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    Reference temperature field and the associated zonal-mean zonal wind for the numerical simulations. The temperature is used as a reference state for the thermal relaxation. It is obtained from the displayed zonal winds using the thermal wind relation. The contour intervals are 5 m s−1 for the winds and 10°C for the temperatures

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    Imposed dipole forcing of zonal momentum used in the model. The contour interval is 2 × 10−6 m s−2

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    (a) The zonal-mean zonal wind averaged from day 3000– 6000 of the control run. The contour interval is 5 m s−1. (b) As in (a) but for EP-flux divergence. The contour interval is 10 × 10−6 m s−2. (c) Zonal-mean zonal wind anomaly regressed on the principal component of the leading EOF of the zonally averaged zonal winds. The contour interval is 0.2 m s−1. (d) As in (c) but for EP-flux divergence. The contour interval is 0.5 × 10−6 m s−2

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    (a) Zonal-mean wind difference, forced − control, for the Northern Hemisphere. The contour interval is 1 m s−1. The strength of the forcing in the forced experiment is 1.5 × 10−5 m s−2. (b) As in (a) but for the EP-flux divergence. The contour interval is 1 × 10−6 m s−2. (c) As in (b) but for wavenumbers 1 to 3

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    As in Fig. 4 but for the Southern Hemisphere

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    (a) Forced − control differences of the zonal-mean zonal winds and the EP vectors in the Northern Hemisphere. The contour interval is 2 m s−1. (b) As in (a) but for the Southern Hemisphere

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    (a) Forced − control differences of the zonal-mean zonal winds in the Northern Hemisphere computed using the zonally symmetric model. The contour interval is 1 m s−1. (b) As in (a) but eddy forcing is included

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    (a) Zonal-mean zonal wind difference, forced damped − damped, for the Northern Hemisphere. The forcing strength in the forced experiment is 1.5 × 10−5 m s−2. The contour interval is 1 m s−1. (b) As in (a) but for the Southern Hemisphere

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    As in Fig. 8 but for the doubled forced − doubled experiment

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    Diagnoses of the forced − control experiment using the zonally symmetric model. (a) Difference between the response to total eddy forcing and to long-wave eddy forcing only. The contour interval is 1 m s−1. (b) As in (a) but the difference between the response to total eddy forcing and to short-wave eddy forcing only

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    (a) The EP-flux divergence due to wavenumber 3 in the control run. The contour interval is 1 × 10−6 m s−2. (b) As in (a) but for the forced run. (c) Composite structure of wavenumber 3 (see text) for the control run. The shading shows the amplitude of the wavenumber-3 geopotential height, with an interval of 10 m, and the contours show its phase, with a contour interval of 10°. (d) As in (c) but for the forced run

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    (a) Zonal-mean zonal wind difference, doubled − control, for the Northern Hemisphere. The contour interval is 1 m s−1. (b) As in (a) but for the EP-flux divergence, with a contour interval of 1 × 10−6 m s−2. (c) As in (b) but for wavenumbers 1 to 3

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    Zonal-mean zonal wind difference, doubled damped − damped, for the Northern Hemisphere. The contour interval is 1 m s−1

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Dynamical Mechanisms for Stratospheric Influences on the Troposphere

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  • 1 RSIS/Climate Prediction Center, NCEP, Washington, D.C
  • | 2 Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
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Abstract

The dynamical mechanisms through which stratospheric forcing can influence tropospheric annular modes are explored. A torque is applied to the stratosphere of an idealized general circulation model, and, under some circumstances, a robust tropospheric response is observed. These tropospheric responses, while initiated by stratospheric forcing, are maintained locally by interactions with transient eddies, and they closely resemble the intrinsic annular modes of the model. Manipulations of the model are consistent in showing that planetary waves, and not only the zonally symmetric secondary circulations induced by stratospheric forcing, are important for transmitting dynamical signals to the troposphere. Specifically, it is found that the tropospheric response is significantly reduced when planetary waves are suppressed in the stratosphere by additional damping or when the strength of the stratospheric jet is increased. Wave diagnoses indicate that the confinement of these waves within the troposphere, when stratospheric winds are enhanced, leads to increased planetary wave deceleration of the zonal winds in the high-latitude upper troposphere.

Corresponding author address: Walter A. Robinson, Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, 105 South Gregory Street, Urbana, IL 61801. Email: robinson@atmos.uiuc.edu

Abstract

The dynamical mechanisms through which stratospheric forcing can influence tropospheric annular modes are explored. A torque is applied to the stratosphere of an idealized general circulation model, and, under some circumstances, a robust tropospheric response is observed. These tropospheric responses, while initiated by stratospheric forcing, are maintained locally by interactions with transient eddies, and they closely resemble the intrinsic annular modes of the model. Manipulations of the model are consistent in showing that planetary waves, and not only the zonally symmetric secondary circulations induced by stratospheric forcing, are important for transmitting dynamical signals to the troposphere. Specifically, it is found that the tropospheric response is significantly reduced when planetary waves are suppressed in the stratosphere by additional damping or when the strength of the stratospheric jet is increased. Wave diagnoses indicate that the confinement of these waves within the troposphere, when stratospheric winds are enhanced, leads to increased planetary wave deceleration of the zonal winds in the high-latitude upper troposphere.

