mid-plate islands also changed sea level as well as created space for the addition of ..... Grand Cayman Island (West Indies) and found mean rates of 0.37 and ...
Coral Reefs 0990) 9:51-62
Coral Reefs 9 Springer-Verlag 1990
A simulation model of island reef morphology: the effects of sea level fluctuations, growth, subsidence and erosion Gustav Paulay * and Larry R. McEdward **
Friday Harbor Laboratories, University of Washington, Friday Harbor, Washington 98250, USA, and Department of Zoology NJ-I 5, University of Washington, Seattle, Washington 98195, USA Accepted 21 November 1989
Abstract. Glacioeustatic sea level fluctuations contin-
ually cover and expose reefs, alternately allowing growth or erosion to operate. In a simulation model we examine the simultaneous effects of sea level change, island subsidence, reef growth, subaerial erosion, marine backwearing, and fluvial erosion (from central highlands) on reef development. Using values obtained from the literature, we vary the rates of these processes and compare the reefs produced. Our results indicate that subaerial erosion, subsidence and growth are of comparable importance in determining reef morphology. Fore reef terraces, as developed by the model, are primarily drowned growth features; marine backwearing is of little importance in their development. Reef terraces form readily at depths that never had a stable sea stand, their depth is influenced by growth, subaerial erosion, and subsidence rates. Thus reef terraces often do not indicate former sea stands. We examine the causes of reef drowning and attribute it primarily to rapid subsidence and subaerial erosion, not to truncation through marine backwearing. We propose that reefs deeply submerged today are not necessarily "drowned out", but may be vertically stable through many sea level cycles. Fluvial erosion is likely an important agent of lagoon formation on high islands in areas with high erosion rates.
Introduction
Since Darwin (1842) proposed that island reefs change through time by a combination of growth and subsidence, several additional processes have been invoked to explain the development of oceanic island reef systems. The principal factors that entered the "coral reef problem" since Darwin's formulation were late Tertiary and * P r e s e n t address: Department of Paleobiology, National Museum of Natural History, Washington, DC 20560, USA ** P r e s e n t address: Department of Zoology, University of Florida, Gainesville, Florida 32611, USA
Quaternary sea level fluctuations and the various erosional processes they make possible. The history of the "coral reef problem" has often been summarized (e. g. Stoddart 1969; Steers and Stoddart 1977). While acknowledging that both contribute to reef development (Hopley 1982), some authors favor erosional processes (Flint et al. 1953; MacNeil 1954; Purdy 1974), while others emphasize growth as more important (Adey 1978; Chappell 1980; 1983; Searle 1983). Late Cenozoic glacio-eustatic sea level fluctuations provided a complex environment for reef development, subjecting different parts of reefs to growth and subaerial erosion as these parts became submerged or exposed respectively. Water depths and thus reef growth rates also varied over submerged reefs as sea level changed. Finally isostatic effects, such as the usually steady subsidence of mid-plate islands also changed sea level as well as created space for the addition of more reef materials. The importance of individual factors affecting reef development may be evaluated by field work, but the interactions of growth, various erosional processes, subsidence and eustatic sea level fluctuations make long term reef development complex and difficult to study directly or by qualitative, verbal models. Quantitative simulation models thus provide some of the best tools for examining long term reef development through the Quaternary. Our purpose was to use a simulation model to study reef development through several glacio-eustatic sea level cycles; to examine the effects, importance, and interactions of 6 basic processes that affect reef morphology: sea level fluctuations, subsidence, growth, subaerial erosion, fluvial erosion, and marine erosion.Values for the rates of these processes were obtained from the literature. We focused our study on oceanic "island reefs", such as are found in the Central Pacific, surrounding or capping volcanic islands situated away from plate margins, and thus in locations largely dominated by subsidence (Parsons and Sclater 1977). Rate estimates (only) from other reef systems were used where deemed appropriate. Most previous models of reef development analyzed the growth of shallow reefs thru the Holocene (or last in-
52
terglacial) trangression, modeling variation in growth rate due to a variety of environmental factors (Adey 1978; Chappell 1980; Graus et al. 1984, 1985). As these studies focused on a single transgression, erosional processes associated with regressions were not included. Holpley (i 982: Fig. 8.11) presented a verbal model outlining the development of a typical Great Barrier Reef shelf reef through an entire glacial sea level cycle, from the last interglacial to the present. Additional studies encompassing at least an entire sea level cycle are needed to understand reef development during the Quaternary, when erosional and growth processes alternated as sea level varied. An important qualification must accompany the analysis of our simulations: several processes that modify reef structure and development were not included in the simulations and thus their effects cannot be evaluated. This reduces the complexity of the model and facilitates analysis of the basic processes in the simulation. Also, field data on the nature and rates of some of these additional processes are lacking. Important processes excluded from the model include topographical variations in growth (except with depth) and erosion rates, accumulation and movement of loose sediments, and slope collapse. Rate estimates Eustatic sea level fluctuations
We used the last glacial sea level cycle (last interglacial to present) as presented by Chappell and Shackleton (1986) as the basis for our sea level curve (Fig. 1), and repeated it four times (there were 17 sea level cycles in the past 1.7 My; Kukla 1977). We chose to repeat the last sea level cycle instead of using empirical sea level data for the past 0.5 My because (1) earlier sea level cycles are poorly known, and (2) repetition of the same cycle allowed us to study the iterative effects of similar sea level cycles. Subsidence." Isostatic changes in sea level
