P redictions of sea-level in the GBR region (Thom and C h ap p ell 1978, N akada and Lambeck 1989) show seaw ard tilting of the continental shelf, so that sea-level at inshore sites reaches its present sea-level before offshore and oceanic sites. In a simplistic consideration, in which ice m elting ceases at 6 ka, uplift on the inner p a rt of the shelf w o u ld resu lt in sea-level reaching its present level before this time, rising to a highstand at 6 ka, and falling from then until the present. On the edge of a w ide shelf, subsidence m eans th at even after the ad d itio n of w ater to the ocean has sto p p ed , relative sea-level keeps rising, so that present-day sea-level is not reached until the present (Figure 6.3). In fact, there are at least two other significant processes w hich alter th is p a ttern . First, any co n tin u ed a d d itio n of m eltw ater to the oceans th ro u g h o u t the late Holocene ten d s to low er the sea-level curves described above, so that the time present sea-level is first reached (henceforth called "first attainm ent time") becomes later. Second,
+
0
inner shelf mid-shelf
outer shelf oceanic
time (ka BP)
Figure 6.3 : Predicted sea-level curves at sites on a transect of the GBR. Predictions were m ade u sin g the stan d ard ice and earth m odels, and only one iteration of the sea-level equation. (From N akada and Lambeck 1989).
the subsidence of the ice sheets' peripheral bulges results in sea-level fall in the far field, increasing the h eig h t of the m id-H olocene h ig h stan d and causing present sea-level to be reached earlier. This is the process referred to as "equatorial ocean siphoning" (Mitrovica and Peltier 1991, Johnston 1993). In the predictions used here, late Holocene m elting is not initially included, but equatorial ocean siphoning is, so the predicted first attainm ent tim es can be expected to be earlier than the observed tim es at each site. A lthough the late Holocene m elting is a eustatic contribution and has no spatial variation, the effect which it has on the first attainm ent time m ay vary considerably, according to the relative size of the isostatic and eustatic com ponents. This is d em o n strated in Figure 6.4, u sin g the stan d ard earth m odel an d late Holocene m elting of 3 m, proportional to the m elting proposed by Lambeck (1993b). At inshore sites (Figure 6.4 b), the isostatic highstand is greater than the a m o u n t of late m elting, so the first attain m en t tim e rem ains in the steeply-rising p a rt of the sea-level curve, and is only delayed by a few h u n d re d years. At the shelf edge, the p red icted isostatic h ig h stan d is roughly equal in m agnitude to the late m elting (Figure 6.4 c), so the first attainm ent time moves to the p art of the sea-level curve w ith low gradient, w here it is highly sensitive to small changes in the eustatic com ponent. At m id-ocean sites, w here the p red icted h ig h stan d is sm all, due solely to
time (ka BP)
Figure 6.4 : Predicted sea-level histories on a transect of the north Queensland coast, using two eustatic sea-level models. The "standard" model is ARC3+ANT3 (Nakada and Lambeck 1988). The late Holocene melting in the other model is based on the results of Lambeck (1993b) scaled to 3 m at 6 ka.
sea-level to rise continuously th ro u g h the Holocene. The effect of late H olocene m elting on the m agnitude and tim ing of the Holocene sea-level highstand is discussed in the next section.
The first attainm ent tim e at each site has been determ ined here using the num erical m odel described in the introduction to this chapter (Section 6.1). Relative sea-level w as calculated at 100 year intervals th ro u g h the m id H olocene, and the tim e at w hich p resen t sea-level is first reached w as estim ated by linear interpolation.
Figure 6.5 show s the predicted first attainm ent tim e contoured over the A ustralian region. Two features are evident: first, inland sites reach present sea-level earlier than offshore sites, due to isostatic tilting at the continental m argin. The contour lines are unaffected by the sm aller islands, w hich are effectively loaded equally on all sides. Second, at oceanic sites, sea-level is reached later in the south than in the north. This is because the southern end of the region show n is affected by the subsidence of the peripheral bulge around Antarctica, causing sea-level rise up to the present.
C ontour m aps of the predicted first attainm ent tim e in the G reat Barrier Reef region (Figures 6.6 and 6.7) show the influence of lith o sp h eric thickness and u p p e r and low er m antle viscosity. A th in n er lithosphere (Figure 6.7) can deform at sh o rter w av elen g th s, so the co n to u rs of
deform ation pro d u ced by the ocean load follow the coastline m ore closely th an w h en a thicker lithosphere is p resent (Figure 6.6). Increasing the viscosity of the u p p e r m antle increases the gradient of tilting across the continental shelf, because m uch of the relaxation is already com pleted by this tim e for m odels w ith a low er viscosity u p p er m antle. This causes the first attainm ent time to vary m ore rapidly across this region, as show n by the closer spaced contours in Figures 6.6 d) and 6.7 d) com pared to Figures 6.6 b) and 6.7 b). The viscosity of the lower m antle has a negligible effect, indicated by the sim ilarity betw een the pairs of m aps Figures 6.6 a) and c), and Figures 6.7 a) and c).
Figure 6.5 : P red icted tim e at w hich sea-level first reached its p resen t level in the A ustralian region. Two iterations of the sea-level equation were perform ed to degree 256, using the standard ice and earth models. Contour interval is 200 years, labelled in thousands of years. Box indicates the study region on the Great Barrier Reef.
Figure 6.6 : Predicted first attainment time in the study area on the GBR, for the standard ice model and a range of earth models with a 100 km lithosphere. The earth model parameters are listed in Table 6.1. Sites from which reef cores have been collected are indicated.
