Modern-day coral reefs have well defined environmental envelopes for light, sea surface temperature (SST) and seawater aragonite saturation state (Ωarag). We examine the changes in global coral reef habitat on multimillennial timescales with regard to SST and Ωaragusing a climate model including a three-dimensional ocean general circulation model, a fully coupled carbon cycle, and six different parameterizations for continental weathering (the UVic Earth System Climate Model). The model is forced with emission scenarios ranging from 1,000 Pg C to 5,000 Pg C total emissions. We find that the long-term climate change response is independent of the rate at which CO2 is emitted over the next few centuries. On millennial timescales, the weathering feedback introduces a significant uncertainty even for low emission scenarios. Weathering parameterizations based on atmospheric CO2 only display a different transient response than weathering parameterizations that are dependent on temperature. Although environmental conditions for SST and Ωaragstay globally hostile for coral reefs for millennia for our high emission scenarios, some weathering parameterizations induce a near-complete recovery of coral reef habitat to current conditions after 10,000 years, while others result in a collapse of coral reef habitat throughout our simulations. We find that the multimillennial response in sea surface temperature (SST) substantially lags the aragonite saturation recovery in all configurations. This implies that if corals can naturally adapt over millennia by selecting thermally tolerant species to match warmer ocean temperatures, prospects for long-term recovery of coral reefs are better since Ωarag recovers more quickly than SST.
 To date, humans have emitted over 337 Pg carbon (C) to the atmosphere through fossil fuel burning and cement production (T. A. Boden et al., Global, regional, and national fossil-fuel CO2 emissions, 2009, http://cdiac.ornl.gov/trends/emis/overview_2006.html). These emissions are ongoing at accelerating rates and have led to a present-day atmospheric CO2 concentration of 392 ppm; a level that has not been experienced within the last 20–30 million years [Beerling and Royer, 2011; Zachos et al., 2008]. Decades of climate research have led us to a relatively good understanding of most physical feedbacks in the climate system (such as the longwave radiation feedback, or the albedo and water vapor feedbacks), and how these feedbacks will respond to increasing emissions. However, our understanding of some biogeochemical feedbacks in the climate system is still rudimentary. In particular the rate of continental weathering and its impact on ocean biogeochemistry on multimillennial timescales is still unclear.
 Chemical weathering can be split into two different main reactions: hydrolysis of silicates and dissolution of carbonates. Dissolution occurs when rocks and/or minerals are dissolved by carbonic acid (H2CO3). The ions created by the dissolution process are then transported by rivers into the ocean, where the formation of biogenic or abiogenic carbonate sediments consumes the Ca2+ ion as well as the bicarbonate and returns one CO2molecule into the ocean-atmosphere system:
On the other hand, hydrolysis occurs when hydrogen ions (H+) replace other positively charged ions in the minerals. For example, silicate minerals typically are made up of positively charged cations (Na+, K+, Fe2+, Mg2+, Al3+, Ca2+) that are chemically bonded to negatively charged SiO4 (silicate) structures. A simple example of a schematic pair of reactions for hydrolysis of calcium silicate is given by [e.g., Berner, 1999; Derry, 2009]:
Here two molecules of CO2 are consumed during the hydrolysis of one molecule of silicate (equation (3)). When the bicarbonate and calcium precipitate later in the ocean to form carbonate, one molecule of CO2 is released again (equation (4)), leading to a net removal of one molecule of CO2 per molecule of silicate [Ebelmen, 1845; Urey, 1952]:
To summarize, hydrolysis leads to a net drawdown of atmospheric CO2 and acts on timescales of several thousands of years [e.g., Caldeira, 2006]. Dissolution on the other hand does not in itself lead to a net drawdown of atmospheric CO2 and acts on a faster timescale than hydrolysis. Both processes add alkalinity to the surface ocean.
 Rates of chemical weathering are mainly influenced by three environmental factors: temperature, precipitation and vegetation. Higher temperatures cause enhanced weathering. Higher precipitation increases the level of groundwater held in soil, and therefore also increases the weathering rates. A warmer Earth is likely to be a wetter Earth, although changes in precipitation will be spatially heterogeneous and dependent of changes in vegetation and evapotranspiration. Finally, plants increase the CO2 content in the soils where it combines with groundwater to form carbonic and organic acids [Caldeira, 2006]. The concept of feedbacks between climate, atmospheric CO2 and weathering were first quantified with computer models in the 1980s [Berner et al., 1983; Walker et al., 1981].
Sarmiento and Gruber describe a self-regulating mechanism that is depicted here in a simplified form inFigure 1: Higher atmospheric CO2 concentrations lead to an increase in temperature, precipitation and net terrestrial primary productivity, which in turn increase the alkalinity flux into the ocean and therefore increase the carbonate concentration in the surface ocean. This results in an increase in calcite saturation (Ω), a deepening of the saturation horizon, and a reduction of the area of sediments exposed to corrosive waters. The burial of CaCO3 increases, which in turn decreases the carbonate concentration. At the same time, the increase in ocean mean alkalinity due to increased weathering decreases the oceanic buffer factor, leading to a decrease in oceanic pCO2 and an imbalance of inorganic carbon between the ocean and atmosphere. This imbalance is restored by oceanic CO2 uptake from the atmosphere, causing a decrease in atmospheric CO2concentrations. The e-folding timescale for the oceanic adjustment in alkalinity is surprisingly short, 5–10 kyr [Archer et al., 1997, 2000; Ridgwell and Hargreaves, 2007].
