1. Introduction
A strong annual cycle occurs in the mean upwelling circulation near the tropical tropopause, with approximately a factor-of-2 variation between boreal winter and summer seasons. This climatological annual cycle of upwelling is an important feature that affects many physical and chemical properties of the tropical tropopause layer (TTL) and lower stratosphere and strongly modulates troposphere-to-stratosphere transport (Holton et al. 1995). In response to the upwelling, distinct annual cycles in temperature (Reed and Vlcek 1969; Yulaeva et al. 1994; Fueglistaler et al. 2011) and water vapor (Mote et al. 1996; Randel and Jensen 2013) have been observed in the TTL and lower stratosphere. In general, strong upwelling is observed in the TTL during the Northern Hemisphere (NH) winter, leading to roughly 4–8-K colder and 1-ppmv drier TTL in the NH winter compared to the summer. In addition, tropical upwelling transports tropospheric air into the stratosphere, and thus an annual cycle is also found in the chemical composition of the tropical lower stratosphere for tracers with strong vertical gradients [e.g., in O3 and CO (e.g., Schoeberl et al. 2006; Randel et al. 2008; Abalos et al. 2012; Stolarski et al. 2014)].
It is well known that tropical upwelling is a mechanically forced phenomenon (Haynes et al. 1991; Holton et al. 1995; Plumb and Eluszkiewicz 1999). Tropical upwelling is part of the global-scale stratospheric overturning circulation, which comprises ascent in the tropics and poleward and descending motion in the midlatitude and polar region [known as the Brewer–Dobson circulation (BDC); Brewer et al. 1949; Dobson 1956]. Recent work has highlighted that the BDC is composed of two branches: a deep branch driven by wave forcing in the deep stratosphere and a shallow branch driven by wave forcing in the subtropical and midlatitude lower stratosphere (Plumb 2002; Birner and Bönisch 2011). The deep branch is largely forced by planetary-scale waves that break in the extratropical (Garcia 1987; Yulaeva et al. 1994; Holton et al. 1995) and subtropical stratosphere (Plumb and Eluszkiewicz 1999; Ueyama et al. 2013), while the shallow branch is primarily forced by planetary and synoptic-scale waves that break in the subtropical lowermost stratosphere (Randel et al. 2008; Abalos et al. 2014). Although these two branches have similar driving mechanisms, the shallow branch is distinguished from the deep branch as it has more rapid circulation and confined vertical structure in the lower stratosphere (Birner and Bönisch 2011). Additionally, the upper and lower BDC branches behave independently on subseasonal time scales (Ueyama et al. 2013; Abalos et al. 2014; Randel and Wu 2015). The large annual cycle near the tropopause and lower stratosphere is associated primarily with the lower branch of the BDC.
However, despite the known links between wave forcing and tropical upwelling, the annual cycle in TTL upwelling is still poorly understood. It is clear that a seasonal difference in wave driving is the major mechanism of the annual cycle in upwelling, but the type and origin of the wave(s) that contributes to this seasonality are still unclear [see discussion in Fueglistaler et al. (2009)]. Yulaeva et al. (1994) and Holton et al. (1995) argued that the annual cycle could be explained by the deep BDC and the seasonal cycle in extratropical planetary-scale waves. This idea is supported by a strong negative correlation between time series of tropical and extratropical temperature in the lower stratosphere, which is observed from satellite measurements using Microwave Sounding Unit channel 4 (MSU-4; Yulaeva et al. 1994). However, Fueglistaler et al. (2011) revealed that this strong correlation is partly a coincidence associated with the weighting function of the measurement. Plumb and Eluszkiewicz (1999) showed that low-frequency wave forcing needs to reach deep into the subtropics to force tropical upwelling. This led to an appreciation that wave dissipation in the subtropics associated with synoptic-scale waves could influence upwelling near the tropical tropopause (Randel et al. 2008; Taguchi 2009; Chen and Sun 2011; Jucker et al. 2013; Kim and Son 2015). Additionally, several recent studies have focused on the contribution of tropical planetary waves forced by deep convection to forced upwelling near the tropopause. Kerr-Munslow and Norton (2006), Norton (2006), and Ortland and Alexander (2014) emphasized the role of equatorial planetary-scale waves in the annual cycle using reanalysis and idealized global circulation model (GCM) experiments. Randel et al. (2008) explained the annual cycle as a combined result of enhanced tropical and extratropical waves in the NH winter using reanalysis data. They also suggested that both planetary and synoptic-scale waves are important for the extratropical wave forcing. Garny et al. (2011) also pointed out the importance of tropical and extratropical waves, but they focused more on the synoptic-scale waves for the extratropical component. Overall, there is no consensus on the waves that maintain the annual cycle in tropical upwelling.
