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1 ~ INTRODUCTION Long-Term Aspects of Future Atmospheric CO2 and Sea-Level Changes ERIC T. SUNDQUIST U.S. Geological Survey, Woods Hole The primary motivation for recent concern about future sea-level change is the anthropogenic production of car- bon dioxide and other infrared-absorbing trace gases. Climate models predict a rise of about 1.5 to 4.5C in mean global temperatures for a doubling of atmospheric CO2 levels, expected to occur during the next century (National Research Council, 1983~. More extreme warm- ing is predicted for higher latitudes. Analyses of air trapped in polar ice have shown that the warming that marked the end of the most recent ice age was accompanied by a rise of atmospheric CO2 from about 200 to 280 ppm (Berner et al., 1980; Delmas et al., 1980; Neftel et al., 1982~. That event was accompanied by the melting of enough polar ice to cause a sea-level rise of about 100 m (see Matthews, Chapter 5, this volume). Thus, both climate theory and history strongly suggest a close interconnection among CO2, climate, and sea level. However, the ice core data do not tell us whether CO2 caused climate and sea level to change. The most viable hypotheses to explain the CO2 changes observed in ice cores call on climate-induced redistributions of carbon within the ocean-atmosphere system (for example, see the section entitled "The Last De~laciation" in Sund~uist and Broecker, 19851. On the other hand, some manifestations of CO2 change appear to lead climate-sensitive oxygen 193 isotope changes in the deep-sea sedimentary record (Shack- leton and Pisias, 1985~. The sequence of events and the details of cause and effect are still vague. Such uncertainties will probably persist for a long time to come. Perhaps, rather than trying to discern whether CO2 or climate has been cause or effect, we would do better to work toward models in which climate and the carbon cycle are considered parts of the same system. This approach was suggested long ago by Chamberlin (1898) and has recently reappeared in the work of Walker and Hays (1981) and Berner et al. (1983~. The geochemical model of Berner et al. suggests that very high CO2 concen- trations were associated with high volcanic activity 100 million years ago (Ma). To simulate the reduction in CO2 concentrations to present levels, the model connects CO2 level to climate by including equations for the increase in chemical weathering rates caused by the temperatures associated with high CO2 concentrations. An updated version of this model, incorporating the effects of sulfur and organic carbon cycling, suggests that late Cretaceous atmospheric CO2 concentrations were 13 times their pres- ent level (Lasaga et al., 19851. One of the key problems in further developing this approach is to sort out which processes and inter- relationships are important to which time scales. Sea- level change encompasses a broad range of time scales, with different mechanisms associated with change over

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194 different time scales. This volume includes discussion of sea-level records ranging over seasons to hundreds of millions of years. The oceanographer concerned with storm tides would have relatively little interest in the fac- tors explaining Cretaceous sea levels; likewise, the geolo- gists' glacioeustatic theories have little application to seasonal events. The problem of sorting out time scales and processes afflicts studies of climate change in general, and of the carbon cycle. The complexities multiply in any attempt to link the two together. As a first step toward resolving these difficulties, it is useful to examine a very simplistic summary of mecha- nisms for sea-level and carbon cycle change over time scales ranging from decades to tens of thousands of years. This summary treats sea level and carbon cycling sepa- rately, and there is no guarantee that their mutual interac- tion does not entail distinct time characteristics of its own. But some intriguing conclusions emerge, particularly with regard to time scales of 1000 yr and longer. TIME SCALES OF SEA-LEVEL CHANGE Table 12.1 summarizes mechanisms of sea-level change by time scale and magnitude. Although these estimates are derived from several sources, they are somewhat subjec- tive. For example, heat exchange is relatively rapid within the uppermost few hundred meters of the oceans. A one- dimensional treatment (e.g., Munk, 1966) implies that thermal expansion of these waters can occur on time scales of years to decades. Sea level will rise about 10 cm for every degree of temperature increase throughout the up- permost 500 m. (In this chapter, relationships between seawater volumes and sea-level changes are calculated assuming no isostatic adjustment.) Heat exchange with deep ocean waters is slower, occurring on the time scale of deep ocean mixing and probably longer (e.g., Hoffert et al., 1980~. If the deep ocean were to warm everywhere by about 10C, as was perhaps the case during the early Tertiary (Brass et al., 1982), sea level would rise by about 6 m. The time scales and magnitudes of melting ice can be estimated from both historical data and mass balance considerations. The present Greenland and Antarctic ice sheets are remnants of the late Pleistocene ice sheets that increased sea levels