New constraints on the postglacial shallow-water carbonate accumulation in the Great Barrier Reef

More accurate global volumetric estimations of shallow-water reef deposits are needed to better inform climate and carbon cycle models. Using recently acquired datasets and International Ocean Discovery Program (IODP) Expedition 325 cores, we calculated shallow-water CaCO3 volumetrics and mass for the Great Barrier Reef region and extrapolated these results globally. In our estimates, we include deposits that have been neglected in global carbonate budgets: Holocene Halimeda bioherms located on the shelf, and postglacial pre-Holocene (now) drowned coral reefs located on the shelf edge. Our results show that in the Great Barrier Reef alone, these drowned reef deposits represent ca. 135 Gt CaCO3, comparatively representing 16–20% of the younger Holocene reef deposits. Globally, under plausible assumptions, we estimate the presence of ca. 8100 Gt CaCO3 of Holocene reef deposits, ca. 1500 Gt CaCO3 of drowned reef deposits and ca. 590 Gt CaCO3 of Halimeda shelf bioherms. Significantly, we found that in our scenarios the periods of pronounced reefal mass accumulation broadly encompass the occurrence of the Younger Dryas and periods of CO2 surge (14.9–14.4 ka, 13.0–11.5 ka) observed in Antarctic ice cores. Our estimations are consistent with reef accretion episodes inferred from previous global carbon cycle models and with the chronology from reef cores from the shelf edge of the Great Barrier Reef.

The role of calcium carbonate deposits in the carbon cycle, and the influence on climate change during the late-Quaternary is poorly constrained. The fifth assessment report of the Intergovernmental Panel on Climate Change 1 identifies the major contributors for atmospheric CO 2 (atm-CO 2 ) concentration changes from the last glacial maximum (LGM) to present. The authors assigned a medium degree of confidence to the current estimates of atm-CO 2 contributions from coral reef accretion and carbonate compensation depth changes. This uncertainty derives not just from the use of proxy data and their limited availability, but from the complex relationships between the carbon and other biogeochemical cycles. Such uncertainty is reflected in the range of the contributions to postglacial atm-CO 2 attributed to shallow-water reefs in global carbon models (− 9 to 30 ppm [2][3][4][5].
The role that coral reefs may have played in this process has been termed the coral reef hypothesis [5][6][7] . This hypothesis proposes that the increase of the atm-CO 2 is at least partly due to the enhanced shallow-water CaCO 3 accretion by corals. This hypothesis relies on the availability of new areas of marine flooded shelf during the last transgression and on the consequent increase in coral reef development. This would have changed the alkalinity balance, at least locally, and ultimately increasing the transfer of CO 2 to the atmosphere 6,8 . Because of the reduced marine shelf area during glacial times and the subsequent increase in reef area from glacial to Holocene times, it is assumed that the coral reefs acted as secondary amplifiers-not precursors-of a climatic change that had already initiated 9,10 with early atm-CO 2 rise generally preceding global surface temperature increase 11 .
The coral reef hypothesis is supported by the extensive coral reefs of Holocene age worldwide [12][13][14][15][16] . Moreover, a possible lower contribution from terrestrial sources in this same period 3,17 argues in favour of alternative carbon sources, such as that represented by reef accretion. Simplified box models 6,7 have suggested that the activity of the coral reefs can explain a significant rise of the atm-CO 2 during postglacial times. However, the dissolution ratios, accretion rates and calcite saturation depth informing these models are poorly constrained and they possibly overestimate the total carbon derived from corals.
More complex models have considered the effect of coral reefs in postglacial atm-CO 2 2-5,18,19 . Notably, Ridgwell et al. 5 inferred two possible minor episodes of global reef growth from 17.0 to 13.8 ka BP and from 12.3

Regional setting
The GBR shelf along the northeastern coast of Australia (Fig. 1) accommodates a thick succession of reef deposits over the last 600 ± 280 ky 37,38 controlled by major glacial-interglacial sea-level fluctuations. The last glacialinterglacial fluctuation initiated during the LGM 21,30 when sea level was approaching minimum levels (120-130 m below present) 31,39 .
