A simple model for the CaCO₃ saturation state of the ocean: The “Strangelove,” the “Neritan,” and the “Cretan” Ocean

2.1. Timescales

[10] The time scale of the model is of the order of 1,000 to 10,000 years and we neglect all processes that may change [CO₃²⁻] on time scales smaller or larger than this. The dominant processes affecting [CO₃²⁻] on this time scale are the riverine flux of Ca²⁺ and CO₃²⁻ ions (weathering), the inorganic or biogenic precipitation of CaCO₃ within the ocean, and the burial of CaCO₃ in shallow-water environments or in the deep sea. Time scales smaller than 1,000 years cannot be represented by the model because the deep sea reservoir is assumed to be well mixed which takes about 1,000 years. On time scales larger than 10,000 years, the riverine flux and whole ocean inventories of ΣCO₂, TA, and Ca²⁺ may change (Ca²⁺ only on Ma time scale) and the model solutions do no longer apply. However, the model is always applicable to individual time intervals (shorter than 10,000 years) at any given time in the past using appropriate boundary conditions for that time interval.

[11] For example, assume a two-fold higher oceanic Ca²⁺ concentration at some time in the past [cf. Horita et al., 2002]. If the saturation state was similar to today's, then [CO₃²⁻] was simply two-fold lower than today, if effects of temperature, salinity, seawater composition, etc. are neglected. (Note that the assumption of a roughly constant saturation state appears reasonable for the last 100 Ma in the current context, cf. section 3.2 and Tyrrell and Zeebe (Reconstructing ocean carbonate chemistry and atmospheric CO₂ over the last 100 My–A new approach, manuscript submitted to Geochimica et Cosmochimica Acta, 2003)). The two-fold lower [CO₃²⁻] follows directly from equation (1) using constant Ω and K*_sp, and considering that the in situ and saturation concentration of Ca²⁺ are equal because Ca²⁺ is virtually constant throughout the ocean:

where “sw” and “sat” refer to the actual seawater and saturation concentration. It shows that x must indeed be equal to 1/2, i.e., past [CO₃²⁻]_sw was half of modern [CO₃²⁻]_sw. Thus although the absolute value of [CO₃²⁻] may change over long time scales, the model results pertaining to [CO₃²⁻] relative to a given saturation concentration are still valid. This greater generality will be expressed by the use of dimensionless symbols (c' s) which signify CO₃²⁻ concentrations divided by the saturation concentration at 1 km depth.

2.2. The Steady-State Equation

[12] The fundamental assumption underlying the model is that the ocean operates in a steady-state on the time scale considered (a non steady-state situation is considered in 22). In other words, the carbonate ion concentration in the deep sea is constant which requires that the weathering must equal the burial. Otherwise, c would steadily increase or decrease. This is expressed by:

where t is time, F_in and F_out are the input and output fluxes due to weathering of CaCO₃ on the continents and burial of CaCO₃ on the shelves and ocean floor, respectively. For the sake of simplicity, all fluxes will be expressed in terms of the input flux, i.e., all fluxes are dimensionless and we set F_in = 1. Since we are considering a steady-state here, we do not have to worry about the units of the left hand side of equation (3). However, this will be necessary in 22.

[13] Next we have to specify the possible output fluxes on the right-hand side of equation (3) and then—provided that a steady-state solution exists—solve the equation for c. In order to do this, information on the solubility of calcite and aragonite has to be provided.

2.3. Solubility of Calcite and Aragonite

[14] In the model, the intercept of the deep ocean carbonate ion concentration and the carbonate ion concentration at calcite saturation (short: saturation concentration) determines the position of the lysocline. The solubility of calcite and thus the saturation concentration increases with depth. For the sake of simplicity, we assume a linear increase of the saturation concentration with depth, and set the value at 1 and 6.5 km to 52 and 147 μmol kg⁻¹, respectively. This approximation is quite reasonable as the comparison with the curve given by Broecker and Takahashi [1978] and refined by Jansen et al. [2002] shows (Figure 3).

[15] As mentioned above, concentrations will in the following be expressed in terms of the saturation concentration at 1 km (52 μmol kg⁻¹). For example, the saturation concentration at 1 and 6.5 km, which is denoted by c_s and c_d, is then equal to 1 and 2.83, respectively (Figure 3). Note that indices “s” and “d” stand for shallow (1 km) and deep (6.5 km); all symbols used for characteristic saturation concentrations in the model are given in Table 1.

[16] The saturation concentration is one of the essential parameters determining the deep ocean carbonate ion concentration. It is therefore interesting to note that this is a purely thermodynamic quantity given by the solubility of calcite which can be determined in the laboratory as it is solely determined by the physicochemical properties of calcite and seawater.

[17] For the calculation of precipitation fluxes in the neritic environment, aragonite saturation needs to be considered which is probably the most important polymorph of CaCO₃ deposited in shallow-water areas [Opdyke and Wilkinson, 1993]. The surface water carbonate ion aragonite saturation concentration at T = 25° C, S = 35, and P = 1 atm is 63 μmol kg⁻¹ [Mucci, 1983] which has to be translated into a corresponding deep ocean concentration because this is the state variable of the model. Today's average surface ocean [CO₃²⁻] is roughly two times that of the deep ocean. Assuming that surface saturation decreases proportionally to the deep saturation when the latter approaches zero, the surface aragonite saturation corresponds to a deep ocean concentration of 32 μmol kg⁻¹ or c_n = 0.62 in terms of c_s, where c_n will be called the neritic saturation. The value assumed for c_n has no essential effect on the model outcome as presented here, see 19.

