Abstract
In this note we show how the use of a semi-implicit time discretization in a linearized non-hydrostatic model can permit very large non-modal perturbation energy growth. This occurs in a single normal-length time step when a hydrostatically unbalanced increment at initial time is mapped to an approximately balanced increment. The energy growth is typically far larger than that of the leading meteorological singular vector (SV) over the course of a 12-hour optimization time interval so, unless action is taken, the leading SVs obtained with this discretization are meteorologically spurious. We show that the excess growths can be prevented by imposing a condition on the relation between the predictor (explicit) step and corrector (implicit) step of the semi-implicit method. We apply this condition to the Met Office's ‘perturbation forecast’ model to obtain SVs with admissible growth rates. Copyright © 2006 Royal Meteorological Society
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