Abstract

This study explores the climatological annual cycle of temperature, circulation, and wave driving distributions in the tropical lower stratosphere as produced in a 50-yr simulation of the Whole Atmosphere Community Climate Model (WACCM). The simulation is forced with a climatological sea surface temperature and sea ice condition. The present diagnoses verify the primary balances of the annual cycle in this region, consistent with lower temperatures, stronger residual circulation (upwelling and local meridional outflow), and nearby stronger wave driving for Northern Hemisphere (NH) winter. An in-detail analysis on the wave driving further reveals that the stronger driving, occurring mostly in the northern tropics and subtropics, is contributed by northward and upward propagation (associated with meridional and vertical fluxes of zonal momentum, respectively) of equatorial Rossby waves forced by convective heating, and also by equatorward propagation of NH extratropical planetary and synoptic waves. The results are used to discuss implications about possible factors that may affect the different observations of the wave driving. The present framework and results will be extended to investigate ENSO-induced changes in this region during NH winter in a forthcoming paper.

1. Introduction

The thermal structure near the tropical tropopause is vital to the stratospheric climate; for example, it controls stratospheric humidity to a high degree over various time scales that affect stratospheric radiation and chemistry (Kley et al. 2000; SPARC 2000). This study focuses on the climatological annual cycle of temperature, circulation, and wave-driving distributions in the tropical lower stratosphere as simulated by Whole Atmosphere Community Climate Model (WACCM), whereas we will investigate El Niño–Southern Oscillation (ENSO)-induced changes during Northern Hemisphere (NH) winter in a future paper (Taguchi 2009, manuscript submitted to J. Atmos. Sci., hereafter TAG).

It is well known that temperatures in the tropical lower stratosphere exhibit a notable annual cycle: the region is coldest during NH winter and warmest during Southern Hemisphere (SH) winter (Yulaeva et al. 1994; Holton et al. 1995). The observed annual cycle in tropical temperatures is strongly coupled to the annual cycle in stratospheric water vapor (Mote et al. 1996). It has been long held that the annual cycle in temperatures in the tropical lower stratosphere arises from the so-called “extratropical stratospheric pump” mechanism (Holton et al. 1995). The zonal body force due to dissipating planetary and gravity waves drives the mean meridional (Brewer–Dobson) circulation in which air is drawn upward from the tropical troposphere and then poleward, especially in the winter hemisphere. Because the planetary wave drag, playing a dominant role in the stratosphere, is much stronger in the NH winter stratosphere than in the SH counterpart, it drives stronger upwelling and hence leads to lower temperatures in the tropical lower stratosphere during NH winter. Plumb (2002) noted that the effects of synoptic-scale tropospheric disturbances, present throughout the year, are probably responsible for inducing the strong two-cell circulation in the lower stratosphere and upper troposphere.

There have been also a few indications, however, that the influence of the extratropical planetary wave drag would be limited to the extratropics on the annual time scale (e.g., Shepherd 2002). Plumb and Eluszkiewicz (1999) found in their numerical experiments that the extratropical wave drag alone is unable to produce tropical upwelling as observed, whereas the equatorward edge of the drag is required to be unrealistically close to the equator for realistic tropical upwelling.

Recently, Kerr-Munslow and Norton (2006) performed a diagnosis of the heat budget near the tropical tropopause with the 15-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-15) data to suggest that the annual cycle in tropical tropopause temperatures is driven by the seasonal contrast of equatorial Rossby waves, with the vertical flux of the zonal momentum playing a large role. Here, “equatorial Rossby waves” means stationary large-scale waves in low latitudes, especially over Indonesia for NH winter and India for NH summer (part of the Asia monsoon), that are forced by convective heating in the troposphere and are prevalent in monthly and seasonal means (e.g., Newell et al. 1972; Gill 1980; Highwood and Hoskins 1998). The suggestion is further supported in simple numerical experiments in which localized distributions of tropical convective heating are applied to a primitive equation model (Norton 2006). The experiments demonstrated that the tropical tropopause is colder in an experiment for a NH winter-like situation when the convective heating placed on the equator forces equatorial Rossby waves in the deep tropics, thus inducing stronger equatorial upwelling. When the heating is placed off the equator at 15°N to mimic a NH summerlike condition, the response is characterized by a dominant monsoon pattern in the subtropics.

In contrast, a further observational analysis by Randel et al. (2008) using the National Centers of Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) and 40-yr ECMWF Re-Analysis (ERA-40) data stresses the importance of the meridional flux of the zonal momentum of extratropical waves (synoptic waves and, in the NH, planetary waves) and also equatorial waves in subtropical wave driving, without supporting the role of the vertical momentum flux. Boehm and Lee (2003) also claim that equatorial Rossby waves play an important role through the meridional momentum flux in driving the upwelling of the Brewer–Dobson circulation near the tropical tropopause.

The purpose of this study is to explore the thermodynamics and dynamics (especially wave driving) of the climatological annual cycle in the tropical lower stratosphere as simulated by WACCM. This study takes a different approach of utilizing a 50-yr simulation of WACCM, one of stratosphere-resolving general circulation models (GCMs), for a re-examination of the tropical and subtropical wave driving, with the observed discrepancy kept in mind (Kerr-Munslow and Norton 2006; Randel et al. 2008) as stated above. Our analysis of the WACCM simulation benefits from temporal/spatial homogeneity and physical consistency of the data, whereas observational analyses may suffer some data uncertainties. The WACCM simulation is also advantageous in that it is forced with climatological conditions and hence can provide a robust picture of the annual cycle, whereas observational results on the annual cycle may be affected by interannual variability. Furthermore, the good representation of the stratosphere in WACCM contributes to reliability of our results. The present GCM-based approach is also useful for our better understanding of this vital region, as we discuss implications of the results in comparison to some existing studies. Such a re-examination of the annual cycle, also serving as a model evaluation, is indispensable before we proceed to study ENSO-induced changes in the tropical stratosphere during NH winter using perpetual WACCM experiments in a future paper (TAG).

The rest of this paper is organized as follows: Section 2 briefly describes the WACCM simulation as well as the analysis framework used in this study. Section 3 presents the diagnostic results on the climatological annual cycle in the simulation, including details of wave driving. Finally, section 4 provides a summary and discussion.

2. Simulation and analysis framework

a. Simulation

This study diagnoses the climatological annual cycle, especially in the tropical lower stratosphere simulated by WACCM (version 1b). WACCM is a version of the NCAR Community Climate Model (CCM) that is extended to include the middle and upper atmosphere up to about 140 km altitude. The details of the model are documented in Sassi et al. (2002). The horizontal resolution is T63 (model output on 2.8° × 2.8° grids), which can reasonably simulate synoptic and planetary scales. Small-scale waves, which are not resolved in the model, may have a substantial role in the tropics, as suggested, for example, for the quasi-biennial oscillation (QBO; Baldwin et al. 2001). The model has 66 vertical levels, corresponding to grid spacing dz ∼ 1.2 km in the upper troposphere and lower stratosphere. The QBO in the tropical stratosphere is not simulated or included in the run used here.

