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2. Coupling of Dynamical Core and Parameterization Suite
The CAM 3.0 cleanly
separates the parameterization suite from the dynamical core, and
makes it easier to replace or modify each in isolation. The dynamical
core can be coupled to the parameterization suite in a purely time
split manner or in a purely process split one, as described below.
Consider the general prediction equation for a generic variable
,
|
(2.1) |
where denotes a prognostic variable such as temperature or
horizontal wind component. The dynamical core component is
denoted and the physical parameterization suite .
A three-time-level notation is employed which is appropriate for the
semi-implicit Eulerian spectral transform dynamical core. However, the
numerical characteristics of the physical parameterizations are more
like those of diffusive processes rather than advective ones. They are
therefore approximated with forward or backward differences, rather
than centered three-time-level forms.
The Process Split coupling is approximated by
|
(2.2) |
where
is calculated first from
|
(2.3) |
The Time Split coupling is approximated by
The distinction is that in the Process Split approximation the
calculations of and are both based on the same past state,
, while in the Time Split approximations and
are calculated sequentially, each based on the state produced by the
other.
As mentioned above, the Eulerian core employs the three-time-level
notation in (2.2)-(2.5). Eqns. (2.2)-(2.5) also apply
to two-time-level semi-Lagrangian and finite volume cores by dropping
centered term dependencies, and replacing -1 by and
by .
The parameterization package can be applied to produce an updated
field as indicated in (2.3) and (2.5). Thus (2.5) can be
written with an operator notation
|
(2.6) |
where only the past state is included in the operator dependency for
notational convenience. The implicit predicted state dependency is understood.
The Process Split equation (2.2) can also be written in operator
notation as
|
(2.7) |
where the first argument of
denotes the prognostic variable
input to the dynamical core and the second denotes the forcing rate
from the parameterization package, e.g. the heating rate in the
thermodynamic equation. Again only the past state is included in the
operator dependency, with the implicit predicted state dependency left understood.
With this notation the Time Split system
(2.5) and (2.5) can be written
|
(2.8) |
The total parameterization package in CAM 3.0 consists of a sequence of
components, indicated by
|
(2.9) |
where denotes (Moist) precipitation processes, denotes clouds
and Radiation, denotes the Surface model, and denotes
Turbulent mixing. Each of these in turn is subdivided into various
components: includes an optional dry adiabatic adjustment (normally
applied only in the stratosphere), moist penetrative
convection, shallow convection, and large-scale stable
condensation; first calculates the cloud parameterization
followed by the radiation parameterization; provides the
surface fluxes obtained from land, ocean and sea ice
models, or calculates them based on specified surface conditions such
as sea surface temperatures and sea ice distribution. These surface
fluxes provide lower flux boundary conditions for the turbulent mixing
which is comprised of the planetary boundary layer
parameterization, vertical diffusion, and
gravity wave drag.
Defining operators following (2.6) for each of the parameterization
components, the couplings in CAM 3.0 are summarized as:
TIME SPLIT
The labels Time Split and Process Split refer to the coupling of the
dynamical core with the complete parameterization suite. The components
within the parameterization suite are coupled via time splitting in both forms.
The Process Split form is convenient for spectral transform
models. With Time Split approximations extra spectral transforms
are required to convert the updated momentum variables provided by the
parameterizations to vorticity and divergence for the Eulerian
spectral core, or to recalculate the temperature gradient for the
semi-Lagrangian spectral core. The Time Split form is
convenient for the finite-volume core which adopts a Lagrangian
vertical coordinate. Since the scheme is explicit and restricted to
small time-steps by its non-advective component, it sub-steps the
dynamics multiple times during a longer parameterization time step.
With Process Split approximations the forcing terms must be
interpolated to an evolving Lagrangian vertical coordinate every
sub-step of the dynamical core. Besides the expense involved, it is
not completely obvious how to interpolate the parameterized forcing,
which can have a vertical grid scale component arising from vertical
grid scale clouds, to a different vertical grid. [182]
compares simulations with the Eulerian spectral transform dynamical
core coupled to the CCM3 parameterization suite via Process
Split and Time Split approximations.
Next: 3. Dynamics
Up: description
Previous: 1.2 Overview of CAM
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Jim McCaa
2004-06-22