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Stationary wave nonlinearity describes the self-interaction of stationary waves and is important in maintaining the zonally asymmetric atmospheric general circulation. However, the dynamics of stationary wave nonlinearity, which is often calculated explicitly in stationary wave models, is not well understood. Stationary wave nonlinearity is examined here in the simplified setting of the response to localized topographic forcing in quasigeostrophic barotropic dynamics in the presence and absence of transient eddies. It is shown that stationary wave nonlinearity accounts for most of the difference between the linear and full nonlinear response, particularly if the adjustment of the zonal-mean flow to the stationary waves is taken into account. The separate impact of transient eddy forcing is also quantified. Wave activity analysis shows that stationary wave nonlinearity in this setting is associated with Rossby wave critical layer reflection. A nonlinear stationary wave model, similar to those used in baroclinic stationary wave model studies, is also tested and is shown to capture the basic features of the full nonlinear stationary wave solution. DOI: 10.1175/2010JAS3332.1

A simple atmospheric general circulation model (GCM) is used to investigate the transient response of the stratosphere-troposphere system to externally imposed pulses of lower-tropospheric planetary wave activity. The atmospheric GCM is a dry, hydrostatic, global primitive-equations model, whose circulation includes an active polar vortex and a tropospheric jet maintained by baroclinic eddies. Planetary wave activity pulses are generated by a perturbation of the solid lower boundary that grow and decay over a period of 10 days. The planetary wave pulses propagate upward and break in the stratosphere. Subsequently, a zonal-mean circulation anomaly propagates downward, often into the troposphere, at lags of 30-100 days. The evolution of the response is found to be dependent on the state of the stratosphere-troposphere system at the time the pulse is generated. In particular, on the basis of a large ensemble of these simulations, it is found that the length of time the signal takes to propagate downward from the stratosphere is controlled by initial anomalies in the zonal-mean circulation and in the zonal-mean wave drag. Criteria based on these anomaly patterns can be used, therefore, to predict the long-term surface response of the stratosphere troposphere system to a planetary wave pulse up to 90 days after the pulse is generated. In an independent test, it is verified that the initial states that most strongly satisfy these criteria respond in the expected way to the lower-tropospheric wave activity pulse.

An exceptionally strong stratospheric sudden warming (SSW) that spontaneously occurs in a very simple stratosphere--troposphere AGCM is discussed. The model is a dry, hydrostatic, primitive equation model without planetary stationary waves. Transient baroclinic wave-wave interaction in the troposphere thus provides the only source of upward-propagating wave activity into the stratosphere. The model's SSW is grossly similar to the Southern Hemisphere major SSW of 2002: it occurs after weaker warmings 'precondition' the polar vortex for breaking, it involves a split of the polar vortex, and it has a downward-propagating signature. These similarities suggest that the Southern Hemisphere SSW of 2002 might itself have been caused by transient baroclinic wave-wave interaction. The simple model used for this study also provides some insight into how often such extreme events might occur. The frequency distribution of SSWs in the model has exponential, as opposed to Gaussian, tails. This suggests that very large amplitude SSWs, though rare, might occur with higher frequency than might be naively expected.

The influence of zonally asymmetric boundary conditions on the leading modes of variability in a suite of atmospheric general circulation models is investigated. The set of experiments consists of nine model configurations, with varying degrees and types of zonal asymmetry in their boundary conditions. The structure of the leading EOF varies with the zonal asymmetry of the base state for each model configuration. In particular, a close relationship is found between the structure of the EOF and the model storm tracks. An approximately linear relationship is found to hold between the magnitude of the zonal asymmetry of the leading EOF and of the storm tracks in the models. It is shown that this linear relationship extends to the observations. One-point correlation maps centered on the regions where the EOFs reach their maximum amplitude show similar structures for all configurations. These structures consist of a north-south dipole, resembling the observed structure of the North Atlantic Oscillation (NAO). They are significantly more zonally localized than the leading EOF, but do resemble one-point correlation maps and sector EOFs calculated for a simulation with zonally symmetric boundary conditions. Thus, the leading EOF for each simulation appears to represent the longitudinal distribution of zonally localized NAO-like patterns. This longitudinal distribution appears to be tied to the distribution of high-frequency eddies, as represented by the storm tracks. A detailed momentum budget for each case confirms that high-frequency eddies play a crucial role in producing the NAO-like patterns. Other dynamical processes also play an important role, but vary with the details of the simulation.

