CARGAS Y GRAVAMENES Por subrogación:

Wave propagation and momentum deposition (in the form of a convergence of EP flux) can be observed particularly well in the Northern Hemisphere winter stratosphere, with extreme events of EP flux convergence during stratospheric sudden warmings associated with a weakening of the zonal mean flow. This chapter will investigate the relative contribution of the terms in the TEM momentum Equation (1.3) to a change in zonal mean wind in the atmosphere. In addition the location, timing and magnitude of the redistribution of momentum in the atmosphere will be investigated. Before a sudden warming happens, it is not clear to what extent the loss of mo- mentum, which is large enough to strongly influence the stratospheric flow, is able to induce a change in the much greater mass of the troposphere. In addition, it is unclear to what extent the waves are amplified within the stratosphere.

After a warming takes place in the stratosphere, it has been shown that the troposphere can be impacted by the change in the stratospheric flow. The question arises if this tropospheric response after the warming is

A) the lingering response to the tropospheric loss of easterly momentum in the lead-up to the warming,

B) a response to a downward influence from the stratosphere, or

C) a tropospheric response to the change in wave propagation properties of the lower stratosphere after a change in stratospheric mean wind distribution.

The dynamics of tropospheric processes suggests dominant tropospheric time scales of 6 - 10 days [e.g. Feldstein (2000)], while mechanism A would require a tropospheric memory of several weeks. Gerber et al. (2009) have further examined the tropospheric response in the light of this mechanism in a three dimensional dynamical core ensem- ble model run. They perturb the tropospheric flow by small random perturbations to wave numbers 4 to 10 in the winter hemisphere midlatitudes starting 10 days before the stratospheric sudden warming in order to wipe out tropospheric memory. They

then verify the subsequent tropospheric response and find that similarly to Bald- win and Dunkerton (2001), a tropospheric response can be identified in an average over the ensemble members, suggesting that the troposphere responds to a change in stratospheric properties, rather than reacting to a lingering response to tropospheric anomalies.

Options B and C, however, are more difficult to separate. Lower stratospheric anomalies may have a strong influence on the troposphere: The shear (Chen and Robinson, 1992) and magnitude (Charney and Drazin, 1961) of the lower stratospheric winds is of great importance for determining wave propagation into the stratosphere, and there have been suggestions of the lower stratospheric winds influencing upper tropospheric eddy phase speeds (Chen and Held, 2007). This indicates that a tro- pospheric response could be induced by the state of the lower stratosphere, either passively by influencing upward wave propagation or actively by changing the tropo- spheric eddy properties.

In general, stratospheric signals are too weak to induce a detectable tropospheric response, and often only an ensemble or a composite of several stratospheric events may show a tropospheric response to a forcing. However, it has been suggested that a significant response can be detected after strong stratospheric forcings such as stratospheric warmings. The strength of the tropospheric response is strongly dependent both on the depth and magnitude of the lower stratospheric response to the forcing in the upper stratosphere as well as on the state of the troposphere at the time of downward propagation of the stratospheric signal (Chan and Plumb, 2009).

5.2.1

Mechanisms of Momentum Transport within the Strato-

sphere

While lower stratospheric anomalies may have an influence on the tropospheric flow, the question arises how a possible downward momentum exchange from the location of the wave convergence in the upper stratosphere to the lower stratosphere occurs in the first place.

It has both been theoretically predicted (Haynes et al., 1991) as well as observed in both models as well as reanalysis data that the weakening of the mean flow through wave breaking induces a residual circulation in the latitude/height plane which spreads beyond (and in particular below) the forcing location. This mecha- nism of downward influence has been termed downward control after Haynes et al. (1991), or balanced response. Downward control can be understood from the TEM Equations (1.3) to (1.7): Following Plumb (1982), Garcia (1987) and Haynes (2005), three of the four independent variables (u, θ, v∗, w∗) in the TEM equations can be eliminated to solve for the fourth, e.g. for the vertical part of the residual circulation w∗, in order to be able to examine the effect of the wave forcing on the residual circu- lation. This yields an equation for w∗ governed by an elliptical operator, indicating that the response to a localized wave forcing spreads beyond the forcing location. The spread of the residual circulation is determined by the ratio of the frequency of the forcing to frictional relaxation (which is small or negligible in the stratosphere) and thermal relaxation. Both Haynes et al. (1991) and Holton et al. (1995) have per- formed idealized numerical experiments estimating the residual circulation response to a localized longitudinally symmetric easterly momentum forcing. For an increase in the forcing frequency relative to the radiative damping rate, the response to the forcing narrows in latitude and strengthens in magnitude, so that in steady state the meridional extent of the circulation is about equal to the meridional extent of the forcing, while extending all the way to the surface where it is balanced by friction. For a comparably short forcing pulse in midlatitudes the response is weaker but can extend into the opposite hemisphere, and an additional residual circulation cell can appear above the forcing region. If the forcing pulse is considerably shorter than the radiative relaxation time scale, the response reduces to the Eliassen response [Eliassen (1951), Plumb (1982)].

