REMOTE SENSING OF GEOMORPHOLOGY AND FACIES … · 2019-12-20 · Journal of Sedimentary Research, 2005, v. 75, 861–876 DOI: 10.2110/jsr.2005.067 REMOTE SENSING OF GEOMORPHOLOGY

Journal of Sedimentary Research, 2005, v. 75, 861–876

DOI: 10.2110/jsr.2005.067

REMOTE SENSING OF GEOMORPHOLOGY AND FACIES PATTERNS ON A MODERN CARBONATE RAMP(ARABIAN GULF, DUBAI, U.A.E.)

SAMUEL J. PURKIS,1 BERNHARD M. RIEGL,1 AND SERGE ANDREFOUET2

1National Coral Reef Institute, Nova Southeastern University Oceanographic Center, 8000 North Ocean Drive, Dania Beach, Florida 33004, U.S.A.2UR Coreus, Institut de Recherche pour le Developpement, BP A5, 98848 Noumea, Nouvelle Caledonie

e-mail: [email protected]

ABSTRACT: The occurrence of power law relationships in the spatialdistribution of sedimentary lithotopes has been identified in both modernand ancient carbonate depositional bodies. In this study, facies patterns andtheir spatial relationships are investigated quantitatively in an Arabian Gulfshallow subtidal carbonate ramp setting, using a synergy of IKONOSsatellite imagery and vessel-based acoustic bathymetry survey. Three-dimensional reconstruction of the facies distribution on the seabed enabledquantification of relationships between eight dominant facies classes and theassociation of particular lithotopes to water depth. Fractal behavior wasinvestigated using a combination of boundary- and patch-based metrics, andthe spatial distribution of early diagenetically cemented hardgrounds andunconsolidated carbonate sand were shown to display strong fractalproperties. In contrast, we show that landscape-scale processes can betreated as essentially deterministic and facies neighborhood patterns arestrongly probabilistic. Identifying that the heterogeneity of shallow subtidalcarbonate facies scales with a power law within certain thresholds has thepotential to serve as a tool in environmental reconstruction in the ancient,where information on the lateral persistence of facies units is difficult toobtain. The findings are relevant to the interpretation of stratigraphicsequences and paleo-depth analysis.

INTRODUCTION

A key feature of sedimentological research is the attempt to understandthe lateral relationship between facies and whether spatial patterns areordered and deterministic or essentially stochastic (Adams and Grotzin-ger 1996; Wilkinson et al. 1999; Davis 2002; Rankey 2002). Much of thisinformation is encoded in spatial patterns, visible in sequence thicknessesand/or lateral extent (Wilkinson et al. 1999; Wilkinson and Drummond2004). Recent carbonate depositional systems, such as investigated in thispaper, can serve as analogues to comparable ancient systems, assist faciesinterpretation and, by examining spatial patterns, help to elucidatedepositional dynamics. Of particular interest is the increasing body ofevidence that many components of carbonate depositional systemsexhibit scale-invariant (fractal) properties (Rankey 2002). While follow-ing facies laterally is easy on the surfaces of recent sedimentary systems,detailed and, most of all, accurate maps of facies of larger study areas,important for obtaining patch-size statistics (Rankey 2002; Wilkinsonand Drummond 2004), can be difficult to achieve. It is here that mappingfrom remotely sensed data, like satellite imagery, has gained increasingsupport in the sedimentary and biological research communities (Rankeyand Morgan 2002; Andrefouet and Riegl 2004).

A key question is whether landscape spatial patterns are deterministicand therefore predictable, or probabilistic or random. Thus, many studieshave explored metrics capable of characterizing the patterning in bothstratigraphic sequences and lateral facies patterns. Among the manystatistics applied to landscapes, fractals have been shown to be meaning-

ful and have recently received much publicity (Li 2000; Rankey 2002;Halley et al. 2004). Fractal patterns have been observed in the small-scalestructure of shallow-water coral colonies (Bradbury and Reichelt 1983;Basillais 1997) as well as in the frequency distribution of deep-waterLophelia corals (O’Reilly et al. 2003; Huvenne et al. 2003). Furthermore,relationships between reefs and fish habitats at the community andpopulation level have also been shown to be largely independent of thescale of observation. Chittaro (2004) and Rankey (2002) showed scale-invariance of patch size and gaps in a Bahamian tidal flat environment.

Here we investigate an entirely subtidal Arabian Gulf carbonateenvironment and therefore extend a comparable study of Rankey (2002)into the sublittoral zone and investigate not only passively accretingcarbonate facies (intertidal muds and sands), but also actively accretingbiotic systems, here represented by corals. The aims of this paper are: (1)to quantify the spatial distributions of sedimentary lithotopes in a shallowsubtidal carbonate ramp setting, (2) to investigate the extent to which thespatial patterns can be described using fractal concepts, and (3) toinvestigate whether lateral spatial patterns harbor clues about themechanism of system evolution.

We use IKONOS satellite imagery, which has been proven to bea powerful tool for carbonate and coral reef studies (Maeder et al. 2002;Andrefouet et al. 2003; Garza-Perez et al. 2004; Purkis and Riegl 2005).However, because topography can act as a primary control for lithotopedistribution (e.g., James and Ginsburg 1979), satellite imagery alone,which primarily provides a two-dimensional image of a study area, is notsufficient to investigate the mechanisms dictating facies patterns. Wecombine a two-dimensional predictive habitat map of the distribution ofreef lithotopes derived from IKONOS satellite imagery with a high-resolution bathymetric digital elevation model (DEM) acquired froma vessel-based acoustic survey. By combining the satellite-derived habitatmap with the bathymetric DEM, the relationship between bathymetry,geomorphology, and habitat distribution can be investigated quantita-tively in a way that is otherwise at best very difficult, if not impossible,with only one of the two data types.

METHODS

Study Area

The study site was selected for the availability of ancillary data and ispart of an ongoing study. It is situated in the southeastern Arabian Gulf,about halfway between Abu Dhabi and Dubai, near Jebel Ali, in theUnited Arab Emirates (U.A.E.; Fig. 1). The study area extends shore-parallel for , 7 km and extends , 1.5 km offshore, where a typical depthof 6 m beneath lowest astronomical tide is attained (mean slope angle is0.5u). Previous studies (Riegl 1999, 2001; Riegl et al. 2001; Purkis andRiegl 2005) identified five typical coral assemblages of variable live cover,areas covered by unconsolidated carbonate sand, macro-algae, andseagrass, underlain in wide areas by early diagenetically cemented

Copyright E 2005, SEPM (Society for Sedimentary Geology) 1527-1404/05/075-861/$03.00

calcarenites (Shinn 1969; Evans et al. 1973), hereafter referred to ashardground.

The Holocene sediments of the United Arab Emirates (U.A.E.) includeshallow-water marine carbonates in one of the world’s classic moderncarbonate settings (Kirkham 1998). Our study area is defined by thegently sloping bathymetry off the U.A.E. coast, frequently referred to asthe Arabian Homocline (Purser and Seibold 1973). Coastal and nearshoresedimentology has been shaped by rapidly changing sea level throughoutthe Pleistocene and Holocene (Lambeck 1996; Uchupi et al. 1996,Kirkham 1998) and in the shorter term by wind. Daily onshore afternoonbreezes and especially the prevailing (though largely seasonal) northerlyShamal wind, influence the local wave-induced currents, which in turnare important for coastal sedimentology (Kirkham 1998; Alsharhan andEl-Sammak 2004). The northwest-trending coastline of the easternU.A.E. is particularly influenced by Shamal events, because it lies obliqueto the characteristic north wind blowing from the Iranian highlands andlacks any shelter from offshore barriers. The shallow seafloor throughoutthe study area lies above the storm wave base typical for Shamal

conditions, which can extend to a depth of at least 20 m (Purser andSeibold 1973).

Bathymetric Ground Truthing

The bathymetry survey was conducted from a survey vessel equippedwith a differentially corrected Fugro SeaSTAR 3200LR12 globalpositioning system (dGPS). Differential correction of the GPS data wasconducted against the network of omniSTAR satellites which wasconfirmed to yield data of sub-meter accuracy when tested againsta known geodetic point. To ensure an adequate degree of accuracy, threeindependent acoustic surveys were used to build the bathymetric digitalelevation model (DEM). Bathymetry lines were obtained over the entirestudy area using both a 50 and 200 kHz signal on a 5 Hz samplingfrequency. A line spacing of 100 m was used to cover the entire study area(7 km 3 1.5 km). An additional nearshore survey with a 15 m linespacing provided high-resolution bathymetry in the first 500 m fromshore. Throughout the survey period, tidal data were collected in situ at

FIG. 1.— Location of the study area in relation to A) the Arabian Gulf and B) area highlighted on an ASTER satellite image (spatial resolution 15 m 3 15 m). C)Bathymetry of the study area is derived from 50 kHz vessel-based acoustic survey. Depths are in meters beneath lowest astronomical tide datum.

