In the climate model we employ the Geophysical Fluid
Dynamics Laboratory (GFDL) Modular Ocean Model (Pacanowski,
1995), which is based upon the primitive equations
for a Boussinesq, hydrostatic fluid under the rigid lid
approximation. Turbulent closure is parameterized as a Laplacian
mixing process. The horizontal momentum equations (including
nonlinearities) in spherical geometry are then

where

are the
horizontal Laplacian terms representing the
horizontal mixing of momentum; is the horizontal
Laplacian operator;
is longitude; is latitude; and *z* is the
vertical coordinate. Here, the velocity components are
*u*, *v*, and *w* in the zonal, meridional and vertical
directions respectively, *f* is the Coriolis
parameter,
*a* is the radius of the earth, *p* is pressure, is a
representative density for seawater, *t* is time,
and , are the
lateral and vertical eddy viscosities. The model
is assumed hydrostatic, so that

where is density and *g* is the acceleration due
to gravity. The continuity equation is given by

The conservation laws for heat and salt may be written as

where *T* is temperature, *S* is salinity, , and are
the lateral and vertical diffusivities, and ,
are Kronecker delta functions defined as

where *k* is
the vertical depth level, and

the case represents instantaneous
convective adjustment that restores a neutral stratification
whenever unstable stratification occurs (here parameterized
explicitly by Rahmstorf's convection scheme, see
Pacanowski, 1995, sec. 11.11).
The equation of state for seawater can be
written as

with the density a nonlinear equation of temperature, salinity
and pressure (UNESCO, 1981).

At the surface, the model is driven by both wind stress (applied
as a body force over the depth of the first grid box)
and surface buoyancy forcing (see the array **sbcocn**,
Appendix A). The surface boundary conditions
are therefore

where are the zonal and
meridional surface wind stresses. The surface buoyancy forcing
is applied directly to the tracer conservation equations
(2.3.5, 2.3.6).
The net heat flux into/out of the ocean is defined as

The definitions of , , , and
are
the same as those in (2.1.6), (2.1.7), (2.2.3), and (2.2.4); while the
latent heat flux out of the ocean takes the form

the freshwater flux over the ocean takes the form

where are representative salinities for the ocean and
ice respectively, *R* is the runoff from the landmass, and *B*
is the freshwater flux from ice formation or melt given by

At the lower boundary of the ocean model we specify a no
flux condition on tracers (heat/salt), and no normal flow

We further apply a quadratic bottom friction (in cases with
topography) as

where is the drag coefficient, and is the turning
angle. At lateral walls, no flux of tracers is permitted, and
a no slip condition is applied to the horizontal flow:

where *n* is a unit normal to the boundary.

Mon May 5 14:22:13 PDT 1997