As the glaciation ended and sea level rose during the postglacial, extensive fringing-and barrier-reef structures developed along the shelf edge of the GBR until ca. 10 ka BP 21,40 . These reefs currently lie between 40 and

Results and discussion
Holocene carbonate deposits. We estimated the areal trends of the Holocene reefs in the GBR. Reef area was estimated from GIS layers containing polygons representing the outline of the Holocene reefs (Figs. 1 and 2). This layer was obtained from a detailed interpretation of recently available satellite images and shallow bathymetry 29,50 , and excluding continental islands and shelf-edge reefs. These features were sliced into latitudinal 50 km wide slices to assess latitudinal variations. We assumed that the reef area polygons represented the main reef and bioclastic deposits directly related to Holocene reef growth. However, unaccounted fore-and back-reef aprons may constitute a significant portion of the reefal carbonate volume 15,51 .
We estimated the mass of the Holocene CaCO 3 deposits by multiplying the area derived from the interpreted GIS layer by the thickness derived from historical reef cores that have drilled through the Holocene (Appendix 1) and petrophysical parameters (Aragonite density, ρ A = 2930 kg m −3 and formation porosity, Φ R = 35% 30 ). The volumetric and mass calculations were also performed at a sub-regional level in 50 km wide latitudinal slices that allowed reconstruction of latitudinal trends (Fig. 3e, Appendix 2).
Our area estimations show that Holocene reefs occupy approximately 10% of the total GBR shelf area, following a latitudinal trend that correlates with the total shelf area, especially in the central GBR (R 2 = 0.84) between 14° and 21° S (Figs. 1, 3e). This reflects the direct relationship between substrate availability on the shelf and carbonate accumulation. Interestingly, in the northern GBR (near 12° S) the proportion of Holocene reef area-to-shelf area increases due to the wide (up to 30 km) reef structures. The seemingly obvious relationship is, however, a complex one and highly dependent on environmental variables (terrigenous flux, circulation, antecedent substrate, etc.) that can determine the spatial distribution of the carbonate deposits 40,49,[52][53][54] .
Our new GBR Holocene CaCO 3 mass estimates (Table 1) fall between the figures by Rees 13 and Kinsey and Hopley 55 . The Rees 13 reef area estimate of 44,920 km 2 , based on Spalding et al. 56 dataset, is larger than the area presented in this study (26,290 km 2 , Table 2). Their Holocene CaCO 3 estimate is consequently higher (1709 Gt CaCO 3 ) than our best estimate of 751 Gt CaCO 3 . However, Rees 13 include reefs in the Australian region that are not part of the GBR system sensu stricto. The Kinsey and Hopley 55 estimated reef area value is more in agreement with our figure: ca. 20,000 km 2 . A more recent estimate places the GBR's shallow-water reef area at 16,110 km 250 , but they do not include sediment wedges associated with these reefs, which are found at greater depths and constitute up to the double of the reef framework volume 15,51 . If we calculate the mass areal accumulation (MAA) using Rees 13  Shelf edge reef CaCO 3 accumulation. The volume and mass of the shelf edge deposits at a regional scale were ground-truthed in two control zones along the shelf edge of the GBR: Hydrographers Passage and Noggin Passage (Fig. 2). Here, extensive IODP drilling, bathymetric and seismic surveys 30,34,40,47 provided valuable data for the calibration of the parameters required for the regional reconstruction of volumetrics and mass: reef area ratio, formation volume from seismic imaging, mass areal accumulation (MAA), vertical accretion rate, the maximum cumulative thickness and petrophysical parameters. A regional bathymetric dataset 57 provided the basis for the reconstruction for the postglacial marine flooded area in the GBR (analogous to Hinestrosa et al. 49 ).