A simple dynamical model is presented for the basic spatial and temporal structure of the large-scale modes of intraseasonal variability and associated variations in the zonal index. Such variability in the extratropical atmosphere is known to be represented by fairly well-defined patterns, and among the most prominent are the North Atlantic Oscillation (NAO) and a more zonally symmetric pattern known as an annular mode, which is most pronounced in the Southern Hemisphere. These patterns may be produced by the momentum fluxes associated with large-scale midlatitude stirring, such as that provided by baroclinic eddies. It is shown how such stirring, as represented by a simple stochastic forcing in a barotropic model, leads to a variability in the zonal flow via a variability in the eddy momentum flux convergence and to patterns similar to those observed. Typically, the leading modes of variability may be characterized as a mixture of 'wobbles' in the zonal jet position and 'pulses' in the zonal jet strength. If the stochastic forcing is statistically zonally uniform, then the resulting patterns of variability as represented by empirical orthogonal functions are almost zonally uniform and the pressure pattern is dipolar in the meridional direction, resembling an annular mode. If the forcing is enhanced in a zonally localized region, thus mimicking the effects of a storm track over the ocean, then the resulting variability pattern is zonally localized, resembling the North Atlantic Oscillation. This suggests that the North Atlantic Oscillation and annular modes are produced by the same mechanism and are manifestations of the same phenomenon. The time scale of variability of the patterns is longer than the decorrelation time scale of the stochastic forcing, because of the temporal integration of the forcing by the equations of motion limited by the effects of nonlinear dynamics and friction. For reasonable parameters these produce a decorrelation time of the order of 5-10 days. The model also produces some long-term (100 days or longer) variability, without imposing such variability via the external parameters except insofar as it is contained in the nearly white stochastic forcing.

The annular mode simulated by an atmospheric general circulation model with a zonally symmetric lower boundary is investigated. The annular mode, defined as the leading empirical orthogonal function (EOF) of the zonal-mean surface pressure, has a meridional structure consisting of a north-south dipole, similar to observations. The leading EOF of the zonally varying surface pressure has the same meridional structure and is also zonally symmetric. Because the lower boundary is zonally symmetric, composites of days with high projection onto the mode have, to within sampling error, no zonal structure. However, individual periods during which the zonal-mean surface pressure projects strongly onto the annular mode are dominated by zonally localized structures. Thus, the model annular mode represents a zonally homogeneous distribution of zonally localized events with a similar meridional structure, rather than a zonally symmetric mode of variability per se. Individual annular-mode events typically show a north-south teleconnection pattern whose meridional structure closely resembles the annular mode and whose zonal structure extends 60[degrees] to 90[degrees] in longitude, with a slight northwest-southeast offset between its centers of action. Similar structures are found for EOFs calculated over a subset of the domain corresponding to the width of the Atlantic basin. The spatial structure of both the teleconnection pattern and the regional EOFs resemble the observed North Atlantic Oscillation (NAO) pattern.

Longitudinal variations in the upper-tropospheric time-mean flow strongly modulate the structure and amplitude of upper-tropospheric eddies. This barotropic modulation is studied using simple models of wave propagation through zonally varying basic states that consist of contours separating regions of uniform barotropic potential vorticity. Such basic states represent in a simple manner the potential vorticity distribution in the upper troposphere. Predictions of the effect of basic-state zonal variations on the amplitude and spatial structure of eddies and their associated particle displacements are made using conservation of wave action or, equivalently, the linearized 'pseudoenergy' wave activity. The predictions are confirmed using WKB theory and linear numerical calculations. The interaction of finite-amplitude disturbances with the basic flow is also analyzed numerically using nonlinear contour-dynamical simulations. It is found that breaking nonlinear contour waves undergo irreversible amplitude attenuation, scale lengthening, and frequency lowering upon passing through a region of weak basic-state flow.

The use of eddy flux of thickness between density surfaces has become a familiar starting point in oceanographic studies of adiabatic eddy effects on the mean density distribution. In this study, a dynamical analogy with the density thickness flux approach is explored to reexamine the theory of nonzonal wave-mean flow interaction in two-dimensional horizontal flows. By analogy with the density thickness flux, the flux of thickness between potential vorticity (PV) surfaces is used as a starting point for a residual circulation formulation for nonzonal mean flows. Mean equations for barotropic PV dynamics are derived in which a modified mean velocity with an eddy-induced component advects a modified mean PV that also has an eddy-induced component. For small-amplitude eddies, the results are analogous to recent results of McDougall and McIntosh derived for stratified flow. The dynamical implications of this approach are then examined. The modified mean PV equation provides a decomposition of the eddy forcing of the mean flow into contributions from wave transience, wave dissipation, and wave-induced mass redistribution between PV contours. If the mean flow is along the mean PV contours, the contribution from wave-induced mass redistribution is 'workless' in Plumb's sense that it is equivalent to an eddy-induced stress that is perpendicular to the mean flow. This contribution is also associated with the convergence along the mean streamlines of a modified PV flux that is equal to the difference between the PV flux and the rotational PV flux term identified by Illari and Marshall. The cross-stream component of the modified PV flux is related to wave transience and dissipation.

Stationary wave nonlinearity describes the self-interaction of stationary waves and is important in maintaining the zonally asymmetric atmospheric general circulation. However, the dynamics of stationary wave nonlinearity, which is often calculated explicitly in stationary wave models, is not well understood. Stationary wave nonlinearity is examined here in the simplified setting of the response to localized topographic forcing in quasigeostrophic barotropic dynamics in the presence and absence of transient eddies. It is shown that stationary wave nonlinearity accounts for most of the difference between the linear and full nonlinear response, particularly if the adjustment of the zonal-mean flow to the stationary waves is taken into account. The separate impact of transient eddy forcing is also quantified. Wave activity analysis shows that stationary wave nonlinearity in this setting is associated with Rossby wave critical layer reflection. A nonlinear stationary wave model, similar to those used in baroclinic stationary wave model studies, is also tested and is shown to capture the basic features of the full nonlinear stationary wave solution. [ABSTRACT FROM AUTHOR]