862 S.J. PURKIS ET AL. J S R

five-minute intervals, using a submerged Van Essen DI-240 pressurelogger. A duplicate logger was used to record atmospheric pressure abovethe water surface and therefore remove any effect from atmosphericvariation. Tidal influence was removed from the bathymetry data bycorrecting the acoustic lines against the coincident in situ tidal record,with the result that each bathymetry point was normalized to a commonlowest astronomical tide datum. The bathymetric DEM was built bycombining the tidally corrected 50 kHz and nearshore high-resolutionsurvey. Bathymetry data from both surveys were merged and interpolatedto a regular grid of equal size to the pixel elements of the IKONOS image(4 m 3 4 m) using triangle-based linear interpolation, yielding a singledepth value per satellite pixel such that the DEM and imagery weremutually registered. The accuracy of the DEM was assessed against the200 kHz survey lines, and independent soundings made with a weightedline. Throughout the study area, the along-track average deviation indepth prediction was 0.05 m. The between-track depth prediction in thefirst 500 m from shore (surveyed with a maximum line spacing of 15 m)had an average deviation in depth of 0.10 m, and for the remainder of thestudy area (surveyed with a line spacing of 100 m) the average deviationwas 0.35 m (Riegl and Purkis 2005).

Processing of Satellite Images

Discrimination of benthic habitats was conducted using an IKONOS-211-bit multi-spectral satellite image. The IKONOS sensor has a multi-spectral resolution in the blue (, 420–560 nm), green (, 470–635 nm),and red (, 620–740 nm) bands of 4 m and in the panchromatic band(, 450–900 nm) with 1 m resolution. The first three multispectral bandsof the imagery were subsequently processed to remove the spectral effectof the intervening water column using the procedure of Purkis andPasterkamp (2004), resulting in pixel values equivalent to substratereflectance. The thickness of the water column within each pixel ofIKONOS imagery is required for this correction and was derived from thebathymetric DEM constructed from the in situ 50 kHz acoustic survey.Each IKONOS image pixel was assigned to one of eight substrate classesusing a classifier trained solely using in situ optical measurements ofsubstrate reflectance. A thorough description of the procedures used toprocess and classify the imagery is provided in the Appendix. The resultingclassified image, which can be considered as a predictive map of benthichabitat distribution, was smoothed using a median filter constructed usinga 3 3 3 pixel neighborhood to reduce the number of isolated erroneouslyclassified pixels resulting from image noise (Wilson 1992; Lillesand andKiefer 1994). The quality of the filtered eight-class thematic map (Fig. 2A)was assessed against extensive observations made in the field and wasshown to have an overall accuracy of 81% (Purkis 2005).

GEOSPATIAL ANALYSIS

Inter-Facies and Facies–Depth Relationships

In order to investigate quantitatively the geospatial relationshipsbetween facies types on the seafloor, an algorithm was developed toevaluate class membership of the eight pixels surrounding each evaluatedpixel (i.e., only those touching the sides and corners of the seed pixel).Pixels situated adjacent to the image boundary where omitted from theanalysis, because they did not possess a full suite of 8-connectedneighbors. The data were tabulated to show which facies classes weremost frequently associated with each other. Relating the spatialdistribution of facies to depth as determined from the DEM, thefrequency of occurrence of each lithotope within 4 depth bins (0–2 m, 2–4 m and 4–6 m) was also computed. This was done in order to evaluate ifcertain facies are preferentially encountered within a particular depthrange and provides an overview of the spatial distribution of the differentbenthic substrates with regard to bathymetry.

Fractals and the Fractal Dimension (D)

Fractals have two intrinsic properties, scale invariance and self-similarity. Scale invariance means that an object looks the same on allscales; self-similarity means that any part of the system, appropriatelyenlarged, looks like the whole. Fractals generated mathematically areinfinite, a property that cannot occur in nature (Halley et al. 2004).However, real-world systems frequently display both scale invariance andself-similarity within certain thresholds and therefore are akin toa mathematical fractal over a limited range of scales. The literature doesnot define a critical range of scales that must be exceeded before a patterncan be described as fractal. Indeed, Avnir et al. (1998) showed that themajority of cases labeled as fractal in the literature span only a singledecade of magnitude and rarely achieve three decades. Similarly, powerlaws identified in the behavior of laboratory-scale avalanches typicallyhold over 1–2 orders (e.g., Jensen 1998). However, Hergarten (2002)postulates that distinguishing a power law over two or fewer decadesrequires at least some belief in scale invariance. In a comparable study,Rankey (2002) identified fractal behavior in exceedence probability vs.area spanning three decades, which we consider to be a reasonable andconservative benchmark and is supported by the literature (Lovejoy 1982;Schroeder 1991). Fractal behavior is quantified by the fractal dimension(D), which can be calculated in many ways but typically relates to theslope of a power law relationship. It should be noted that D does notprovide information on the goodness of fit to a power function, which inthe subsequent analysis is quantified using the adjusted coefficient ofdetermination (Radj

2). The statistic is essentially the standard R2, modifiedto account for the sample size using Wherry’s (1931) correction and istherefore appropriate for comparison between cases with varyingnumbers of data. Values of Radj

2 close to 1 indicate a strong relationshipand values above 0.90 are considered as a good fit to the power law(Carlson and Grotzinger 2001). The statistic is used in the followinganalysis to test the robustness of fractal relationships. There area multitude of methods with which to analyze an object for its complexityand fractal character, and for this study we employ a combination ofboth boundary-based metrics (box counting) and patch-based metrics(size-frequency distribution and exceedence probability) to investigatethe degree to which the mapped facies patches satisfy the fractalcondition.

Box Counting

Analysis was conducted on the eight-class thematic map of substratedistribution resulting from classification of the IKONOS satelliteimagery. The locations of patch boundaries were extracted for each ofthe eight facies classes by creating a binary image containing only theperimeter pixels of patches containing a minimum of two connected pixelsof constant facies type. A pixel was considered to be part of the perimeterif it was both nonzero and was connected to at least one zero-valued pixel.There are numerous permutations of the basic box counting technique toquantify D, which have been extensively investigated in the literature(Tarboton et al. 1988; Hall and Wood 1993; Pruess 1995; Middleton 2000;Seuront and Spilmont 2002). In this study, the degree of convolution ofthe patch boundaries was tested by box counting (Rodriguez-Iturbe andRinaldo 1997; Turcotte 1997) using code written in Matlab 6.1. Thistechnique measures the ‘‘wiggliness’’ of a curve and tests for fractalproperties by covering the entire curve with progressively smaller boxesand plotting box size against the number of boxes needed to cover thecurve. A straight-line (power law) relationship in a bilogarithmic plotsuggests a fractal and the slope of the resulting function provides anestimate for D (Pruess 1995), the goodness of fit of which can beevaluated using Radj

2. To ensure that the automated box countingalgorithm written in Matlab produced reproducible results, a test casewas taken in which the Matlab script was applied to a dataset which had

REMOTELY SENSED FACIES PATTERNS ON A MODERN CARBONATE RAMP 863J S R

been box counted manually for box sizes 221 to 2210, with the result thatthe automated technique was proven reliable. It should be noted that theautomated box counting method approaches a horizontal trend at highorders (2210) as compared to the manual solution that rolls off onto the

function of a one-dimensional line. This difference is not to the detrimentof either method but arises from the fact that the manual technique isvector-based, counting boxes eclipsed by line segments (Euclideandimension of 1), whereas the Matlab code is raster-based and counts

FIG. 2.—A) The spatial distribution of submerged lithotopes on the classified IKONOS image (spatial resolution 4 m 3 4 m) in plan view with B) a detail of the linearstructures that were identified as overthrust tepees following ground-truthing. Coordinates are decimal latitudes and longitudes. C) The classified image was draped overthe bathymetric DEM highlighting the topographic approximation to a homoclinal ramp, D) the longshore-oriented channel in the immediate nearshore, E) and theshore-perpendicular ridge and valley systems. For the 3D views, the vertical axis has been exaggerated 3500 in order to highlight the relief of the DEM. A description ofthe assemblage composition of the facies groups is given in Table 1.


boxes containing point data (Euclidean dimension of 0). Because thisartifact is manifested solely at high orders, beyond the break in the log-log function, it does not affect the estimate of D. As is common for thetechnique (e.g., Schlager 2004) the trend line does not readily passthrough the origin and can be attributed to ‘‘edge effects’’ whereby aninitial transient is observed prior to the definitive trend emerging at higherorders (Fig. 3).

Frequency–Area Relations and Exceedence Probability

Patch area and frequency were computed by extracting the area of allobjects within the binary image for each of the eight facies classes. Benthicpatchiness typically follows a trend where there is a high frequency ofsmall patches in a landscape and large patches are rare. Furthermore therelationship between patch frequency and patch area often approximatesto a power law model (Connell and Keough 1985; Li 2000; Langmead andSheppard 2004). To investigate the degree to which our data conformedto this pattern, the number of the pixels assigned during classification toeach class was used to yield an estimate of the total area covered by eachfacies. Patches in the imagery were defined as being composed of single ormultiple connected pixels of the same substrate type (encoded by the sameinteger class value). Diagonally adjacent pixels as well as pixels on thesame row or column (i.e., sharing an edge) were considered connected.Exceedence probability for patch area was calculated according toRodriguez-Iturbe and Rinaldo (1997) and Rankey (2002) under theassumption that a linear relationship between patch area and probabilityin the log-log domain can be interpreted as further evidence for fractalbehavior. D was taken to be equal to the slope of the resulting power

TABLE 1.— Summary of the typical substrate assemblages encompassed within each of the eight facies classes.

