Variability of the Earth’s orbit: The astronomical theory - Ice Ages and Interglacials: Measurements, Interpretation, and Models - page 251

Thus, we see that peak solar intensity in summer at higher latitudes (north or
south) will be a maximum when (a) the longitude of perihelion occurs near
local midsummer (north or south), (b) eccentricity is high at such a maximum,
and (c) obliquity is high at such a maximum. The combined effect of high eccen-
tricity and the longitude of perihelion coinciding with local midsummer (north or
south) assures that peak solar intensity at the local high latitude will occur in
summer (when high latitudes receive almost all their solar input anyway). The
effect of obliquity is general: higher obliquity shifts more solar irradiance from
low latitudes to high latitudes. As obliquity approaches 45 , there is little differ-
ence between the equator and the poles. When obliquity exceeds about 54 , there
is greater solar intensity at the poles than at the equator. As these parameters
evolve with time, peak solar intensity in summer at higher latitudes undergoes
quasi-periodic variations and will tend to maximize either in the north or south
when local conditions (a), (b), and (c) are satisfied.
While variations in obliquity change the distribution of solar input between
high and low latitudes, and changes in the longitude of perihelion change the
season of closest approach to the Sun, neither of these parameters affect total
yearly solar input to the Earth. However, increases in eccentricity slightly increase
total yearly solar input to the Earth because, when the Earth is closer to the Sun,
the 1 r 2 law causes the increase in solar intensity at closest approach to be greater

than the decrease in solar intensity when the Earth is farthest from the Sun.
If the appropriate measure of solar input to high latitudes is not peak solar
intensity in summer, but yearly total solar intensity, then the formula given
previously should be used. In this case, eccentricity has only a minor influence
and, indeed, total solar input over a year hardly varies from year to year. This
does not seem to lead to a viable theory for ice ages.
A great deal of research has used spectral analysis applied to ice age isotope
data and to modeled solar variability. Unfortunately, some of these researchers
compared the astronomical theory with isotope data as if each of the factors—
eccentricity, longitude of perihelion, and obliquity—acted independently in con-
tributing to changes in climate. If the forcing function from the astronomical
theory is peak solar intensity in summer, which is dependent on all three factors
in the manner previously described, no single factor acts alone. On the other hand,
one must consider the possibility that changes in the Earth's orbit might not only
change peak solar intensity in summer, but also other relevant global parameters.
The buildup of budding ice sheets depends not only on the rate at which solar
input can deplete ice sheets in summer at high latitudes, but also on the amount
of precipitation (primarily in winter) at high latitudes to replenish budding ice
sheets. If precipitation is primarily affected by a single Earth orbital parameter, it
may skew the dependence of ice age cycles on other Earth orbital parameters. Lee
and Poulsen (2009) used a climate model to examine how precipitation in Arctic
areas depends on the Earth's orbital parameters. Unfortunately, their model was
not very representative. Aside from the generic inadequacies of climate models
regarding clouds, aerosols, humidity, and other feedback processes, for reasons
that seem inexplicable they used greenhouse gas concentrations corresponding to

=