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model, it would not be clear how solar variations should be compared with
isotope ratios even if the astronomical theory was obeyed perfectly.
Most of the models developed so far have dealt with the variability of ice
volume resulting from solar variability in the NH. Calculated peak solar intensity
in the NH year by year is used as a forcing function. However, none of the models
yet developed seem to be completely a priori. The models utilize a certain amount
of physical logic to set up mathematical expressions for the rate of change of ice
volume as a function of solar intensity and ice volume, but the models contain
parameters that are adjusted to obtain a best fit between the model and the time
dependence of ice volume inferred from isotope measurements. If the chronology
of the data was initially inferred by tuning to the astronomical theory, implicit
circular reasoning may be involved. The significance of such comparisons is argu-
able. A skeptic might claim that the entire exercise is merely curve fitting to find a
mathematical representation of the isotope data that is connected to solar data via
mathematical artifices. However, the proponents of these models would argue that
the models have a physical basis and adjustment of the parameters merely sets the
details—not the underlying form of the result. The truth probably lies somewhere
between these extremes.
A number of models were developed as early as the late 1960s. Some models
dealt with the question of whether known variability of solar intensity was great
enough to cause climate shifts leading to ice ages. Later studies attempted to
model the effects of variability of solar intensity on the time evolution of ice sheet
formation and decay. The goal of such models was to produce an estimate of ice
sheet volume vs. time that could be compared with the variation of isotope ratios
with time, as a test of the astronomical theory.
An early paper estimated the change in temperature produced by changing
solar intensity, but it used current atmospheric and surface properties and did not
account for changes in albedo due to ice sheet growth or other secondary factors.
The temperature changes calculated appeared to be too small to suggest ice sheet
formation (Shaw and Donn, 1968). Several other papers reached similar conclu-
sions in the 1970s. North (1975) developed an energy balance climate model that
predicted larger temperature changes due to variability of solar intensity, although
ice sheets were not included in this model. This paper is dicult to follow and
makes many assumptions. Pollard (1978) attempted to incorporate the feedback
effect due to the albedo of ice sheets into such models. Unlike North, he produced
specific curves of climate variability over the past 300,000 years. However, his
model included a dozen adjustable parameters and it seems likely that he could
have produced almost any result by choosing them appropriately.
Calder (1974) compared variations in the oxygen isotope ratio of marine
sediments with calculated solar irradiance at 50
N. He made an issue of choosing
50
N, which does not make much sense to this writer, but as it turns out it doesn't
matter much whether one chooses 50
Nor65
N since all solar variations at differ-
ent latitudes have similar shapes (see
Figure 9.9
, for example). He made a few vital
assumptions without providing justification. He assumed that the rate of decrease
(or increase) in ice volume is proportional to the amount by which solar intensity
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