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2.2 Timestepping
The equations of motion integrated by the model involve four
prognostic equations for flow,
and
, temperature,
, and
salt/moisture,
, and three diagnostic equations for vertical flow,
, density/buoyancy,
/
, and pressure/geopotential,
. In addition, the surface pressure or height may by
described by either a prognostic or diagnostic equation and if
nonhydrostatics terms are included then a diagnostic equation for
nonhydrostatic pressure is also solved. The combination of prognostic
and diagnostic equations requires a model algorithm that can march
forward prognostic variables while satisfying constraints imposed by
diagnostic equations.
Since the model comes in several flavors and formulation, it would be
confusing to present the model algorithm exactly as written into code
along with all the switches and optional terms. Instead, we present
the algorithm for each of the basic formulations which are:
 the semiimplicit pressure method for hydrostatic equations
with a rigidlid, variables colocated in time and with
AdamsBashforth timestepping,
 as 1. but with an implicit linear freesurface,
 as 1. or 2. but with variables staggered in time,
 as 1. or 2. but with nonhydrostatic terms included,
 as 2. or 3. but with nonlinear freesurface.
In all the above configurations it is also possible to substitute the
AdamsBashforth with an alternative timestepping scheme for terms
evaluated explicitly in time. Since the overarching algorithm is
independent of the particular timestepping scheme chosen we will
describe first the overarching algorithm, known as the pressure
method, with a rigidlid model in section
2.3. This algorithm is essentially
unchanged, apart for some coefficients, when the rigid lid assumption
is replaced with a linearized implicit freesurface, described in
section 2.4. These two flavors
of the pressuremethod encompass all formulations of the model as it
exists today. The integration of explicit in time terms is outlined
in section 2.5 and put into the context of the
overall algorithm in sections 2.7 and
2.8. Inclusion of nonhydrostatic
terms requires applying the pressure method in three dimensions
instead of two and this algorithm modification is described in section
2.9. Finally, the freesurface equation may be
treated more exactly, including nonlinear terms, and this is
described in section 2.10.2.
Next: 2.3 Pressure method with
Up: 2. Discretization and Algorithm
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