Another way to determine the downward influence of a sudden warming is the inversion of the induced stratospheric potential vorticity anomaly. Note that a north- ward eddy flux of potential vorticity is related to the divergence of EP flux observed during sudden warmings, as given under quasi-geostrophic scaling by v0_q0 _{= ρ}−1

Hartley et al. (1998) found that the tropopause geopotential height field is signifi- cantly impacted by the redistribution of potential vorticity induced by a stratospheric sudden warming as compared to an undisturbed polar vortex.

Critical level mechanics in addition play an important role in the vertical coupling within the stratosphere: Due to the descent of the critical level (where the wind speed matches the phase speed of the propagating waves) the waves tend to break at subsequently lower levels and induce additional residual circulations at lower levels. The critical level may however not descend at the same rate or in the same fashion at all longitudes, complicating the description of this mechanism. Plumb and Semeniuk (2003) found the downward progression of the critical level is solely caused by the interaction of the zonal mean flow with the waves, as opposed to other mechanisms such as wave reflection or the induced meridional circulation.

5.2.2

Momentum Exchange between the Stratosphere and

the Troposphere

The above described induced residual circulation is an established signal within the stratosphere which has a strong influence all the way down to the tropopause. How- ever, it is not clear how and if a lower stratospheric or tropopause signal is transferred to the troposphere. Song and Robinson (2004) suggest that the tropospheric response has to be coordinated by synoptic-scale Rossby waves, which organize the response to the stratospheric signal into the intrinsic tropospheric response given by the tropo- spheric annular modes, a mechanism they termed downward control with eddy feed- back. Several studies find that the observed change in the surface winds is observed to be and, according to theory, needs to be accompanied by a change in tropospheric eddy momentum fluxes [e.g. Chen and Zurita-Gotor (2008), Chen and Held (2007)] in order to produce the observed annular mode response, and a tropospheric annular mode response can be observed in both observations as well as model simulations of sudden warmings as described in Chapter 1.

anomalous lower stratospheric wave drag is sufficient to induce the observed surface wind anomalies for the longterm effect of ozone depletion in the stratosphere, meaning that the surface winds respond to changes in the induced meridional circulation as opposed to the tropospheric eddy feedback. They simulate the tropospheric response to stratospheric momentum forcing and radiative heating in a zonally symmetric quasi-geostrophic linear model, where the forcings are estimated from observations. Similar forcings can be observed as a response to sudden warmings, although on dif- ferent time scales. They find that the balanced response to the stratospheric forcing in their model is able to account for the magnitude of the tropospheric response ob- served in more complex models, while in addition the stratospheric radiative heating increases the persistence of the tropospheric response.

Other mechanisms can be observed to influence the vertical momentum exchange and the connection between the stratosphere and the troposphere. Harnik and Lindzen (2001) find evidence of downward reflection of planetary-scale waves in the winter stratosphere. However, it is not yet resolved how wave reflection events are re- lated to sudden warming events (Shaw and Perlwitz, in press), and the identification of wave reflection events is more involved than the detection of sudden warmings and beyond the scope of this study.

This chapter will examine the exchange of momentum within the atmosphere and between the terms of the TEM equations with the intention to identify the impact of the wave forcing on both the change in mean zonal wind and the induced residual circulation. Ideally, this will hint at the mechanism of momentum exchange between the troposphere and the stratosphere. In particular, the goal is to identify if there is a possibility for a balanced response to anomalous stratospheric wave drag, which would be indicated by the tropospheric residual circulation dominating the response in the troposphere in the absence of meridional momentum fluxes induced by the waves, i.e. Fy. On the other hand, an annular mode response in the troposphere

along with significant meridional EP fluxes indicates a smaller role by the meridional residual circulation.