 While a number of studies have addressed the climatic consequences of anthropogenic CO2emissions for the twenty-first century, the long-term consequences remain uncertain [Archer et al., 2009; Eby et al., 2009; Montenegro et al., 2007]. For example, most climate models assume constant alkalinity in the oceans, and neglect the weathering-alkalinity feedback.Lenton and Britton added parameterizations for silicate and carbonate weathering to a seven-box global carbon cycle model, coupled to an energy-balance approximation of global temperature [Lenton, 2000]. Forced with a range of emission scenarios spanning from 7,350 Pg C to 15,000 Pg C in total, they find that enhanced carbonate and silicate weathering accelerate subsequent CO2 removal from the atmosphere by up to a factor 4. For total emissions of 1,100–4,000 Pg C, enhanced weathering accelerates CO2 removal by a factor of 1.5–2.5. Uchikawa and Zeebe use the LOSCAR model, a carbon-cycle reservoir model [Walker and Kasting, 1992] coupled to a sediment model [Zeebe and Zachos, 2007] to investigate whether continental weathering can mitigate future ocean acidification by sequestering atmospheric CO2. They conclude that on centennial timescales, weathering has little effect on future atmospheric CO2concentrations and ocean acidification, regardless of the assumed weathering feedback strength. On millennial timescales, however, weathering may be a very important factor determining the long-term decrease in atmospheric CO2 levels, the cooling of sea surface temperatures and the oceanic pH recovery to preindustrial levels.
 The potential long-term recovery of sea surface temperatures and pH is most relevant to the Earth's coral reef habitat, since coral reefs are vulnerable to ocean warming and acidification and their habitat has been shown to follow tight thresholds related to oceanic environmental parameters [Kleypas et al., 1999b]. Here we implement six different weathering parameterizations into the UVic Earth System Climate Model to better understand the recovery of important environmental parameters for coral reef habitat (sea surface temperature and aragonite saturation state; Ωarag). This allows us to identify and understand the potential long-term recovery of coral reefs for a range of future emission scenarios with total emissions after year 1999 ranging from 1,000 Pg C to 5,000 Pg C.
2. Model Description
 The UVic Earth System Climate Model (UVic ESCM) consists of an ocean general circulation model (Modular Ocean Model, Version 2) [Pacanowski, 1995] coupled to a vertically integrated two dimensional energy-moisture balance model of the atmosphere, a dynamic-thermodynamic sea-ice model based onSemtner , Hibler , and Hunke and Dukowicz , a land surface scheme, a dynamic global vegetation model [Meissner et al., 2003] and a sediment model [Archer, 1996a]. The model is driven by seasonal variations in solar insolation at the top of the atmosphere and seasonally varying wind stress and wind fields [Kalnay et al., 1996]. The coupled model has a resolution of 3.6° in longitude and 1.8° in latitude and conserves energy, water and carbon to machine precision without the use of flux adjustment. The physical components of the model are described in Weaver et al. .
 The UVic ESCM also includes a fully coupled carbon cycle taking into account the terrestrial carbon fluxes and reservoirs [Matthews et al., 2005; Meissner et al., 2003] as well as the inorganic [Ewen et al., 2004] and organic [Schmittner et al., 2008] carbon cycle in the ocean. The dynamic global vegetation model (DGVM) incorporated is called TRIFFID [Cox et al., 2000; Cox, 2001]. TRIFFID includes five plant functional types (PFT) and is coupled to a simplified version of MOSES [Meissner et al., 2003]. The UVic ESCM also includes a marine ecosystem/biogeochemical model, which is an improved NPZD (nutrient, phytoplankton, zooplankton, detritus) model with a parameterization of fast nutrient recycling due to microbial activity [Schartau and Oschlies, 2003]. It includes two phytoplankton classes (nitrogen fixers and other phytoplankton), two nutrients (nitrate and phosphate), oxygen, dissolved inorganic carbon and alkalinity as prognostic tracers. Carbonate production is calculated as a fixed proportion of primary production. A complete description of the ecosystem/biogeochemical model can be found in Schmittner et al. . The ocean biogeochemical model calculates carbon fluxes to the sediments as well as their rain ratios. Sediment processes are represented using a model of deep ocean sediment respiration [Archer, 1996a]. This model assumes oxic conditions, therefore all incoming organic carbon is assumed to respire. The remaining CaCO3 and clay is added to the first sediment layer, eventually passes through the pore layer to be added to more stable layers, and finally the lithosphere. The UVic ESCM is computationally very efficient and has been developed to address scientific questions related to climate variability on time scales of hundreds of years to millennia. The systematic comparison of the coupled model with observations shows good agreement [Eby et al., 2009; Meissner et al., 2003; Weaver et al., 2001]. In the past, the UVic ESCM has been used to address a broad range of scientific questions related to future climate change and paleoclimates.
