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 E(s). We find two distinct broad log-linear regimes, one for E below 2% of E(s) and the other for E above. In each, log (E/E(s)) grows as if satisfying a linear differential equation. When plotting d log(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.