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3. Model runs

Since the injection simulations are based on the abiotic DIC runs, modelers must have read the related Abiotic HOWTO, also on this Web site. In the rest of this Injection-HOWTO, we describe only the sequestration of CO2 within the ocean and its effects on atmospheric CO2 and oceanic DIC.

3.1 Injection sites

Seven injection sites have been designated by GOSAC participants:

  1. Bay of Biscay
  2. New York
  3. Rio de Janeiro
  4. San Francisco
  5. Tokyo
  6. Jakarta
  7. Bombay

Exact locations of these sites are shown in Fig. 1. They are also listed in the ASCII file sitepos.dat. All sites are located along coastlines near populated areas where large amounts of CO2 are emitted to the atmosphere. Only two of these sites are in the Southern Hemisphere. Protocols call for each model to make injections at all sites simultaneously. Models will make separate simulations for up to three injection depths: 800 m, 1500 m, 3000 m.

To determine the 7 grid cells in your model where CO2 is to be injected, we use a simple algorithm (see initgos.f) to find each site's nearest grid cell that has a water column of at least 3000 m and is within 1000 km of the nearest coastline. These constraints are considered, roughly, as the current technical and economical limits of feasibility.

3.2 Tracers

Ten tracers are necessary to perform an injection simulation. Each of the ten tracers is carried simply as total dissolved inorganic carbon (DIC). These oceanic tracers exchange CO2 with three different atmospheric boxes, all of which are defined in section Three Atmospheres. The ten oceanic tracers are defined as follows:

Tracer 1

Control scenario: no effect of the anthropogenic perturbation on atmospheric CO2 is included. This tracer is used to remove the drift of the model.

Tracer 2

Future scenario: The effect of the anthropogenic perturbation on atmospheric CO2 is included, as is the resulting invasion of anthropogenic CO2 into the ocean; however, no injection is performed. Reference to this tracer allows us to determine, by difference, the total effect of ocean injection on atmospheric pCO2 and oceanic DIC.

Tracer 3

Injection scenario (``Permanent sequestration''): Like Tracer 2 but in addition it includes the effect due to the reduction of atmospheric CO2 caused by the diversion of fossil carbon into the deep ocean (sequestration) instead of the atmosphere. However, Tracer 3 ignores the impact of direct injection of CO2 within the deep ocean on the oceanic DIC. Tracer 3 differs from Tracer 2 when atmospheric CO2 is computed (i.e., in the Emission case E1500), but not when atmospheric CO2 is prescribed (scenarios C800, C1500, and C3000). For the Emission case, Tracer 3 is used to compute atmospheric CO2, air-sea CO2 fluxes, and the distribution of oceanic DIC when CO2 sequestration is made in an ideal permanent reservoir that allows no leakage back to the atmosphere.

Tracers 4-10

These seven tracers simulate, individually for each injection site, the effects of injected CO2 on oceanic DIC. The impact of CO2 sequestration on atmospheric pCO2 is also considered, just as with Tracer 3. Tracers 4-10 are summed along with Tracer 3 to determine the loss of sequestered CO2 to the atmosphere and to evaluate the direct effect of the injection on the DIC distribution. These seven tracers are necessary to determine the efficiency of each site in retaining injected CO2.

3.3 Conservation equations

Each of the ten tracers is carried as dissolved inorganic carbon (DIC) and has the following conservation equation

(1)   d[DIC]/dt = L([DIC]) + Jv + J + Ji    


The source-sink terms Jv and J are added only as surface boundary conditions. That is, they are equal to zero in all subsurface layers. These two source-sink terms are equivalent to the corresponding fluxes (described in the Abiotic-HOWTO) divided by the surface layer thickness dz1.

    Jv = Fv/dz1

    J = F/dz1

The virtual flux Fv is described in the Abiotic-HOWTO (Section 2.2).

For the last seven tracers (4-10), which are used to study the injection efficiency, each source term Ji is added only to the grid cell of the model located nearest the corresponding injection site. Conversely, Ji is set to zero for the first three tracers. The Ji source is equivalent to the quantity of CO2 injected at each site (Q) divided by the volume dV of the corresponding grid cell of the model.

    Ji = Q/dV

3.4 Air-sea gas exchange fluxes (F)

For simulations of CO2 sequestration, air-sea fluxes F for each tracer must be modeled according the OCMIP-2 guidelines described in the related Abiotic-HOWTO,

(2)   F = Kw (Csat - Csurf)


(3)   Csat = alphaC * pCO2atm * P/Po


The three terms P, Kw, and alphaC are identical for all the ten tracers. They are described in the Abiotic-HOWTO. Conversely, Csurf depends on which of the 10 tracers is considered. Furthermore, pCO2atm depends on which oceanic tracer is considered for the Emissions run (E1500) but not for the other simulations. The dependencies of both terms are described below.

3.5 Oceanic Component

The oceanic term Csurf is not carried as a tracer. Thus to determine gas exchange, it must be computed each timestep for each of the ten tracers.

Csurf is the surface [CO2] concentration [mol/m^3], which is computed from the model's surface [DIC], T, S, and [Alk] through the equations and constants found in the subroutine co2calc.f. We inject anthropogenic carbon as CO2, which does not affect Alkalinity. Thus Alkalinity is identical for all ten tracers. It is determined as a normalized linear function of salinity:

(4)    [Alk] = Alkbar * S/Sbar

where [Alkbar] is 2310 microeq/kg and Sbar is the model's annual mean surface salinity, integrated globally (horizontally).

