Effect of Tropical Waves on the Tropical Tropopause ... - AMS Journals

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Effect of Tropical Waves on the Tropical Tropopause Transition Layer Upwelling JUNG-HEE RYU* AND SUKYOUNG LEE Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania (Manuscript received 31 December 2009, in final form 13 May 2010) ABSTRACT An initial-value problem is employed with a GCM to investigate the role of the convectively driven Rossby and Kelvin waves for tropopause transition layer (TTL) upwelling in the tropics. The convective heating is mimicked with a prescribed heating field, and the Lagrangian upwelling is identified by examining the evolution of passive tracer fields whose initial distribution is identical to the initial heating field. This study shows that an overturning circulation, induced by the tropical Rossby waves, is capable of generating the TTL upwelling. Even when the heating is placed in the eastern Pacific, the TTL upwelling occurs only over the western tropical Pacific, indicating that the background flow plays a crucial role. The results from a Rossby wave source analysis suggest that a key feature of the background flow is the strong absolute vorticity gradient associated with the Asian subtropical jet. In addition, static stability is relatively weak over the western Pacific, suggesting that this may also contribute to the TTL upwelling in that region. The background flow also modulates the internal Kelvin waves in such a manner that the coldest region in the TTL (resembling the observed ‘‘cold trap’’) occurs over the western tropical Pacific. As a consequence, the upwelling air, induced by the meridional momentum flux of the Rossby wave, passes through the cold trap generated by the Kelvin wave. Since in reality the background flow is shaped by the convective heating, the climatological western tropical Pacific heating is ultimately responsible for both the TTL upwelling and the cold trap; however, both processes are realized indirectly through its impact on the background flow and the generation of the tropical waves.

1. Introduction The observed long-term variations of stratospheric water vapor and cooling in the lower stratosphere (Oltmans et al. 2000; Zhou et al. 2001; Rosenlof et al. 2001; Rosenlof and Reid 2008; Thompson and Solomon 2005; Randel et al. 2006) underscore the importance of tropopause transition layer (TTL) physical processes in the tropics. The TTL is a layer that has properties of both the troposphere and stratosphere (Highwood and Hoskins 1998; Folkins et al. 1999) and is defined as a layer between the typical level of convective outflow (;12 km) and the cold point tropopause at 16–17 km (Gettleman and Forster 2002). While it has been widely accepted that most of the water vapor in the stratosphere

* Current affiliation: Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado.

Corresponding author address: Jung-Hee Ryu, Department of Atmospheric and Oceanic Sciences, University of Colorado, UCB 311, Boulder, CO 80309–0311. E-mail: [email protected] DOI: 10.1175/2010JAS3434.1 Ó 2010 American Meteorological Society

is transported from the tropical troposphere through the TTL, the question of how this TTL transport occurs is still an unsettled problem. There are two main schools of hypotheses for this problem of TTL upwelling. One hypothesis is that convective overshooting brings air from the troposphere up to the cold point tropopause (CPT), which occurs at a height of about 17 km, where the temperature is a local minimum (e.g., Johnston and Solomon 1979; Danielsen 1982, 1993; Schmetz et al. 1997; Simpson et al. 1998; Sherwood and Dessler 2000, 2001). However, the low amount of overshooting convection, which accounts for only 1.5% of the total convective rain (Alcala and Dessler 2002), is a limitation of this mechanism. The other hypothesis is that the TTL transport is realized through slow, large-scale tropical upwelling (Brewer 1949; Newell and Gould-Stewart 1981; Folkins et al. 1999; Highwood and Hoskins 1998). Most previous studies of the large-scale ascent have attributed the tropical upwelling process to the influence of the surf zone ‘‘wave drag’’ [see the review by Holton et al. (1995) and references therein], where the upwelling comprises part of the global-scale circulation, known as the