Two methods were applied to obtain the volumetrics and mass of the shelf-edge deposits: (1) the mass areal accumulation method and (2) the postglacial thickness method. The former is a bulk calculation of volume based on flooded area and the accumulation represented by the MAA, scaled back by the proportion of bathymetric surface covered by reefs (reef area ratio) without considering any temporal evolution. The latter, the postglacialthickness method, attempts to reconstruct the temporal evolution of the reef accretion by considering the change in flooded area since the LGM. It is layer-based, with each layer corresponding to a 5 m sea-level step in which data-derived thickness constraints (Fig. 4a, Appendix 3) are applied in such a way that vertical reef accumulation does not exceed observed thicknesses (Fig. 4b). It relies on the assumption that the reef area ratio, vertical accretion rate and maximum cumulative thickness values observed in the control zones can be extended to other locations along the GBR shelf edge. A composite sea-level curve based on Lambeck et al. 39 and Yokoyama et al. 31 (Fig. 5, Appendix 6) enabled the translation between past sea levels and geological ages to reconstruct the temporal evolution of the deposits.
The estimates obtained applying the mass areal accumulation method are lower than those estimated by applying the postglacial thickness method but are within the same order of magnitude. Not surprisingly, the application of both methods results in similar latitudinal trends (Fig. 3e) because in both the flooded area is a direct factor in the calculations.
Control zones. In the control zones, Noggin Passage and Hydrographers Passage (Fig. 2), ca. 20% of the shelf edge is covered in reef structures (i.e., reef area ratio = ca. 20%). This proportion is almost twice the reef area ratio estimated at a regional scale for the shallower, Holocene reefs when considering the whole of the GBR shelf.
In both control zones ( www.nature.com/scientificreports/ barrier). This is consistent with a thinner reef veneer (< 10 m) in the terrace and outer geomorphic areas and less distinguishable barrier structures found at Noggin Passage 40 .
Shelf edge trends. Volumetrically, the carbonate deposits of the shelf edge wane in the northern GBR when compared to the central and southern GBR (Fig. 3d, e). In the northern GBR, the Holocene and the shelf edge pre-Holocene reef trends are also contrasting: the Holocene reef deposits increase dramatically near 12° S, whereas the shelf edge deposits at those latitudes diminish, possibly due to limited substrate availability 40 . On the contrary, in the southern-central GBR (e.g. Hydrographers Passage control zone) wider and a more gentle gradient provides more substrate availability 34 . It is useful to establish some comparisons to appreciate the magnitude of the shelf edge deposits. At the shelf edge, our estimates suggest that the area covered by reef formations is between 3000 and 11,000 km 2 (Table 1), which would represent 8% (minimum case) to 30% (maximum case) of the total area occupied by all the banks in Harris et al. 50 , and between 12% (minimum case) and 48% (maximum case) of the area occupied by banks with no Holocene cover in that same study. Kleypas 58 inferred that the global area available for reef growth during the LGM lowstand was approximately 20% of that available today. In the GBR, that figure is at least within the   27 shows that the postglacial Halimeda deposits are equivalent in mass to 5.5-10.5% of the Holocene reef mass on the GBR shelf (Table 1).
Halimeda can form mounds in inter-reef areas of the GBR up to a thickness of 20 m [25][26][27]59,60 . Recent reviews of published and new high-resolution bathymetry have revealed that at least 6000 km 2 of the northern and central GBR are covered by Halimeda bioherms 26,27 . This is a considerable increase from the ca. 2000 km 2 from previous estimations 59 .
Halimeda-like morphologies have also been detected on the shelf edge in seismic profiles 47 and Halimeda floatstones recovered in dredges from the shelf edge dated to 11.8-7.2 ka (D24B, D22, D11B in Abbey et al. 36 ). Global and regional estimates. We extrapolated the estimates and trends of CaCO 3 deposits for the GBR to the entire globe using the reef area estimate of Spalding et al. 56 . Using this area, we applied the parameters ground-truthed in the GBR dataset. The global reef area (RA GLOBAL ) was multiplied by average thickness and petrophysical parameters (ρ A , Φ R ) to obtain global postglacial CaCO 3 deposits. We accounted for the drowned postglacial reefs by applying two factors to the global Holocene estimates: a factor based in the ratio of shelf edge-to-Holocene reef area (area adjustment factor, AF A ) and a factor based in the mass ratio (mass adjustment factor, AF M ) ( Table 3). These factors and the global extrapolation as such, have large associated uncertainties given the gaps in knowledge of total global extent, accretion trends and morphology of the less accessible postglacial drowned reefs. We also calculated the global volumetrics and mass globally using the reef areas from past studies (Tables 4, 5; Appendix 4). We found that the reef area ratio at the shelf edge (ca. 20%) is twice the reef area ratio estimated for the whole GBR shelf (ca. 10% for Holocene reefs, Table 1). The structures with Holocene reefs occupy more absolute area but are sparse and separated by large extensions of flat sediment-covered submarine topography. At a global scale, previous studies suggest lower reef area ratio values: reef area (584 to 746 × 10 3 km 2 ) and shelf area in low latitudes (11,686 × 10 3 km 2 ) as reported in Kleypas 58 , suggesting a global reef area ratio of 5 to 6%. This percentage would be even lower if we apply the global reef areas of 300 × 10 3 km 261 , 255 × 10 3 km 216 or 284 × 10 3 km 256 . The lower value of the global reef area ratio (5-6%) compared to the GBR values of this study (ca. 10%) could be partly explained by uncertainties in the topographic/bathymetric datasets used by Kleypas 58 (e.g., ETOPO5 62 ), and by difficulties in predicting reef habitat using the ReefHab model 58 , or by the inclusion of shelf areas that are not potential reef habitats. It is also possible that the GBR had more favourable regional conditions for reef development compared to other global locations.