IMPORTANT: The carbonate chemistry subroutine co2calc.f was originally designed to require tracer input (DIC, Alk, PO4, and SiO2) on a per mass basis (umol/kg); however, for OCMIP-2 co2calc.f has been modified to pass tracer concentrations on a per volume basis (mol/m^3), as carried in ocean models. To do so, we use the mean surface density of the ocean (1024.5 kg/m^3) as a constant conversion factor; we do NOT use model-predicted densities. For example, OCMIP-2 modelers should used SiO2 = 7.7e-03 mol/m^3 and PO4 = 5.1e-04 mol/m^3 as input arguments; again both are constant for the abiotic simulation. The output arguments co2star (Csurf) and dco2star (Csat - Csurf) are also returned in mol/m^3.

3.6 Three atmospheres

Atmosphere description

In the injection simulation, a set of three different atmospheric boxes, each which is global in nature, exchange CO2 with the ocean:

  1. The first atmospheric box B(1) is related to the control scenario. In equation (2), Csurf is calculated from Tracer 1.
  2. The second atmospheric box B(2) is related to the future scenario. Csurf is computed from Tracer 2.
  3. The third atmospheric box B(3) is related to the injection scenario. Csurf is computed from Tracers 3-10.

Each of the three atmospheres is defined as an homogeneous box B(i) (with i=1,2,3), with global coverage, having a uniform atmospheric concentration of CO2 pCO2atm(i) (in uatm). To this concentration corresponds an atmospheric content of CO2 (in GtC) MCO2atm(i). The two variables are related by the following equation:

(5)   MCO2atm(i) = Matm * (WCO2/Watm) * (pCO2atm(i)*1.0e-06)


Conservation equation for the atmosphere

In each of the three atmospheric boxes B(i), the atmospheric mass of CO2 MCO2atm(i) depends on the following conservation equation:

(6)    d MCO2atm(i) / dt = E(i) + S(i) - I(i)


The total sea-to-air flux of CO2 S(i) (for atmospheric boxes i=1,3) is a global integral related to the air-to-sea CO2 flux F(n) at each surface grid box (for Tracers n=1,10)---see definition of F in Conservation equations and Air-sea gas exchange fluxes (F). The value of S(i) depends on the atmospheric box: S(1) is equivalent to the spatial integration over the whole surface ocean of the corresponding sea-to-air flux, i.e., -F(1); likewise, S(2) is the globally integrated sea-to-air flux -F(2); however, S(3) is more complicated. That is, for S(3), we must additionally account for the sea-to-air flux due to loss of injected CO2. For atmospheric box B(3), the sum of both air-to-sea fluxes at each grid box is then

(7)    F' = F(3) + sum[F(n)-F(3)]       n = [4-10]


Thus, the global sea-to-air flux S(3) equals -F' integrated horizontally over the entire surface of the global ocean.

Regarding the injection rate, I(1) and I(2) are always zero. Conversely, I(3) is non-zero, but only during the 100-year injection period. The reason is that unlike B(1) and B(2), atmospheric box B(3) accounts for the effect of CO2 injection. Furthermore, I(3) is not exactly equivalent to the total amount of CO2 that is injected into the deep ocean. In fact, I(3) is a little less because it requires energy to separate, transport, and pump CO2 to the deep ocean. Thus we remove less CO2 from the atmosphere than is added to the ocean. We assume a 14% energy penalty, based on removing CO2 from gas-fired plants or advanced technology coal-fired plants. Thus

(8)     I(3) = N * Q / 1.14


E and d(MCO2atm)/ dt

To close equation (6), either E or d(MCO2atm)/dt must be specified a priori; the remaining term is calculated based on the computed air-sea CO2 flux. The specified term determines the type of run.

Standard case - Required

For the "C" runs, we specify the time evolution of the atmospheric CO2 d(MCO2atm)/dt and the injection scenario; then with modeled air-sea CO2 exchange, each model computes the corresponding time evolution of anthropogenic carbon emissions E to each atmospheric box B(1)-B(3).

Emissions case - Optional

For the "E" run , we specify the history of the anthropogenic emissions E and the history of injected CO2; then with modeled air-sea CO2 exchange, each model computes its corresponding time evolution of atmospheric pCO2atm for each atmospheric box B(1)-B(3).

When specified, pCO2atm and E should be interpolated temporally to each time step of the model.

3.7 Gain

The primary emphasis of these runs is to determine the efficiency of the ocean to retain artificially injected CO2. For each injection site m, we define a Gain G(m) equal to the amount of CO2 injected at that site which remains in the ocean. The more efficient the injection site m, the greater is its G(m). Thus

(9)     d G(m) / dt = Q - R(m)


R(m) is the integral of -(F(m+3)-F(3)) with respect to the global surface area of the ocean. We use the m+3 index because the seven injection sites (m=1,7) correspond to the last seven of the ten ocean tracers (n=4,10).

3.8 Technical notes

The following routines are used in the IPSL ocean model to perform the injection simulations. There are provided as templates that modelers may adapt and use in their own models. All the routines are coded in FORTRAN 77.

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