20
The testing of the statistical significance of reported regime shifts is
problematical if they were not predicted a priori; especially if the record
is not much longer than the duration of the regimes, as is often the case
when one is dealing with interdecadal variability in the historical record.
Even in random time series with red spectra, chance superposition of the
various Fourier harmonics can sometimes create structures that could be
interpreted as regime shifts by an analyst intent on finding them. Impressive looking regime shifts can be created artificially by selecting a posteriori
(i.e., after inspecting the data) a number of 'key dates' characterized by
large positive or negative time derivatives, and compositing segments of
the time series relative to these key dates. One can be assured that the
larger the number of events included in the composite, the more clearly the
'regime shift', centered on the key date, will stand out above the temporal
variability within the artificial 'regimes' that precede and follow it.
The physical and statistical significance of what I will refer to as "unprecedented events" (e.g., record high or low values, the longest uninterrupted sequence with anomalies of the same polarity, the highest frequency
of record high or low values within an interval of prescribed length, the
strongest linear trend within an interval of prescribed length, the longest
interval between events of some prescribed type) in climatic time series of
finite length is also bound to be controversial. Even random time series exhibit record high and low values from time to time, and extrema of like sign
are likely to be clustered in time if the time series is even slightly red. The
pervasive nonstationarity inherent in many climatic time series increases
the likelihood of encountering unprecedented events. In particular, the
time series associated with chaotic nonlinear systems are full of surprises
which may involve changes in time-mean state and/or changes in the character of the variability about the time-mean state; e.g., the amplitude, the
dominant frequency, the tendency for periodic or aperiodic behaviour. In
a time series of finite length one is never sure that one has sampled the full
range of possible behaviour of the natural variability. Just because some
new kind of behaviour is noted doesn't necessarily imply that the earth has
entered into a new climatic regime or that anthropogenic influences must
be responsible for it.
The ENSO time series in Fig. 8 is a case in point. The mean state and
the character of the variability about the mean state have varied substantially from one decade to the next. For example, the 1930's and 40's were
notable for the absence of a strong ENSO cycle; the '60's and early 70's
The testing of the statistical significance of reported regime shifts is
problematical if they were not predicted a priori; especially if the record
is not much longer than the duration of the regimes, as is often the case
when one is dealing with interdecadal variability in the historical record.
Even in random time series with red spectra, chance superposition of the
various Fourier harmonics can sometimes create structures that could be
interpreted as regime shifts by an analyst intent on finding them. Impressive looking regime shifts can be created artificially by selecting a posteriori
(i.e., after inspecting the data) a number of 'key dates' characterized by
large positive or negative time derivatives, and compositing segments of
the time series relative to these key dates. One can be assured that the
larger the number of events included in the composite, the more clearly the
'regime shift', centered on the key date, will stand out above the temporal
variability within the artificial 'regimes' that precede and follow it.
The physical and statistical significance of what I will refer to as "unprecedented events" (e.g., record high or low values, the longest uninterrupted sequence with anomalies of the same polarity, the highest frequency
of record high or low values within an interval of prescribed length, the
strongest linear trend within an interval of prescribed length, the longest
interval between events of some prescribed type) in climatic time series of
finite length is also bound to be controversial. Even random time series exhibit record high and low values from time to time, and extrema of like sign
are likely to be clustered in time if the time series is even slightly red. The
pervasive nonstationarity inherent in many climatic time series increases
the likelihood of encountering unprecedented events. In particular, the
time series associated with chaotic nonlinear systems are full of surprises
which may involve changes in time-mean state and/or changes in the character of the variability about the time-mean state; e.g., the amplitude, the
dominant frequency, the tendency for periodic or aperiodic behaviour. In
a time series of finite length one is never sure that one has sampled the full
range of possible behaviour of the natural variability. Just because some
new kind of behaviour is noted doesn't necessarily imply that the earth has
entered into a new climatic regime or that anthropogenic influences must
be responsible for it.
The ENSO time series in Fig. 8 is a case in point. The mean state and
the character of the variability about the mean state have varied substantially from one decade to the next. For example, the 1930's and 40's were
notable for the absence of a strong ENSO cycle; the '60's and early 70's