about 100 m by melting over a period of several thousand years encompassing the end of the Pleistocene (see Matthews, Chapter 5, this volume). The mass balance estimates shown in Table 12.2 itaken largely from Lamb (1972) and Meier (19831] suggest modern ice residence times on the order of 104 years (see also L'vovich, 1974~. The Antarctic ice sheet contains enough water to raise sea level by about 60 m, and the Greenland ice sheet contains water equivalent to a 6-m sea-level rise. Moun ERIC T. SUNDQUIST TABLE 12.1 Mechanisms of Eustatic Sea-Level Change Order of Time Scale (vr) Magnitude (cm) Ocean Thermal Expansion Shallow (0 to 500 m) Deep (500 to 4000 m) Melting Ice Mountain glaciers Greenland ice sheet Antarctic ice sheet West Antarctic ice sheet Crustal Deformation Glacial rebound Tectonism 10 to 102 102 to 104 10 to 102 4+ 4+ 1 03? 103 to 104 1 o6+ 10 to 102 102 to 104 10 to 102 <103 103 to 104 <103 variable 1 o4+ TABLE 12.2 Polar Ice Mass Balance Inputs (km3/yr) Mass (km3) Outputs (km3/yr) Accumulation Antarctic ice Surface ablation (0 to 100) (1000 to 2000) sheet (30 x 106) Ablation under ice shelves (100 to 300) Icebergs (500 to 1500) Accumulation Greenland ice Surface ablation (100 to 300) (400 to 600) sheet (2.6 x 106) Icebergs (200 to 300) SOURCES: Lamb (1972) and Meier (1983~. lain glaciers are discussed by Meier (Chapter 10, this volume). The magnitude and time scales of their influence on sea level appear to be comparable to those for thermal expansion in the upper ocean. The West Antarctic ice sheet has attracted much con- troversy as a potential source of relatively rapid and large sea-level rise. On the one hand, dynamical arguments suggest that it may be very sensitive to any climate change that might cause grounding-line retreat (Hughes, 1973; Weertman, 1974~. On the other hand, its diminution dur- ing the Holocene appears to have been gradual, and per- haps nil for the last 1000 yr (Stuiver et al., 1981; Bentley, 1983~. On the basis of actual and anticipated ice stream flow rates, Bentley (1983, 1984) has estimated that 500 yr would be the minimum time required for disintegration of the West Antarctic ice sheet. From worldwide correlations of coastal onlap and offlap sedimentary sequences, eustatic sea-level changes of hun- dreds of meters are inferred to have been caused by defor- mation of the Earth's crust (see, e.g., Chapter 7, this volume). These changes occurred over time scales of mil- lions to hundreds of millions of years.

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LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES From the data in Table 12.1, it appears that sea-level changes on the order of meters or more require times on the order of hundreds of years or longer. In light of this relationship between larger sea-level changes and longer time scales, it is logical to subject the carbon cycle to a similar analysis, with a view toward estimating the time scale of the fossil-fuel CO2 perturbation. TIME SCALES OF CARBON CYCLE CHANGE The carbon cycle can be broadly subdivided according to characteristic time scales. Figure 12.1 illustrates one such subdivision, emphasizing long-term effects. Using this scheme, the most rapid changes the order of hundreds of years occur within the ocean-atmosphere- biosphere system. Over longer time scales, "reactive sediments" must be added to the system. These are sedi- ments that can interact readily with the ocean-atmosphere- biosphere system on time scales of thousands to tens of thousands of years. Finally, over time scales approaching 100,000 yr or longer, the carbon cycle must be viewed as including interactions with the Earth's crust. (For a more complete and mathematically rigorous discussion of time scales of carbon cycle change, see Sundquist, 1985.) From a consideration of both the historical record and the mechanisms of cycling carbon, it appears that there are limits to the magnitude of natural variations in atmospheric CO2 within the system delineated in Figure 12.1 as the atmosphere, biosphere, oceans, and reactive sediments. It ATMOSPHERE 550- 590 Weathering of Carbonates and SIIIc' Tee (CO2) 7" 029 :~t Weathering of Volcanism, Org. C (CON ) Metamorphlem (C02) CRUST: CARBONATES 70 x 106 ELEMENTAL C 20 x 1 o6 3~ - 8~) 195 has been hypothesized that atmospheric CO2 could not have changed by greater than a factor of 2 within this system prior to man's activities (Sundquist, 1986~. There- fore, if we are interested in geologic analogs of greater than twofold atmospheric CO2 changes, we must study the record of processes having time scales longer than 100,000 yr. Similarly, the relationships between magnitudes and time scales of sea-level change lead to questions about carbon cycle dynamics over time scales longer than the decades spanned by most CO2 predictive studies. Once fossil-fuel CO2 has been put in the atmosphere, how long will it stay there? Will high CO2 levels persist long enough to approach the response times of the polar heat and water budgets? Answering these questions will require the development of a new generation of unified climate/car- bon cycle models. In the meantime, some very general conclusions can be derived from a geochemical model of the ocean-atmosphere-sediment carbon cycle. EXTENDING PREDICTIVE CO2 MODELS TO LONGER TIME SCALES Efforts to predict the effects of