3.1. Weathering Parameterizations
 When equilibrating the standard model, the net deposition of CaCO3 in sediments is balanced by the incoming flux of alkalinity (FAlk,w) and dissolved inorganic carbon (FDIC,w) via river discharge in order to conserve alkalinity and dissolved inorganic carbon (DIC) in the ocean. This parameterization inhibits the continental flux of alkalinity to adjust to climate change and therefore suppresses the weathering feedback. Under preindustrial boundary conditions, the UVic model's equilibrium global carbon flux from ocean to sediments equals 1.206 × 1013 mol/year C, which aligns well with Milliman 's estimate of the total deep sea accumulation of CaCO3 of 1.1 × 1013 mol/year C. Therefore, the preindustrial flux of inorganic carbon via river discharge (FDIC,w,0) is set to 1.206 × 1013 mol C/year, while the alkalinity flux (FAlk,w,0) equals 2.4125 × 1013 mol/year (FAlk,w,0 = 2 × FDIC,w,0, in order to balance the proportions in which carbon and alkalinity are removed from the system). Walker and Kasting estimate the present-day silicate weathering flux at 5 × 1012 mol/year C, while Morse and Mackenzie estimate the present-day carbonate weathering flux at 12 × 1012 mol/year C; these two values add up to 1.7 × 1013mol/year C, which is slightly higher than the value used here. On the other hand, the UVic model does not simulate shallow-water carbonates (benthic production); accumulation of CaCO3in sediments is exclusively in deep-water resulting from planktonic carbonate production. The simulated percent dry weight CaCO3 at year 2000 is in reasonable agreement with core top data [Archer, 1996b] and shown in Figure 2. The global average percent of CaCO3 in sediments is 34.5% for the data compared to 37.8% for the model; this discrepancy is mainly due to the fact that the model slightly overestimates CaCO3 in the Indian Ocean, the western tropical Pacific and the North Atlantic. The sediment cover at high latitudes is in better agreement with observations than for an earlier version of this model [Eby et al., 2009, Figure 5]. This is due to the fact that the organic/CaCO3 rain ratio of sinking particles is now explicitly calculated and not fixed.
 We introduce six different parameterizations of carbonate and silicate weathering as a function of environmental variables into the UVic ESCM in order to test the parameter space of global weathering parameterizations available in the literature. Following the parameterization used first in the GEOCARB II model [Berner, 1994] and later in the GEOCARB III [Berner and Kothavala, 2001] and COPSE [Bergman et al., 2004] models, our model version called UVic_BERNER incorporates a flux of inorganic carbon (FDIC,w) and alkalinity (FAlk,w) via river discharge expressed as:
and FAlk,w,0 and FDIC,w,0 are the preindustrial flux of alkalinity and dissolved inorganic carbon (DIC) via river runoff, pCO2 is the atmospheric concentration of CO2, SAT the global mean surface air temperature and the index 0 stands for preindustrial values. A similar dependence of CO2 is also used in the COMBINE model [Goddéris and Joachimski, 2004]. The factors fSi and fCa stand for the fraction of silicate (0.25) and carbonate (0.75) weathering, respectively. These factors are unchanged in all our parameterizations and are based on Lenton and Britton  and references therein.
 Our second model version is called UVic_LB and follows the parameterization of Lenton and Britton , in which the temperature response of carbonate and silicate weathering is still taken from the GEOCARB II model [Berner, 1994]. Instead of introducing a dependence on atmospheric CO2, Lenton and Britton  include plant productivity (NPP):
where NPP is the global mean net primary production, and the index 0 stands for preindustrial values.
UVic_T_ONLYincorporates a parameterization that is only based on the temperature-dependent part of the GEOCARB II parameterization:
where nSi and nCa are two parameters that are set to 0.6 and 1.0 respectively [Uchikawa and Zeebe, 2008] for our UVic_ZEEBE model version and to 0.2 and 0.4 respectively [Zeebe et al., 2008] in our UVic_ZEEBE_LOW model version.
 Finally our last parameterization, called UVic_PI hereafter, has fixed fluxes of inorganic carbon and alkalinity via river discharge (FDIC,w = FDIC,w,0; FAlk,w = FAlk,w,0), in these simulations weathering fluxes equal preindustrial fluxes.
3.2. Initial Conditions and Emission Scenarios
 We integrated six initial transient simulations, each with a different parameterization of the weathering feedback described in Section 3.1. All started from the same preindustrial equilibrium simulation, which was integrated for over 10,000 years under boundary conditions consistent with year 1800. The simulations were then integrated until present-day while being forced with historical natural and anthropogenic emissions. By year 2009, the simulations were almost identical: atmospheric carbon dioxide concentrations differed by 0.4 ppm, global ocean alkalinity by 3 × 10−4 mol/m3, surface ocean alkalinity by 22 × 10−4 mol/m3, surface ocean pH by 10−3, global DIC by 2 × 10−4 mol/m3and sediment carbon budget by 0.022 Pg. These values are too small to be detected in present-day measurements; the weathering parameterizations used in the present study have therefore a negligible impact for transient simulations between preindustrial and present-day.
 Starting at integration year 2000, six different CO2pulse releases as well as one A2-type emission scenario were considered. For the first six pulse releases (called PULSE hereafter), an additional amount of carbon is emitted to the atmosphere over the period of one year, after which the emissions are set equal zero. The additional amount of carbon added at year 2000 varies between 1,000 and 5,000 Pg C (seeTable 1). The last emission scenario (called A2 hereafter) is forced with emissions following the SRES A2 scenario until year 2100, after which emissions decline linearly with time until year 2315, so that the integral of emissions over time starting from year 2000 equals 5,000 Pg C. We integrated the six different versions of the UVic model (six different weathering parameterizations) with a combination of the seven emission scenarios. A total of 24 simulations were integrated to year 12,000 (see Table 1).