The global reef area estimate of 284,000 km 2 by Spalding et al. 56 is lower than estimates from other authors ( Table 5), but it is based on a more comprehensive dataset compared to other studies. However, this dataset originates from a collection of data from different origins and scales which brings uncertainty, especially at a local scale. Their estimates refer mainly to the area occupied by modern coral reefs and would only represent a proxy for Holocene deposits rather for than the entire postglacial reef system, which should include early-and mid-postglacial drowned reefs.
Applying the global reef area above and the parameters ground-truthed on the GBR shelf, we obtain a global Holocene reef deposits estimate of ca. 8100 Gt CaCO 3 in the best-case scenario (Table 3). This is very similar to past estimates reported in Rees et al. 63 (Table 6). However, we must also consider other calcium carbonate deposits: inter-reef carbonates, Halimeda bioherms and drowned reefs. Applying a similar Halimeda-to-reef ratio to the one estimated in the GBR (Table 1) an extra 592 Gt CaCO 3 would be added to the global carbonate budget of the last 8 ky (Table 3). The choice of the global reef area as a parameter is critical: a simple comparison of the same calculations but using areas from other studies (Table 5) reveals a large variation in total postglacial CaCO 3 (Holocene + drowned reefs + Halimeda deposits) ranging from 4073 Gt CaCO 3 64 to a maximum of 54,550 Gt CaCO 3 65 (Table 4).
Incorporating the drowned reefs in global CaCO 3 budgets. The role of coral reefs in postglacial oceanic alkalinity changes and atmospheric CO 2 input is poorly constrained and partly relies on CaCO 3 deposits estimates that are uncertain. The estimates of area covered by shallow-water carbonates, from which some global estimates are derived, are mainly associated with Holocene reefs 13,16,61 (Table 5) and ignore the more elusive (now) drowned, deeper deposits. The submerged reefs discovered in different parts of the world 21,23,24 should be incorporated into updated postglacial CaCO 3 deposits estimates.
In the GBR, there is strong evidence of almost continuous shallow reef accretion from ca. 30 until ca. 9.5 ka BP along the shelf edge, albeit characterised by ~ five brief demise events 21 . We estimate that the total net CaCO 3 deposits of the submerged shelf-edge reefs are equivalent to ca. 16 to 20% of the Holocene reef deposits mass in our best-estimate scenario, and up to ca. 40% if we consider higher values of reef area ratio, postglacial reef thickness or mass areal deposits (Table 1).
If we extend the shelf edge-to-Holocene reef ratios estimated in the GBR to global scales (mass adjustment factor AF M and areal adjustment factor AF A ), we obtain a global value of 1460-1785 Gt CaCO 3 accumulated in the drowned reefs from 19 to 10 ka BP. These results are modest compared to the combined Holocene reef deposits (ca. 8100 Gt CaCO 3 ). However, given the direct evidence on large-scale pre-Holocene shelf edge reef systems in the GBR (only surveyed at scale in the last decade 30 ) and past evidence of other large-scale drowned reefs in global locations 23,24 , the question of the impact of drowned reefs on the LGM-to-postglacial global CaCO 3 budgets remains relevant.
