**Sardeshmukh, P. D.**, **M. Newman**, and **M. D. Borges**, 1997:
Free barotropic Rossby wave dynamics of the wintertime low-frequency flow.
*J. Atmos. Sci.*, **54**, 5-23.

**ABSTRACT**

In recent years much attention has been given to Rossby wave propagation and dispersion on representative zonally and meridionally varying background flows in the atmosphere. Particular emphasis has been placed on the 300-mb flow as shaping the structure and evolution of extratropical low-frequency eddies. In this paper an attempt is made to check this hypothesis against the observed evolution of low-pass filtered 300-mb streamfunction anomalies during the eight northern winters of 1985-93. The filter passes periods greater than ~10 days. The focus is on explaining the observed evolution of these low-pass anomalies over 10 days. This evolution is expected to be nonmodal, that is, a mix of several evolving normal modes rather than a single mode. Two questions are asked: 1) given an initial anomaly, to what extent can one explain the observed subsequent evolution with an unforced barotropic vorticity equation linearized about the climatological 300-mb flow, and 2) in instances of anomaly growth, to what extent is the growth optimally nonmodal, that is, associated with the maximum possible constructive interference of the normal modes.

Concerning question 1, it is found that regardless of the linear drag specified in the model, it cannot reproduce the 10-day lag-covariance structure of the observations. If the model is interpreted as an equivalent barotropic model applied at the 300-mb level, a 5-day drag is appropriate; however, the modeled anomalies lose significant amplitude by day 10 in this case. Question 2 is addressed in two ways. First, a theoretical analysis is performed to determine the optimal as well as expected nonmodal growth of global perturbation kinetic energy in the model. The optimal growth can be as large as a factor of 8 over 3.5 days, even in the presence of the 5-day drag, if certain optimal perturbations (singular vectors) occur as the initial condition. The expected growth, given the statistical structure of the observed "initial" conditions, is however actually a decay. Second, 21 cases of global anomaly growth sustained over at least 7 days are isolated in the data record. The model is run for 7 days with the observed initial condition in each case. In each case, it predicts a decay instead of growth, more consistent with the expected growth (i.e., decay) than optimal growth. The same result is obtained with nonlinear integrations. Somewhat better results are obtained by considering "instantaneous" background flows in the 21 cases; however, the model still predicts a decay. An interesting ambiguity in the interpretation of these latter runs is highlighted.

These results imply that an unforced barotropic vorticity equation linearized about a representative 300-mb flow cannot explain the observed evolution of low-frequency anomalies except possibly in isolated cases. In particular they imply that extratropical low-frequency variability cannot be viewed solely as free Rossby wave propagation and dispersion on a zonally and meridionally varying 300-mb flow, with the forcing acting mainly as a provider of initial perturbations in certain sensitive regions of the atmosphere. Rather the forcing, which in a barotropic model represents the combined effects of diabatic heating, interactions with orography, synoptic-eddy feedbacks, and baroclinic dynamics, is important throughout the development of low-frequency anomalies.