The first letters indicate the weathering parameterization used, the following number the total amount of carbon emitted after year 1999. The A2 simulations have an “A2” suffix whereas the PULSE simulations have no suffix after the emission value.
1000 Pg C PULSE
2000 Pg C PULSE
3000 Pg C PULSE
3734 Pg C PULSE
4000 Pg C PULSE
5000 Pg C PULSE
5000 Pg C A2
3.3. Defining the Global Coral Reef Habitat
 Coral reef ecosystems are built around a framework of calcium carbonate (CaCO3) produced by reef-building corals that coexist with symbiotic micro-algae. When coral reef communities experience abnormally warm temperatures, the thermal stress affects the photosynthetic reactions of the symbiotic dinoflagellates causing dysfunction and bleaching to occur [Glynn, 1988; Hoegh-Guldberg, 1999; Hoegh-Guldberg et al., 2005]. On the other hand, abnormally low temperatures can inhibit photosynthesis of symbiotic algae and induce direct mortality [Kemp et al., 2011]. Temperature thresholds have been therefore primarily used to define coral reef habitats [e.g., Donner et al., 2005; Meissner et al., 2012]. Present-day coral reefs exist predominantly between a minimum winter SST of 18°C and a maximum summer SST of 31°C. Translating this to annual mean SSTs, most coral reefs exist between 21°C and 28°C [Kleypas et al., 1999b].
 To test our model's reproducibility of coral reef habitat parameters, we compare our present-day simulation to global observations.Figure 3 shows the simulated surface Ωarag for year 1994 compared to GLODAP data [Key et al., 2004]. The largest discrepancy can be found in the tropical and subtropical Atlantic, where the model underestimates Ωarag. This is due to an underestimation of sea surface salinities in these regions [Weaver et al., 2001]. Overall, the simulated aragonite saturation shows good agreement with observations. Other parameters, such as SSTs, sea surface salinities, dissolved inorganic carbon and atmosphere-ocean carbon flux have been evaluated and compared to observations in former publications [e.g.,Weaver et al., 2001; Schmittner et al., 2008; Eby et al., 2009].
 This study investigates changes in open ocean temperature and aragonite saturation and their impact on coral reefs. It should be noted that local physical and biogeochemical conditions at the reef sites are often different from open ocean conditions [Meissner et al., 2012], and that other important stress factors including changes in nutrient levels, coastal development, changes to the freshwater balance or overfishing are not being taken into account.
4.1. Global Carbon Budgets Until 12,000 AD
 Time series of the carbon reservoirs for scenarios releasing 5,000 Pg C at or after year 2000 are shown in Figure 4. From 2700 onwards, LB_5000_A2 (red dashed) show the same results as LB_5000 (red) (same for PI_5000_A2 (orange dashed) and PI_5000 (orange)), which corroborates Eby et al. 's conclusion that the long-term climate response appears to be independent of the rate at which CO2 is emitted over the next few centuries. During the first 200 years, all PULSE simulations (solid lines) and all A2 simulations (dashed lines) are similar, supporting Uchikawa and Zeebe 's conclusion that weathering has little effect on atmospheric CO2 and ocean acidification on short timescales (see also Figure 5c). On timescales beyond centuries, chemical weathering and an increase in alkalinity flux have a discernable effect on the climate system; the time series diverge with time. After 10,000 years (year 12,000), less than 20% of the emitted carbon is still in the atmosphere for the UVic_LB (red) and UVic_ZEEBE (blue) simulations, whereas 40% of the carbon remains for the UVic_PI (orange) simulation. About 80% of the maximum surface air temperature (SAT) anomalies remain after 10,000 years for the UVic_PI simulation, whereas less than 50% of the maximum anomaly remains in the simulations with the largest increase in weathering (UVic_LB and UVic_ZEEBE, Figure 5a). Global mean surface aragonite saturation experiences a drop below 1 in the first years of the simulations (Figure 5d). The saturation rates recover fastest in the UVic_ZEEBE (blue) simulation, followed by UVic_LB (red), UVic_BERNER (green), UVic_T_ONLY (black), UVic_ZEEBE_LOW (cyan), and UVic_PI (orange). Finally, after 10,000 years, the global mean pH anomaly has slowly recovered to about 0.54 below the preindustrial value in the UVic_PI simulation while it recovers to about 0.21 below preindustrial in the UVic_ZEEBE simulation (Figure 5c).
 It is interesting to note that the UVic_ZEEBE simulation, with a dependence on atmospheric CO2 only, behaves differently from other parameterizations used in this study. During the first part of the simulations, the weathering feedback is stronger in UVic_ZEEBE than in any of the other simulations (Figure 6a), due to the fact that the rise in SAT is slower than the rise in CO2. Although the total drawdown of atmospheric CO2 in UVic_LB almost equals that of UVic_ZEEBE at the end of the simulation (difference of 4 ppm or 8.5 Pg between UVic_LB and UVic_ZEEBE at year 12,000, Figure 4a), the history of sustained higher weathering rates during the UVic_ZEEBE simulation can be seen in the ocean reservoirs at the end of the simulations (difference of 987 Pg between UVic_LB and UVic_ZEEBE, Figure 4b). At year 12,000, the atmospheric CO2 and surface air temperature for simulations UVic_ZEEBE and UVic_LB are therefore similar, whereas the carbon budget in ocean and sediments is different. This legacy effect due to different timescales in the recovery of atmospheric CO2 and SAT would not be apparent in a carbon cycle reservoir model, where temperature and atmospheric CO2 are directly linked [e.g., Uchikawa and Zeebe, 2008, Figure 1].