The impact of the global reef area applied can be assessed by looking at average CaCO 3 fluxes for the whole postglacial period (Table 3), which can vary from a minimum of 0.2 Gt CaCO 3 y −1 (using area in De Vooys 64 ) to a maximum of 3.2 Gt CaCO 3 y −1 (using area in Copper 65 ). However, if we split the averages between Holocene and pre-Holocene, we find the differences are of one order of magnitude (1.0 vs 0.2 Gt CaCO 3 y −1 ; Table 3). This can be compared to some recent estimates of reef productivity of 1.9 Gt CaCO 3 y −1 for the Holocene and 2.5-4.5 Gt CaCO 3 y −1 for the late deglacial 19 , which were hard to reconcile with common carbon cycle models 18   . These were periods of high substrate availability and favourable environmental conditions for reef growth, as influenced by shelf physiography and sea-level rise 21,49 . The postglacial thickness method cannot establish a precise chronology for CaCO 3 mass accumulation at regional level, but it can provide a broad temporal trend. The periods of higher CaCO 3 accumulation in the shelf edge (15.1-13.7 ka BP and 13.3-11.3 ka BP applying the 20 m maximum reef thickness assumption, Fig. 3b, Appendix 5) envelope at least two of the three episodes of increased slope of the atm-CO 2 curve since the LGM (ca. 14.9-14.4 ka and ca. 13.0-11.5 ka BP 67 ) (Fig. 3a,b). These periods of higher CaCO 3 accumulation at the shelf edge also coincide with the episodes inferred by Ridgwell et al. 5 in their models (17.0-13.8 ky and 12.3-11.2 ky BP). These findings are consistent with a more recent analysis of all available postglacial vertical reef accretion Table 2. Deposits at the control zones of Hydrographer's and Noggin Passages: total area, CaCO 3 volume, CaCO 3 mass and mass areal accumulation for different geomorphic zones 47 . Reef area ratio in the area comprised between the outer GBR fore-reef and the 130-m contour is similar in both sites. These figures are based on seismic three-dimensional reconstructions, geomorphic interpretations and core data 30,34,40,47 . www.nature.com/scientificreports/ data (including IODP Exp. 325), which shows rapid accretion rates (9.6 to more than 20 mm yr −1 ) during these periods of higher CaCO 3 accumulation (see Fig. S6 in Webster et al. 21 ).
Our new estimates of postglacial, pre-Holocene carbonate deposits in the GBR (ca. 130 Gt CaCO 3 ) and their global extrapolations (1500 Gt CaCO 3 ) suggest that pre-Holocene reef accretion is likely to be more relevant to the global CaCO 3 budgets (hence in the global carbon cycle) than currently recognized. The impact of these deposits in the atm-CO 2 should be assessed by global process-based carbon models that reflect the full complexity of the atmosphere-ocean-land biogeochemical cycles (Fig. 6).

Conclusions
1. The assembled dataset provides new constraints on Holocene reef deposits in the GBR: 751 Gt CaCO 3 as per our best estimate, varying between 520 and 1001 Gt CaCO 3 , distributed latitudinally with a strong correlation to the available shelf area. these (now) drowned reefs occupy an area of between 3000 and 12,000 km 2 , equivalent to ca. 10-45% of the total Holocene reef area in the GBR. In the GBR, these drowned reefs accumulated ca. 135 Gt of reefal CaCO 3 , equivalent to ca. 18% of the mass estimated for the more recent Holocene deposits (best estimate). The latitudinal distribution of the shelf edge reefs is also strongly correlated to shelf availability. 3. By globally extrapolating the GBR constraints, we estimate a total accumulation of 8100 Gt CaCO 3 from Holocene reefs (best estimate), which is consistent with previously published estimates.   www.nature.com/scientificreports/ 5. Our results support a more prominent role in the postglacial carbon cycle for pre-Holocene shallow-water coral reefs. Significantly, the timing of higher CaCO 3 deposition in the GBR is broadly coeval with two distinct episodes of postglacial atm-CO 2 increase (ca. 14.9-14.4 ka and ca. 13.0-11.5 ka BP 67 ). Any causal relationship must be confirmed by more complex, process-based models of the global carbon and other biogeochemical cycles and global surveys of drowned reefs and reef areas.

