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CHAPTER 7 • Astronomical Control of Solar Radiation 129

The changing values of sinω affect the extreme insolation does not arrive at Earth’s surface because
perihelion and aphelion positions shown in Figure 7-13 clouds and other features in the climate system alter
by altering the distance between Earth and the Sun. the amount that actually penetrates the atmosphere
With greater eccentricity, the differences in distance (companion Web site, pp. 2-4). Still, these calculations
between a close pass and a distant pass are magnified. of insolation are the best guide to the effects of orbital
With a nearly circular orbit, differences in distance changes on Earth’s climate.
nearly vanish.
7-6 Insolation Changes by Month and Season
IN SUMMARY, changes in eccentricity magnify or The long-term trends of tilt (see Figure 7-4) and sinω
suppress contrasts in Earth-Sun distance around the (see Figure 7-15) contain all the information needed to
orbit at the 23,000-year precession cycle. These calculate the amount of insolation arriving at any lati-
changes in distance to the Sun in turn alter the tude and season. By convention, climate scientists usu-
amount of solar radiation received on Earth (more ally show the amount of insolation (or the departures of
radiation at the perihelion close-pass position, less insolation from a long-term average) during the solstice
at the distant-pass aphelion position). months of June and December in watts per square
2
meter (W/m ). Some studies use an alternate form,
calories per square centimeter per second.
The modulation of the sinω signal by eccentricity June and December insolation values over the
is not a real cycle (see Box 7–1), even though this state- last 300,000 years show a strong dominance of the
ment probably goes against your intuition. You have 23,000-year precession cycle at lower and middle lati-
learned that eccentricity varies at cycles of 100,000 and tudes and also at higher latitudes during the summer
413,000 years (see Figures 7–7 and 7–14), and you can season (Figure 7-16). Just like the sinω precessional
see that the upper and lower envelopes of the sinω sig- index, individual insolation cycles at lower latitudes
nal vary at these periods (see Figure 7-15). But the off- occur at wavelengths near 23,000 years, but their ampli-
setting effects of the upper and lower envelopes cancel tudes are modulated at periods of 100,000 and 413,000
each other out. years. The June and December monthly insolation
For example, when the 23,000-year cycle is vary- curves at each latitude in Figure 7-16 are also opposite
ing between large minima and large maxima, these adja- in sign. Both can vary by as much as 12% (40 W/m )
2
cent minima and maxima are approximately equal in around the long-term mean value for each latitude.
size. Over the longer (100,000-year) wavelengths of the The 41,000-year cycle of tilt (obliquity) is not
eccentricity variations, the amplitudes of the shorter- evident at lower latitudes but is visible in the low-
term (23,000-year) oscillations cancel each other out, amplitude variations of winter-season insolation at
leaving a negligible amount of net variation. Similarly, higher mid-latitudes (northern hemisphere January
short-term variations between small-amplitude max- and southern hemisphere June at 60°). Summer season
ima and minima at other times also offset each other. insolation changes at the tilt cycle are actually larger
The importance of this point will become obvious in than those in winter, although this excess is not evident
Chapters 9 and 11.
in these precession-dominated plots. One example is
two precession cycles that are evident near 50,000 years
IN SUMMARY, the combined effects of eccentricity and ago in the June insolation signal for latitude 20°N but
precession cause the distance from the Earth to the gradually blend and merge into a single tilt cycle at
Sun to vary by season, primarily at a cycle of 23,000 latitude 80°N (see Figure 7-16).
years. Times of high eccentricity produce the largest Changes in annual mean insolation at the 41,000-
contrasts in Earth-Sun distance within the orbit, year tilt signal at high latitudes have the same sign as the
and conversely. As Earth precesses in its orbit, the summer insolation anomalies, but they are lower in
changes in Earth-Sun distance are registered as amplitude. The lesser significance of winter season
seasonal changes in arriving radiation. changes in tilt at full-polar latitudes results from the
fact that no insolation at all arrives during long
stretches of polar winter.
Changes in Insolation Received on Earth
IN SUMMARY, monthly seasonal insolation changes
Changes in Earth’s orbit alter the amount of solar are dominated by precession at low and middle
radiation received by latitude and by season. Climate latitudes, with the effects of tilt evident only at
scientists refer to the radiation arriving at the top of higher latitudes.
Earth’s atmosphere as insolation. Some of this incoming