Figure 6c shows time series of the sediment calcite pore layer portion for scenarios releasing 5,000 Pg C at or after year 2000. The amount of calcite in sediments stays surprisingly constant during the first 1000 years of all simulations. This is due to an increase in global mean photosynthesis and calcium carbonate production in the ocean due to higher temperatures (Figure 6b) concurrent with an increase in dissolution in sediments (Figure 6d). After year 4000, dissolution becomes larger than the downward flux of calcite and the global amount of calcite in the pore layer decreases.
Figures 7a and 7b show time series for a total release of 3,000 Pg in year 2000. Similar to the 5,000 Pg C time series, the five simulations diverge with time. The different behavior of UVic_ZEEBE due to the response time of global mean temperature is apparent again (ocean budget anomalies not shown here). The total discrepancy between all parameterizations at year 12,000 amounts to 271 ppm for atmospheric CO2, and 2.4°C for global mean atmospheric temperature. The strongest weathering feedback is given by UVic_ZEEBE (blue) and UVic_LB (red), followed by UVic_BERNER (green), UVic_T_ONLY (black) and UVic_PI (orange).
 Time series for a total release of 1,000 Pg C are shown in Figures 7c and 7d. Although the total emission is low for these simulations, the different weathering feedbacks still introduce a significant divergence with time. At year 12,000 atmospheric CO2 values span between 422 ppm (UVic_PI, orange) and 358 ppm (UVic_LB, red), while global mean surface air temperature varies between 14.7°C (UVic_PI) and 13.9°C (UVic_LB). It is also worth noting that for low emissions, UVic_LB becomes more efficient in absorbing atmospheric CO2 than UVic_ZEEBE. The sudden increase in temperature and atmospheric CO2 between year 4,000 and 6,000 for simulations UVic_T_ONLY, UVic_BERNER and UVic_LB are caused by vigorous deep water formation events in the Southern Ocean as described in Meissner et al. . These deep water formation events cool the deep ocean worldwide. After each event, the deep ocean warms slowly again and CO2 is taken up by the ocean until the stratification becomes unstable again at high latitudes thousands of years later. Effects of this internal oscillation can also be seen during the last years of simulation LB_3000 in Figure 7b.
 Finally, Figures 7e and 7f show time series of all the remaining simulations (2,000 Pg C, 3,734 Pg C and 4,000 Pg C). Three of the nine emission scenarios used in Lenton and Britton  (L4, L5, L6) have a total emission of 4,212 Pg C (4,000 Pg C fossil emissions plus 212 Pg C land use change emissions). We chose to integrate two simulations (LB_lb and PI_lb) with a pulse of 3,734 Pg C at year 2000 so that the total emitted (including emissions up to 1999) is the same as for the L4, L5 and L6 simulations in Lenton and Britton . Lenton and Britton  integrated simulations including both silicate and carbonate weathering (equivalent to our simulation LB_lb), as well as simulations with a fixed weathering rate of Falk = 2 × 1013 mol/year (equivalent to our simulation PI_lb). When integrating with fixed weathering rates, Lenton and Britton 's model yields an atmospheric CO2 concentration of 602 ppm and a remaining temperature anomaly of 3.2°C at year 10,000 compared to 948 ppm and 5.3°C in our PI_lb simulation. Lenton and Britton 's simulation with variable weathering fluxes computes an atmospheric CO2 concentration of 510 ppm and a remaining temperature anomaly of 2.35°C at year 10,000 compared to 579 ppm and 2.97°C in our LB_lb simulation. Therefore, adding variable instead of fixed weathering rates has a larger impact on the atmospheric carbon drawdown in the UVic ESCM (40% after 10,000 years for a total emission of 4212 Pg C) than in Lenton and Britton 's box model (15% after 10,000 years for a total emission of 4,212 Pg C). In all cases, the UVic ESCM is slower to absorb the additional atmospheric carbon than Lenton and Britton 's box model. The millennial scale oscillation that can be seen in LB_2000 is again a manifestation of an internal oscillation of the UVic model described in Meissner et al. .
4.2. Coral Reef Habitat Changes Until 12,000 AD
Figure 8 shows the full fields of surface aragonite saturation (Ωarag) as well as sea surface temperature (SST) anomalies for the two extreme simulations PI_5000 and Z_5000 at year 10,000. While aragonite saturation rates are globally below 2.5 for simulation PI_5000, the saturation rates have recovered at a much faster rate for the simulation including the most effective weathering parameterization (Z_5000). At the same time, the SST anomalies in the tropical and subtropical oceans are below 4.5°C in simulation Z_5000, compared to values between 5 and 8.5°C in simulation PI_5000.
