25
the positive polarity of EOF2 appears exactly 1/4 cycle after the spatial
pattern associated with the positive polarity of EOF1; the spatial pattern
associated with the negative polarity of EOF1 appears exactly 1/4 cycle
after the pattern associated with the positive polarity of EOF2, etc. In abbreviated notation: +EOF1 -++EOF2 -+-EOF1 -+-EOF2 -++EOF1 ...... .
This kind of sequence may be viewed as the canonical form a progressive
oscillation.
Although their time dependence is not perfectly periodic, normal mode
solutions exhibit a behaviour similar, in some respects, to the progressive oscillation described in the previous paragraph. The general form
\IT = exp( O"t) [A cos wt + B sin wt] may be represented either as an expanding or decaying spiral pattern depending upon whether w is positive or
negative. (For example, if A = cos kx and B = sin kx, and 0" = 0 , \IT is
simply an eastward propagating wave.) If such modal behaviour is evident
in observational data or model output, it should be possible to represent
it in a two-dimensional phase space. Statistical analysis methods such as
complex EOF analysis (Barnett 1981), Principal Oscillation Pattern (POP)
analysis; (Hasselmann 1988), and Multi-channel Singular Spectrum Analysis (MCSSA; Vautard and Chil 1989) are well-suited for detecting such
oscillations, if they exist, though if not used in conjunction with stringent
tests of statistical significance, they are also capable of detecting spurious
oscillations.
Some normal mode solutions, and some quasi-periodic phenomena lack a
statistically significant "imaginary component" (i.e., a second EOF whose
expansion coefficient time series oscillates in quadrature with that of the
leading EOF). Periodic or quasi-periodic phenomena may possess progressive wave signatures when viewed in the appropriate phase space, but they
may be detectable only as standing oscillations if the phase space chosen for
the analysis does not include the variables or spatial patterns that exhibit
a sufficient range of phase lags relative to the leading EOF. In the presence of sampling variability, standing oscillations can easily be mistaken
for progressive oscillations if careful significance testing is not performed.
In general, the more periodic the phenomenon, the more its evolution is
constrained to resemble a progressive or standing oscillation in some appropriately chosen two-dimensional phase space. Strong bandpass filtering or
methods of analysis that have a predilection for quasi-periodic modes (i.e.,
POP analysis and MCSSA) will inevitably tend to focus the investigator's
attention on such phenomena, regardless of whether they have any physical
the positive polarity of EOF2 appears exactly 1/4 cycle after the spatial
pattern associated with the positive polarity of EOF1; the spatial pattern
associated with the negative polarity of EOF1 appears exactly 1/4 cycle
after the pattern associated with the positive polarity of EOF2, etc. In abbreviated notation: +EOF1 -++EOF2 -+-EOF1 -+-EOF2 -++EOF1 ...... .
This kind of sequence may be viewed as the canonical form a progressive
oscillation.
Although their time dependence is not perfectly periodic, normal mode
solutions exhibit a behaviour similar, in some respects, to the progressive oscillation described in the previous paragraph. The general form
\IT = exp( O"t) [A cos wt + B sin wt] may be represented either as an expanding or decaying spiral pattern depending upon whether w is positive or
negative. (For example, if A = cos kx and B = sin kx, and 0" = 0 , \IT is
simply an eastward propagating wave.) If such modal behaviour is evident
in observational data or model output, it should be possible to represent
it in a two-dimensional phase space. Statistical analysis methods such as
complex EOF analysis (Barnett 1981), Principal Oscillation Pattern (POP)
analysis; (Hasselmann 1988), and Multi-channel Singular Spectrum Analysis (MCSSA; Vautard and Chil 1989) are well-suited for detecting such
oscillations, if they exist, though if not used in conjunction with stringent
tests of statistical significance, they are also capable of detecting spurious
oscillations.
Some normal mode solutions, and some quasi-periodic phenomena lack a
statistically significant "imaginary component" (i.e., a second EOF whose
expansion coefficient time series oscillates in quadrature with that of the
leading EOF). Periodic or quasi-periodic phenomena may possess progressive wave signatures when viewed in the appropriate phase space, but they
may be detectable only as standing oscillations if the phase space chosen for
the analysis does not include the variables or spatial patterns that exhibit
a sufficient range of phase lags relative to the leading EOF. In the presence of sampling variability, standing oscillations can easily be mistaken
for progressive oscillations if careful significance testing is not performed.
In general, the more periodic the phenomenon, the more its evolution is
constrained to resemble a progressive or standing oscillation in some appropriately chosen two-dimensional phase space. Strong bandpass filtering or
methods of analysis that have a predilection for quasi-periodic modes (i.e.,
POP analysis and MCSSA) will inevitably tend to focus the investigator's
attention on such phenomena, regardless of whether they have any physical