1. Introduction
A recent observational study by Thompson and Solomon (2009) revealed that a decreasing temperature trend in the lower stratosphere during 1979–2006, except for the three years following the El Chichón and Mount Pinatubo eruptions, is strongly related to the global overturning circulation. Upwelling equatorward of 50° and downwelling in the polar regions are respectively enhancing and attenuating the ozone-induced cooling trend. This provides additional observational support for acceleration of the stratospheric mean meridional circulation, the so-called Brewer–Dobson (BD) circulation, in the warming atmosphere, as revealed in various recent climate change simulations (e.g., Butchart et al. 2006; Olsen et al. 2007; Fomichev et al. 2007; Li et al. 2008; Garcia and Randel 2008; McLandress and Shepherd 2009; Butchart et al. 2010).
Tropical upwelling, the upward branch of the BD circulation, is important in the stratospheric climate, as it influences the concentration of water vapor entering the stratosphere, which in turn affects radiation and chemistry in the middle atmosphere. Observational studies (e.g., Randel et al. 2003; Kerr-Munslow and Norton 2006) show a clear annual cycle in the tropical upwelling, with a maximum during the Northern Hemisphere (NH) winter and a minimum during the NH summer. It has been recognized that tropical upwelling, as a part of the BD circulation, is driven primarily by extratropical wave forcing due to dissipation of planetary and gravity waves (Holton et al. 1995), and its annual cycle could be related to the annual cycle of planetary-wave forcing. However, Plumb and Eluszkiewicz (1999) showed from their numerical simulations that the extratropical wave forcing is not sufficient to drive upwelling near the equator and that wave drag within 20° of the equator is required. They suggested that vertically propagating equatorial planetary and/or gravity waves may contribute to the angular momentum budget in the tropical region, analogous to the role played by viscosity in their model. Recently, there have been increasing numbers of observational (e.g., Kerr-Munslow and Norton 2006; Randel et al. 2008, hereafter RGW08) and numerical modeling [e.g., Norton 2006; Taguchi 2009 (hereafter T09), 2010; Ryu and Lee 2010] studies that have emphasized the role of the tropical and subtropical wave driving in the annual cycle of tropical upwelling.
Despite recent progress in our understanding of wave driving in the tropical upwelling, it is not clear yet which waves are involved in this process, where they dissipate, and how they interact with each other to drive tropical upwelling. One example that has been explored more recently is the role of gravity waves. Using a high-resolution (horizontal grid spacing of 0.56° and vertical grid spacing of about 300 m) general circulation model (GCM) that explicitly resolves small-scale waves including gravity waves, Miyazaki et al. (2010) showed that the Eliassen–Palm flux divergence (EPD) of the small-scale gravity waves induces mean equatorward flow in the extratropical tropopause region, which partially cancels the poleward flows induced by the planetary and synoptic waves, while it induces mean poleward flow in the subtropical lower stratosphere and mean downward flow in the midlatitude lower stratosphere. From chemistry–climate models that performed twenty-first century reference simulations—the Atmospheric Model with Transport and Chemistry (AMTRAC) by Li et al. (2008), Canadian Middle Atmosphere Model (CMAM) by McLandress and Shepherd (2009), Center for Climate System Research (CCSR)–National Institute for Environmental Studies (NIES) model by Okamoto et al. (2011), and 11 chemistry–climate models including three models by Butchart et al. (2010)—it is shown that the parameterized orographic gravity wave drag (GWD) can contribute to the long-term trend in the net upward mass flux at 70 hPa up to 40%–59% during the NH wintertime. These studies suggested that this rather significant contribution by orographic gravity wave drag is due to an enhanced and upward-shifted gravity wave drag under the stronger subtropical jets in the lower stratosphere as a consequence of climate change, which allows more planetary waves and gravity waves to propagate into the stratosphere.
