Variability of the Earth’s orbit: The astronomical theory - Ice Ages and Interglacials: Measurements, Interpretation, and Models - page 259

estimates of the properties of ice and bedrock, as well as some additional guesses,
he estimated that h (the height of the snow line at the northern edge of the ice
sheet) would have to be between 0 and 540m to enable a stable ice sheet to
persist. In his model, when h ) 0, L ) 2,500 km. When h rises to 540m, the ice
sheet becomes unstable and ablates away. He derived an expression for the rate of
change of ice volume with time that depends on h. He made the connection
to solar variations by assuming that h is proportional to the variation in solar
intensity at some latitude (he chose 50 N). As Weertman put it: ''We assume that
in this naive way the solar radiation variations can be related to changes in the
elevation of the snowline.'' The proportionality constant was selected somewhat
arbitrarily. He was then able to derive a result for ice volume in the ice sheet vs.
time over the past 500,000 years. It is dicult to ascertain the degree of rigor in his
various assumptions. He seems to have encountered a rather extreme sensitivity to
the ratio between the rates of accumulation and ablation. A change in this ratio
from 2.745 to 2.750 seems to have produced dramatic changes in the results. For
example, depending on this choice (2.745 or 2.750) his result for the future either
predicts no ice age in the next 120,000 years or an ice age should be starting right
now.
He concluded that variations in solar irradiance were large enough to have
produced ice ages. However, to reach this conclusion, it was necessary to assume
that accumulation and ablation rates were substantially higher than those that
occur today in Greenland and Antarctica. He also found a significant sensitivity
of the possibility of ice ages to the location of northern landmasses. His results
suggest that if Greenland were moved 500 km north (or south) we would either be
in a perpetual ice age or forever free from ice ages. Weertman's study provided
some valuable insights into ice sheet formation, but his model clearly needs
refinement.
Imbrie and Imbrie (1980) reviewed the status of various models for ice volume
variability and concluded: ''As described above, Pollard and Weertman have made
considerable progress in this direction—yet results fall short of an adequate simu-
lation.'' The Imbries advocated the use of simple models because, as they put it,
''even if a complex model yields a successful simulation, it may be dicult to
understand what features of the model are the basis of its success.'' However,
after advocating this fundamental wisdom, they went on to say:

''Tuning a model to the climatic record is an essential feature of our strategy
for developing a simple class of differential models. To see how drastically one's
ability to tune a model is affected by complexity, define the complexity (C)tobe
the total number of adjustable parameters. We include in this total any parameter
that can be adjusted within the constraints of physical plausibility to make
significant changes in the system function. Some of these parameters may vary
over a large range and make large changes in the system function, while others
may be relatively restricted. For purposes of comparison, however, we count all
of them equally. Some of the parameters (C F ) will occur in the system function
...

while others (C I ) will occur in the input, so that C ¼ C F þ C I . In previous