Subsidence explains the succession of island reef types (Darwin 1842). Subsidence of oceanic islands can be due to several factors, most importantly to cooling and concomittant sinking of aging lithosphere. Subsidence rate of ocean floor is inversely correlated with the square root
v
E
500
09 9 03
-50
k~
| -100 r',-
i
0
i
i
i
I
25
i
i
i
i
I
1
50 Time
i
l'l
I
75 (ty)
J ~
i
i
[
1 O0
i
i
i
125
Fig.l, The 125 ty seatevei record used (reiterated 4 times) in the model. Adapted from Chappell and Shackleton's (1986: Fig. lc) curve for the last interglacial to the present. 0 = mean sealevel
of plate age (Detrick and Crough 1978; Menard 1983); it is 0.15 m/ty for new crust at the ridge crest compared with 0.03 m/ty for 25 My old lithospheric plate material (calculated from Fig. 13 of Parsons and Sclater 1977). Hotspots locally thin and thus raise the lithosphere, so new islands are born on locally modified plate material raised to the depth of effectively much younger lithosphere, and subside at rates characteristic of such younger plates (Detrick and Crough 1978; Menard and McNutt 1982; Menard 1983). Several conflicting estimates are available as to the amount of thermal rejuvenation associated with hotspots. Crough (1978) estimates rejuvenation to an equivalent thermal age of 25 My (thus a subsidence rate of 0.03 m/ty) for all new islands, while Menard (1983) presents evidence that the new thermal age will be 0-3 My (subsidence rate of 0.15 m/ty), and Menard and McNutt (1982) argue that the amount of rejuvenation is dependent on original crustal age: "crust younger than 10 m. y. is reelevated to depths comparable to the depth of the ridge crest [0 My]", while "crust aged 10-90 m.y. is reelevated on average about a third of the amount it has subsided since it was at a ridge crest." Only Menard's (1983) data are derived from island subsidence rates; Crough's (1978) and Menard and McNutt's (1982) data are derived largely from observations on the subsidence of lithospheric swells associated with hot-spot traces. Menard (1983) calculated average rates of subsidence for a variety of Pacific plate islands based on estimates of reef thickness made from bathymetric profiles. He obtained subsidence rates of 0.04-023 m/ty for islands varying in age between 14 and 1.5 My (calculated from Table 1 of Menard 1983). Direct estimates of subsidence are available from dated reef cores. The Miocene/Pliocene boundary lies at a depth of 210 m, 185 m and 139 m in cores from Bikini (Marshall Is.), Enewetak and Midway (Hawaiian Is.) atolls (Ladd et al. 1967), respectively. On all 3 islands the late Miocene and Pliocene sequences are characterized by shallow water communities (Schlanger 1963; Ladd et al. 1967). Assuming near sea level deposition and a sea stand 10-80 m above the present stand at the Miocene/Pliocene boundary (Hallam 1984; Haq et al. 1987) yields subsidence rates of 0.043-0.057, 0.038-0.052 and 0.0290.043 m/ty respectively for the 3 islands. The volcanic basement reached at a depth of 1263 m under Enewetak was dated as 51-59 My old (Kulp 1963). This basalt basement, lying under the present reef rim, was quickly submerged if not formed underwater, as it is overlain by Tertiary b fossils (Schlanger 1963). Assuming that the dated basalt was near sea level and a sea stand 60-220 m above present 51-59 My ago (Hallam 1984; Haq et al. 1987) yields a subsidence rate of 0.0220.029 m/ty. Considering the thickness of the section, these subsidence rates are well bufferred against errors in estimating depth or elevation of basalt at time of formation. On Midway, basalt from a depth of 363 m was dated as 27.0 4-0.6 My old (Dalrymple et al. 1977). These flows were probably near sea level as (1) they were not laid down in deep water (Ladd et al. 1967) and (2) they were quickly submerged if not formed submerged as evidenced
53 by overlying Tertiary e fossils and latest Oligocene to earliest Miocene ostracods (Dalrymple et al. 1977). Assuming the basalt formed near sea level, 15-75 m above the present sea stand (Hallam 1984; Haq et al. 1987), yields subsidence rates of 0.014-0.016 m/ty. On Mururoa Atoll (Tuamotu Is.) the Miocene/ Pliocene boundary lies at a depth of 556 m in a bed of coral carbonates (Trichet et al. 1984), indicating a subsidence rate of 0.111-0.125 m/ty (calculated as for atolls above). Trichet et al. (1984) estimate a subsidence rate of 0.08 m/ty for Mururoa, based on an age of 7.2 My for basalt on the volcanic summit now 240 m below sea level, but estimated, from geophysical information, to have originally been ca. 300 m above sea level. Additional estimates of short term subsidence rates are available where past sea level signatures are lowered by subsequent subsidence. Thus by measuring the present day emergence of coral conglomerates formed at the marine phreatic/vadose interface at a known higher Holocene sea stand, Pirazzoli et al (1985) calculate a subsidence rate of 0.15 mm/y for Tahiti and 0.14 mm/y for Moorea. These are in good agreement with Menard's (1983) estimate of a subsidence rate of 0.18-0.23 m/ty for Moorea (calculated from his Table 1), and demonstrate the rapid subsidence of young islands. While an island is volcanically active, subsidence rates are up to two orders of magnitude greater due to isostatic adjustment to the load added by the growing island; the active volcano of Hawaii subsides at a rate of 1.2-4.1 m/ ty (Moore and Fornari 1984). Additional processes affecting reef subsidence rates away from plate margins include movement over possible asthenospheric bumps (Menard 1973), lithospheric flexure around active hotspots (McNutt and Menard 1978; Spencer et al. 1987), and riding over lithospheric swells caused by hotspots (Crough 1984). These processes may cause either uplift or increased subsidence but have localized effects and were not considered for this model. We used subsidence rates of 0, 0.05 and 0.2 m/ty in the model, corresponding to an island that is not subsiding, an old (,-~ 10-20 My), and a young ( ~ 1 My) island (ages based on Menard's 1983 estimates).
