth and patch linearity; a theoretical interpretation prompts the question ‘why?’ The explanatory power of the theory might be a good indicator of its utility, although it is important to emphasise that the model, which incorporates the combined influence of adjacent groove depths and incident wave power, enables us to explain 81% of the variation in the linearity of seagrass and sand patches across the overall habitat map. This does not necessarily imply predictive success; merely it reveals a relationship that may well be determined by a covariate of the variable examined. The focus, therefore, moves on to the criteria whereby one explanatory account may be preferred over another. New hypotheses and experiments must now be devised to provide even more stringent tests of the model. In such a remote location, with the focus being phenomena that are largely underwater, which precludes their comprehensive field sampling, this represents the best available account for the time being.

Acknowledgements The following organisations and people are thanked for their assistance with work at Alphonse: Khaled bin Sultan Living Oceans Foundation, Seychelles Centre for Marine Research and Technology, Dr. Annelise Hagan of the Cambridge Coastal

Research Unit, The Island Development Company (Seychelles) and Great Plains Seychelles. References ACORN, 2001. Atmospheric correction now: Analytical imaging and geophysics LLC, version 3.12. Bierwirth, P.N., Lee, T.J., Burne, R.V., 1993. Shallow sea-floor reflectance and water depth derived by unmixing multispectral imagery. Photogrammetric Engineering and Remote Sensing 59, 331–338. Cambridge, M.L., 1975. Seagrasses of southwestern Australia with special reference to the ecology of Posidonia australis in a polluted environment. Aquatic Botany 1, 149–162. Childs, C., 2004. Interpolating Surfaces in ArcGIS Spatial Analyst. ESRI Education Services. Chorley, R.J., 1972. Spatial analysis in geomorphology. In: Chorley, R.J. (Ed.), Spatial Analysis in Geomorphology. Methuen, London, pp. 3–17. Congalton, R., 1991. A review of assessing the accuracy of classifications of remotely sensed data. Remote Sensing of the Environment 6, 35–46. Darwin, C.R., 1842. The Structure and Distribution of Coral Reefs. Smith, Elder & Co., London. Den Hartog, C., 1971. The dynamic aspect in the ecology of seagrass communities. Thalassia jogoslavia 7 (1), 101–112. Done, T.J., 1992. Phase shifts in coral reef communities and their ecological significance. Hydrobiologia 247, 121–132. Erdas Inc., 1997. Erdas field guide. fourth ed., Erdas, Atlanta. Fairbridge, R.W., 1950. Recent and Pleistocene coral reefs of Australia. Journal of Geology 58, 330–401. Flood, P.G., Orme, G.R., 1977. A sedimentation model for platform reefs of the Great Barrier Reef, Australia. In: Proceedings of the third International Coral Reef Symposium, Miami, vol. 2, pp. 111–117. Fonseca, M.S., Bell, S.S., Robbins, B.D., 2006. Foreward. Special issue on seagrass landscapes. Estuarine Coastal and Shelf Science 68, 380–382. Fonseca, M.S., Bell, S.S., 1998. Influence of physical setting on seagrass landscapes near Beaufort, North Carolina, USA. Marine Ecology Progress Series 171, 109–121. Fox, J., 1997. Applied Regression Analysis, Linear Models, and Related Methods. Sage Publications Inc., London. Frohn, R.C., 1998. Remote Sensing for Landscape Ecology: New Metric Indicators for Monitoring, Modeling, and Assessment of Ecosystems. Lewis Publishers, Boca Raton. Gourlay, M.R., 1996. Wave set-up on coral reefs. II. Set-up on reefs with various profiles. Coastal Engineering 28 (4), 17–55. Guilcher, A., 1958. Coastal and Submarine Morphology. Methuen, London. Gustafson, E.J., Parker, G.R., 1992. Relationships between landcover proportion and indices of landscape spatial pattern. Landscape Ecology 2, 101–110. Hopley, D., 1982, The Geomorphology of the Great Barrier Reef: Quaternary Development of Coral reefs. Wiley-Interscience, New York. Hopley, D., Parnell, K.E., Isdale, P.J., 1989. The Great Barrier Reef Marine Park: dimensions and regional patterns. Australian Geographical Studies 27, 47–66. Hubbard, D.K., 1997. Reefs as dynamic systems. In: Birkeland, C. (Ed.), The Life and Death of Coral Reefs. Chapman and Hall, London, pp. 43–67. Jenness, J., 2006. Radiating Lines and Points (rad_lines.avx) Extension for ArcView 3.x, v. 1.1. Jenness Enterprises at: /http://www.jennessent.com/arcview/ radiating_lines.htmS. Jerlov, N.G., 1976. Marine Optics. Elsevier, Amsterdam. Jupp, D.L., 1988. Background and extensions to depth of penetration (DOP) mapping in shallow coastal waters. In: Symposium on Remote Sensing of the Coastal Zone, pp. IV.2.1–IV.2.19. Gold Coast, Queensland. Kench, P., Perry, C.T., Spencer, T., 2009. Coral reefs. In: Slaymaker, O., Spencer, T., Embleton-Hamman, C. (Eds.), Geomorphology and Global Climate Change. Cambridge University Press, Cambridge, pp. 180–213. Komar, P.D., 1998. Beach Processes and Sedimentation, Second ed Prentice-Hall, Upper Saddle River. Kuchler, D.A., 1986. Geomorphological separability, Landsat MSS and aerial photographic data: Heron Island, Great Barrier Reef. Technical Memorandum 10, Great Barrier Reef Marine Park Authority, Townsville, pp. 1–12. Langrebe, D., 1998. Information extraction principles and methods for multispectral and hyperspectral image data. In: Chen, L. (Ed.), Information Processing for Remote Sensing. Word Scientific Publishing Co. Pte. Ltd., Singapore, pp. 1–38. Liu, T.W., Tang, W., Xie, X., 2008. Wind power distribution over the ocean. Geophysical Research Letters, vol. 35, L13808, doi: 1029/2008GL034172. Marba, N., Duarte, C.M., 1994. Growth response of the seagrass Cynlodocea nodosa to experimental burial and erosion. Marine Ecology Progress Series 107, 307–311. Mather, P.M., 1979. Theory and quantitative methods in geomorphology. Progress in Physical Geography 3, 471–487. Mather, P.M., 2004. Computer Processing of Remotely Sensed Images: An Introduction, second ed John Wiley & Sons, Chichester. Maxwell, W.G.H., 1968. Atlas of the Great Barrier Reef. Elsevier, Amsterdam. Mumby, P.J., Harborne, A.R., 1999. Development of a systematic classification scheme of marine habitats to facilitate regional management and mapping of Caribbean coral reefs. Biological Conservation 88, 155–163.