Quantifying the sources of waves that drive the annual cycle is a crucial aspect for understanding variability in the TTL and related troposphere–stratosphere coupling processes. In this study, we revisit this problem to better understand the type and origin of the waves contributing to the annual cycle. Recent studies have shown that temperature variability near the tropical tropopause is largely independent from that in the deep stratosphere (e.g., Ueyama et al. 2013; Grise and Thompson 2013; Randel and Wu 2015); thus, we focus on wave forcing in the lower stratosphere, which directly induces the tropopause upwelling. The wave forcing is decomposed as a function of the zonal wavenumber in order to identify the scale and origin of the waves. We analyze the detailed structure of the wave forcing, including tropical and extratropical wave components, sources and propagation characteristics. Section 2 describes data and methodology. The results are presented in section 3 and summarized in section 4.
2. Data and methodology
a. ERA-Interim and NOAA OLR data
Wave forcing and upwelling are computed at every 6 h using temperature and wind from the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim; ECMWF 2009; Dee et al. 2011) archived in pressure coordinates. Daily and monthly means are obtained by averaging the 6-hourly calculation. Vertical resolution of the data is roughly 25 hPa near the TTL (levels are 150, 125, 100, 70, and 50 hPa), and data up to 10 hPa are used for the upwelling calculation. We use N128 Gaussian grid data (512 × 256 grid points in longitude and latitude) with a horizontal resolution of about 0.7°. The climatologies shown in this study are based on the period of 1979–2012 (34 yr). Monthly National Oceanic and Atmospheric Administration (NOAA) outgoing longwave radiation (OLR; Liebmann and Smith 1996) is also used to understand the relationship between wave forcing and convective activity in the tropics.
b. Upwelling calculation
The momentum-based estimate is based on the zonal-mean momentum equation, in which wave drag (DF) is balanced by the Coriolis torque of a poleward motion and zonal wind tendencies; the poleward motion is estimated using the momentum balance, and then upwelling is computed from the estimated poleward motion using mass continuity [leading to Eq. (2)]. Under steady-state conditions (
c. Spectral decomposition of wave forcing
3. Results
The analyses in this paper focus on the annual cycle of wave activity and the associated forcing in the subtropical lower stratosphere. Tropical upwelling is first computed and analyzed using Eq. (2); then the spectrum of the wave forcing is examined in detail. Finally, the sources and propagation characteristics of the waves that are responsible for the annual cycle are discussed.
a. Annual cycle of upwelling
Figure 1 presents the momentum-based estimates 
Estimates of daily upwelling over 15°S–15°N based on thermodynamic balance (
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
It is worth noting that Fig. 1 shows that 
To understand the scale of wave forcing that contributes to the annual cycle, 
Daily 
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
Monthly climatology (1979–2012) of 
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
December–February (black) and June–August (gray) climatologies (1979–2012) of 
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
b. Zonal wavenumber spectrum of wave forcing
To characterize the behavior of upwelling, the zonal spectrum of wave forcing (DF) at 100 hPa is examined as a function of latitude in Fig. 5. The DF spectrum in DJF (Fig. 5a) shows a pronounced forcing in the NH subtropics (~10°–20°N) at k = 3 and a secondary maximum in the SH subtropics (~10°–30°S) over a broader range of wavenumbers (k = 2–4). These forcings are mostly absent in JJA (Fig. 5d), indicating that the forcings are responsible for the annual cycle. Further decomposition of the DF spectrum into horizontal (Figs. 5b,e) and vertical components (Figs. 5c,f) reveals that the strong NH forcing at k = 3 is largely as a result of horizontal convergence of waves propagating both from the tropics and extratropics (Fig. 5b). Strong poleward EP flux from the tropics and equatorward EP flux from the extratropics converge near 15°N and produce a large momentum forcing at k = 1–3. This is very similar to the momentum flux (proportional to the horizontal EP flux) reported in Randel et al. (2008). However, the horizontal EP-flux convergence is largely cancelled by its vertical divergence for k = 1 and 2 (Fig. 5c), and therefore only k = 3 forcing dominates the DF spectrum in DJF. A similar behavior is also found at 70 hPa (not shown), except that extratropical waves dominate the forcing spectrum (the EP flux from the tropics is negligibly small at 70 hPa).
