21
for the regularity of the cycle with a tendency for 'phase locking' with the
annual cycle (as evidenced by the fact that most warm and cold episodes
reached peak amplitude during the season July-November); the late '70's
and '80's for the high mean SST relative to the previous deca<;les. Whether
these interdecadal changes are statistically significant is difficult to judge.
One could perform Monte Carlo tests on randomly generated time series to
determine the probability that the observed changes could have occurred
by chance, but in order to do so one would need to justify the choice of
an algorithm for generating the random time series and to quantitatively
define the features in the time series that were observed to change on the
interdecadal time scale. If these definitions were made on an a posteriori
basis, in such a way that they tended to accentuate the importance of the
apparent regime shifts or unprecedented events in the record, the integrity
of the significance test would be compromised.
3 The view from "phase-space"
Although it may be conceptually useful to envision the entire climate system as residing in a multi-dimensional "phase space" , in which each of the
coordinate axes represents an independent "degree of freedom" , this concept is too abstract to apply to real observations. Any serious attempt at
a comprehensive representation of the evolution of the climate system over
the past few decades or centuries would require a phase space with so many
dimensions that the observational record would literally be lost in it (i.e.,
most of the space would be empty) and the description of the behaviour
would involve keeping track of so many variables that it would be very difficult to digest it and distill any useful information from the exercise. Even
the task of determining what coordinate axes to use to define the space
would be a daunting one. In practice, it is feasible to perform analyses
only in a very small subspace selected to illuminate some particular aspect
of climate variability. As implied by the first paragraph of this chapter,
the selection of that subspace may prove to be the most important step in
the analysis.
Periodic and quasi-periodic variations lend themselves to a representation in a one- or a two-dimensional phase space, depending upon whether
they can be described as "standing oscillations" or "progressive oscillations". In the former, all time series fluctuate either in-phase or one half
cycle out of phase, apart from sampling variability, whereas in the latter
for the regularity of the cycle with a tendency for 'phase locking' with the
annual cycle (as evidenced by the fact that most warm and cold episodes
reached peak amplitude during the season July-November); the late '70's
and '80's for the high mean SST relative to the previous deca<;les. Whether
these interdecadal changes are statistically significant is difficult to judge.
One could perform Monte Carlo tests on randomly generated time series to
determine the probability that the observed changes could have occurred
by chance, but in order to do so one would need to justify the choice of
an algorithm for generating the random time series and to quantitatively
define the features in the time series that were observed to change on the
interdecadal time scale. If these definitions were made on an a posteriori
basis, in such a way that they tended to accentuate the importance of the
apparent regime shifts or unprecedented events in the record, the integrity
of the significance test would be compromised.
3 The view from "phase-space"
Although it may be conceptually useful to envision the entire climate system as residing in a multi-dimensional "phase space" , in which each of the
coordinate axes represents an independent "degree of freedom" , this concept is too abstract to apply to real observations. Any serious attempt at
a comprehensive representation of the evolution of the climate system over
the past few decades or centuries would require a phase space with so many
dimensions that the observational record would literally be lost in it (i.e.,
most of the space would be empty) and the description of the behaviour
would involve keeping track of so many variables that it would be very difficult to digest it and distill any useful information from the exercise. Even
the task of determining what coordinate axes to use to define the space
would be a daunting one. In practice, it is feasible to perform analyses
only in a very small subspace selected to illuminate some particular aspect
of climate variability. As implied by the first paragraph of this chapter,
the selection of that subspace may prove to be the most important step in
the analysis.
Periodic and quasi-periodic variations lend themselves to a representation in a one- or a two-dimensional phase space, depending upon whether
they can be described as "standing oscillations" or "progressive oscillations". In the former, all time series fluctuate either in-phase or one half
cycle out of phase, apart from sampling variability, whereas in the latter