title: Convex error growth patterns in a global weather model.
abstract: 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.
authors.affiliation: Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA. jharlim@math.umd.edu
authors.forename: John
authors.initials: J
authors.lastname: Harlim
authors.forename: Michael
authors.initials: M
authors.lastname: Oczkowski
authors.forename: James A
authors.initials: JA
authors.lastname: Yorke
authors.forename: Eugenia
authors.initials: E
authors.lastname: Kalnay
authors.forename: Brian R
authors.initials: BR
authors.lastname: Hunt