From what I have seen, people trip over three things: (1) Variability in deterministic
models as a function of
initial and boundary conditions, and the measurement errors associated with those; (2) variability due to residuals of non-explanation due to limits of mesh
grading and imperfections in the physical
modeling of materials and physical processes; and (3) variability due to having imperfect descriptions of variability itself, notably linearizations of residuals as if they were i.i.d. which may continue to exhibit dependent behavior.