Page 157 - Earth's Climate Past and Future

CHAPTER 7 • Astronomical Control of Solar Radiation 133

We can combine these three cycles by adding them change in amplitude through time (see Figures 7-4 and
together in various ways (Figure 7-20B). When the 7-15). Obviously, it will be impossible to disentangle all
23,000-year and 100,000-year cycles are combined, the this information simply by eye.
resulting signal is obviously a simple addition of the two
separate cycles. The two cycles are easy to distinguish
because they differ in period by a factor of more than 4 7-8 Time Series Analysis
(100,000 divided by 23,000 = 4.3). To simplify analyses of cyclic variations in climate
It becomes more difficult to detect the two original changes, scientists use time series analysis. The term
signals when only the 23,000-year and 41,000-year “time series” refers to records plotted against age (time).
cycles are combined. Because the periods of these two These techniques extract rhythmic cycles embedded
cycles are more similar, they reinforce and cancel each within records of climate.
other in somewhat complicated ways. The task becomes The first step in time series analysis is to convert cli-
even more difficult when all three cycles are combined, matic records to a time framework. After individual
as in the bottom curve of Figure 7-20B. It is not at all measurements of a climatic indicator have been made
obvious to the eye that this signal is a simple addition of (for example, across an interval in a sediment core), all
three perfect sine waves. available sources of dating are used to define the ages of
In the case of Earth’s actual climate records, the sit- particular levels within the sequence. A complete time
uation is even more complex because the three cycles scale for the sequence is then created by interpolating
are not only superimposed on each other but also the ages of all sediment depths between the dated levels.
This time scale can then be used to plot the climatic
record against time for further analysis.
One technique is spectral analysis. Modern tech-
100,000
1
1 –1 niques of spectral analysis are beyond the scope of this
book, but we need at least a basic sense of how this tech-
Cycle amplitudes –1 41,000 –1 nique detects cycles in records of past climate change.
–1
One way to visualize what happens in spectral analysis is
1
1
to imagine taking a climate record plotted on a time axis
and gradually sliding a series of sine waves of different
1 23,000 1 periods across it. As this is done, the correlation between
each sine wave and the full climatic signal is measured
–1 –1
for each point in the sliding process. If the climate
Time record that is being examined contains a strong cycle at
A Individual sine-wave cycles
one of the sine wave periods, the climate record will
100,000 + 23,000 show a strong correlation with that sine wave at some
2 2 point in the sliding process. The strong correlation indi-
cates that the climatic signal contains a strong cycle at
–2 41,000 + 23,000 –2 that period. As this process is repeated for different sine
waves with different periods, other cycles may emerge.
Signal amplitudes –2 –2 posed cycles in the bottom part of Figure 7-20B. A
Now we return to the example of the three superim-
2
2
spectral analysis run on this signal will extract the three
component (orbital) cycles, which can be displayed on a

zontal axis shows a range of periods plotted on a log
3 100,000 + 41,000 + 23,000 3 plot called a power spectrum (Figure 7-21). The hori-
scale, with the shorter periods to the right. The vertical
axis represents the amplitude of the cycles (see Box 7-1),
also known as their “power.” The height of the lines
–3 –3 plotted on the power spectrum is related to the square
Time of the amplitude of the cycle at that period.
B Combination of cycles For the example shown in Figure 7-21, all three
FIGURE 7-20 Complications from overlapping cycles If cycles detected by spectral analysis plot as narrow “line
perfect sine wave cycles with periods of 100,000, 41,000, and spectra,” with their power concentrated entirely at the
23,000 years are added together so that they are periods shown by the solid vertical lines. In this ideal-
superimposed on top of one another, the original cycles are ized example, no power occurs anywhere else in the
almost impossible to detect by eye in the combined signal. spectrum than at these three cycles.