Corresponding author address: Walter A. Robinson, Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, 105 South Gregory Street, Urbana, IL 61801. Email: robinson@atmos.uiuc.edu

1. Introduction

Recent observational studies (Thomson and Wallace 1998; Kuroda and Kodera 1999; Baldwin and Dunkerton 1999, 2001) have suggested that variations in the stratospheric flow can propagate downward and affect the weather and climate in the troposphere. When height fields are regressed onto the leading principal component of the sea level pressure, deep structures reflecting coupling between the surface and the stratosphere are revealed (Thomson and Wallace 1998). During winter periods in which the polar vortex is strong the tropospheric westerlies along 55°N are also anomalously strong (Baldwin and Dunkerton 2001). It is, therefore, reasonable to hypothesize that the tropospheric annular mode is influenced by variations in the strength of the wintertime stratospheric polar vortex.

The observational results have stimulated numerous modeling studies, using both idealized and realistic models. The approach shared by these studies is to induce a change in the stratosphere and then observe the resulting response in the troposphere. The first such experiment was, in fact, performed nearly 20 years ago by Boville (1984), who demonstrated that “degrading” the stratosphere of a general circulation model (GCM) led to substantial modifications of its tropospheric circulation. More recently, similar experiments, at least in spirit, have been carried out by Polvani and Kushner (2002, hereafter PK), Taguchi (2003), and Norton (2003). The details of these models and the experimental designs differ appreciably, but certain aspects of the results are robust. Changes in the stratosphere, induced in different ways, often, though not always, lead to significant modifications in the tropospheric circulation. When they are strong these tropospheric changes project strongly on the leading intrinsic modes of tropospheric variability, the annular modes of the models.

Despite this growing body of observational and modeling evidence for stratospheric influences on the tropospheric flow, a clear exposition of the dynamical mechanisms for such downward influence remains elusive. Several mechanisms have been proposed:

  1. Planetary wave propagation: Using a linear model, Chen and Robinson (1992) found that the vertical propagation of planetary waves from the troposphere to the stratosphere is sensitive to the vertical wind shear across the extratropical tropopause. This shear is found to vary with the annular modes (Limpasuvan and Hartmann 1999). The results of Perlwitz and Harnik (2003) suggest that the vertical reflection of planetary waves within the stratosphere may contribute to downward influence.
  2. Wave–zonal flow interaction: The planetary wave– zonal flow interaction that leads to downward propagation of wind anomalies in the stratosphere (Holton and Mass 1976; Christiansen 1999), could continue into the troposphere and reach the surface.
  3. Remote responses to the rearrangement of stratospheric potential vorticity: Baldwin and Dunkerton (1999) suggested that the redistribution of mass in the stratosphere, in response to changes in wave driving, may be sufficient to influence the surface pressure significantly, consistent with the theoretical results of Haynes and Shepherd (1989). From calculated changes in the tropospheric flow induced by stratospheric redistributions of potential vorticity, Hartley et al. (1998) and Black (2002) argued that changes in the zonal flow in the lower stratosphere can induce significant changes in the tropopause height and tropospheric winds.
  4. Downward control: If anomalous wave driving is sustained for a sufficiently long time, the wave transport of potential vorticity equilibrates with its creation and destruction by radiative damping. In this equilibrium, the influence of altered stratospheric wave driving is transmitted to the surface through secondary circulations that extend downward from the region of anomalous wave driving, and close in the planetary boundary layer. Following the important work on these dynamics by Haynes et al. (1991) this process is now generally denoted “downward control.” We adhere to that usage—the term downward control is used herein to denote only that downward influence associated with equilibrated or nearly equilibrated downward closing secondary circulations.
  5. Intrinsic mode amplification: The annular modes are free intrinsic modes of the nonlinear tropospheric dynamics, as indicated by their presence in troposphere-only models with static lower boundaries (e.g., Robinson 1991). As such, they may respond significantly to modest stratospheric forcing.

It is not clear which of these mechanisms is important for downward influence from the stratosphere. In this study, we approach the problem from the perspective that a necessary, if not sufficient, condition for true downward influence is that the tropospheric annular mode can respond to large changes in stratospheric wave driving. By “true downward influence,” we mean that the change in stratospheric wave driving dynamically causes subsequent changes in the troposphere. Our experiments are motivated, at least initially, as tests of a specific dynamical mechanism, a combination of items 4 and 5 described earlier. We hypothesize that anomalous stratospheric wave driving produces a secondary circulation that transmits the stratospheric forcing to the surface. The response to this forcing is manifest as a weak and downward decaying modification of tropospheric winds, which mirrors the meridional structure of the anomalous stratospheric wave driving. If a typical anomaly in stratospheric wave driving is on the order of 1 m s−1 day−1, distributed over a stratospheric layer about 50-hPa deep, then, assuming a boundary layer thickness of 100 hPa and a time scale for boundary layer drag of 1 day, the equilibrated surface wind response to anomalous stratospheric wave driving is roughly 0.5 m s−1. This signal is much weaker than is implied by observations. For example, Hartmann et al. (2000) found that anomalous stratospheric wave driving of the magnitude described earlier was associated with anomalies of about 5 m s−1 in zonally averaged near-surface zonal winds. Moreover, the zonal wind structure of the annular mode in the troposphere does not mirror that in the stratosphere. Rather it is significantly narrower, with the strongest tropospheric wind anomalies coinciding in latitude with the equatorial edge of those in the stratosphere. Finally, anomalous stratospheric wave driving appears concurrently with strong anomalies in tropospheric wave driving (Hartmann et al. 2000). These facts suggest that the stratospherically forced response is both amplified and modified by tropospheric dynamics, presumably the same interactions with both transient and stationary eddies that cause the annular mode to emerge as an intrinsic dynamical mode of the troposphere (Robinson 1991; Hartmann and Lo 1998; Limpasuvan and Hartmann 1999; Lorenz and Hartmann 2001, 2003; DeWeaver and Nigam 2000).