The present analysis on the mean annual cycle makes use of a 55-yr simulation forced with a climatological sea surface temperature and sea ice distribution that correspond to the climatology of observed distributions from 1950 to 1999 (cf. the NCEP Reynolds dataset at http://podaac.jpl.nasa.gov/PRODUCTS/p118.html). The first 5 yr are discarded as an initial spinup period, leaving 50 yr for the analysis. The 50-yr dataset is useful for the present analysis on the annual cycle in the tropical lower stratosphere, where interannual variability is not large in the absence of the QBO.

b. Analysis framework

Our diagnosis is based on the transformed Eulerian mean (TEM) equations on log-pressure coordinates (Andrews et al. 1987) as follows:

 
formula
 
formula
 
formula

where

 
formula

Here, our notations follow the conventions used in Andrews et al. (1987), except that square brackets denote the zonal mean and asterisks denote wave components (departure from the zonal mean). The residual meridional and vertical winds are expressed as [υ] and [w], respectively.

The wave driving, (ρ0a cos ϕ)−1∇ · F, is represented with the aid of divergence of the Eliassen–Palm (EP) flux F = (Fy, Fz) as given below:

 
formula
 
formula
 
formula

It is useful to further decompose each component of Fy and Fz into two terms as Fy = Fy1 + Fy2 and FzFz1 + Fz2, where

 
formula

and

 
formula

Note that Fy1 and Fz1 are assigned to the first terms in Eqs. (4a) and (4b) that are dominant under the quasigeostrophic scaling. Using these decompositions, the wave driving is symbolically expressed as the sum of the contributions from the four terms ∂Fy1/∂y + ∂Fy2/∂y + ∂Fz1/∂z + ∂Fz2/∂z.

3. Results

a. General aspects

We first examine general aspects of the global stratosphere and troposphere simulated in the WACCM run (Fig. 1) compared to observations (e.g., Randel and Newman 1998). The simulation reproduces the familiar features of the zonal mean states (Figs. 1a–f) in the middle and upper stratosphere generally well, such as the polar night jet and Brewer–Dobson circulation. Model biases are notable in the NH (e.g., the polar winter stratosphere is too cold and the polar night jet is too strong), whereas such biases are relatively unclear in the SH. The interhemispheric differences are nonetheless reproduced, with the higher polar temperatures, the weaker polar night jet, and the stronger Brewer–Dobson circulation in the NH during its winter. These differences are associated with the stronger planetary wave forcing in the winter NH (Figs. 1g,h).

Fig. 1.

Climatological states in the WACCM simulation for (left) January and (right) July: (a),(b) zonal mean temperature [T] (K), (c),(d) zonal mean zonal wind [U] (m s−1), (e),(f) residual circulation [υ] and [w], and (g),(h) EP flux Fy and Fz. Contours in (e) and (f) show [υ] drawn at 0, ±0.1, ±0.25, ±0.5, and ±1 m s−1. The EP flux vectors are weighted by 1/p. The wave driving is contoured in (g) and (h) at 0, ±0.5, ±1, and ±2 m s−1 day−1.

Fig. 1.

Climatological states in the WACCM simulation for (left) January and (right) July: (a),(b) zonal mean temperature [T] (K), (c),(d) zonal mean zonal wind [U] (m s−1), (e),(f) residual circulation [υ] and [w], and (g),(h) EP flux Fy and Fz. Contours in (e) and (f) show [υ] drawn at 0, ±0.1, ±0.25, ±0.5, and ±1 m s−1. The EP flux vectors are weighted by 1/p. The wave driving is contoured in (g) and (h) at 0, ±0.5, ±1, and ±2 m s−1 day−1.

Some broad features of the residual circulation and wave driving are noticeable in the lower stratosphere and upper troposphere of low latitudes. The residual circulation in this region is characterized by the two-cell patterns, with the prevalent cross-equatorial meridional flow to the winter subtropics and upwelling in the summer hemisphere flank of the equator, whereas the wave driving exhibits multipolar patterns for both seasons. The circulation and wave driving in the lower stratosphere and upper troposphere of the tropics and subtropics are our focus and will be examined in detail. Hitchman and Huesmann (2007) present observed wave-driving distributions for the global troposphere and stratosphere and point out dynamical origins of the driving from both equatorial and extratropical waves (see also Edmon et al. 1980).

The annual cycle of tropical tropopause temperatures (averaged between 30°S and 30°N near 100 hPa) is also reproduced in the WACCM simulation notably well, including the minima during NH winter and the maxima during SH winter (Fig. 2), compared to the ERA-40 reanalysis data (Simmons and Gibson 2000). The degree to which the WACCM run simulates the annual cycle is beyond or near the best results in the GCM intercomparison project of Pawson et al. (2000). Some model biases are also noticeable; for instance, it is interesting to note that the WACCM simulation delays the maximum temperatures by 1 month. In NH autumn to winter, the decline of model temperatures is smaller and slower, leading to higher temperatures in January and February. The annual cycle in the tropical tropopause temperatures is related to the heat budget in this region examined in section 3b. Interannual variations are much smaller in the simulation, which are mainly due to the absence of the QBO and also volcanic effects from the model. The temperature annual cycle in the simulation is centered in the equatorial lower stratosphere (approximately 70–80 hPa), also in good agreement with the reanalysis results (Fig. 1 of Kerr-Munslow and Norton 2006).

Fig. 2.

Time series of zonal and monthly mean temperature [T] (K) near the tropical tropopause level: 50-yr WACCM simulation (solid) and ERA-40 data (dotted) from January 1958 to December 2001. The ERA-40 climatology is also drawn with a thick dotted line. A latitudinal average between 30°S and 30°N is taken at 101 hPa for the WACCM data and at 100 hPa for the ERA-40 data.

Fig. 2.