anthropogenic CO2 have stimulated many advances in modeling the carbon cycle. These advances can be applied fruitfully to long-term aspects of the problem. However, predictive CO2 models cannot be extended to long-term geochemical modeling by simply running them for longer times. A primary reason 1 - _ TERRESTRIAL BIOSPHERE 560 Sedimentation (Org. C) OCEANS 36,600 500- 1000 (Inorg. C) (Org. C) Sedimentatlon (Org. C) (CaCO3) 71 1 - ?1| 1 0.7110.491` , Oxidstlon Oxidation of Org. C of Ora. C (CO2) (C(52) REACTIVE SEDIMENTS SOIL ORG C 1400 Burial (Ors. C) 0.05 l , Dlssolutlon of CaCO3 (Ca'~CO3) MARINE ORG C MARNE CACOa 1 000 5000 (Or . C) Burial (Cat 'Owl 0.22 _ 3544 Runot, (SCOT ) (Org. C) UNITS: RESERVOIRS GIGATONS C FLUXES GIGATONS C/YR FIGURE 12.1 The carbon cycle, subdi- vided to emphasize the components and processes important to different time scales. Changes over time scales up to hundreds of years will occur within the ocean, at- mosphere, and biosphere. Changes over time scales of thousands to tens of thou- sands of years will involve "reactive sedi- ments." Changes over time scales longer than 100,000 yr will involve carbon in the Earth's crust. (From Sundquist, 1986)

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196 Ocean ~ Sediment I ~Relative area lo 13 I_ ~ i: FIGURE 12.2 Basic geometry of an ocean-sediment box model, based on global seafloor hypsometry. 5 for this difficulty is that the predictive models usually do not incorporate specific interactions with marine sediments. The most conspicuous feature in the worldwide distri- bution of marine pelagic sediments is the transition from carbonate-rich sediments at shallow depths to carbonate- depleted sediments in the deep ocean. This transition reflects the difference between shallow and deep seawa- ters in their state of saturation with respect to the carbon- ate minerals calcite and aragonite (Li et al., 1969; Bro- ecker and Takahashi, 1978; Plummer and Sundquist, 19821. As anthropogenic CO2 is absorbed by the oceans, the undersaturated regions of the ocean will become more undersaturated, and some regions that are now supersatu- rated will become undersaturated. These changes, which can be predicted from fundamental chemical equilibrium calculations, imply that increasing atmospheric CO2 will increase the extent of carbonate dissolution in marine sediments. Because adding dissolved carbonate to seawa- ter increases its capacity to absorb CO2 from the atmo- sphere, this mechanism is a principal sink for added CO2 over time scales of thousands to tens of thousands of years. Other feedbacks most notably biological may also be important (see, e.g., Revelle and Munk, 1977), but they are not considered here because their mechanisms are poorly understood (particularly over such long time scales). The importance of carbonate dissolution to long-term predictions can be illustrated by a simple calculation (Broecker, 1977; Sundquist, 19791. If all of the world's fossil-fuel resources were instantaneously added to the oceans as CO2 and distributed in proportion to present dissolved inorganic carbon concentrations, the resultant atmospheric CO2 concentration would be about three times its present value. However, if the same amount of CO2 were allowed to react with an equal molar amount of ERIC T. SUNDQUIST Depth sedimentary calcium carbonate, the resultant atmospheric (he ) CO2 concentration would be only about 30 percent above its present value. Thus, it is of considerable interest to develop a predictive model capable of examining the ef- fectiveness of CO2 buffering by dissolution of carbonate sediments. To incorporate "reactive" marine sediments into carbon cycle models, it is necessary for the model oceans to have a specified bottom topography. Figure 12.2 shows how ocean hypsometry can be explicitly included in ocean box models. The areas of the surfaces between adjoining ocean boxes can be calculated from the global seafloor hypso- metric curve. With linear interpolation, these areas imply a volume and a seafloor area for each box. The seafloor area is assumed to be the surface of contact between each ocean box and an associated sediment box. This hypsometric ocean model permits a realistic ap- proach to the relationships between the sedimentation and dissolution of carbonate particles. Calcite and aragonite, precipitated by organisms in the ocean surface, settle into the deep sea. Because nearly all of the aragonite dissolves before or soon after it reaches most of the seafloor, only calcite need be included in a model incorporating "reac- tive" sediments. Calcite appears to dissolve after it has reached the seafloor rather than while it is settling, which is relatively rapid (Vinogradov, 1961; Berger and Piper, 1972; Honjo, 1975~. Thus, calcite sedimentation can be approximated by a flux from the ocean surface to the seafloor, with dissolution occurring only from those sedi- ments that lie below the "saturation horizon" (Figure 12.3~. - ~~ `..... ma.. . ::::N A,::: ~ ~ -a N: . :? _ Saturation Horizon- - - ~,::::N x::: I| Settling x:.:: :~' , ~; . . :, j ~ --- - Dissolution He. ~ N--N I' FIGURE 12.3 Carbonate sedimentation and dissolution in a hypsometric ocean-sediment box model. Carbonate particles are supplied to the sediments everywhere from the surface ocean box, but dissolution occurs only below the saturation horizon.