Growth Reef growth rates have been reviewed often (e. g. Highsmith et al. 1980; Hopley 1982; Davies 1983; Davies et al. 1985; Graus et al. 1985) and range between 0.2-21 m/ty (= meters/1000 years). Most relevant to our study are direct rate measurements from cores dated by 14C at different levels during the Holocene transgression. Davies et al. (1985) present a summary of their work in the north and central Great Barrier Reef, based on 85 drill holes in 27 reefs. They found growth rates ranging from 1.3-14.2 m/ ty with a mean of ,~ 6 m/ty. Hopley (1982) estimated reef growth on the Great Barrier Reef to average between 25 m/ty, varying regionally, based on dating the commencement and end of 24 Holocene reef sequences. Drill core studies in the Carribbean show similar growth rates, ranging from 0.3-12.0 m/ty depending on facies and environmental conditions (Graus et al. 1985). These values
Table
1. Simulation parameters used in model Rate(m/ty)
Process
Low
S t a n d a r d High
Growth Subsidence Subaerial erosion Fluvial erosion Marine erosion
1 0 0 0 0
4 0.05 0.15 1 1
Other variations
Standard
Variation
Max. growth at... depth Max. depth of growth
0m 50 m
5m 13 m
8 0.20 0.50 4 4
are comparable to those obtained from the best studied Holocene reef core for a central Pacific island, Tarawa Atoll (Kiribati), where growth ranged between 5.08.2 m/ty (Marshall and Jacobson 1985). We selected maximum growth rates of 1, 4 and 8 m/ty to represent slow, average, and rapid growth. Variation in reef growth rate with depth is still poorly documented. Although reef growth rate usually decreases with increasing depth,at shallow depths this trend may be reversed. On the basis of Holocene cores from the Great Barrier Reef, Davies (1983) and Davies et al. (1985) show a gradually increasing growth rate from the surface to ,-~3 m depth, a stable to slightly increasing growth rate to a depth of 15 m, followed by a markedly decreasing growth rate toward deeper water. Adey (1978), on the basis of coring data, presents growth/depth curves from St. Croix and Alacran in the Caribbean, with maximum growth rates at 2 and 8 m depths respectively. Additional estimates of how reef growth rate varies with depth can be inferrerd from indirect studies on (1) reef carbonate budgets and (2) growth rates of bioliths. Smith and Harrison (1977) calculated the weighted sum of coral and coralline algal cover and calcium carbonate production on the windward slope of Enewetak atoll (Marshall Is.) and found it to be highest on the reef crest, whereas on the fore reef production peaked at 11 m depth. Sheppard (1982), in his review of reef slope corals, concluded that coral cover tends to increase to a depth of 5-10 m, to decrease past a depth of 30 m, and to be relatively uniform in between. Coral growth rate usually decreases with depth, although sometimes only slightly (e.g. Buddemeier and Kinzie 1976; Highsmith 1979; Graus and Macintyre 1982; Huston 1985). The principal limit to growth at increasing depths is probably decreasing light intensity (Graus and Macintyre 1976, 1982). At shallow depths wave energy may also limit growth (Adey 1979; ChappeU 1980). Calcareous algae may add substantially to reef growth at very shallow depths (Smith and Kinsey 1976). We examined the effects of 2 relationships between growth rate and depth. In one, growth rate decreased steadily with increasing depth. In the other, growth rate peaked at 5 m depth and decreased both with increasing depth and towards the surface. Relative position within a reef system might have important effects on reef growth rates (Smith and Kinsey
54
1976; Smith and Harrison 1977; Jokiel and Maragos 1978; Neumann and Macintyre 1985), as might the topography and nature of antecedent substratum (Marshall and Davies 1982; Hopley 1982, 1983). Positional information may explain a large portion of reef morphology, such as certain barrier reefs (Chappell 1983). In the present model we did not simulate variation in growth rate with reef topography, except that inner reef areas landward of exposed reefs had zero growth rates.
Subaerial erosion
Subaerial erosion during low sea stands has been claimed to be the most important process affecting the overall morphology of present-day reef systems (Fling et al. 1953; MacNeil 1954; Purdy 1974). Rates of erosion may be estimated in several ways; best perhaps are rates calculated from reef cores through one interglacial-glacial-interglacial sea level cycle. In reef cores, the "Thurber discontinuity" (Stoddart 1969) separates deposits of the last interglacial period ( ~ 125/ty BP) from Holocene sediments. The Thurber discontinuity lies at a depth of 610 m on Mururoa (Labeyrie et al. 1969), at 10.8-14.4 m (Mu7 drill core) and 18-24 m (E-1 and F-1 drill cores) on Enewetak (Sackett and Potratz 1963) and at 11-17 m on Tarawa (Marshall and Jacobson 1985). Assuming that at their time of formation these last interglacial reefs were at sea level (a likely scenario as the cores are located on reef rims that during high sea stands are near sea level), assuming a global sea level 6 m above the present stand during the last interglacial (Chappell 1983), and assuming the subsidence rates estimated for these islands above, one may calculate the amount of material eroded since the last interglacial: Holocene re&thickness = Growth = Subsidence + Erosion -6 m
(1) Using subsidence rates on the most recent time period available (Miocene/Pliocene boundary to Recent), calculated erosion rates are 0-0.017 m/ty for Mururoa, 0.0820.125 m/ty (Mu7 drill core), 0.140-0.202 m/ty (E-1 and F-1 drill cores) for Enewetak, and 0.011-0.146 m/ty for Tarawa, the latter estimated using subsidence rates from both Mururoa and Enewetak. The low erosion rate on Mururoa may reflect either actually low rate of erosion, a rapidly decreasing subsidence rate since the Early Pliocene, or an effective uplift of the atoll. Labeyrie et al. (1969) argue for a recent uplift of 3 m on Mururoa. Using the same calculation (1), Marshall and Davies (1984) estimate an erosion rate of 0.07-0.14 m/ty for shelf reefs of the Great Barrier Reef. Stoddart et al. (1971) calculated the potential amount of subaerial erosion on Aldabra Atoll to be 0.005 m/ty by estimating the amount of calcite that rainwater would remove. Opdyke et al. (1984) estimated karst erosion in Northern Florida to be 0.026-0.08 m/ty based on estimates of amount of calcium carbonate lost through spring flow and subsurface seepage. Trudgill (1976a, 1979) measured short term erosion with a micro-erosion meter on Aldabra and found a range of 0.09-0.62 mm/y,
with mean values ranging from 0.09-0.51 mm/y for a variety of uplifted reef surfaces. Under deep organic soils, limited in extent on Aldabra, erosion was much more rapid, with a mean rate of 12.5 mm/y. Spencer (1985a) measured erosion rates with a micro-erosion meter on Grand Cayman Island (West Indies) and found mean rates of 0.37 and 0.16 mm/y inland and subsoil respectively, with a range of site means of 0.11-0.69 and 0.060.27 mm/y respectively. Menard (1982)noted a correlation between the occurrence of uplifted islands and low rainfall, presumably due to less erosion and thus a longer lifespan of limestone islands under low rainfall conditions. A correlation between the depth of atoll lagoons and amount of rainfall is also evident (Purdy 1974; Menard 1982). Erosion rates are highly dependent on the resistance of rocks to weathering and thus on the age of the limestone (T. Spencer personal communication). During the frequent sea level fluctuations of the Pleistocene it is mostly the uppermost, youngest, least remineralized, least resistant reef rocks that are exposed and eroded. We used subaerial erosion rates of 0, 0.15 and 0.5 m/ty to correspond to no erosion, average, and high erosion rates.
