Page 146 - Earth's Climate Past and Future

122 PART III • Orbital-Scale Climate Change

BOX 7-1 TOOLS OF CLIMATE SCIENCE
Cycles and Modulation

low changes in Earth’s orbit around the Sun occur in a
amplitude
Scyclic or rhythmic way, as do the changes in amount of
incoming solar radiation they produce. The science of
wave physics provides the terminology needed to
describe these changes. The length of a cycle is referred to
Wavelength = period (in years)
as its wavelength. Expressed in units of time, the wave- 1
Frequency =
length of a cycle is called the period, the time span period
A Sine-wave cycle
between successive pairs of peaks or valleys.
The opposite (or inverse) of the period of a cycle is its
Individual cycles
frequency, the number of cycles (or in this case fractions
of one cycle) that occur in one year. If a cycle has a period
of 10,000 years, its frequency is 0.0001 cycle per year (one
cycle every 10,000 years). In this book, we will refer to
cycles in terms of their periods.
Modulation of cycles
Another important aspect of cycles is their ampli- B Amplitude modulation
tude, a measure of the amount by which they vary around
Description of wave behavior (A) Perfectly cyclic behavior
their long-term average. Low-amplitude cycles barely
can be represented by a sine wave with a particular period
depart from the long-term mean trend; high-amplitude and amplitude. (B) Cycles may show regular variations in
cycles fluctuate more widely. amplitude, or modulation.
Not all cycles are perfectly regular. Commonly the
sizes of peaks and valleys oscillate irregularly around the If variations in a particular signal are regular in both
long-term mean value through time. Behavior in which period and amplitude, it is appropriate to use the term
the amplitude of peaks and valleys changes in a repetitive “cycle.” For the case of perfect cyclicity, this behavior is
or cyclic way is called modulation, a concept that lies described as “sinusoidal” or sine waves.If the variations are
behind the principle of AM (amplitude modulation) radio. irregular in period, the term “cyclical” is technically incor-
Modulation creates an envelope that encompasses the rect; “quasi-cyclical” or “quasi-periodic” is preferable. In the
changing amplitudes that occur at a specific cycle. Note case of orbital-scale changes, we will informally use the
that modulation of a cycle is not in itself a cycle; it simply adds term “cyclic” or “periodic” for climatic signals that are
amplitude variations to an actual cycle. nearly regular but vary slightly in wavelength or amplitude.

radiation received at any latitude. As a result, solstices of this range, and the angle is currently decreasing. Cyclic
and equinoxes do not even exist because every day has changes in tilt angle occur mainly at a period of 41,000
the same length. A tilted axis is necessary for Earth to years, the time interval that separates successive peaks or
have seasons. successive valleys (see Box 7–1). The cycles are fairly reg-
Next consider the opposite extreme with a maxi- ular, both in period (wavelength) and in amplitude.
mum tilt of 90° (Figure 7-3B). Solar radiation is Changes in tilt amplify or suppress the strength of
directed straight at the summer-season pole, while the the seasons, especially at high latitudes (Figure 7-5).
winter-season pole lies in complete darkness. Six Larger tilt angles turn the summer hemisphere poles
months later, the two poles have completely reversed more directly toward the Sun and increase the amount
position. The difference between these two extreme of solar radiation received. The increase in tilt that
configurations shows that tilt is an important control on turns the North Pole more directly toward the Sun at
solar radiation at polar latitudes. its summer solstice on June 21 also turns the South Pole
The angle of Earth’s tilt has varied through time more directly toward the Sun at its summer solstice six
within a narrow range, between values as small as 22.2° months later (December 21). On the other hand, the
and as large as almost 24.5° (Figure 7-4). The French increased angle of tilt that turns each polar region more
astronomer Urbain Leverrier discovered these variations directly toward the Sun in summer also turns each win-
in the 1840s. Today Earth’s tilt (23.5°) is near the middle ter season pole away from the Sun.