Facies class Typical assemblage composition CommentsProportion of study

area (%)Total area

(km2)Max patch size

(km2)

Dense live coral Porites lutea and columnar Poritesharrisoni intermingled withFavia spp. and Platygyra spp.

Dense colonies over caprock, commonlymaintaining a low relief but in places formingnon-framebuilding coral carpets. Coverage50–100%

3.78 0.32 0.01

Dense dead coral Acropora clathrata andA. downingi

Dense dead tabular colonies, frequentlyovertopping and heavily overgrown withalgal turf and corraline algae. In places thetabular framework has disintegrated intopiles of branch rubble. Average size of intactcolonies is 1 to 1.5 m, and coverage is 80–100%

7.11 0.59 0.14

Sparse coral Porites, Favia spp., andSiderastrea savignyana, withoccasional small colonies ofAcropora clathrata

Widely spaced patches of Faviid andSiderastreid colonies on caprock withoccasional large Porites boulder corals. TheAcropora were mostly dead at the time ofimage acquisition. Coverage is generally 10–40%

16.31 1.36 0.07

Seagrass Mainly Halodule uninervis withoccasional H. ovalis

Dense seagrass stands are generally found oversandy-silty substrate and have a coverage of60–80%

5.73 0.48 0.01

Algal mats Rhizoclonium tortuosum,Chaetomorpha gracilis,and Cladophora coelothrix

Extensive mats over sandy-silty substrates,often associated with seagrasses. Coverage80–100%

12.27 1.02 0.21

Macro-algae Sargassum binderi, S. decurrens,Avrainvillea amedelpha, and Padina

Moderately dense stands of macro-algae onpatches of unconsolidated sediment.Coverage 30–60%

12.69 1.06 0.02

Hardground - Large slabs of lithified carbonate sediment,fringed by ‘‘tepee’’ structures. Coverage100%

21.33 1.78 0.42

Sand - Unconsolidated carbonate sand. Coverage100%

20.78 1.73 0.29

Coverage refers to the percentage of the seabed occupied when a 1 m 3 1 m area of substrate is viewed from nadir at an altitude of 1 m. Assemblage description isbased on Purkis and Riegl (2005). For each class, summary statistics for patch size and total coverage derived through image analysis of the classified IKONOS data areprovided.

FIG. 3.—Validation of the raster-based box counting algorithm programmed inMatlab against a hand-counted dataset. The results demonstrate the initialtransient deemed to arise through edge effects, prior to the definitive linear trendbecoming established. At higher orders the automated algorithm returns resultsthat roll off towards horizontal (zero-dimensional Euclid) whereas the hand-counted (vector-based) data adopts the trend of a one-dimensional Euclid. Theresult is an artifact of the metric (see text) and does not affect the returned valueof D.


function plus the Euclidean dimension (here 2, because we considersubstrate distribution in plan view and therefore in two dimensions)(Rankey 2002). The fit was quantified using Radj

2. Power functions werefitted for each substrate to the portion of the dataset displaying a linearrelationship rather than for the whole series, because in all cases the datarolled off the trend for smaller patch sizes.

RESULTS

Topographic Distribution

The classified IKONOS image was draped over the processedbathymetric DEM, yielding a quantitative three-dimensional model offacies distribution and topography (Fig. 2A). The classified image showeda first-order trend of shore-parallel zonation into three crude zones. In thefirst 500 m from shore, a shallow facies assemblage of sand (yellow inFig. 2A), seagrass (red in Fig. 2A), and algal mats (light green in Fig. 2A)was found. Only relatively small areas of hardground were observed inthe nearshore zone. A middle zone extended from 500 to 1000 m offshoreand consisted predominantly of sand and hardground (orange in Fig. 2A).Farther down the ramp profile, the deep zone that extended from 1000 to1500 m from shore exhibited a deep facies mosaic characterized mainly byhardgrounds, which were bare or covered by coral growth of variabledensity (blue and two shades of purple in Fig. 2A), interspersed by densemacro-algal growth (dark green in Fig. 2A).

On the digital elevation model, a differentiation into two zones basedprimarily on seafloor morphology rather than optically resolvable faciespatterns was seen. The nearshore zone of mainly unconsolidated sedimentexhibited a trough-like, shore-parallel depressed morphology (Fig. 2D).The offshore zone of mainly consolidated sediment and coral growthshowed an undulating surface with along-strike orientation perpendicularto the nearshore features. Within this surface, several distinct featurescould be observed. Large-scale undulations formed a shore-perpendicularmorphology throughout most of the study area at a scale of several tensof meters width and spacing (Fig. 2E). The ridge to trough to ridgesequences were at scales of up to and more than 100 m. Highest elevationbetween a trough and an adjacent ridge was 2 m. This trough and ridgesystem was found mainly in the area covered by corals. It did not extendinto the longshore trough that characterized the nearshore zone ofunconsolidated sediment. A second system of much smaller ridges wasalso observed. Their orientation was less clearly shore-perpendicular andthey were not found at comparable frequencies over the entire study area.In the imagery, these ridges were frequently a composite of an upward-turned hardground, with a leeward accumulation of unconsolidated sand.The maximum positive topography associated with these ridges was onemeter.

Facies–Facies and Facies–Depth Relationships

Examining the frequency with which each of the eight facies types areassociated allows a quantitative analysis of the probability that twosubstrates occur as neighbors. The classes encoding carbonate framework(dense live and dead corals) were most frequently associated with eachother (Fig. 4), but sparse corals (small isolated colonies of Porites, Faviaspp., and Siderastrea savignyana) frequently neighbored pixels dominatedby macro-algae or hardgrounds. Non-accreting facies (sand, algal mats,and seagrass) were similarly associated, with the exception of macro-algae, which frequently neighbored both corals and hardground.

In order to evaluate whether facies neighborhoods are random orprobabilistic, we investigated the existence of the Markov property(Roberts 1976; Pielou 1977; Davis 2002). We populated a transitionmatrix with state-to-state transitions from the 8 classified IKONOSfacies. When allowing for transition to the same state (i.e., as a regularMarkov chain; Roberts 1976) we found that the facies mosaic exhibited

a high-order (tested up to fourth order) Markov property (Chi-squaretests, p % 0.001). This is not surprising, because the 4 m pixel is so smallin relation to the average habitat patch that a high level of self-to-selftransition can be expected. We therefore further evaluated the faciesmosaic as an embedded Markov chain (Davis 2002), which does not allowself-to-self transitions. Again we were able to demonstrate clearly theMarkov property (Chi-square p % 0.001). Facies in the study area areclearly not randomly distributed, but there exists a very clear probabilisticdependence in neighborhood patterns. Total landscape statistics based ontransition frequencies are given in Figure 4.

Interpretation of the tabulation of facies occurrence versus depth(Fig. 5) reveals that, although there is a degree of depth zonation of faciesgroups, several classes exhibit an equally high probability of occurring intwo or more depth intervals. The probability of macro-algae occurring inthe 2–4 m depth interval was the same as in the 4–6 m depth interval.Similarly, unconsolidated sand is equally prevalent in the intervals 0–2 mand 2–4 m. Exhibiting the greatest degree of depth preference, denseframework-building corals (live and dead) were found most frequently ingreater water depths. This corresponds to the very low occurrence ofhardground in the deep areas, because the corals rapidly cover anyavailable consolidated substratum. Sparse corals were most abundant indepths , 4 m and followed the same trend as hardground, because thetwo facies were commonly associated (Fig. 4) and the sparse coverageleaves large areas of vacant hardground. The data clearly contradict thetheory of ‘‘one facies 5 one water depth’’ and is in concert with thefindings of Rankey (2004), who showed that substrate type exhibited littledepth organization across a section of the shallow (, 8 m) South Floridashelf. The observation has relevance to the interpretation of stratigraphicsections as evidence for paleo-bathymetry.

Box Counting

Box counting provides a measure of the relative tortuosity and thuscontortion of patch boundaries. The more contorted the boundary, thehigher its complexity and fractal dimension. Each of the eight substratetypes displayed a robust linear relationship in bilogarithmic plots of boxsize versus number of filled boxes over nine decades of box reduction(Fig. 6). There was no obvious correlation between substrate type andgoodness of fit to the linear slope function, with all data points adheringstrictly to the relationship (Radj

2 exceeds 0.99 in all cases) up until thetransition towards a horizontal trend beyond 229, equivalent to a box sizeof 1024 m2. Image resolution is reached at 16 m2 (equivalent to 212 stepsof log2(box size)) and is the point where the number of boxes equals thenumber of image pixels. The fact that the log-log relationship rolled offthe trend three log2 cycles prior to reaching the image resolution suggeststhat there is a threshold of minimum patch size which must be attainedbefore the definitive spatial trend is satisfied. The linear trend terminatesfor box sizes , 1024 m2 (Fig. 6). We interpret this to indicate that at least64 pixels (1024 m2) are required to estimate the size of a patch properly.The observation is relevant because it suggests that the spatialdistribution of patches of lesser area do not display scale invariance.The box counted estimates of D did not display a relation to whethera substrate type is dominant in the nearshore or in deeper water, butthey did correlate (R2 5 0.58) with the percentage of the total land-scape area occupied (Fig. 7A), with substrates covering greater areasreturning higher values of D. Similarly, there was a moderate correlation(R2 5 0.48) between D and the number of patches, where facies withfewer patches returned a lower fractal dimension. Conversely, nocorrelation existed between the percentage of landscape area occupiedby a substrate versus the number of patches (Fig. 7C). However, therewas a general trend that the most patchy facies types (macro-algae,sparse coral, and hardground) accounted for the largest areas of thelandscape.