2.4. The “Strangelove Ocean”

[18] First, we specify the output flux in a hypothetical ocean in which inorganic precipitation is the dominant mode of CaCO₃ removal from seawater. This scenario will be termed the “Strangelove Ocean” which is usually used in the literature to denote an ocean in which all life has been eliminated. In the current paper, however, the term “Strangelove Ocean” is used for an ocean in which life may indeed exist but in which biogenic precipitation of CaCO₃ is essentially absent (to be defined more precisely later on).

[19] The only output flux in the Strangelove Ocean is the inorganic precipitation of CaCO₃ above a critical supersaturation, c_c. If c is smaller than or equal to c_c, no output flux is generated; if c is larger than c_c, precipitation is initiated which generates an output flux, F_out. At higher concentration, this flux should increase. We express this by the following equation which is a modified version of a relationship often used for inorganic precipitation rates (see next section):

where γ is an arbitrary constant and the number 3 in the exponent represents the reaction order chosen at the upper end of the spectrum to indicate the inorganic character of the precipitation [Zhong and Mucci, 1993]. It is emphasized that neither the precise value assumed for c_c, nor for γ, nor for the reaction order is crucial to our analysis. The point that matters is that the critical supersaturation is usually much higher than the CaCO₃ saturation concentration. This may be justified by the observation that today's surface ocean is about 4 and 6 times supersaturated with respect to aragonite and calcite, respectively, but that inorganic precipitation is very rarely observed. Obviously, a much higher supersaturation is required to trigger significant inorganic precipitation.

[20] In summary, the assumption is that c_c is distinctly higher than the solubility concentration at calcite saturation in the deep ocean, c_s or c_d. Figure 4a shows the output flux in the Strangelove Ocean for c_c = 4 × c_s and γ = 500. The value for c_c was picked arbitrary just to produce the figure, the value for γ was assumed to be large, implying that once inorganic precipitation is triggered, it is supposed to be rapid and widespread. One may, however, pick different values. Because a steady-state is required, also the Strangelove Ocean must obey that input equals output, i.e., weathering equals burial. The only output in the Strangelove Ocean is generated at c > c_c, which means that the steady-state concentration is always higher than the saturation concentration in the deepest part of the ocean, i.e., c > c_d. It follows immediately that there cannot be any seafloor dissolution in the Strangelove Ocean since even the deepest part of the ocean floor is bathed in supersaturated waters.

2.5. The “Neritan Ocean”

[21] In contrast to the Strangelove Ocean, now an ocean is considered that harbors organisms capable of inducing or directly precipitating CaCO₃ biogenically. The habitat of those organisms shall be restricted to the shallow-water environment. We will call this the “Neritan Ocean.” (The term Nerita refers to a genus of marine molluscs and probably stems from Nerites, a Greek God who was transformed into a mussel because he refused to follow Aphrodite to the Olympus. The commonly used term “neritic” refers to the marine shelf areas of less than ∼200 m depth). In this sense, the neritic organisms that produce CaCO₃ such as corals, calcareous algae, snails, or mussels and all organisms that can mediate CaCO₃ precipitation are the “Neritans” or the protagonists of the Neritan Ocean. The term shall emphasize the difference to the Strangelove Ocean where there may well be calcium carbonate precipitation—but no protagonists.

2.5.1. CaCO₃ Production in the Neritan Ocean

[22] In the model, CaCO₃ production in shallow-water environments is assumed to be biologically controlled or at least biologically mediated. The CaCO₃ produced in those environments shall escape dissolution. For the description of the neritic CaCO₃ production, F_n, we adopt a relationship which has frequently been employed for shallow-water production but is actually common in studies of inorganic precipitation rates:

where Ω is the saturation state, k is a rate constant and η = 2 is the order of reaction (modified after Opdyke and Wilkinson [1993] [cf. Caldeira and Rampino, 1993]). This relationship expresses the observation that calcification in shallow-water facies such as coral reefs increases with saturation state (see 19 for further details and justification). Equation (5) can be written in terms of model concentrations:

where c_n is the carbonate ion saturation concentration at which the biogenic/biologically mediated precipitation in shallow-water environments approaches zero and was called the neritic saturation (4, Table 1). It corresponds to the CO₃²⁻ concentration at say, surface aragonite saturation at given [Ca²⁺] translated into a deep ocean concentration. Furthermore, we can write

and finally normalized with respect to c_s:

with F_n⁰ = k × c_s²/c_n². The neritic, biogenic output flux then reads:

The pre-factor F_n⁰ scales the neritic production and is just equal to it at c = c_n + c_s, i.e., at this point F_n⁰ = F_n (Figure 4b shows an example with F_n⁰ = 1.1).

[23] The relation between the model parameterization of neritic CaCO₃ production and natural processes occurring in the ocean may be described as follows. The pre-factor F_n⁰ is a measure of the CaCO₃ production of the total population of shallow-water calcifiers in the Neritan Ocean. This includes factors such as the ecological success of those groups but also the areal extent of shelves, i.e., the size of the habitat available to neritic organisms which may change, for instance, due to sea-level fluctuations. On the other hand, the ability of the individual organism to either produce CaCO₃ or induce CaCO₃ precipitation is reflected in the second term of our parameterization [(c − c_n)² in equation (6)] which strongly depends on the saturation state of the surrounding seawater. Together, the pre-factor F_n⁰ and the dependence on the saturation state determine the total neritic flux at any given saturation state as shown in Figure 4b.

2.6. The “Cretan Ocean”

[24] In the current section we consider an ocean which harbors pelagic calcifiers capable of precipitating CaCO₃ biogenically at a supersaturation significantly lower than the critical inorganic supersaturation, c_c. The CaCO₃ production shall be entirely biologically controlled and to a large degree independent of the external supersaturation. Because in this ocean CaCO₃ production occurs in the open ocean, deep sea accumulation and dissolution comes into play. We will call this the “Cretan Ocean.” (Creta is the Latin word for chalk, cf. “Cretaceous.”) In this sense, the pelagic CaCO₃ producing organisms such as foraminifera and coccolithophorids are the “Cretans” or the protagonists of the Cretan Ocean. The term shall emphasize the difference to the (1) Strangelove Ocean where there may be precipitation but no protagonists and (2) to the Neritan Ocean where the protagonists are restricted to the shallow-water environment and their production strongly depends on the saturation state.