Zonal wavenumber spectra of DF (m s−1 day−1) at 100 hPa in (a)–(c) December–February and (d)–(f) June–August. The DF computed from (a),(d) total; (b),(e) horizontal; and (c),(f) vertical EP flux components are shaded. (b),(e) The horizontal (106 kg s−2) and (c),(f) vertical EP fluxes (104 kg s−2) are also shown (counter interval is 1, and ±0.5 contours are also shown). The letters A and B indicate the maximum and minimum of the horizontal EP flux at k = 3, which are found at 3.8° and 29.1°N, respectively.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
The wave forcing in the SH subtropics is dominated by vertical convergence of EP flux (Fig. 5c). This maximum is related to the horizontal heat flux 
We further examine the spatial structure of the wavenumber-3 EP flux that is related to the annual cycle in upwelling. Figure 6 shows seasonal differences (DJF minus JJA) in k = 3 EP flux and DF over the entire 1979–2012 record. As expected from the previous result (Fig. 5), the seasonal difference in DF shows a strong forcing (negative DF) near 100 hPa in the NH subtropics and a weaker maximum in the SH subtropics. The most pronounced feature in the EP-flux difference is a convergence of two branches of wave activity propagating from the NH extratropics and SH tropics. In the SH tropics, there is a region of positive EP-flux divergence centered near 200 hPa, which is a signature of a source of wave activity likely associated with persistent deep convection (e.g., Dima et al. 2005). The two branches of k = 3 EP fluxes converge in the NH subtropics (~15°N) and produce the strong wave forcing over approximately 70–200 hPa. The magnitude of the tropical and extratropical wave fluxes is qualitatively similar at 100 hPa, suggesting that both components are important for the annual cycle in the TTL upwelling. Note that the seasonal differences in EP flux and DF observed in the tropics are qualitatively similar to those of DJF climatology, because tropical k = 3 forcing is relatively weak in JJA.
Differences in k = 3 EP flux (vectors) and DF (m s−1 day−1; shading) between DJF and JJA. Insignificant DF difference is hatched in white, and only significant EP flux is shown (based on a Student’s t test at the 99% confidence level). EP flux vectors are weighted in height by multiplying by ez/H for visual clarity.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
It is worth noting that the subtropical wave forcing below 100 hPa may affect vertical motion at 100 hPa as a part of the transient response, which is observed on subseasonal time scales (e.g., Grise and Thompson 2013; Abalos et al. 2014). However, on seasonal or longer time scales, which could be assumed as steady state (
c. Propagation and potential sources of wavenumber-3 waves
All extratropical planetary-scale waves (wavenumbers 1–3) exhibit maximum amplitudes in the troposphere during NH winter. Why is the wavenumber-3 contribution so dominant to the annual cycle of tropical upwelling? The extratropical EP fluxes in the NH (Fig. 6) provide a hint for this question. The k = 3 waves originating from the midlatitudes are refracted mostly toward the subtropics while they propagate upward, with relatively little vertical transport to the stratosphere. Although they are attenuated significantly while traveling in the troposphere, still a good portion of the waves propagate into the subtropical upper troposphere–lower stratosphere (UTLS). This is a general feature of the extratropical k = 3 waves during DJF (note that they are almost absent in JJA; refer to Fig. 5).
