Section 15.5: POPs as Normal Modes
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of these processes is reasonable.
Indeed, Schnur et al. found two categories of POPs. One is in good
correspondence with the most unstable normal modes of the theoretical A in
terms of both the frequency and wavelength of the waves and the meridionalheight structure of the waves. The only inconsistency between this category
of POPs and the baroclinic unstable waves lies in the damping and growth
rates. For a stationary time series, a POP analysis always gets damped POP
with corresponding eigenvalues lAI< 1 whereas the most unstable modes
have always a growth rate with lAI> 1. This inconsistency is a consequence
of the artifical set up of the theoretical approach in which only linear growth
phase of the waves is considered. In reality, after waves grow out of noisy
background, other processes take place. The growing modes appear in the
data as stationary waves.
The second category of POPs describes the decaying phase of the baroclinically unstable modes. These modes were associated with patterns of
Eliassen-Palm flux vectors and their divergence which characterize the decaying phase.
Schnur et al. demonstrated that at least in the case of baroclinic unstable
waves, the empirical A is capable of approximating processes which are responsible for both the growing and decaying phase of the waves. Although the
decaying phase itself is nonlinear, Simmons and Hoskins (1978) have shown
that this nonlinear process is only important at the point where the linear
growth of a wave comes to an end and barotropic decay begins. The evolution following this transition point displays linear character. That might be
the reason why the linear POP analysis can describe also this phase.
Schnur et al. 's example shows the ability of empirical A in approximating the linear behavior of processes which generate the climate data. This
implication can be extended to the situation where it is diflicult to get the
theoretical A. An attempt was done by Xu (1993) in which a combined atmospheric and oceanic data set was used to approximate the processes in the
coupled system.
297
of these processes is reasonable.
Indeed, Schnur et al. found two categories of POPs. One is in good
correspondence with the most unstable normal modes of the theoretical A in
terms of both the frequency and wavelength of the waves and the meridionalheight structure of the waves. The only inconsistency between this category
of POPs and the baroclinic unstable waves lies in the damping and growth
rates. For a stationary time series, a POP analysis always gets damped POP
with corresponding eigenvalues lAI< 1 whereas the most unstable modes
have always a growth rate with lAI> 1. This inconsistency is a consequence
of the artifical set up of the theoretical approach in which only linear growth
phase of the waves is considered. In reality, after waves grow out of noisy
background, other processes take place. The growing modes appear in the
data as stationary waves.
The second category of POPs describes the decaying phase of the baroclinically unstable modes. These modes were associated with patterns of
Eliassen-Palm flux vectors and their divergence which characterize the decaying phase.
Schnur et al. demonstrated that at least in the case of baroclinic unstable
waves, the empirical A is capable of approximating processes which are responsible for both the growing and decaying phase of the waves. Although the
decaying phase itself is nonlinear, Simmons and Hoskins (1978) have shown
that this nonlinear process is only important at the point where the linear
growth of a wave comes to an end and barotropic decay begins. The evolution following this transition point displays linear character. That might be
the reason why the linear POP analysis can describe also this phase.
Schnur et al. 's example shows the ability of empirical A in approximating the linear behavior of processes which generate the climate data. This
implication can be extended to the situation where it is diflicult to get the
theoretical A. An attempt was done by Xu (1993) in which a combined atmospheric and oceanic data set was used to approximate the processes in the
coupled system.