In a system such as the climate, we can never include enough variables to describe the actual system
on all relevant length
scales (e.g. the butterfly effect —
MICROSCOPIC perturbations grow exponentially in time to drive the system to completely different states over macroscopic time) so the best that we can
often do is model it as a complex nonlinear set of ordinary differential equations with stochastic noise terms — a generalized Langevin equation or generalized Master equation, as it were — and average behaviors over what one hopes is a spanning set of butterfly - wing perturbations to assess whether or not the resulting system trajectories fill the available phase space uniformly or perhaps are restricted or constrained in some way.