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LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES The depth of this horizon can be determined from the~o- dynamic calculations using the known distributions of alkalinity, dissolved inorganic carbon, and dissolved cal- cium as functions of depth. These distributions imply depth-dependent carbonate-ion concentrations and calcite solubilities. As illustrated in Figure 12.4, the saturation horizon corresponds to the depth at which the curve repre- senting the carbonate-ion concentration intersects the curve representing carbonate-ion concentrations at equilibrium with calcite. Undersaturation occurs wherever the latter curve, termed ~e"critical carbonate-ion curve" by Broecker and Takahashi (1978), lies to the right of the carbonate-ion concentration profile. At any undersaturated depth, the distance between these curves represents the degree of undersaturation, a quantity needed to calculate dissolution rates. In ocean box models, both the depth of the saturation horizon and the degree of undersaturation can be approximated by interpolation between the carbonate-ion concentrations and critical carbonate-ion concentrations in adjacent boxes (Figure 12.4, inset). Calcite dissolution adds alkalinity to seawater, and, in turn, variations in ocean alkalinities affect the carbonate- ion concentrations that control calcite dissolution. Whereas nearly all CO2 predictive models treat alkalinity as a con- stant parameter, any ocean model that incorporates calcite dissolution must treat alkalinity as a time-dependent vari- able. Like dissolved inorganic carbon, alkalinity is con- servative with respect to ocean mixing processes. Thus, model equations for alkalinity will include mixing terms very similar to those for dissolved inorganic carbon. Moreover, the stoichiometry of carbonate dissolution implies that dissolution fluxes of alkalinity (in equiva- lents) will be exactly twice as large as the corresponding dissolution fluxes of dissolved inorganic carbon (in moles). Calcite dissolution rates depend not only on the degree of undersaturation but also on the amount of calcite avail- able for dissolution. The hypsometric ocean model (Fig- ure 12.2), together with interpolative determination of the saturation horizon (Figure 12.4), provides a straightfor- ward representation of the relative seafloor areas exposed to dissolution. The most difficult aspect of modeling global calcite dissolution is approximating the time de- pendence of the calcite content relative to the noncarbon- ate components in sediments. This difficulty is illustrated by the scenario shown in Figure 12.5. At steady state (Figure 12.5a), sediments above the saturation horizon have a high calcite content, while dissolution causes those below the saturation horizon to have a low calcite content. If CO2 is added to the oceans (Figure 12.5b), the conse- quent decrease in carbonate-ion concentrations causes the saturation horizon to rise. This process exposes calcite- rich sediments to undersaturated waters. The dissolution flux from these sediments may exceed the dissolution flux 1 - lo - x co cY 2 ~4 Cal Is CRITICAL CARBONATE IONS ,~ _. I 197 WON BOX MODEL REPRESENTAT7 - 1 " . .. ~ ma a 7s~ ala1.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.762.002.25 CONCENTRAT I ON ( MOLE/KG X 1 0 4) FIGURE 12.4 The carbonate saturation horizon in an ocean- sediment box model. The critical carbonate-ion curve agrees closely with the equilibrium carbonate-ion profile (Broecker and Takahashi, 1978~. The inset shows how box model interpolation is a reasonable way of estimating the depth of the saturation horizon. from calcite-depleted sediments that, although exposed to greater degrees of undersaturation, cannot supply calcite for dissolution at a rate greater than the flux of calcite settling to the seafloor. Dissolution, of course, decreases the calcite content of the sediments that were not previ- ously exposed to undersaturated waters. If the amount of calcite dissolved is enough to cause carbonate-ion concen- trations to increase (Figure 12.5c), the saturation horizon falls toward its original steady-state depth. As this occurs, some calcite-depleted sediments pass from undersaturated to oversaturated waters. The calcite content in these sedi- ments increases as the continuous supply of settling calcite is no longer offset by loss due to dissolution. This example demonstrates several fundamental prob- lems in extending global atmosphere-ocean models to include calcite dissolution. The distribution of the disso- lution flux is discontinuous; it exists only in undersatu- rated waters, which must be located by reference to a saturation horizon that can move through a wide range of depths. Care must be taken that the physical discontinui- ties implicit in the saturation horizon are neither ignored by spatial averaging nor allowed to generate exaggerated discontinuities in the numerical solutions to the model equations. The magnitude of the dissolution flux and the calcite content of the sediments must also be modeled to interact with each other. This interaction requires that the ocean model be coupled to a sediment model with its own additional time-dependent variables. Finally, the behavior of the model sediments must include a wide range of possible changes in the calcite content of sediments ex

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198 : I 1~ ~ TACO $' _ ~ ~ ~ o _ ~ ~ 0 0 - ~ ~ - ~ CL, ~ ~ ~ ~ 1~ i,'. ~ ~ ~ o ~ so o ~4 ~ to o ~ ~ ~ o a ~ Ct Cat ~ ~ ~ ~ '' OCR for page 193
LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES posed to both undersaturated and oversaturated waters. It is clear that the areal resolution of the coupled sediment model must be comparable to the spatial resolution of the ocean model, and that an ocean-sediment box model may require further resolution to distinguish between under- saturated and oversaturated behavior within a single ocean box. A COUPLET;) ATMOSPHERE-OCEAN-SEDIMENT MODEL The model shown in Figure 12.6 (from Sundquist, 1986) has been used to simulate the response of ocean and sedi- ment chemistry to anthropogenic CO'. The global ocean is divided into three regions representing waters south of latitude 50S, north of latitude 50N (55N in the Pacific Ocean), and all waters between these polar regions. Ocean areas for these regions are taken from Baumgartner and Reichel (19751. Each polar region is divided into two vertical boxes by a boundary at 300 m. Temperate ocean boxes are separated by boundaries at 100, 300, 500, 700, 1000, 2000, 3000, 4000, and 5000 m. Each ocean box is coupled to a sediment box. The volume and area for each ocean box, and the area for each sediment box, are calcu- lated using the hypsometric data of Menard and Smith (1966) (for the temperate and south polar regions) and Gorshkov (198-0) (for the north polar region) to define the ocean bottom. The model represents seawater chemistry, ocean mix- ing, and gas exchange using parameterizations similar to those employed in many CO2 predictive models. For each ocean box, the speciation of dissolved inorganic carbon is calculated from total alkalinity and total dissolved inor ATM06~RE CONS Ino 2000 3000 - etere 4 000 - SOOO _ 6000 _ 1i O _E NORTH POUR T1 ' .. I 1 ~ = 199 ganic carbon using an iterative procedure and appropriate equilibrium constants from Lyman (1957), Culberson and Pytkowicz (1968), Mehrbach et al. (1973), Millero (1979), and Dickson and Riley (1979~. Dissolved calcium and total borate are assumed to be proportional to salinity (Culkin, 1965~. In the ocean surface boxes, air-sea exchange of CO2 is assumed to be proportional to the difference between the partial pressure of CO2 in the atmosphere and the partial pressure of CO2 at equilibrium with the surface mixed layer. CO2 solubilities are taken from Weiss (1974), and the gas-exchange rate is assumed to be 7 x 10 - moles m-2atm-~yr' (Broecker et al., 1980; Siegenthaler, 19831. Mixing across ocean boundar~es is represented by both diffusive and advective terms. Diffusive terms, which appear only in the equations for the temperate ocean boxes, have the form ~z',+~ _ 7' ~ (12.1 ~ where the subscripts i and i+1 refer to vertically contigu- ous boxes, X represents the concentration of either total alkalinity or total dissolved inorganic carbon, z represents the box depth, and Kv represents the vertical diffusion coefficient. Values for Kv range from 1.7 cm2/s below the temperate ocean surface mixed layer (Li et al., 1984) to 0.6 cm2/s in the deep ocean (Ku et al., 1980~. Advective fluxes are represented simply by Wij Xi, where wij repre- sents the flux of water from box i to box j. Values for wit are derived from the fluxes assumed for the polar produc- tion of cold deep and interinediate waters. Following Gordon and Taylor (1975), the for~:nation of Antarctic bottom water is represented by advective flux terms total FIGURE 12.6 The atmosphere-ocean- sediment box model used to assess the carbonate dissolution response to fossil- fuel CO2. The double arrow in the temper- ate ocean represents eddy diffusion; single ~7 arrows represent generalized exchange fluxes. See text for further de':ails.

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200 ing 40 x 106 m3/s from the deep south polar box to the temperate boxes deeper than 3000 m; the formation of North Atlantic deep water is represented by flux terms totaling 10 x 106 m3/s from the deep north polar box to the temperate boxes deeper than 1000 m; and the formation of Antarctic intermediate water is represented by flux terms totaling 20 x 106 m3/s from the south polar surface box to temperate boxes between 300 and 2000 m. These flux terms imply additional advective terms representing upwelling throughout the temperate water column. Sediment coupling is based on the sediment model shown in Figure 12.7. The model assumes that the sediment box associated with each ocean box can be represented as a homogeneous bioturbated layer 10 cm thick (Berger and Heath, 1968; Peng et al., 1977; Sundquist et al., 1977; Peng and Broecker, 1978~. Calcite and noncarbonate particles settle continuously to the surface of each sedi- ment box, where they are incorporated as sedimentation fluxes into the homogeneous box. If the sediment surface is exposed to undersaturated waters, dissolution removes some of the calcite from the box. The sediment burial flux is equivalent to the difference between the sedimentation fluxes and the dissolution flux. Model calcite and noncarbonate sedimentation fluxes are assigned constant values that are consistent with the known distribution of oceanic sedimentation rates. Fol- lowing Broecker (1982), the calcite sedimentation flux is evaluated at 10 g/m2yr for sediments deeper than 300 m and shallower than 3000 m. For sediments deeper than 3000 m, the calcite sedimentation flux is assumed to be 8 g/m2yr. The calcite flux per area to sediments shallower than 300 m is assumed to be three to four times the flux per area to the deep sea. Noncarbonate sedimentation fluxes are assigned values that are consistent with the distribu- tion of sediment carbonate fractions as a function of depth Dissolution Sedimentation flux flux Bottom water . T ! ~ . . Homogeneous Mixed ~instantaneous . ~ _ Radioactive layer it: ~ '. mixing . . ~decay flux 1 '-I -~ ' ~ ,, ,:. ,~ . Hi, - Buried sediment Burial flux FIGURE 12.7 Sediment model used in the ocean-atmosphere- sediment model (after Sundquist et al., 1977). The homogeneous mixed layer is assumed to be 10 cm thick. ERIC T. SUNDQUIST (Milkman, 1974; Broecker and Takahashi, 1977) and with the global flux of suspended sediments delivered by rivers to the oceans (Milkman and Meade, 1983~. Model noncar- bonate sedimentation values are extremely depth-dependent, ranging from 120 g/m2yr for sediments shallower than 300 m to 1 g/m2yr for sediments deeper than 3000 m. Calcite dissolution is modeled from laboratory rate measurements and a sediment pore water model. The exponential rate law determined experimentally by Keir (1980) is incorporated into a steady-state pore water model (Berner, 1980) to yield the dissolution flux term KdiS [ffq/c~n~d/q~n+l] 5, (12.2) where f is the sediment calcite fraction, q is the ratio of the carbonate-ion gradient to the total dissolved inorganic carbon gradient, c is the critical carbonate-ion concentra- tion in the bottom water, d is the difference between the pore-water carbonate-ion concentration and the critical carbonate-ion concentration at the sea-sediment interface, and n is an experimental constant equal to 4.5 for calcite (Keir, 19804. The constant KdiS is derived from estimates for the sediment density and porosity, the pore-water dif- fusion coefficient for bicarbonate ion, the experimental dissolution rate constant, and the specific surface area of sedimentary calcite. Typical values for KdiS and q are 3300 moles/m2yr and 0.6, respectively. The