Refractive index squared (shading) and EP flux climatology (vectors) for each wavenumber (k = 1–4) during DJF. Refractive indices are computed from DJF zonal wind climatology (1979–2012). EP flux vectors are weighted in height by multiplying by ez/H for visual clarity.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
It is worth noting that some portion of k = 1 waves also propagate into the subtropical UTLS in DJF (Fig. 7a). This is the reason there is a nonnegligible k = 1 forcing in DF spectra at 100 hPa (Fig. 5a). Although k = 1 upwelling shows a semiannual cycle as a result of additional wave forcing in JJA, the extratropical k = 1 wave is a minor contributor for the observed annual cycle. Also note that k = 1 EP flux vectors are heading downward near the tropical tropopause (~15°N and ~100–125 hPa). This feature is consistent with vertical divergence of EP flux observed in k = 1 waves (Fig. 5c).
We now discuss potential sources of the k = 3 waves focusing on the forcing in the NH subtropics (highlighted by the cross in Fig. 5a). We use the interannual variability of the wavenumber-3 forcing during DJF (over 1979–2012) to quantify forcing mechanisms and find the relevant forcing regions by avoiding spurious relationships from coincident annual cycles. Figure 8 presents interannual variability of the monthly 
Monthly 
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
The extratropical component FEXT shows significant relationships with midlatitude regions. The 100-hPa geopotential height regressed onto FEXT (shading in Fig. 9a) shows three high pressure centers, which are collocated with the exit regions of the climatological jet maxima (contours in Fig. 9a). These anomalies have a deep vertical structure, extending from the surface to lower stratosphere levels (~70 hPa; not shown). Particularly, the anomalies over the central Pacific and Atlantic Oceans have a westward-tilted structure in the vertical (
(a) Geopotential height (m; shading) and wind (vectors) at 100 hPa and (b) potential vorticity at 350 K [PV units (PVU; 1 PVU = 10−6 K kg−1 m2 s−1); shading] regressed to FEXT during DJF. Climatology of the zonal wind (m s−1) at 200 hPa and potential vorticity (PVU) at 350 K, respectively, are also shown (gray contours). The insignificant area for shading is hatched in white, and only significant wind is shown (based on a Student’s t test at the 95% confidence level).
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
Frequency distribution of PV difference between two regions defined in Fig. 9b (region C minus region D). Lines indicate the 10 individual months in the DJF season with maximum (red) and minimum (blue) FEXT, and gray shading presents the DJF climatology for 1979–2012. The 6-hourly PV at 350 K is used for the computation. A positive value implies a potential PV overturning event over the northeastern Pacific.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
Relationships of tropical k = 3 forcing FTRO to deep convection and 100-hPa wind speed in the tropics are shown in Fig. 11. The regressed OLR shows a strong minimum (linked to maximum convection) over the western Pacific and maximum over the central eastern Pacific. This is basically an enhanced pattern of climatological convection. In DJF, climatological convection has three maxima over the western Pacific, South America, and central Africa. This climatological structure could produce a wavenumber-3 component in the convectively driven equatorial waves. The horizontal wind anomaly over the OLR minimum and maximum shows a westward-tilted structure (
OLR (shading) and 100-hPa temperature (contours) and wind (vectors) regressed to FTRO. Insignificant OLR is hatched in white, and only significant wind is shown (based on a Student’s t test at the 95% confidence level). Temperatures are shown from −0.3 to +0.3 K, which is roughly significant at the same confidence level.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
It is worth noting that k = 1 and 2 structures are also shown (particularly k = 2) in the regressed fields (e.g., OLR in Fig. 11). This implies that k = 1 and 2 waves are also enhanced when FTRO (k = 3 wave) is strong. It may be natural that strong convective heating in the tropics (e.g., over the western Pacific) forces tropical waves at various scales. However, it is not clearly understood why k = 1 and 2 tropical waves cannot make significant forcing at and above 100 hPa. Further study is required.
4. Summary and discussion
The annual cycle in upwelling is the main cause of seasonal variation in many properties in the TTL, including temperature, moisture, and chemical constituents. The upwelling in the TTL, associated with the shallow branch of the BDC, is mechanically forced by tropical and extratropical waves, which dissipate in the subtropics, and it is largely independent of the deep stratospheric circulation (Ueyama et al. 2013; Abalos et al. 2014; Randel and Wu 2015). Thus, our study focuses on wave forcing in the subtropical lower stratosphere, which directly induces tropical upwelling in a shallow vertical depth (70–100 hPa).