We denote this hypothesis, which involves the eddy reinforcement within the troposphere of a weak signal transmitted downward by the zonally averaged secondary circulation, “downward control with eddy feedback” (DCWEF). To test this hypothesis, we apply, to the stratosphere of an idealized dynamical model, a zonally symmetric zonal torque that mimics changes in wave driving. We observe the resulting tropospheric response, in comparison with a control run, in which no such torque is applied. While this is a very artificial setup, it provides all conditions necessary for a test of DCWEF. The response to the imposed torque should exhibit downward control in the same way as a response to internally generated wave driving. Our model resolves tropospheric transient eddies, and it supports an intrinsic tropospheric annular mode, so the tropospheric dynamics that are expected to amplify and modify the response to stratospheric forcing are present.

A prediction of DCWEF is that, since the direct stratospheric signal is weak in the troposphere, the dynamical forcing of the tropospheric response should be dominated by that due to tropospheric eddies. As is shown later, this prediction fares well in our model experiments, as it does in the results shown by PK.

A second prediction of DCWEF is that the tropospheric response to the imposed torque should be largely insensitive to the state of the stratosphere. The secondary circulation generated by the imposed torque depends on the strength and structure of the torque, and it should be independent of the preexisting stratospheric flow— this is exactly correct in the quasigeostrophic limit, and it is approximately correct in the primitive equations outside of the Tropics. Even on the flanks of the stratospheric jets in our model, the relative vorticity is less then 40% of the planetary vorticity in our control simulations, though it is larger in high latitudes in some forced experiments. The downward influence by the secondary circulation is different from that by planetary wave propagation, since planetary waves are sensitive to the mean state.

As is seen later, however, our extensive suite of experiments and diagnoses reveals that the tropospheric response to stratospheric forcing depends strongly on the state and dynamics of the stratosphere. Thus, we are led to the conclusion that, while downward control and tropospheric eddy feedback operate in our model, these processes do not comprise a complete description of the dynamics through which the influence of stratospheric forcing is transmitted to the troposphere.

For the present study, we use a version of our model, with neither topography nor zonally varying thermal boundary conditions to generate planetary waves. Planetary waves are present in the model, generated by instabilities and/or by interactions with shorter-scale disturbances, but they are far weaker than those observed in the Northern Hemisphere. This study, then, is an exploration of the dynamics of downward influence in the presence of weak planetary wave feedbacks. Still, we find that these relatively weak waves, especially those at intermediate planetary wavenumbers (s ∼ 3), are important in the dynamics of downward influence. Results of experiments with orographically forced waves will be reported in a subsequent paper.

The details of the model configuration, the suite of experiments, and diagnostic techniques are given in section 2. The responses of our model to imposed stratospheric forcing are described in section 3. Section 4 describes the responses to changing the background thermal state of the stratosphere, experiments similar to those performed by PK. The final section summarizes our results and their implications for the dynamics of downward influence.

2. Model, diagnostics, and experiments

a. Model

The model is similar to that of Held and Suarez (1994), with some changes made for the purposes of this study. The vertical levels and the radiative-equilibrium temperature are similar to those used by Scinocca and Haynes (1998; see appendix for details). The horizontal resolution corresponds to a rhomboidal 30 spectral truncation. That this resolution is sufficient for resolving tropospheric eddies and their interactions with annular modes of variability is suggested by the result (Limpasuvan and Hartmann 2000) that a general circulation model at this resolution displays annular modes of variability very similar to those found in observations.

Temperatures in our model are linearly relaxed everywhere towards a latitude- and altitude-dependent reference profile. These reference temperatures are computed, using the thermal wind relation, from a radiative-equilibrium zonal-wind profile. The radiative-equilibrium winds and temperatures are shown in Fig. 1. The Newtonian cooling coefficient is (25 days)−1.

Rayleigh friction is used to parameterize surface drag. Its coefficient, k, is given by,
i1520-0469-61-14-1711-e1
where τ is the damping time scale, 0.5 days.
In order to prevent inertial instability in the equatorial mesosphere, which leads to numerical instability if unchecked, vertical diffusion is added. The same coefficient of vertical diffusion is taken for momentum and temperature,
i1520-0469-61-14-1711-e2
Here z is a logσ approximate altitude, computed using a uniform scale height of 7 km. Sixth-order horizontal diffusion is used throughout the domain, with a minimum damping time scale of 0.1 day for the smallest horizontal scales resolved in the model.

b. Diagnostics

Diagnostic quantities are computed on the model σ surfaces, thereby avoiding possible inaccuracies introduced in interpolation to constant-pressure surfaces. This is unlikely to be a significant problem in the present simulations without topography, but we implement this approach to simplify comparisons with later simulations that include topography. D. Andrews (2002, personal communication) kindly provided his derivation of the Eliassen–Palm relations in σ coordinates (slight modifications are made for this study), following the approach described by Andrews and McIntyre (1978). In the transformed-Eulerian mean sense, the zonal momentum equation becomes
i1520-0469-61-14-1711-e3
where P is the surface pressure and all other quantities are defined as follows:
i1520-0469-61-14-1711-e4a
The derivation differs from the quasigeostrophic version in that the residual circulation does not treat the isentropic surface as quasi horizontal, and the projection of transport by eddies along isentropic surfaces is, therefore, more accurate. In comparison with the primitive equation form in pressure coordinates, there is an additional term on the right-hand side of the momentum equation that cannot be expressed as the divergence of a flux.