Fluvial erosion
Uplifted islands where fossil reefs surround a central volcanic massif show evidence of a distinct erosional process, here termed fluvial erosion, that may be important in lagoon formation on high islands. Fluvial erosion creates inland facing limestone cliffs at the volcanic-karst junction due to corrosion by streams and flood water draining centrally located volcanic hinterlands (Fig. 2) (Hoffmeister 1930; Stoddart et al. 1985; Stoddart and Spencer 1987). Water from the volcanic highlands drains through conduits in the karst, but "these conduits cannot accomodate flood discharges, so that aggressive waters are dammed back, causing solutional undercutting along the swamp-makatea junction" (Stoddart and Spencer 1987, p. 9). This process was studied in detail by Stoddart et al. (1985) on Mangaia (Cook Is.) and by Stoddart and Spencer (1987, their Fig. 4 is an excellent illustration of this process) on Rurutu; its effects are also clearly evident on other uplifted islands in the Cook-Austral and Tongan Groups (Hoffmeister 1930; Spencer et al. 1985; G. Paulay personal observation). Fluvial erosion is analogous to Purdy's (1974) karst marginal plain erosion. The rate of horizontal fluvial erosion in such settings may be estimated as follows. Mangaia has an uplifted reef about 70 m high, terminating inland in cliffs that range up to 60 m high and surround a central volcanic dome of 169 m elevation. The volcanic interior averages 3 km in radius and the 70 m altitude (equivalent to the height of the uplifted reef) is reached 1-2 km inland of the cliff face. Thus a 1-3 km wide portion of fossil reef has been removed by fluvial erosion, depending on how much higher (and thus further inland) the fossil reef extended before subaerial erosion reduced its height to the present 70 m. The uplift of Mangaia is thought to be due to lithospheric flexure around the 1.1-2.3 My old vol-
55 s u b a e r i a l erosion fluvial erosion
I
I
[ !rosioFi
IANBNCNgN[ Fig. 2. Mode of operation of the 3 erosional processes simulated in the model. Scale is not proportional. A = antecedent basalt slope, B = reef material remaining after erosion, C = reef material removed by subaerial erosion, D = reef material removed by marine erosion, E = reef material removed by fluvial erosion
cano of Rarotonga (McNutt and Menard 1978; Turner and Jarrard 1982; Stoddart et al. 1985). On neighboring Atiu, 1-2 km of limestone was removed in the same time interval. Fluvial erosion rates for these islands are therefore about I m/ty horizontally. These rates would be higher if the islands were atolls prior to uplift, a likely possibility (see Appendix). The rate of fluvial erosion is dependent on the amount and irregularity of rainfall. We used 0, 1 and 4 m/ty as low, average and high rates of fluvial erosion in the model. Marine erosion
Marine erosion cuts back limestone coastlines, often producing seaward cliffs (Fig. 2). Daly (1910) advocated the importance of marine erosion in his glacial control theory, estimating the rate at which backwearing would destroy an exposed reef from rates measured on the Cretaceous chalk cliffs of Dover. He concluded that even large islands would be rapidly reduced to banks during glacial periods. Chalk is much less resistant to marine erosion than reef limestones however, and rates of marine erosion on reef systems are now known to be several orders of magnitude less than Daly assumed. Hodgkin (1964), with a variety of techniques, estimated the rate of intertidal erosion to be around I mm/y. Trudgill (1976b) examined the rate of, and the physical and biological processes yielding, marine erosion on Aldabra using a micro-erosion meter. He measured a notch retreat of 1.01-1.25 mm/y on the sheltered coast and about 4 mm/y on the exposed coast. Spencer (1985b) measured marine backwearing rates of 0.45 mm/y (mean) on protected and 2.77 mm/y (mean) on exposed coasts of Grand Cayman, an island with a microtidal regime compared to the macrotidal coast of Aldabra. He also reviewed the literature and gave a range of 0.3-6.4 mm/y for marine erosional processes. We used 0, 1 and 4 m/ty as low, average, and high rates of marine erosion in the model. Methods: the simulation model A computer-based simulation model was used to examine the relative influence and interaction of reef growth, sea level fluctuations,
erosion, and subsidence on the morphology of a hypothetical, midoceanic reef surrounding a volcanic island (Fig. 3). The profile of the island was described by 1120 islels ( = island elements), each representing I horizontal meter of island surface. The maximum horizontal resolution of the model was therefore 1 m. Initially the island consisted of a uniform 15 ~ slope and sea level was set at half the island height. The model operated through repetitive generations, each generation representing 1000 years. A generation consisted of 6 sequential steps: (1) island subsidence, (2) sea level fluctuation, (3) reef growth, (4) subaerial erosion, (5) fluvial erosion and (6) marine erosion. For steps 3-6 of each generation, the elevation of each of the 1120 islels was modified by the various processes as described below. Rates of all processes were constant within each 1 ty generation. Reef development was simulated for 500 generations, corresponding to 4 repetitions of a 125 ty long interglacial-glacial-interglacial sea level cycle. 