Methods
We estimated the carbonate volume in the GBR for: (1) early postglacial reef deposits (21-10 ka); and (2) Holocene reef deposits. We also attempted a global extrapolation of these carbonate deposits based on these new and well-constrained regional GBR estimates. Data were available across the whole GBR: bathymetry at ~ 100 m resolution 57 , GIS layers with reef locations and extensions 50 ; previous GBR Holocene drill cores (see Appendix 1 for summary and Hopley et al. 68 for data Table 4. Extrapolations of global CaCO 3 deposits applying the parameters of this study (Table 3) but using the broad range of past global reef area estimates shown in Table 5.  www.nature.com/scientificreports/ sources). We distinguished the areas at the shelf edge (defined here between the modern outer GBR reef front and the 130 m isobath) from the other areas of the shelf and extracted the corresponding bathymetric subset. More locally, data were available for two densely surveyed control zones at the shelf edge (Noggin Passage and Hydrographers Passage; Fig. 2) where reef volumetrics and mass accumulation were estimated with a high degree of confidence for Quaternary reefs. This was possible due to: (1) availability of seismic-derived three-dimensional reconstructions of the reef patterns and volumetrics 40,47 ; (2) extensive and precise chronologic database (> 580 published U-Th and 14 C ages), lithological and petrophysical properties directly measured from the IODP Exp. 325 drill holes and cores 30,31 ; (3) high-resolution (5 m) bathymetric coverage in these sites 34 ; and (4) extensive knowledge on the development history and age structure of the shelf-edge reef system 21 .
To estimate the postglacial Pleistocene carbonate deposits, we first produced the following input for both of the estimation methods we applied: • Reef area ratio [%] at the shelf-edge control zones: the percentage of reef formation area extension compared to total shelf edge area (Fig. 2). This value was obtained by digitising the area occupied by reef banks and comparing it to the total shelf-edge area. The identification of the banks was supported by the bathymetry, backscatter, seismic and GIS data 34,40,47,50 . The results of both control zones were averaged and rounded to the nearest ten to obtain a best estimate of 20%. To capture plausible uncertainties, arbitrary minimum and maximum values were set: a minimum reef area ratio of 10% equivalent to the proportion of Holocene reef area ratio in the whole GBR shelf; and a maximum value of twice the best estimate. • Formation volume [m 3 ] at the shelf-edge control zones: the volume contained between the present day, seafloor bathymetry and the antecedent basal substrate (Reflector 1) as obtained from the seismic interpretations 40,47 .
The three different velocity scenarios (1700-3300 m s −1 ) to convert from seismic time to true depth 47 were considered to obtain a minimum, best estimate, and maximum values for each set of maps. • Mass areal accumulation (MAA) [kg m −2 ] at the shelf-edge control zones: these values were calculated for each control zone by transforming each formation volume estimate to carbonate mass (CaCO 3 mass = formation volume × ρ A × (1-Φ R )) and subsequently dividing the mass by the total shelf edge area of the control zones (MAA = mass · [shelf edge area] −1 ). The calculations were also applied for each of the main geomorphic zones 47 : inner barrier, outer barrier, terrace and shelf break combined, and inner and outer platforms combined. Three values were applied to account for plausible minimum, best and maximum scenarios: the average MAA value of all reef locations, and the minimum and the maximum MAA value in any reef location ( Table 2). Table 6. Global estimates of CaCO 3 mass and/or accumulation rate of present-day shallow-water reefs, Holocene reefs and Halimeda bioherms according to different authors. To establish a comparison among new and past estimates, some of the values were calculated using the parameters highlighted in bold.