c. EOF analysis

Since there are no preferred longitudes in our zonally homogeneous model, an empirical orthogonal function (EOF) analysis is performed on zonal-mean zonal winds between the surface and 50 km (the lowest 18 model layers). So as to represent both the troposphere and the stratosphere in the resulting EOFs, no mass weighting is applied. A low-pass Lanczos filter retaining periods longer than 10 days is applied to the zonal-mean zonal wind before computing the covariance matrix and its eigenvalues.

d. Zonally symmetric model

A zonally symmetric version of the model is used diagnostically, to determine the separate contributions made to the overall response from baroclinic eddies, planetary waves, and the imposed forcing itself. Because interactions between short and long waves do not directly contribute to the zonal-mean flow, short- and long-wave forcing of the zonal flow can be considered separately. The zonally averaged model employs the same radiative forcing and dissipation as the full model. It is driven by zonally and time-averaged heat and momentum fluxes of long (wavenumbers 1, 2, and 3) and short waves (all other waves). The zonally symmetric model is integrated for 1000 days and the time average is taken from day 300 to 1000.

e. Composite planetary wave structures

In this model, with no stationary wave forcing, simple time averages of planetary waves yield near-zero values. To obtain meaningful averages of planetary wave structures, planetary wave amplitudes and phases at every latitude and height are saved daily. The wave phase on each day is then rotated, at all latitudes and levels, so that the wave ridge is at 0° longitude at some reference latitude and level. The resulting rotated waves are then averaged over time, and amplitudes and phases are computed from these averages.

f. Imposed torque

The zonally symmetric zonal torque is intended to mimic changes in the wave driving of the polar-night jet, such as are observed to occur in association with fluctuations in the Artic Oscillation index (Hartmann et al. 2000). This torque is included as an additional term in the zonal momentum equation,
i1520-0469-61-14-1711-e5
where Fϕ is chosen so as not to alter the globally averaged angular momentum, that is,
i1520-0469-61-14-1711-e6
We choose a symmetric dipole forcing of the form
i1520-0469-61-14-1711-e7
In the present experiments, ϕ0 is 57°N. The value of δ is increased smoothly from 0 over the first 100 days of each experiment to final values of 1.5 × 10−5, 1.0 × 10−5, or 0.5 × 10−5 m s−1. The results with these values are qualitatively similar, so only the strongest forcing case is discussed in detail. The vertical profile of the forcing, Λ(z) is a Gaussian, centered at 30 km,
i1520-0469-61-14-1711-e8
where z0 and Δz are 30 km and 10 km (again, these are logσ heights computed using a scale height of 7 km). The resulting forcing is shown in Fig. 2.

g. Damped stratospheric planetary wave experiments

Several runs are carried out in which planetary waves, with zonal wavenumbers 1, 2, and 3, are strongly damped by enhanced diffusion above the tropopause. In these experiments, denoted damped runs, planetary waves in the upper 20 model levels, above σ = 0.1, are subject to enhanced diffusion, with a damping time scale of 0.5 day. The full suite of experiments is listed in Table 1.

h. Doubled jet experiments

We perform several model runs (see Table 1) in which the strength of the stratospheric jet is essentially doubled. This is accomplished by increasing the stratospheric maximum value of the radiative-equilibrium wind, from which radiative-equilibrium temperatures are computed, from 62 to 124 m s−1.

3. Results

Our basic experimental approach is to examine the differences between the equilibrated states of model runs with and without the earlier-described forcing imposed in the stratosphere. In all cases we consider the averages over the final 3000 days of 6000-day runs. Next (sections 3a and 3b) we first describe the results of a basic experiment. This experiment reveals a significant tropospheric response to stratospheric forcing. To elucidate the dynamics of this response, the results of follow-up experiments are described in the subsequent sections.

a. Control run

Figure 1 shows the specified model equilibrium temperature profile Teq and the winds associated with these temperatures by thermal wind balance. These profiles are similar to those used by Scinocca and Haynes (1998). The model spins up from rest, and achieves a profile of zonally averaged winds, similar to the time average shown in Fig. 3a, after about 110 days. Figure 3b shows the associated time-averaged Eliassen–Palm (EP) flux divergence (expressed in units of zonal flow acceleration). The dominant pattern is a vertical dipole, with divergence near the surface and convergence in the upper troposphere—a pattern associated with baroclinic eddies (Edmon et al. 1980). Wave driving in the stratosphere is weak, consistent with the absence of explicitly forced planetary waves.

The leading pattern of internal variability for the control experiment is shown in Figs. 3c,d. These are the zonally averaged zonal wind and EP-flux divergence regressed on the principal component of the leading EOF of the zonally averaged zonal wind, computed as described in section 2c. This EOF includes tropospheric zonal-wind anomalies that straddle the subtropical jet, as well as poleward-sloping connections to the stratosphere. While this pattern is different from that of the observed annular modes (Thompson and Wallace 2000), this model “annular mode” is similar to the observed mode in that it is eddy driven. The EP-flux divergences (Fig. 3d) are such as to reinforce the pattern of zonal-wind anomalies, especially in the troposphere.

b. Imposed forcing experiment

The stratospheric forcing, described in section 2f, is applied steadily in a 6000-day model run, and the time-averaged differences (day 3000–6000) between this run and the control run (forced–control) are examined. Figure 4 shows the differences in the zonally averaged zonal winds and in the EP-flux divergences. Tropospheric zonal winds respond to the stratospheric forcing with four anomalies centered around 250 hPa. The response in the stratosphere is at the larger meridional scale of the imposed forcing, but in the troposphere, it is similar in structure to the EOF shown in Fig. 3. The EP-flux divergences (Fig. 4b) indicate that the tropospheric wind anomalies are driven by local eddy forcing, a result that is confirmed later using the zonally symmetric model.