2.6.1. CaCO₃ Production in the Cretan Ocean

[25] It is assumed that pelagic organisms can produce calcite at a constant rate over a wide range of supersaturation. In other words, the biogenically controlled precipitation of pelagic calcite in the Cretan Ocean is largely independent of the external supersaturation of seawater. This assumption is probably reasonable at high supersaturation [Riebesell et al., 2000; Zondervan et al., 2001; Bijma et al., 1999; Wolf-Gladrow et al., 1999]. However, at low supersaturation or undersaturation the biogenic production is decreasing as in the limit c → 0, the substrate for calcification is absent and there cannot be any more calcite production. We may assume for simplicity, that the pelagic, biogenic CaCO₃ output flux, F_p, is linearly increasing between zero and a maximum biogenic flux, F_p^m. As a result, the output flux generated by pelagic, biogenic CaCO₃ production in the Cretan Ocean is mathematically expressed by:

where c_b is the threshold concentration below which the biogenic precipitation is decreasing—c_b will be called the biogenic, pelagic saturation (Figure 4b).

[26] In the Cretan Ocean, the relation between model parameterization of pelagic, biogenic calcite production and natural processes is as follows. The maximum biogenic flux corresponds to the total CaCO₃ production of the total population of calcifiers in the open ocean if the production is not diminished by low saturation state. For example, increasing F_p^m therefore signifies a larger population and variations in the ecological competitiveness between e.g., calcifying and non-calcifying groups are reflected in F_p^m. On the other hand, the dependence of the calcification rate on the saturation state below the biogenic saturation reflects the ability of the individual organism to produce calcite (cf. 18). Together, the maximum biogenic flux and the biogenic saturation determine the total biogenic flux at any given saturation state (Figure 4b).

[27] It is noted that our pelagic CaCO₃ production fluxes refer to that portion of CaCO₃ which settles down to the depth of the saturation horizon (SH). CaCO₃ redissolved in the upper water column, say in the upper 1000 m, is irrelevant to the current model because this carbonate cannot be buried even if the SH rises. It therefore does not affect the inventories of Ca²⁺, ΣCO₂, and TA (see 16).

[28] The relative importance of neritic and pelagic production may be expressed by the ratio of the neritic production, F_n, to the total production F_n + F_p and will be called f:

For example, f = 0.1 signifies that 10% of the total production is neritic.

2.6.2. Dissolution in the Cretan Ocean

[29] In contrast to the Strangelove and Neritan Ocean where either the high supersaturation or the absence of pelagic production prevents CaCO₃ dissolution in the deep sea, in the Cretan Ocean dissolution of CaCO₃ in the deep sea is feasible. It is this dissolution that is crucial to maintaining the steady-state between weathering and burial at a low saturation state.

[30] For the description of the dissolution in the Cretan Ocean, four different domains have to be considered of which two are very simple to describe. If the deep sea carbonate ion concentration, c, is greater than the solubility concentration in equilibrium with calcite at the ocean's deepest spot, c_d (here 6.5 km), then no calcite can be dissolved since the entire ocean floor is bathed in supersaturated waters—the dissolution flux is zero (Figures 4c and 5a). On the other hand, if c is smaller than the solubility concentration at the ocean's shallowest spot, c_s (here 1 km), then all calcite must dissolve since the entire ocean floor is bathed in undersaturated waters (Figure 5b). It follows for the latter domain that the dissolution flux must be equal to the production flux with a negative sign.

[31] If c is smaller than the calcite saturation at the deepest spot, c_d, but larger than the biogenic, pelagic saturation, c_b, then the dissolution flux is proportional to the maximum pelagic flux, F_p^m, and proportional to the area of the seafloor below the lysocline (Figure 5c). Now the area of the seafloor below the lysocline is proportional to the difference between the depth of the lysocline and the ocean's deepest spot, 6.5 km. Since the lysocline is located at the intercept of the actual concentration, c, and the solubility concentration, and we assumed a linear relationship between depth and solubility concentration (Figure 3), the area of the seafloor below the lysocline is simply proportional to the difference c_d − c_s. A similar reasoning holds for the domain in which c is smaller than the biogenic saturation, c_b, but larger than c_s.

[32] In summary, the dissolution in Cretan Ocean can mathematically be expressed by:

with

where F_p^m is the maximum pelagic flux, c_b is the biogenic, pelagic saturation, and c_d and c_s are the solubility concentrations in equilibrium with calcite at 6.5 and 1 km, respectively. The dissolution flux in the Cretan Ocean is graphically shown in Figure 4c and illustrated in Figure 5.

3.1. Today's Deep Ocean Carbonate Ion Concentration

[40] In this section we aim to demonstrate that despite the limitations of our highly simplified model, it is capable of reproducing the deep ocean carbonate ion concentration as observed in the modern ocean. As already stated above, today's ocean operates in a mode corresponding to Domain 2. On the basis of the assumption that this mode is largely dominated by pelagic production (see 14) we therefore employ equation (12) for the Cretan Ocean to calculate today's deep ocean carbonate ion concentration:

Using c_s = 1 and c_d = 2.83, corresponding to [CO₃²⁻] being 52 and 147 μmol kg⁻¹ (Figure 3), a pelagic biogenic saturation of c_b = 1.73, corresponding to [CO₃²⁻] being 90 μmol kg⁻¹ (see 18), and an overproduction at biogenic saturation of r = 4.3, the result is:

It is noted that the values picked for the pelagic biogenic saturation, c_b, and the pelagic overproduction at biogenic saturation, r, are not crucial to this result. Varying c_b between 70 and 110 μmol kg⁻¹, yields a deep ocean [CO₃²⁻] between 73 and 82 μmol kg⁻¹. Likewise, varying r between 3 and 5, gives [CO₃²⁻] between 75 and 85 μmol kg⁻¹. Using parameters as given above, our simple model calculates a value of 78 μmol kg⁻¹ for the deep ocean carbonate ion concentration. How does this compare to observations in the real ocean?

