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The governing equation of model atmospheric dynamics is the 2D
anelastic system (Ogura and
Phillips, 1962).
The effect of planetary rotation is not considered.
(A.1), (A.2) are the horizontal and
vertical component of equation of motion, respectively.
(A.3) is the continuity equation
and (A.4) is the
thermodynamic equation.
 are horizontal, vertical and time
coordinate, respectively.
are horizontal and vertical velocity, and
 are potential temperature and
nondimensional pressure function deviation from those of basic
state, respectively.
 are density, potential temperature and
temperature in basic state.
 is gravitational acceleration whose value
is equal to 3.72 msec-2.
 is radiative heating (cooling) rate per
unit mass which is calculated by convergence of the radiative heat flux
(see appendix A.d).
 is heating rate per unit mass owing to
dissipation of turbulent kinetic energy, which is given by turbulent parameterization.
 in equation (A.1) 〜 (A.4)
represents the turbulent diffusion owing to subgrid scale turbulent
mixing.
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(A.5) |
K is turbulent diffusion coefficient which
is calculated by (A.9) and (A.10).
The nondimensional pressure function and potential temperature are
defined as follows.
where  and  are pressure
and basic state pressure,  is reference
pressure (= 7 hPa),  ,  is specific
heat of constant pressure per unit mass and  is
atmospheric gas constant per unit mass.
The values of and are set to be
those of CO2 (734.9
Jkg-1K-1,
189.0
Jkg-1K-1).
The basic state atmospheric structure is calculated by using
the hydrostatic equation as follows.
The deviation of nondimensional pressure function is calculated
by using the following equation which is derived
from (A.1) ˜ (A.3)
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