So far, there have been no proper studies on the contribution of gravity waves generated by individual sources other than orography to the tropical upwelling. One candidate is the gravity waves generated by convective clouds, which can provide significant drag in the tropical lower stratosphere as shown in several GCMs with a convective gravity wave parameterization (e.g., Chun et al. 2004; Song et al. 2007; Jeon et al. 2010; Richter et al. 2010). Also, when the tropical upwelling is estimated by downward mass flux in the extratropical regions, as done by Li et al. (2008), McLandress and Shepherd (2009), and Butchart et al. (2010), gravity waves generated by fronts/jet streams (e.g., Charron and Manzini 2002; Richter et al. 2010) could be important. Because there is no proper observational dataset to derive momentum forcing induced by gravity waves generated by individual sources, using GCM results that include individual GWD parameterizations might be one feasible way. The gravity waves parameterized in GCMs represent subgrid-scale gravity waves with horizontal wavelengths smaller than a few hundred kilometers, and they are the ones that are missed mostly even in current high-resolution GCMs and that are most important for momentum budget in the mesosphere.
In the present study, we examine the annual cycle of tropical upwelling based on a 12-yr simulation of the Whole Atmosphere Community Climate Model (WACCM) including three GWD parameterizations (orographic, nonstationary background, and convective). Contributions of the resolved planetary waves and parameterized gravity waves generated by individual sources are presented. The impact of convective gravity waves, which could be important, especially in the tropical region, is also investigated by comparing results from an additional WACCM simulation without convective GWD parameterization.
2. Experimental design
The climate model used in this study is the WACCM version 1b (WACCM1b) developed at the National Center for Atmospheric Research (NCAR) (Sassi et al. 2002). The WACCM1b is a global spectral model with T63 horizontal resolution at 66 vertical levels from the surface to about 140 km. The model description and physical processes included in WACCM1b can be found in Song et al. (2007). The two 12-yr simulations with and without convective GWD parameterization are performed from an initial condition of 1 July 1978 using the climatological ozone (Wang et al. 1995) and sea surface temperature (SST) (Shea et al. 1992). The constant sea ice thickness is assigned when the SST is less than about −1.8°C (Collins et al. 2004). We refer to the simulations with and without convective GWD parameterization as the GWDC and CTL simulations, respectively. The GWDC and CTL simulations both include the orographic GWD parameterization by McFarlane (1987) and the background GWD parameterization that represents nonstationary gravity waves observable in the atmosphere based on Lindzen (1981). The convective GWD parameterization implemented in the GWDC simulation is the ray-based parameterization to represent the three-dimensional propagation of GWs proposed by Song and Chun (2008). A recent study by Choi et al. (2009) showed that the ray-based parameterization by Song and Chun (2008) represents the global temperature variances observed in Microwave Limb Sounder (MLS) on the Upper Atmosphere Research Satellite (UARS) better than the columnar parameterization by Song and Chun (2005). The model climatology for each simulation is made by averaging results over the last 10 yr after a spinup period of 2 yr. The results shown in section 3 are based on the GWDC simulation except in section 3b, where differences between the GWDC and CTL simulations will be presented.
3. Results
a. GWDC simulation
Figure 1 shows the annual cycle in 
Annual cycle in 
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
The gravity waves included in the present WACCM simulations are orographic GWD, background GWD, and convective GWD (hereafter OGWD, BGWD, and CGWD, respectively). The CGWD is included only in the GWDC simulation. Unlike the OGWD and CGWD, for which the momentum flux source spectrum is determined explicitly based on the linear gravity wave theory using topography (McFarlane 1987) and model-produced diabatic heating information (Song and Chun 2005), respectively, constant values depending only on latitude are assigned to the source spectrum of BGWD. In the BGWD scheme used in the present WACCM simulation, the source-level momentum flux is set to be large in the midlatitudes, so it represents primarily the gravity waves associated with the fronts/jet streams. Recently, Richter et al. (2010) showed that including a jet stream–related GWD parameterization from which gravity waves are launched at certain grids based on the frontogenesis function can replace BGWD and provide better results in WACCM simulations.
