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Simulated Anthropogenic Changes in the Brewer–Dobson Circulation, Including Its Extension to High Latitudes

Charles McLandress Department of Physics, University of Toronto, Toronto, Ontario, Canada

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Theodore G. Shepherd Department of Physics, University of Toronto, Toronto, Ontario, Canada

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Print Publication:
15 Mar 2009
DOI:
https://doi.org/10.1175/2008JCLI2679.1
Page(s):
1516–1540
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Abstract

Recent studies using comprehensive middle atmosphere models predict a strengthening of the Brewer–Dobson circulation in response to climate change. To gain confidence in the realism of this result it is important to quantify and understand the contributions from the different components of stratospheric wave drag that cause this increase. Such an analysis is performed here using three 150-yr transient simulations from the Canadian Middle Atmosphere Model (CMAM), a Chemistry–Climate Model that simulates climate change and ozone depletion and recovery. Resolved wave drag and parameterized orographic gravity wave drag account for 60% and 40%, respectively, of the long-term trend in annual mean net upward mass flux at 70 hPa, with planetary waves accounting for 60% of the resolved wave drag trend. Synoptic wave drag has the strongest impact in northern winter, where it accounts for nearly as much of the upward mass flux trend as planetary wave drag. Owing to differences in the latitudinal structure of the wave drag changes, the relative contribution of resolved and parameterized wave drag to the tropical upward mass flux trend over any particular latitude range is highly sensitive to the range of latitudes considered. An examination of the spatial structure of the climate change response reveals no straightforward connection between the low-latitude and high-latitude changes: while the model results show an increase in Arctic downwelling in winter, they also show a decrease in Antarctic downwelling in spring. Both changes are attributed to changes in the flux of stationary planetary wave activity into the stratosphere.

Corresponding author address: Charles McLandress, Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada. Email: charles@atmosp.physics.utoronto.ca

Abstract

Recent studies using comprehensive middle atmosphere models predict a strengthening of the Brewer–Dobson circulation in response to climate change. To gain confidence in the realism of this result it is important to quantify and understand the contributions from the different components of stratospheric wave drag that cause this increase. Such an analysis is performed here using three 150-yr transient simulations from the Canadian Middle Atmosphere Model (CMAM), a Chemistry–Climate Model that simulates climate change and ozone depletion and recovery. Resolved wave drag and parameterized orographic gravity wave drag account for 60% and 40%, respectively, of the long-term trend in annual mean net upward mass flux at 70 hPa, with planetary waves accounting for 60% of the resolved wave drag trend. Synoptic wave drag has the strongest impact in northern winter, where it accounts for nearly as much of the upward mass flux trend as planetary wave drag. Owing to differences in the latitudinal structure of the wave drag changes, the relative contribution of resolved and parameterized wave drag to the tropical upward mass flux trend over any particular latitude range is highly sensitive to the range of latitudes considered. An examination of the spatial structure of the climate change response reveals no straightforward connection between the low-latitude and high-latitude changes: while the model results show an increase in Arctic downwelling in winter, they also show a decrease in Antarctic downwelling in spring. Both changes are attributed to changes in the flux of stationary planetary wave activity into the stratosphere.

Corresponding author address: Charles McLandress, Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada. Email: charles@atmosp.physics.utoronto.ca

Keywords: Anthropogenic effects; Climate change; Middle atmosphere; Atmospheric circulation; Orographic effects

1. Introduction

Recent simulations using comprehensive middle atmosphere models predict an increase in the Brewer–Dobson circulation (BDC) in response to climate change, as diagnosed by changes in lower stratospheric tropical upwelling (Butchart et al. 2000; Butchart and Scaife 2001; Sigmond et al. 2004; Butchart et al. 2006; Fomichev et al. 2007; Li et al. 2008; Garcia and Randel 2008). This increase is due to an increase in wave drag in the extratropical stratosphere, as confirmed from diagnostic analyses of the model simulations and as expected from theory. A strengthened BDC will affect the recovery of stratospheric ozone from anthropogenic halogens by speeding up the removal of the halogens (Butchart and Scaife 2001) and changing the latitudinal distribution of ozone. In particular, Shepherd (2008) has shown that a strengthened BDC leads to a super recovery of total ozone in Northern Hemisphere (NH) midlatitudes and a subrecovery in the tropics.

It is well accepted that climate change will warm the troposphere and cool the stratosphere. Because the troposphere is much deeper in the tropics than in the extratropics, one can generically expect an increased equatorward temperature gradient in the subtropical upper troposphere/lower stratosphere, which implies strengthened westerlies in the upper flank of the subtropical jet. This basic response to climate change is seen in all model simulations, and it has been noted by many authors (e.g., Rind et al. 1998; Shindell et al. 1999) that the zonal wind change has the potential to affect the spatial structure of wave drag within the stratosphere, thereby affecting the BDC. However, the tropospheric response to climate change also has the potential to affect the BDC through changes in the flux of wave activity entering the stratosphere. This latter possibility has been less explored.

While models unanimously predict an increase in tropical upwelling (Butchart et al. 2006), there is as yet no consensus on the specific mechanisms behind the increase. Butchart et al. (2006) find the resolved wave drag to account, on average, for 60% of the upwelling trend in the models, which suggests the remaining 40% is due to parameterized processes [presumably gravity wave drag (GWD)]. Li et al. (2008) and Garcia and Randel (2008) have specifically quantified the role of orographic GWD in their model simulations, but come to very different conclusions as to its importance for tropical upwelling trends. Concerning the impact of resolved wave drag, there has been no serious attempt to quantify the relative roles of planetary waves and synoptic waves as well as stationary and transient waves. Since their tropospheric forcing mechanisms are distinct, each may respond differently to climate change. It is therefore important to separate their effects when diagnosing stratospheric wave driving.

In contrast to the situation with respect to tropical upwelling, there is no clear consensus as to even the sign of the climate change response at high latitudes, with some models predicting increased downwelling in the Arctic lower stratosphere and others predicting reduced downwelling (Austin et al. 2003—also inferred from temperatures in Eyring et al. 2007) and in most cases with the trends not being statistically significant. This lack of consensus arises in part from a lack of long simulations with ensembles, which are required to obtain statistically significant results in polar winter where interannual variablity is large (Butchart et al. 2000; Fomichev et al. 2007). Since future changes in the BDC at high latitudes are critical for future Arctic ozone loss, it is important to assess the robustness of the polar responses in many models in order to arrive at some consensus.

Herein we examine an ensemble of three transient simulations using the Canadian Middle Atmosphere Model (CMAM), a Chemistry–Climate Model (CCM) that simulates climate change as well as ozone depletion and recovery. A detailed diagnostic analysis is performed to identify and quantify the factors responsible for the increase in the BDC. The roles of planetary and synoptic wave drag and parameterized orographic GWD, and the connection between tropical upwelling and polar downwelling, are examined in detail. While changes in the upward flux of wave activity into the stratosphere are quantified, an attribution of those changes to changes within the troposphere is beyond the scope of this study. As discussed in the final section, the diagnostic tools for such an analysis are not well developed and represent a priority for future research.

The paper is organized as follows. Section 2 provides a general description of the model and gives pertinent information about the simulations. Section 3 describes the results. There the general features of the simulated BDC are described before investigating the causes of its increase. The latter begins with a downward control analysis of the residual vertical velocity at 70 hPa (generally considered the base of the BDC) and ends with a discussion of the causes of wave drag changes in northern winter and southern spring and summer. The final subsection ties together the previous results with an examination of tropical upwelling. While our main focus is on the net upward mass flux, as this directly relates to the mass exchange between the troposphere and stratosphere, we also examine the sensitivity of the tropical upwelling trend to the range of latitudes considered (and find it to be considerable). Section 4 summarizes our findings and discusses some of the implications as well as the relation to previous work.

2. Description of model and simulations

The Canadian Middle Atmosphere Model is the upward extension of the Canadian Centre for Climate Modelling and Analysis (CCCma) general circulation model (Beagley et al. 1997; Scinocca et al. 2008). It includes a fully interactive stratospheric chemistry module, a comprehensive radiation scheme, as well as a suite of other parameterizations relevant to physical processes from the earth’s surface up to the model lid at ∼100 km. As with all current CCMs, sea surface temperatures and sea ice distributions (SSTs for short) are prescribed. The simulations described here employ 71 vertical levels, having a vertical resolution that varies from several hundred meters in the lower troposphere to ∼1.5 km near 20 km and ∼2.5 km above 60 km. In the horizontal direction a T31 spectral resolution is used, corresponding to a grid spacing of ∼6°. This resolution is adequate for resolving the Rossby waves that affect the stratosphere. A detailed description of this version of the model is given in Scinocca et al. (2008).

The results presented here comprise an ensemble of three transient simulations extending from 1950 to 2099, with the first 10 years considered as spinup and discarded. Greenhouse gases and ozone-depleting substances are prescribed according to the CCM Validation Activity (CCMVal) for Stratospheric Processes and their Role in Climate (SPARC) reference simulation 2 (REF2) scenario (Eyring et al. 2005). SSTs are obtained from three transient simulations of a coupled atmosphere–ocean version of the CCCma model. This approach differs from other modeling groups participating in CCMVal whose REF2 ensembles were generated from simulations using different initial conditions but a single set of SSTs (Eyring et al. 2007). Using different but equally plausible realizations of the SSTs, as we have done, should give a more realistic estimate of the uncertainty in long-term changes due to natural variability.

