East Asia and Western Pacific METEOROLOGY AND CLIMATE

240
NORMAL MODES OF CLIMATOLOGICAL MEAN FLOW AND THEIR
ROLES IN ATMOSPHERIC GENERAL CIRCULATION
Zhang Zuojun
Institute of Atmospheric Physics, Academia Sinica
ABSTRACT
The loss of orthogonality between unstable normal modes is
general for any kind of eigen-analysis, in particular for an observed
climatological mean flow this is found to be very significant for the
development of perturbations. A small perturbation can have a very
large projection onto the most unstable normal mode. The adjoint eigen
mode is most efficient at exciting the normal mode. The "gain" on
projection is described by the projectibility. In general, growth rate
and frequency information should be augmented with the projectibility
and eigen vectors should be augmented by the corresponding adjoint
eigen vectors.
For the 300 hPa January climatological mean flow, the maximum
projectibility is found to be 7.8 and the adjoint mode corresponding
to the most unstable normal mode has large amplitude over the
subtropical Indian Ocean and southeast Asia. The adjoint mode when
used as initial perturbation yields an energy increase of a factor of
50 within 10 days even when a damping is added to make the system
stable. Both the initial value and forcing problems show that the
linear barotropic vorticity equation gives important ideas on the
atmospheric low-frequency variability and the role of the tropics.
Initial studies suggest that growth rates and projectibility
together give important information on the likely accuracy of mediumrange
weather forecasts.