Figure 2 shows latitudinal distributions of annual average upwelling at 100 hPa estimated from (1) and (2) (Fig. 2a) and the annual cycle of the tropical upwelling averaged over 15°S and 15°N (Fig. 2b). Note that the estimate of 
(a) Latitudinal distribution of the annual means of 
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
Figure 3 shows latitude–height cross sections of (top) the zonal-mean zonal wind, and the EPD, BGWD, CGWD, and OGWD forcing terms during (middle) January and (bottom) July. The zonal-mean zonal wind shown in Fig. 3 exhibits the characteristic features of the zonal wind observed in solstice seasons such as the hemispheric difference in the strength of the polar night jets, zonal wind reversal near the mesopause level, and the cross-equatorial westerly flow from the winter mesosphere to the summer thermosphere. However, compared with Upper Atmosphere Research Satellite (UARS) Reference Atmosphere Project (URAP) (Swinbank and Ortland 2003), the zonal-mean zonal wind above z = 90 km in the present simulation is significantly small, as also shown in Song and Chun (2008). Although this discrepancy may induce unrealistic wave forcings in the upper mesosphere and lower thermosphere, this is unlikely to influence in the present upwelling calculation significantly, given that the wave forcing below z = 50 km is effective to the upwelling estimation at 100 hPa, as will be shown in Fig. 4. In EPD, negative forcing is dominant in the troposphere and most of the winter middle atmosphere. During January, the maximum negative forcing is −19 m s−1 day−1 near z = 60 km at 45°N and maximum positive forcing is 10 m s−1 day−1 in the NH polar stratopause. During July, their magnitudes increase to −21 and 12 m s−1 day−1, respectively, both at similar heights and latitudes in the Southern Hemisphere (SH). The magnitude of BGWD is largest among the four wave forcing terms, with maximum positive forcing during January of 127 m s−1 day−1 in the SH midlatitudes near z = 80 km and the maximum negative forcing during January of −60 m s−1 day−1 in the NH midlatitudes near z = 60 km. During July, the areas of negative and positive BGWD forcing are reversed in the different hemispheres, with a slightly less positive forcing maximum (124 m s−1 day−1) and significantly larger negative forcing maximum (−88 m s−1 day−1).
(top) Latitude–height cross sections of the zonal-mean zonal wind during (left) January and (right) July, and EPD, BGWD, CGWD, and OGWD forcing terms during (middle) January and (bottom) July. Contour interval of the zonal-mean zonal wind is 10 m s−1. Contours drawn in the forcing terms are 0.5, 1, 2, 5, 10, 20, 50, and 100 m s−1 day−1 and absolute values larger than 5 m s−1 day−1 are shaded. In all figures, negative values are dashed. The OGWD forcing is cut off at 30 hPa (z ≅ 24.5 km).
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
Latitude–height cross sections of the effective (a) EPD, (b) BGWD, (c) CGWD, and (d) OGWD forcing terms that are multiplied by ρ(z)/ρ(100 hPa) during (top) January and (bottom) July. The thick line in each plot is the height at which 90% of contribution is made in the vertical integration of (2). Contours are 0, 0.005, 0.01, 0.02, 0.05, 0.1, 0.2, and 0.5 m s−1 day−1, and negative values are dashed. Values less than −0.01 m s−1 day−1 are shaded in blue and those greater than 0.01 m s−1 day−1 are shaded in orange.
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
The CGWD forcing also shows clear seasonal variation, with negative forcing in the winter mesosphere subtropics and midlatitudes and positive forcing in the tropics and most of the summer hemisphere above z = 60 km. The maximum positive and negative forcing during January are 31 and −7.6 m s−1 day−1, respectively, while they are much larger during July at 41 and −49 m s−1 day−1, respectively. The stronger negative forcing during the SH midlatitude wintertime compared with the NH wintertime is due to the larger SH wintertime convective forcing and resultant cloud-top momentum flux in the storm-track region in which the main convective sources exist during the winter. The OGWD is restricted below 30 hPa (z ≅ 24.5 km) in the model, and its magnitude is much less than the other three forcing terms. As will be shown below, however, its contribution can be significant when the density is weighted to the forcing terms.