[41] A range for the global average value of today's deep ocean carbonate ion concentration was obtained as follows. We used the global data set for total dissolved inorganic carbon (ΣCO₂) and total alkalinity (TA) from Goyet et al. [2000] at a depth of 3.5 km. From this data, we used a range of values for ΣCO₂ and TA representative for the major ocean basins, weighed them by the respective area fraction of the basins, and then calculated a range for the global average CO₃²⁻ ion concentration, using carbonate chemistry dissociation constants as summarized in Zeebe and Wolf-Gladrow [2001]. The procedure gives a global average value of 71–85 μmol kg⁻¹ (Table 2). Thus the model-calculated value of 78 μmol kg⁻¹ compares well to observations in the real ocean.

3.2. Summary: Steady-State Solutions

[42] The entirety of the steady-state solutions for all five model domains as a function of the biogenic flux is shown in Figure 7. Three distinctly different modes of operation can be identified. First, if the biogenic flux—no matter whether neritic or pelagic—is smaller than the riverine flux, then the saturation state of the ocean is close to the critical inorganic supersaturation (e.g., c ≃ 4). The ocean operates in the Strangelove Ocean mode and its fate is a high supersaturation (the mathematical definition for the Strangelove Ocean in the current paper hence is: F_b < F_in). Second, if in the absence of pelagic fluxes, the neritic flux is as large as the riverine flux, the saturation state can vary dramatically and can take on any value between the high supersaturation of the Strangelove Ocean and the low saturation at which aragonite starts to dissolve in the surface ocean. This is the Neritan Ocean. Because there is no dissolution, the constraint for steady-state being that the neritic flux must always be equal to the riverine flux at any saturation which leads to the vertical dot-dashed line in Figure 7 at F_b = F_in = 1. Third, if in the absence of neritic fluxes, the pelagic flux exceeds the riverine flux, then the ocean operates in a mode of a much lower saturation state than the Strangelove Ocean: The Cretan Ocean. In the Cretan Ocean, the low saturation state can be maintained over a large range of pelagic production, the only constraint being that F_b > F_in.

[43] These are remarkable results. If the model outcome is robust and applicable to the real ocean (see below) it tells us that as long as the pelagic, biogenic production of CaCO₃ exceeded the riverine flux of Ca²⁺ and CO₃²⁻ ions in Earth's history, then the saturation state of the ocean was fairly constant. For example, if the pelagic flux varied between two and ten times the riverine flux (2 × F_in < F_b < 10 × F_in), then c was roughly between 1.2 and 1.9. At today's calcium concentration, this translates into deep sea [CO₃²⁻] of about 62 and 100 μmol kg⁻¹. Note that the result in terms of c still holds even if oceanic [Ca²⁺] has varied on long time scales (2). This explains the overall constancy of the saturation state of the ocean documented over the last 100 Ma (van Andel et al. [1977], Thierstein [1979], but see comment below). It is emphasized that this is mostly a consequence of the interplay of two independent variables: (1) the pelagic, biogenic calcite production at low supersaturation exceeding the riverine flux and (2) the solubility of calcite in seawater—of which the former is controlled by biologic processes, while the latter is controlled by the physicochemical properties of seawater and calcite.

[44] Regarding the saturation state of the Neritan Ocean, the model tells us that as long as the neritic production has balanced the riverine flux in Earth's history (in the absence of pelagic calcifiers), then the saturation state of the ocean was probably highly unstable [Ridgwell et al., 2003]. Any change in the population or ecological success of Neritans and/or in the neritic area (F_n⁰) directly impacts upon the saturation state. For example, in the Neritan Ocean an increased population or a larger neritic area leads to an immediate drop in the saturation state which in turn reduces the precipitation rate of each individual Neritan until the total production again balances the influx. If the population or neritic area is large, saturation state must be low and vice versa (cf. lower and upper end of vertical dot-dashed line in Figure 7). Mathematically, this is easily seen by considering F_n⁰ × (c − c_n)² = const. There is no freedom in the biogenic production as compared to the Cretan Ocean where increased deep sea dissolution can compensate for higher production.

[45] To give an example, and to put it less mathematically, say an armada of massively calcifying organisms would suddenly conquer the ocean and their production of CaCO₃ would rapidly reduce the CaCO₃ saturation state of the ocean. If the organisms are pelagic, then in the Cretan Ocean two stabilizing feedbacks are active. On the one hand, the saturation horizon would rise leading to more dissolution which counteracts the reduction in saturation state. On the other hand, if at some point the saturation state would drop to a value such that the ability of each individual organism to calcify would be impaired, then the CaCO₃ production stagnates and the saturation state finally stabilizes. Together, these two feedbacks lead to the very stable saturation state for the Cretan Ocean in Domain 2 (see Figure 7). In the Neritan Ocean, only the second feedback is active. In any case, this feedback prevents the ocean from rapidly running out of ingredients for CaCO₃ manufacturing due to overproduction.