Eyring et al. (2006) performed an intercomparison of many CCMs, including CMAM, based on process-oriented diagnostics applied to a reference simulation for the recent past constrained by observed SSTs (the so-called REF1 simulation). CMAM compared very favorably with observations. The CMAM REF2 simulations were compared with other CCMs in Eyring et al. (2007) and further examined in Shepherd (2008). In Shepherd (2008) they were shown to agree with past observations in terms of column ozone decreases except in the Arctic where, like many CCMs, CMAM ozone is generally too high and the model does not fully capture the severely depleted values found in the coldest Arctic winters.

Comparisons of the REF2 simulations with observed dynamical fields were limited in Eyring et al. (2007) and Shepherd (2008). Although a comprehensive validation of the CMAM REF2 simulations cannot be presented here, several basic dynamical quantities (computed from the ensemble average) are compared to the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996) to demonstrate the credibility of CMAM’s climate for the recent past (1979–2006). Figure 1 shows the seasonal cycle of zonal average zonal wind at 58°N and 58°S at 30 hPa and zonal average temperature near the poles at 50 hPa. In the NH the agreement is excellent. In the Southern Hemisphere (SH) CMAM exhibits a cold bias of ∼10 K in late winter and spring, which is associated with an eastward wind bias of ∼15 m s−1 and a late (by several weeks) breakdown of the polar vortex: these biases are common to all the CCMs compared in Eyring et al. (2006). Figure 2 shows the zonal average zonal wind for the NH winter months December–February (DJF). The strength and position of the tropospheric and stratospheric jets are well reproduced by CMAM. As will be discussed shortly, these features play an important role in the propagation and dissipation of resolved and parameterized waves. The meridional heat flux at 100 hPa, which is generally regarded as the key metric for resolved wave forcing of the stratospheric circulation, is shown in Fig. 3. The CMAM results are, again, in good overall agreement with NCEP except that the SH heat flux persists too long in the summer, a bias that is associated with the too-late breakdown of the vortex.

In the results that follow, we shall use the residual (i.e., transformed Eulerian mean) circulation as a proxy for the BDC (Andrews et al. 1987). The residual vertical velocity w* is computed from the mass streamfunction Ψ as follows:
i1520-0442-22-6-1516-e1
and
i1520-0442-22-6-1516-e2
where is the residual meridional velocity, p pressure, ϕ latitude, g gravity, a the earth’s radius; H is the pressure scale height (7 km), and the boundary condition Ψ = 0 has been applied at p = 0. (Note that the log-pressure height that is shown in the figures is also computed using H = 7 km.) We will refer to Ψ as the direct streamfunction to distinguish it from the downward control streamfunction that is introduced later. This method yields similar but somewhat smoother results than w* computed using the standard definition given in Andrews et al. (1987, p. 128) as well as a smaller residual term in the mass continuity equation when computed numerically.

3. Results

a. General features of the BDC

Before discussing the climatological means, it is instructive to first examine time series to get an overall sense of the temporal changes in the BDC. Figure 4 shows the zonal average temperature T (black) and residual vertical velocity w* (gray) at 70 hPa in the tropics (annual mean) and during Arctic winter (DJF) and Antarctic spring, September–November (SON), for the three simulations (dotted) and the ensemble average (thick). In the tropics there is a gradual and nearly linear increase in upwelling and an associated steady cooling, with both exhibiting little interannual variability and almost no perceptible differences between the three simulations. In Arctic winter there is a gradual increase in downwelling and an associated weak but steady warming—features that are also seen in each of the simulations but with greater variability. The linear nature of these trends suggests that they are due to climate change. In Antarctic spring the behavior is quite different, with decreasing downwelling occurring in conjunction with cooling. Moreover, the temperature trend is not linear but exhibits a more rapid decrease before about 2010, flattening out to a near-zero trend thereafter. This change in trend is attributed to the combined effects of the ozone hole, which produces a cooling in the late twentieth century and a subsequent warming as ozone levels recover, and climate change, which produces the steady dynamical cooling that must occur in response to the steadily decreasing downwelling. These results confirm the sense of the circulation changes in CMAM due to climate change inferred by Shepherd (2008) from the changes in both ozone and temperature. The cooling trend in Antarctic spring before 2010 (Fig. 4c) is observed and is a robust feature that is simulated by most CCMs (Eyring et al. 2006). However, clear secular temperature trends in the Arctic winter or tropical lower stratosphere are not detectable in observations. In the former case this is because of the large interannual variability, whereas in the latter case it is because of the small signal and biases in radiosonde and satellite data (Randel and Wu 2006).

Guided by the structure of these time series, climatological means are computed from the first (1960–79) and last (2080–99) 20 years of the ensemble average. These averaging periods are short enough to avoid the impact of ozone depletion and recovery, yet long enough to yield statistically significant results given that we have three ensemble members. The climatological means for these two periods will be referred to henceforth as the past and the future. Significance levels for the differences of the means are computed using the Student’s t test, assuming each year is independent. This assumption is supported by the lack of statistically significant lag-one autocorrelations in polar cap temperatures in the midstratosphere in these simulations.

Figure 5 shows the annual mean T and w* for the past and the corresponding differences between the future and past. The shading indicates that the differences are statistically significant at the 99% level over almost all of the plotted domain. Increased CO2 concentrations in the future have warmed the troposphere and cooled the stratosphere (Fig. 5b). Most of the stratospheric cooling above about 70 hPa is only weakly dependent on latitude, indicating the dominance of the radiative response to the increase in CO2. However, dynamics is responsible for the departures from the global average cooling at high latitudes in the stratosphere, with the warming in the NH resulting from increased downwelling and the cooling in the SH resulting from reduced downwelling (Fig. 5d). The increase in tropical upwelling extends over the entire depicted height range from 100 to 10 hPa, with the width of the region of positive differences increasing with height. Below about 70 hPa the width of the region of tropical upwelling narrows in the future (red lines in Fig. 5d). For consistency with the intercomparison study of Butchart et al. (2006), we shall focus primarily on the 70-hPa level when discussing the future changes in w*. The vertical structure of the w* changes is examined in later subsections.

The seasonal cycle of w* at 70 hPa for the past is shown in Fig. 6a. Tropical upwelling maximizes in the summer hemisphere, in agreement with observations (Rosenlof 1995; Plumb and Eluszkiewicz 1999). Extratropical downwelling is strongest in the NH, maximizing at high latitudes in winter, again in agreement with observations (Rosenlof 1995). To highlight the impact of dynamics on lower stratospheric temperatures, deviations of the zonal average temperature from the global mean (δT) at 70 hPa for the past are shown in Fig. 6c. In accordance with observations, the tropics are coldest in the NH winter months when upwelling is strongest and warmest in the SH winter months when upwelling is weakest (Yulaeva et al. 1994). Differences between the future and past are shown in Figs. 6b,d. The NH extratropics experience increased downwelling and warming, which maximize in the winter months at high latitudes (cf. Figure 4b). The picture in the SH is more complicated, as the region of increased downwelling and warming does not extend to the pole. Rather, the Antarctic undergoes reduced downwelling and cooling in winter and, especially, spring (cf. Figure 4c).

The BDC also has a strong impact on the simulated ozone field, as can be seen in Figs. 6e,f which show the deviation of the zonal average total ozone column from the global mean (δ) for the past and the difference with the future. (Note that the ozone column is largely determined by lower-stratospheric ozone, which is mainly under dynamical control. Furthermore, the past and future time periods were specifically chosen to avoid the years of severe chemical ozone depletion. Hence, the differences seen here are almost entirely due to transport.) In regions where upwelling increases in the future ozone generally decreases, and vice versa. The largest decreases of tropical ozone and the largest increases of extratropical ozone in the NH are found in February when the changes in w* are the largest. Likewise, the reduction in ozone in Antarctic spring is a direct consequence of the reduced downwelling there. The good agreement between the future changes in column ozone and w* also indicates that w* is a good proxy for the Lagrangian mean vertical velocity, in accordance with the findings of Pendlebury and Shepherd (2003).

b. Causes of predicted increase in the BDC

To diagnose the contributions of different types of wave drag to changes in the residual circulation, the downward control principle of Haynes et al. (1991) is used. The downward control mass streamfunction Ψdc is given by
i1520-0442-22-6-1516-e3
where f̂ = f −(a cos ϕ)−1 ∂(u cos ϕ)/∂ϕ; f is the Coriolis parameter, u the zonal average zonal wind, and F the zonal average wave drag, which comprises the tendency terms in the zonal momentum equation due to resolved wave drag and parameterized GWD. Resolved wave drag is given by ∇ · F/(ρa cos ϕ), where F is the Eliassen–Palm (EP) flux given in Andrews et al. (1987, p. 128); ρ = ρsexp(−z/H), z = −Hln(p/ps), ρs = ps/(gH), and ps = 1000 hPa. The integral is evaluated along lines of constant latitude with the upper boundary condition that Ψdc vanishes at p = 0. Note that downward control cannot be used in the tropics: plotted results between 20°N and 20°S are therefore masked out. Exact agreement with Ψ is not expected owing to the neglect of transience and integration along lines of constant latitude. The corresponding downward control residual vertical velocity wdc* is computed using Eq. (1).

