Abstract
Abstract 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 certa...
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