[46] In the following, a comment on past CCD variations is added. It was stated above that the saturation state was on the whole constant over the last 100 Ma. In fact, the CCD—which is thought to be a good proxy for saturation state—has varied over this period of time and was approximately 1 km shallower at the end of the Cretaceous. In a different context, this may be considered as significant [Sclater et al., 1979; Delaney and Boyle, 1988]. However, viewed from our current perspective these variations are rather small as a 1 km change of the SH translates into a change of [CO₃²⁻] by ∼17 μmol kg⁻¹ (at today's calcium) and of pCO₂ by ∼25 μatm (see 23). What we would consider significant is, for example, if the total biogenic flux would have ever fallen close to or below the riverine flux. The consequence would have been a dramatic drop of the CCD below the ocean floor. This has obviously never happened during the last 100 Ma.

3.3. Combining Open Ocean and Shallow-Water Production

[47] So far only the two end-member scenarios of possible modes of biogenic carbonate deposition have been discussed, namely exclusive pelagic or shallow-water production. In reality, however, the ocean has probably operated in a combination mode of the two over a large portion of its recent history. In today's ocean, the majority of the global CaCO₃ production is pelagic as estimates of the observed CaCO₃ production range from 65 to 85% for the open ocean [Morse and Mackenzie, 1990; Milliman and Droxler, 1996; Milliman et al., 1999]. Therefore pelagic production was also considered the major player in the model and the modern ocean was thought to operate in the Cretan Ocean mode.

[48] On the other hand, when accumulation is considered, shallow-water environments may not be negligible in the modern ocean [Iglesias-Rodriguez et al., 2001]—although a definite statement on this issue has to await more accurate estimates of the marine CaCO₃ budget. Another reason to consider shallow-water production and accumulation has to do with the geologic history of calcification, as CaCO₃ production in shallow-water environments was probably very important before pelagic calcifiers became increasingly abundant in the late Mesozoic. Biogenic shallow-water carbonate accumulation may provide an important feedback controlling the ocean's saturation state both in Paleozoic-to-middle Mesozoic oceans and after catastrophic events such as the Cretaceous/Tertiary (K/T) boundary impact when pelagic production was reduced [Caldeira and Rampino, 1993].

[49] Figure 8 shows the calculated steady-state concentrations for the coexistence of pelagic and neritic production as a function of the total biogenic flux for different values of f = F_n/(F_n + F_p), the ratio of neritic to total production (cf. 6 and see appendix A for analytical solution). First, starting at the Cretan Ocean and adding neritic production (compare, for example, the curves labeled “Cretan” and “f = 0.1”) lowers the steady-state concentration at a given total biogenic flux. This is because now some portion of the CaCO₃ production is buried on the shelf and accordingly a smaller portion is buried in the deep sea in order to balance the riverine flux. This is accomplished by a rise of the saturation horizon and a drop of deep [CO₃²⁻]. Thus an increase of the fraction buried on the shelf should lead to a rise of the CCD. This may have been the case 100 million years ago which would explain the shallower CCD reconstructed for this time period [Sclater et al., 1979].

[50] Second, if shelf production is included, our general conclusions regarding the strong saturation-stabilizing feedback which is active in the Cretan Ocean (cf. Figure 7) only holds if the pelagic production is dominant. If shallow-water accumulation becomes a larger portion of the production, the feedback is much weaker. For instance, if the neritic production is more than half of the total (cf. curve for f = 0.5), then dramatic variations of the saturation state (0.6 < c <3) are possible for only small variations of the total biogenic flux (1 < F_b < 2).

[51] If the saturation drops below the calcite saturation at 1 km depth (c_s), all pelagic calcite must dissolve and because there is no deep sea accumulation anymore, the influx must be balanced by the neritic accumulation alone. In steady-state, the latter must be exactly equal to the influx and hence the neritic flux for all curves shown in Figure 8 (where f > 0) is constant and equal to 1 for c < c_s. It follows that because we assumed a fixed ratio of neritic to pelagic production, also the pelagic production is constant below c_s. This leads to the vertical lines for all values of f > 0 between c_n and c_s.

4.1. Calcite Lysocline, Ca²⁺ Concentration, and Water Column Dissolution

[53] The dominant mineral of CaCO₃ precipitated in today's open ocean and buried in the deep sea is coccolithophorid and foraminiferal calcite. As a result, the model calculates the calcite lysocline. The carbonate ion concentration in equilibrium with calcite as a function of depth adapted in the model follows Jansen et al. [2002]. Our linear approximation to their exponential curve underestimates the calculated depth of the saturation horizon at maximum by roughly 500 m (Figure 3). The calcium concentration in today's ocean is large and constant throughout the ocean. As a corollary, variations in the concentration of CO₃²⁻ determines the CaCO₃ saturation state of seawater and the model uses the carbonate ion concentration as the state variable.

[54] Recent studies of the CaCO₃ cycle indicate large amounts of water column dissolution, particularly in the top 1000 m of the ocean [Milliman et al., 1999; Feely et al., 2002]. Although very important for our understanding of the CaCO₃ export and dissolution, upper water column dissolution is irrelevant to the current model. Our CaCO₃ production fluxes refer to that portion of CaCO₃ which settles down to the depth of the saturation horizon only. CaCO₃ redissolved in the upper water column, say in the upper 1000 m, is ignored because this carbonate cannot be buried even if the saturation horizon rises and therefore does not affect the balance between riverine flux and burial. Water column dissolution may well affect the distribution of Ca²⁺, ΣCO₂, and TA in the upper ocean but not their whole ocean inventories.

4.2. Topography

[55] Figure 9 shows the topography used in the model (solid line), and the topography derived from the ETOPO5 bathymetric data base (dashed line, National Oceanic and Atmospheric Administration (NOAA), 1988]). The linear approximation between 1 and 6.5 km appears reasonable for depths greater than 2 km but is quite bad for the shelf areas. Because shallow-water environments and their CaCO₃ production is considered separately in the model, the bad shelf topography should not be too problematic.