Note in (2) that the wave forcing contributes to the upwelling with a weighting of density. Therefore, the forcing terms shown in Fig. 3 are not the ones that directly contribute to the vertical integration. To understand the forcing that actually contributes to the upwelling calculation in (2) at 100 hPa, effective wave forcing multiplied by ρ(z)/ρ(100 hPa) is shown in Fig. 4. The negative (positive) values are dashed (solid) lines, while areas with values less (larger) than −0.01 m s−1 day−1 (0.01 m s−1 day−1) are shaded with blue (orange). The thick black solid lines denote the height at which a 90% contribution is made for each individual forcing term in the vertical integration of (2). The figure clearly shows that effective EPD forcing predominates, with mostly negative values except in the winter hemisphere polar region. To represent 90% of the upwelling at 100 hPa, vertical integration of EPD up to 50 km is required in the tropics and winter hemisphere midlatitudes, whereas vertical integration of EPD below 30 km is enough in the summer hemisphere. Among the three effective GWD forcing terms, effective OGWD forcing is largest in the winter hemisphere subtropics and midlatitudes below z = 25 km. The magnitudes of the effective BGWD and CGWD forcing terms are comparable, although effective BGWD forcing is distributed widely in latitude. For the effective BGWD and CGWD forcing terms, integration up to 70 km is required in most regions, except in the summer hemisphere midlatitudes where integration of CGWD forcing below 30 km is enough. This result implies that integration of the effective forcing in a sufficiently deep vertical layer is required to estimate balanced upwelling accurately, especially for nonorographic GWD forcing and even for the EPD forcing in the tropical region.
Figure 5 shows latitudinal distributions of 
Latitudinal distribution of 
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
Figure 6 shows the annual cycle of 
Annual cycle of 
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
Given that EPD forcing is the dominant component of tropical upwelling, we calculated 
As in Fig. 6, but for the annual cycle of 
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
In the present study, the contribution of meridional heat flux 
b. Impact of CGWD on tropical upwelling
To understand effects of convective gravity waves on tropical upwelling, results from GWDC and CTL simulations are compared. Figure 8 shows differences between the GWDC and CTL simulations in the annual cycle of 
Differences in (a) the annual cycle of 
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
Figure 9 shows the difference between the GWDC and CTL simulations for each of the forcing terms determining 
Differences in the annual cycle of 
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
c. Upwelling estimation from net upward mass flux
In the previous figures, upwelling averaged over 15°S and 15°N and seasonal contribution of each forcing terms in those latitudes are considered exclusively. This latitude band is selected because 
To take into account the contribution of each wave forcing term in a wider latitudinal band in which tropical upwelling actually occurs, we estimate the net upward mass flux between turnaround latitudes where tropical upwelling changes extratropical downwelling, from the mass streamfunctions obtained from the simulated residual mean meridional 
Figure 10a shows vertical profiles of annual-mean net upward mass flux calculated using the direct mass streamfunction and downward-control mass streamfunction contributed by individual forcing terms in the CGWD simulation. The annual cycles of the upward mass flux at 70 hPa contributed by the three GWD forcing terms are shown in Fig. 10b, and downward-control mass streamfunctions for December–February (DJF) at 70 hPa induced by each forcing terms are shown in Fig. 10c along with the direct mass streamfunction. The annual and seasonal means of the net upward mass fluxes at 70 hPa are shown in Fig. 10d as color bars with their values in Table 1.
+Net upward mass flux calculated from the direct mass streamfunction and from downward-control mass streamfunctions using the EPD and three GWD forcing terms in the CGWD simulation: (a) vertical profiles of the annual mean net upward mass flux, (b) the annual cycle of the net upward mass flux at 70 hPa from the three GWD forcing terms, (c) mass streamfunctions for DJF at 70 hPa, and (d) annual, DJF, and June–August (JJA) means of net upward mass flux at 70 hPa. The mass flux is computed between the turnaround latitudes (see text for details).
Citation: Journal of the Atmospheric Sciences 68, 11; 10.1175/JAS-D-11-022.1
The annual, DJF, and JJA means of net upward mass flux at 70 hPa (×109 kg s−1) from the direct mass streamfunction and from the downward-control mass streamfunctions using the EPD and three GWD forcing terms in the CGWD simulation. The mass flux is computed between the turnaround latitudes (see text for details). Definitions of the direct and downward-control mass streamfunctions and the net upward mass flux can be found in the appendix.