Frequency–Area Relations and Exceedence Probability

The data plotted in Figure 8 represent the probability (y axis) thata given patch will be of an area equal to or greater than a given area (xaxis). All substrates were consistent in displaying a decrease in exceedenceprobability (E.P.) with increasing patch area, confirming that thefrequency of occurrence decreases when moving from smaller to largerpatch sizes (large patches were rare, small patches were common).Furthermore, all substrates were characterized by a change in the natureof the relationship with an inflection point at a patch area ofapproximately 1000 m2 (103). This is interesting in that it correspondsto the observation made during box counting that patches containing

fewer than 64 pixels (1024 m2) behave differently than larger patches.Furthermore, and in concert with the patterns observed with boxcounting, it was for patches greater than 1000 m2 that the probability ofpatch size exceeding the area of the x axis rapidly decreased withincreasing area and followed a robust power law. For example, the powerlaw equation for hardground takes the form of E.P. 5 e4.58(Area)20.71

where 20.71 describes the slope of the function which with the additionof the Euclidean dimension of the system (2) yields D (1.29). Allsubstrates returned Radj

2 . 0.94, which can be described as good powerlaw relationships (Carlson and Grotzinger 2001; Rankey 2002), and thedata can be inferred to display scale-invariant properties. In order todetermine whether the scale invariance can be interpreted as fractal

FIG. 4.— Inter-facies associations showingthe geospatial relationships between faciestypes on the seafloor. For each facies type, classmembership was evaluated for the 8-connectedpixels surrounding each pixel (i.e., only thosetouching the sides and corners of the seedpixel).


behavior, it must be shown to persist over several orders of magnitude.The number of orders spanned is dependent on the slope of the linearregression line and therefore on D. Facies types spanning the most ordersare characterized by higher values of D and conspicuously stronger valuesof Radj

2. Dense live coral and seagrass displayed scale invariance overa single order, sparse and dense dead coral extended the range to slightlyover 2 orders and hardground as far as 2.5 orders of magnitude(equivalent to patch sizes 1000 m2–500,000 m2). Although displayinga degree of scale invariance, it would be misleading to conclude that eitherseagrass or dense live coral behave as fractals. Similarly, the 2 ordersoffered by dead and sparse corals are not sufficient to characterizeexplicitly as fractal, but according to Avnir et al. (1998) and Jensen (1998)at least suggests fractal behavior. Hardground and sand are the onlyfacies types that approach three orders of scale-invariance, and even if theterm is used conservatively they would seem solid candidates for a fractal.

DISCUSSION

Figure 2C (looking obliquely offshore) shows clearly that theresearched area can best be described as part of a homoclinal ramp, ashas indeed been described previously (Kirkham 1998). It is also very clearthat the coral area does not form a three-dimensional buildup but simplydrapes the underlying morphology. It can therefore not be called a coralreef: it is simply a thin veneer that can at best be described as a biostromalframework (coral carpet) or a non-framebuilding community, in whichcorals are sufficiently widely spaced that no framework is formed (Riegland Piller 1999, 2000). Other clear sedimentary features are a longshore-oriented channel in the immediate nearshore area (the first 100 m)(Fig. 2D), which is most likely due to scour by the eastward-flowingcurrents that are typical of the study area. Both the predictive map andthe ground-truth data confirm that the channel bed is dominated byunconsolidated sand, covered to varying degrees by patches of seagrassand algal mats.

From about 500 m offshore, the orientation of structures changes fromshore-parallel to shore-perpendicular. Two types of shore-perpendicularstructures were observed in both the plan view and the three dimensionalview. Firstly, the plan view clearly shows linear structures (Fig. 2B) that,upon ground-truthing, were identified as overthrust tepees (Shinn 1969),which are formed by synsedimentary cementation.

In the proximal portion of the ramp (1000–1500 m from shore), a gentlealong-shore undulation of the substratum is found (Fig. 2E). The mostpronounced ridges and valleys exhibit up to a 2 m difference in depth(5 m in valley, 3 m on crest, with three such undulations spread across the7 km study area). The ridges are characterized by dense live and deadcoral growth, whereas the valleys are commonly occupied by sand,hardground, and sparse corals. Repeated sampling with a hammerconfirmed the total absence of any coral-built framework on the ridges(all corals grew on the original hardground). These structures are vaguelyreminiscent of spur-and-groove systems, as found commonly on high-energy upper reef slopes in comparable depth settings, although far lesspronounced in their undulations. Because there is neither enough coralframework to build spurs nor enough water energy to induce seriousscour, we believe that the corals and the substratum undulations might becoincidental. However, moderate- to high-energy beaches also exhibitundulations (transverse bar-and-rip system; Short and Aagard 1993) inresponse to preferential localized runoff and ensuing stronger off-beachsediment transport in areas of wave setdown at a comparable scale. It ispossible that the observed offshore features could be paleo-structuresfrom a lower sea level 7500 to 7000 yr BP (Lambeck 1996). Thesecemented ridges might secondarily have led to preferential coralsettlement (James and Ginsburg 1979), in which case their co-occurrencewith corals would be explained.

It is clear from the classified IKONOS imagery (Fig. 2A) and Figure 5that ‘‘hard’’ carbonate facies (live and dead corals) are preferentiallysituated in deeper water than ‘‘soft’’ unconsolidated facies and theirassociated biota (algae and seagrass). Of particular relevance to thisobservation is the action of wave energy dissipating on the shoreline andthe depth at which fair-weather wavebase makes contact with the seabed.Personal observation confirms that for the homoclinal ramp of Jebel Alithe fair-weather wavebase lies at water depths of 3–4 m. At this depth,sediment is kept in motion and forms elongate shore-parallel sedimentaryfeatures (Fig. 2A) and the constant reworking of the nearshore sands bywaves and current prevents consolidation by hardground formation.Uchupi et al. (1996) have shown that the Southern Arabian Gulf isa province of extensive formation of marine hardgrounds, whichcorresponds to the high occurrence in the remotely sensed predictivemap, where hardground is the most prevalent facies type, covering inexcess of 1.78 km2 (21%) of the total area mapped (Table 1). Hardground

FIG. 5.— Normalized relationship of faciesdistribution with water depth. The abundance ofeach of the eight facies classes is binned withinthree water depth intervals (0–2, 2–4, and 4–6 m); depths are in meters beneath lowestastronomical tide datum. Inset gives the totalnumber of IKONOS image pixels within eachdepth interval.


is found to be more widespread than unconsolidated sand (whichoccupies 1.73 km2 of the landscape) and dominates the seafloor . 500 mfrom the coast (Fig. 2). This supports our suspicion that constant shiftingby currents and waves, such as in the nearshore scour channel, isnecessary to keep sediment unconsolidated. Our findings thus supportShinn (1969), who observed the strongest lithification in the areas oflowest sedimentation. This would correspond to the deeper zone (. 4 m)in the Jebel Ali–Ras Hasyan area, where sedimentation by wavesresuspending unconsolidated sediment is episodic. The occurrence ofhardground provides a suitable substratum for coral recruitment, andsubsequently this is where corals become established. Therefore, theoccurrence of the hardground class in depths . 4 m is low, because muchof the available vacant hardground is colonized by corals, whichdominate this depth range (Fig. 5). Unconsolidated sand collects indepressions within the coral framework. Algae colonize both barehardground and sand, which accounts for the high occurrence of algaeat depths . 4 m (Fig. 5). The spatial expression of sand and algae inwater depths . 4 m is one of filling the negative spaces in betweenpatches of coral. Conversely, in depths , 4 m, sand is not constrained by‘‘hard’’ coral patches and forms shore-parallel bedforms that providesuitable substratum for algal mats and seagrass beds.