4.3. Biogenic, Pelagic Saturation

[56] The biogenic saturation below which the biological production of calcite decreases was set to 90 μmol kg⁻¹ in the model. This is based on calcification rates in the most important pelagic calcifyers, coccolithophorids and foraminifera which show a dependence on [CO₃²⁻] (Figure 10, cf. Riebesell et al. [2000], Zondervan et al. [2001], Bijma et al. [1999]; Wolf-Gladrow et al. [1999]). The calcification rate in these organisms decreases below a threshold value of approximately 250 μmol kg⁻¹ [CO₃²⁻], under culture conditions representative for the surface ocean. This threshold value is a little higher than the typical [CO₃²⁻] of today's surface ocean. In order to translate this into a threshold value for the deep ocean, we have to take into account that the surface ocean has a much higher [CO₃²⁻] than the deep ocean. The biogenic saturation expressed in terms of the deep ocean [CO₃²⁻] was therefore taken as 90 μmol kg⁻¹, a little higher than the typical [CO₃²⁻] of today's deep ocean. Although this value is a rough estimate, it is not of major importance for our purpose. It was already stated in 12 that variations in the biogenic saturation have a minor influence on the calculated results. Varying the biogenic saturation between 70 and 110 μmol kg⁻¹, yields a deep ocean [CO₃²⁻] between 73 and 82 μmol kg⁻¹.

[57] As noted in 8, the biogenic saturation reflects the response of the calcification rate to changing saturation state of a calcifying species on the organisms level. The ecological success of calcifying groups, i.e., their abundance and thus total production is reflected in F_p^m.

4.4. Biogenic, Neritic Production

[58] As said earlier, CaCO₃ production in shallow-water environments is assumed to be biologically controlled or mediated. In the following, we justify the mathematical expression used to describe the neritic production in the model (6). In contrast to the pelagic realm, many investigators have shown that precipitation rates in neritic organisms such as individual corals or in experimental coral reefs appear to increase over a wide range of increasing saturation state rather than being constant above a certain level (see summary in Leclercq et al. [2000]). One exception to this is the work by Gattuso et al. [1998] on the coral Stylophora pistillata in which the calcification rate approached a saturation level above Ω_arag ≃ 3. It is noted, however, that in this study [Ca²⁺] was manipulated and not [CO₃²⁻].

[59] The relationship between calcification rate, R, in corals or coral reef communities and the saturation state, Ω, can often be expressed by an equation used to describe precipitation rates of inorganic CaCO₃ in the laboratory:

where k is a rate constant and η is the order of reaction. While some studies found a reaction order of η = 1 (i.e., a linear relationship [cf. Leclercq et al., 2000], Borowitzka [1981] found a more parabolic relationship in coralline red algae. Langdon et al. [2000] also preferred a linear dependence on [CO₃²⁻] to describe calcification rates of the BIOSPHERE-2 coral reef mesocosm. Although a good first-order approximation, their data (see their Figure 5) also shows a second-order effect which indicates a rather parabolic relationship between R and [CO₃²⁻] (i.e., η > 1). Finally, Opdyke and Wilkinson [1993] examined accumulation rates in Holocene tropical and temperate shallow marine platforms and found a good fit to the data at latitudes less than 30° for η = 1.7 (aragonite, 25°C). We feel that the relationship found in the latter study (η ∼ 2) is most appropriate for our modeling of modern neritic production in the ocean because (1) in addition to reefs, also carbonate mud, sand, and ooids were considered and (2) a geologically significant period was covered. We do not claim, however, that this relationship is a universal remedy.

[60] In summary, we followed Opdyke and Wilkinson [1993] but used a value of 2 for the rate order η instead of 1.7 in order to maintain analytic tractability (for a model approach using η = 1.7, see Caldeira and Rampino [1993]).

[61] The neritic saturation, c_n, i.e., the deep ocean concentration that corresponds to the surface aragonite saturation was set to 32 μmol kg⁻¹ or c_n = 0.62 (see 4). Assuming another value for c_n would shift the lowest possible concentration of the Neritan Ocean (Figure 7) up and down but does in no way change our conclusions. Variation of c_n has no effect on the model outcome presented in Figure 8 because the neritic production was set at a fixed ratio to the total production.

4.5. Biological Pump, Organic Carbon Burial, and Rain Ratio

[62] In today's ocean, the biological pump produces vertical gradients in ΣCO₂ and TA by extracting organic carbon and CaCO₃ from the surface ocean. This process—in combination with ocean circulation—leads to vertical as well as horizontal gradients of [CO₃²⁻]. It is important to note, however, that these processes do not lead to a change of the inventory as they merely affect the distribution of [CO₃²⁻] but not the budget. On the contrary, if e.g., changes in the burial of organic carbon (C_org) in sediments would occur, the ΣCO₂ inventory would change. Is this likely and if yes, is it of significance for the current model?

[63] Considering the long-term carbon cycle, Berner and Caldeira [1997] have pointed out that the fluxes between the combined surficial reservoir (ocean, atmosphere, biota, and soils) and the carbonate rock reservoir must be closely balanced. Otherwise, untenable changes of atmospheric CO₂ would occur. If this also holds true for the input and burial of C_org in the ocean, these fluxes can be ignored because they are in steady-state on the time scale of 10 ky considered here. If, however, there are imbalances in the C_org input and burial, their impact on the steady-state deep sea [CO₃²⁻] may be estimated as follows. The C_org burial is approximately 1/4 of the CaCO₃ burial [Berner, 1991]. Using 12 × 10¹² mol C y⁻¹ = 0.144 Gt C y⁻¹ as CaCO₃ burial flux [Archer et al., 1998], the C_org burial is 0.036 Gt C y⁻¹ or 360 Gt C per 10 ky. Thus if the C_org burial would cease entirely or double for a period of 10 ky (these are unrealistically large changes), ΣCO₂ in the ocean would change by ∼1% and deep [CO₃²⁻] by ∼10 μmol kg⁻¹. It therefore appears that changes in organic burial—although they need to be quite large—could affect the deep sea [CO₃²⁻] as calculated in our model. However, we will show that this is incorrect because our consideration is yet incomplete.

