The Imbries model for rate of rise and fall of ice ages is reviewed here.
In 1980, John Imbrie and John Z. Imbrie published an influential paper “Modeling the Climatic Response to Orbital Variations” in Science 207, 943-953 (to be denoted as “MCROV”). They proposed a simple formula for modeling the effect of variations of solar input to high latitudes (SIHL) on the northern ice volume. They proposed the equation:
dV/dt = – {(1 ± B)/t} {S + V}
where S is a measure (not yet specified) of solar input to high latitudes (SIHL) and V is supposedly a measure of the ice volume, to be determined by integration over time. B and t are constants. The ± sign in front of B requires that we use the + sign when dV/dt is negative, and the – sign when dV/dt is positive. That allows the rate of change of V with time to be slower when the ice is building up, and faster when ice is diminishing.
The original idea was that S is physically, a negative driving force for ice volume. When S is large-positive, it contributes a large negative term to dV/dt.
The model is analyzed and discussed in detail.