Figure 7 (left panels) show wdc* at 70 hPa for the past computed using resolved and parameterized (orographic and nonorographic combined) wave drag. The good qualitative agreement between wdc* and w* (Figs. 7a and 6a) indicates that downward control provides reasonable estimates of the residual vertical velocity in the extratropical lower stratosphere, which gives us confidence in using it to attribute the causes of w* in the past and its changes in the future. Figure 7c shows that resolved wave drag accounts for most of the past downwelling in Arctic winter/spring and Antarctic spring. Parameterized orographic GWD (OGWD) (Fig. 7e) accounts for a significant fraction of the downwelling at midlatitudes, a large fraction of the downwelling in Antarctic winter, and most of the upwelling in the subtropical winter hemispheres. Nonorographic GWD has a negligible impact at these heights.

Displayed on the rhs of Fig. 7 are the corresponding differences (future minus past) in wdc*. Comparison to the differences in w* (Fig. 6b) again shows reasonable agreement. Resolved wave drag (Fig. 7d) accounts for nearly all of the future changes in downwelling at high latitudes, in particular the decrease in Antarctic spring and the increase in Arctic winter. Owing to the strong interannual variability of planetary wave activity in Arctic winter, the differences are only significant at the 80% level in that region. [Note also that near the pole, wdc* due to resolved wave drag should be treated with caution because of the amplification of finite difference errors in the EP flux divergence by the division by the cosine of latitude, which are compounded by the finite difference evaluation of Eq. (1).] Except in the NH during summer, OGWD (Fig. 7f) accounts for a significant fraction of the increase in downwelling at midlatitudes and most of the increase in upwelling in the subtropics. In the SH the future changes in wdc* due to OGWD are substantially smaller than in the NH and more uniform throughout the year. Interestingly, in the NH the OGWD and resolved wave drag contributions to wdc* exhibit difference patterns of opposite sign equatorward of ∼60°N in winter, spring, and fall, with increased upwelling from OGWD partially compensated by increased downwelling from resolved drag and vice versa. We will return to this point later.

As stated in the introduction, the relative roles of planetary waves and synoptic waves in causing the increase in the BDC have never been analyzed in previous climate change simulations. Since each may respond differently to climate change, it is important to determine their separate contributions to wdc*. Here we consider two zonal wavenumber (k) bands: k ≤ 3 (planetary waves) and k ≥ 4 (synoptic and small-scale waves, which for simplicity are referred to henceforth as synoptic waves). Figure 8 shows the contributions to wdc* from planetary waves (top) and synoptic waves (bottom). Comparison to Fig. 7 reveals that planetary wave drag accounts for nearly all of the resolved wave downwelling at high latitudes in the past and the corresponding changes in the future. Synoptic wave drag provides some downwelling at midlatitudes in the past, which is strongest in NH winter and weaker and more uniformly distributed over the course of the year in the SH, as well as upwelling at low latitudes (Fig. 8c). Future changes in wdc* due to synoptic waves (Fig. 8d), which are largest in NH winter at low latitudes, are substantially less than for the planetary waves.

As will be discussed in more detail shortly, much of the change in the stratospheric residual circulation is caused by changes in the flux of planetary wave activity into the stratosphere. Since the upward EP flux (Fz) at 100 hPa (or more typically the meridional heat flux) is the standard metric for quantifying the resolved wave forcing of the stratosphere (Newman et al. 2001), it is useful to examine it here. The top panels in Fig. 9 show Fz for the past and the corresponding differences between the future and past; the middle panels show the breakdown of those differences into planetary and synoptic waves. Consistent with our previous findings, planetary waves account for most of the future changes in Fz. The NH winter results, with positive differences between 30° and 60°N, indicate an increase in Fz at those latitudes. In SH winter and spring there is an overall decrease in planetary wave Fz in the extratropics with negative differences maximizing at high latitudes. Both NH winter and SH winter/spring changes in planetary wave Fz are consistent with the changes noted earlier in wdc* (Fig. 8b). Figure 9b also serves to show that averaging Fz (or heat flux) over latitude, as is done in the Newman et al. (2001) diagnostic, could yield an erroneous picture of future changes in wave forcing because of the strong cancellation between the positive and negative differences seen at mid and high latitudes in the NH during DJF.

Although the physical mechanisms responsible for the predicted changes in tropospheric planetary waves are extremely difficult to untangle in a model like the CMAM, some indication about the possible causes can be obtained by decomposing the EP fluxes into contributions from stationary (monthly means) and transient (deviations from monthly means) waves, which are shown in Fig. 9 (bottom panels) for the differences between the future and past. Stationary waves account for the increase in wave forcing in NH midlatitudes in winter/spring, the decrease in Antarctic winter/spring, and for almost all future changes at low latitudes. Changes in transient waves are significant in midlatitudes, where an increase in Fz occurs, and in NH high latitudes in winter and spring, where a decrease occurs. The latter is due to transient planetary waves that are ubiquitous features in NH winter and spring.

1) NH winter

The previous results have shown that the predicted increase in downwelling during Arctic winter in the lower stratosphere is caused primarily by planetary waves, suggesting that future increases in the upward EP flux from tropospherically forced stationary waves are responsible. Increased resolved wave drag was also seen to cause an increase in subtropical downwelling, which could be an indication of increased equatorward propagation and/or altered refraction. In addition to these changes, OGWD was shown to have a strong impact at low and midlatitudes. In this section we examine the vertical structure of the wave drag in NH winter and attribute possible physical causes to the changes. Since the contribution to annual mean tropical upwelling is largest in NH winter (e.g., Rosenlof 1995), a detailed analysis of NH winter wave drag will also provide insight into the causes of the overall increase in the BDC.

The meridional mass streamfunction is a convenient way to capture the two-dimensional structure of the residual circulation. The left panels of Fig. 10 show results for DJF for the past. The direct streamfunction (Ψ) is displayed in the top panel, and the downward control estimates (Ψdc) using planetary wave drag and OGWD are shown in the middle and bottom panels, respectively. (Ψdc as the sum of the total resolved and parameterized drag is in good agreement with Ψ and is not shown.) The direct streamfunction Ψ consists of a two-celled structure with upwelling centered at low latitudes in the SH and downwelling at middle and high latitudes in both hemispheres. The NH cell extends higher into the stratosphere as a result of the interhemispheric differences in the planetary wave drag in winter, which can be inferred from Fig. 10c. Poleward of ∼60°N planetary wave drag accounts for nearly all of the past downwelling. The circulation induced by OGWD is confined primarily to midlatitudes in the NH (Fig. 10e). The effects of synoptic wave drag (not shown) are confined to low latitudes in the NH and do not extend far into the stratosphere.

The corresponding differences between the future and past mass streamfunction (ΔΨ) are displayed in Fig. 10 (right panels). As can be seen, ΔΨ consists of two cells of the same sign as Ψ, indicating a future strengthening of the residual circulation at all heights. The NH cell is broader in latitudinal extent and reaches farther into the stratosphere. At high latitudes the mass flux differences are nearly constant with height (as indicated by the nearly vertical alignment of the contours), while at low latitudes they decay quite rapidly in the vertical. The contrast between the subtropics and high latitudes reflects the fact that the change in the NH circulation driven by planetary wave drag (Fig. 10d) consists of not one but two cells—one at low latitudes, the other at high latitudes. These two cells are bridged by a single cell due to OGWD (Fig. 10f). The impact of synoptic wave drag (not shown) is small and confined to low latitudes in the lower stratosphere. Thus, the strengthening of the equator-to-pole branch of the BDC in NH winter seen in Fig. 10b is, in fact, a combination of several elements and is not a single dynamical response.

The downward control analysis has revealed that future changes in planetary waves have resulted in two regions of increased wave drag separated by a region of zero or positive differences near 40°N in NH winter. That these differences have quite a different structure from the past suggests that future changes in the refractive properties of the background state may be responsible. To investigate the role of wave refraction we therefore examine the EP flux vector F shown in Fig. 11 along with the resolved wave drag (F has been divided by ρ to highlight changes in the stratosphere).

Considering first the EP flux for the past, Fig. 11a indicates two paths of wave propagation out of the troposphere: one between 45° and 60°N that is nearly vertical, the other between 30° and 45°N that has a strong equatorward component. The suppression of propagation near 40°N and 70 hPa is explainable in qualitative terms by the quasigeostrophic refractive index squared R2 (Matsuno 1970), shown in Fig. 12a for zonal wavenumber zero: the region of negative R2 near 40°N and 70 hPa, indicative of wave evanescence, is coincident with the region of suppressed propagation. A very similar structure is also seen in the NCEP reanalyses (not shown). For both CMAM and NCEP this region of negative R2 is a result of the vertical shear term in the zonal average quasigeostrophic potential vorticity. Use of a latitude- and height-dependent buoyancy frequency does not significantly change the result.

Concerning the differences between future and past EP fluxes (Fig. 11b), we see an increase in vertical propagation at midlatitudes over the entire height region, which produces the negative wave drag differences near 20 hPa. A second branch of increased wave propagation occurs at lower latitudes where enhanced equatorward propagation is seen, resulting in the fairly broad region of negative wave drag differences near 50 hPa and 20°N. However, the fact that equatorward of ∼50°N and below 50 hPa ΔF and F are nearly aligned indicates that future changes in the direction of wave propagation are not large in this region, a finding which is further supported by the absence of any significant change in shape or location of the region of negative R2 in the future (Fig. 12b). Rather, it is increased upward EP flux in the upper troposphere at midlatitudes (Fig. 9b) and refraction about the region of small R2 near 40°N and 70 hPa that is primarily responsible for the increase in wave drag at both low and high latitudes in the lower stratosphere. Higher up, where wave amplitudes are larger, nonlinear effects play an important role, and the concept of a refractive index makes little sense.