The zonal-wind response in the extratropical troposphere in the Southern Hemisphere, where the imposed forcing is westward, is approximately half as strong as its counterpart in the Northern Hemisphere. The EP-flux divergence shows similarly weaker changes in the troposphere, but it displays a strong increase in the Southern Hemisphere subpolar stratosphere, which cancels about half of the imposed forcing there. The total forcing, imposed and planetary wave, of the zonal flow in the Southern Hemisphere stratosphere is, therefore, much weaker than that in the Northern Hemisphere, consistent with the much weaker tropospheric response. Figures 4c and 5c show the contributions of planetary waves (zonal wavenumbers 1, 2, and 3) to the EP-flux divergences. Comparisons between Figs. 4b and 4c and between 5b and 5c show, as expected, that stratospheric wave driving is entirely due to long waves, while in the troposphere it is due to the shorter waves, wavenumbers 4 and higher. Long-wave wave driving is also important in the upper troposphere poleward of 60°, a point to which we return later.

Additional experiments are performed with the same spatial pattern of imposed forcing, but at a strength reduced by one-third or two-thirds. In the Northern Hemisphere, where the forcing is eastward, the response in both the stratospheric and tropospheric winds scales roughly with the strength of the forcing (see Table 2). In the Southern Hemisphere, however, where the forcing is westward, even the weakest forcing induces a large change in the stratospheric zonal winds—the response is nonlinear in the strength of the forcing. The tropospheric response is weaker than in the Northern Hemisphere for all strengths of forcing, but it scales approximately with the strength of the forcing.

The differences in the EP vectors between the forced and control runs (Fig. 6) reflect both the behavior of baroclinic eddies, which are dominant in the troposphere, and the planetary-scale waves, which are dominant in the stratosphere. The tropospheric eddies show enhanced upward propagation where zonal winds are strengthened in the upper troposphere. The coincidence of enhanced upward EP fluxes from the lower boundary with latitudes of increased vertical shear in the zonal winds suggests that baroclinic eddy generation is enhanced where the zonally averaged baroclinicity, as indicated by the increased vertical shear, is increased. These eddies propagate away from their latitude of generation, inducing momentum fluxes that reinforce the anomalously strong zonal winds in the upper troposphere, between 40° and 50°N and, to a lesser extent, between 20° and 30°S. This positive feedback is as described by Robinson (2000).

In the SH stratosphere, the EP flux is directed from high latitudes into the jet, which is displaced equatorward in comparison with the control run. This implies a downshear momentum flux that may be a consequence of barotropic instability within the stratosphere, the possibility of which was first explored by Hartmann (1983). In the total zonally averaged zonal wind and EP-flux divergence for the forced run (not shown), there is a broad region of EP-flux divergence poleward of 50°S in the Southern Hemisphere that is not present in the Northern Hemisphere. This in situ generation of wave activity within the stratosphere strongly suggests the presence of instability. In addition, the divergent EP fluxes (momentum flux convergence) coincide with weak westerly and easterly zonal winds, with strong positive curvature in their meridional profile. These winds lead to a weakly reversed gradient of absolute vorticity, a necessary condition for barotropic instability. The presence of instability is further supported by enhanced week-to-week variability in the stratospheric zonal winds in the high latitudes, in comparison with both the Northern Hemisphere and the control run. It appears, then, that barotropic instability of the forced zonally averaged zonal winds in the model's Southern Hemisphere is responsible for the negative feedback on the westward-imposed forcing and the resulting weakness of the tropospheric response.

c. Diagnoses using the zonally symmetric model

Figure 7a shows the zonal-wind response, in the zonally symmetric model, to the imposed forcing alone. The zonally symmetric model is forced with the time-averaged transports of heat and momentum from the control run of the full model and run for 1000 days. This is then repeated with the imposed forcing added to the zonal momentum equation. The result is consistent with the predictions of the principle of downward control. The tropical wind anomalies far from the applied forcing are presumably slowly decaying remnants of the spinup process, their slow decay permitted by the weakness of the thermal wind constraint in the Tropics. Temperature and vertical velocity anomalies at levels below the forcing (not shown) nearly vanish, as expected, equatorward of 30° latitude. The zonal-wind response is nearly barotropic above the forcing level, and it decays rapidly below. The stratospheric anomalies extend downward to about 250 mb, but no further. In contrast, when the full time-averaged eddy forcing from the forced run is included (Fig. 7b), the zonally symmetric model reproduces the entire response to imposed forcing produced by the full model (Figs. 4 and 5). This includes the structure of the zonal-wind anomalies in the troposphere, and the greater strength of these anomalies in the NH (eastward-imposed forcing) than in the SH (westward-imposed forcing; not shown).

d. The roles of planetary waves

The results thus far are consistent with the DCWEF hypothesis. The direct influence of the imposed forcing in the troposphere is weak (Fig. 7a), but is reinforced by tropospheric eddies of less than planetary scale (wavenumbers 4 and higher) to produce a robust tropospheric response. These results do not, however, rule out a role for zonally asymmetric motions in transmitting the dynamical signal downward from the stratosphere. Therefore, two additional pairs (forced and control runs) of experiments are carried out. In the first, forced damped − damped, planetary wave coupling between the troposphere and stratosphere is explicitly reduced or eliminated, by strongly damping the planetary waves in the stratosphere (as described in section 2g). In the second, doubled forced − doubled, the stratospheric behavior of planetary waves is modified by doubling the strength of the stratospheric jet.