[64] What would happen is the following. Say the C_org burial suddenly rises, then ΣCO₂ drops and [CO₃²⁻] increases. This, however, leads to increased burial of CaCO₃ because now the riverine CaCO₃ flux is not balanced! Owing to the excess burial, oceanic ΣCO₂ and TA decrease in a ratio 1:2 until the old [CO₃²⁻] is restored and CaCO₃ weathering again equals burial. The opposite happens if the C_org burial is initially reduced. Thus calcite compensation restores the old steady-state with respect to CaCO₃ despite changes in C_org input or burial (compensation e-folding time is ∼6,000 y, see Appendix B). Only, the new steady-state has a different ΣCO₂ and TA than before. Calculating the overall carbonate chemistry changes, including C_org burial change and CaCO₃ compensation, shows that the overall ratio of change in ΣCO₂ and TA is roughly 1:1. This has a small effect on atmospheric CO₂. In summary, the biological pump and organic carbon burial can be ignored in the current model. As a corollary, a global average value of the observed [CO₃²⁻] in the deep ocean at steady-sate should be well described by the model without considering organic carbon pump or burial. This was shown in 12.

[65] Another parameter that may be relevant to the model outcome is the rain ratio, the ratio of organic carbon to inorganic carbon (C_org/CaCO₃) of the biogenic rain to the sediments. It has been suggested that an increased rain ratio and increased respiration of organic carbon in the sediments, e.g., during glacials, may lead to dissolution of CaCO₃ well above the saturation horizon [Archer and Maier-Reimer, 1994]. This calls upon a strong decoupling of the saturation horizon and the lysocline. The deep ocean carbonate ion concentration would then no longer be coupled in a simple way to the weathering and burial of CaCO₃. However, the following arguments make a strong case against it: (1) the observed correspondence of today's lysocline depth with the depth of calcite saturation, (2) the similar depth of the CCD during glacial times and today [Catubig et al., 1998; Archer et al., 2000], (3) evidence from modeling results for the glacial ocean [Sigman and Boyle, 2000; Jansen, 2001], and (4) the most recent reconstructions of glacial deep sea [CO₃²⁻] [Broecker and Clark, 2001; Anderson and Archer, 2002].

5.1. Biogenic Calcification and Fossil Fuel Neutralization

[67] Mankind will presumably have almost tripled the natural concentration of CO₂ in the atmosphere by the end of this century. The ultimate fate of most of this anthropogenic CO₂ is to end up as dissolved HCO₃⁻ in the ocean:

The ocean is currently taking up about one third of the annually produced manmade CO₂ which is transported to the deep sea by means of vertical mixing and advection by the thermohaline circulation. Because CO₂ is an acid, the pH of the ocean is currently dropping and will continue to do so. The seawater is getting more corrosive and the excess CO₂ will react with CaCO₃ in the sediments:

This process is part of what is called fossil fuel neutralization in the literature [Broecker and Takahashi, 1977; Sundquist, 1986; Archer et al., 1998].

[68] As a result of the fossil fuel-carbon uptake, the deep sea carbonate ion concentration is expected to decrease strongly during this process and the saturation horizon will significantly shallow from today's depth of about 4 km to perhaps less than 500 m in the year 3500 [Archer et al., 1998]. Consequently, there will be an imbalance between input and output because the burial will be greatly reduced as it will only occur at very shallow depth. (A potential increase in weathering at higher pCO₂ is ignored here as it will not affect our main result, see below). Once the fossil fuel resources have been used up, taken up by the ocean, and have reacted with sediment CaCO₃, a new steady-state between weathering and burial will start to be restored by the excess influx which tends to increase [CO₃²⁻] and therefore to deepen the saturation horizon. The latter process is a general feedback and is called calcite compensation [Broecker and Peng, 1987] and its timescale has been estimated as 6,000 to 14,000 y [Sundquist, 1990; Archer et al., 1998].

[69] The question to be addressed in the following is: What is the role of the pelagic biogenic calcite production during the recovery of the CaCO₃ saturation state from fossil fuel neutralization? It has been demonstrated that coccolithophores and foraminifera show diminished calcite precipitation under conditions of high CO₂ and low [CO₃²⁻] [Riebesell et al., 2000; Zondervan et al., 2001; Bijma et al., 1999; Wolf-Gladrow et al., 1999]. We will show that this effect will accelerate the restoring of the steady-state because it provides a negative feedback to a reduction of the saturation state of the ocean on this time scale. (Note, however, that on long time scales the saturation state is stabilized and assuming a generally reduced marine calcification during periods of high pCO₂ such as the Cretaceous is a misconception, 24).

[70] The effect works as follows (consider Figure 4b): Initially, c will drop and so does the biogenic output flux. Now the subsequent increase of the ocean's inventory of Ca²⁺ and CO₃²⁻ is given by the riverine flux minus burial, where the latter is given by the portion of the biogenic production not being dissolved (equation (10)). That part of the biogenic output produced over undersaturated bottom water will completely redissolve and thus has no effect on the flux balance. On the other hand, that part produced over supersaturated bottom water will be buried and this is less at reduced production. The result is that in addition to reduced burial due to the lower saturation state, the burial is even more reduced at diminished biogenic calcification and [CO₃²⁻] will increase more rapidly.

