FRED T. MACKENZIE: Research Models: SOCM

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Model Methodology:

The Shallow–water Ocean Carbonate Model (SOCM) is a process–driven biogeochemical box model representative of the global shallow-water ocean environment including coastal zones, reefs, banks and continental shelves (28.3 x 106 km2) (Milliman, 1974). Details and some of the earlier results of the model are given in Andersson (ms, 2003), Andersson and others (2003), Andersson and Mackenzie (2004) and Mackenzie and others (2004a, 2004b). The SOCM consists of two different major domains, a surface water domain and a pore water–sediment domain (fig. 1). The surface water domain contains the reservoirs of dissolved inorganic carbon (DIC) and organic matter [dissolved organic carbon (DOC), organic detritus and living biota]. The pore water–sediment domain contains the reservoirs of organic matter, refractive particulate inorganic carbon (originating from continental erosion), in situ produced calcite, aragonite, 15 mol percent magnesian calcite representative of magnesian calcite compositions, and a pore water reservoir of average composition based on data from the Bahamas and elsewhere (Thorstenson and Mackenzie, 1974; Morse and others, 1985; Morse and Mackenzie, 1990). Differential equations are expressed in the general form (table 1, where fluxes F are denoted CF):

where C is the mass of carbon in reservoir i, Fij is the flux of carbon from reservoir i to reservoir j, and Fji is the flux of carbon from reservoir j to reservoir i. The fluxes include the physical transport as well as chemical production or consumption terms. The most commonly adopted flux between reservoirs is described by equations of first order kinetics:

where Fij is the flux of carbon from reservoir i to reservoir j, which is linearly dependent on the mass of carbon in reservoirCi, and kij is the rate constant. In the present model, kij was defined based on the initial reservoir mass and the initial flux adopted at the initial quasi–steady state in the year 1700 (fig. 1), that is:

Fig. 1. Schematic of the Shallow–water Ocean Carbonate Model (SOCM) and pre–industrial carbon estimates adopted in the current simulations (Andersson, ms, 2003). SOCM consists of two major domains representing the water column (surface water and organic matter) and the pore water–sediment system (pore water, sediment organic matter, river–derived particulate inorganic carbon (PIC), calcite, aragonite, and 15 mol % magnesian calcite). Reservoir masses (shown in italics) are in 1012 mol C. Arrows denote carbon fluxes between reservoirs in 1012 mol C yr–1 (shown inside parentheses). For two–way arrows the direction of the net flux is shown next to the flux estimate. The dashed lines indicate carbon flux owing to CaCO3 production (eq 16). 2 mol of C are removed from the water column for every mol of CaCO3 precipitated, 1 mol of C is released back to the water column as CO2 from which 0.4 mol C remains in the surface water reservoir and 0.6 mol C evades to the atmosphere.

Essential Mathematical Relationships of the Model

Biogenic calcification.— Biogenic calcification is related to the concentration of total dissolved inorganic carbon (DIC) in surface water, carbonate saturation state, and sea surface temperature. The dependence of marine primary production on DIC content can be viewed as a first order relationship assuming that marine primary production is directly related to this parameter (Riebesell and others, 1993; Raven, 1993, 1997). Although this assumption is contentious, the overall increase in DIC relative to its initial concentration due to increased atmospheric CO2 is small and has only a minor effect on the rate of calcification in the current model simulations; hence, the first-order relationship provides a conservative estimate of the effect of decreasing carbonate saturation state on the rate of calcification. In model simulations, dependence of biogenic calcification on carbonate saturation state was expressed in a first case as a linear relationship derived from multiple experiments on corals and coralline algae (Gattuso and others, 1999):

and in a second case by a curvilinear relationship based on the experimental results for the coral Stylophora pistillata (Gattuso and others, 1998; Leclerq and others, 2002):

where R(omega) is the relative rate of calcification (approximately equal to 100 at the initial conditions) and (Omega) is the surface seawater saturation state with respect to aragonite. (Omega) is defined in equation (24). It should be pointed out that the relationship derived for Stylophora pistillata may not be fully representative of the response of this species to increasing CO2 and subsequent changes in seawater carbonate chemistry because the saturation state (Omega) was manipulated by altering the calcium concentration rather than the carbonate chemistry. However, we chose to investigate this relationship in order to cover the full range of possible effects on biogenic calcification arising from decreasing seawater carbonate saturation state.