Returning to Fig. 11, the bottom two rows show the resolved wave drag and EP fluxes (past and differences) for both planetary waves and synoptic waves. (Note that the contour intervals and scaling of the vectors are different for the four panels.) The close correspondence between the middle and upper panels indicates that planetary waves account for most of the changes in the wave drag and EP flux. Consistent with the previous results, the impact of synoptic waves is confined to the troposphere and subtropical lower stratosphere. Figure 11e shows a large equatorward tilt in the past F for the synoptic waves and an associated low-latitude wave drag maximum near 30°N and 50 hPa, while Fig. 11f reveals a future increase in synoptic wave drag in this region. Like the planetary waves, the synoptic wave EP flux differences are nearly parallel to the past EP fluxes, indicating that significant changes in wave refraction in the stratosphere do not occur. However, the synoptic waves appear to penetrate slightly higher into the subtropical lower stratosphere. Randel and Held (1991) showed that synoptic wave drag in the upper troposphere and lower stratosphere is shaped by the zonal wind through critical-layer absorption. Based on this reasoning, a plausible explanation for the upward shift in synoptic wave drag is the strengthened westerlies in this region (see Fig. 14d), which would shift the critical levels upward.

The differences between the future and past resolved wave drag and EP fluxes for stationary and transient planetary waves are shown in Fig. 13. Comparison to Figs. 11c,d indicates that changes in stationary planetary waves are largely responsible for the increases in the mid and high latitude planetary wave drag in the middle stratosphere, thus explaining the increased polar downwelling in the lower stratosphere discussed earlier. Stationary and transient planetary waves both contribute to the low-latitude wave drag maximum in the lower stratosphere.

Turning now to the impact of parameterized orographic gravity waves, Fig. 14 (top panels) shows the zonal average zonal component of OGWD for NH winter for the past and the corresponding difference between the future and past. The dipole structure in the difference implies an upward shift in the location of the OGWD maximum, which explains the future increase in subtropical upwelling and midlatitude downwelling in the lower stratosphere (Fig. 7f). The upward shift in OGWD is associated with a strengthening of the subtropical westerly jet at and above its maximum (bottom panels of Fig. 14), which is the thermal wind response to the increased meridional temperature gradient in the upper troposphere that results from increased CO2 (Fig. 5b).

For a fixed momentum flux at the source level, this change in zonal wind raises the breaking height of the gravity waves, which would explain the upward shift in the OGWD profile. A similar effect on the OGWD distribution was discussed in detail by Li et al. (2008) and noted in passing by Garcia and Randel (2008). Since the momentum flux for the orographic gravity waves in these simulations was not saved, it is not possible to quantify how much of the change in OGWD is due to a change in the source flux and how much is due to a change in the zonal wind. However, the negligible change in the zonal average zonal wind in the lower troposphere (results not shown), together with the dipole nature of the drag change (note that all but two of the contours seen in Fig. 10f are closed above 200 hPa, indicating that the OGWD-induced circulation is largely closed within the stratosphere) suggests that a change in the source flux due to a change in the surface winds is not the dominant mechanism.

2) SH spring and summer

In contrast to Arctic winter when downwelling increases in the future, Antarctic spring was shown to undergo reduced downwelling. The downward control estimates of w* indicated that this was due to reduced planetary wave drag. Here we briefly examine the vertical structure of the changes in wave drag in SH spring. We also address the issue of an ozone-hole-induced increase in downwelling in SH summer that has been discussed in previous modeling studies (e.g., Manzini et al. 2003; Li et al. 2008).

The top panels of Fig. 15 show the mass streamfunction Ψ for SON for the past and the corresponding differences between the future and past. The streamfunction difference ΔΨ consists of a two-celled structure in the SH that produces the reduced downwelling in Antarctic spring (Fig. 4c). The middle panels of Fig. 15 indicate that planetary waves are largely responsible for this reduction. As in NH winter, the impact of OGWD (Fig. 15, bottom) is confined to midlatitudes. Note also that the two-celled structure in the planetary-wave-induced ΔΨ seen before in NH winter (Fig. 10d) is also seen here in NH fall (Fig. 15d) but with reduced amplitude, indicating that it is a robust feature of the NH planetary wave response to climate change in these simulations.

The resolved wave drag and corresponding EP fluxes for SH spring are shown in Fig. 16 (top) for the past and differences. The past shows a region of negative wave drag centered at ∼60°S that increases with height. The differences indicate a future reduction in this drag that is associated with a decrease in the upward component of the EP flux that extends down into the troposphere at high latitudes. Figure 16 (bottom) indicates that stationary planetary waves are largely responsible for the changes in high-latitude wave drag. This behavior is in contrast to the predicted changes in NH winter (Fig. 11b) when an increase in planetary wave Fz and drag occur.

The final results in this section pertain to changes in polar downwelling in SH summer due to the ozone hole. As is well known, the ozone hole cools the vortex and delays its breakdown by several weeks. This allows planetary waves to propagate into the stratosphere for a longer period of time and leads to a dynamical warming in late spring/early summer, as discussed by Manzini et al. (2003) and Li et al. (2008). Figure 17a shows time series of resolved wave drag at midlatitudes at 50 hPa (solid black) and polar cap average w* at 70 hPa (gray) for SH summer. From 1960 to about 2000 there is an increase in downwelling and wave drag, with a flattening out in the twenty-first century. The dashed line indicates that planetary waves are responsible for this behavior—a point that was never, in fact, demonstrated in previous studies. This increase is due to the mechanism described above, as can be seen in Fig. 17b, which shows the average height of the zero-wind line for December increasing from about 50 hPa in 1960 to 15 hPa in 2000. There is a very slight reduction in the height of the zero-wind line, but far from a reversal, by 2100. Thus, as the ozone hole disappears over the course of the twenty-first century, the delay in vortex breakdown is maintained by the dynamical cooling from climate change in Antarctic spring discussed earlier (Fig. 4c). A rough comparison of w* to that in Arctic winter (Fig. 4b) shows that from 1960 to 2000 the increase in downwelling is about twice as large in Antarctic summer.

c. Tropical mass flux

We now quantify the net upward mass flux (equivalently, troposphere to stratosphere mass exchange) and identify the reasons for its predicted strengthening as a result of climate change. Following Holton (1990), the area-averaged extratropical vertical mass flux across a pressure surface in the NH and SH, Fmnh and Fmsh, is expressed as
i1520-0442-22-6-1516-e4
and
i1520-0442-22-6-1516-e5
in which ϕtsh and ϕtnh are the so-called turnaround latitudes where tropical upwelling changes to extratropical downwelling, which are located at the minimum and maximum values of the mass streamfunction Ψ, respectively. This is illustrated in Fig. 18a, which shows Ψ (thin black curves) at 70 hPa for the past for DJF. In this example, ϕtsh and ϕtnh are located at ∼35°S and 30°N, respectively. Expressed in terms of Ψ, and noting that Ψ vanishes at the poles, the net downward mass fluxes in the two hemispheres are given by Fmnh = 2πaΨ(ϕtnh) and Fmsh = − 2πaΨ(ϕtsh). The net upward mass flux, which occurs mainly in the tropics, follows from the constraint of zero global average mass flux and is given by Fmtr = 2πa[Ψ(ϕtnh) − Ψ(ϕtsh)]. Similarly, the net upward mass flux using downward control is given by 2πa[Ψdc(ϕtnh) − Ψdc(ϕtsh)], where Ψdc is evaluated at the turnaround latitudes computed from Ψ. The mass fluxes are computed for each month (and year), and seasonal and annual means are computed from the monthly values.

Figure 19 shows time series of the net upward mass flux at 70 hPa for the four seasons, including March–May (MAM) and June–August (JJA). The mass flux computed from Ψ (black) has a strong seasonal cycle, which peaks in DJF in agreement with the majority of the CCMs examined in Butchart et al. (2006) and as inferred from the observed seasonal cycle of tropical temperature (Yulaeva et al. 1994). It exhibits a steady and nearly linear increase with time in each season, consistent with the secular trend in w* shown in Fig. 4a. The trend is largest in DJF, again in agreement with Butchart et al. (2006).

The colored curves in Fig. 19 denote the contributions of different types of wave drag to the net upward mass flux, as estimated from downward control. (The downward control estimate from the combined wave drag is very similar to the direct mass flux and is not shown.) Planetary wave drag (green) accounts for more than half of the past upward mass flux. However, except in JJA, the trends in synoptic wave drag (yellow) and OGWD (red) are just as important as the trend in planetary wave drag. The OGWD mass flux decrease with time after about 2080 in DJF is attributed to the combination of the equatorward shift in the turnaround latitudes at 70 hPa in the latter part of the twenty-first century (Fig. 5d) and the rapid latitudinal variation of Ψdc near the NH turnaround latitude (Fig. 18).

Table 1 summarizes the linear trends in the net upward mass flux at 70 hPa for the four seasons and the annual mean. Resolved wave drag and OGWD account for about 60% and 40%, respectively, of the total annual mean trend, with planetary waves accounting for about 60% of the resolved wave drag trend. The largest trend occurs in DJF and is nearly a factor of two larger than in JJA. Increases in resolved wave drag account for ∼70% of the total trend in DJF. Synoptic wave drag has the strongest impact in DJF when it accounts for nearly as much of the trend as does planetary wave drag.