Figure 8 shows the difference between the forced and control experiments with planetary waves suppressed in the stratosphere (damped forced–damped), again averaged from day 3000 to day 6000. In the absence of stratospheric planetary waves the influence of the stratospheric forcing on tropospheric zonal winds in middle and high latitudes is significantly reduced, especially in the Northern Hemisphere, as can be seen by comparing Fig. 8a. to Fig. 4a (see also Table 2). There is a strong asymmetry between the hemispheres in the stratospheric response to forcing in the damped experiments. In particular, the Southern Hemisphere polar stratosphere responds very strongly to the forcing (Fig. 8b). An almost identical stratospheric response is found in our zonally symmetric model. The forcing is sufficiently strong in high latitudes that the absolute vorticity of the polar cap is reduced in the Southern Hemisphere to slightly greater than half the planetary vorticity. This permits a stronger zonal wind response in the Southern Hemisphere, and breaks the symmetry of the response to forcing that would be expected from quasigeostrophic theory.

As expected, there is essentially no wave driving in the stratosphere when the long waves are damped. Because planetary wave feedback on the stratospheric zonal winds is weak in the forced and control experiments and absent in the damped forced and damped control experiments, the weakness of the tropospheric response in the Northern Hemisphere of the damped experiments cannot be attributed to stratospheric planetary wave feedback. At the same time, the structure of the tropospheric intrinsic variability in the damped model is nearly identical to that in the undamped model, indicating that the eddy–zonal flow dynamics that reinforces the tropospheric response in the undamped model is available in the damped model. These results suggest that planetary waves themselves transmit a significant part of the dynamical signal from the stratosphere to the troposphere.

Because damping waves of only some scales in some regions may be construed as contrived, we perform yet another set of forced and control experiments, this time without extra damping but with the strength of the stratospheric jet doubled (doubled forced − doubled, see section 2f ). The zonal flow response is shown in Fig. 9. In the stratosphere, it is as strong as in the original forced − control experiment, but in the Northern Hemisphere, the tropospheric response (Fig. 9a) is much weaker. In this case the difference in stratospheric wave driving between the forced and control experiments is similar to that found for the original forced − control, so the weaker tropospheric response again cannot be attributed to planetary wave feedback in the stratosphere.

In summary, the results of the damped forced − damped, and doubled forced − doubled experiments, in particular the weakness of the tropospheric response in comparison with the original forced − control experiment, argue against DCWEF as a complete explanation for the influence of stratospheric forcing on the troposphere, and they, therefore, support a direct role for planetary waves. To diagnose these effects, we return to the original model (with unsuppressed planetary waves), and use the time-averaged eddy forcing (forced − control) by short waves, and by long waves, and by both together, to drive the zonally symmetric model. Figure 10 shows that the short waves (Fig. 10a) are primarily responsible for the tropospheric response, but that the tropospheric influences of planetary waves are not negligible. Zonally averaged zonal-wind anomalies forced by the planetary waves tilt poleward with increasing altitude. A weak signal (∼1 m s−1) extends below σ = 0.3. This is of the same order as the direct tropospheric response to the imposed forcing (Fig. 7a). The weakness of the tropospheric response when planetary waves are suppressed suggests that this modest tropospheric response to planetary wave forcing is important for communicating the influence of the imposed forcing down into the troposphere.

Much of the difference between the forced and control runs in tropospheric planetary wave driving (Figs. 4c and 5c) is associated with wavenumber 3. The wave driving due to wavenumber 3 in these two runs is shown in Figs. 11a and 11b. A vertically oriented dipole spanning the tropopause and centered near 70°N is seen in both parts of Fig. 11, but it is much stronger in Fig. 11b, the forced run. This westward wave driving in the high-latitude upper troposphere is needed to generate a robust tropospheric response to stratospheric forcing in our model. It is found in all cases in which the tropospheric response is strong and displays a close similarity to the intrinsic modes of variability shown in Fig. 3c. How is this feature generated by the imposed forcing? Addressing questions of causality is difficult in a set of equilibrated model runs. Some hints, however, come from examining the composite structure of wavenumber 3, computed as described in section 2e. Figures 11c and 11d show the composite amplitudes and phases of wavenumber 3 in the control and forced runs, using a base point at 70°N and σ = 0.2. (The structures displayed are insensitive to the choice of base point.) In both the control and forced runs, wavenumber 3 has an amplitude maximum in the high-latitude (65°N) upper troposphere, and a secondary maximum in the stratosphere at lower latitudes. The stratospheric maximum is higher and farther south in the control run than in the forced run. The wave phase shows a more striking difference between the experiments. In the control run, but not in the forced run, the phase of wavenumber 3 increases rapidly with height in the stratosphere and with decreasing latitude, indicating upward and equatorward propagation. From this result we infer that the increased lower-stratospheric westerlies induced by the imposed forcing trap wavenumber 3 within the troposphere, leading to greater wave driving at the high-latitude tropopause.

The vertical dipole in wavenumber-3 wave driving (Figs. 11a,b), with a region of EP-flux divergence near the surface and a region of convergence aloft, is characteristic of baroclinic instability (Edmon et al. 1980). Tanaka and Tokinaga (2002) proposed that high-latitude baroclinic instability of planetary waves provides a mechanism to couple the stratospheric polar vortex to the tropospheric annular mode. Consistent with the present results, they find that high-latitude planetary wave baroclinic instability is stronger when the polar vortex is stronger, as occurs in the present experiments when the imposed forcing is eastward. In contradistinction to the present results, however, Tanaka and Tokinaga find that the high-latitude baroclinic instability accelerates high-latitude westerlies in the upper troposphere, while in our results, stronger planetary waves in high latitudes gives rise to an easterly high-latitude response to westerly imposed forcing.