1. Island subsidence was simulated by increasing the sea level relative to the island. Subsidence rates varied among 0, 0.05 and 0.2 m/ ty in different simulations (see Table 1 for summary of rates used). 2. Sea level fluctuations were based on Chappell and Shackleton's (1986) curve from the last interglacial to the present (Fig. 1). Sea level was specified every 1 ty and was used to modify the simulated sea level once each generation. 3. Reef growth occured on all submerged surfaces down to a depth of either 13 m or 50 m. Actual reef growth at any isM was a function of water depth. For depths shallower than the depth where maximum growth occured, the rate of growth was a linear, increasing function of depth (2). Below the depth of maximum growth, growth was a linear, decreasing function of depth (3). Gi = Gin,,, * (Di/Dgmax),
(2)
G i = Gma,, * ((Dde~p-Di)/(Daoop-Dg,~a,,).
(3)
Gi is the actual growth rate for any given islel, Gma x is the maximum growth rate, D i is the depth of any given islel prior to growth, Ddeop is the maximum depth at which reef growth occurs, and Dgm,x is the depth at which the maximum rate of reef growth occurs. Three types of variations were run: a) Gma x w a s varied among 1, 4 and 8 m/ ty; b) Dgma x w a s varied between 0 m and 5 m, and c) Dae~p was varied between 13 m and 50 m. 4. All reef surfaces exposed above sea level were eroded vertically (subaerial erosion, Fig.2). The rate of erosion was constant throughout a simulation but varied among 0, 0.15 and 0.5 m/ty among simulations. The subaerial erosion rate was the same for all parts of the exposed reef, and was 0 below sea level or on the base slope. 5. Fluvial erosion removed all reef material above the baseline slope from the most landward isM of exposed reef seaward for a number of islels equivalent to the fluvial erosion rate (0, 1, or 4) or until reaching a point where elevation of the baseline slope was equal to sea level, whichever happened first. It thus eliminated all previous reef growth in the area eroded and left a vertical cliff at the edge of erosion (Fig. 2). Fluvial erosion rate varied among 0, l, or 4 m/ty among simulations. 6. Marine erosion occurred from the most seaward exposed isM landward for a number ofisMs equivalent to the marine erosion rate (0, 1, or 4) or until baseline slope was reached, whichever happend first. Marine erosion was simulated by reducing the elevation of isMs in the erosion zone to sea level, creating a terrace at sea level (Fig. 2). Marine erosion rate varied among 0, 1 and 4 m/ty among simulations. A "standard" set of parameters was defined to represent estimated average rates (see above) for each process simulated: 0.05 m/ ty subsidence rate, 4 m/ty maximum growth rate with the maximum growth at the surface (0 m) and a maximum depth at which growth occurs of 50 m, 0.15 m/ty subaerial erosion rate, 1 m/ty fluvial erosion rate and 1 m/ty marine erosion rate. To reduce the very large number of possible permutations, simulations were run using the standard parameters for all but one process, while varying the pa-
I
decrement islel
r__~_~,.
elev = SL
basalt < SL
elev > SL
yes
islel >= tart islel -
islel with elev >SL
"'--'--'-''--.....~
-
- -""
no
; ..............
9 ";-._
gen #
increment
t
elevs
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store
marine erosion
erosion~
fluvial
subaerial erosion
1
growth
~
subsidence
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setup
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(sub
9 gen #)
SL = SL(gen)
~
@
t .... I ~
n
elev = basalt
o
start at rain isle1 w i t h eleY > basalt
no
increment
............................................................
......
......
store final elevs
.......................................................
Ft
t
no
Jr
= elev - ER
basal'(
elev = greater of SL or
elev
" " "
rainislel
initialize elevs= basalt
parameters
no
no
el
ment
Fig. 3. Flowchart 9 Diagrams logic of the simulation model. Flow is indicated by solid arrows. Rectangles represent actions and diamonds represent decisions. Procedures are delimited by solid, bold lines and are connected to the main program by dashed arrows. Islels are horizontal location (1 m) along a radial transect o f the island with the minimum islel at the landwardmost location and the maximum islel at the seawardmost location. AE = subaerial erosion (depth); ELEV = elevation at given islel; F E = fluvial erosion (distance); G E N = generation; MAX = maximum; M E = marine erosion (distance); M I N = minimum; SL = sea level; SUB = subsidence (depth)
elev = SL
function
increaseelev bg growth
start at max islel with elev > SL
+ input
57 rameter of that process among low, standard, and high values (Table 1). Terrace depths on simulated reefs were determined from a numerical output of islel elevations, not from graphical output. Where terraces were not clearly defined, i. e. were slightly sloping, the average depth of the terrace was estimated (estimates are accompanied by a " ~ " sign).