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Brewer–Dobson circulation (Brewer 1949). Plumb and Eluszkiewicz (1999) suggested that the Hadley circulation may play an important role for the TTL upwelling, since their calculation revealed that the Brewer–Dobson circulation will not reach far enough into the deep tropics unless the wave drag occurs in uncharacteristically low latitudes. As an alternative to the mechanisms that involve either surf zone wave drag or the Hadley circulation, Boehm and Lee (2003) suggested that the tropical TTL upwelling can be generated as a response to poleward propagating Rossby waves that are driven by tropical convection. With an idealized general circulation model (GCM), they forced the zonal momentum equation with the tropical upper tropospheric eddy momentum flux convergence derived from the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) reanalysis dataset. [With the same dataset, Lee (1999) showed that the eddy momentum convergence in the tropical upper troposphere is associated with poleward propagating Rossby waves that are driven by tropical convection.] They found that the resulting overturning circulation produced TTL upwelling velocity that is reasonably close to that observed in the atmosphere. In an independent study, Norton (2006) attributed the ascent in his model’s tropical upper troposphere to horizontal eddy vorticity flux. His interpretation is as follows: convective outflow generates a Rossby wave (Sardeshmukh and Hoskins 1988), and the horizontal eddy vorticity flux associated with this wave induces divergent flow (i.e., a secondary circulation, which includes upwelling). Although quasigeostrophic (QG) theory is invalid in the tropics, to address this concern in a precise manner we borrow some concepts from QG theory. In QG theory, in response to momentum and/or heat sources (which include wave momentum and heat fluxes), to restore an O(1) balanced state, an overturning circulation must develop, and this overturning circulation can be described by the solution of the omega equation. In this interpretation, the local upwelling corresponds to that part of the O() response (within the QG framework) whose impact is to maintain an O(1) balanced state (Pedlosky 1987, section 3.12). From this perspective, the zonal mean upwelling represents the zonal mean of the local O() response, and the zonal mean solution of Boehm and Lee (2003) is equivalent to the zonal mean of the local upwelling described by Norton (2006). Accordingly, this Rossby wave–driven upwelling mechanism will be referred to as the Boehm– Lee–Norton (BLN) mechanism. In support of this mechanism, Randel et al. (2008) showed that upwelling across the tropical tropopause is forced by horizontal eddy

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momentum flux convergence associated with both equatorial planetary waves and waves originating from the extratropics. In addition to the Rossby waves, gravity waves have also been suggested as an agent for tropical TTL upwelling (Potter and Holton 1995). Indeed, as will be shown in this study, our initial-value calculations suggest that both the Rossby and Kelvin waves (the latter wave is a common type of gravity wave in the atmosphere) contribute to the TTL upwelling. In addition to the TTL upwelling itself, there is another related element known as the ‘‘cold trap,’’ the coldest region within the CPT, which occurs over the western tropical Pacific. Like the TTL upwelling, the formation process for the cold trap also remains an open question. In his seminal paper on the Brewer–Dobson circulation, Brewer (1949) proposed that the upwelling air is dried through condensation as it passes through the coldest region in the equatorial CPT. It was found later that the coldest region in the tropical upper troposphere– lower stratosphere (UTLS) occurs over the western Pacific, and this led to the stratospheric ‘‘water fountain’’ hypothesis (Newell and Gould-Stewart 1981). Trajectorybased studies have indeed demonstrated that tropical troposphere-to-stratosphere transport preferably occurs over the western Pacific (Fueglistaler et al. 2004; Ploeger et al. 2010) and that the majority of the trajectories pass through the coldest regions (Bonazzola and Haynes 2004). There are two main groups of hypotheses for the formation of the cold trap, one being turbulent entrainment of cold stratospheric air associated with convection (Sherwood et al. 2003; Kuang and Bretherton 2004), and the other being cooling associated with convectively forced Kelvin waves (Tsuda et al. 1994; Zhou and Holton 2002; Randel and Wu 2005). Ryu et al. (2008, hereafter RLS), using wave action conservation, further suggested that the strongest cooling occurs over the western Pacific because Kelvin waves are modulated by the background flow. Since the background flow is influenced by climatological convective heating, the RLS mechanism also ultimately arises from convection. Synthesizing the studies summarized above, a picture emerges whereby either of two ideas—one that hinges on the direct impact of convection, and the other that relies on convection-driven wave dynamics—is able to provide self-contained explanations for the formation of the TTL upwelling and the cold trap. For the former perspective, convective overshooting can carry moist air into the TTL, while the same convection, through smallscale turbulence entrainment, can also form the cold trap. In this manner, the cold trap can ideally situate itself where the upwelling is strongest. For the latter perspective, we hypothesize that an equally ideal situation

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can also arise because the convection simultaneously excites both Rossby and Kelvin waves. In this hypothesis, the Rossby waves, via the BLN mechanism, can drive the TTL upwelling, while the vertically propagating Kelvin waves, via the RLS mechanism of wave modulation, can generate the cold trap. In this manner, once again, the cold trap can position itself where upwelling takes place. In this study, we test the BLN and RLS mechanisms, using tracer transport calculations, to examine whether poleward propagating Rossby waves can force the tracer to rise through the TTL, and whether the bulk of this tracer enters the Kelvin-wave generated cold trap (hereafter referred to as the Kelvin-wave cold trap for brevity). A dry, global spectral model is used as our tool. In this model, a prescribed idealized heating field is used to represent the tropical convective heating, and a passive tracer is used to mimic the water vapor. Because neither convective overshooting nor turbulence entrainment is present, this model is suitable for testing the proposed hypotheses. Section 2 provides a description of the model and experimental design. The results from the tracer-transport calculations are presented in section 3. Section 4 examines mechanisms for the TTL upwelling, including the workings of the BLN mechanism. Section 5 addresses the question of whether the bulk of the upwelling tracer transits the Kelvin wave cold trap. The conclusions are presented in section 6.

