268
Chapter 14: Patterns in Time: SSA and MSSA
The estimation of power spectra associated with SSA elements can be
done in a very neat way by combining Maximum entropy estimation with
SSA (Vautard et al., 1992). For SSA, this implies an autoregressive model of
order m* -1, and for MSSA, this involves building a multichannel autoregressive model of the same order. This latter model looks like the POP model
described in Chapter 15, but' ,with a higher order than 1. The estimation
of the coeflicients of these models is tricky. A very nice description of the
problems encountered in this estimation can be found ill Ulrych and Bishop
(1975).
14.4 Climatic Applications of SSA
Along the line of statistical climate analysis, SSA and MSSA have been applied to climatic data, on various time scales. In the analysis of oceanic
sediment al cores (Vautard and Ghil, 1989), the dominant cycles (100 ka, 40
ka and 20 ka)2 of the paleoclimate have been extracted as pairs of oscillatory components in the oxygen isotopes ratio series, and SSA allowed to
exhibit strong modulations of the amplitude of these cycles along the quaternary epoch. On a shorter time scale, SSA has been applied to global
surface temperature records (Ghil and Vautard, 1991), like the ones presented in Chapter 4, and allowed to distinguish an interdecadal oscillation,
albeit poorly significant, owing to the shortness of the record. The analysis
of the Southern oscillation index (SOl) has been carried out by Rassmusson
et al. (1990), who demonstrated the existence of two dominant periods in
the ENSO signal. Finally, the intraseasonal variability has been investigated
by the analysis of geopotential heights (Ghil and Mo, 1991; Plaut and Vautard, 1994), and the atmospheric angular moment um (Penland et al., 1991).
Strongly intermittent intraseasonal oscillations have been found in the midlatitudes. We shall, as an example, focus on the intraseasonal variability, by
showing two applications of MSSA.
14.4.1 The Analysis of Intraseasonal Oscillations
For details about the contents of this section, the reader is referred to Plaut
and Vautard (1994). The series to be analyzed here is the NMC final analysis
of 700 hPa geopotential heights, covering aperiod of 32 years (1954-1986).
The analysis has been carried out over the Atlantic domain, the Pacific domain, and the global Northern hemisphere, but for the sake of conciseness,
we shall present here results for the Atlantic domain only. The NMC grid on
which data was provided is the diamond grid, including 113 points over the
mid-Iatitude Atlantic (80 0 W - 40 0 E; 30 0 - 70 0 N). Since we are interested
in periods in the range of 10-100 days, the remarks of Section 14.3 about the
window length lead us to consider a window of 200 days. In order to avoid
21 ka represents 1000 years, Le., a "kiloyear".
Chapter 14: Patterns in Time: SSA and MSSA
The estimation of power spectra associated with SSA elements can be
done in a very neat way by combining Maximum entropy estimation with
SSA (Vautard et al., 1992). For SSA, this implies an autoregressive model of
order m* -1, and for MSSA, this involves building a multichannel autoregressive model of the same order. This latter model looks like the POP model
described in Chapter 15, but' ,with a higher order than 1. The estimation
of the coeflicients of these models is tricky. A very nice description of the
problems encountered in this estimation can be found ill Ulrych and Bishop
(1975).
14.4 Climatic Applications of SSA
Along the line of statistical climate analysis, SSA and MSSA have been applied to climatic data, on various time scales. In the analysis of oceanic
sediment al cores (Vautard and Ghil, 1989), the dominant cycles (100 ka, 40
ka and 20 ka)2 of the paleoclimate have been extracted as pairs of oscillatory components in the oxygen isotopes ratio series, and SSA allowed to
exhibit strong modulations of the amplitude of these cycles along the quaternary epoch. On a shorter time scale, SSA has been applied to global
surface temperature records (Ghil and Vautard, 1991), like the ones presented in Chapter 4, and allowed to distinguish an interdecadal oscillation,
albeit poorly significant, owing to the shortness of the record. The analysis
of the Southern oscillation index (SOl) has been carried out by Rassmusson
et al. (1990), who demonstrated the existence of two dominant periods in
the ENSO signal. Finally, the intraseasonal variability has been investigated
by the analysis of geopotential heights (Ghil and Mo, 1991; Plaut and Vautard, 1994), and the atmospheric angular moment um (Penland et al., 1991).
Strongly intermittent intraseasonal oscillations have been found in the midlatitudes. We shall, as an example, focus on the intraseasonal variability, by
showing two applications of MSSA.
14.4.1 The Analysis of Intraseasonal Oscillations
For details about the contents of this section, the reader is referred to Plaut
and Vautard (1994). The series to be analyzed here is the NMC final analysis
of 700 hPa geopotential heights, covering aperiod of 32 years (1954-1986).
The analysis has been carried out over the Atlantic domain, the Pacific domain, and the global Northern hemisphere, but for the sake of conciseness,
we shall present here results for the Atlantic domain only. The NMC grid on
which data was provided is the diamond grid, including 113 points over the
mid-Iatitude Atlantic (80 0 W - 40 0 E; 30 0 - 70 0 N). Since we are interested
in periods in the range of 10-100 days, the remarks of Section 14.3 about the
window length lead us to consider a window of 200 days. In order to avoid
21 ka represents 1000 years, Le., a "kiloyear".