Variability of the Earth’s orbit: The astronomical theory - Ice Ages and Interglacials: Measurements, Interpretation, and Models - page 262

model to the (tuned) geological record of the past 150,000 years. They found a
best fit with B ¼ 0.6 and T ¼ 17,000 years, so that the time constants for buildup
and decay of ice sheets were claimed to be 42,500 years and 10,600 years, respec-
tively (ice sheet decay is four times faster than ice sheet buildup when B ¼ 0.6).
Their solar intensity was taken at 65 N at noon on July 21 (it would have made
little difference had they chosen 50 N). The Imbries claimed: ''This simple model's
simulation of the past 150,000 years of climate is reasonably good—in fact, some-
what better than that achieved by the more complex but untuned models.''
However, it is arguable whether tuning a mathematical expression to (tuned) data
validates the astronomical theory or merely defines the best fit to this model
assuming the astronomical theory is correct. It is well known that geological data
tend to show slow buildups and rapid decays of ice volume with time, and the use
of the constant B in the above equations assures that the model will produce this
kind of sawtooth behavior.
Paillard (1998) sought to model the time evolution of ice volume over the past
2 million years in order to validate the astronomical theory. He emphasized the
''100 kyr problem'' and pointed out that previous investigators suggested that non-
linear responses of ice sheet dynamics to forcing were probably responsible. He
claimed: ''although some of these models compare well with the geological record
in the spectral domain, all of them fail to reproduce the correct amplitude and
phase of each glacial-interglacial cycle.''
Paillard (1998) presented a simple model which he claimed reproduces
reasonably well the succession of glacial-interglacial cycles over the Late
Pleistocene. He utilized daily insolation at 65 N at the summer solstice as his
forcing function, thereby assuming (as most have done) ''that summer insolation
at high northern latitudes controls the ice-sheet volume, and hence the global
climate.''
He assumed that, depending on insolation forcing and ice volume, the climate
system could enter three different regimes—i (interglacial), g (mild glacial), and G
(full glacial)—and that transitions between them are regulated by a set of rules as
follows.
i ) g transitions occur when insolation falls below i 0
g ) G transitions occur when the ice volume exceeds a threshold v max although this
parameter need not be specified in this model
It is assumed that an ice sheet needs some minimal time t g in order to grow to the
point where volume exceeds v max and that the insolation maxima preceding the
g ) G transition must remain below the level i 3 . The g ) G transition then can
occur at the next insolation decrease when it falls below i 2 . Apparently (it is
dicult to follow exactly what was done), if the system remains in the g state for
a time t g , during which the peaks in insolation remain below i 3 and the average
insolation lies below i 2 , the system will make a sudden transition to state G.
G ) i transitions occur when insolation increases above i 1