Figure 4 shows that dense live and dead corals are most frequentlyassociated with each other, which is logical considering that stands ofdead corals can form only in areas previously monopolized by live coralsand given the fact that dead coral framework frequently serves asa suitable substratum onto which juvenile coral recruits can settle (e.g.,Carleton and Sammarco 1987). Most striking is the fact that areas of barecarbonate hardground (which is the optimum substrata for coral growth)are frequently associated with the sparse coral assemblage but never withdense live or dead corals. Examination of the classified imagery (Fig. 2A)reveals that areas of live and dead coral are fully encompassed in a zoneof sparse coral cover on hardground, which in turn is most frequentlyassociated with algal dominated sediments (Fig. 4). Ground verificationreveals that coral frameworks occur solely on areas of hardground wherethe slightly higher elevation as compared to the surrounding seafloorprovides protection against mobile sand sheets that inhibit both coralsettlement and subsequent growth (e.g., Rogers 1990). In concert with thisobservation is the finding that image pixels classified as unconsolidatedsand are never found adjacent to pixels dominated by coral facies.However, unconsolidated sand patches are commonly associated withhardground (i.e., sand sheets onlapping hardground plates) and algal andseagrass stands, which require unconsolidated sediment as a substratum.

FIG. 6.—Implementing the box counting metric on patch boundaries yields a robust log-log relationship over nine base 2 logarithms of box size, with the relationshipfailing for box sizes , 1024 m2. Image resolution is reached at step 212 when box size equals a single image pixel (16 m2). In all cases Radj

2 values exceed 0.99, indicatingan excellent fit to the power law (cf. Carlson and Grotzinger 2001).


The stratified arrangement of corals on hardground patches (dead corals,fringed by dense live corals, fringed by a sparse assemblage of corals) isinvestigated by Purkis and Riegl (2005) and can be explained by thedisturbing influence of recurrent temperature anomalies in the area,which repeatedly inhibit reef framework accretion (Riegl 2001).

The detailed map of facies distribution and relationships, coupled withour knowledge of the area (see Riegl 1999, Purkis and Riegl 2005) allowsus to speculate about the processes shaping this landscape using graphtheory (Roberts 1976; Harris and Stocker 1998) (Fig. 9). We believe thatwe are dealing with a young landscape that exhibits strong influence ofneither antecedent topography nor flooding history. This is reflected bythe absence of any dramatic geomorphologic features. The major factorsshaping the landscape are: (1) movement of sediments by currents andwaves; (2) synsedimentary cementation due to the water chemistry of thearea (Shinn 1969; Uchupi et al. 1996); and (3) subsequent settlement ofalgae and corals on the newly available hardgrounds. We assume thatimmediately after flooding the entire area consisted of unconsolidatedsand, which now is maintained only in areas with enough hydrodynamicenergy to constantly rework the sediment. Where this does not happen,the stabilized, but uncemented sand is first covered by algal mats andlater by seagrass (and the two states can change from one to the other).Alternatively, hardgrounds are formed and sparse corals and/or macro-algae settle. Sparse coral becomes dense coral, which subsequently

changes to dense dead coral and from there to macro-algae, which coverthe dead skeletons (Purkis and Riegl 2005). After breakdown of the coral-covered skeletons (Riegl 2001), the sparse coral state is regained. Thus,once hardground is formed, the system enters an ergodic state (i.e., onceentered, the system remains in that state) with a loop between sparse coraland macro-algae, with no path leading back to unconsolidated sand(Fig. 9A). The condensation graph in Figure 9B identifies the strongcomponents of the system (Roberts 1976; Harris and Stocker 1998),within which all nodes can be reached from one another. Polarized pathsexist between these strong components, such that there is strictly one-waytransition between K1 (sand, algal mats, seagrass), K2 (hardground), andK3 (sparse coral, dense live coral, dense dead coral, macro-algae).

Fractal Metrics

Analysis of the substrate distribution using a combination ofboundary-based and patch-based metrics yields evidence of scaleinvariance over several orders of magnitude. Most striking is the factthat both a boundary-based (box counting) and a patch-based(exceedence-probability) metric support the observation that 1000 m2

marks a lower cutoff in size, above which scale invariance is observed.The pattern is partly reflected in data presented by Rankey (2002), whosimilarly demonstrated scale invariance in facies patterns on a carbonate

FIG. 7.—A) Cross plot of box counted D vs.total percentage of the landscape occupied byeach facies type, for which a strong correlationis observed. B) Cross plot of box counted D vs.number of patches, displaying moderate cor-relation. C) Cross plot of number of patchesvs. total percentage of landscape for eachfacies type, which is shown to be uncorrelated.


tidal flat. Plotting E.P. vs. area, Rankey demonstrates a log-logrelationship spanning patch areas of 103 m2 to 105–106 m2, dependingon facies type. Data for patch areas , 103 m2 is not presented, and so it isnot possible to comment on whether the linear trend fails for smallerpatch sizes. The lower bound of 103 m2 may be an artifact arising as theresolution of the IKONOS data is approached. It is also plausible that thebreak in the trend indicates that 103 m2 represents a threshold ofminimum patch size that must be attained before the definitive spatialtrend is satisfied. At the other end of the spatial scale, all facies types ofRankey (2002) begin to roll off the linear trend between 105 and 106 m2,as observed in this analysis. Whether the failure of the trend at such largepatch sizes is an inherent property of both systems or an edge effectresulting from the limited size of the landscape is difficult to judge. Withdimensions of 7 3 1.5 km2, the study area in Jebel Ali covers an area ofapproximately 107 m2, and therefore it is not surprising that the lineartrend starts to fail. Evidence that the landscape size is a limiting factorwould be if the larger patches were seen to be truncated by the landscapeboundary, which seems not to be the case (Fig. 2A). However, prior todrawing conclusions on the fractal nature of coral reef facies, we wouldpropose reanalyzing a larger landscape.

Having identified patterns that can be defined as fractal in the spatialdistribution of lithotopes on the Jebel Ali ramp, it is worthwhile

postulating which mechanisms may be at work to result in sucha fragmented system. Factors serving to maintain a patchy landscapeare the natural processes of competition for space between adjacentecological groups (e.g., corals and algae), natural and anthropogenicdisturbance, and both hydraulically and biomediated erosion. Actingagainst these are factors that serve to produce large homogeneous patchesof constant facies type, such as sedimentation, growth of a particularbiotic group at the expense of a less able competitor, and rapidsynsedimentary lithification of sand sheets (e.g., Shinn 1969). It isa balance between these mechanisms that maintains both the universalpatchiness and the zonation in coral environments. Coral reef landscapesare spatially and temporally nonlinear, exhibiting instability at meter todecimeter levels on timescales of months to years but complex meta-stability at scales of tens of kilometers for decades, centuries, and evenmillennia. In the case of Jebel Ali, the potential for large scalemetastability as attained by reefs in comparable high-latitude settings(e.g., the Red Sea), is not realized. On the basis of the size of acroporidcolonies and analysis of archive sea-surface-temperature data, Purkis andRiegl (2005) confirmed that the area is subjected to recurrent mortalityevents resulting from cyclic temperature anomalies at frequencies near orexceeding 15 years. Temperature-induced mass mortality events in reefenvironments often result in widespread coral death, followed by

FIG. 8.— A) Bilogarithmic plots of exceedence probability (E.P.) vs. area for six facies types (for clarity the two algal facies have been omitted). The data plottedrepresent the probability ( y axis) that a given patch will be of an area equal or greater than a given area (x axis). All substrates display a linear trend for patches of area. 103 m2, but the slope of the linear function is notably different. Hardground, sand, and sparse and dense dead coral display scale-invariance over . 2 orders ofmagnitude, which strongly suggests fractal behavior. In each case, fractal dimension (D) and the power law equation from which it was calculated is provided. Goodnessof fit to the linear trend is quantified by Radj

2 which exceeds 0.90 in all cases. The inset B) shows the relationship between E.P. and area for sparse coral and seagrass forpatch sizes 101–103 m2. The expanded E.P. axis demonstrates that the relationship cannot be described by a linear function and therefore it cannot be inferred that thesystem is bifractal. This is also the case for all other facies classes (not shown).


a protracted phase shift to an algae dominated environment (Hughes1994; McCook 1999; Dustan et al. 2001; Bellwood et al. 2004). Also, inthe Arabian Gulf, compensatory mortality events are observed,disadvantaging the most aggressive coral species (the acroporids) andthus assuring the survival of weaker competitors in the system (e.g.,Connell 1978, Riegl 1999, Purkis and Riegl 2005). The relevance is thatthe disturbance regime in the Gulf serves to increase heterogeneity, in thesense both of biotic diversity and the spatial extent of the dense coralfacies. It is thus a plausible candidate for maintaining a highly fragmentedlandscape with fractal properties. Relating this observation to the fractaldimension (D) of the patch boundaries (as quantified through boxcounting), we observe that the higher the fragmentation of the landscape,the more complex the patch boundaries become and the higher the valueof D. Therefore, a high D shows more intimate contact between adjacentlithotopes. If the lithotopes are structures by living organisms, thissituation may promote competition. Such a situation is likely to maintainspatial instability and prevent (or at least delay) the system from revertingto a more homogeneous state. Interestingly, the facies with the lowest boxcounted D, the dense live coral facies (Fig. 7), is also the one thatexperiences the highest known disturbance, namely at roughly decadaltimescales as a result of recurring temperature anomalies (Riegl 1999;Purkis and Riegl 2005). This coincides with the finding of Li (2000), whopostulates that a more fragile or vulnerable habitat may be associatedwith a smaller fractal dimension (i.e., habitat fragility and D are inverselycorrelated). This tallies with our findings that the highest D is observedfor facies postulated to be the most temporarily stable (i.e., sand,hardground, sparse coral, and macro-algae), which correspond to p* ofthe strong components (Fig. 9B) in the weighted digraph (i.e., the facieswith the greatest self-to-self transition probability).