Results
The average rates (Table 1) of each o f the simulated processes was used to create a standard simulation. The ontogeny of this reef is depicted in Fig. 4B by plotting the reef structure at an initial high sea level (9 ty), at the lowest sea level o f the first cycle (108 ty), at the high sea level at the end of the first cycle (125 ty), and at the end of 4 cycles (500 ty). The reef starts as a small fringing reef which is displaced downslope due to erosion and growth as the sea level falls (108 ty). By the end o f the first sea level cycle the reef rises to form a large fringing reef with a minor lagoon and with a shallow drowned fore reef terrace. The reef grows by raising the fore reef terrace and extending the fore reef seaward through the next 3 cycles. In this and subsequent figures this standard simulation is reproduced in the center, with the results of a low rate simulation above and a high rate simulation below it. The low growth rate (1 m/ty) simulation results in a largely drowned reef, with a wide shallow fore reef terrace at 33 m depth. This terrace keeps up with subsidence, i. e.
3oo] 200
33,~
1 0
0
250
.0. . . . . .
--
it is vertically stable, staying at the same depth through successive repetitions of the 125 ty sea level cycle (Fig. 4A). Both the low growth rate and the standard growth rate (4 m/ty) simulations produce a deep fore reef terrace, deeper in the former (,-~ 125 m depth and 102 m depth respectively). The high growth rate (8 m/ty) simulation yields a larger reef, with both the lagoon and fore reef terrace filling in. At the end of the first 125 ty sea level cycle though, a deep terrace (108 m depth) is still evident (Fig. 4C). Comparing the standard (maximum growth rate at surface) with a variation where the maximum growth rate is at a depth of 5 m reveal few differences (Fig. 5A, B). By decreasing the maximum depth at which growth can occur from 50 m (standard) to 13 m, a small reef with large fore reef terraces is created (Fig. 5C). Both this and the low growth rate (Fig. 4A) simulations decrease reef accumulation rate by three-fourths relative to the standard, and produce reefs similar in shape. The simulation where subsidence was set at 0 m/ty (Fig. 6A) yields a reef that is not as thick vertically as subsiding reefs (Fig. 6B, C) as no new potential space is added on top by subsidence. It is more extensive horizontally seaward, however, as growth continues to occur in the deeper reaches that become drowned in subsiding reefs. As a result the outer reef slope is relatively smooth, because potential fore reef terraces loose their distinctiveness as they grow toward sea level. In contrast, the high subsidence rate (0.2 m/ty) simulation yields a reef that is largely drowned, as it is unable to keep up with subsidence except at its shoreward margin where it is supported by the shallow antecendent slope. Most of the reef surface consists of a wide, shallow, fore reef terrace (at 16 m depth) that is vertically stable through successive 125 ty sea level cycles, which in turn is interrupted by
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Fig. 9 A-C. Variation in marine erosion rate. M a r k on right indicates final sea stand. A Low (0 m/ty) erosion rate simulation.
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B Standard (1 m/ty) erosion rate simulation. C High (4 m/ty) erosion rate simulation
large, drowned lagoons that are not interconnected as each is the result of fluvial erosion during a separate 125 ty sea level cycle (Fig. 6C). A deep fore reef terrace is also found in the high subsidence rate simulation, and is deeper there than in the standard subsidence rate simulation ( ~ 125 m depth and 102 m depth respectively). Extent of reef development is inversely correlated with rate of subaerial erosion. A low subaerial erosion rate (0 m/ty) results in a reef with more extensive growth seaward, and with more extensive lagoon development (Fig. 7A) than produced by higher erosion rate simulations. In contrast a largely drowned reef, dominated by
a wide, shallow fore reef terrace (38 m depth) that is vertically stable through successive sea level cycles, is produced in the high erosion rate (0.5 m/ty) simulation (Fig. 7C). A deep fore reef terrace is formed in all 3 simulations (Fig.7); its depth (111 m, 102m, 9 8 m ) is inversely related to subaerial erosion rate. All deep fore reef terraces are vertically stable through successive sea level cycles. Increasing the rate o f fluvial erosion has a drastic effect on the resulting reef; while lagoon development is minor in the standard (1 m/ty) and absent in the low fluvial erosion rate (0 m/ty) simulations, a very large, undi-
59 vided lagoon is produced by the high fluvial erosion rate (4 m/ty) simulation (Fig. 8). Thus the increase from I to 4 m/ty erosion rate is in the critical range for lagoon formation by this process, given the other parameters of the model. Varying marine erosion rates within the range of 04 m/ty yields only minor differences in reef morphology (Fig. 9). There is slightly more terrace formation at higher rates, but except for a small expansion in a terrace at 40 m depth with the high erosion rate simulation, the changes are hardly discernible. Marine erosion is not necessary for terrace development, as terraces of similar size developed in the simulation where marine erosion rate was set to 0 m/ty (Fig. 9A). The deep fore reef terrace is at the same depth (102 m) in all 3 simulations. Discussion
The large scale, eustatic sea level fluctuations of the late Cenozoic caused different reef forming processes to be effective over different lengths of time. Nevertheless the rates of growth, subsidence, and erosion are such that when integrated over the time period during which they are effective, their net influence on reefs is similar. Thus it is only during ca. 33% of the time (in the sea level cycles we used) that growth can occur in the upper 30 m of the reef, and in little more than 15% of the time can growth occur in the top 10 m. It is in the top 10 m that most new reef is added during the final rise and highstand of the sea in each cycle. Conversely, erosional processes operate over this top portion for the remaining 85% of the time. Subsidence is mostly independent of sea level fluctuations and occurs at a constant rate. Although growth occurs for only one tenth as long as erosion or subsidence, it occurs at rates that are about an order of magnitude greater than erosion or subsidence. For a reef to survive at sea level, the amount of growth over time