This strong contribution from synoptic waves may at first seem surprising in light of the discussion in the previous sections. The reason can be seen in Fig. 8: although Δwdc* due to planetary wave drag is larger at any single latitude than that due to synoptic wave drag, the positive and negative differences in the NH tend to cancel out when the extratropical area average is computed, thus boosting the relative contribution to the net upward mass flux from synoptic wave drag whose wdc* differences are of one sign.

The slight narrowing of the region of upwelling at 70 hPa, noted above, has also resulted in the OGWD mass flux trend being smaller than the resolved wave drag trend (see Fig. 19a). If the mass fluxes are computed from the seasonally averaged streamfunction (instead of the monthly averaged values), this shift in the turnaround latitude is weaker and the relative contribution of OGWD to the total trend is larger, but with the trend due to the combined resolved wave drag and OGWD remaining about the same.

Tabulated results for the net downward mass flux trends at 70 hPa for both hemispheres are given in Table 2. The largest trend occurs in NH winter and is more than a factor of 2 larger than in SH winter. The negative trend in resolved wave drag in SH spring (reduced downwelling) is offset by the increase due to OGWD. The contribution from synoptic waves is largest in NH winter.

Earlier we showed (Fig. 17) that the increased vertical propagation of planetary waves into the SH summer stratosphere during the development of the ozone hole caused increased downwelling in the Antarctic lower stratosphere during those years. As in Li et al. (2008), this has a significant influence on the net upward mass flux trends in DJF. Table 3 shows that the trend in DJF is nearly 60% stronger before 2004 than after and that it is largely due to the much stronger trend in the net downward SH mass flux before 2004. An additional calculation (results not shown) reveals that 75% of that trend occurs poleward of 60°S, indicating that increased downwelling in the Antarctic is responsible. The similarity between our results and those of Li et al. (2008) is somewhat surprising given that the model used in the latter study had too much ozone loss in the SH and too much cooling throughout the SH extratropics (Eyring et al. 2006). It is reasonable to presume that the reason the two models nevertheless yield similar results is because of the excessive cooling through ozone loss in the model used by Li et al. being spread out meridionally so that the latitudinal temperature gradient and corresponding zonal wind changes were not that much different from those in the CMAM.

While 70 hPa is conventionally chosen to define the base of the BDC (e.g., Butchart et al. 2006), to some extent this choice is arbitrary. Also, age of air is affected by the circulation throughout the stratosphere. It is therefore of interest to examine the vertical structure of the changes in upwelling. Vertical profiles of the annual mean net upward mass flux for the past and the 140-yr trend computed from the seasonal means for each year are shown in Fig. 20. Results are not shown below 80 hPa because the turnaround latitudes approach too close to the equator to yield accurate downward control estimates, or above 40 hPa because the turnaround latitudes are not well defined in the summer hemisphere. Resolved wave drag (solid blue) accounts for most of the past mass flux, with the relative contribution from planetary wave drag (dashed–dotted blue) increasing with height. The contribution from OGWD (red) is about a factor of 3 smaller than resolved wave drag in the lower stratosphere. However, the trend due to OGWD is as large as or larger than that due to resolved wave drag above ∼60 hPa. Below 70 hPa the OGWD trend falls off rapidly, becoming negative at ∼80 hPa. This behavior is attributed to the upward shift in the OGWD in the future (Fig. 14d). Below 70 hPa resolved wave drag accounts for nearly all of the trend, resulting in a fairly smoothly decaying total trend profile (black). The trend due to planetary wave drag closely follows that due to resolved wave drag. Synoptic waves (dotted blue) play a nonnegligible role, matching that of planetary waves near 50 hPa where synoptic wave drag exhibits a future increase in the subtropics (Fig. 11f).

In contrast to our results (and also those of Li et al. 2008), Garcia and Randel (2008) found that below about 22 km the resolved wave drag contribution to tropical upwelling was substantially larger than that from parameterized GWD. However, their conclusion was based on averaging the upwelling over a fixed latitude range, namely, 22°S–22°N, which is deep within the region of net upwelling and thus does not account for the significant upwelling in the subtropics. From Fig. 18b it is evident that the magnitude of the OGWD and resolved wave drag contributions to tropical upwelling trends are sensitive functions of the latitude range used in defining the upwelling region. Figure 21 shows vertical profiles of the annual mean mass flux trend computed over three different latitude ranges centered about the equator. For the wide latitude range (solid curves) the trend is largest for OGWD, except close to 100 hPa where resolved wave drag is dominant. However, for the narrow latitude range (dashed–dotted curves), the relative contributions from OGWD and resolved wave drag reverse, with resolved wave drag now dominating, as in Garcia and Randel (2008). This behavior results from the oppositely signed differences in wdc* due to OGWD and planetary wave drag south of 35° in the NH seen in Figs. 7 and 8. Thus, when comparing model results it is important to appreciate the sensitivity of the computed mass flux to the way in which the spatial averaging is done.

4. Summary and discussion

Three 150-yr transient simulations using the Canadian Middle Atmosphere Model (CMAM) are used to examine the response of the Brewer–Dobson circulation (BDC) to climate change. Consistent with previous modeling studies (e.g., Butchart et al. 2006), the BDC is found to increase in strength as greenhouse gas concentrations increase. Such an increase requires an increase in wave drag in the extratropical stratosphere. A downward control analysis is performed to identify the causes for this increase and to quantify the contributions from different types of wave drag.

The predicted increase in the annual mean net upward mass flux at 70 hPa is mainly due to an increase in resolved wave drag (mainly planetary waves k = 1–3), with a significant secondary contribution from parameterized orographic gravity wave drag (OGWD). A seasonal and hemispheric breakdown reveals that increased NH winter wave drag is mainly responsible for the annual mean trend. The impact of synoptic wave drag (k ≥ 4) is largest in NH winter, providing nearly half of the net downward mass flux trend from resolved waves in NH winter.

The relative contributions of resolved and parameterized wave drag to the trends in area-averaged lower stratospheric tropical upwelling are found to be extremely sensitive to the latitudinal ranges used in computing those averages. This sensitivity results from differences in the latitudinal structure of the wave drag and appears to account for the opposite conclusions of Li et al. (2008) and Garcia and Randel (2008) regarding the importance of parameterized orographic gravity wave drag.

In agreement with Li et al., the development of the ozone hole is found to have a significant impact on the net upward mass flux trend in DJF during the last part of the past century. The increased trend in the net upward mass flux during this period is attributed to increased resolved wave drag in SH summer due to the late breakdown of the vortex as a result of ozone-hole-induced cooling in the Antarctic lower stratosphere. Planetary waves are identified as being responsible for this increased wave drag.

At high latitudes in NH winter, climate change leads to increased downwelling and a warming in the lower stratosphere that is attributed to increased stationary planetary wave drag. In contrast to Arctic winter, reduced downwelling and cooling are found in Antarctic spring. This is attributed to a decrease in the vertical flux of stationary planetary waves. The reasons for the hemispheric asymmetry in the planetary wave changes in our simulations are not understood and, if reproduced in other models, would present an interesting challenge for dynamicists to explain.

At middle and subtropical latitudes in NH winter, increases in both OGWD and resolved wave drag are found. The increase in OGWD is attributed to an upward shift in the breaking heights of the parameterized orographic gravity waves, which results from an increase in the strength of the subtropical jet in the lower stratosphere. The increase in the resolved subtropical wave drag is associated with stationary and transient planetary waves and to a somewhat lesser extent with synoptic waves. Since the differences (future minus past) in the EP fluxes are nearly parallel to the past EP fluxes, changes in the propagation direction of the resolved waves in the stratosphere do not appear to be important. Rather, it is increased upward EP flux from resolved waves in the troposphere that best explains the increased stratospheric wave drag.

Previous studies have suggested changes in the quasigeostrophic refractive index R2 as an important cause of changes in resolved wave drag in the stratosphere in response to climate change (e.g., Rind et al. 1998; Shindell et al. 1999). Although future changes in R2 in our simulations are consistent with the climate change response of the zonal average zonal winds in the lower stratosphere (i.e., the slight upward shift in the region of negative R2 located near 40°N and 70 hPa seen in Fig. 12), they are certainly not large enough to account for the future changes in EP flux in the stratosphere. Our results are consistent with those of Butchart and Scaife (2001), who also did not find any evidence of altered wave refraction in their simulations.

Using an earlier version of the CMAM, Fomichev et al. (2007) found an increase in tropical upwelling as a result of CO2 doubling but no statistically significant change in Arctic winter temperature in the lower stratosphere or upward EP flux at midlatitudes at 100 hPa. The latter two nonresults, which are of course related, reflect the limited length of the dataset, which was half that considered here. Nevertheless, their midlatitude average 100-hPa EP flux shows an increase in NH winter/spring and a slight decrease in SH spring between the CO2 doubling and control simulations, which is consistent with our results. Note also that area averaging EP flux differences that contain positive and negative values (Fig. 9b) will reduce the average difference and therefore reduce the statistical significance. Fomichev et al. attributed the increase in tropical upwelling to an increase in resolved wave drag at low latitudes based on an increase in subtropical EP flux. However, since a downward control analysis was not performed, one cannot state with certainty that this was the only cause (nor was there any split into planetary and synoptic waves.) The impact of parameterized OGWD, which was not diagnosed in Fomichev et al. (2007), most likely contributed to a significant fraction of the upwelling.