4. Thermally forced experiments

The experiments described in section 3 involve the response to an imposed stratospheric body force. The control run for the double-jet experiment, together with our standard control run, allows us to examine the tropospheric response to stratospheric thermal forcing. This experiment, doubled − control, is very similar to that described by PK. The results are shown in Fig. 12. Doubling the strength of the thermally forced stratospheric jet produces, consistent with their results, a very strong response in tropospheric winds (Fig. 12a). As for the forced − control experiments, the change in tropospheric winds is attributable to changes in the tropospheric wave driving (Fig. 12b), to which planetary waves contribute in high latitudes (Fig. 12c). Because no body force is imposed in this experiment, downward control can contribute to the tropospheric response only if the change in the strength of the stratospheric jet leads to a significant change in the stratospheric wave driving. Only weak changes are found, however. The largest changes in stratospheric wave driving between the doubled and control runs are only 2 × 10−6 m s−2, in the upper stratosphere. Once again, then, it is found that waves, presumably planetary waves, and not only the zonally symmetric secondary circulations, are needed to transmit the full of effects of a stratospheric change downward into the troposphere. This is supported by our final experiment, doubled damped − damped, the results of which are shown in Fig. 13. With planetary waves damped in the stratosphere, doubling the strength of the stratospheric jet has a greatly reduced influence on tropospheric winds.

5. Summary and discussion

It is found, consistent with results of earlier studies by Boville (1984) and by Polvani and Kushner (2002), that a dynamical signal introduced in the stratosphere is readily transmitted to the troposphere, where it projects upon the tropospheric annular mode. Further analyses using a zonally symmetric model confirm that the proximate forcing of the tropospheric response is the anomalous momentum transport by tropospheric transient eddies. Such anomalous momentum fluxes come about as the baroclinic lower-tropospheric source of these eddies shifts toward latitudes at the base of the anomalous tropospheric jet. These tropospheric dynamics are consistent with our present understanding of the dynamics of the intrinsic annular mode, at least as such dynamics are manifest in idealized, zonally homogeneous models (Robinson 1991, 1994, 2000).

Taken at face value, the results of our forced − control experiments are consistent with the hypothesis we denote DCWEF, downward control with eddy feedback. The direct response to the imposed forcing, calculated using the zonally symmetric model is small but not zero in the troposphere. This weak signal is then amplified by transient-eddy feedbacks, and the result is a robust tropospheric response that projects on the model's intrinsic annular modes. Also consistent with DCWEF is the result that when, as in our easterly forced (SH) case, stratospheric planetary wave driving partially cancels the imposed forcing, the tropospheric response is reduced proportionately.

If, however, DCWEF were a complete explanation for the downward influence in our model, then the model should produce similar results when planetary waves are suppressed. This is not the result we obtain. Rather, the tropospheric responses are weaker when planetary waves are damped in the stratosphere, and they bear much less resemblance to the intrinsic annular mode. Similarly, the strong tropospheric influence of a thermally strengthened stratospheric jet nearly disappears when planetary waves are damped in the stratosphere.

Moreover, it is noteworthy that the sign of the high-latitude wind anomalies in the troposphere in response to the stratospheric torque is opposite that in the stratosphere, whereas zonally symmetric dynamics alone give the same sign in both locations. This equatorward “slope” of the response going from the stratosphere to the troposphere is also found in observations (e.g., Black 2002), but is exaggerated in our model. A straightforward application of DCWEF would suggest that an eastward stratospheric torque should favor stimulation of the intrinsic tropospheric EOF (Fig. 3c) with the opposite sign from what we find, that is, with anomalous westerlies and easterlies aligned between the troposphere and stratosphere.

Diagnoses of the planetary waves in the forced and control runs shows that in the forced run, planetary waves contribute a significantly greater deceleration to the upper-tropospheric zonal winds in high latitudes than in the control run. Most of this deceleration is accomplished by wavenumber 3. There is a similar, but stronger, difference in high-latitude upper-tropospheric deceleration by planetary waves between the doubled and control runs. In these sets of experiments, there is a significant tropospheric response to the stratospheric change—imposed torque or doubled jet—that projects on the intrinsic annular mode. When planetary waves are damped in the stratosphere, this upper-tropospheric deceleration is not enhanced by the imposed stratospheric torque. Similarly, the high-latitude upper-tropospheric deceleration is strong, compared to that in the control run, when the jet is doubled, but it does not increase significantly when stratospheric torque is applied to the doubled-jet experiment. In these experiments, in which the stratospheric change does not enhance the high-latitude deceleration by planetary waves, the impact of stratospheric changes on the tropospheric winds is weak. These results suggest that the planetary wave–induced high-latitude deceleration is an important step in the downward influence of stratospheric changes. From this point the transient-eddy feedback takes over, and gives rise to the meridionally alternating pattern of anomalous easterlies and westerlies that characterizes both the response to the imposed forcing, and the internal variability. In this regard, it should be noted that the response to forcing is stronger in high latitudes than is the leading EOF.

While the structure of wavenumber 3 (Figs. 11c,d), as well as its influence on the zonal flow, is clearly different between the forced and control runs, the dynamics of these differences are not entirely clear. While it is plausible that the stronger stratospheric winds in the forced run confine wavenumber 3 to the troposphere and thereby enhance its baroclinic instability, it is perhaps surprising that this effect is readily extinguished by damping the wave only within the stratosphere. This issue could possibly be resolved by an extensive set of forced and free linear calculations. In the case of the doubled and doubled forced runs, it is again plausible, but not demonstrated, that wavenumber 3 is already very unstable in the doubled case, so that the addition of lower-stratospheric vertical shear by the imposed torque has little or no additional effect.