Time series of zonal and monthly mean temperature [T] (K) near the tropical tropopause level: 50-yr WACCM simulation (solid) and ERA-40 data (dotted) from January 1958 to December 2001. The ERA-40 climatology is also drawn with a thick dotted line. A latitudinal average between 30°S and 30°N is taken at 101 hPa for the WACCM data and at 100 hPa for the ERA-40 data.

b. Heat and momentum budget diagnoses

Given the reasonable simulation of the annual cycle of tropical tropopause temperatures, in this section we seek to diagnose how it arises. It turns out that our model results basically accord with Kerr-Munslow and Norton (2006) in this respect as introduced in section 1. Figure 3 displays all terms of Eq. (2) averaged between 10°S and 10°N in the lower stratosphere (86 hPa) as a function of the annual cycle. The tropical latitudinal band in the lower stratosphere is chosen where the temperature annual cycle is large. The radiative heating [Q] and vertical advection −[w][θ]z make the largest contributions and oppose each other, with the advection term somewhat preceding. The [θ] tendency roughly follows the change in the vertical advection. Using a highly simplified model, Kerr-Munslow and Norton (2006) show that the annual cycle in tropical tropopause temperatures is driven by the change in the adiabatic cooling or tropical upwelling. It is also noted here that the change in the vertical advection term can be well reproduced when [θ]z is replaced by its annual mean (not displayed). This underlines the importance of the upwelling in the annual cycle of the vertical advection term. Some differences of the modeled annual changes (such as [θ]t, −[w][θ]z, and [Q]) in the magnitude and timing of local extrema are suggested from a close comparison of Fig. 3 to its observational counterpart (i.e., Fig. 3 of Kerr-Munslow and Norton 2006).

Fig. 3.

Terms of the TEM thermodynamic Eq. (2) as a function of the annual cycle at 86 hPa averaged between 10°S and 10°N: [θ] tendency (thin solid), meridional advection (thin dotted), vertical advection (thick dotted), radiative heating (thick solid), and residual eddy flux term (dotted–dashed).

Fig. 3.

Terms of the TEM thermodynamic Eq. (2) as a function of the annual cycle at 86 hPa averaged between 10°S and 10°N: [θ] tendency (thin solid), meridional advection (thin dotted), vertical advection (thick dotted), radiative heating (thick solid), and residual eddy flux term (dotted–dashed).

The annual cycle in the equatorial upwelling reflects a seasonal change in latitudinal distributions of the vertical wind (Fig. 4a). In NH winter (December to March), the upwelling clearly exhibits maxima in the SH (summer hemisphere) flank of the equator (between 5°S and 10°S), with values near 0.4 mm s−1 at the equator. In SH winter (June to August), the maxima are located more poleward in NH (near 15°N or higher latitudes) and are smaller in magnitude. The upwelling over the equator is thus larger in NH winter than in SH winter, consistent with the annual cycle in the adiabatic cooling (Fig. 3). The model picture of the tropical upwelling well agrees with observations (e.g., Plumb and Eluszkiewicz 1999; Randel et al. 2008).

Fig. 4.

Time–latitude sections of the residual circulation at 86 hPa: (a) [w] (mm s−1) and (b) [υ] (m s−1).

Fig. 4.

Time–latitude sections of the residual circulation at 86 hPa: (a) [w] (mm s−1) and (b) [υ] (m s−1).

The equatorial upwelling can be related to meridional outflow from the tropics through the TEM continuity Eq. (3). Some mathematical manipulations yield

 
formula

where

 
formula

and the upper boundary condition of [w] = 0 at z = ∞ is used. Equation (5) states that the vertical wind averaged between −ϕL and +ϕL is proportional to vertical integral of meridional wind difference between the latitudes from level z to the top of the atmosphere. Note that 〈[w]〉 is close to latitudinally averaged [w] when the latitudinal integrations are taken near the equator because ϕL = 10° is used below. An examination of the integrand in the rhs of Eq. (5) verifies a primary balance of the annual cycle in the tropical upwelling at 86 hPa (Figs. 3 and 4a) with that in the outflow from the tropics at and just above the level (not displayed).

The annual cycle in the outflow from the tropics, [υ](10°N) − [υ](10°S), at 86 hPa is also noticeable in a time–latitude section of the meridional wind at the level (Fig. 4b; see also Figs. 1e,f). The poleward flow at 10°N is much stronger for NH winter (especially December to February) than for NH summer. On the other hand, [υ] at 10°S is relatively time invariant, although it is somewhat stronger for SH winter. Thus, the stronger poleward flow at 10°N in NH winter largely contributes to the stronger outflow from the tropics and hence the stronger tropical upwelling for the season.

The meridional wind is then related to wave driving through the TEM zonal momentum Eq. (1). Rearranging Eq. (1) as

 
formula

this equation enables us to examine which term largely balances with the meridional wind of interest. Figure 5a displays all terms in Eq. (6) subtracted between the NH and SH flanks of the equator (NH minus SH) in the lower stratosphere. To extract representative features in the tropical lower stratosphere, latitudinal and vertical averagings (5°–15° in each hemisphere and 50–100 hPa) are applied to each term in Eq. (6). The vertical averaging roughly corresponds to the case in which the equatorial upwelling at 86 hPa balances well with the outflow averaged vertically in the lower stratosphere. The wave-driving term is calculated by using resolved wave fields in the model output, whereas the [X] term is calculated as a residual of all other terms. A clear feature is that the annual cycle in the outflow from the tropics (thick solid line) is largely in balance with that in the wave driving (thick dashed line). The primary balance between the outflow and wave driving holds when values at the grid points of 10°N and 10°S at 86 hPa are used (Fig. 5b). This ensures that the balance is a robust feature in the tropical lower stratosphere.

Fig. 5.

Contributions to [υ] (m s−1) in the TEM zonal momentum Eq. (6) as a function of the annual cycle: [υ] (thick solid), zonal wind tendency (thin solid), vertical advection (thin dotted), wave driving (thick dotted), and residual (dotted–dashed): (a) NH minus SH differences, each averaged over 5°–15° and 50–100 hPa and (b) differences taken between 10°N and 10°S at 86 hPa.

Fig. 5.

Contributions to [υ] (m s−1) in the TEM zonal momentum Eq. (6) as a function of the annual cycle: [υ] (thick solid), zonal wind tendency (thin solid), vertical advection (thin dotted), wave driving (thick dotted), and residual (dotted–dashed): (a) NH minus SH differences, each averaged over 5°–15° and 50–100 hPa and (b) differences taken between 10°N and 10°S at 86 hPa.

The residual [X] (dotted–dashed line in Fig. 5) is much smaller in magnitude than the two dominant terms but is comparable to the tendency and vertical advection terms. This residual will be related to parameterized gravity wave drag (which is not archived) and also other factors, including errors in the present calculations. Randel et al. (2008) compared 100-hPa [w] derived from the WACCM3 simulation output with momentum balance estimates to suggest the importance of the gravity wave drag in the residual circulation, especially near the top of the subtropical jets. Here it is emphasized, however, that the primary balance between the outflow and wave driving (by resolved waves) is a robust result in our diagnosis of the momentum equation.