The dependence of biogenic calcification on temperature is also given by two different relationships in SOCM. In the first case, a negative parabolic relationship between calcification rate and temperature was assumed based on experimental results for the coral Pocillopora damicornis (Clausen and Roth, 1975), and the coralline alga Porolithon gardineri (Agegian, ms, 1985; Mackenzie and Agegian, 1989). Although the latter was based on extension rates rather than actual calcification rates, the relationship between temperature and calcification rate or extension rate from the two studies are very similar when normalized to the maximum rate of calcification and maximum extension rate. The relationship adopted that describes the rate of calcification as a function of temperature is:

where RT is the relative rate of calcification expressed as a percentage of the rate at the initial temperature in the year 1700 and (Delta)T is the temperature change in degrees Celsius. A recent study of two species of scleractinian corals shows a similar trend of calcification rate versus temperature (Marshall and Clode, 2004), although the parabolic trend of this study is more convex than that used in SOCM, indicating that changes in temperature could have an even larger effect on the rate of calcification than our model calculations show. It also should be emphasized that the calculated rates of calcification are positive even though the adopted relationship is termed negative parabolic. In the second case, a positive linear relationship was obtained from the observed rates of calcification of multiple coral colonies from the Great Barrier Reef, Hawaii and Thailand (Grigg, 1982, 1997; Scoffin and others, 1992; Lough and Barnes, 2000):

There are some potential problems with applying this relationship, which are discussed in the Effect of surface water temperature section. The overall equation describing the flux of biogenic carbonate production (F) is:

where F is the flux of carbon in mol yr–1, k is the rate constant based on the initial flux and the initial reservoir size (see eq 3), CDIC is the total mass of DIC in the surface water in mol C, and R(Delta) and RT are the relative rates of calcification as a function of carbonate saturation state and temperature, as given in equations (4) to (7).

Inorganic dissolution and precipitation.— Inorganic dissolution (Rd) and precipitation (Rp) of carbonate minerals within the pore water–sediment system are described by kinetic rate equations of the general form:

and

where kd is the rate constant for dissolution and kp is the rate constant for precipitation, (Omega) the pore water carbonate saturation state, and nd and np the reaction order for dissolution and precipitation, respectively (table 2). The constant parameters were obtained from the experimental results of Zhong and Mucci (1989) for precipitation, and Walter and Morse (1985) for dissolution. The reaction rates were calculated based on the total mass of calcium carbonate in the sediments by converting the calculated rates per unit area to mass per unit time using average specific surface areas (0.1-0.5 m2 g–1) and the ratio between reactive surface area and total area (0.003-0.66) for typical shallow-water biogenic sediment components (Walter and Morse, 1984, 1985). Inhibition by dissolved phosphate (10 µmol L–1) and dissolved organic matter (10 mg kg–1) (Morse and others, 1985) was also taken into account following the work of Berner and others (1978) by multiplying the rate equations by inhibition factors corresponding to these concentrations (table 1) (Andersson, ms, 2003). Because pore water chemistry is significantly heterogeneous spatially and the reaction kinetics of carbonate minerals in the natural environment are poorly known, sensitivity analyses (the Sensitivity Analyses section) were used to evaluate if the above assumptions were realistic relative to the global estimates of total calcium carbonate production and dissolution.

Air–sea CO2 exchange.— For a coastal ocean water reservoir, as shown in figure 1, the balance of dissolved inorganic carbon (DIC) is the difference between its inputs and outputs as fluxes Fx1yr, where fluxes are in units of mol C per year:

The organic carbon balance is expressed, similarly to that of DIC:

The sum of (11) and (12), with the notation of (Delta)DIC = [DICeq] –[DIC0], is:

The individual terms in equations (11) to (13) and their initial values at the end of pre-industrial time, taken as the year 1700 (Andersson, ms, 2003), are (fig. 1):

• [DICeq] is the DIC concentration at equilibrium with atmospheric CO2 after all the other input and removal fluxes have been accounted for. The value of DICeq depends on (1) the atmospheric CO2 concentration and (2) a change in total alkalinity of seawater due to the net input of alkalinity via rivers, runoff and upwelling, and precipitation and dissolution of CaCO3. [DIC0] is the initial DIC concentration (2000 µmol kg–1).
  
• FDIC inflow is the DIC input from land and by upwelling from deeper ocean to the coastal ocean (1536.2 x 1012 mol C yr–1) and FDIC outflow is its output by water exchange with the open ocean (1503 x 1012 mol C yr–1); FCorg inflow (26 + 8 = 34 x 1012 mol C yr–1) and FCorg outflow (18 x 1012 mol C yr–1) are the inflows and outflows, respectively, of organic carbon that consists of dissolved organic carbon (DOC), living biota, and particulate detritus; FCorg S is the permanent burial and net organic carbon storage rate in sediments, taken here as 9 x 1012 mol C yr–1 (see Mackenzie and others, 2004a).
  
