15
0.5
o~------~------~~~--~
10°
10 1
10 2
10 3
lifL-------~--------~------~
10°
101
10 2
Jag (dayS)
averaging interval (days)
2.-~------~----~------~
3r-------~--------~----~
el1.5
o§
2
~
a>
§
.~ 0.5
o~~----~------~----~~
10
100
1000
10000
10- 2
10- 1
sample length (days)
frequency
Figure 10: Hemispheric-mean 500-hPa height statistics derived from a 100,000 day perpetual January integration ofthe NOAA/GFDL R15 truncation general circulation model
run with fixed climatological mean SST. Upper left: lag-1 autocorrelation for the aggregated time series as a function of lag between successive data points. Upper right: variance
of the aggregated time series as a function of averaging interval, plotted on a log scale in
arbitrary units. The slope of the dotted line corresponds to an inverse relation between
variance and averaging interva1. Lower left: average variance of consecutive segments of
the time series as a function of sample length. Lower right: log/log plot of the power
spectral density (variance per unit frequency interval) as a function of frequency in cycles
per day. Note that variance is not proportional to area under the curve. All statistics
represent approximations based on the 10 leading EOF's of the simulated 500-hPa height
field.
clearly visible when this spectrum is plotted on a linear frequency scale
(not shown).
Although each involves a different way of analyzing the time series, the
four displays in Fig. 10 contain essentially equivalent information about
the transition between aperiodic and random behaviour. Such redundancy
0.5
o~------~------~~~--~
10°
10 1
10 2
10 3
lifL-------~--------~------~
10°
101
10 2
Jag (dayS)
averaging interval (days)
2.-~------~----~------~
3r-------~--------~----~
el1.5
o§
2
~
a>
§
.~ 0.5
o~~----~------~----~~
10
100
1000
10000
10- 2
10- 1
sample length (days)
frequency
Figure 10: Hemispheric-mean 500-hPa height statistics derived from a 100,000 day perpetual January integration ofthe NOAA/GFDL R15 truncation general circulation model
run with fixed climatological mean SST. Upper left: lag-1 autocorrelation for the aggregated time series as a function of lag between successive data points. Upper right: variance
of the aggregated time series as a function of averaging interval, plotted on a log scale in
arbitrary units. The slope of the dotted line corresponds to an inverse relation between
variance and averaging interva1. Lower left: average variance of consecutive segments of
the time series as a function of sample length. Lower right: log/log plot of the power
spectral density (variance per unit frequency interval) as a function of frequency in cycles
per day. Note that variance is not proportional to area under the curve. All statistics
represent approximations based on the 10 leading EOF's of the simulated 500-hPa height
field.
clearly visible when this spectrum is plotted on a linear frequency scale
(not shown).
Although each involves a different way of analyzing the time series, the
four displays in Fig. 10 contain essentially equivalent information about
the transition between aperiodic and random behaviour. Such redundancy