It is also possible to relate the residual circulation [υ] (and [w]) to the wave driving by solving a differential equation for [υ] [such as Eq. (3.5.8) in Andrews et al. 1987] with the wave driving, diabatic heating, and friction imposed. One should be careful, however, about how to give the diabatic heating in solving such an equation because the term depends on temperature or on a part of the solution. Some difficulty will also remain in determining which region of the wave driving and/or diabatic heating is important for the residual circulation of interest because the response [υ] to the forcings is nonlocal on account of the elliptic operator for [υ]. Note that our diagnostic results, in which Eqs. (2) and (6) are used to show the primary balances between the adiabatic cooling and radiative heating and between the meridional outflow and wave driving, are consistent with the elliptic differential equation for [υ]. Another way to examine the relationship between the residual circulation and wave driving is to use momentum balance estimates, which is a generalization of the downward control (Haynes et al. 1991), as done in Randel et al. (2002 and 2008). The present use of Eqs. (5) and (6) is useful enough to make the point that the annual cycle in [υ] and [w] in the tropical lower stratosphere largely balances with that in the nearby wave driving.

c. Wave driving

Having shown that the annual cycle in the wave driving plays a key role in the tropical lower stratosphere, we now explore the wave driving in detail. Figure 6a plots the total wave driving summed at the NH and SH tropics in the lower stratosphere (each averaged over 5°–15°, 50–100 hPa and then summed for both hemispheres) as a function of the annual cycle, together with its decomposition into contributions from the four terms. Note that negative wave driving, corresponding to EP flux convergence, at either NH and SH flank of the equator leads to poleward flow there [Eq. (6)]. The annual cycle of the total wave driving (solid line), with larger (more negative) values in NH winter (November to January) and smaller (less negative) values in SH winter (July to September), is consistent with the result in the momentum budget (Fig. 5).

Fig. 6.

Wave driving (m s−1 day−1) as a function of the annual cycle summed from the NH and SH tropical stratosphere for (a) averages at 5°–15° and 50–100 hPa and (b) values at 10°N and 10°S at 86 hPa. Solid line shows the total. Contributions from the four terms are also plotted: thick dotted for ∂Fy1/∂y, thin dotted for ∂Fy2/∂y, thick dashed for ∂Fz1/∂z, and thin dashed for ∂Fz2/∂z. Shadings denote the months of August and December.

Fig. 6.

Wave driving (m s−1 day−1) as a function of the annual cycle summed from the NH and SH tropical stratosphere for (a) averages at 5°–15° and 50–100 hPa and (b) values at 10°N and 10°S at 86 hPa. Solid line shows the total. Contributions from the four terms are also plotted: thick dotted for ∂Fy1/∂y, thin dotted for ∂Fy2/∂y, thick dashed for ∂Fz1/∂z, and thin dashed for ∂Fz2/∂z. Shadings denote the months of August and December.

The difference of the total wave driving between December and August is −0.58 m s−1 day−1 summed for both hemispheres (see Fig. 6a). The four terms [Eq. (4)] make different contributions to the total December–August difference, as summarized in Fig. 7 (left set): it is ∂Fy1/∂y and ∂Fz2/∂z that make the largest contributions (32.5 and 51.6% of −0.58 m s−1 day−1, respectively). The contributions from the two others are much smaller. Here, the two months are used when the total wave driving is largest or smallest (Fig. 6a). Our results are insensitive to the choice of the months, so that the following results are representative of the wave driving for NH winter and summer conditions.

Fig. 7.

Bar chart showing December minus August differences of the wave driving (m s−1 day−1): (left) sums from the NH and SH averages (5–15°, 50–100 hPa) and (right) values at 10°S and 10°N at 86 hPa. Each set consists of the total (leftmost) and contributions from the four terms (second left to right) ∂Fy1/∂y, ∂Fy2/∂y, ∂Fz1/∂z, and ∂Fz2/∂z. Shadings show the sums from both hemispheres. Dotted lines show contributions from the NH.

Fig. 7.

Bar chart showing December minus August differences of the wave driving (m s−1 day−1): (left) sums from the NH and SH averages (5–15°, 50–100 hPa) and (right) values at 10°S and 10°N at 86 hPa. Each set consists of the total (leftmost) and contributions from the four terms (second left to right) ∂Fy1/∂y, ∂Fy2/∂y, ∂Fz1/∂z, and ∂Fz2/∂z. Shadings show the sums from both hemispheres. Dotted lines show contributions from the NH.

It is also noticeable in Fig. 7 (left set) that the NH part explains most of the seasonal contrast of the total wave driving summed for both hemispheres. This reflects that SH ∂Fy1/∂y (stronger driving for August) partially cancels the NH contribution and that the ∂Fz2/∂z contribution occurs mostly in the NH part. These features are basically robust when gridpoint values at 10°N and 10°S at 86 hPa are used (Fig. 6b and right set of Fig. 7) The contribution from ∂Fz1/∂z increases when focusing on the lower stratospheric grid points.

The seasonal contrast of the total wave driving in the tropical lower stratosphere, especially in the NH tropics, is clearly seen in its latitude–height distributions (Figs. 8a,e). The distributions of the total wave driving in the model resemble the observations (see Fig. 7 of Hitchman and Huesmann 2007). The significant contributions from ∂Fy1/∂y and ∂Fz2/∂z (Fig. 7) are also related to their spatial distributions below.

Fig. 8.

Latitude–height sections of the wave driving (m s−1 day−1) for (top) December and (bottom) August, showing contributions from the three terms—(b),(f) ∂Fy1/∂y, (c),(g) ∂Fz1/∂z, and (d),(h) ∂Fz2/∂z—and also (a),(e) the totals. Contours are drawn at 0, ±0.25, ±0.5, ±1, and ±3 m s−1 day−1. EP flux vectors are shown by arrows in (a) and (e) weighted by 1 – 2|ϕ|/90 and 1/p for graphic purposes. The vectors are further magnified by 2.5 above 100 hPa. Solid lines denote the latitudes 5° and 15° between 50 and 100 hPa. Crosses denote 10°S and 10°N at 86 hPa.

Fig. 8.

Latitude–height sections of the wave driving (m s−1 day−1) for (top) December and (bottom) August, showing contributions from the three terms—(b),(f) ∂Fy1/∂y, (c),(g) ∂Fz1/∂z, and (d),(h) ∂Fz2/∂z—and also (a),(e) the totals. Contours are drawn at 0, ±0.25, ±0.5, ±1, and ±3 m s−1 day−1. EP flux vectors are shown by arrows in (a) and (e) weighted by 1 – 2|ϕ|/90 and 1/p for graphic purposes. The vectors are further magnified by 2.5 above 100 hPa. Solid lines denote the latitudes 5° and 15° between 50 and 100 hPa. Crosses denote 10°S and 10°N at 86 hPa.

The following argues that stationary equatorial Rossby waves (through both ∂Fy1/∂y and ∂Fz2/∂z) and NH extratropical planetary and synoptic waves (through ∂Fy1/∂y) play roles inducing the strong driving in the NH tropical lower stratosphere for its winter.