S.M. Hamylton, T. Spencer / Continental Shelf Research 31 (2011) S151–S161

Patriquin, D.G., 1975. ‘‘Migration’’ of blowouts in seagrass beds at Barbados and carriacou, West Indies and its ecological and geological applications. Aquatic Biology 1, 163–189. Perry, C.T., Spencer, T., Kench, P.S., 2008. Carbonate budgets and reef production states: a geomorphic perspective on the ecological phase-shift concept. Coral Reefs 27, 853–866. Richards, K., Brooks, S., Clifford, N., Harris, T., Lane, S., 1997. Theory, measurement and testing in ‘real’ geomorphology and physical geography. In: Stoddart, D.R. (Ed.), Process and Form in Geomorphology. Routledge, London, pp. 265–292. Richards, K.S., 2003. Geography and the physical science tradition. In: Holloway, S.L., Rice, S.P., Valentine, G. (Eds.), Key Concepts in Geography. Pion, London, pp. 23–50. Robbins, B.D., Bell, S.S., 1994. Seagrass landscapes: a terrestrial approach to the marine subtidal environment. Trends in Ecology and Evolution 9, 301–304. Roberts, H.H., 1974. Variability of reefs with regard to changes in wave power around an island. In: Proceedings of the Second International Coral Reef Symposium, Brisbane, vol. 2, pp. 497–512. Slaymaker, O., Spencer, T., Dadson, S., 2009. Landscape and landscape-scale processes as the unfilled niche in the global environmental change debate: an introduction. In: Slaymaker, O., Spencer, T., Embleton-Hamann, C. (Eds.), Geomorphology and Global Environmental Change. Cambridge University Press, Cambridge, pp. 1–36.

S161

Spencer, T., Teleki, K.A., Bradshaw, C., Spalding, M.D., 2000. Coral bleaching in the Southern Seychelles during the 1997–1998 Indian Ocean Warm Event. Marine Pollution Bulletin 40 (7), 569–586. Spencer, T., Hagan, A.B., Hamylton, S.M., Renaud, P.G., 2009. Atlas of the Amirantes. Cambridge Coastal Research Unit, Cambridge. Stoddart, D.R., 1984. Coral reefs of the Seychelles and adjacent regions. In: Stoddart, D.R. (Ed.), Biogeography and Ecology of the Seychelles Islands. W. Junk, The Hague, pp. 63–81. Summerfield, M.A., 1991. Global Geomorphology. Longman Publishing, London. US Navy, 1976. Marine Climatic Atlas of the World. Chief of Naval Operations, Washington DC. Verstappen, H.T., 1977. Remote Sensing in Geomorphology. Elsevier Scientific, Amsterdam. Walsh, R.P.D., 1984. Climate of the Seychelles. In: Stoddart, D.R. (Ed.), Biogeography and Ecology of the Seychelles Islands. W. Junk, The Hague, pp. 39–62. Wilkinson, C., 2008. Status of Coral Reefs of the World: 2008. Global Coral Reef Monitoring Network and Reef and Rainforest Research Center, Townsville. Wiegel, R.L., 1964. Oceanographical Engineering. Prentice Hall, New York. Woodroffe, C.D., 2002. Coasts: Form, Process and Evolution. Cambridge University Press, Cambridge. Wright, D.J., Heyman, W.D., 2008. Introduction. Special issue on marine and coastal GIS for geomorphology, habitat mapping and marine reserves. Marine Geodesy 31, 223–230.