   ## 3.1 Gas exchange flux

For simulations of He-3 and He-4, we will directly model the finite air-sea flux F. In other words, surface helium concentrations will NOT be set equal to temperature-derived equilibrium values determined from the solubility. Instead, modelers must use the formulation for the standard OCMIP-2 air-to-sea flux,

(1a)   F = Kw (Csat - Csurf)

with

(1b)   Csat = alpha * pHe

where

• Kw is the gas transfer (piston) velocity [m/s] ;
• Csurf is the modeled surface ocean He-3 (or He-4) concentration [mol/m^3] ;
• alpha is the He-3 (or He-4) solubility for water-vapor saturated air (in mol/(m^3 * atm)). For He-4,    alpha(He-4) = exp[A1+A2*100/T+A3*ln(T/100)+S*(B1+B2*T/100+B3*(T/100)^2)]/22400, where T is the temperature (in Degrees Kelvin), S is the salinity (on the psu scale), and where the coefficients A1, A2, A3, B1, B2, and B3 are all taken from Wanninkhof (1992, Table A2).
• To check that you have correctly implemented this equation, the He-4 solubility should be 0.3299 mol/(m^3 * atm_He4) at a temperature of 10C (283.15K) and a salinity of 35. Thus for this same T and S, Csat would be 1.7288*10^-6 mol/m^3, (from equation 1(b) and the partial pressure of He-4 in the atmosphere, given below).
• The He-3 solubility (alpha[He-3]) is equal to He-4 solubility multiplied by the isotope fractionation factor = 0.984 (Weiss, 1970; Top et al., 1987; Fuchs et al., 1987)
• pHe is the partial pressure of He-3 (or He-4) in dry air at one atmosphere total pressure [in atm] Specifically, pHe-4 = 5.24 *10^-6 and pHe-3 = pHe-4*1.38*10^-6.

All right hand terms, in equations (1a) and (1b) are different for He-3 and He-4.

## 3.2 The Piston Velocity Kw

For simulations of He-3 and He-4, 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 the 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 for He-4 given by Wanninkhof (1992, Table A1), derived from Jähne (1987a). For He-3, we reduce the Schmidt number (relative to He-4) by 15% (ScHe-3 = ScHe-4 / 1.15) based on the ratio of the reduced masses, which is consistent with helium isotopic fractionation measurements from Jähne (1987b). The function sc_helium.f computes the Sc's (unit-less) for both He-3 and He-4.

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 2-D gas exchange fields, written in netCDF format. 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 is used for some of the analysis during OCMIP-2. We encourage OCMIP members to become familiar with 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
```

## 3.3 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 constant specified a priori via the three remaining terms:

1. alpha: The solubility alpha, different for He-3 and He-4, will be computed using modeled SST and SSS, both of which vary in time at each grid point. For He-4 we use the solubility formulation provided by Wanninkhof (1992, Table A2), a temperature-dependant polynomial for He solubility, which was derived from measurements by Weiss (1971).The function sol_he.f determines alpha for both He-3 and He-4, but changes the units to [mol/(m^3 * atm)] so that model helium concentrations can then be carried in SI units [mol/m^3].
2. pHe: For these simulations we set the partial pressure of atmospheric He-4 (pHe-4) to 5.24 *10^-6 atm, constant in time and space; similarly, pHe-3 = pHe-4*1.38*10^-6.= 7.23 *10^-12 atm. ?

## 3.4 Helium mantle source

He-3 is injected at the seafloor along ocean ridges at a global rate of around 1000 mol/yr (Clarke et al., 1969; Craig et al., 1975; Jean-Baptiste, 1992; Farley et al., 1995). We hold the He-3/He-4 ratio of injected mantle helium to a constant value of 8 x 1.38. x 1.38*10^-6 (Farley et al., 1995). Thus the globally integrated source for He-4 is 1000/8/1.38E-6 (i.e.,  90.6 x 10^6) mol/yr. The mass of mantle helium that is injected is partioned geographically as a function of ridge positions, lengths, and spreading rates (Farley et al., 1995).

For consistent simulations, we need to position mantle helium sources as a function of the REAL ocean's ridge positions, spreading rates, and depths. To facilitate making these simulations in any model, we have provided the mass/year of injection helium partitioned, as a SCALAR field, on the same 1 x 1 degree grid as used for the OCMIP-2 boundary condition for air-sea gas exchange. To derive that 1 x 1 degree field, we calculated length of the ridges falling within each grid box and multiplied each length by its corresponding spreading rate (i.e., see program src_helium.f). The injection points, which define the ridge lengths, and corresponding rates are those used by Farley et al. (1995) (Maier-Reimer, personal communication, 1998). However, that data set does not include known sites in the Western Pacific (Philippe: references?), which we have also included in this study. The complete list of sites and spreading rates is given in sitespread.dat.

To account for the mantle source, each modeling group will need to interpolate our standard 1 x 1 degree grid of helium sources and corresponding ridge depths to their model. Then, groups will need to adjust the vertical position of helium injection point, where necessary

• If the model bathymetry is deeper than the injection point, then NO Vertical adjustment
• If the model bathymetry is equal to or shallower than the injection point, then inject mantle helium into the deepest ocean box in the same water column.

Technical notes:

1. The 1 x 1 degree grid of sources and sinks is provided as a netCDF file src_helium.nc.
2. Variables in that file are
• zHe: the ridge depth already adjusted upward by 300 m (see following note)
• rateHe3flux: the rate of injection of He-3 (mol/yr)
• rateHe4flux: the rate of injection of He-4 (mol/yr)
3. Note that our "ridge depths" are already 300 m shallower than those actually observed, thereby accounting for the typical rise of the warm mantle source waters from the ridge up into the water column. Therefore, modelers should avoid additional coding to account for this effect.
4. Interpolation: When interpolating the mantle source (scalar) information from the 1 x 1 degree grid to your grid, please be sure that you conserve mass. Globally, the rate of injection of He-3 must be 1000 mol/year; that for He-4 should be around 90.6 x 10^6 mol/year. Groups should scale all local injection rates by a constant to exactly obtain those globally integrated rates.   