470
(Plaut and Vautard 1994). The properties of pairs of near-equal eigenvalues
that satisfy suitable significance criteria can also be transposed to M-SSA:
RCs based on pairs isolate elementary spatio-temporal oscillations. The
ideas of Monte Carlo noise tests can also be applied to M-SSA (Allen and
Robertson 1996), by paying additional attention to the spatial structure(s)
assumed by the null hypothesis.
An M-SSA application to low-frequency atmospheric variability is shown
in Fig. 12, adapted from Plaut and Vautard (1994). M-SSA is applied to
a time series of geopotential height anomalies at 70 kPa, covering 45 boreal winters between 1949 and 1994. The analysis is performed on five-day
averages (pentads), using ten channels (L = 10) obtained as the leading
PCs of a spatial EOF analysis (Preisendorfer 1988) of the anomaly fields
defined over the Pacific sector (30 0 -70 o N, 140o-260 0 E). The annual cycle
was removed and a time window of 180 days (M = 36) is used. The succession of panels in Fig. 12 shows the progression of an oscillating pattern,
keyed to the phase index associated with the EOF pair (11,12); the associated period is 40-45 days. This spatio-temporal evolution could be related
to the 50-day Madden-Julian (1971, 1972) oscillation in the tropical IndoPacific Ocean or to the -possibly independent - extratropical oscillation
reviewed by Ghil et al. (1991) and studied further by Marcus et al. (1994,
1996) and Strong et al. (1993, 1995), whose period is closer to 40 days.
M-SSA has also been applied to both observations and model results
on intraseasonal variability by Kimoto et al. (1991) and Keppenne and
Ghil (1993). It helped in the study of seasonal-to-interannual variability
in the tropical Pacific, for the analysis of data (Jiang et al. 1995) and
model simulations (Robertson et al. 1995a, b), as well as to investigate
interannual and interdecadal variability in global sea level data (Unal and
Ghi11995) and in United States surface air temperatures (Dettinger et al.
1995b). The channels can be the leading spatial PCs, as in the example of
Fig. 12, or a set of low-resolution grid-point time series, as in Jiang et al.
(1995), Robertson et al. (1995a, b) or Unal and Ghil (1995).
5 Whereto next?
We have introduced in Sec. 1 the concept of a ghost limit cycle (Fig. 1) as
the underpinning of the dynamic usefulness of a spectral peak. In a number of instances, from intraseasonal oscillations (Ghil et al. 1991) through
paleoclimatic variability (Ghil 1994), the robust identification of an SSA
(Plaut and Vautard 1994). The properties of pairs of near-equal eigenvalues
that satisfy suitable significance criteria can also be transposed to M-SSA:
RCs based on pairs isolate elementary spatio-temporal oscillations. The
ideas of Monte Carlo noise tests can also be applied to M-SSA (Allen and
Robertson 1996), by paying additional attention to the spatial structure(s)
assumed by the null hypothesis.
An M-SSA application to low-frequency atmospheric variability is shown
in Fig. 12, adapted from Plaut and Vautard (1994). M-SSA is applied to
a time series of geopotential height anomalies at 70 kPa, covering 45 boreal winters between 1949 and 1994. The analysis is performed on five-day
averages (pentads), using ten channels (L = 10) obtained as the leading
PCs of a spatial EOF analysis (Preisendorfer 1988) of the anomaly fields
defined over the Pacific sector (30 0 -70 o N, 140o-260 0 E). The annual cycle
was removed and a time window of 180 days (M = 36) is used. The succession of panels in Fig. 12 shows the progression of an oscillating pattern,
keyed to the phase index associated with the EOF pair (11,12); the associated period is 40-45 days. This spatio-temporal evolution could be related
to the 50-day Madden-Julian (1971, 1972) oscillation in the tropical IndoPacific Ocean or to the -possibly independent - extratropical oscillation
reviewed by Ghil et al. (1991) and studied further by Marcus et al. (1994,
1996) and Strong et al. (1993, 1995), whose period is closer to 40 days.
M-SSA has also been applied to both observations and model results
on intraseasonal variability by Kimoto et al. (1991) and Keppenne and
Ghil (1993). It helped in the study of seasonal-to-interannual variability
in the tropical Pacific, for the analysis of data (Jiang et al. 1995) and
model simulations (Robertson et al. 1995a, b), as well as to investigate
interannual and interdecadal variability in global sea level data (Unal and
Ghi11995) and in United States surface air temperatures (Dettinger et al.
1995b). The channels can be the leading spatial PCs, as in the example of
Fig. 12, or a set of low-resolution grid-point time series, as in Jiang et al.
(1995), Robertson et al. (1995a, b) or Unal and Ghil (1995).
5 Whereto next?
We have introduced in Sec. 1 the concept of a ghost limit cycle (Fig. 1) as
the underpinning of the dynamic usefulness of a spectral peak. In a number of instances, from intraseasonal oscillations (Ghil et al. 1991) through
paleoclimatic variability (Ghil 1994), the robust identification of an SSA