Multi-scale randomness (combinations of random processes operatingat different resolutions) generates statistical fractal output patterns (DeCola 1989; Halley 1996; Halley and Kunin 1999). Although the landscapetrajectory presented (Fig. 9) can be treated as deterministic, strongrandom components remain. It remains impossible to predict exactlywhere hardground patches will form, where corals and/or algae willsettle, or where sand sheets will migrate, because these depend ona multitude of factors which can be considered essentially random.Therefore, the deterministic landscape trajectory is translated intoa probabilistic facies mosaic in which it is not possible to predict theexact position of any given unit. It is however possible to predict thatthe facies will exist within certain broad bands. We postulate thata landscape evolving along a deterministic path can also have fractalproperties, because the determinism exists only at landscape scale, whileits fractal components reflect their forcing by essentially randomprocesses at all other scales. This begs the question whether the fractalpatterns observed in the small-scale structure of corals (e.g., Bradburyand Reichelt 1983; Basillais 1997) are related to the scale invarianceobserved at reef-scale. A multi-scale experiment looking at coral structurefrom colony scale to reef scale would be required to shed light on thisissue.

For geologists, data on the horizontal persistence of carbonate faciesare difficult to obtain from outcrops and in the subsurface (Wilkinson etal. 1999). However, the mechanisms of deposition in modern environ-ments are usually assumed to be essentially the same as for buried ancientsystems and therefore the spatial patterns in modern analogues can assistinterpretation of the inaccessible ancient (e.g., Harris 1996). The findingthat facies distribution in modern carbonate depositional environmentscan, within certain thresholds, be explained using fractal concepts is

FIG. 9.— A) Weighted digraph where prepresents transition probability, p* & 1-np andp < 1-np, illustrating the suspected geneticrelationship between the observed facies. Anergodic state exists on Hardground (Coral–Macro-algae loop). B) Condensation graphshowing the strong components of part A of thisfigure, where K1 5 {Sand, Algal mats, Sea-grass}, K2 5 {Hardground}, K3 5 {Sparsecoral, Dense live coral, Dense dead coral,Macro-algae}; K3 is ergodic, K1 and K2

transient, the entire system moves towards K3,i.e., hardground with algae or corals. C) Theadjacency matrix for part A of this figure.


particularly exciting because it offers a predictive tool for use in thesubsurface. Three-dimensional reflection seismics is arguably the onlytool capable of resolving facies distribution in the subsurface in plan view.As with all remote sensing technologies, seismic images have a finitespatial resolution. With the knowledge that the system statisticallyfollows predictable relationships over a range of spatial scales, there is thepotential that fractal concepts can be used to offer insight intomechanisms operating beyond the spatial resolution of the seismic image.However, this study shows that the degree of fractal behavior and thespatial scales over which scale invariance holds is substrate specific.Boundary-based and patch-based metrics return inconsistent informationabout the spatial patterns within the facies mosaic, because they analyzedifferent properties of the system. While identifying that facies distribu-tions on a limited portion of the Arabian Homocline do display fractalproperties, our study also shows that a generic statistical solution topredict lithographic heterogeneity in modern or ancient carbonatesystems remains enigmatic.

ACKNOWLEDGMENTS

We thank reviewers P. Burgess, B. Wilkinson, G. Rankey, an anonymousreviewer, and editor D. Budd for their constructive comments on themanuscript. We benefited from discussion with W. Schlager, J. Kenter, andR. Dodge. We thank H.K. Al Shaer, M.A.H.A. Deshgooni, S.M. Ahmed,and the crew of the Municipality survey vessel. N. Al Shaiba, H. Braaksma, S.Knottnerus, and C. Purkis aided the fieldwork. The PRR600-610 was lent byBiospherical Instruments Inc., and we thank J. Morrow and M. Holas. Wewish to acknowledge M. Moerman (Physics and Electronics Laboratory,FEL-TNO) for the use of the sun photometer and H. van der Woerd(Institute for Environmental Studies, IVM) for the loan of the spectro-radiometers. BR and SJP were supported by National Oceanic andAtmospheric Administration (NOAA) grant NA16OA1443 to the NationalCoral Reef Institute (NCRI). The IKONOS image was provided via theNational Aeronautics and Space Administration (NASA) Scientific DataPurchase program. This is NCRI contribution 55.

REFERENCES

ADAMS, R.D., AND GROTZINGER, J.P., 1996, Lateral continuity of facies andparasequences in middle Cambrian platform carbonates, Carrara Formation,southeastern California, U.S.A.: Journal of Sedimentary Research, v. 66, p.1079–1090.

AL-HINAI, K.G., MOORE, J.M., AND BUSH, P.R., 1987, Landsat image enhancementstudy of possible submerged sand-dunes in the Arabian Gulf: International Journal ofRemote Sensing, v. 8, p. 251–258.

ALSHARHAN, A.S., AND EL-SAMMAK, A.A., 2004, Grain-size analysis and characterizationof sedimentary environments of The United Arab Emirates coastal area: Journal ofCoastal Research, v. 20, p. 464–477.

ANDREFOUET, S., AND RIEGL, B., 2004, Remote sensing: a key tool for interdisciplinaryassessment of coral reef processes: Coral Reefs, v. 23, p. 1–4.

ANDREFOUET, S., KRAMER, P., TORRES-PULLIZA, D., JOYCE, K.E., HOCHBERG, E.J.,GARZA-PEREZ, R., MUMBY, P.J., RIEGL, B., YAMANO, H., WHITE, W.H., ZUBIA, M.,BROCK, J.C., PHINN, S.R., NASEER, A., HATCHER, B.G., AND MULLER-KARGER, F.E.,2003, Multi-sites evaluation of IKONOS data for classification of tropical coral reefenvironments: Remote Sensing of Environment, v. 88, p. 128–143.

AVNIR, D., BIHAM, O., LIDAR, D., AND MALCAI, O., 1998, Is the geometry of naturefractal?: Science, v. 279, p. 39–40.

BASILLAIS, E., 1997, Coral surfaces and fractal dimensions: a new method: Academie desSciences (Paris), Comptes Rendus, Life Sciences, v. 320, p. 653–657.

BELLWOOD, D.R., HUGHES, T.P., FOLKE, C., AND NYSTROM, M., 2004, Confronting thecoral reef crisis: Science, v. 429, p. 827–833.

BRADBURY, R.H., AND REICHELT, R.E., 1983, Fractal dimension of a coral reef atecological scales: Marine Ecology, Progress Series, v. 10, p. 169–171.

CARLETON, J.H., AND SAMMARCO, P.W., 1987, Effects of substratum irregularity onsuccess of coral settlement: quantification by comparative geomorphologicaltechniques: Bulletin of Marine Science, v. 40, p. 85–98.

CARLSON, J., AND GROTZINGER, J.P., 2001, Submarine fan environment inferred fromturbidite thickness distributions: Sedimentology, v. 48, p. 1331–1351.

CHITTARO, P.M., 2004, Fish-habitat associations across multiple spatial scales: CoralReefs, v. 23, p. 235–244.

CONNELL, J.H., 1978, Diversity in tropical rain forests and coral reefs: Science, v. 199, p.1302–1310.

CONNELL, J.H., AND KEOUGH, M.J., 1985, Disturbance and patch dynamics of subtidalmarine animals on hard substrata, in Pickett, S.T.A., and White, P.S., eds., TheEcology of Natural Disturbance and Patch Dynamics: New York, Academic Press, p.125–151.

DAVIS, J.C., 2002. Statistics and Data Analysis in Geology, Third Edition: New York,John Wiley & Sons, 638 p.

DE COLA, L., 1989, Fractal analysis of a classified Landsat scene: PhotogrammetricEngineering and Remote Sensing, v. 55, p. 601–610.

DUSTAN, P., DOBSON, E., AND NELSON, G., 2001, Landsat thematic mapper: detection ofshifts in community composition of coral reefs: Conservation Biology, v. 15, p.892–902.

EMBABBI, N.S., AND SHARKAWI, F.M., 1989, Landform systems of the United ArabEmirates (abstract) : First symposium on remote sensing in the United Arab Emirates:U.A.E. University, Al Ain, April 16–19.

EVANS, G., MURRAY, J.W., BIGGS, H.E.J., BATE, R., AND BUSH, P.R., 1973, Theoceanography, ecology, sedimentology and geomorphology of parts of the TrucialCoast barrier island complex, Persian Gulf, in Purser, B.H., ed., The Persian Gulf;Holocene Carbonate Sedimentation and Diagenesis in a Shallow Epicontinental Sea:Heidelberg, Springer-Verlag, p. 234–269.

GARZA-PEREZ, J.R., LEHMANN, A., AND ARIAS-GONZALEZ, J.E., 2004, Spatial predictionof coral reef habitats: integrating ecology with spatial modelling and remote sensing:Marine Ecology, Progress Series, v. 269, p. 141–152.

