Error growth in baroclinic waves

Growth of perturbations in baroclinic waves is considered through observational and theoretical approaches. The observational approach documents the dominant structure of analysis and forecast errors using a small ensemble of operational analyses. Results for the meridional wind show that analysis and forecast errors share the same dominant vertical structure as the analyses. This structure peaks near the tropopause and decays smoothly toward small values in the middle and lower troposphere. The dominant vertical structure for analysis errors exhibits upshear tilt, and peaks just below the tropopause, suggesting an asymmetry in errors of the tropopause location, with a bias toward greater errors for downward tropopause displacements. Linear regression of forecast errors onto analysis errors for the western North Pacific is used to assess the non-separable zonal--height structure of errors and their propagation. Analysis errors near the tropopause rapidly develop into a spreading wave packet, with a group speed that matches the mean zonal-wind speed of 31 m/s.

For the theoretical approach, Floquet theory is applied to the stability of time-periodic, non-parallel shear flows consisting of a baroclinic jet plus a neutral wave as an idealized representation of baroclinic waves in a storm track. Two useful attributes of Floquet theory relevant to this problem are that the period-average mode growth rate is norm independent, and the t->infinity stability limit is determined by the stability over one period. Exponentially growing Floquet modes are found for arbitrarily small departures from parallel flows. Approximately 70% of Floquet mode growth in energy is due to barotropic conversion, with the remainder due to zonal heat flux. Initial-value problems demonstrate that the periodic basic states are absolutely unstable, with Floquet modes spreading faster than the basic-state flow both upstream and downstream of an initially localized disturbance. This behavior dominates the convective instability of parallel-flow jets when the neutral baroclinic wave amplitude exceeds a threshold value of about 8--10 K. This result suggests that forecast errors in a storm track may spread faster, and affect upstream locations, for sufficiently wavy jets.