  • A remarkable ∂Fy1/∂y feature is that its latitude–height distributions include tripolar patterns in both December and August; they consist of positive values (corresponding to EP flux divergence) centering in the upper troposphere and lower stratosphere of the summer tropics and surrounding negative values in higher latitudes of both hemispheres (Figs. 8b,f). Inspection of EP flux vectors (plotted in Figs. 8a,e) shows that in low latitudes waves mainly propagate from the region of the EP flux divergence (wave source region) to the winter tropics for both seasons. The meridional wave propagation signature to the summer subtropics may be masked by the equatorward propagation of extratropical waves described below. Such tripolar ∂Fy1/∂y patterns in low latitudes are a characteristic of equatorial Rossby waves forced by convective heating near the equator (Hitchman and Huesmann 2007; Norton 2006). Because such patterns are present for both seasons, this suggests persistent existence of the waves near the equator in the simulation. It is also noteworthy that extratropical waves propagate equatorward from midlatitudes of both hemispheres in the troposphere and lower stratosphere for both seasons, with enhanced activity for local winter. This contributes to the negative ∂Fy1/∂y driving that strengthens and extends more equatorward for local winter: this feature is more distinct in the NH. The antiphase annual changes between NH and SH correspond to the partial cancellation of this term seen in Fig. 7. The enhanced equatorward propagation during local winter seems to be in line with the the zonal wind in the simulation having a region of westerlies (reflecting the existence of “westerly ducts”) in the upper troposphere of the winter tropics, especially in the NH (Figs. 1c,d).

  • The ∂Fz2/∂z distribution in December is characterized by a paired structure of positive values (EP flux divergence) in the tropical middle troposphere around 350 hPa and negative values above it (Fig. 8d), again characteristic of equatorial Rossby waves as compared with Norton (2006). Also note that ∂Fz2/∂z includes contributions from the midlatitudes. The distribution in August suggests a similar but less coherent structure in the tropics (Fig. 8h). It is consistent with Fig. 7 that the ∂Fz2/∂z driving is markedly stronger in the NH tropical lower stratosphere for its winter.

  • The seasonal contrast of ∂Fz1/∂z in the tropical lower stratosphere is unclear compared to those of ∂Fy1/∂y and ∂Fz2/∂z (Figs. 8c,g).

Figure 9a displays a time–latitude section of [u*υ*]cosϕ in the lower stratosphere (averaged for 50–100 hPa), which is proportional to Fy1 and hence to ∂Fy1/∂y. Note that positive [u*υ*]cosϕ corresponds to equatorward Fy1 and vice versa. The meridional eddy flux of the zonal momentum (weighted by cosϕ) suggests strong convergence of Fy1 in the NH tropics for its winter (December to February), associated with the equatorial negative extremum and the equatorward extension of large (positive) values from NH midlatitudes. On the other hand, such strong convergence is absent from the region for NH summer. This seasonality is consistent with Figs. 8a,b,e,f.

Fig. 9.

(a)–(c) Time–latitude sections of the climatological [u*υ*]cosϕ averaged between 50 and 100 hPa explained by (a) all waves, (b) planetary waves 1–3, and (c) synoptic waves 4–10. The contour interval is 2.5 m2 s−2, with additional contours drawn at ±1 m2 s−2. (d),(e) Time–height sections of the climatology of all waves averaged for (d) 0°–10°N and (e) 10°–20°N. The contour interval is 5 m2 s−2.

Fig. 9.

(a)–(c) Time–latitude sections of the climatological [u*υ*]cosϕ averaged between 50 and 100 hPa explained by (a) all waves, (b) planetary waves 1–3, and (c) synoptic waves 4–10. The contour interval is 2.5 m2 s−2, with additional contours drawn at ±1 m2 s−2. (d),(e) Time–height sections of the climatology of all waves averaged for (d) 0°–10°N and (e) 10°–20°N. The contour interval is 5 m2 s−2.

To study which spatial scales contribute to the seasonal contrast of [u*υ*]cosϕ, the calculation is repeated using planetary waves of zonal wavenumbers 1–3 (Fig. 9b). Contribution of synoptic waves 4–10 is also calculated (Fig. 9c). This test shows that planetary waves largely explains the seasonality of [u*υ*]cosϕ of all waves, whereas synoptic waves add some contribution, especially in midlatitudes of both hemispheres. Time–height sections of [u*υ*]cosϕ of all waves (averaged over 0°–10°N and 10°–20°N) show northward Fy1 from the equatorial region and notable equatorward Fy1 from NH midlatitudes in the upper troposphere and lower stratosphere for NH winter (Figs. 9d,e).

A similar examination is made of [u*w*]cosϕ, the characteristic term of equatorial Rossby waves, which contributes to Fz2 and ∂Fz2/∂z (Fig. 10). Note again that [u*w*]cosϕ and Fz2 have opposite signs. The vertical momentum flux averaged in the NH tropics (0°–10°N) exhibits a clear seasonal contrast, with negative values (upward Fz2) extending to the lower stratosphere above 100 hPa and decaying with height for NH winter (Fig. 10a). The decay of [u*w*]cosϕ, along with the density factor in Fz2, implies convergence of Fz2 or negative ∂Fz2/∂z, consistent with Figs. 8a,d. The seasonality in [u*w*]cosϕ of all waves is explained largely by planetary scales and also by synoptic scales to a lesser degree (Figs. 10,cb). It is consistent with the fact that stationary equatorial Rossby waves consist of planetary and also synoptic scales, as examined below. A time–latitude section of this term in the upper troposphere (200 hPa) confirms the enhanced upward Fz2 in the NH tropics for its winter, whereas a hint of upward Fz2 is also found in the SH tropics for its winter (Fig. 10d).

Fig. 10.

(a)–(c) Time–height sections of the climatological ([u*w*]cosϕ × 103) averaged for 0°–10°N explained by (a) all waves, (b) waves 1–3, and (c) waves 4–10. Contour interval is 10 m2 s−2, with additional contours drawn at −2.5 m2 s−2. (d) A time–latitude section of the climatology of all waves at 200 hPa. Contour interval is 20 m2 s−2.

Fig. 10.

(a)–(c) Time–height sections of the climatological ([u*w*]cosϕ × 103) averaged for 0°–10°N explained by (a) all waves, (b) waves 1–3, and (c) waves 4–10. Contour interval is 10 m2 s−2, with additional contours drawn at −2.5 m2 s−2. (d) A time–latitude section of the climatology of all waves at 200 hPa. Contour interval is 20 m2 s−2.