above flux term, which represents the flux per unit area at the sea-sediment interface, must be integrated over the seafloor area ex- posed to undersaturated conditions. The value of the inte- gral is estimated for variable c and d using the weighted mean value theorem (Apostol, 1967, p. 154~. As suggested in the discussion of Figure 12.5, it is possible that the dissolution flux may exceed the total sedimentation flux under certain conditions. This situ- ation results in a "negative" burial flux; that is, previously buried sediments are exhumed and incorporated into the bioturbated layer. This possibility requires that the sedi- ment model "remember" the properties of previously bur- ied sediments. Another modeling necessity suggested by Figure 12.5 is the distinction between sediments above and below a saturation horizon. In any box that is found to contain a saturation horizon, the model implements separate equa- tions to distinguish sediments that are dissolving from those that are not. The calcite contents of these two classes of sediments are therefore treated independently. As the saturation horizon moves up or down, conservation of mass requires that some of the sediments of one class be transferred to those of the other class. As shown in Figure 12.8, the sediment model is modified to include this lateral flux whenever the associated ocean box contains a satura- tion horizon. The calculation of steady-state solutions for ocean box

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LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES models is a significant modeling problem, requiring many compromises between model parameterizations and em- pirical observations (see, e.g., Wunsch and Minster, 1982; Bolin et al., 19831. For this study, the flux terms for CO2 gas exchange, ocean mixing, and calcite sedimentation and dissolution are assumed to conform to the parameteri- zations described above. The steady state for the entire model system is defined by the overall balance between inputs from rivers, volcanoes, and weathering of organic carbon and losses to sediment burial and CO2 consumption during weathering. Additional terms in the steady-state equation account for the alkalinity sink and CO2 source associated with deep-sea hydrothermal activity. A test of the coupled model's self-consistency is its representation of sedimentation and dissolution in a way that yields a reasonable value for the steady state global calcite burial flux. This flux is estimated to be 1.75 x 10'3 moles/yr, equal to the flux of calcium ions delivered to the oceans by rivers (Holland, 1978), plus a small calcium-ion contribu- tion from deep-sea hydrothermal reactions (Edmond et al., 1979; Mottl, 19831. This burial rate is a net flux, repre- senting the difference between calcite particle fluxes to the global ocean bottom and calcite dissolution fluxes from those areas of the seafloor where calcite dissolves. The model can be tuned to yield this global burial flux exactly, with only minor adjustment of the shallow-water calcite sedimentation fluxes. Likewise, ocean-surface dissolved inorganic carbon concentrations can be tuned slightly to yield air-sea exchange fluxes that conform exactly to the steady-state equation for atmospheric CO2. Thus it is assumed that the model parameterizations are a reasonable approximation of steady-state behavior. In practice, this assumption requires the introduction of re- sidual terms to satisfy the steady-state equations for alka- linity and dissolved inorganic carbon in each ocean box. These residuals, which are held constant throughout each modeling experiment, represent processes (such as organic carbon cycling) that are not represented by the parameteri- zations described above. The model equations therefore represent perturbations relative to an assumed network of steady-state processes, many of which are poorly under- stood. Steady-state concentrations are calculated using an iterative procedure that assures that the model concentra- tions for the year 1973 agree with the volume-weighted GEOSECS measurements (Takahashi et al., 1981 ) and the seasonally adjusted atmospheric measurement from Mauna Loa (Keeling and Bacastow, 1977~. THE LONG-TERM PERSISTENCE OF FOSSIL-FUEL CO2 This model is grossly oversimplified, but nevertheless it suggests an answer to our question about the persistence 201 MODEL CHANGES IN DEPTH OF SATURATION HOR17t)N \\~________ __ NO \ DISSOLUTION OVERSATURATIQ~ \\;t, - ~\,,`~DERSA TUR ~ TION DISH FIGURE 12.8 The relationship between sediment dissolution and the position of the saturation horizon in the atmosphere- ocean-sediment box model. Sediments above and below the saturation horizon must be categorized and modeled separately even though they may be associated with a single ocean box. Changes in the depth of the saturation horizon require a corre- sponding transfer of sediments from the dissolving to the nondis- solving category, or vice versa. of fossil-fuel CO2. This answer emerges from the results of two modeling experiments representing the addition of different amounts of fossil-fuel CO2. These amounts are selected to be well within the range of fossil-fuel resource estimates shown in Table 12.3, which shows both identi- fied and ultimately recoverable resources as an index of the uncertainty in the estimates. The two modeling experi- ments simulate the addition of 2500 and 5000 billion tons of carbon as CO2. The lower number is somewhat less than the world's total identified resources, while the high number is near the median between the identified and ultimately recoverable resource estimates. The time dependence of these scenarios for CO2 release is shown in Figure 12.9. CO2 production through the year 1980 is based on the yearly production estimates of Rotty (as compiled by Watts, 19821. Extrapolation beyond 1980 is based on the logistic resource-depletion function sug- gested by Perry and Landsberg (19779. The peakedness of these curves is perhaps steeper than recent growth of fos- sil-fuel consumption would indicate, but the primary fac- tor in long-term effects is the total integral under the curves rather than their short-term derivatives. The model equations are solved numerically using fifth- and sixth-order Runge-Kutta formulas implemented in the subroutine DVERK (IMSL, 1982~. Repetitive runs, using different error control options, established that the global numerical error never exceeds 0.5 percent for any model variable.

