Variability of the Earth’s orbit: The astronomical theory - Ice Ages and Interglacials: Measurements, Interpretation, and Models - page 260

models, C ranges from 4 to 12. If each parameter is adjusted over only three
levels, then 3C [calculations] are necessary [to tune the model]. Such a search
procedure for Calder's model (81 [calculations]) is relatively easy, but for
Pollard's it would require more than 500,000 [calculations].''
From the point of view of the Imbries, the task at hand was to adjust
parameters in a model (i.e., to tune the model) to seek maximum agreement with
isotope data. In their view, there was no doubt at all a priori that the astronomical
theory was correct in principle, even though it was not clear how the variability of
solar intensity led to variability in isotope time series. The belief was that by
tuning the model one would identify the quantitative connection between solar
variability and climate change, and there was no underlying doubt that such a
connection existed. The second point was that if too many parameters are
included in the model the number of possibilities increased rapidly, making the
process of identifying the best fit cumbersome and arbitrary. Of course, there is
no guarantee that there is only one unique answer.
The Imbries discussed the number of parameters involved in input (solar
intensity). For a high-resolution global model that includes solar input to all lati-
tudes there are no parameters. Solar input to any latitude is uniquely determined
by the three orbital parameters: e ¼ eccentricity, q ¼ obliquity, and w ¼ longitude
of precession. These parameters can be calculated by methods given previously
(see Sections 9.2 to 9.5). As the Imbries pointed out, in most models a more
limited approach is used involving ''linear combinations of irradiation curves at
various latitudes and seasons.'' However (as Figure 9.9 suggests), the irradiation
curve at any high latitude in midsummer is likely to be adequate. At this point,
the Imbries embarked on a discussion of the orbital parameters that control solar
irradiance which seems illogical to this writer. They discussed the effect of the
three orbital parameters as if each acts independently on climate and they
attempted to attribute changes in climate to one or other orbital parameter and,
in some cases, more than one. But these orbital parameters do not act separately.
They act in concert to determine solar irradiance, and solar irradiance is the
forcing function of interest in the astronomical theory. The only two parameters
in such calculations should be season and latitude. In fact, if one takes summer as
the season and utilizes any latitude at, say, 50 or greater the results are essentially
the same. Once they are chosen, solar irradiance is essentially uniquely determined
and the Imbries actually showed this in their Figure 3. Thus, there should really be
only one parameter of interest regarding input, and that is whether the latitude for
solar input is chosen in the south or the far north.
The Imbries then went on to discuss how the system functions. They pointed
out that the simplest system they could imagine was the one described by the
equation:

1
T ð x þ y Þ
In this equation, y is a variable that characterizes the climate (in their case, ice
sheet volume), x is a parameter that characterizes variations in solar input (in their

dy
dt ¼