HALL, P., AND WOOD, A., 1993, On the performance of box-counting estimators offractal dimension: Biometrika, v. 80, p. 246–252.

HALLEY, J.M., 1996, Ecology, evolution and 1/f-noise: Trends in Ecology and Evolution,v. 11, p. 33–37.

HALLEY, J.M., AND KUNIN, W.E., 1999, Extinction risk and the 1/f-noise family of noisemodels: Theoretical Population Biology, v. 56, p. 215–230.

HALLEY, J.M., HARTLEY, S., KALLIMANIS, A.S., KUNIN, W.E., LENNON, J.J., AND

SGARDELIS, S.P., 2004, Uses and abuses of fractal methodology in ecology: EcologyLetters, v. 7, p. 254–271.

HARRIS, J.W., AND STOCKER, H., 1998. Handbook of Mathematics and ComputationalScience: New York, Springer-Verlag, 1028 p.

HARRIS, P.M., 1996, Reef styles of modern carbonate platforms: Bulletin of CanadianPetroleum Geology, v. 44, p. 72–81.

HERGARTEN, S., 2002. Self-organised criticality in earth systems: Heidelberg, Springer,272 p.

HUGHES, T.P., 1994, Catastrophes, phase-shifts and large-scale degradation ofa Caribbean coral reef: Science, v. 265, p. 1547–1551.

HUVENNE, V.A.I., DE MOL, B., AND HENRIET, J.-P., 2003, A 3D seismic study of themorphology and spatial distribution of buried coral banks in the Porcupine Basin, SWof Ireland: Marine Geology, v. 198, p. 2–25.

JAMES, N.P., AND GINSBURG, R.N., 1979, The Seaward Margin of Belize Barrier andAtoll Reefs: International Association of Sedimentologists, Special Publication 3, 191p.

JENSEN, H.J., 1998. Self-Organized Criticality: Cambridge, U.K., Cambridge UniversityPress, 167 p.

KHAN, M.A., FADLALLAH, H., AND AL-HINAI, K.G., 1992, Thematic mapping of subtidalcoastal habitats in the western Arabian Gulf using Landsat TM data—Abu Ali Bay,Saudi Arabia: International Journal of Remote Sensing, v. 13, p. 605–614.

KIRKHAM, A., 1998, A Quaternary proximal foreland ramp and its continental fringe,Arabian Gulf, U.A.E., in Wright, V.P., and Burchette, T.P., eds., Carbonate Ramps:Geological Society of London, Special Publication 149, p. 15–42.

LAMBECK, K., 1996, Shoreline reconstructions for the Persian Gulf since the last glacialmaximum: Earth and Planetary Science Letters, v. 142, p. 43–57.

LANGMEAD, O., AND SHEPPARD, C., 2004, Coral reef community dynamics anddisturbance: a simulation model: Ecological Modelling, v. 175, p. 271–290.

LI, B.-L., 2000, Fractal geometry applications in description and analysis of patchpatterns and patch dynamics: Ecological Modelling, v. 132, p. 33–50.

LILLESAND, T.M., AND KIEFER, R.W., 1994. Remote Sensing and Image Interpretation,Third Edition: New York, John Wiley & Sons, 750 p.

LOVEJOY, S., 1982, Area–perimeter relation for rain and cloud areas: Science, v. 216, p.185–187.

MAEDER, J., NARUMALANI, S., RUNDQUIST, D.C., PERK, R.L., SCHALLES, J., HUTCHINS, K.,AND KECK, J., 2002, Classifying and mapping general coral-reef structure usingIKONOS data: Photogrammetric Engineering and Remote Sensing, v. 68, p.1297–1305.

MCCOOK, L.J., 1999, Macroalgae, nutrients and phase shifts on coral reefs: scientificissues and management consequences for the Great Barrier Reef: Coral Reefs, v. 18, p.357–367.

MIDDLETON, G.V., 2000. Data Analysis in the Earth Sciences using Matlab: New York,Prentice Hall, 260 p.

MUELLER, J.L., 2003, In-water radiometric profile measurements and data analysisprotocols, in Mueller, J.L., Fargion, G.S., and McClain, C.R., eds., Ocean OpticsProtocols for Satellite Ocean Color Sensor Validation, Revision 4, Volume III:NASA/TM-2003-21621/Rev4-Vol.III: Greenbelt, National Aeronautics and SpaceAdministration, p. 1–77.

O’REILLY, B.M., READMAN, P.W., SHANNON, P.M., AND JACOB, A.W.B., 2003, Amodel for the development of a carbonate mound population in the RockallTrough based on deep-towed sidescan sonar data: Marine Geology, v. 198,p. 55–66.


PETERSON, B., 2001. IKONOS relative spectral response and radiometric calibrationcoefficients: Revision A: Thornton, Space Imaging, Document number SE-REF-016,27 p.

PIELOU, E.C., 1977. Mathematical Ecology: New York, John Wiley & Sons,384 p.

PRUESS, S.A., 1995, Some remarks on the numerical estimation of fractal dimension, inBarton, C.C., and La Pointe, P.R., eds., Fractals and the Earth Sciences: London,Plenum Press, p. 65–75.

PURKIS, S.J., 2005, A ‘‘reef-up’’ approach to classifying coral habitats from IKONOSimagery: IEEE Transactions on Geoscience and Remote Sensing, v. 43, p. 1375–1390.

PURKIS, S.J., AND PASTERKAMP, R., 2004, Integrating in situ reef-top reflectance spectrawith Landsat TM imagery to aid shallow-tropical benthic habitat mapping: CoralReefs, v. 23, p. 5–20.

PURKIS, S.J., AND RIEGL, B., 2005, Spatial and temporal dynamics of Arabian Gulf coralassemblages quantified from remote-sensing and in situ monitoring data: MarineEcology, Progress Series, v. 287, p. 99–113.

PURSER, B.H., AND SEIBOLD, E., 1973, The principal environmental factors influencingHolocene sedimentation and diagenesis, in Purser, B.H., ed., The Persian Gulf;Holocene Carbonate Sedimentation and Diagenesis in a Shallow Epicontinental Sea:Heidelberg, Springer, p. 234–269.

RANKEY, E.C., 2002, Spatial patterns of sediment accumulation on a Holocenecarbonate tidal flat, Northwest Andros Island, Bahamas: Journal of SedimentaryResearch, v. 72, p. 591–601.

RANKEY, E.C., 2004, On the interpretation of shallow shelf carbonate facies andhabitats: How much does water depth matter?: Journal of Sedimentary Research,v. 74, p. 2–6.

RANKEY, E.C., AND MORGAN, J., 2002, Quantified rates of geomorphic change ona modern carbonate tidal flat, Bahamas: Geology, v. 30, p. 583–586.

RIEGL, B., 1999, Corals in a non-reef setting in the Arabian Gulf (Dubai, U.A.E.): faunaand community structure in response to recurring mass mortality: Coral Reefs, v. 18,p. 63–73.

RIEGL, B., 2001, Inhibition of reef framework by frequent disturbance: examples fromthe Arabian Gulf, South Africa, and the Cayman Islands: Palaeogeography,Palaeoclimatology, Palaeoecology, v. 175, p. 79–101.

RIEGL, B., AND PILLER, W.E., 1999, Coral frameworks revisited: reefs and coral carpetsin the northern Red Sea: Coral Reefs, v. 18, p. 241–254.

RIEGL, B., AND PILLER, W.E., 2000, Reefs and coral carpets in the northern Red Sea asmodels for organism—environment feedback in coral communities and its reflectionin growth fabrics, in Insalaco, E., Skelton, P.W., and Palmer, T.J., eds., Carbonateplatform systems: components and interactions: Geological Society of London,Special Publication 178, p. 71–88.

RIEGL, B., AND PURKIS, S.J., 2005, Detection of shallow subtidal corals from IKONOSsatellite and QTC View (50, 200 kHz) single-beam sonar data (Arabian Gulf; Dubai,UAE): Remote Sensing of Environment, v. 95, p. 96–114.

RIEGL, B., KORRUBEL, J.L., AND MARTIN, C., 2001, Mapping and monitoring of coralreef communities and their spatial patterns using a surface based video method froma vessel: Bulletin of Marine Science, v. 69, p. 869–880.

ROBERTS, F.S., 1976. Discrete Mathematical Models: Englewood Cliffs, New Jersey,Prentice Hall, 559 p.

RODRIGUEZ-ITURBE, I., AND RINALDO, A., 1997. Fractal river basins; Chance and Self-Organization: Cambridge, U.K., Cambridge University Press, 540 p.

ROGERS, C.S., 1990, Responses of coral reefs and reef organisms to sedimentation:Marine Ecology Progress Series, v. 62, p. 185–202.

SCHLAGER, W., 2004, Fractal nature of stratigraphic sequences: Geology, v. 32, p.185–188.

SCHROEDER, M., 1991. Fractals, Chaos, Power Laws; Minutes from an Infinite Paradise:New York, Freeman, 196 p.

SEURONT, L., AND SPILMONT, N., 2002, Self-organised criticality in intertidal micro-phytobenthos patch patterns: Physica A, v. 313, p. 513–539.

