14
series for each individual gridpoint and then area averaged over the entire
domain to form a single plot for each type of calculation. First a set of
'aggregated' time series was generated from each of the daily time series
derived from the GCM run: the first N daily values were averaged to form
the first data point of the aggregate time series, daily values from N + 1
to 2N were averaged to form the second data point, etc. This procedure
is designed to emulate the conventional formatting of climate time series
in terms of non-overlapping monthly means, annual means, decadal means
etc. The autocorrelation was then computed at a lag of one data point for
the daily time series and the entire set of aggregated time series generated
from them. The results are shown in the upper left panel. Lag on the
abscissa refers to the averaging interval N used in forming the aggregated
time series. The figure shows that for averaging intervals less than about
100 days, successive values of the aggregated time series are positively
correlated (i.e., the series are "red"), whereas for longer intervals they are
uncorrelated (Le., the series resemble white noise).
The upper right panel shows how the variance of the 500-hPa height
field in the GCM drops off with increasing averaging interval N. For averaging intervals longer than 100 days the curve becomes tangent to the
dotted straight line, whose slope is indicative of an inverse proportionality between variance and averaging interval, the characteristic signature of
white noise. The lower left panel shows the variance based on subsamples
of the record N days in length, averaged over all such samples obtained
from the 100,000 day record. Variance increases with the length of the
subsamples for subsample lengths up to around 100 days, beyond which
only a very small further increase is evident.
The lower right panel shows the corresponding frequency spectra based
on the Tukey lag-correlation method, using a maximum lag of 1000 days
(1% of the length of the record), the longest that was found to yield an
acceptably smooth spectrum. The spectral resolution (which is also the
lowest frequency that can be resolved) corresponds to one cycle per two
lag intervals (2000 days) and the curve in Fig. 10 begins with the second
spectral estimate (1 cycle per 500 days): the lowest frequency that is not
affected by the detrending of the time series. The transition from white
to red, where the variance begins to drop off with increasing frequency, is
seen to occur around a period of a few hundred days, which corresponds
to the around the 5th spectral estimate. The white (flat) segment of the
spectrum is confined to the region so close to zero frequency that it is not
series for each individual gridpoint and then area averaged over the entire
domain to form a single plot for each type of calculation. First a set of
'aggregated' time series was generated from each of the daily time series
derived from the GCM run: the first N daily values were averaged to form
the first data point of the aggregate time series, daily values from N + 1
to 2N were averaged to form the second data point, etc. This procedure
is designed to emulate the conventional formatting of climate time series
in terms of non-overlapping monthly means, annual means, decadal means
etc. The autocorrelation was then computed at a lag of one data point for
the daily time series and the entire set of aggregated time series generated
from them. The results are shown in the upper left panel. Lag on the
abscissa refers to the averaging interval N used in forming the aggregated
time series. The figure shows that for averaging intervals less than about
100 days, successive values of the aggregated time series are positively
correlated (i.e., the series are "red"), whereas for longer intervals they are
uncorrelated (Le., the series resemble white noise).
The upper right panel shows how the variance of the 500-hPa height
field in the GCM drops off with increasing averaging interval N. For averaging intervals longer than 100 days the curve becomes tangent to the
dotted straight line, whose slope is indicative of an inverse proportionality between variance and averaging interval, the characteristic signature of
white noise. The lower left panel shows the variance based on subsamples
of the record N days in length, averaged over all such samples obtained
from the 100,000 day record. Variance increases with the length of the
subsamples for subsample lengths up to around 100 days, beyond which
only a very small further increase is evident.
The lower right panel shows the corresponding frequency spectra based
on the Tukey lag-correlation method, using a maximum lag of 1000 days
(1% of the length of the record), the longest that was found to yield an
acceptably smooth spectrum. The spectral resolution (which is also the
lowest frequency that can be resolved) corresponds to one cycle per two
lag intervals (2000 days) and the curve in Fig. 10 begins with the second
spectral estimate (1 cycle per 500 days): the lowest frequency that is not
affected by the detrending of the time series. The transition from white
to red, where the variance begins to drop off with increasing frequency, is
seen to occur around a period of a few hundred days, which corresponds
to the around the 5th spectral estimate. The white (flat) segment of the
spectrum is confined to the region so close to zero frequency that it is not