• FCaCO3 ppt is precipitation of CaCO3 from biological and/or inorganic processes (24.5 x 1012 mol C yr–1);
  
• FCaCO3 diss is dissolution of CaCO3 minerals (6 x 1012 mol C yr–1);
  
• FGPP is the consumption of CO2 in gross primary production (600 x 1012 mol C yr–1);
  
• FR is the production of CO2 by autotrophic and heterotrophic respiration of organic carbon that includes Corg from external inputs and from in situ primary production (607 x 1012 mol C yr–1);
  
• FCO2 is the air-sea CO2 flux, taken as negative for a flow from seawater to the atmosphere (that is, coastal water is a CO2 source) and positive for transfer from the atmosphere (that is, coastal water is a CO2 sink) (–21.7 x 1012 mol C yr–1).
  

The CO2 air-sea flux (FCO2) in equation (13) is negative when CO2 is emitted from coastal water, making the coastal water a source of CO2 to the atmosphere, and it is positive when the coastal zone is a CO2 sink. With this notation, equation (13) can be written in the following form:

Because the surface water is assumed to attain equilibrium with the atmosphere instantaneously, (Delta)DIC is effectively the time rate of change of total dissolved inorganic carbon content (CDIC) of the surface water, dCDIC/dt, as a function of changes in the inorganic carbon content of the atmosphere (CATM). The relationship is essentially a modification of the Revelle-Munk function and can be derived from the following expression:

The Revelle constant (D) was taken as 4, and the factor R0 as 9. The latter value indicates that the buffer mechanism of seawater causes a fractional rise of CO2 in the surface water that is one ninth of the increase in the atmosphere (Bacastow and Keeling, 1973; Revelle and Munk, 1977; Ver, ms, 1998).

At the onset of the simulation, the shallow-water ocean environment was set to be a net source of CO2 to the atmosphere of –21.7 x 1012 mol C yr–1 (fig. 1) owing to the assumption that this region was net heterotrophic at this time by –7 x 1012 mol C yr–1 (Smith and Mackenzie, 1987; Wollast and Mackenzie, 1989; Smith and Hollibaugh, 1993; Mackenzie and others, 1998; Mackenzie and others, 2004b) and because of calcium carbonate production of 24.5 x 1012 mol C yr–1 (Milliman, 1993; Milliman and Droxler, 1996), resulting in a release of –14.7 x 1012 mol C yr–1 to the atmosphere assuming that 0.6 mol of CO2 is released to the atmosphere for every mol CaCO3 precipitated (Smith, 1985; Ware and others, 1992; Frankignoulle and others, 1994; Lerman and Mackenzie, 2004, 2005). It is customary to write the precipitation reaction of CaCO3 in seawater or fresh water as:

Thus for every two moles of HCO3– removed from the aqueous solution, one mole of CaCO3 is precipitated and one mole of CO2 is released back to the solution and eventually escapes to the atmosphere as gaseous CO2. However, as Smith (1985) has shown, the stoichiometry of this reaction is only correct for a relatively low pH fresh water solution but not for seawater. Surface seawater is a slightly basic solution with a pH of about 8.2. It has a relatively high carbonate buffer capacity and seawater pH decreases only slightly in response to CaCO3 precipitation. The CO2 that is formed as a result of the precipitation of CaCO3 reacts with the water and leads to a reapportionment of the H+, HCO3–, and CO32– ions and H2CO3 (CO2aq) in the seawater. Because of this, at 25°C and a pCO2 of 10–3.5 atm, the CO2 gas loss from the seawater is only about 60 percent as large as the dissolved inorganic carbon incorporated into the solid phase CaCO3. The remaining 40 percent of the carbon enters the DIC pool of seawater. Smith (1985) also showed that the released CO2 is probably incorporated into organic matter so that the net reaction for the precipitation of CaCO3 and the fate of the carbon that enters the DIC pool of seawater is:

Frankignoulle and others (1994) and Lerman and Mackenzie (2004, 2005) subsequently showed that the amount of the gaseous CO2 that escapes seawater because of the precipitation of CaCO3 is variable and dependent on several environmental factors including temperature, salinity, atmospheric CO2 concentration, DIC speciation, and the rate at which the CaCO3 precipitates from the water. The ratio of CO2 released from seawater of normal salinity to CaCO3 removed by precipitation is 0.51 to 0.66 mol/mol, between 15° and 25°C, and the atmospheric CO2 concentration between the pre-industrial 280 ppmv and the early 21st century 375 ppmv (Lerman and Mackenzie, 2005).