 The zonal mean values of SST and Ωaragfor year 2000 (present-day) and year 10,000 after a release of 5,000 Pg C (PI_5000, ZL_5000, T_5000, B_5000, LB_5000, Z_5000) are shown inFigure 9. If we consider fixed temperature thresholds (21°C < mean annual SST < 28°C), the potential coral reef habitat expands poleward compared to modern day (Figure 9a) and the tropical oceans exceed the maximum temperature threshold for all simulations at year 10,000. PI_5000 shows the largest shift of potential habitat with regard to temperature (orange boxes), whereas Z_5000 shows the smallest shift (blue boxes). In terms of aragonite saturation, only two simulations (Z_5000 and LB_5000) display any potential habitat recovery at year 10,000, zonal mean surface aragonite saturation in the remaining four simulations stay globally under 3. The gray box in Figure 9bindicates the present-day potential coral habitat whereas the blue and red boxes indicate the recovery of potential coral habitat by year 10,000 according to simulations Z_5000 and LB_5000.
Figures 10 and 11 show the future evolution of the global surface area of potential coral reef habitat within the geographical limits of preindustrial environmental thresholds for coral reefs (see blue line in Figure 3). The time series depict the percentage of the coral reef habitat surface area that was warm enough under preindustrial conditions to allow for shallow water coral growth (winter temperature higher than 18°C, called ‘PI coral habitat’ hereafter), and that at the same time remains above a certain Ωarag threshold during the future simulations (1, 1.5, 2 and 3; respectively). For the extreme and geochemically corrosive threshold of 1, the surface area of potential coral habitat drops by 5 to 10% within the first 300 years (PI_5000_A2 and LB_5000_A2). For all parameterizations, the full extent of potential coral habitat is characterized by saturation values over 1 within 5000 years of the perturbation (Figure 10a). If we consider a threshold of 1.5, all potential preindustrial habitat falls under the threshold for at least 300 years for all simulations but Z_5000 and LB_5000_A2 (Figure 10b). The simulations with interactive weathering fluxes (Z_5000, LB_5000, B_5000, T_5000, ZL_5000) recover faster than the control simulation with fixed weathering rates (PI_5000). They reach preindustrial values of surface extent by year 5000–9000. The control simulation does not recover completely; PI_5000 reaches 98% at year 12,000. A threshold of 2 clearly separates the response of the models with interactive weathering parameterizations from the model without (Figure 10c). For the models with interactive weathering parameterizations, small surface areas with saturation levels over 2, start to emerge between year 3000 (Z_5000) and year 4350 (ZL_5000). The surface area recovers fully by year 10,000 for simulations Z_5000 and LB_5000. B_5000 has recovered by 97% by year 10,000, while T_5000, ZL_5000 and PI_5000 recover by 92%, 86%, and 15.5%, respectively. Finally, if we consider Ωarag equal or greater as 3 as a liveable threshold for shallow water carbonates, the ocean is inhospitable for coral for over 3000 years (Figure 10d). The Z_5000 and LB_5000 simulations show a slow recovery of surface areas with saturation rates over 3 starting in year 5150 and 6350, respectively. B_5000 is inhospitable until year 8350 and T_5000 and ZL_5000 only start to recover by a few percent within the last 2000 years of integration. By year 10,000, 90% of the initial surface area has recovered in Z_5000, compared to 63% for LB_5000 and 2.5% for B_5000; by year 12,000 the recovery rate exceeds 90% for Z_5000 and LB_5000. The control simulation (PI_5000) does not show any recovery within the 10,000 years of integration after the perturbation.
 For a pulse release of 3,000 Pg C at year 2000, more than 99.5% of preindustrial potential coral habitat sustains surface aragonite saturation rates larger than 1 throughout the simulations (Figure 11a). Aragonite saturation rates recover to values above 1.5 for all simulations within the first 4,000 years of integration (Figure 11b). For a threshold of 2, the recovery is slower. By year 10,000 over 99% of the potential habitat has recovered for simulations T_3000, B_3000, LB_3000 and Z_3000, whereas 96.5% of the area has recovered for simulation PI_3000 (Figure 11c). With a threshold of 3, Z_3000 and LB_3000 recover by over 95% by year 10,000, whereas B_3000, T_3000 and PI_3000 recover by 69%, 46% and 2% respectively (Figure 11d).
 Finally, the thresholds of 1 and 1.5 are never violated within the preindustrial potential habitat when total emissions after year 1999 equal 1,000 Pg C. Furthermore, 98% of the habitat sustains Ωarag values greater than 2 throughout the simulations (Figure 11e). By year 10,000, all simulations with interactive weathering parameterizations have recovered by 96% or more, and PI_1000 reaches 92% of recovery (Figure 11f).
5.1. The Importance of Weathering for the Long-Term Recovery of Coral Reefs
 Coral reefs cover up to 600,000 km2 of the world's low latitude oceans, representing about 1% of the global continental shelf [Crossland et al., 1991]. Due to the large global distribution across a range of environmental limits [Kleypas et al., 1999b] and their ability to reproduce asexually, corals are unlikely to become extinct as discussed by Hoegh-Guldberg . Modern coral reefs have evolved over multimillennial timescales and are generally 6 to 8 kyr old [Kiessling, 2009; Montaggioni, 2005]. This age reflects the more than doubling of global coral reef habitat since the Last Glacial Maximum (21 kyr BP) due to higher available space via post-glacial flooding of continental shelves along with warmer temperatures conducive for coral development [Kleypas, 1997]. We find that under all future scenarios analyzed here (low to high scenarios), aragonite saturation state and temperature warming will be hostile to coral reef habitat over the later part of the 21st century. It is only after multiple millennia, that coral reef habitat may start to recover as a function of the terrestrial weathering feedback.
