Variability of the Earth’s orbit: The astronomical theory - Ice Ages and Interglacials: Measurements, Interpretation, and Models - page 265

Figure 9.14. Dependence of the Imbries' integration on starting values for relative ice volume.
The dashed lines are for starting values of 0.0, 0.2, and 0.8, while the solid line is for 0.5.
65 N over the past 800,000 years was obtained from Figure 9.11 . The values of x
are then measured from the average in units of the standard deviation.
The resultant values of y obtained by stepwise integration 2 are measured in
units of the standard deviation of x. There remains the question of which starting
value to use for y to begin the integration but, as it turns out, the result is not
sensitive to this choice (see Figure 9.14 ). Regardless of the starting value (0.0, 0.2,
0.5, or 0.8) all the curves approach a common result after about 50,000 years.
The dependence of the modeled ice volume history on the two parameters (B
and T) is illustrated in Figures 9.15 and 9.16 . Regardless of the values of these
parameters, the maxima and minima in modeled ice volume occur in the same
time periods. Only the magnitudes of the peaks and valleys change with the
parameters. Shorter time periods produce wider ranges of variation. Larger values
of B raise the ice volume curve and lower values of B lower it. What is important
here is that the locations of peaks and valleys in the ice volume curve vs. time are
independent of the choice of parameters and, furthermore, the dynamic range of
the peaks and valleys is not extremely sensitive to the choice of parameters.
Physical arguments can be made to support the belief that T should be in the
general range of 10,000 to 20,000 years, and B ought to be somewhere in the
range 0.4 to 0.8. Hence, there is no need to keep an eye on SPECMAP data when
applying the Imbrie model. The model, to the extent that T and B are predictable,
2 These calculations were carried out by the present author in 2008.