Figure 12.2: Coloured lines:
power spectra of global mean temperatures in the unforced control integrations
that are used to provide estimates of internal climate variability in Figure
12.12. All series were linearly detrended prior to analysis, and spectra computed
using a standard Tukey window with the window width (maximum lag used in the estimate)
set to one-fifth of the series length, giving each spectral estimate the same
uncertainty range, as shown (see, e.g., Priestley, 1981). The first 300 years
were omitted from ECHAM3-LSG, CGCM1 and CGCM2 models as potentially trend-contaminated.
Solid black line: spectrum of observed global mean temperatures (Jones et al.,
2001) over the period 1861 to 1998 after removing a best-fit linear trend. This
estimate is unreliable on inter-decadal time-scales because of the likely impact
of external forcing on the observed series and the negative bias introduced by
the detrending. Dotted black line: spectrum of observed global mean temperatures
after removing an independent estimate of the externally forced response provided
by the ensemble mean of a coupled model simulation (Stott et al., 2000b, and Figure
12.7c). This estimate will be contaminated by uncertainty in the model-simulated
forced response, together with observation noise and sampling error. However,
unlike the detrending procedure, all of these introduce a positive (upward) bias
in the resulting estimate of the observed spectrum. The dotted line therefore
provides a conservative (high) estimate of observed internal variability at all
frequencies. Asterisks indicate models whose variability is significantly less
than observed variability on 10 to 60 year time-scales after removing either a
best-fit linear trend or an independent estimate of the forced response from the
observed series. Significance is based on an F-test on the ratio observed/model
mean power over this frequency interval and quoted at the 5% level. Power spectral
density (PSD) is defined such that unit-variance uncorrelated noise would have
an expected PSD of unity (see Allen et al., 2000a, for details). Note that different
normalisation conventions can lead to different values, which appear as a constant
offset up or down on the logarithmic vertical scale used here. Differences between
the spectra shown here and the corresponding figure in Stouffer et al. (2000)
shown in Chapter 8, Figure 8.18
are due to the use here of a longer (1861 to 2000) observational record, as opposed
to 1881 to 1991 in Figure 8.18. That figure also
shows 2.5 to 97.5% uncertainty ranges, while for consistency with other figures
in this chapter, the 5 to 95% range is displayed here.