The importance of parameterized OGWD on the predicted increase in tropical upwelling has been discussed before (Li et al. 2008) and inferred from differences between actual upwelling and downward control estimates using resolved wave drag (Butchart et al. 2006). In our simulations, this is due to an upward shift in the OGWD maximum. The strengthening of the lower stratospheric winds that causes this upward shift is a direct consequence of climate change, which warms the tropical upper troposphere and cools the extratropical lower stratosphere (Fig. 5b), and through thermal wind balance causes the observed wind changes. This suggests that the predicted increase in the net upward mass flux in the lower stratosphere due to OGWD is a robust response to climate change. Although the magnitude of the change in mass flux may differ among models, the overall effect should not, as is borne out by the similarity of our results to those of Li et al. In comparison to nonorographic gravity wave drag parameterizations where the source spectrum is poorly constrained, the wave source in OGWD parameterizations is much more realistic, which suggests that the climate change response is physically realistic. In our simulations, the OGWD parameterization of Scinocca and McFarlane (2000) is employed, which takes into account the shape and orientation of subgrid-scale topography. Parameterized OGWD has another important role, particularly in NH winter, where it causes a separation of the tropospheric and stratospheric zonal jets (McFarlane 1987). This will influence planetary wave propagation, thus providing an important indirect impact of OGWD on the BDC.

The causes of the changes in the resolved tropospheric wave activity in our simulations are not understood. The response of planetary waves to climate change appears to have received almost no attention in the scientific literature. With the exception of the modeling study of Joseph et al. (2004), diagnostic analyses of the forced stationary wave response to thermal and orographic forcings from climate model simulations are never performed. Such analyses may shed light on the mechanisms responsible for the hemispheric asymmetry in the planetary wave differences in our simulations. In terms of synoptic waves, the large changes in the temperature and zonal wind structure in the subtropical upper troposphere and lower stratosphere (Figs. 5b and 14d) allow the possibility of significant changes in the contributions of synoptic waves to the driving of the BDC, which have not been discussed much. Future modeling studies will require detailed diagnostic analyses of planetary and synoptic wave forcing in order to assess the robustness of the resolved wave–driven response of the BDC to climate change.

Acknowledgments

CM thanks Diane Pendlebury and Neal Butchart for helpful discussions. Rolando Garcia and an anonymous reviewer provided valuable reviews. This work was supported by the Canadian Foundation for Climate and Atmospheric Sciences through the C-SPARC project.

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Fig. 1.
Fig. 1.

Monthly and zonal average (a) zonal wind (u) at 30 hPa and 58°N/S and (b) temperature (T) at 50 hPa and 85°N/S for CMAM (solid) and NCEP (dash) for the years 1979–2006.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 2.
Fig. 2.

Zonal average zonal wind (u) during NH winter (DJF) for (a) CMAM and (b) NCEP for the years 1979–2006. Contour interval is 5 m s−1; easterlies are shaded.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 3.
Fig. 3.

Monthly and zonal average meridional heat flux () at 100 hPa for (a) CMAM and (b) NCEP for the years 1979–2006. Contour intervals are 4 K m s−1; southward (negative) heat fluxes < −2 K m s−1 are shaded.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 4.
Fig. 4.

Time series of zonal average temperature T (black) and residual vertical velocity w* (gray) at 70 hPa for (a) tropics (annual mean), (b) Arctic winter (DJF), and (c) Antarctic spring (SON): T and w* have been area averaged from 15°S to 15°N in (a) and from 60°N/S to 90°N/S in (b) and (c). Thick lines denote the ensemble average, dotted lines the three ensemble members. Linear trends computed over the 140-yr period are given by the thin solid lines in (b) and (c).

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 5.
Fig. 5.

Annual and zonal mean (a) temperature (T) for the past, (b) difference in T (future minus past), (c) residual vertical velocity (w*), and (d) difference in w* (future minus past). Note the different range of vertical axes. Contour intervals are (left) 10 K and 0.1 mm s−1 and (right) 1 K and 0.02 mm s−1. Blue and red lines in (d) denote the w* = 0 line for the past and future, respectively. Light and dark shading denote the 90% and 99% confidence levels, respectively. The extension of the shading across the zero contour in places is an artifact of the interpolation used in the plotting software.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 6.
Fig. 6.

Monthly mean residual vertical velocity (w*) at 70 hPa for (a) past and (b) difference (future minus past). (c),(d) As in (a),(b) but for zonal average temperature (δT) and (e),(f) as in (a),(b) but for zonal average total ozone column (δO3); δT and δO3 are deviations from the global average. Contour intervals in (a)–(f) are 0.1 mm s−1, 0.05 mm s−1, 5 K, 1 K, 20 DU, and 10 DU, respectively. Light and dark shading in the extratropics denotes the 90% and 99% confidence levels, respectively.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 7.
Fig. 7.

Monthly-mean residual vertical velocity wdc* at 70 hPa computed from downward control using resolved and parameterized wave drag for (a) past and (b) difference (future minus past). (c),(d) As in (a),(b) but using only resolved wave drag and (e),(f) as in (a),(b) but using only parameterized orographic GWD. Contour intervals are (left) 0.1 and (right) 0.05 mm s−1. Light and dark shading in the extratropics denotes the 90% and 99% confidence levels, respectively.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 8.
Fig. 8.

As in Fig. 7 but using resolved wave drag for (top) planetary waves and (bottom) synoptic waves.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 9.
Fig. 9.

Monthly-mean vertical component of EP flux (Fz) at 100 hPa for (a) past and (b) difference (future minus past). (c)–(f) As in (b) but for planetary waves (k = 1–3), synoptic waves (k = 4–32), stationary waves (k = 1–32), and transient waves (k = 1–32), respectively. Contour intervals are 4 × 10 kg m3 s−2 in (a) and 0.6 × 10−4 kg m3 s−2 in (b)–(f). Light and dark shading denote the 90% and 99% confidence levels, respectively.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 10.
Fig. 10.

Mass streamfunction for DJF for (left) past and (right) difference (future minus past). (top) Direct calculation and downward control calculations using (middle) resolved planetary wave drag, and (bottom) parameterized orographic GWD. Contour intervals are (left) 20 and (right) 6 kg m−2 s−1. Since a uniform contour interval is used, the mass flux is proportional to the distance between adjacent contour lines. The arrows indicate the direction of the circulation.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 11.
Fig. 11.

Resolved wave drag and EP flux F for NH winter (DJF) for (a) past and (b) difference (future minus past). (c),(d) As in (a),(b) but for planetary waves and (e),(f) as in (a),(b) but for synoptic waves. Contour intervals are 0.5 m s−1 day−1 in (a),(c); 0.2 m s−1 day−1 in (b),(d),(e); and 0.1 m s−1 day−1 in (f). Light and dark shading denote the 90% and 99% confidence levels for the wave drag, respectively; F has been divided by the background density ρo. The black arrows in the top left corner of each panel denote the magnitude of the plotted vector components. The flux F for synoptic waves is a factor of 2 smaller than for planetary waves; ΔF is a factor of 5 smaller than F.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 12.
Fig. 12.

Quasigeostrophic refractive index squared R2 for zonal wavenumber 0 for DJF (a) past and (b) future: a constant buoyancy frequency of 0.0173 s−1 is used. The refractive index squared has been multiplied by the square of the radius of the earth, and is dimensionless. Shading denotes regions of negative R2.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 13.
Fig. 13.

Differences (future minus past) in resolved wave drag and EP flux F for DJF for (a) stationary and (b) transient planetary waves. Contour intervals are 0.2 m s−1 day−1. Refer to Fig. 11 for details.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 14.
Fig. 14.

Zonal average zonal component of (top) orographic GWD and (bottom) zonal wind for DJF for (left) past and (right) difference (future minus past). Contour intervals for OGWD are 0.5 and 0.2 m s−1 day−1 and for zonal winds 5 and 2 m s−1, respectively. Light and dark shading denote the 90% and 99% confidence levels, respectively.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 15.
Fig. 15.

As in Fig. 10 but for SON.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 16.
Fig. 16.

Resolved wave drag and EP flux F for SH spring (SON) for (a) past and (b) difference (future minus past). (c),(d) Differences for stationary and transient planetary waves, respectively. Refer to Fig. 11 caption for details. Scale factors for the difference vectors are all the same.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 17.
Fig. 17.

(a) Resolved wave drag at 50 hPa (solid black) and residual vertical velocity (w*) at 70 hPa (gray) for SH summer (DJF). Dashed line denotes planetary wave drag. The residual vertical velocity w* has been area averaged between 60° and 90°S, wave drag between 40° and 80°S. (b) Height of the zero wind line computed from the December zonal-mean zonal wind profiles after area averaging between 50° and 90°S. Axis showing (left) pressure height and (right) corresponding log pressure height using a scale height of 7 km.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 18.
Fig. 18.

Downward control mass streamfunction for DJF at 70 hPa for (a) past and (b) difference (future minus past): combined resolved and parameterized wave drag (thick black); resolved wave drag (solid blue); parameterized orographic GWD (red); planetary wave drag (dotted–dashed); and synoptic wave drag (dotted). The thin black line denotes the direct streamfunction.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 19.
Fig. 19.