The upwelling estimate based on wave forcing and momentum balance (downward control) shows good agreement with the thermodynamic estimate (Fig. 1), and this calculation demonstrates the importance of zonal wavenumber-3 forcing in the annual cycle (Figs. 2–4). Detailed analyses of the wave forcing show a large convergence of the wavenumber-3 component in the NH subtropics at 100 hPa during NH winter (Fig. 5a). These waves are originating both from the NH extratropics and SH tropics. Both tropical and extratropical waves show strong activity at 100 hPa in DJF, but they are almost absent in JJA. A secondary wave forcing in DJF is also found in the SH subtropics over a relatively broader wavenumber band (k = 2–4), and this is mostly related to vertical convergence of EP flux likely originating from deep convection in the tropics.
The reason why wavenumber-3 forcing dominates the annual cycle can be partly understood based on its propagation characteristics. Although all extratropical planetary-scale waves (k = 1–3) have strong activities during the NH winter, only the k = 3 component is trapped in the vertical (based on quasigeostrophic refractive index calculations). A large portion of the k = 3 component propagates into the subtropical lower stratosphere and produces an enhanced tropical upwelling in DJF at 100 hPa. This extratropical forcing is particularly noticeable over the eastern Pacific and Atlantic Oceans in the exit regions of the climatological jets. In addition, there is a large k = 3 component of wave activity originating in the tropics, likely linked to the climatological structure of deep convection (which has three maxima during DJF). The possible forcing structure is summarized in a schematic diagram (Fig. 12). The combination of the tropical and extratropical waves, which maximize during boreal winter, produces the dominant annual cycle in wave forcing and associated tropical upwelling near the tropopause.
Schematic diagram for potential sources and forcing mechanisms of climatological k = 3 waves in the tropics and extratropics.
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
The relative importance of tropical and extratropical waves in forcing the annual cycle has been the subject of recent research, with conflicting results (e.g., Jucker et al. 2013; Ortland and Alexander 2014). From our analysis, the tropical and extratropical waves have roughly equal contributions to the forcing in the NH subtropics, which is the main cause of the annual cycle in k = 3 upwelling. As expected, the amplitude of the k = 3 upwelling is sensitive to interannual variations of the separate (tropical and extratropical) forcings (Fig. 13a). We have used the interannual variability to quantify links to forcing mechanisms in the tropics and extratropics. Enhanced NH extratropical k = 3 wave fluxes are related to modulations of the winter storm tracks and wave breaking over the northeastern Pacific and North Atlantic Oceans, but detailed mechanisms in this process are still unclear. For tropical waves, it is worth noting that the regressed OLR and temperature patterns (Fig. 11) are similar to that of La Niña (cold phase of the El Niño–Southern Oscillation). In addition, FTRO and 
(a) Monthly 
Citation: Journal of the Atmospheric Sciences 73, 2; 10.1175/JAS-D-15-0096.1
It is worth noting that total upwelling is stronger with a positive SST anomaly over the Niño-3.4 region compared to that with negative SST anomaly (dotted lines in Fig. 13b). During the positive SST phase, k = 1 forcing is as strong as k = 3 forcing, and this implies a strong capability of the k = 1 wave in driving tropical upwelling. This can be caused by a stronger source of the k = 1 wave or change in waveguide (or both). In addition, smaller-scale waves (k ≥ 4) also show a larger contribution to tropical upwelling during the positive phase. Forcing by resolved synoptic-scale and gravity waves (Calvo et al. 2010) likely increases in the subtropical lower stratosphere during the positive phase; however, this issue needs more comprehensive analysis and understanding.
We thank John Albers, Seok-Woo Son, and Rolando Garcia for helpful discussions and comments on this idea and manuscript. We also thank three anonymous reviewers for their constructive comments. This work was partially supported under the NASA GNSS Remote Sensing and Aura Science Teams.
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