must equal the amount of reef material buried by subsidence and destroyed by erosion [Eq. (1)]. If growth is sufficiently rapid to balance long term erosion and subsidence, then the rates of subsidence and erosion become important determinants of reef development by creating less or more space in shallow water for growth of new reef. Both subsidence and erosion occur at similar rates: 0.02-0.2 m/ty for subsidence with a strong dependence on island age, and 0.05~0.5 m/ty for erosion with a strong dependence on the amount of rainfall. One might expect the former to be more important in providing space for reef growth on younger and drier islands, and the latter on older and wetter islands. Whether erosion or subsidence predominates in creating space for more reef is of more than trivial importance; while subsidence lowers all the land surface evenly, topographic variation in erosion rate can be pronounced and lead to similar topographic variation in reefs developing over such eroded foundations (Flint et al. 1953; MacNeil 1954; Purdy 1974). Because the rates of reef forming processes are such that when integrated over time they have comparable effects on reefs, reef development is very pluralistic; subsi-
dence, erosion and growth all exert a strong influence (Hopley 1982). For example large, shallow ( < 5 0 m depth), drowned fore reef terraces are formed when growth rates are low (Fig. 4A), subsidence rates are high (Fig. 6C), or subaerial erosion rates are high (Fig. 7C). Under a high rainfall regime, where erosion is accelerated, shallow reef terraces may be due to the effect of erosion, an explanation less likely to apply in low rainfall areas. In the Cook-Austral and Pitcairn Islands, located around and south of the Tropic of Capricorn and thus presumably at latitudes where reef growth might be limited by low temperatures, extensive shallow drowned terraces are common, occuring on Rarotonga, Mangaia, Rimatara, areas of Rurutu, Tubuai, Raivavae, and Ducie Islands (G. Paulay personal observation). On these islands, terraces are probably due to low rates of reef growth. Because we used the same sea level curve repeated 4 times, the origin of, development of, and variation between terraces is regular and thus amenable to analysis. Fore reef terraces, as developed by the model, are primarily drowned growth features. They can develop without subaerial erosion (Fig. 7A), marine erosion (Fig. 9A), or subsidence (Fig. 6A, although here the terrace is mostly filled in by the end of the simulation). Once formed,terraces may (1) be vertically stable in their position through successive sea level cycles (e. g. shallow, 33 m terrace of Fig. 4A), (2) permanently drown or (3) catch up with sea level to form a surface reef (e. g. deep 108 m terrace in Fig. 4C). Two types of vertically stable terraces were commonly formed by the model: a shallow (16-38 m depth) and a deep (98-125 m depth) one. Deep terraces are due to the reef keeping up with the initially slower sea level rise following the lowest sea stand of the sea level cycle (109 ty); thus they always lie above the glacial sea level minimum @130 m). This is well illustrated in the development of the deep terrace in the high growth rate simulations. During the first sea level minimum at 109 ty (Fig.4C, coarse dashed line), the deepest part of the fore reef is an uneven slope, which, however, develops into a terrace by catching up with and following the rising sea level, and drowns subsequently as the rate of sea level rise increases toward the end of the first 125 ty sea level cycle (Fig. 4C, fine dashed line). The shallower terraces form during extended time periods when sea level fluctuates at intermediate depths; they drown due to the rapid post-glacial rise in sea level, as well documented for several actual reefs (e. g. Adey and Burke 1976; Grigg and Epp 1989). Because the vertical position of terraces is strongly influenced by all processes that raise and lower reefs, terraces are not useful indicators of past sea levels. Shallow terraces formed during low growth rate (at 33 m depth, Fig.4A), high subsidence rate (at 16 m depth, Fig. 6C), and high subaerial erosion rate simulations (at 38 m, Fig. 7C). Deep terraces are more common and decrease in depth with increasing growth rate ( ~ 1 2 5 m , 102m depths and filled in, Fig. 4), with decreasing subsidence rate ( ~ 125 m, 102 m depths and mostly filled in, Fig. 6), and with decreasing subaerial erosion rate (111 m, 102 m and 98 m depths), Fig. 7. Sea level was never stable at any
60 of these depths for more than one 1000 yr generation (Fig. l). Terraces are usually vertically stable through successive sea level cycles (e. g. Fig. 4A), indicating that a single terrace has a long and complex constructional history, as observed by Coulbourn et al. (1974) for Hawaiian reefs. We did not find marine erosion to be an important factor in generating fore reef terraces; terraces developed to almost the same extent when marine erosion was absent (Fig. 9A). In our simulations sea level was stable only during the last 6 ty of each sea level cycle when the reef was submerged (Fig. 1). In nature, marine erosion may be more important at low stillstands if and when such occur, but such stillstands would have to be of long duration to allow substantial terraces to form considering that marine backwearing occurs at rates of 0-7 m/ty. How can reefs drown? Schlager (1981) pointed out the paradox that while subsidence rates by long term processes are very slow relative to typical rates of reef growth, drowned reefs are not uncommon in the Phanerozoic. Schlager (1981) and Hallock and Schlager (1986) argue that drowned reefs result either from very slow growth rates of bioliths, as in nutrient-enriched systems, or from short term, very rapid rises in sea level. It is interesting to consider what happens with recurrent rapid sea level fluctuations, such as Pleistocene glacio-eustatic cycles, when sea level might be stable in the long run. Schlager (1981) concluded that symmetrical sea level fluctuations could drown reefs only if high sea stands were delayed "until subsidence has lowered the platform top below the bottom of the euphotic zone during the next low stand." With cyclic sea level change, (1) reef growth becomes limited to times of high sea stands when the reef is submerged; thus it is effectively reduced in rate when integrated over a whole sea level cycle, and (2) subaerial erosion as well as subsidence enters as a variable that can reduce reef height. Although both erosion and subsidence