SHINN, E.A., 1969, Submarine lithification of Holocene carbonate sediments in thePersian Gulf: Sedimentology, v. 12, p. 109–144.

SHORT, A.D., AND AAGAARD, T., 1993, Single and multi-bar change models: Journal ofCoastal Research, v. 15, p. 141–157.

TARBOTON, D.G., BRAS, R.L., AND RODRIGUEZ-ITURBE, I., 1988, The fractal nature ofriver networks: Water Resources Research, v. 24, p. 1317–1322.

TURCOTTE, D.L., 1997. Fractals in Geology and Geophysics: Cambridge, U.K.,Cambridge University Press, 412 p.

UCHUPI, E., SWIFT, S.A., AND ROSS, D.A., 1996, Gas venting and late Quaternarysedimentation in the Persian (Arabian) Gulf: Marine Geology, v. 129, p. 237–269.

WHERRY, R.J., 1931, A new formula for predicting the shrinkage of the coefficient ofmultiple correlation: Annals of Mathematical Statistics, v. 2, p. 440–457.

WILKINSON, B.H., AND DRUMMOND, C.N., 2004, Facies mosaics across the PersianGulf and around Antigua—stochastic and deterministic products of shallow-water sediment accumulation: Journal of Sedimentary Research, v. 74,p. 513–526.

WILKINSON, B.H., DRUMMOND, C.N., DIEDRICH, N.W., AND ROTHMAN, E.D., 1999,Poisson processes of carbonate accumulation on Paleozoic and Holocene platforms:Journal of Sedimentary Research, v. 69, p. 338–350.

WILSON, J.D., 1992, A comparison of procedures for classifying remotely-sensed datausing simulated data sets: International Journal of Remote Sensing, v. 13, p. 365–386.

Received 21 November 2003; accepted 6 January 2005.

APPENDIX—OPTICAL METHODOLOGY

Image Acquisition

Remote sensing has been employed in the Arabian Gulf for shallow-marine habitat mapping from both satellite (Al-Hinai et al. 1987;Embabbi and Sharkawi 1989; Khan et al. 1992; Andrefouet et al. 2003;Purkis and Riegl 2005) and vessel-based (Riegl et al. 2001) sensors. Forremote-sensing-based reef mapping, we employed two types of satelliteimagery. 15 m 3 15 m pixel-resolution ASTER imagery for site orientationand use as a navigational map in the hydrographic survey (imported intothe survey software Hypack for line selection) and 4 m 3 4 m pixelresolution IKONOS imagery was used for optical discrimination of benthichabitats. We selected an IKONOS-2 11-bit multispectral satellite imageacquired on 2 May 2001 (scene 75209) at 06:49 GMT. Sun elevation andnominal collection azimuth at the time of acquisition were 67u and 65u,respectively, the tidal stage was 3 hours after high water, water clarity washigh, and the surface was calm. The image was unaffected by atmosphericdust, and there was no cloud cover. Although the level of geographicaccuracy of the raw image was reasonable, further geocorrection wasconducted against 40 ground-control points acquired using a portableLeica 500 dGPS system with a horizontal accuracy of 6 30 cm, yielding anaverage root-mean-square error of 0.66 pixel, or 2.65 m.

‘‘Reef-Up’’ Classification Strategy

Monitoring coral-reef benthos with satellites typically follows a ‘‘sen-sor-down’’ approach, with the classification algorithm driven by statisticsderived from the imagery. We adopt the ‘‘reef-up’’ method proposedby Purkis (2005), with a classifier trained exclusively using in situoptical measurements, linking the satellite and in situ data usingcommon units of substrate reflectance. Meter-scale ground verificationwas used to determine the dominant benthic substrates, which weresubsequently targeted for optical measurement. The measurementstrategy employed a suite of four intercalibrated field spectroradiometersto coincidently parameterize the optical properties of the atmosphere,the water column, and the benthic substrates in rapid succession. Alloptical measurements were conducted over suitably large and spatiallyhomogeneous patches of substrate, between 10:00 and 17:45 hr localtime, therefore ensuring that the sun was a minimum of 30u above thehorizon, to preclude the effects of directional illumination. Theequipment setup is shown in Figure 10, and the specifications of theoptical instruments and procedures adopted are detailed by Purkis (2005).For brevity, from here onwards the symbol l has been suppressed forwavelength-specific terms.

For each target, the suite of radiometers were used to concurrentlyevaluate: (1) the attenuation of the water body (k), (2) the downwellingirradiance in air (Ead), (3) downward radiance of skylight (Lsky), (4)reflectance just above the water–air boundary (Rrs(z5a)) and (5) a signalapproximating to substrate reflectance, evaluated in close proximity tothe seabed (Rb) (Fig. 10). Image classification was implemented usinga multivariate-normal probability density function implemented usingcode written in Matlab 6.1 (Purkis and Pasterkamp 2004). In line withancillary ground-based ecological studies of the area and the naturalgrouping of the spectral data following hierarchical cluster analysis, eightspectral classes were defined. For classifier training, the Rb spectraevaluated close to the submerged target using a SD2000 radiometer wereused (Fig. 11).

The spectra assigned to each of the eight spectral classes weretransformed to simulate values for the three visible spectral bands ofthe IKONOS sensor by integrating the data over the width of each bandwith respect to its published radiometric sensitivity. The within-classmean (m), standard deviation, and covariance matrix (S) of dimensionsn 3 n were subsequently calculated for each of the eight spectral groups.


Each pixel of the IKONOS image (X) was analyzed and the probability(W) of membership to each spectral class calculated (eq. 1).

W~exp { 1

2X{mð Þ’S{1 X{mð Þ

� �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pð Þn S½ �Þ

p ð1Þ

The output from the analysis was an eight-band ‘‘probability image,’’which was reduced to a single band thematic map by extracting the bandnumber accounting for the highest W value, on a pixel-by-pixel basis.

Prior to classification, the IKONOS image was calibrated radiomet-rically using the coefficients of Peterson (2001) to yield pixel values ofradiance (W m21 ster21 mm21). The imagery was further corrected forthe effect of atmospheric path radiance against terrestrial pseudoinvariantfeatures, the spectral properties of which were parameterized in situ usinga PR650 radiometer. The first three bands of the imagery (blue, green,and red) were then processed to remove the spectral effect of theintervening water column using the optical model of Purkis andPasterkamp (2004), (eq. 2),

Rb~1

0:54Rrs z~að Þ{ 1{e{2kz

� �Rw

e{2kzð2Þ

resulting in pixel values presumed to be equivalent to substrate reflectance(Rb).

The Rrs(z5a) are the atmospherically corrected pixel values in units ofapparent surface reflectance (%). The thickness of the water column (z)within each pixel of IKONOS imagery is required for this procedure andwas derived from the mutually registered bathymetric DEM constructedfrom the 50 kHz acoustic survey. Also required are data pertaining to theattenuation of the water body (k) and the reflectance of optically deepwater (Rw). The PR650 radiometer was used to measure Rw, which wasretrospectively matched to the imagery over a deep-water target (Purkis2005). k was evaluated in the field using a PRR-600 Profiling ReflectanceRadiometer system (Biospherical Instruments Inc.). The hand-deployedunit instantaneously profiles downwelling irradiance (Ed), upwellingradiance (Lu), and depth (z). These data can be used to calculate theattenuation of the water body (k). The PRR-600 was operated in unisonwith a PRR-610 Reference Radiometer, equipped with a cosine corrector

FIG. 10.—Cartoon detailing the measure-ment strategy used to quantify the componentsof the radiative transfer sequence betweensatellite and substrate.

FIG. 11.— Representative substrate reflectance spectra evaluated beneath thewater surface and in close proximity (0.1 m elevation) to the sea bed, obtainedfrom the eight predetermined substrate classes used for training the classificationalgorithm.


to simultaneously measure downwelling irradiance in air (Ed) in the samewavelength bands. The data from this reference instrument were usedaccording to the protocols of Mueller (2003) to normalize the profilemeasurements to Ead, yielding normalized downwelling irradiance (E9d).Profiles of k were conducted in areas where water depth was sufficient tofacilitate a profile over a minimum Dz of 4 m and calculated according to(eq. 3).

k zð Þ~ln E0d zð Þ� �

dzð3Þ

For the reef-up classification strategy to function, a reasonable degree ofoptical closure must be achieved between reflectance values acquired from

the satellite and values evaluated in situ. Radiative-transfer modeling candeliver only pseudo optical closure, because absolute closure is unattain-able in shallow water because adjacency and surface effects (e.g., whitecaps) are not accounted for in the model. However, the reef-up strategyoperates under the assumption that errors in the model are balanced bythe flexibility of the probability-driven classifier, so that a close matchbetween the two datasets is sufficient to allow the correct assignment ofpixels to classes. Indeed, this seems to be the case, because the classi-fication result is satisfactory and optically similar substrates such as algaeand seagrass are successfully separated. The inclusion of covariance in theclassifier is likely to aid this process by providing an additional datacharacteristic with which to discriminate between spectral classes.


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