East Asia and Western Pacific METEOROLOGY AND CLIMATE

506
The coefficients Z, T, H, and T are spectral coefficients of the
vertically averaged and vertically differenced geopotential, the
topography and the radiative equilibrium^temperature, respectively.
In the above spectral representations, T is represented by mode Al
only. Only one zonal wave number, n=3, is retained in the model and
two kinds of meridional truncation m=l and m=l,2,3 are used in this
study. In the case m=l, the topography is represented by mode LI
with H LI = 250 m. In the case m=l,2,3, the topography is represented
by a superposition of LI and L3 modes, with H LI = -3 H L3 = 250 m.
3. MULTIPLE EQUILIBRIA (STEADY SOLUTIONS)
With only one meridional mode (m=l), this is the simplest case
that includes nonlinear interaction between the mean zonal flow,
waves, and topography. With this truncation, the governing equations
are reduced to six ordinary differential equations with six dependent
variables. By requiring all tendency of the six equations to be
zero, we can solve the six nonlinear algebra equations with six
unknowns. As we searched for a forcing range of AT = 20°C to 80°C,
we found more than one (three) stationary solutions (equilibria) whe
AT* is greater than 76°C.
Fig. 2 shows the AT vs AT plot for the equilibria states.
There are three branches in the region 20°K < AT < 80°K, Branches
1, 2, and 3, which correspond to the high-index equilibrium,
intermediate equilibrium and low-index equilibrium, respectively.
A linear stability analysis has been performed by perturbing the
spectral coefficients of the equilibria in the form of cj>' = cj) e .
For Branch 3 all equilibrium states are stable, for Branch 2 all
equilibrium states are monotonically unstable (real 0) t and for Branch
1 all equilibrium states are oscillatorily unstable (complex O ).
We identify the monotonic instability as the baroclinic version of
orographic instability. It can be inferred qualitatively in the AT
vs. AT diagram (Fig. 2) . The orographic instability is due to the
existence of the resonance that makes a perturbation in AT deviate
from its equilibrium state through a change of the eddy heat flux
divergence larger than the change of Newtonian heating. Again,
unlike the barotropic case, a change in eddy heat flux rather than
mountain torque is responsible for this instability. We find that
all equilibria are unstable with respect to m=2 perturbations,except
for the low-index equilibrium at very low AT , AT < 29°K.
To allow eddy momentum flux and possible double jets pattern
zonal flows in the model, we have relaxed the spectral truncation to
additionally include second and their meridional modes (m—1,2,3) in
the model. The thermal forcing is kept the same with only mode Al,
while a third mode component is added in the topography spectrum. By
choosing H^ = -1/3 H LI , the topography is flattened near the lateral
boundaries. There are 18 variables in the system, 6 for mean zonal
components and 12 for wave components, with 18 ordinary differential