 It is important to note that the environmental thresholds here and previously reported should not be viewed as mechanistic thresholds but rather as empirical thresholds based on the current global distribution of coral reefs relative to these environmental parameters. Furthermore, the importance of natural variability (both diurnal and seasonal) and the co-linearity with other important parameters like light levels are unclear.
 Without an interactive terrestrial weathering feedback, sea surface temperature averaged over PI coral habitat exceeds 30°C within 200 years for simulation PI_5000_A2 (not shown). The SSTs averaged over PI coral habitat then increase up to 6°C compared to pre-industrial levels, and remain at high levels up until 10,000 AD (Figure 8). All waters between 20°S and 20°N become ‘extremely marginal’ in relation to temperature alone (Figure 9a), while optimal temperatures exist between a narrow band of 20°–40° in both hemispheres in year 10,000 (Figures 9a and 12a). Yamano et al.  find evidence of a poleward expansions of coral reefs with a speed of up to 14 km year−1, indicating some level of adaptation on centennial time-scales. The extremely low aragonite saturation rates (Ωarag = 1–1.75, Figure 8a) within that latitudinal band of optimal temperature would be a rate-limiting step though. Therefore, while corals could potentially migrate to optimal temperature ranges, the low Ωarag conditions, in the control simulation (PI_5000), would most likely limit this coral reef habitat from developing over the first 10,000 years.
 Introducing an interactive terrestrial weathering feedback, however, significantly improves the prospects of coral reef habitat recovery on timescales of millennia. Terrestrial weathering provides a strong negative feedback on atmospheric CO2 on millennial timescales, lowering atmospheric CO2 from a range of 1830–2010 ppm at 2500 AD to a range of 666–1046 ppm at 10,000 AD (Figure 4a). Global mean surface air temperature cools by 2–3.8°C from year 2500 to 10,000 AD in conjunction with the drawdown of atmospheric CO2 associated with interactive terrestrial weathering (Figure 5a). 90% of the coral reef habitat recovers by year 10,000 in terms of aragonite saturation when considering the most efficient weathering parameterization (Z_5000) (Figure 10d). At the same time, the zonal mean Ωarag of surface waters between 25°S and 25°N rise above 3 (Figure 9b) for the two most efficient parameterizations (Z_5000 and LB_5000), which is above the marginal threshold for today's modern coral reef habitat [Guinotte et al., 2003; Kleypas et al., 1999b]. In a large section of the subtropical Pacific, Ωarag recovers to above 3.5 (Figure 8c), which is adequate for today's modern corals [Guinotte et al., 2003]. The terrestrial weathering feedback is therefore critically important in allowing the subtropical surface oceans carbonate saturation state to recover to near modern day levels.
 Aragonite saturation state recovers faster than SST since sea surface carbonate ion changes are directly related to atmospheric CO2levels via air-sea gas exchange. The relationship between SST and atmospheric CO2 is not linear and SST changes are therefore dictated by a considerable lag to atmospheric CO2 changes [Eby et al., 2009; Meissner et al., 2012]. Figure 12 shows the potential global coral habitat at year 10,000 for emission scenarios of 5,000 Pg C based on both Ωarag and SST.
 A very important question for the long-term prospects of recovery for coral reefs is therefore a better understanding of an upper limit of SST to coral reef development. Our simulations including the most effective weathering parameterizations allow the coral reef habitat to recover its necessary carbonate ion availability (Ωarag > 3) in a large portion of the ocean (25°S–25°N) by 10,000 AD, so as to give a wider coral reef habitat the chance to select thermally tolerant species over multimillennia (Figure 12b). This implies that if corals can naturally adapt over millennia to warmer ocean temperatures, prospects for long-term recovery of coral reefs are better since Ωarag recovers more quickly than SST.
5.3.1. Weathering Parameterizations and Sedimentation Processes
 None of these parameterizations takes changes in physical weathering rates into account. For example, one would expect an increase in chemical weathering during mountain glacial and continental ice sheet (e.g., Greenland) retreat. These glaciers leave behind large amounts of fresh, finely ground rock that provide fertile substrates for chemical weathering [Vance et al., 2009]. Changes in the total surface area of exposed rock due to sea level change are also not taken into account [Ludwig et al., 1999; Munhoven, 2002]. Finally, Meehl et al.  note a likely increase in intensity in tropical cyclones and a likely decrease in number but increase in intensity of midlatitude storms in the future. Changes in storm pattern and intensity will impact physical erosion and are not considered here.
 It should also be noted that not all the global parameterization schemes available in the literature were implemented and tested in the present study. Goddéris and Joachimski  use a different dependency on temperature and runoff in their COMBINE model, although the dependency on atmospheric CO2 is similar to GEOCARB II [Berner, 1994]. An updated parameterization of the original COMBINE model has also been used in the GEOCLIM model [Donnadieu et al., 2006] and in GEOCLIM reloaded [Arndt et al., 2011]. Finally, there are more comprehensive and regional chemical weathering models such as WITCH [Goddéris et al., 2006], which include a number of prognostic variables and which were constructed to work at the catchment scale, and are therefore not suited for the present study.
 The sediment model employed here is only valid for deep-sea sediments under oxic conditions [Archer, 1996a]. The contribution of shallow water sediments to fossil fuel neutralization is considered to be smaller than that of the deep ocean, feedbacks associated with shallow sediments are neglected in this study [Archer et al., 1997]. CaCO3 on the deep seafloor available for dissolution is dependent on both the geometry of surface sediments and the rate of bioturbation. In our parameterization, the depth of the first sediment layer is constant, assuming uniform and constant bioturbation rates.