In conclusion, we find that even when planetary waves are weak, as they are in the present models that lack explicit planetary wave forcing, these weak planetary waves are necessary to transmit much of the stratospheric influence to the troposphere. The relevant planetary waves in our simulations are internally generated, possibly by baroclinic instability. As suggested by Tanaka and Tokinaga (2002), such waves are sensitive to conditions in the lower stratosphere. Finally, it is expected that the role of planetary waves in coupling the troposphere to the stratosphere will increase in importance in the presence of realistically strong planetary waves.

Acknowledgments

The authors thank Dr. Mingfang Ting for providing the GCM dynamical core and for helpful discussions. The authors also thank Dr. David Andrews for providing his derivation of the generalized Charney–Drazin theorem in sigma coordinates. We thank Prof. P. H. Haynes and two anonymous reviewers for their insightful and helpful comments. This research is funded by the Climate Dynamics program of the National Science Foundation, ATM-0139101.

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APPENDIX

Model Details

Model equations

The dynamic-core GCM for this study is a modified version of the spectral model used by Held and Suarez (1994). The model equations are
i1520-0469-61-14-1711-ea1
where ζ, D, T, lnP, and Φ are the relative vorticity (vertical component), divergence, temperature, logarithm of surface pressure, and geopotential height. Here, F indicates forcing terms with corresponding subscripts. The tildes represent vertical averages, while σ is the vertical coordinate. The value S is defined as
i1520-0469-61-14-1711-ea7

Vertical levels

The model employs a total of 30 levels (Scinocca and Haynes 1998). There are 9 levels in the troposphere, which are linearly spaced up to σtran = 0.1 while there are 21 levels in the stratosphere. The lowest and highest half-levels are σbottom = 1 − (1 − σtran)/ntrop(ntrop = 9) and σtop = 6.0 × 10−7.

Fig. 1.
Fig. 1.

Reference temperature field and the associated zonal-mean zonal wind for the numerical simulations. The temperature is used as a reference state for the thermal relaxation. It is obtained from the displayed zonal winds using the thermal wind relation. The contour intervals are 5 m s−1 for the winds and 10°C for the temperatures

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 2.
Fig. 2.

Imposed dipole forcing of zonal momentum used in the model. The contour interval is 2 × 10−6 m s−2

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 3.
 Fig. 3.

(a) The zonal-mean zonal wind averaged from day 3000– 6000 of the control run. The contour interval is 5 m s−1. (b) As in (a) but for EP-flux divergence. The contour interval is 10 × 10−6 m s−2. (c) Zonal-mean zonal wind anomaly regressed on the principal component of the leading EOF of the zonally averaged zonal winds. The contour interval is 0.2 m s−1. (d) As in (c) but for EP-flux divergence. The contour interval is 0.5 × 10−6 m s−2

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 4.
Fig. 4.

(a) Zonal-mean wind difference, forced − control, for the Northern Hemisphere. The contour interval is 1 m s−1. The strength of the forcing in the forced experiment is 1.5 × 10−5 m s−2. (b) As in (a) but for the EP-flux divergence. The contour interval is 1 × 10−6 m s−2. (c) As in (b) but for wavenumbers 1 to 3

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 5.
Fig. 5.

As in Fig. 4 but for the Southern Hemisphere

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 6.
Fig. 6.

(a) Forced − control differences of the zonal-mean zonal winds and the EP vectors in the Northern Hemisphere. The contour interval is 2 m s−1. (b) As in (a) but for the Southern Hemisphere

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 7.
Fig. 7.

(a) Forced − control differences of the zonal-mean zonal winds in the Northern Hemisphere computed using the zonally symmetric model. The contour interval is 1 m s−1. (b) As in (a) but eddy forcing is included

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 8.
Fig. 8.

(a) Zonal-mean zonal wind difference, forced damped − damped, for the Northern Hemisphere. The forcing strength in the forced experiment is 1.5 × 10−5 m s−2. The contour interval is 1 m s−1. (b) As in (a) but for the Southern Hemisphere

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 9.
Fig. 9.

As in Fig. 8 but for the doubled forced − doubled experiment

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 10.
Fig. 10.

Diagnoses of the forced − control experiment using the zonally symmetric model. (a) Difference between the response to total eddy forcing and to long-wave eddy forcing only. The contour interval is 1 m s−1. (b) As in (a) but the difference between the response to total eddy forcing and to short-wave eddy forcing only

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 11.
 Fig. 11.

(a) The EP-flux divergence due to wavenumber 3 in the control run. The contour interval is 1 × 10−6 m s−2. (b) As in (a) but for the forced run. (c) Composite structure of wavenumber 3 (see text) for the control run. The shading shows the amplitude of the wavenumber-3 geopotential height, with an interval of 10 m, and the contours show its phase, with a contour interval of 10°. (d) As in (c) but for the forced run

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 12.
Fig. 12.

(a) Zonal-mean zonal wind difference, doubled − control, for the Northern Hemisphere. The contour interval is 1 m s−1. (b) As in (a) but for the EP-flux divergence, with a contour interval of 1 × 10−6 m s−2. (c) As in (b) but for wavenumbers 1 to 3

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Fig. 13.
Fig. 13.

Zonal-mean zonal wind difference, doubled damped − damped, for the Northern Hemisphere. The contour interval is 1 m s−1

Citation: Journal of the Atmospheric Sciences 61, 14; 10.1175/1520-0469(2004)061<1711:DMFSIO>2.0.CO;2

Table 1.

A list of model runs

Table 1.
Table 2.

A summary of the results of model experiments

Table 2.
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