In Fig. 10a, net upward mass fluxes generally decrease with height except for those by CGWD and BGWD that increase below about 70 and about 50 hPa, respectively. Among the three GWD forcings, contribution by OGWD is largest during January, February, March, and November, while that by CGWD is largest during the rest of months except December, where contribution by BGWD is largest (Fig. 10b). Compared with 11 chemistry–climate model results reported by Butchart et al. (2010, see their Fig. 11), the upward mass flux by OGWD in the present study is much less, especially during DJF. One possible reason for relatively small contribution by OGWD in the present study, especially for DJF, is that the turnaround latitude in the NH side of the direct mass streamfunction (26°N), which is used for mass flux calculation, is located equatorward of that of downward-control mass streamfunction induced by the OGWD forcing (37°N) (Fig. 10c). Consequently, downwelling by the OGWD forcing between 26° and 37°N cancels the upwelling poleward of 37°N by the OGWD forcing. Compared with McLandress and Shepherd (2009), the turnaround latitude in the NH side in the present DJF mean shifts somewhat equatorward (30°N vs 26°N). When we calculate net upward mass flux using the turnaround latitudes derived from the downward-control mass streamfunction including all forcing terms (EPD+GWDs), which is 29°N during DJF (Fig. 10c), the mass flux by OGWD during DJF becomes almost twice as large as the present result (0.61 vs 0.33 × 109 kg s−1). This implies that small changes in turnaround latitudes are likely to make significant differences in the mass flux calculation.
Contributions by the EPD, OGWD, CGWD, and BGWD forcings to upward mass flux are 81%, 9%, 7%, and 3%, respectively, in the annual mean (Fig. 10d). The contribution by CGWD, which could not be considered in the previous studies, is comparable to that by OGWD. This implies that CGWD can contribute to tropical upwelling significantly, as much as by OGWD, and proper treatment of convective gravity waves in GCMs through CGWD parameterization may be required for realistic climate and climate change simulations. Compared with previous studies based on chemistry–climate models (e.g., Butchart et al. 2010), the relative contribution by the present EPD (OGWD) forcing is generally larger (smaller). Considering that the present results are based on a 10-yr annual simulation using climatological boundary conditions without chemical processes, it is not straightforward to directly compare the present results with those from the previous chemistry–climate modeling for more than 100 yr.
4. Summary and conclusions
Seasonal variations of tropical stratospheric upwelling are investigated from the results of the 10-yr WACCM simulations including mountain, convection, and background GWD parameterizations. The tropical upwelling is estimated by the residual mean vertical velocity 
A clear annual cycle of tropical upwelling is found, with a maximum during the NH wintertime and a minimum during the NH summertime, and it is determined primarily by the EPD contribution along with the secondary contribution from dU/dt. Among the four components consisting of EPD, contribution by the horizontal momentum flux (EPD-Y1) is dominant, while smaller contributions from vertical momentum flux (EPD-Z2) and meridional heat flux (EPD-Z1) are similar to each other. Compared with some previous studies, however, the contribution from EPD-Y1 is relatively small while that of EPD-Z1 is larger in the present study, likely due to using deeper vertical integration of forcing terms in calculating upwelling in the present study. Gravity waves mostly increase tropical upwelling throughout the year, and among the three sources the contribution of convective gravity waves is largest, especially during NH springtime. However, the total contribution of all three gravity waves to tropical upwelling is not larger than 5%. When upwelling is extended to the subtropics (25°S–25°N), the relative contribution from all three gravity wave forcings is larger than 10% during the NH wintertime, mainly due to the increase from OGWD.
To investigate effects of convective gravity waves, an additional WACCM simulation without CGWD parameterization (CTL simulation) is conducted, and differences between the GWDC and CTL simulations are examined for each wave contribution as well as the annual cycle of upwelling. The analysis shows that including CGWD parameterization increases tropical upwelling during most months by about 5%, which is larger than the single contribution by CGWD. The increase of tropical upwelling caused by including CGWD is due not only to the direct CGWD forcing but also to the changes in EPD and dU/dt forcing terms that are modulated by including CGWD parameterization.