are slow (usually < 0.5 or < 0.2 m/ty respectively), the combination of high erosion and subsidence rates, as on young, wet islands, can cause reefs to drown even if they have rapid growth rates. This is clearly shown in both the high subsidence rate and high subaerial erosion rate simulations (Figs. 6C and 7C). All but the most shoreward fraction of the reef (based on the shallow antecedent slope) drowns in both cases, creating large, shallow, fore reef terraces. We found marine erosion to be ineffectual in truncating and thus drowning reefs; in the northwestern Hawaiian Islands, however, Grigg and Epp 0989) present indirect evidence that such horizontal erosion may cause reefs to drown. A drowned reef may not be lost from the photic zone, however. Grigg (1982) proposed that the "Darwin Point" be used to designate the latitude at which net reef growth rate is so limited by temperature that reefs can no longer keep up with subsidence and consequently drown. The stability of the depth of many drowned reef terraces through successive sea level in several of our simulations points to the possibility that past the Darwin Point (i. e. at latitudes where temperature is more limiting, or in areas where overabundant nutrients slow reef growth cf. Hallock and Schlager 1986) there exists another
threshold, between which and the Darwin Point reefs can survive as submerged banks at a depth that remains stable through successive sea level cycles. Such "halfdrowned" reefs are explained by the fact that reefs that remain submerged during high sea stands are subjected to erosion for shorter time periods and growth for longer time periods than reefs that reach the sea surface. The depth at which such vertically stable, submerged reefs lie is influenced by local growth, erosion, and subsidence rates, as well as by the nature of sea level fluctuations. That such vertically stable, drowned reefs may be common is indicated by the abundance of drowned banks in the Northern Hawaiian islands at depths of 20-80 m (Grigg and Epp 1989). In our simulations, lagoon development could occur only through fluvial erosion, however topographic variation in growth (Adey 1978; Hopley 1982; Chappell 1983) and in erosion (Flint et al. 1953; MacNeil 1954; Purdy 1974) have also been invoked to explain lagoon formation. Hoffmeister (1930), Stoddart et al. (1985), and Stoddart and Spencer (1987) demonstrated that lagoon-like cavities can be formed by fluvial erosion in uplifted landscapes. Our simulations indicate that fluvial erosion is also an effective agent of lagoon formation in reefs experiencing oeustatic sea level fluctuations. It is interesting to note that the threshold of lagoon formation by fluvial erosion in our model is in the range of estimated rates for fluvial erosion on uplifted islands. At a fluvial erosion rate of 1 m/ty lagoon development is poor, but at 4 m/ty it is extensive (Fig. 8B, C). Thus in areas with high rainfall and less resistant (younger) substratum, fluvial erosion is likely to be an important component of lagoon formation, but not on dryer or more resistant (older) islands. The depth of atoll lagoons correlates with the amount of rainfall (Purdy 1974; Menard 1982) indicating the potential importance of erosional processes in lagoon formation, although fluvial erosion by runoff from central highlands is not possible in such settings. Lagoon development by fluvial erosion is enhanced by subsidence and retarded by subaerial erosion. Additional simulations (not illustrated) using antecedent slopes of different inclinations (e. g. 10~ 20 ~ indicate that lagoon formation is further facilitated by an increase in slope contrary to Chappell's (1980, 1983) observations. This apparent contradiction is explained by the fact that our lagoons are erosional features while Chappelfs lagoons are the result of reef growth. Deeper erosional lagoons are produced on steeper slopes, and are less likely to be filled in by growth or reduced in extent by subaerial erosion.
Acknowledgements. We thank B.V. Holthuis, A.J. Kohn, T. Spencer, and 3 anonymousreviewers for comments on the manuscript. A.O.D. Willows (Director) provided computer facilitiesat the FridayHarbor Laborutories.J. Adicottand M. Jourdan assisted with computer graphics. References
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Appendix The following argument is presented to support the claim that Mangaia and Atiu (as well as other uplifted Cook Islands: Mauke and Mitiaro) were atolls prior to uplift. We will base the argument entirely on Mangaia, as that island has the greatest elevation (169 m) and its volcanic center rises furthest above (ca. 100 m) the encircling karst ring, thus was the least likely to have been an atoll prior to uplift. 1. Mangaia is the oldest reliably-dated island with exposed volcanics on the Pacific plate (1219.4 My, Turner and Jarrard 1982). Uplift of Mangaia is thought to be due to emplacement of the Pliocene (maximum surface age 2.3 My - Turner and Jarrard 1982) volcano of Rarotonga (McNutt and Menard 1978). Assuming uplift was due to Rarotonga, uplift of Mangaia began when Mangaia was ca. 14-17 My old. No reliably-dated volcanic exposures are known on the Pacific plate to be as old as Mangaia was prior to uplift (Jarrard and Clague 1977; D. Epp compilation 1982), all islands of such age having subsided below sea level. Thus unless subsidence on Mangaia was much slower than elsewhere on the Pacific plate, Mangaia should have been an atoll by 3 My BP. 2. The uplifted reef facies surrounding Mangaia have been dated paleontologicallyto be of Oligocene to Mid Miocene age for the oldest deposits (Marshall 1927; Wood and Hay 1970), and to be (15.5)16.5-17.6 My old for deposits near the top of the section (Yonekura et al. 1986; Tsuchi 1986). Thus the present uplifted reef facies surrounding the island were formed soon after the volcanic edifice. All overlying post-Early Middle Miocene deposits (if ever formed) have been eroded off. 3. Even considering a slow erosion rate of 0.05 m/ty, and a situation where uplift did not commence until Rarotonga reached the sea surface (2.3 My BP), 115 vertical meters of reef limestones would have been removed from Mangaia since uplift. Considering subsidence rates in the Cook-Austral swell, Crough (1978, 1984) estimated that Mangaia had an original reef thickness of 400 m. Thus much of the pre-uplift reef of Mangaia was removed by erosion, and the pre-uplift reef likely covered the central volcanic edifice which today lies about 100 m above the encircling fossil reef.
