The nature of singular vector growth and structure

The aim of this paper is to produce a basic understanding of the nature of singular vector growth and structure. The approach is through a sequence of singular vector calculations based on the European Centre for Medium-Range Weather Forecasts Ensemble Prediction System. Comparison is made for a range of cases based on trajectories that are evolving or constant atmosphere states, all cases having the same optimization time interval and resolution in the singular vector calculation From these it is deduced that the constant or evolutionary nature of the trajectory is not as relevant as the smoothness of the trajectory. Unless the trajectory is very smooth, singular vectors tend to propagate from the upstream end of the storm-track baroclinic regions into their downstream end. The upscale transfer of energy in singular vector development is seen mostly as a kinematic effect of the strengthening flow in the downstream direction. Short-optimization-time singular vectors are found to grow by unshielding potential-vorticity (PV) structures associated with their compactness in the vertical and by untilting their westward tilted troughs as they propagate upwards. Longer-optimization-time singular vectors are lower in the troposphere and their interaction with the near-surface region enables longer-term normal-mode-like growth through PV coupling in the vertical. The division between short and longer optimization times is consistent with the time taken to propagate to the tropopause.