Study
Kinsey and Hopley 55 Milliman and Droxler 12 Ryan et al. 15 Rees 13 Hillis (   We extracted the shelf-edge areas defining them as the areas between the outer GBR and the 130 m depth contour (Appendix 7). The bathymetric surface was sliced into thirty-three 50 km wide latitudinal zones after Hinestrosa et al. 49 . Each of the zones was flooded using sea levels ranging from 130 to 0 m in 5 m steps to obtain marine-flooded area in km 2 . To represent the timing of the flooded area at each sea-level increment, we applied a composite relative sea-level curve to the results in Hinestrosa et al. 49 (Fig. 5, Appendix 6). The relative sea level was reconstructed from data in Lambeck et al. 39 , Yokoyama et al. 31 and Webster et al. 21 The The Holocene reef CaCO 3 accumulation was calculated using the following parameters: • Reef area [m 2 ] from the Queensland coast to the outer GBR: the reef area was estimated from GIS layers containing polygons representing the outline of the Holocene reefs (Figs. 1 and 2, Supplementary data). This layer was obtained from a detailed interpretation of recently available satellite images and shallow bathymetry 29,50 . Continental islands and reefs belonging to the shelf edge were excluded to better approximate Holocene reef area. These features were sliced into thirty-three latitudinal zones 50 km wide to capture the latitudinal variations (Figs. 1, 3e). We assumed that the reef area polygons represent the main reef and bioclastic deposits directly related to Holocene reef growth. However, unaccounted fore-and back-reef aprons may constitute a significant portion of the reefal carbonate volume 15,51 . There are of course, uncertainties inherent to the original sources (satellite imagery and bathymetric mapping) and their interpretation, which could result in an overestimation of the reef area in the northern GBR, the under or overestimation of the extent of the bioclastic cover, or the misrepresentation of some locations as Holocene reefs when they might be older Pleistocene outcrops 50 27 and considered these values in our Holocene totals (Table 1).
For the global extrapolations, we also considered the following parameters: • Global reef area [km 2 ]: values for global reef area were extracted from the observational study by Spalding et al. 56 , but other past values (Table 5) were considered for comparison (Table 4). • Area adjustment factor [%]: defined as the ratio of shelf-edge reef area to the Holocene reef area. According to our estimates in the GBR, this corresponds to 22% (Table 1). • Mass adjustment factor [%]: defined as the ratio of CaCO 3 mass at the shelf edge to the CaCO 3 mass of the Holocene reef. According to our estimates in the GBR, this corresponds to 18% (Table 1).
Postglacial pleistocene carbonate deposits. We followed two approaches. The postglacial-thickness method attempts to reconstruct the temporal evolution of the reef accretion by considering the change in flooded area since the LGM. The mass areal accumulation method does not consider the change in marine flooding area and outputs the cumulative postglacial volume and CaCO 3 mass.
Shelf edge carbonate deposits-mass areal accumulation method. The mass areal accumulation method is based on one key assumption: that the reef area ratio and mass areal accumulation variables calculated locally at the Exp. 325 control zones are valid along the entire extension of the shelf edge. For each latitudinal zone in the shelf edge bathymetric subset, the maximum highstand flooded area (FA) was multiplied by the reef area ratio (RAR) and mass areal accumulation (MAA) values to obtain CaCO 3 accumulation values in the GBR shelf margin (Table 1).

• Pleistocene CaCO 3 mass = FA × RAR × MAA
Shelf edge carbonate deposits-postglacial-thickness method. The postglacial-thickness method relies on the assumption that reef area ratio, vertical accretion rate and maximum cumulative thickness values observed in the control zones can be extended to other locations along the GBR shelf edge. It also assumes that the parameters remain constant through time. By considering accretion rates and maximum thickness, this method allows us to approximate the temporal evolution of the shelf-edge deposits.
Firstly, the vertical accretion rate for each reef development episode  was converted to an equivalent rate relative to past sea-level steps. This allowed us to associate an incremental reef thickness to each of the 5 m sea-level steps considered. Conversion from geological age to equivalent sea level was performed using a simplified relative sea-level curve based on Lambeck et al. 39 for ages more recent than 10 ka BP, and based on Webster et al. 21 , Yokoyama et al. 31 for ages before 10 ka BP (Fig. 5, Appendix 6).