An additional support for the role of stationary planetary waves in Fz2 in the NH tropics during its winter can be obtained by applying a time–space cospectral analysis to [u*w*]cosϕ for a NH cold season (November through March) when the momentum flux is strongest (Fig. 10; see also Fig. 6 for ∂Fz2/∂z). This analysis can decompose contributions from different zonal wavenumbers and frequencies (phase speeds) to the total [u*w*]cosϕ of interest. The calculation of the cospectrum is made for each of the 50 yr, via a method introduced by Mechoso and Hartmann (1982), before a 50-yr climatology is obtained. Figure 11 plots zonal wavenumber dependences of the cospectrum by highlighting contributions from stationary components in comparison to those from eastward- or westward-moving components. The plot shows that the stationary components of planetary scales play the largest role in the total [u*w*]cosϕ, consistent with Kerr-Munslow and Norton (2006). This is insensitive to the choice of the months. This result can be obtained by a much simpler method by just comparing contributions from stationary components (monthly or seasonal means of u* and w*) to the daily calculated [u*w*]cosϕ (not shown).

Fig. 11.

Zonal wavenumber dependence of [u*w*]cosϕ during November through March averaged for 0°–10°N at 200 hPa. The solid line indicates stationary components; thin and thick broken lines indicate eastward- and westward-moving components, respectively.

Fig. 11.

Zonal wavenumber dependence of [u*w*]cosϕ during November through March averaged for 0°–10°N at 200 hPa. The solid line indicates stationary components; thin and thick broken lines indicate eastward- and westward-moving components, respectively.

d. Stationary wave patterns

Figures 12a and 12b examine climatological patterns of stationary waves at 200 hPa for the November–January (NDJ) and July–September (JAS) periods. The upper tropospheric level of 200 hPa is chosen here because the momentum fluxes [u*υ*] and [u*w*] are larger in magnitude in the upper troposphere than in the lower stratosphere (Figs. 9 and 10), although circulation features are generally similar between the two regions. The 3-month periods when the wave driving is largest or smallest in magnitude (Fig. 6) are used to obtain smooth patterns, but similar patterns are also found during NH winter and summer seasons. The 200-hPa circulation distribution for NDJ includes a quadrupole structure of geopotential height, and associated horizontal winds, over a tropical/subtropical region of approximately 120°–240°E (Fig. 12a). The horizontal winds have significant amplitudes near the equator. On the other hand, the circulation in the deep tropics is much less for JAS, although there persists a pair of weak anticyclones over the equatorial Pacific (Fig. 12b). Monsoonal circulations over the Asia and western Pacific in the NH subtropics are a dominant feature for JAS.

Fig. 12.

Climatological circulation patterns at 200 hPa for (a) NDJ and (b) JAS. Black contours show geopotential height. Zonal and meridional winds are drawn with arrows. Light blue (pink) shading shows vertical wind over +5 (−5) mm s−1. Wave components of 1–6 are used in the height and wind distributions. Blue contours show OLR at 200 (thick) and 240 (thin) W m−2. (c),(d) Longitudinal distributions of u* m s−1 (thick solid), υ* × 3 m s−1 (thin solid), and w* mm s−1 (dotted). Latitudinal averages are taken for (c) 0°–10°N and (d) 0°–10°S.

Fig. 12.

Climatological circulation patterns at 200 hPa for (a) NDJ and (b) JAS. Black contours show geopotential height. Zonal and meridional winds are drawn with arrows. Light blue (pink) shading shows vertical wind over +5 (−5) mm s−1. Wave components of 1–6 are used in the height and wind distributions. Blue contours show OLR at 200 (thick) and 240 (thin) W m−2. (c),(d) Longitudinal distributions of u* m s−1 (thick solid), υ* × 3 m s−1 (thin solid), and w* mm s−1 (dotted). Latitudinal averages are taken for (c) 0°–10°N and (d) 0°–10°S.

The seasonal circulation changes well agree with observations (e.g., Newell et al. 1972; Kerr-Munslow and Norton 2006). The changes can be understood as stationary Rossby wave responses to seasonally varying distributions of convective heating (Gill 1980; Highwood and Hoskins 1998; Norton 2006). Modeled outgoing longwave radiation (OLR; blue contours in Figs. 12a,b) implies the existence of active convection centering over Indonesia for NDJ and extending over South and Southeast Asia for JAS. It is also noted that active convection persists in the deep tropics near Indonesia for JAS, although the latitudinal scale of the low-OLR region (e.g., <240 W m−2) seems smaller.

To relate these stationary wave patterns in low latitudes to the eddy momentum fluxes [u*υ*] and [u*w*] (or Fy1 and Fz2) examined in Figs. 9 and 10, longitudinal distributions of u*, υ*, and w* are plotted in Figs. 12c,d. Different latitudinal averages are applied to focus on the latitudes of the characteristic momentum fluxes: 0°–10°N for NDJ and 0°–10°S for JAS (cf. Figs. 9a and 10d). The quadrupole height pattern over the Pacific and Indonesia for NDJ makes a significant contribution to the negative [u*υ*] (northward Fy1) in the NH tropics because the pattern includes poleward winds corresponding to westward winds, or vice versa. A strong negative covariance between u* and w* is also found in the pattern around 60°–90°E, where westward and upward winds coincide. The negative [u*w*] in the SH tropics for JAS is contributed by the anticyclonic flow over Indonesia, including westward and upward winds, and also by the cyclonic flow over the Atlantic and South America around 0°–60°W.

4. Summary and discussion

This paper has presented a diagnostic analysis of the climatological annual cycle of temperature, circulation, and wave-driving distributions in the tropical lower stratosphere as produced in a 50-yr control simulation of WACCM. Our diagnosis, in particular, includes an in-detail analysis on the wave driving in the tropical–subtropical lower stratosphere and upper troposphere that is relevant to the dynamics of the Brewer–Dobson circulation there. This study is motivated by the intention to re-examine, with the stratosphere-resolving GCM data, the observations of the wave driving (e.g., Kerr-Munslow and Norton 2006; Randel et al. 2008), which lead different results as discussed in section 1.

Our WACCM results can be summarized as follows:

  1. The annual cycle in temperatures in the tropical lower stratosphere is dynamically consistent with that in the adiabatic cooling and hence the tropical upwelling. The tropical upwelling largely balances with the local meridional outflow from the tropics. The annual cycle in the outflow is then well associated with that in the nearby wave driving in the tropical/subtropical lower stratosphere. The annual cycle in this region is characterized, for NH winter, by lower temperatures, stronger residual circulation, and enhanced wave driving. It is further shown that the annual cycle in the outflow and wave driving mostly reflects the contribution from the NH flank of the equator, where their seasonal contrast is clear, with strong wave driving for NH winter. Because the present results are purely diagnostic, they do not prove any causality between the residual circulation and wave driving. However, it seems natural that the annual cycle in the wave driving induces that in the residual circulation (and hence temperature), whereas the opposite is unlikely [as argued by Kerr-Munslow and Norton (2006)].