Based on the above considerations, our model partitions the carbon released to seawater upon the precipitation of CaCO3 as 60 percent gaseous release to the atmosphere and 40 percent incorporation into the DIC pool of seawater, which is a boundary condition of the model and the CO2 flux equation at the initial quasi-steady state (fig. 1). This assumption implies that at steady state for every 2 mol HCO3– brought in via rivers and upwelling and every mol CaCO3 precipitated, 0.6 mol of C is released to the atmosphere and 0.4 mol of C is fixed into organic matter or exported to the open ocean. Although we recognize that the partitioning of CO2 released owing to calcification varies as a function of the previously described parameters, we did not vary this parameter throughout the model simulation runs. Taking into account the partitioning of CO2 from CaCO3 production (fig. 1), as discussed above, and the resulting change in DIC from equation (15), the final CO2 flux relationship that is given in equation (14) can be written as:

where NEC is the net ecosystem calcification (CaCO3 production flux – dissolution flux) and NEM* is the net ecosystem metabolism which is defined as (Andersson and Mackenzie, 2004; Mackenzie and others, 2004b):

At the onset of simulation in the year 1700, equation (18) yields (in 1012 mol C yr–1):

Bearing in mind the uncertainties of the flux estimates that are given in the literature and in figure 1, the calculated CO2 emission of –21.7 x 1012 mol C yr–1 is in very good agreement with the result of –21 ± 5 x 1012 mol C yr–1, obtained from the CO2 air–sea transfer model of Lerman and Mackenzie (2005) over a range of temperature and other environmental conditions that takes into account inflows and outflows of DIC and reactive Corg, as well as the formation and net storage of CaCO3 and Corg in sediments.

TABLE 1 SOCM mass balance and flux equations. Reservoirs are annotated Ci, where Ci refers to the total mass of carbon in reservoir i. Fluxes are annotated CFij, where CFij refers to the flux of carbon between reservoirs i and j. Rate constants are annotated kCij. A two-way arrow indicates that the flux can be either positive or negative.

TABLE 2 Adopted constants for inorganic CaCO3 precipitation and dissolution rates (R)

Example Paper Abstract: Coastal Ocean and Carbonate Systems in the High CO2 World of the Anthropocene

Andreas J. Andersson*, Fred T. Mackenzie* and Abraham Lerman**
American Journal of Science, Vol. 305, November 2005, P.875-918

The behavior of the ocean carbon cycle has been, and will continue to be, modified by the increase in atmospheric CO2 due to fossil fuel combustion and land-use emissions of this gas. The consequences of a high-CO2 world and increasing riverine transport of organic matter and nutrients arising from human activities were investigated by means of two biogeochemical box models. Model numerical simulations ranging from the year 1700 to 2300 show that the global coastal ocean changes from a net source to a net sink of atmospheric CO2 over time; in the 18th and 19th centuries, the direction of the CO2 flux was from coastal surface waters to the atmosphere, whereas at present or in the near future the net CO2 flux is into coastal surface waters. These results agree well with recent syntheses of measurements of air-sea CO2 exchange fluxes from various coastal ocean environments. The model calculations also show that coastal ocean surface water carbonate saturation state would decrease 46 percent by the year 2100 and 73 percent by 2300. Observational evidence from the Pacific and Atlantic Oceans shows that the carbonate saturation state of surface ocean waters has already declined during recent decades. For atolls and other semi-enclosed carbonate systems, the rate of decline depends strongly on the residence time of the water in the system. Based on the experimentally observed positive relationship between saturation state and calcification rate for many calcifying organisms, biogenic production of CaCO3 may decrease by 42 percent by the year 2100 and by 85 to 90 percent by 2300 relative to its value of about 24 x 1012 moles C/yr in the year 2000. If the predicted change in carbonate production were to occur along with rising temperatures, it would make it difficult for coral reef and other carbonate systems, to exist as we know them now into future centuries. Because high-latitude, cold-water carbonates presently occur in waters closer to saturation with respect to carbonate minerals than the more strongly supersaturated waters of the lower latitudes, it might be anticipated that the cool-water carbonate systems might feel the effects of rising atmospheric CO2 (and temperature) before those at lower latitudes. In addition, modeling results show that the carbonate saturation state of coastal sediment pore water will decrease in the future owing to a decreasing pore water pH and increasing CO2 concentrations attributable to greater deposition and remineralization of land-derived and in situ produced organic matter in sediments. The lowered carbonate saturation state drives selective dissolution of metastable carbonate minerals while a metastable equilibrium is maintained between the pore water and the most soluble carbonate phase present in the sediments. In the future, the average composition of carbonate sediments and cements may change as the more soluble Mg-calcites and aragonite are preferentially dissolved and phases of lower solubility, such as calcites with lower magnesium content, increase in percentage abundance in the sediments.