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202 TABLE 12.3 World Remaining Fossil-Fuel Resources (gigatons equivalent carbon content) Ultimately 0. 8 Identified Recoverable Coal Crude oil Natural gas Oil shale Oil sands/heavy crude aWorld Energy Congress (1980~. bHalbouty and Moody (19801. CNehring (1981~. Ovcharenko (1981). 3226a 97b 41C 233 97a 6743a 253a 133a 288a 97a Calcite dissolution is represented in Figure 12.10 by the model output for sediments at about 3000 m depth. The lower curve, from the high fossil-fuel case, shows a total depletion of calcite and a response time of tens of thou- sands of years. The upper curve shows less intense disso- lution and a more rapid return to initial conditions for the low fossil-fuel case. In both cases, model sedimentation rates (Figure 12.1 1) for the same water depth fall to negative values for about 1000 yr. That is, the rate of dissolution exceeds the rate of incoming sediments, and chemical erosion occurs. The lower curve is the high fossil-fuel case, again showing much more intense dissolution. Once calcite is depleted in the burrowed sediment layer, the sedimentation rate re 3.0 _ 2.5 He o 1 .5 1 .0 C) o o O . 5 _ / '` ". \ 0.0 I J I I I""" 1.7 1.8 ~ .S 2.0 2. ~2.2 2.3 2.4 2.5 YEAR ( X 103 ~ FIGURE 12.9 Fossil-fuel consumption scenarios used in model- ing experiments. The solid curve represents the "high fossil- fuel" case; the dashed curve represents the "low fossil-fuel" case. See text for details. ERIC T. SUNDQUIST ~ - o.o 1 1 ~1 1 1 1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 YEAR ( X 104 ) FIGURE 12.10 Model sediment calcite fractions in sediments at 3000 m depth. The solid and dashed curves correspond to the fossil-fuel consumption scenarios shown in Figure 12.9. turns to a positive value representing the noncarbonate sedimentation rate. The sedimentation rate in the high fossil-fuel case eventually rises to its initial value as cal- cite is replenished in the burrowed layer, over about 25,000 years. The importance of different processes to different time scales is perhaps best illustrated in this model by the behavior of its calcite saturation horizon. On a time scale of 1000 yr (Figure 12.12), in both the high and low fossil- fuel cases, water at depths corresponding to the dissolved ~ .o 0.5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 C.5 0.6 0.7 0.8 0.9 1.0 1.1 YEAR ( X 104 ) FIGURE 12.1 1 Model sedimentation rates at 3000 m depth. The rates shown are for total sediments, including noncarbonate. The solid and dashed curves correspond to the fossil-fuel scenarios shown in Figure 12.9.

