19.1.2.1 Interpolations to ocean grid

Unlike in Section 19.1.1, there are no complications since the ocean domain is assumed to be contained within the atmosphere domain as shown in Figure 19.4. Each surface boundary condition is interpolated one at a time with the essential steps being:

• Set cyclic conditions of . This assumes a global atmosphere domain.

• Extrapolate into land areas on the atmosphere grid. This is done as in Section 19.1.1 by solving $\nabla^2\xi_{i^\prime,j^\prime}=0$ over land areas using values of $\xi_{i^\prime,j^\prime}$ over non-land areas as boundaries where $\xi_{i^\prime,j^\prime}$ represents windstress components, heatflux, etc^19.21. The idea, as on the ocean grid, is to get reasonable $\xi_{i^\prime,j^\prime}$ adjacent to coastlines while not trying to produce accurate $\xi_{i^\prime,j^\prime}$ in the middle of continents. Where land and ocean areas on the ocean and atmosphere grids are mismatched, this will ameliorate the sensing of erroneous $\xi_{i^\prime,j^\prime}$ by the ocean.

• Interpolate to . Since ocean resolution is typically higher than that of the atmosphere due to the difference in Rossby radius scales, the interpolation is linear. The interpolation is carried out using subroutine ctf from file util.F. Note that linear interpolation does not exactly conserve the quantity being interpolated. However, linear interpolation has been used without causing noticable drift in coupled integrations (without flux correction) of up to 20 years at GFDL.

  For integrations simulating thousands of years, linear interpolation may not be good enough. To conserve fluxes exactly, one possibility (although drastic) is to design the grids such that an integral number of ocean cells overlay each atmospheric grid cell. Then the quantity to be interpolated can simply be broadcast from each atmospheric cell to all underlying ocean cells. However, this is really not necessary. Assume that the value of the quantity being interpolated is constant over the entire atmospheric grid cell. For exact conservation, the value in each ocean cell is just an integral of the atmospheric quantity over the area of the ocean cell. It would be a matter of writing a subroutine to do it and substituting this subroutine for the call to ctf.

• Set cyclic conditions on and convert to units expected by the ocean. MOM expects units of cgs.

• Compute global mean of

Caveat

In the process of constructing no attempt has been made at removing small scale spatial features from the grid which could potentially be a source of noise for the ocean model.