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The core algorithm is based on the ``C grid'' discretization of the
continuity equation which can be summarized as:



(2.87) 



(2.88) 



(2.89) 



(2.90) 
where the continuity equation has been most naturally discretized by
staggering the three components of velocity as shown in
Fig. 2.9. The grid lengths
and
are the lengths between tracer points (cell centers). The grid lengths
,
are the grid lengths between cell
corners.
and
are the distance (in units of
) between level interfaces (wlevel) and level centers (tracer
level). The surface area presented in the vertical is denoted
. The factors
and
are nondimensional fractions
(between 0 and 1) that represent the fraction cell depth that is
``open'' for fluid flow.
The last equation, the discrete continuity equation, can be summed in
the vertical to yield the freesurface equation:

(2.91) 
The source term
on the rhs of continuity accounts for the local
addition of volume due to excess precipitation and runoff over
evaporation and only enters the toplevel of the ocean model.
Next: 2.13 Hydrostatic balance
Up: 2. Discretization and Algorithm
Previous: 2.11.6 Topography: partially filled
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