Seasonal mean net upward mass flux (Fmtr) at 70 hPa for (a) DJF; (b) JJA; (c) MAM; and (d) SON: direct calculation (black); downward control estimates using parameterized OGWD (red); resolved wave drag (blue); planetary wave drag (green); and synoptic wave drag (yellow). The mass flux is computed between the turnaround latitudes (refer to text for details).

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 20.
Fig. 20.

Vertical profiles of annual mean net upward mass flux (Fmtr) for (a) past and (b) linear trend from 1960 to 2099: direct calculation (black); downward control estimates using parameterized orographic GWD (red); resolved wave drag (solid blue); planetary wave drag (blue, dashed–dotted); synoptic wave drag (blue dots); and total wave drag (black dots). Note the logarithmic scale for the mass flux. Trends are computed using least squares. The mass flux is computed between the turnaround latitudes (see text for details), which vary as a function of altitude.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Fig. 21.
Fig. 21.

Vertical profiles of linear trends of annual mean upward mass flux computed over fixed latitude ranges centered about the equator: ±36.0° (solid), ±30.5° (dotted), and ±24.9° (dashed–dotted) for (a) resolved wave drag and (b) parameterized orographic GWD computed using downward control. Note the logarithmic scale for the mass flux. Trends are computed from 1960 to 2099 using least squares.

Citation: Journal of Climate 22, 6; 10.1175/2008JCLI2679.1

Table 1.

Linear trends in seasonal mean net upward mass flux at 70 hPa calculated from the direct streamfunction and from downward control using resolved wave drag (all waves k = 1–32; planetary waves k = 1–3; and synoptic waves k = 4–32) and parameterized orographic and nonorographic GWD. Quantities in parentheses are the 1-σ uncertainties. Trends are computed from 1960 to 2099 using least squares. Negative values indicate a decrease in upwelling. Units are kt s−1 yr−1. The mass flux is computed between the turnaround latitudes (see text for details).

Table 1.
Table 2.

As in Table 1 but showing linear trends in seasonal mean net downward mass flux for each hemisphere at 70 hPa. Negative values indicate a decrease in downwelling.

Table 2.
Table 3.

Linear trends in seasonal mean net upward and downward mass fluxes at 70 hPa computed for the ozone depletion period (1960–2004) and for the ozone recovery period (2005–99). Quantities in parentheses are the 1-σ uncertainties in the trends. Units are kt s−1 yr−1. The mass fluxes are computed using the turnaround latitudes (see text for details).

Table 3.
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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Monthly and zonal average (a) zonal wind (u) at 30 hPa and 58°N/S and (b) temperature (T) at 50 hPa and 85°N/S for CMAM (solid) and NCEP (dash) for the years 1979–2006.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Zonal average zonal wind (u) during NH winter (DJF) for (a) CMAM and (b) NCEP for the years 1979–2006. Contour interval is 5 m s−1; easterlies are shaded.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Monthly and zonal average meridional heat flux () at 100 hPa for (a) CMAM and (b) NCEP for the years 1979–2006. Contour intervals are 4 K m s−1; southward (negative) heat fluxes < −2 K m s−1 are shaded.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Time series of zonal average temperature T (black) and residual vertical velocity w* (gray) at 70 hPa for (a) tropics (annual mean), (b) Arctic winter (DJF), and (c) Antarctic spring (SON): T and w* have been area averaged from 15°S to 15°N in (a) and from 60°N/S to 90°N/S in (b) and (c). Thick lines denote the ensemble average, dotted lines the three ensemble members. Linear trends computed over the 140-yr period are given by the thin solid lines in (b) and (c).

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Annual and zonal mean (a) temperature (T) for the past, (b) difference in T (future minus past), (c) residual vertical velocity (w*), and (d) difference in w* (future minus past). Note the different range of vertical axes. Contour intervals are (left) 10 K and 0.1 mm s−1 and (right) 1 K and 0.02 mm s−1. Blue and red lines in (d) denote the w* = 0 line for the past and future, respectively. Light and dark shading denote the 90% and 99% confidence levels, respectively. The extension of the shading across the zero contour in places is an artifact of the interpolation used in the plotting software.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Monthly mean residual vertical velocity (w*) at 70 hPa for (a) past and (b) difference (future minus past). (c),(d) As in (a),(b) but for zonal average temperature (δT) and (e),(f) as in (a),(b) but for zonal average total ozone column (δO3); δT and δO3 are deviations from the global average. Contour intervals in (a)–(f) are 0.1 mm s−1, 0.05 mm s−1, 5 K, 1 K, 20 DU, and 10 DU, respectively. Light and dark shading in the extratropics denotes the 90% and 99% confidence levels, respectively.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Monthly-mean residual vertical velocity wdc* at 70 hPa computed from downward control using resolved and parameterized wave drag for (a) past and (b) difference (future minus past). (c),(d) As in (a),(b) but using only resolved wave drag and (e),(f) as in (a),(b) but using only parameterized orographic GWD. Contour intervals are (left) 0.1 and (right) 0.05 mm s−1. Light and dark shading in the extratropics denotes the 90% and 99% confidence levels, respectively.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    As in Fig. 7 but using resolved wave drag for (top) planetary waves and (bottom) synoptic waves.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Monthly-mean vertical component of EP flux (Fz) at 100 hPa for (a) past and (b) difference (future minus past). (c)–(f) As in (b) but for planetary waves (k = 1–3), synoptic waves (k = 4–32), stationary waves (k = 1–32), and transient waves (k = 1–32), respectively. Contour intervals are 4 × 10 kg m3 s−2 in (a) and 0.6 × 10−4 kg m3 s−2 in (b)–(f). Light and dark shading denote the 90% and 99% confidence levels, respectively.

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Mass streamfunction for DJF for (left) past and (right) difference (future minus past). (top) Direct calculation and downward control calculations using (middle) resolved planetary wave drag, and (bottom) parameterized orographic GWD. Contour intervals are (left) 20 and (right) 6 kg m−2 s−1. Since a uniform contour interval is used, the mass flux is proportional to the distance between adjacent contour lines. The arrows indicate the direction of the circulation.

  • <sc>Fig</sc>. 11.
    View in gallery
    Fig. 11.

    Resolved wave drag and EP flux F for NH winter (DJF) for (a) past and (b) difference (future minus past). (c),(d) As in (a),(b) but for planetary waves and (e),(f) as in (a),(b) but for synoptic waves. Contour intervals are 0.5 m s−1 day−1 in (a),(c); 0.2 m s−1 day−1 in (b),(d),(e); and 0.1 m s−1 day−1 in (f). Light and dark shading denote the 90% and 99% confidence levels for the wave drag, respectively; F has been divided by the background density ρo. The black arrows in the top left corner of each panel denote the magnitude of the plotted vector components. The flux F for synoptic waves is a factor of 2 smaller than for planetary waves; ΔF is a factor of 5 smaller than F.

  • <sc>Fig</sc>. 12.
    View in gallery
    Fig. 12.

    Quasigeostrophic refractive index squared R2 for zonal wavenumber 0 for DJF (a) past and (b) future: a constant buoyancy frequency of 0.0173 s−1 is used. The refractive index squared has been multiplied by the square of the radius of the earth, and is dimensionless. Shading denotes regions of negative R2.

  • <sc>Fig</sc>. 13.
    View in gallery
    Fig. 13.

    Differences (future minus past) in resolved wave drag and EP flux F for DJF for (a) stationary and (b) transient planetary waves. Contour intervals are 0.2 m s−1 day−1. Refer to Fig. 11 for details.

  • <sc>Fig</sc>. 14.
    View in gallery
    Fig. 14.

    Zonal average zonal component of (top) orographic GWD and (bottom) zonal wind for DJF for (left) past and (right) difference (future minus past). Contour intervals for OGWD are 0.5 and 0.2 m s−1 day−1 and for zonal winds 5 and 2 m s−1, respectively. Light and dark shading denote the 90% and 99% confidence levels, respectively.

  • <sc>Fig</sc>. 15.
    View in gallery
    Fig. 15.

    As in Fig. 10 but for SON.

  • <sc>Fig</sc>. 16.
    View in gallery
    Fig. 16.

    Resolved wave drag and EP flux F for SH spring (SON) for (a) past and (b) difference (future minus past). (c),(d) Differences for stationary and transient planetary waves, respectively. Refer to Fig. 11 caption for details. Scale factors for the difference vectors are all the same.

  • <sc>Fig</sc>. 17.
    View in gallery
    Fig. 17.

    (a) Resolved wave drag at 50 hPa (solid black) and residual vertical velocity (w*) at 70 hPa (gray) for SH summer (DJF). Dashed line denotes planetary wave drag. The residual vertical velocity w* has been area averaged between 60° and 90°S, wave drag between 40° and 80°S. (b) Height of the zero wind line computed from the December zonal-mean zonal wind profiles after area averaging between 50° and 90°S. Axis showing (left) pressure height and (right) corresponding log pressure height using a scale height of 7 km.

  • <sc>Fig</sc>. 18.
    View in gallery
    Fig. 18.

    Downward control mass streamfunction for DJF at 70 hPa for (a) past and (b) difference (future minus past): combined resolved and parameterized wave drag (thick black); resolved wave drag (solid blue); parameterized orographic GWD (red); planetary wave drag (dotted–dashed); and synoptic wave drag (dotted). The thin black line denotes the direct streamfunction.

