   ## 2.1 Gas exchange flux

For simulations of CFC-11 and CFC-12, we will directly model the finite air-sea flux F. In other words, surface CFC concentrations will NOT be set equal to temperature-derived equilibrium values determined from the solubility. Modelers must use the formulation for the standard OCMIP-2 air-to-sea flux,

(1a)   F = Kw (Csat - Csurf)

with

(1b)   Csat = alpha * pCFC * P/Po

where

• Kw is the gas transfer (piston) velocity [m/s] ;
• Csurf is the modeled surface ocean CFC-11 (or CFC-12) concentration [mol/m^3];
• alpha is the CFC solubility for water-vapor saturated air [mol/(m^3 * picoatm)];
• pCFC is the partial pressure of CFC-11 (or CFC-12) in dry air at one atmosphere total pressure [in picoatm], which is the same as the dry air mixing ratio of CFC-11 or (CFC-12) multiplied by 10^12 ;
• P is the total air pressure at sea level [atm], locally;
• Po is 1 atm.

All right hand terms, except P and Po, in equations (1a) and (1b) are different for CFC-11 and CFC-12, as well as other tracers.

## 2.2 The Piston Velocity Kw

For simulations of CFC-11 and CFC-12, modelers must use the standard OCMIP-2 formulation for the piston velocity Kw. 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):

(2)    Kw = (1 - Fice) [Xconv * a *(u2 + v)] (Sc/660)**-1/2

where

• Fice is the fraction of the sea surface covered with ice, which varies from 0.0 to 1.0, and is given as monthly averages from the Walsh (1978) and Zwally et al. (1983) climatology (OCMIP-2 modelers must resest Fice values less than 0.2 to zero, after interpolation to their model grid)
• u2 is the instantaneous SSMI wind speed, averaged for each month, then squared, and subsequently averaged over th e same month of all years to give the monthly climatology. (see the OCMIP-1 README.satdat for further details);
• v is the variance of the instantaneous SSMI wind speed computed over one month temporal resolution And 2.5 degree spatial resolution, and subsequently averaged over the same month of all years to give the monthly climatology. Again, see the OCMIP-1 README.satdat for further details.
• a is the coefficient of 0.337, consistent with a piston velocity in cm/hr. We adjusted the coefficient a for OCMIP-2, in order to obtain Broecker et al.'s (1986) radiocarbon-calibrated, global CO2 gas exchange of 0.061 mol CO2 /(m^2 * yr * uatm), when using the satellite SSMI wind information (u2 + v) from Boutin and Etcheto (pers. comm.). Our computed value for a is similar to that determined by Wanninkhof (a = 0.31), who used a different wind speed data set and assumptions about wind speed variance; we use the observed variance.
• Xconv = 1/3.6e+05, is a constant factor to convert the piston velocity from [cm/hr] to [m/s]. This conversion factor is already included in the forcing field xKw, provided below.
• Sc is the Schmidt number which is to be computed using modeled SST, using the formulation from Zheng et al (1998). The function sc_cfc.f computes the Sc's (unit-less) for both CFC-11 and CFC-12.

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

• the variable Fice,
• the second term, [Xconv * a * (u2 + v)], denoted as xKw [m/s]
• the mask Tmask (1 if ocean; 0 if land),
• the total atmospheric pressure at sea level P [atm]
• the longitude Lon at the center of each 1 x 1 degree grid box,
• the latitude Lat at the center of each 1 x 1 degree grid box.

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 cfc1112.atm into your interpolation routines. After compilation, to link and use rgasx_ocmip2.f, one must have already installed netCDF.

The file `gasx_ocmip2.nc` 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
```

## 2.3 Oceanic and Atmospheric Components

Apart from Kw, there are two other terms in equation (1a). The ocean component Csurf [in mol/m^3] is computed by the model each timestep; the atmospheric component Csat is specified a priori via the three remaining terms:

1. alpha: The CFC solubility alpha is to be computed using modeled SST and SSS, both of which vary in time at each grid point. For OCMIP-2 we use the solubility formulation determined by Warner and Weiss (1985, Table 5 for solubility in [mol/(l * atm)]). The function sol_cfc.f determines alpha accordingly, for both CFC-11 and CFC-12, but changes the units to [mol/(m^3 * picoatm)] so that model CFC concentrations can then be carried in SI units [mol/m^3].
2. pCFC: Extrapolated records for observed CFC-11 and CFC-12 [in picoatm] constructed at 41S and 45N (Walker et al., pers. comm.). For OCMIP-2, each station will be treated as representative of its own hemisphere, except between 10S and 10N where those station values will be interpolated linearly as a function of latitude. Thus there are 3 zones:
• 90S-10S, where CFC's are held to same value as at the station at 41S;
• 10S-10N, a buffer zone where values are interpolated linearly; and
• 10N-90N where values are held to the same value as at the measuring station at 45N.
3. P: Is the total atmospheric pressure [atm] from the monthly mean climatology of Esbensen and Kushnir (1981). The latter, given originally on a 4 x 5 degree grid (latitude x longitude) in bars, is converted to atm by multiplying by (1/1.101325). Land and sea ice values in the original data set were filled with average values from adjacent ocean points. These monthly mean arrays were then linearly interpolated to the 1 x 1 degree grid of Levitus (see netCDF file gasx_ocmip2.nc).

Technical notes:

1. The Fortran subroutine cfc_interp.f interpolates pCFC spatially following the above algorithm. The code allows, in one pass, to spatially interpolate atmospheric pCFC-11 and pCFC-12, at a given timestep, to all grid points as a function of latitude.
2. The ASCII file cfc1112.atm provides mid-year values of atmospheric pCFC-11 and pCFC-12 [in picoatm] at both stations for the period from 1931 to 1997. See the program read_cfcatm.f.
3. Temporal interpolation of atmospheric pCFC-11 and pCFC-12 is to be made linearly for each time step, based on mid-year values (file cfc1112.atm).   