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.
Harlim
John
J
Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA. jharlim@math.umd.edu
Oczkowski
Michael
M
Yorke
James A
JA
Kalnay
Eugenia
E
Hunt
Brian R
BR