5 10 5 1 3 51 4 515
C om p arison w ith observation s
To com pare the predictions and observations, the observed first attainm ent tim es show n in Table 2.11 w ere plotted as sh ore-perpendicular transects. The offshore distance was defined for each m odel as the shortest distance to the predicted 6.6 ka contour, w hich runs through the m iddle of the study area in m ost cases. The predicted contours are alm ost parallel th ro u g h o u t the region, so choosing another contour has no significant effect on the appearance of the results.
earth model 0 610 * 613 □ 614 a 615 o © o°oo oo o o 'OOD O o o o c o o o o o o o o O 00 o o offshore distance (km)
F igure 6.8 : Predicted and observed spatial gradients in the first attainm ent time, for the sta n d a rd ice m odel and earth m odels w ith a 100 km lithosphere. O ffshore distance is defined as the shortest distance to the 6.6 ka contour on the appropriate m odel in Figure 6.6. G raph a) shows the dependance of the onshore-offshore gradient on u p p er m antle viscosity, and indicates that the effect of varying the lower m antle viscosity is negligible. G raphs b) to e) com pare the observations (circles) w ith the predicted gradients (lines) for each earth m odel.
The predicted and observed first attainm ent times are com pared in Figures 6.8 and 6.9. A lth o u g h the d ata are sp arse, the u p p e r lim it to the observations seem s to confirm the predicted decrease seaw ards in the age of the first attain m en t of present sea-level. Because the slope of this u p p er bound is usually constrained by only three of four sites, it it not possible to determ ine w hich rheological m odel is m ost appropriate.
One of the predicted effects of late Holocene melting, described above, is the sensitivity of the first attainm ent tim e at offshore sites to the m agnitude of m elting. If late Holocene m elting causes sea-level rise greater than the fall due to eq u ato rial ocean siphoning, then the first attainm ent tim e occurs during the late Holocene, instead of during the period of rapid sea-level rise, w hich ended around 6 ka. On the transects show n in Figures 6.8 and 6.9, this w ould appear as a steepening of the gradient at the seaw ard end of the transect. In the m odels using an u pper m antle viscosity of 2 x 1020 Pa.s, the value considered m ost appropriate for the A ustralian region (N akada and Lambeck 1989), there is some suggestion of this steepening in the observed
earth model 0510 + 513 c 514 a 515 o © S 6.0 oo o o © © o o o © o offshore distance (km)
first attainm ent times (Figures 6.8 a & c, and 6.9 a & c), b u t the data are too sparse for this to conclude that it exists.
Predictions of the first attainm ent time w ere also m ade using two m odels of late Holocene melting. The first is based on that of Lambeck (1993b), derived from observations in the British Isles, b u t restricted to the last 8 000 years. This m odel allows 1.7 m of eustatic sea-level rise since 6 ka. The second is proportional to the first model, b u t scaled so that 3 m of ESL rise occurs since 6 ka, w hich is in closer agreem ent w ith p rev io u s estim ates from the A u stralian region (N akada and Lam beck 1989). Both these m odels are w ithin the uncertainties of previous estim ates of the late Holocene m elting. M odel 1 (Figures 6.10 and 6.11) reduces the p red icted age of the first attainm ent of present sea-level by about 200 years. The predictions rem ain a plausible upper b ound to the observations, except for the Cape Tribulation sites, w hich are estim ated to have reached present sea-level about 100 years before the predicted time.
M odel 2 (Figures 6.12 and 6.13) predicts even later first attainm ent times, ab o u t 300 years y o u n g er than the sta n d a rd m odel. For som e m antle rheologies, this late m elting m odel causes the p red icted first attain m en t tim e at some outer shelf sites to be delayed until 4 ka (using the 100 km lith o sp h ere m odel) or even rem oves the H olocene h ig h stan d altogether, causing the first attainm ent time to be the present (Figure 6.12 a & d). The predictions of this m odel are not an u p p er bound to the observations, w ith several sites reaching sea-level before the m odel predicts. These results, therefore, suggest that late Holocene m elting is unlikely to have been as m uch as 3 m, if the rheological m odels used are representative of the region. The lag time of coral grow th behind sea-level change rem ains an unknow n factor in the relationship betw een eustasy, isostasy and the reef grow th record. How ever, the predicted first attainm ent tim es using the ESL m odel 1 form a close u p p er bound to the observations, suggesting that this lag time is negligible.
6.0 'r
offshore distance (km)
Figure 6.10 : Same as Figure 6.8, but including 1.7 m of late Holocene melting.
offshore distance (km)
offshore distance (km)
Figure 6.12 : Same as Figure 6.8, b u t including 3 m of late Holocene m elting. The rapid decrease in the age of the first attain m en t tim e at far offshore sites indicates th at the transition betw een the scenarios of Figures 6.4 c) and 6.4 d) has been reached, which does not occur w ith smaller am ounts of Holocene melting.
cu CQ O £ 4—* D £ £ ' 5 C3 •— OO ÖOOO o c r bCDOOO O O O O 1 o - t'O - O D O & P O offshore distance (km)
Figure 6.13 : Same as Figure 6.9, b ut including 3 m of late Holocene m elting. The rapid decrease in the age of the first attainm ent time at far offshore sites indicates th at the transition betw een the scenarios of Figures 6.4 c) and 6.4 d) has been reached, which does not occur w ith smaller amounts of Holocene melting.