458
Carlo simulations, gives confidence intervals outside which a time series
can be considered to be significantly different from a generic red-noise simulation. For instance, if an eigenvalue Ak lies above a 90% noise percentile,
then the red-noise null hypothesis for the associated EOF (and PC) can be
rejected with this confidence. Otherwise, that particular SSA component
of the time series cannot be considered as significantly different from red
noise.
As the next step in the analysis our SOl time series, we apply an MCSSA noise test to it. In order to enhance the readability of the diagrams
for the SSA spectra in the presence of MC-SSA error bars, we associate
a dominant frequency with each EOF detected by SSA, as suggested by
Vautard et al. (1992), and plot in Fig. 7 SSA eigenvalues (diamonds) vs.
frequency, following Allen and Smith (1996). Such a plot is easier to interpret, with respect to the MC-SSA error bars, than plotting vs. SSA rank
k as in Fig. 3. Care needs to be exercised, however, since the dominantfrequency estimate may be uncertain due to the possible anharmonicity of
the EOFs, especially for low frequencies. The error bars in Fig. 7 represent
90% of the range of the eigenvalues obtained at that (dominant) frequency
over the given ensemble of 1000 red-noise realizations (i.e., they denote
the interval between the 5th and 95th percentile). Hence, the eigenvalues
lying outside the bars have a 90% chance not to be due merely to red
noise. The high values exhibit a significant quasi-biennial oscillation and
an oscillatory component with a period between 5 and 6 years. The low
values near 1 cycle yr- 1 are probably associated with nonlinear side effects
of the seasonal cycle (Jin et al. 1994, Tziperman et al. 1994) which have
not been properly removed.
The MC-SSA algorithm described above can be adapted to eliminate
known periodic components and test the residual against noise. This adaptation might provide a sharper insight into the dynamics captured by the
data, since known periodicities (like orbital forcing on the Quaternary time
scale or seasonal forcing on the intraseasonal-to-interannual one) often generate much of the variance at the lower frequencies manifest in a time series and alter the rest of the spectrum. Allen (1992) and Allen and Smith
(1996) describe this refinement of MC-SSA which consists in restricting the
projections given by Eq. (11) to the EOFs that do not account for known
periodic behavior.
Carlo simulations, gives confidence intervals outside which a time series
can be considered to be significantly different from a generic red-noise simulation. For instance, if an eigenvalue Ak lies above a 90% noise percentile,
then the red-noise null hypothesis for the associated EOF (and PC) can be
rejected with this confidence. Otherwise, that particular SSA component
of the time series cannot be considered as significantly different from red
noise.
As the next step in the analysis our SOl time series, we apply an MCSSA noise test to it. In order to enhance the readability of the diagrams
for the SSA spectra in the presence of MC-SSA error bars, we associate
a dominant frequency with each EOF detected by SSA, as suggested by
Vautard et al. (1992), and plot in Fig. 7 SSA eigenvalues (diamonds) vs.
frequency, following Allen and Smith (1996). Such a plot is easier to interpret, with respect to the MC-SSA error bars, than plotting vs. SSA rank
k as in Fig. 3. Care needs to be exercised, however, since the dominantfrequency estimate may be uncertain due to the possible anharmonicity of
the EOFs, especially for low frequencies. The error bars in Fig. 7 represent
90% of the range of the eigenvalues obtained at that (dominant) frequency
over the given ensemble of 1000 red-noise realizations (i.e., they denote
the interval between the 5th and 95th percentile). Hence, the eigenvalues
lying outside the bars have a 90% chance not to be due merely to red
noise. The high values exhibit a significant quasi-biennial oscillation and
an oscillatory component with a period between 5 and 6 years. The low
values near 1 cycle yr- 1 are probably associated with nonlinear side effects
of the seasonal cycle (Jin et al. 1994, Tziperman et al. 1994) which have
not been properly removed.
The MC-SSA algorithm described above can be adapted to eliminate
known periodic components and test the residual against noise. This adaptation might provide a sharper insight into the dynamics captured by the
data, since known periodicities (like orbital forcing on the Quaternary time
scale or seasonal forcing on the intraseasonal-to-interannual one) often generate much of the variance at the lower frequencies manifest in a time series and alter the rest of the spectrum. Allen (1992) and Allen and Smith
(1996) describe this refinement of MC-SSA which consists in restricting the
projections given by Eq. (11) to the EOFs that do not account for known
periodic behavior.