  2. Our detailed analysis of the wave driving has revealed that the strong driving in the NH tropics–subtropics for its winter is induced by equatorial Rossby waves forced by convective heating through marked northward and upward propagation (in Fy1 and Fz2) and by NH extratropical planetary and synoptic waves through the enhanced equatorward propagation (in Fy1). The role of equatorial Rossby waves for NH winter is clarified here because the EP flux and its divergence distributions in low latitudes are largely explained by stationary planetary waves, together with consistent stationary wave patterns. The distributions also generally agree with theoretical and modeling studies of such waves (Gill 1980; Highwood and Hoskins 1998; Norton 2006). Simply stated, the configuration of continents appears to favor the near-equatorial massive distribution of active convection for NH winter, contributing to the strong driving of equatorial Rossby waves in the NH tropical–subtropical lower stratosphere; it also favors enhanced propagation (and generation) of NH extratropical waves, leading to the strong driving in the region. The wave driving in the SH tropical lower stratosphere is relatively time invariant: equatorial Rossby wave activity does not extend there despite the persistent (year round) existence of the waves in the deep tropics suggested, whereas such latitudinal extension–retreat of extratropical waves (in Fy1) is relatively unclear.

Figure 13 provides support for the role of synoptic Rossby waves in the driving in the tropical/subtropical lower stratosphere, using data from the 15th year of the 50-yr WACCM simulation. It is shown that some events of the strong (negative) wave driving around 15°–20°N at 86 hPa are contributed by the ∂Fy1/∂y term associated with enhanced equatorward Fy1 in the NH (Figs. 13a,b). Such enhancement of equatorward wave propagation corresponds to intrusions of synoptic Rossby waves from mid to lower latitudes, as seen in Fig. 13c for 14 January of that year. It is known that in the real world synoptic Rossby waves originating from extratropics propagate to the tropics and break (Postel and Hitchman 1999; Waugh and Polvani 2000). Note also that the QBO and ENSO may play some role affecting such equatorward intrusions of extratropical waves in the real world, although these effects (if any) are absent from the simulation. The tropical waves in Fig. 13c exist regardless of extratropical variability, since they broadly resemble the stationary wave patterns in Fig. 12a.

Fig. 13.

(a),(b) Time–latitude sections of the wave driving at 86 hPa for NH winter of the 15th year (contours and shadings); the total driving is plotted in (a), whereas (b) shows the contribution from ∂Fy1/∂y. Contour interval is 0.5 m s−1 day−1. The EP flux component Fy1 is drawn in (b) with dot contours at ±5 and −15 in 106 kg s−2 and arrows. The downward arrows above the panels denote the day of 14 January. (c) 200-hPa geopotential height waves on 14 January, with a contour interval of 100 m.

Fig. 13.

(a),(b) Time–latitude sections of the wave driving at 86 hPa for NH winter of the 15th year (contours and shadings); the total driving is plotted in (a), whereas (b) shows the contribution from ∂Fy1/∂y. Contour interval is 0.5 m s−1 day−1. The EP flux component Fy1 is drawn in (b) with dot contours at ±5 and −15 in 106 kg s−2 and arrows. The downward arrows above the panels denote the day of 14 January. (c) 200-hPa geopotential height waves on 14 January, with a contour interval of 100 m.

The above results in this study are compared with existing studies as follows: The first result correlates with and hence supports the overall balances observed by Kerr-Munslow and Norton (2006). The large contribution from the NH in this result has not been previously emphasized but can be broadly seen in the observational results of, for example, Hitchman and Huesmann (2007) and Randel et al. (2008); suggesting that the NH tropics are a key factor in the tropical lower stratosphere.

The second result provides a few implications about tropical–subtropical wave driving, including the discrepancy observed by Kerr-Munslow and Norton (2006) and Randel et al. (2008). Kerr-Munslow and Norton (2006) and Norton (2006) emphasize the importance of ∂Fz2/∂z by equatorial Rossby waves, whereas Randel et al. (2008) do not support it but rather stress the role of ∂Fy1/∂y in equatorial and extratropical waves. Both arguments are included in our second result. It seems certain that the ∂Fy1/∂y driving provides an important contribution to the tropical–subtropical wave driving, as it is consistently shown in some observational studies (Boehm and Lee 2003; Hitchman and Huesmann 2007; Hartmann 2007; Randel et al. 2008) as well as in this GCM study. One should be careful in looking at ∂Fy1/∂y contributions from both hemispheres because they may be complicated as a result of the antiphase seasonal changes between the NH and SH.

On the other hand, the possible role of ∂Fz2/∂z, especially by equatorial Rossby waves, may leave room for some discussion. The discrepancy about ∂Fz2/∂z between the observational studies (Kerr-Munslow and Norton 2006; Randel et al. 2008) can arise at least from two factors. One is the difference in data length: the result of Kerr-Munslow and Norton (2006) using the shorter ERA-15 data may be more sensitive to interannual variability, including trends. Interannual variability in the tropical lower stratosphere occurs in association with the QBO, ENSO, and so on. The other is that the ERA-15 and ERA-40 data themselves are different even for a fixed time (such as a particular day or month), reflecting different assimilation procedures. This ∂Fz2/∂z term, or vertical momentum flux [u*w*], will be thus sensitive to differences, or data quality, especially of vertical wind because of its poor constraint in current data assimilation. It is also known that in GCMs equatorial wave responses can be largely different because convective distributions are simulated differently (e.g., Horinouchi et al. 2003). It will be therefore a useful future work to perform a multi-reanalysis or GCM comparison about the tropical–subtropical wave driving, especially in [u*w*] by stationary equatorial waves.

To conclude, the present diagnostic analysis using the WACCM simulation has provided a support for the overall dynamical balances of the annual cycle in the tropical lower stratosphere, as characterized by lower temperatures, stronger residual circulation, and enhanced wave driving for NH winter. A further examination has revealed the origins of the wave driving in the tropical–subtropical lower stratosphere and upper troposphere: the strong driving in the NH tropics and subtropics for its winter, which is key for the overall annual cycle in the tropical lower stratosphere, is contributed by equatorial Rossby waves propagating northward and upward and by NH extratropical planetary and synoptic waves propagating equatorward. Based on the present framework and results, ENSO-induced changes in the tropical lower stratosphere during NH winter will be investigated using perpetual-January WACCM experiments in a future paper (TAG).

Acknowledgments

The author thanks the developers of WACCM (Sassi et al. 2002), who made the model available. The simulation was performed while the author stayed at University of Washington. The author also acknowledges useful comments provided by three anonymous reviewers. The GFD-DENNOU Library was used to draw the figures. This work was supported by the JSPS Grant-in-Aid for Scientific Research (A) 20244076 and for Young Scientists (B) 20740272.