In the present study, upwelling averaged over 15°S and 15°N at 100 hPa and seasonal contribution of each forcing terms in those latitudes are considered mostly. To take into account the contribution of each wave forcing terms in a wider latitudinal band in which upwelling actually occurs, we also estimate net upward mass flux between turnaround latitudes where tropical upwelling changes extratropical downwelling. It shows that contributions by the EPD, OGWD, CGWD, and BGWD forcings to the annual mean of the net upward mass flux at 70 hPa are 81%, 9%, 7%, and 3%, respectively. The relative contribution by the OGWD forcing in the present study is much less, especially during DJF, while that by the EPD forcing is much larger than the previous studies based on chemistry–climate models. The contribution by CGWD, which was not considered in the previous studies, is comparable to that by the OGWD forcing, implying that proper treatment of convective gravity waves in GCMs through CGWD parameterization may be required for realistic estimation of BD circulation and its trend associated with climate change.
Acknowledgments
The authors thank two anonymous reviewers for their careful reading of the manuscript and helpful comments. This study was partially conducted while the first author was visiting the Jet Propulsion Laboratory of the California Institute of Technology during her sabbatical leave. This work was funded by the Korean Meteorological Administration Research and Development Program under Grant RACS_2010-2008. The authors would like to acknowledge the support from KISTI Supercomputing Center (KSC-2009-S03-0004).
APPENDIX
Derivation of the Net Upward Mass Flux
REFERENCES
Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. Academic Press, 489 pp.
Butchart, N., and Coauthors, 2006: Simulations of anthropogenic change in the strength of the Brewer–Dobson circulation. Climate Dyn., 27, 727–741.
Butchart, N., and Coauthors, 2010: Chemistry–climate model simulations of twenty-first century stratospheric climate and circulation changes. J. Climate, 23, 5349–5374.
Charron, M., and E. Manzini, 2002: Gravity waves from fronts: Parameterization and middle atmosphere response in a general circulation model. J. Atmos. Sci., 59, 923–941.
Choi, H.-J., H.-Y. Chun, and I.-S. Song, 2009: Gravity wave temperature variance calculated using the ray-based spectral parameterization of convective gravity waves and its comparison with Microwave Limb Sounder observations. J. Geophys. Res., 114, D08111, doi:10.1029/2008JD011330.
Chun, H.-Y., I.-S. Song, J.-J. Baik, and Y.-J. Kim, 2004: Impact of a convectively forced gravity wave drag parameterization in NCAR CCM3. J. Climate, 18, 3530–3547.
Collins, W. D., and Coauthors, 2004: Description of the NCAR Community Atmosphere Model (CAM 3.0). NCAR Tech. Note NCAR/TN-464+STR, 214 pp.
Fomichev, V. I., A. I. Jonsson, J. de Grandpré, S. R. Beagley, C. McLandress, K. Semeniuk, and T. G. Shepherd, 2007: Response of the middle atmosphere to CO2 doubling: Results from the Canadian Middle Atmosphere Model. J. Climate, 20, 1121–1144.
Garcia, R. R., and W. J. Randel, 2008: Acceleration of the Brewer–Dobson circulation due to increases in greenhouse gases. J. Atmos. Sci., 65, 2731–2739.
Haynes, P., M. McIntyre, T. Shepherd, C. Marks, and K. Shine, 1991: On the “downward control” of extratropical diabatic circulations by eddy-induced mean zonal forces. J. Atmos. Sci., 48, 651–678.
Holton, J. R., 1990: On the global exchange of mass between the stratosphere and troposphere. J. Atmos. Sci., 47, 392–395.
Holton, J. R., P. Haynes, M. McIntyre, A. Douglass, R. Rood, and L. Pfister, 1995: Stratosphere–troposphere exchange. Rev. Geophys., 33, 403–439.
Jeon, J.-H., S.-Y. Hong, H.-Y. Chun, and I.-S. Song, 2010: Test of a convectively forced gravity wave drag parameterization in a general circulation model. Asia-Pac. J. Atmos. Sci., 46, 1–10.
Kerr-Munslow, A. M., and W. A. Norton, 2006: Tropical wave driving of the annual cycle in tropical tropopause temperature. Part I: ECMWF analyses. J. Atmos. Sci., 63, 1410–1419.
Li, F., J. Austin, and J. Wilson, 2008: The strength of the Brewer–Dobson circulation in a changing climate: Coupled chemistry–climate model simulations. J. Climate, 21, 40–57.
Lindzen, R. S., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86, 9707–9714.
McFarlane, N. A., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44, 1775–1800.