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LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES ~ -- - -- - 1 ~1 1 - 6 FIGURE 12.12 Model calcite saturation horizons over 1000 yr. The solid and dashed curves correspond to the fossil-fuel con- sumption scenarios shown in Figure 12.9. oxygen minimum become undersaturated shortly after the time of peak CO2 additions. This occurs because CO2 is already abundant at these depths, where much of the or- ganic matter settling from the ocean surface is oxidized. For a short time, the waters immediately below the oxygen minimum zone remain supersaturated, causing the model ocean to have three saturation horizons instead of one. (A problem with the model is also apparent in this figure. The sudden jump in the deepest saturation horizon occurs because the model's interpolating equations cannot "see" the saturation reversal between two of its average box depths.) 1 1 1 1 1 ., 1 E o 3 _' o o 4 I_ s 6 l . 1 1 1 1 1 1 1 1 1 _ 1 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.S 1.0 1 1 YEAR ~ x~o4 ~CONCLUSIONS FIGURE 12.13 Model calcite saturation horizons over 10,000 yr. The solid and dashed curves correspond to the fossil-fuel consumption scenarios shown in Figure 12.9. 203 - lo - x cat to Lie =~3 ~ CK I Z 4 _ _. ~ 5 1 . , . _ ; 1 1 1 1 1 1 1 1 1 1 6 1 , 1 1 1 1 1 1 1 1 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2 6 2.7 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5 YEAR ( X 103 ) YEAR ( X 1 04 ) FIGURE 12.14. Model calcite saturation horizons over 50,000 yr. The solid and dashed curves correspond to the fossil-fuel consumption scenarios shown in Figure 12.9. Over a time scale of 10,000 yr (Figure 12.13), the high and low fossil-fuel cases show drastically different influ- ences on the calcite saturation horizon. The high fossil- fuel case maintains undersaturation up to depths shallower than 1000 m, while the low fossil-fuel case returns to a near-normal saturation state. There is simply not enough calcite available in this model to buffer the high fossil-fuel CO2 additions. Instead, the buffering in this case is paced by the much slower return to a balance between the input of dissolved bicarbonate in river water and the sedimenta- tion of calcite. This balance assures that, after 50,000 yr, the model saturation horizon for both cases has returned to its initial depth (Figure 12.14~. Given the exhausted buffering capacity in the high fossil- fuel case, it is not surprising that its atmospheric CO2 level stays higher for a longer period. After 1000 yr, its atmo- sphere contains about four times as much CO2 as it did initially, while the low fossil-fuel case has buffered its atmospheric CO2 increase to less than twofold (Figure 12.15~. After 10,000 yr (Figure 12.16), the high fossil- fuel atmosphere is still at about twice the initial CO2 con- centration, while the low fossil-fuel atmosphere contains about 400 ppm CO2, a level that we will probably ap- proach during the next few decades. Over a time scale of 50,000 yr (Figure 12.17), the model atmospheres approach their new steady-state values of about 380 ppm for the low fossil-fuel case and 450 ppm for the high fossil-fuel case. Before discussing the implications of the results de- scribed above, it is important to reemphasize the short- comings of the model. Several important feedbacks are

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204 2.00 _ - lo 1.75 X 1.50 ~7 lo, CY :~ 1.25 CD o "C 1.00 CU o ~ 0.75 C' - ~ 0.60 o .c 0.26 0.00 I I I I I I -a- ~I I I . ~ , .~ . L I I I I I I -- ~ 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 YEAR ( X 103 ) FIGURE 12.15. Model atmospheric CO2 concentrations over 1000 yr. The solid and dashed curves correspond to the fossil- fuel consumption scenarios shown in Figure 12.9. ignored. Massive production of fossil-fuel CO2 will al- most certainly alter the global cycling of organic carbon, both on land and in the sea. Long-term interactions be- tween the climate system and the carbon cycle are so pervasive that any model that separates them is inherently inadequate. For example, ocean heating will probably be a positive feedback. The solubility of CO2 in seawater decreases with increasing temperature. Although this ef- fect is relatively minor when considered for the ocean surface only, it will be amplified to the extent that warm deep water replaces cold water. This will also profoundly 2.00,, , ~, ~ o.oo 1 1 1 1 1 1 1 1 1 1 _ 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 YEAR ( X 104 ) L FIGURE 12.16. Model atmospheric CO2 concentrations over 10,000 yr. The solid and dashed curves correspond to the fossil- fuel consumption scenarios shown in Figure 12.9. ERIC T. SUNDQUIST affect ocean density stratification and therefore circula- tion. Warming will also affect calcite solubility, decreas- ing its effectiveness as a buffer. Another important feed- back is the effect of high atmospheric CO2 on chemical weathering rates. This feedback is effected in soils, where CO2 is delivered to rocks by organisms that respond to environmental changes in notoriously complex ways. These and other processes must be better understood before the long-term persistence of fossil-fuel CO2 can be reliably predicted. However, principal features of the model results de- scribed above are maintained throughout a number of important sensitivity tests. Ocean mixing and air-sea exchange are relatively rapid, so wide variations in their parameters have little effect on model results beyond a 2.00 ~ .75 - o X 1 50 hJ tar ~ 1.26 CD o I: 1.00 Cal to cat O . 75 C' _4 CY I 0.60 c/) to 0 . 26 ,_ 1 1 1 1 1 1 1 1 1 0.6 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 YEAR ( X 104 ) FIGURE 12.17. Model atmospheric CO2 concentrations over 50,000 yr. The solid and dashed curves correspond to the fossil- fuel consumption scenarios shown in Figure 12.9. few thousand years. The model is likewise insensitive to large variations in the shape of the CO2 production curve for a given total integral under the curve. Calcite dissolu- tion rate parameters also have little influence on the model results beyond a few thousand years. In short, the model results appear to be relatively insensitive to errors in the processes included in the model; the model's principal shortcomings derive from the processes it does not in- clude. The model results suggest that significantly elevated atmospheric CO2 concentrations may persist for a time long enough to approach the response times of the polar heat and water budgets. Moreover, the magnitude of the persistent long-term CO2 increase will depend on the total amount of fossil fuels consumed during coming decades

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