[71] The model was used to simulate this recovery from fossil fuel neutralization (Figure 11) assuming constant (dashed line) and reduced biogenic calcification (solid line) as a response to high pCO₂ and low [CO₃²⁻]. Because in this case a transient process is to be modeled, no steady-state solution of the model is required but rather the integration of equation (3) for [CO₃²⁻] forward in time:

where F_in and F_out are the input and output fluxes now expressed in units of mol C yr⁻¹ as CaCO₃. The factor α ≃ 2 takes into account the buffer capacity of seawater, as the dissolution or precipitation of one mole CaCO₃ does only lead to a change of [CO₃²⁻] in seawater by roughly half a mole; M_oc = 1.4 × 10²¹ kg is the mass of the ocean.

[72] The calcite compensation time scale of the simple model after which a perturbation in [CO₃²⁻] has dropped to 37% of its initial value (e-folding time) is ∼6,000 y under constant biogenic calcification (see Appendix B). The time scale is in agreement with those obtained from atmosphere-ocean-sediment box models (6,000 to 14,000 y [Sundquist, 1990]) and coupled ocean circulation-carbon cycle models (∼8,000 y [Archer et al., 1998]). This result is not surprising because the time scale is essentially given by the time required to refill the [CO₃²⁻] anomaly by the excess weathering flux over burial which depends little on model complexity. The interesting result is that the compensation time scale is about 1,000 y shorter if the biology responds to the initially reduced saturation state by reduced calcite production (Figure 11). This is an important negative feedback that speeds up the restoring of the CaCO₃ saturation state of the ocean after a perturbation.

[73] In our consideration we have ignored increases in weathering at elevated pCO₂ as it would affect the recovery from fossil fuel neutralization equally in the two cases—with or without a response of the biology. An unknown variable in our calculation is a potential increase in coccolithophorid blooms due to expected higher stratification in the future which would tend to counteract the reduction of calcification on the organism level.

5.2. Glacial Changes in Rain Ratio

[74] One of the most important topics in paleo-climate research is the glacial-interglacial change in atmospheric CO₂ (for recent reviews see Sigman and Boyle [2000], Archer et al. [2000]). It is clear that the deep ocean is involved in those cycles because of its huge dissolved CO₂ reservoir and its mixing time of ∼1,000 y during which the ocean and atmosphere carbon reservoirs equilibrate. One mechanism that has frequently been called upon to lower atmospheric CO₂ during glacials are changes in the so-called rain ratio (see above reviews for references). The rain ratio is the export ratio of organic carbon to calcium carbonate carbon (C_org/CaCO₃) from the surface (often taken at ∼100 m) to the deep ocean and estimates of this parameter range from 4:1 to 17:1 [Broecker and Peng, 1982; Sarmiento et al., 2002]. (Note that because most organic carbon is remineralized in the top 1000 m, the rain ratio changes significantly with depth). A glacial increase in this ratio (e.g., through a decrease of CaCO₃ export) may have deepened the saturation horizon, increased the deep sea carbonate ion concentration, and lowered atmospheric CO₂. The magnitude of this change can be estimated using our simple model. It is noted that the aim of the current section is mainly to present an easily accessible approach to the problem. A more detailed approach can be found in Sigman et al. [1998].

[75] There is compelling evidence that, as in today's ocean, the glacial calcite lysocline depth corresponded to the calcite saturation depth (see 20). If this is accepted, then the deepening of the glacial saturation horizon was probably between 0 and 1 km because this is the estimated range of the deepening of the glacial lysocline from observations [Sigman and Boyle, 2000; Archer et al., 2000]. The model can then be used to calculate the corresponding change in the biogenic flux and deep sea [CO₃²⁻]. The result is shown in Figure 12 which is similar to Figure 7 but with different units of c and including the saturation depth and atmospheric pCO₂. The decrease in atmospheric pCO₂ in equilibrium with the surface ocean at T = 20°C and S = 35 can be estimated from the change of ΣCO₂ and TA in a ratio 1:2 given by the prescribed deepening of the saturation horizon and increase of deep sea [CO₃²⁻] at T = 2°C and S = 35. This gives a sensitivity of −20 μatm in pCO₂ per 17 μmol kg⁻¹ increase in [CO₃²⁻] or a 1 km drop of the SH. For comparison, Sigman and Boyle [2000] give a sensitivity of −25 μatm in pCO₂ per 1 km drop of the SH. The latter sensitivity is adopted in Figure 12 and shows that if glacial saturation horizon and lysocline were tightly coupled, then atmospheric pCO₂ dropped by less than 15 μatm due to this mechanism.

5.3. Biogenic Calcification and Periods of High pCO₂ Such as the Cretaceous

[76] After Riebesell et al. [2000] had published evidence for reduced calcification in coccolithophorids at elevated pCO₂, confusion has occasionally arisen as to why then we would observe massive coccolith formations during geologic eras such as the Cretaceous during which pCO₂ was probably high. This confusion is likely due to a misconception of time scales and the neglect of the mechanism described in detail in 22: Calcite compensation.

[77] The biogenic response and its effect on atmospheric CO₂ described in Riebesell et al. [2000] and Zondervan et al. [2001] refers to a time frame of the coming centuries during which the CaCO₃ saturation state of the ocean will temporarily drop. However, as soon as millennia are considered, the saturation state will recover due to calcite compensation. If then the geological past over millions of years is considered, there is no reason to assume that the saturation state was low for intervals of this time period exceeding ∼10 ky. Rather, the feedback between biogenic production and calcite dissolution, explicitly discussed and named the Cretan Ocean in 13, will have maintained a fairly constant CaCO₃ saturation state, at least throughout the Cretaceous and Cenozoic. In regard to the seawater carbonate chemistry during the Cretaceous this means that even very high pCO₂ was likely accompanied by a saturation state similar to today, while ΣCO₂, TA, and [Ca²⁺] in Cretaceous Oceans were probably different from today [Zeebe, 2001; Tyrrell and Zeebe, submitted manuscript, 2003].