McLandress, C., and T. G. Shepherd, 2009: Simulated anthropogenic changes in the Brewer–Dobson circulation, including its extension to high latitudes. J. Climate, 22, 1516–1540.
Miyazaki, K., K. Sato, S. Watanabe, Y. Tomikawa, Y. Kawatani, and M. Takahashi, 2010: Transport and mixing in the extratropical tropopause region in a high-vertical-resolution GCM. Part II: Relative importance of large-scale and small-scale dynamics. J. Atmos. Sci., 67, 1315–1336.
Norton, W. A., 2006: Tropical wave driving of the annual cycle in tropical tropopause temperature. Part II: Model results. J. Atmos. Sci., 63, 1420–1431.
Okamoto, K., K. Sato, and H. Akiyoshi, 2011: A study on the formation and trend of the Brewer–Dobson circulation. J. Geophys. Res., 116, D10117, doi:10.1029/2010JD014953.
Olsen, M. A., M. R. Schoeberl, and J. E. Nielsen, 2007: Response of stratospheric circulation and stratosphere–troposphere exchange to changing sea surface temperature. J. Geophys. Res., 112, D16104, doi:10.1029/2006JD008012.
Plumb, R. A., and J. Eluszkiewicz, 1999: The Brewer–Dobson circulation: Dynamics of the tropical upwelling. J. Atmos. Sci., 56, 868–890.
Randel, W. J., F. Wu, and W. R. Rios, 2003: Thermal variability of the tropical tropopause region derived from GPS/MET observations. J. Geophys. Res., 108, 4024, doi:10.1029/2002JD002595.
Randel, W. J., R. R. Garcia, and F. Wu, 2008: Dynamical balances and tropical stratospheric upwelling. J. Atmos. Sci., 65, 3584–3595.
Richter, J. H., F. Sassi, and R. R. Garcia, 2010: Toward a physically based gravity wave source parameterization in a general circulation model. J. Atmos. Sci., 67, 136–156.
Ryu, J.-H., and S. Lee, 2010: Effect of tropical waves on the tropical tropopause transition layer upwelling. J. Atmos. Sci., 67, 3130–3148.
Sassi, F., R. R. Garcia, B. A. Boville, and H. Liu, 2002: On temperature inversions and the mesospheric surf zone. J. Geophys. Res., 107, 4380, doi:10.1029/2001JD001525.
Shea, D. J., K. E. Trenberth, and R. W. Reynolds, 1992: A global monthly sea surface temperature climatology. J. Climate, 5, 987–1001.
Song, I.-S., and H.-Y. Chun, 2005: Momentum flux spectrum of convectively forced internal gravity waves and its application to gravity wave drag parameterization. Part I: Theory. J. Atmos. Sci., 62, 107–124.
Song, I.-S., and H.-Y. Chun, 2008: A Lagrangian spectral parameterization of gravity wave drag induced by cumulus convection. J. Atmos. Sci., 65, 1204–1224.
Song, I.-S., H.-Y. Chun, R. R. Garcia, and B. Boville, 2007: Momentum flux spectrum of convectively forced internal gravity waves and its application to gravity wave drag parameterization. Part II: Impacts in a GCM (WACCM). J. Atmos. Sci., 64, 2286–2308.
Swinbank, R., and D. A. Ortland, 2003: Compilation of wind data for the Upper Atmosphere Research Satellite (UARS) Reference Atmosphere Project. J. Geophys. Res., 108, 4615, doi:10.1029/2002JD003135.
Taguchi, M., 2009: Wave driving in the tropical lower stratosphere as simulated by WACCM. Part I: Annual cycle. J. Atmos. Sci., 66, 2029–2043.
Taguchi, M., 2010: Wave driving in the tropical lower stratosphere as simulated by WACCM. Part II: ENSO-induced changes in northern winter. J. Atmos. Sci., 67, 543–555.
Thompson, D. W. J., and S. Solomon, 2009: Understanding recent stratospheric climate change. J. Climate, 22, 1934–1943.
Wang, W.-C., X. Liang, M. P. Dudek, D. Pollard, and S. L. Thompson, 1995: Atmospheric ozone as a climate gas. Atmos. Res., 37, 247–256.
