Error growth in flows with finite-amplitude waves or coherent structures

Explanations of error growth in atmospheric flows are often based on the extension of barotropic and baroclinic instabilities from steady parallel flows to weakly nonparallel and time-dependent flows. Consideration of simple flows with finite-amplitude waves, however, suggests an additional scenario for error growth: an initial error that changes the wave amplitude or the medium through which the wave propagates will alter the propagation of the wave and result in a growing phase error. This scenario is illustrated and generalized to other coherent structures through several examples for which analytic solutions are available. For a basic state of a barotropic Rossby wave, growing phase errors account for the most rapidly growing disturbances over time intervals long compared to the basic-state advective timescale; over shorter intervals, amplifications of phase errors are smaller than, but comparable to, the optimal amplification. The role of this mechanism in forecast error growth is less certain, but its importance is suggested by the fact that short-range forecast errors are typically errors in the position or intensity of existing features.