  • <sc>Fig</sc>. 19.
    View in gallery
    Fig. 19.

    Seasonal mean net upward mass flux (Fmtr) at 70 hPa for (a) DJF; (b) JJA; (c) MAM; and (d) SON: direct calculation (black); downward control estimates using parameterized OGWD (red); resolved wave drag (blue); planetary wave drag (green); and synoptic wave drag (yellow). The mass flux is computed between the turnaround latitudes (refer to text for details).

  • <sc>Fig</sc>. 20.
    View in gallery
    Fig. 20.

    Vertical profiles of annual mean net upward mass flux (Fmtr) for (a) past and (b) linear trend from 1960 to 2099: direct calculation (black); downward control estimates using parameterized orographic GWD (red); resolved wave drag (solid blue); planetary wave drag (blue, dashed–dotted); synoptic wave drag (blue dots); and total wave drag (black dots). Note the logarithmic scale for the mass flux. Trends are computed using least squares. The mass flux is computed between the turnaround latitudes (see text for details), which vary as a function of altitude.

  • <sc>Fig</sc>. 21.
    View in gallery
    Fig. 21.

    Vertical profiles of linear trends of annual mean upward mass flux computed over fixed latitude ranges centered about the equator: ±36.0° (solid), ±30.5° (dotted), and ±24.9° (dashed–dotted) for (a) resolved wave drag and (b) parameterized orographic GWD computed using downward control. Note the logarithmic scale for the mass flux. Trends are computed from 1960 to 2099 using least squares.

Fig. 1.

Monthly and zonal average (a) zonal wind (u) at 30 hPa and 58°N/S and (b) temperature (T) at 50 hPa and 85°N/S for CMAM (solid) and NCEP (dash) for the years 1979–2006.
Fig. 2.

Zonal average zonal wind (u) during NH winter (DJF) for (a) CMAM and (b) NCEP for the years 1979–2006. Contour interval is 5 m s−1; easterlies are shaded.
Fig. 3.

Monthly and zonal average meridional heat flux () at 100 hPa for (a) CMAM and (b) NCEP for the years 1979–2006. Contour intervals are 4 K m s−1; southward (negative) heat fluxes < −2 K m s−1 are shaded.
Fig. 4.

Time series of zonal average temperature T (black) and residual vertical velocity w* (gray) at 70 hPa for (a) tropics (annual mean), (b) Arctic winter (DJF), and (c) Antarctic spring (SON): T and w* have been area averaged from 15°S to 15°N in (a) and from 60°N/S to 90°N/S in (b) and (c). Thick lines denote the ensemble average, dotted lines the three ensemble members. Linear trends computed over the 140-yr period are given by the thin solid lines in (b) and (c).
Fig. 5.

Annual and zonal mean (a) temperature (T) for the past, (b) difference in T (future minus past), (c) residual vertical velocity (w*), and (d) difference in w* (future minus past). Note the different range of vertical axes. Contour intervals are (left) 10 K and 0.1 mm s−1 and (right) 1 K and 0.02 mm s−1. Blue and red lines in (d) denote the w* = 0 line for the past and future, respectively. Light and dark shading denote the 90% and 99% confidence levels, respectively. The extension of the shading across the zero contour in places is an artifact of the interpolation used in the plotting software.
Fig. 6.

Monthly mean residual vertical velocity (w*) at 70 hPa for (a) past and (b) difference (future minus past). (c),(d) As in (a),(b) but for zonal average temperature (δT) and (e),(f) as in (a),(b) but for zonal average total ozone column (δO3); δT and δO3 are deviations from the global average. Contour intervals in (a)–(f) are 0.1 mm s−1, 0.05 mm s−1, 5 K, 1 K, 20 DU, and 10 DU, respectively. Light and dark shading in the extratropics denotes the 90% and 99% confidence levels, respectively.
Fig. 7.

Monthly-mean residual vertical velocity wdc* at 70 hPa computed from downward control using resolved and parameterized wave drag for (a) past and (b) difference (future minus past). (c),(d) As in (a),(b) but using only resolved wave drag and (e),(f) as in (a),(b) but using only parameterized orographic GWD. Contour intervals are (left) 0.1 and (right) 0.05 mm s−1. Light and dark shading in the extratropics denotes the 90% and 99% confidence levels, respectively.
Fig. 8.

As in Fig. 7 but using resolved wave drag for (top) planetary waves and (bottom) synoptic waves.
Fig. 9.

Monthly-mean vertical component of EP flux (Fz) at 100 hPa for (a) past and (b) difference (future minus past). (c)–(f) As in (b) but for planetary waves (k = 1–3), synoptic waves (k = 4–32), stationary waves (k = 1–32), and transient waves (k = 1–32), respectively. Contour intervals are 4 × 10 kg m3 s−2 in (a) and 0.6 × 10−4 kg m3 s−2 in (b)–(f). Light and dark shading denote the 90% and 99% confidence levels, respectively.
Fig. 10.

Mass streamfunction for DJF for (left) past and (right) difference (future minus past). (top) Direct calculation and downward control calculations using (middle) resolved planetary wave drag, and (bottom) parameterized orographic GWD. Contour intervals are (left) 20 and (right) 6 kg m−2 s−1. Since a uniform contour interval is used, the mass flux is proportional to the distance between adjacent contour lines. The arrows indicate the direction of the circulation.
Fig. 11.

Resolved wave drag and EP flux F for NH winter (DJF) for (a) past and (b) difference (future minus past). (c),(d) As in (a),(b) but for planetary waves and (e),(f) as in (a),(b) but for synoptic waves. Contour intervals are 0.5 m s−1 day−1 in (a),(c); 0.2 m s−1 day−1 in (b),(d),(e); and 0.1 m s−1 day−1 in (f). Light and dark shading denote the 90% and 99% confidence levels for the wave drag, respectively; F has been divided by the background density ρo. The black arrows in the top left corner of each panel denote the magnitude of the plotted vector components. The flux F for synoptic waves is a factor of 2 smaller than for planetary waves; ΔF is a factor of 5 smaller than F.
Fig. 12.

Quasigeostrophic refractive index squared R2 for zonal wavenumber 0 for DJF (a) past and (b) future: a constant buoyancy frequency of 0.0173 s−1 is used. The refractive index squared has been multiplied by the square of the radius of the earth, and is dimensionless. Shading denotes regions of negative R2.
Fig. 13.

Differences (future minus past) in resolved wave drag and EP flux F for DJF for (a) stationary and (b) transient planetary waves. Contour intervals are 0.2 m s−1 day−1. Refer to Fig. 11 for details.
Fig. 14.

Zonal average zonal component of (top) orographic GWD and (bottom) zonal wind for DJF for (left) past and (right) difference (future minus past). Contour intervals for OGWD are 0.5 and 0.2 m s−1 day−1 and for zonal winds 5 and 2 m s−1, respectively. Light and dark shading denote the 90% and 99% confidence levels, respectively.
Fig. 15.

As in Fig. 10 but for SON.
Fig. 16.

Resolved wave drag and EP flux F for SH spring (SON) for (a) past and (b) difference (future minus past). (c),(d) Differences for stationary and transient planetary waves, respectively. Refer to Fig. 11 caption for details. Scale factors for the difference vectors are all the same.
Fig. 17.

(a) Resolved wave drag at 50 hPa (solid black) and residual vertical velocity (w*) at 70 hPa (gray) for SH summer (DJF). Dashed line denotes planetary wave drag. The residual vertical velocity w* has been area averaged between 60° and 90°S, wave drag between 40° and 80°S. (b) Height of the zero wind line computed from the December zonal-mean zonal wind profiles after area averaging between 50° and 90°S. Axis showing (left) pressure height and (right) corresponding log pressure height using a scale height of 7 km.
Fig. 18.

Downward control mass streamfunction for DJF at 70 hPa for (a) past and (b) difference (future minus past): combined resolved and parameterized wave drag (thick black); resolved wave drag (solid blue); parameterized orographic GWD (red); planetary wave drag (dotted–dashed); and synoptic wave drag (dotted). The thin black line denotes the direct streamfunction.
Fig. 19.

Seasonal mean net upward mass flux (Fmtr) at 70 hPa for (a) DJF; (b) JJA; (c) MAM; and (d) SON: direct calculation (black); downward control estimates using parameterized OGWD (red); resolved wave drag (blue); planetary wave drag (green); and synoptic wave drag (yellow). The mass flux is computed between the turnaround latitudes (refer to text for details).
Fig. 20.

Vertical profiles of annual mean net upward mass flux (Fmtr) for (a) past and (b) linear trend from 1960 to 2099: direct calculation (black); downward control estimates using parameterized orographic GWD (red); resolved wave drag (solid blue); planetary wave drag (blue, dashed–dotted); synoptic wave drag (blue dots); and total wave drag (black dots). Note the logarithmic scale for the mass flux. Trends are computed using least squares. The mass flux is computed between the turnaround latitudes (see text for details), which vary as a function of altitude.
Fig. 21.

Vertical profiles of linear trends of annual mean upward mass flux computed over fixed latitude ranges centered about the equator: ±36.0° (solid), ±30.5° (dotted), and ±24.9° (dashed–dotted) for (a) resolved wave drag and (b) parameterized orographic GWD computed using downward control. Note the logarithmic scale for the mass flux. Trends are computed from 1960 to 2099 using least squares.
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