REFERENCES

REFERENCES
Andrews
,
D. G.
,
J. R.
Holton
, and
C. B.
Leovy
,
1987
:
Middle Atmosphere Dynamics.
Academic Press, 489 pp
.
Baldwin
,
M. P.
, and
Coauthors
,
2001
:
The quasi-biennial oscillation.
Rev. Geophys.
,
39
,
179
229
.
Boehm
,
M. T.
, and
S.
Lee
,
2003
:
The implications of tropical Rossby waves for tropical tropopause cirrus formation and for the equatorial upwelling of the Brewer–Dobson circulation.
J. Atmos. Sci.
,
60
,
247
261
.
Edmon
,
H.
,
B.
Hoskins
, and
M.
McIntyre
,
1980
:
Eliassen–Palm cross sections for the troposphere.
J. Atmos. Sci.
,
37
,
2600
2616
.
Gill
,
A. E.
,
1980
:
Some simple solutions for heat-induced tropical circulation.
Quart. J. Roy. Meteor. Soc.
,
106
,
447
462
.
Hartmann
,
D. L.
,
2007
:
The atmospheric general circulation and its variability.
J. Meteor. Soc. Japan
,
85B
,
123
143
.
Haynes
,
P. H.
,
M. E.
McIntyre
,
T. G.
Shepherd
,
C. J.
Marks
, and
K. P.
Shine
,
1991
:
On the downward control of extratropical diabatic circulations by eddy-induced mean zonal forces.
J. Atmos. Sci.
,
48
,
651
678
.
Highwood
,
E. J.
, and
B. J.
Hoskins
,
1998
:
The tropical tropopause.
Quart. J. Roy. Meteor. Soc.
,
124
,
1579
1604
.
Hitchman
,
M. H.
, and
A. S.
Huesmann
,
2007
:
A seasonal climatology of Rossby wave breaking in the 320–2000-K layer.
J. Atmos. Sci.
,
64
,
1922
1940
.
Holton
,
J. R.
,
P. H.
Haynes
,
M. E.
McIntyre
,
A. R.
Douglass
,
R. B.
Rood
, and
L.
Pfister
,
1995
:
Stratosphere–troposphere exchange.
Rev. Geophys.
,
33
,
403
439
.
Horinouchi
,
T.
, and
Coauthors
,
2003
:
Tropical cumulus convection and upward-propagating waves in middle-atmospheric GCMs.
J. Atmos. Sci.
,
60
,
2765
2782
.
Kerr-Munslow
,
A. M.
, and
W. A.
Norton
,
2006
:
Tropical wave driving of the annual cycle in tropical tropopause temperatures. Part I: ECMWF analyses.
J. Atmos. Sci.
,
63
,
1410
1419
.
Kley
,
D.
,
J. M.
Russell
III
, and
C.
Philips
,
Eds.
2000
:
Assessment of upper tropospheric and stratospheric water vapor.
WMO Tech. Doc. 1043, 312 pp
.
Mechoso
,
C. R.
, and
D. L.
Hartmann
,
1982
:
An observational study of traveling planetary waves in the Southern Hemisphere.
J. Atmos. Sci.
,
39
,
1921
1935
.
Mote
,
P. W.
, and
Coauthors
,
1996
:
An atmospheric tape recorder: The imprint of tropical tropopause temperatures on stratospheric water vapor.
J. Geophys. Res.
,
101
, (
D2
).
3989
4006
.
Newell
,
R. E.
,
J. M.
Kidson
,
D. G.
Vincent
, and
G. J.
Boer
,
1972
:
The General Circulation of the Tropical Atmosphere and Its Interactions with Extratropical Latitudes.
Vol. 1. MIT Press, 258 pp
.
Norton
,
W. A.
,
2006
:
Tropical wave driving of the annual cycle in tropical tropopause temperatures. Part II: Model results.
J. Atmos. Sci.
,
63
,
1420
1431
.
Pawson
,
S.
, and
Coauthors
,
2000
:
The GCM–reality intercomparison project for SPARC (GRIPS): Scientific issues and initial results.
Bull. Amer. Meteor. Soc.
,
81
,
781
796
.
Plumb
,
R. A.
,
2002
:
Stratospheric transport.
J. Meteor. Soc. Japan
,
80
,
793
809
.
Plumb
,
R. A.
, and
J.
Eluszkiewicz
,
1999
:
The Brewer–Dobson circulation: Dynamics of the tropical upwelling.
J. Atmos. Sci.
,
56
,
868
890
.
Postel
,
G. A.
, and
M. H.
Hitchman
,
1999
:
A climatology of Rossby wave breaking along the subtropical tropopause.
J. Atmos. Sci.
,
56
,
359
373
.
Randel
,
W. J.
, and
P. A.
Newman
,
1998
:
The stratosphere in the Southern Hemisphere.
Meteorology of the Southern Hemisphere, Meteor. Monogr., No. 27, Amer. Meteor. Soc., 243–282
.
Randel
,
W. J.
,
R. R.
Garcia
, and
F.
Wu
,
2002
:
Time-dependent upwelling in the tropical lower stratosphere estimated from the zonal-mean momentum budget.
J. Atmos. Sci.
,
59
,
2141
2152
.
Randel
,
W. J.
,
R.
Garcia
, and
F.
Wu
,
2008
:
Dynamical balances and tropical stratospheric upwelling.
J. Atmos. Sci.
,
65
,
3584
3595
.
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
.
Shepherd
,
T. G.
,
2002
:
Issues in stratosphere–troposphere coupling.
J. Meteor. Soc. Japan
,
80
,
769
792
.
Simmons
,
A. J.
, and
J. K.
Gibson
,
2000
:
The ERA-40 project plan.
ECMWF ERA-40 Project Report Series 1, 63 pp
.
SPARC
,
2000
:
SPARC Assessment of water vapor in the upper troposphere and lower stratosphere.
Stratospheric Processes and Their Role in Climate (SPARC) Water Vapor Working Group, WMO/TD-1043, 312 pp
.
Waugh
,
D. W.
, and
L. M.
Polvani
,
2000
:
Climatology of intrusions into the tropical upper troposphere.
Geophys. Res. Lett.
,
27
,
3857
3860
.
Yulaeva
,
E.
,
J. R.
Holton
, and
J. M.
Wallace
,
1994
:
On the cause of the annual cycle in tropical lower-stratospheric temperatures.
J. Atmos. Sci.
,
51
,
169
174
.

Footnotes

Corresponding author address: Masakazu Taguchi, 1 Hirosawa, Igaya-cho, Kariya, Aichi 448–8542, Japan. Email: mtaguchi@auecc.aichi-edu.ac.jp