5.3.2. Carbonate Production
 The biological pump plays an important role in the drawdown of anthropogenic CO2. The ecosystem and oceanic biogeochemical model in the present study is described in Schmittner et al. . The formulation used to compute the temperature dependency of biological rates is the widely applied function from Eppley . Carbonate production is calculated as a fixed proportion of primary production, which is indirectly a function of temperature through the Eppley function. In our model, increasing temperature enhances primary production, thereby increasing particulate organic carbon (POM) and calcite export [Schmittner et al., 2008]. One direct consequence of this parameterization is the fact that during the first 1000 years of our 5,000 Pg C simulations, marine calcite export increases at a similar rate to sediment calcite dissolution (Figures 6b and 6d), leading to an almost neutral sediment carbon budget. On the other hand, Gehlen et al.  and Ridgwell et al.  make carbonate production a function of saturation state, with the consequence that carbonate is reduced by increasing pCO2. There is therefore a large uncertainty in the future of the biological pump and calcite accumulation on the seafloor, calling for a more detailed ecosystem model with different plankton types that distinguishes between calcifiers and noncalcifying organisms. A first step has been taken by Gangstø et al. . They included the marine aragonite cycle in the global biogeochemical model PISCES. Forced with the SRES A2 scenario, they find that production rates of aragonite decrease notably after 2050. By the end of this century, global aragonite production is reduced by 29% relative to preindustrial. In their simulation, the increase of pCO2 is taken into account whereas changes in ocean temperatures and circulation are not.
 We integrate six different weathering parameterizations into a climate model of intermediate complexity (the UVic ESCM) in order to understand the long-term spatial evolution of environmental parameters important for the evolution of coral reefs. Three of these parameterizations (UVic_BERNER, UVic_LB, UVic_T_ONLY) are based on the temperature dependence first formulated for the GEOCARB II model [Berner, 1994], two are based on atmospheric CO2 concentration only, following the parameterization of Walker and Kasting (UVic_ZEEBE, UVic_ZEEBE_LOW), and one employs a constant pre-industrial weathering flux (UVic_PI). We simulate 24 future climate scenarios during which a total of 1,000–5,000 Pg C is emitted after year 2000. Our results suggest that the long-term climate response is independent of the rate at which CO2 is emitted over the next few centuries [Eby et al., 2009]. Our results also support Uchikawa and Zeebe 's conclusion that weathering has little effect on atmospheric CO2 and ocean acidification on centennial timescales. On timescales beyond centuries however, chemical weathering and an increase in alkalinity flux into the ocean have a discernable effect on the climate system and introduce a high uncertainty in future carbon uptake. We find that for most pulse releases UVic_ZEEBE is the most effective weathering parameterization, followed by UVic_LB, UVic_BERNER, UVic_T_ONLY and UVic_ZEEBE_LOW. UVic_PI shows a much slower recovery than parameterizations with climate dependent weathering fluxes. For our lowest pulse release (1,000 Pg C), UVic_LB becomes more efficient than UVic_ZEEBE. It is interesting to note that the UVic_ZEEBE simulation behaves differently from other parameterizations used in this study. The relationship between global mean temperature and atmospheric CO2 is not linear, and temperature changes are dictated by a considerable lag to CO2 changes. Weathering parameterizations based on atmospheric CO2 only respond therefore much faster to high emission scenarios than parameterizations based on temperature plus either CO2 or NPP. This results in a different transient response and recovery history, which also influences the final result: Although atmospheric temperature and CO2 are similar at the end of our simulations, the UVic_ZEEBE simulation leads to a higher ocean carbon budget than the UVic_LB simulation. This legacy effect due to different timescales in the recovery of atmospheric CO2 and SAT would not be apparent in carbon cycle box models, where temperature and atmospheric CO2 are directly linked.
 Depending on the type of weathering parameterization, between 14% and 40% of the emitted carbon remains in the atmosphere in year 12,000 (10,000 years after the initial perturbation of a 5,000 Pg carbon release). The uncertainty in prescribing a weathering parameterization reflects a similar uncertainty in determining multimillennial coral reef habitat. Although environmental conditions for SST and Ωaragstay globally hostile for coral reefs for millennia, some weathering parameterizations induce a near-complete recovery of coral reef habitat to current conditions after 10,000 years, while others result in a collapse of coral reef habitat throughout out simulations. Future research in refining and validating terrestrial weathering parameterizations is critical before we can justify optimism or pessimism with respect to the potential multimillennial recovery of global coral reef habitat.
 Independent of the type of weathering parameterization, the multimillennial response in sea surface temperature (SST) substantially lags the aragonite saturation recovery. This implies that if corals can naturally adapt over millennia by selecting thermally tolerant species to match warmer ocean temperatures, prospects for long-term recovery of coral reefs are better.
 The authors would like to thank two anonymous reviewers, as well as Eric Sundquist and Parvadha Suntharalingam, for their very valuable comments, suggestions and help. Kirsten Zickfeld was helpful with an earlier draft of this paper. We are grateful for research support under the ARC Future Fellowship Grant Program (FF100100443), as well as the ARC Discovery Grant Program and NSERC and CFCAS Operating Grants.