To obtain an estimate of reef volume at each sea-level step, we first estimated reef thickness by multiplying the converted postglacial vertical accretion rate (VA SL ) by each sea-level step (5 m). Subsequently, the product of this thickness and the flooded area at each flooding stage (FA SL ) gave us the formation volume for each one of the thirty-three latitudinal zones and for each sea-level step. The volume was scaled down by the reef area ratio (RAR) values (minimum, best estimate, maximum; Table 1) to obtain a measure representative of the shelf edge geomorphology as observed at the control zones. In the calculations, each flooded area had a cap on cumulative reef thickness: the maximum cumulative thickness (Fig. 4). The CaCO 3 accumulated mass for each sea-level increase was obtained by multiplying these volumes by formation net volume (1-Φ R ) and density (ρ A ): Pleistocene CaCO 3 mass for each sea level (SL) between 130 and 0 m: Holocene veneer carbonate accumulation estimates. To obtain values of total CaCO 3 mass of Holocene carbonate in the GBR, the reef thickness (RT) values were multiplied by the reef area (RA) to obtain cumulative Holocene carbonate volumes for the GBR as a whole and for each one of the thirty-three latitudinal zones (Fig. 1). Mass values were obtained by multiplying these volumes by formation net volume (1-Φ R ) and density (ρ A ) ( Table 1), as summarised below: • Holocene reef volume = RA × RT • Holocene reef CaCO 3 mass = Holocene reef volume × ρ A × (1 − Φ R ) Global estimates. We consider the contribution of drowned postglacial reefs in global CaCO 3 budgets.
We extrapolated the estimates and trends of CaCO 3 deposits for the GBR to the entire globe. We used published estimates of global reef area and parameters ground-truthed by the GBR dataset. The global reef area (RA GLOBAL ) was multiplied by average thickness (RT) and petrophysical parameters (ρ A , Φ R ) to obtain global postglacial CaCO 3 deposits. We accounted for the drowned Pleistocene reefs by applying two assumptions in our calculations to obtain two equivalent results.
• Assumption 1: on average, the proportion of postglacial drowned reefs areas corresponding to a given Holocene reef area is similar across all reef provinces. We expressed this assumption as a ratio of shelf margin area to total Holocene reef area, the area adjustment factor (AF A ), • Assumption 2: on average, the postglacial drowned reefs mass corresponding to a given Holocene reef mass is similar across all reef provinces. We expressed this assumption as a ratio of shelf margin CaCO 3 mass to Holocene reef CaCO 3 mass, the mass adjustment factor (AF M ).
The values for global reef area (RA global ) have a large range of uncertainty as demonstrated by the range of values proposed by different authors (Table 5). We consider those by Spalding et al. 56 more accurate given the ground-truthing datasets. The factors that we applied on the global area (AF A , AF M ) have a large associated uncertainty: despite the evidence for drowned reefs in other geographical locations, the exact global extension and morphology of drowned reefs is not well constrained. Other carbonate provinces might differ in morphology, in accretion trends and in the proportion of Pleistocene reefs present along their margins compared to the more recent Holocene deposits of those provinces. On CO 2 and total C estimates. The chemical equilibrium of the shallow ocean is complex, with the concentration of the main inorganic carbon species (CO 2 , HCO 3 − , CO 3 − ) varying according to temperature, salinity and pressure 69,70 .
According to the coral reef hypothesis 6,71 , reefal CaCO 3 accretion provides CO 2 to the environment by increasing the concentration of CO 2 in the ocean water. The equivalent CO 2 and C mass based on the stoichiometry of the chemical reaction: Ca 2+ + 2HCO 3 − = => CaCO 3 + CO 2 + H 2 O 6,66 gives an incomplete picture because the exact proportion would depend on physical conditions that would have varied during the postglacial period. Experimentally, it has been demonstrated that for each mole of CaCO 3 precipitated in seawater only a fraction of a mole of CO 2 is fed to the surrounding waters due to the buffering effect of marine water 8,72 . It is then unclear how much of this carbon is released into the atmosphere, especially at centennial timescales 66,72 . The pathways for the released CO 2 molecules are varied-they can be absorbed into inorganic or organic marine carbon cycles, or they can also be transferred into the atmosphere by the balancing of the partial pressure of CO 2 . We have not attempted to quantify the corresponding postglacial CO 2 contribution to the surrounding waters and to the atmosphere. This would require more complex carbon models which are beyond the scope of this study.