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.
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.
http://www.unidata.ucar.edu/packages/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
http://ferret.wrc.noaa.gov/Ferret/
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 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:
- 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].
- 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.
- 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:
- 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.
- 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.
- 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).