Convex error growth patterns in a global weather model

We investigate the error growth, that is, the growth in the distance E between two typical solutions of a weather model. Typically E grows until it reaches a saturation value Es. We find two distinct broad log-linear regimes, one for E below 2% of Es and the other for E above. In each, log (E/Es) grows as if satisfying a linear differential equation. When plotting dlog (E)/dt vs log(E), the graph is convex. We argue this behavior is quite different from other dynamics problems with saturation values, which yield concave graphs.