For the inorganic carbon and radiocarbon, both passive tracers, the conservation equations carried in the model are
(1a)   d[DIC]/dt = L([DIC]) + Jv + J
(1b)   d[DIC14]/dt = L([DIC14]) - Lambda * [DIC14] + Jv14 + J14
The source-sink terms Jv, Jv14, J, and J14 are added only as surface boundary conditions. That is they are equal to zero in all subsurface layers. These source-sink terms are equivalent to the fluxes, described below, divided by the surface layer thickness dz1.
Jv = Fv/dz1
Jv14 = Fv14/dz1
J = F/dz1
J14 = F14/dz1
In models where surface salinity is restored to observed values, this results in a surface flux of salt, not a surface flux of water as in the real world. Such surface salt fluxes are typically found in models with a rigid lid, and even in some models with a free surface (e.g., the OGCM from Louvain-la-Neuve). For simplicity, we categorize both classes of models as "rigid-lid-like". Conversely, non-rigid-lid-like models have a free surface and restore surface salinity by an equivalent flux of water leading to dilution or concentration (e.g., the MPI LSG model). Salinity in the latter type of free-surface model is conserved; E-P fluxes are taken into account by the velocity fields and thus do not need to be explicitly formulated in the transport model.
Yet for all rigid-lid-like models, we must explicitly take into account the concentration-dilution effect of E-P (Evaporation minus Precipitation), which changes surface [DIC] and [Alk]. Thus we add the virtual flux to the surface layer, each time step according to
(2a)   Fv = DICg * (E-P)
(2b)   Fv14 = DIC14g * (E-P)
where DICg and DIC14g are the model's globally averaged surface concentrations of DIC and DIC14, respectively. Both global averages must be computed at least once per year. For rigid-lid-like models with only salinity restoring, we suggest that (P - E) be computed as
(3)   P - E =
where S' is the observed local salinity to which modeled local salinity S is being restored, Sg is the model's globally averaged surface salinity, dz1 is the top layer thickness, and Tau is the restoring time scale for salinity. For rigid-lid-like models which in addition include explicit P - E water fluxes, that term must of course also be added to eq (3).
For simulations of DIC and DIC14, OCMIP-2 simulations will directly model the finite air-sea fluxes F and F14, respectively. Modelers must use the formulation for the standard OCMIP-2 air-to-sea flux,
(4a)   F = Kw (Csat - Csurf)
(4b)   F14 = Kw (14Csat - 14Csurf)
(5a)   Csat = alphaC * pCO2atm * P/Po
(5b)   14Csat = Csat * Ratm
(6)   Ratm = (1 + D14Catm/1000)
where D14Catm is the atmospheric Delta C-14, the fractionation corrected ratio of C-14/C-12, given in permil (see below).
Those familiar with C-14, may be surprised that in equation (6) we define Ratm, without multiplying the right hand term by Rstd (1.176e-12). Instead, we prefer to be able to compare [DIC14] to [DIC], directly, in order to simplify early interpretation and code verification. With the above formulation for the OCMIP equilibrium runs (where pCO2atm=278 ppm and D14Catm=0 permil), if both tracers are initialized identically, the only difference between units for the [DIC] and [DIC14] tracers will be due to radioactive decay. For the anthropogenic runs, there will also be contributions due to differences between atmospheric records for pCO2atm and D14Catm.
For simulations of DIC and DIC14, modelers must use the standard OCMIP-2 formulation for the piston velocity Kw for CO2. The monthly climatology of Kw, to be interpolated linearly in time by each modeling group, is computed with the following equation adapted from Wanninkhof (1992, eq. 3):
(7)    Kw = (1 - Fice) [Xconv * a *(u2 + v)] (Sc/660)**-1/2
Practically speaking, to use equation (2) each group will interpolate the OCMIP-2 standard information to their own model grid. The standard information is provided by IPSL/LSCE as a monthly climatology on the 1 x 1 degree grid of Levitus (1982) in netCDF format (in file gasx_ocmip2.nc). Gridded variables in that file include
For the variables Fice and xKw, continents on the 1 x 1 degree standard grid have been flooded with adjacent ocean values. Such an approach avoids discontinuities at land-sea boundaries during interpolation. See the Fortran program rgasx_ocmip2.f for an example of how to read the information in gasx_ocmip2.nc.gz into your interpolation routines. After compilation, to link and use rgasx_ocmip2.f, one must have already installed netCDF.
may also be inspected with software that uses netCDF format, such as ncdump
or Ferret. Ferret will be used for some of the analysis during OCMIP-2.
We encourage participants to become familiar with Ferret now
After installation, one can visualize maps of the standard information in gasx_ocmip2.nc, by using the Ferret script vgasx_ocmip2.jnl.
After launching Ferret, simply issue the following command (at Ferret's "yes?" prompt)
yes? go vgasx_ocmip2.jnl
Apart from Kw, there are a total of four other terms in equation (4a) and (4b) which require further development.
The oceanic terms Csurf and 14Csurf [in mol/m^3] are not carried as tracers, so they must be computed each timestep to determine gas exchange
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. As input, we must provide alkalinity, which we determine as a normalized linear function of salinity.
(8)    [Alk] = Alkbar * S/Sbar
where [Alkbar] is 2310 microeq/kg and Sbar is the model's annual mean surface salinity, integrated globally (horizontally). Two other input arguments, both nutrient concentrations, are needed as input. Although accounting for both of their equilibria makes a difference, neither nutrient is included in the solubility pump run. Hence we take concentrations of both as being constant, equal to the global mean of surface observations: 0.5 micromol/kg for phosphate and 7.5 micromol/kg for silicate. Note that for the later OCMIP-2 run which includes the biological pump, we will use observed seasonal distributions of surface phosphate.
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.
14Csurf is the surface ocean [14CO2], defined as
(9)    14Csurf = Csurf * Rocn,
(10)    Rocn = [DIC14]/[DIC].
Furthermore, for comparison to ocean measurements, we compute
(11)    D14Cocn = 1000*(Rocn - 1).
Following equation (4), we do not include Rstd when calculating D14Cocn in the model.
The atmospheric components Csat and 14Csat in equations (4a) and (4b) are specified a priori via four remaining terms: