Borges, M. D., and P. D. Sardeshmukh, 1995: Barotropic Rossby wave dynamics of zonally varying upper level flows during northern winter. J. Atmos. Sci., 52, 3779-3796.
The evolution of linear Rossby waves on representative zonally varying upper-tropospheric flows is examined. Structures associated with maximum perturbation energy growth over both short and long time intervals are obtained. Sensitivity is determined with respect to the background flow, the manner in which the background flow is maintained, and vertical level. The background flows considered are a 26 winter 250-mb climatology obtained from the National Meteorological Center, 13-winter 300-, 250-, and 150-mb climatologies obtained from the European Centre for Medium-Range Weather Forecasts, flows representative of warm and cold ENSO events, and nearby free steady solutions of the nonlinear barotropic vorticity equation.
The principal finding is that no matter which of the above background flows is used, no matter how the perturbation problem is formulated, no matter whether modal or nonmodal evolution is considered, the growth of free perturbations in a linear barotropic model is too weak to explain by itself the dominant observed structures of extratropical low-frequency variability.
In almost all the cases considered, the normal modes are stabilized by a 5-day drag, which is argued to be appropriate for this problem. It is shown further that although substantial nonmodal growth is still possible in the presence of the drag, it can occur for at most 12 days. Thus, without forcing, all initial perturbations to a climatological flow begin to decay in 12 days or less. The least-damped normal mode, being a decaying structure, can become relatively dominant only in the decaying stages of a perturbation. It takes about 10 days to emerge from its adjoint structure and at least 20 days to emerge from an arbitrary initial condition. These times are long enough that one expects either the perturbation to lose most of its initial amplitude in the presence of the drag or nonlinear effects to become important in its absence.
These results cast doubt on the role of barotropic normal-mode instability in the low-frequency dynamics of the Northern Hemisphere wintertime circulation. A representative zonally varying upper-level flow significantly modifies the propagation and dispersion of Rossby waves, but it does not significantly destabilize them. The spatial structures of the normal modes and optimal initial perturbations for nonmodal growth are apparently more relevant than normal-mode instability. For example, a normal mode with a structure resembling the Pacific-North American (PNA) pattern is found among the most unstable modes in almost all cases. Because it is stable in the presence of a realistic drag, however, such a mode cannot be naturally selected from random disturbances in the atmosphere; it has to be forced. In a system with stable normal modes, mode selection is determined not by relative modal decay rates but by forcing. Our analysis therefore implies that without a knowledge of the forcing, one cannot explain the relative importance of, or the energy contained in, the PNA or any other pattern of extratropical low-frequency variability.