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Chapter 14: Patterns in Time: SSA and MSSA
14.5 Conclusions
The analysis of time patterns provides a dynamical insight to the climate.
SSA and MSSA are statistical analysis tools that describe the structure of
second-order moments of time sequences or space-time sequences, just as
well as EOF analysis does with second-order moments of spatial distributions. There is however a difference in the interpretation of spatial patterns
and time patterns: as explained in Chapter 13, spatial EOFs depend strongly
on the dot product used, and this arbitrariness leads to a difficulty in assessing the dynamical significance of the patterns. They cannot be considered as
"dynamical mo des" of variability. They can still be used as "guess patterns" ,
since a few of them approximate generally quite well the spatial structure of
instantaneous flows. This arbitrariness is still present with the MSSA for the
spatial directions, but it is removed in the delay-coordinate space, i.e., in the
lag domain. Space-time patterns are generally band limited. Spatial structures are tied to a time scale. The natural oscillators of the physical system
under study will come out as pairs of time patterns in phase quadrature.
When a projection is made onto the first few time patterns, one makes
the implicit assumption that the system is the sum of a finite number of
oscillators. Thus SSA and MSSA are particularly suited to study oscillatory
behaviour. At first sight SSA might seem inadequate for the study of strongly
nonlinear systems such as the climate. Such systems may still possess intermittent oscillations due to the presence of unstable periodic orbits. The fact
that the basis functions of SSA are given on a lag window of finite length
allows the localisation of these intermittent spells, unlike classical spectral
analysis which does not allow amplitude modulation.
Finally, we showed two applications of MSSA:
• the description of intraseasonal mid-latitude variability and its dominant oscillations. This application demonstrates that it is possible to
detect oscillatory phenomena without any prior guess of the underlying
physics. MSSA provides an objective index of phase and amplitude of
an oscillation that can serve as a basis for composite studies. We showed
in particular that weather regimes and intraseasonal oscillations are related. This emphasises the need for GCMs to reproduce this oscillatory
behaviour in order to be able to produce valuable long-range forecasts .
• MSSA time-patterns can be used as a basis of predictors for long-range
forecasting. These patterns are optimal in the sense that they achieve a
good compromise between compression of information and extraction of
slowly-varying oscillatory components. We have presented here a possible probabilistic fore casting scheme that is an improved-persistence
Chapter 14: Patterns in Time: SSA and MSSA
14.5 Conclusions
The analysis of time patterns provides a dynamical insight to the climate.
SSA and MSSA are statistical analysis tools that describe the structure of
second-order moments of time sequences or space-time sequences, just as
well as EOF analysis does with second-order moments of spatial distributions. There is however a difference in the interpretation of spatial patterns
and time patterns: as explained in Chapter 13, spatial EOFs depend strongly
on the dot product used, and this arbitrariness leads to a difficulty in assessing the dynamical significance of the patterns. They cannot be considered as
"dynamical mo des" of variability. They can still be used as "guess patterns" ,
since a few of them approximate generally quite well the spatial structure of
instantaneous flows. This arbitrariness is still present with the MSSA for the
spatial directions, but it is removed in the delay-coordinate space, i.e., in the
lag domain. Space-time patterns are generally band limited. Spatial structures are tied to a time scale. The natural oscillators of the physical system
under study will come out as pairs of time patterns in phase quadrature.
When a projection is made onto the first few time patterns, one makes
the implicit assumption that the system is the sum of a finite number of
oscillators. Thus SSA and MSSA are particularly suited to study oscillatory
behaviour. At first sight SSA might seem inadequate for the study of strongly
nonlinear systems such as the climate. Such systems may still possess intermittent oscillations due to the presence of unstable periodic orbits. The fact
that the basis functions of SSA are given on a lag window of finite length
allows the localisation of these intermittent spells, unlike classical spectral
analysis which does not allow amplitude modulation.
Finally, we showed two applications of MSSA:
• the description of intraseasonal mid-latitude variability and its dominant oscillations. This application demonstrates that it is possible to
detect oscillatory phenomena without any prior guess of the underlying
physics. MSSA provides an objective index of phase and amplitude of
an oscillation that can serve as a basis for composite studies. We showed
in particular that weather regimes and intraseasonal oscillations are related. This emphasises the need for GCMs to reproduce this oscillatory
behaviour in order to be able to produce valuable long-range forecasts .
• MSSA time-patterns can be used as a basis of predictors for long-range
forecasting. These patterns are optimal in the sense that they achieve a
good compromise between compression of information and extraction of
slowly-varying oscillatory components. We have presented here a possible probabilistic fore casting scheme that is an improved-persistence