2. Model and experiment design The calculations used for this study are identical to those of RLS, except that passive tracer transport is also calculated for this study. Therefore, the readers are referred to RLS for a more complete description of the model. For this study, we use the spectral dynamical core of the Geophysical Fluid Dynamic Laboratory (GFDL) global model (Gordon and Stern 1982). Two different basic states are used, the first one being the December–February (DJF) time-mean flow (hereafter called the 3D basic state) for the years 1948–96, derived from the NCEP–NCAR reanalysis dataset. The second basic state is the zonal mean of this DJF climatological flow (hereafter called the 2D basic state). For the run with the 3D basic state, a forcing term is added to ensure that the basic state is a solution to the model equations. Newtonian cooling is applied to the perturbation temperature, with time scales of 5 days and 20 days in the stratosphere and troposphere, respectively. An idealized heating profile is adopted to mimic convection heating in the tropics. The heating structure is identical to that used by RLS (see their Fig. 1 for the structure), except that the heating adopted for this study

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is stationary. The maximum heating rate is 4.8 K day21 at 400 hPa. We emphasize that the heating is zero above 175 hPa (;13 km). Therefore, the occurrence of upwelling above ;13 km is not a result of the direct response to the diabatic heating. Two tropical locations are chosen for the heating, one centered at 08, 1508E (hereafter called western Pacific heating) and the other at 08, 1208W (hereafter called eastern Pacific heating). The heat sources are gradually turned on during the first day and turned off during the tenth day of the integration. As stated in the introduction, a passive tracer is used to study the initial transient evolution of the model’s water vapor. A patch of the tracer is released initially, where the patch is collocated with the heating and also takes on the same distribution as that of the heating (again see the heating profile in Fig. 1 of RLS). Although the value of the tracer mixing ratio is arbitrary in this study, its initial value is specified to satisfy the condition that if the tracer were water vapor, then its value would correspond to the amount of water vapor necessary to produce the model’s prescribed condensational heating. The total tracer mixing ratio is conserved by using an adjustment process in which negative mixing ratio values, which are artificially generated by the spectral truncation, are set to zero by borrowing tracer values (water vapor) from neighboring grid points (Son and Lee 2005). For the vertical advection, a centered finite difference scheme is employed. To ensure a reasonable degree of accuracy, fine vertical resolution of about 90 m is used in the TTL region (Fig. 1b of RLS). In the rest of the paper, the response of the model atmosphere to the idealized heating is defined as a deviation from the basic state. One may question whether the transient wave response, which our model solution represents, is relevant for addressing how the climatological TTL upwelling and cold trap are formed. In our view, the climatological background flow can be understood as including both the response to the steady heating and also a time average of the transient response to transient heating. Although not shown in this study, the latter perspective is supported by daily outgoing longwave radiation (OLR) statistics (June 1974–January 2010) over the western tropical Pacific; the typical clearsky OLR is 240–300 W m22 (Ho et al. 1998), whereas our estimate of the OLR value corresponding to maximum cloudiness conditions is approximately 170 W m22. Since the 1-standard-deviation value of OLR over the western tropical Pacific is 75 W m22 (not shown), positive and negative 1-standard-deviation OLR values, respectively, correspond to typical clear-sky and maximum cloudiness conditions. This suggests that the warm pool region is not constantly covered by convective clouds; rather, even in the warm pool region, these OLR values

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suggest that the climatological cloudiness (and therefore climatological convective heating) is an average between periods of active convection and periods when convection is absent. Because a concrete test of this view would require a thorough analysis of the observed transient behavior of the convective heating and associated wave responses, it remains an open question as to whether a stationary response or a time average of a transient response is a better description of the relationship between the circulation and the heating.

3. Tropical wave and tracer transport responses a. Horizontal wave structure Before inspecting the time evolution of the tracer fields, we briefly examine the circulation response to the heating so as to place the tracer-field evolution in the context of the circulation response to the heating. Figure 1 shows the 14-km perturbation pressure and horizontal wind fields, both for the (left) 2D and (right) 3D basic states. For the 3D basic state, the heat source is placed in the western Pacific, centered at 08, 1508E. For both basic states, the day-4 response shows the hallmark of the Gill-type forced tropical wave response (Gill 1980), with an equatorially trapped Kelvin wave to the east and a pair of Rossby waves poleward and to the west of the heating. However, after day 8, the Rossby waves propagate poleward, especially in the Northern Hemisphere (NH). Because the heating is symmetric about the equator, this asymmetry between the NH and the Southern Hemisphere (SH) responses is due to hemispheric differences in the background flow. At day 10 and onward, after the heating is turned off, the unforced Kelvin wave starts to propagate rapidly to the east, while the Rossby waves continue to propagate poleward and eastward, followed by a equatorward reflection at high latitudes. This Rossby wave behavior deviates from the Gill response, which is strictly valid for a steady linear response in a resting background state, but it conforms to the results obtained by Jin and Hoskins (1995).

b. Tracer evolution: Western Pacific heating The equatorial cross sections of the tracer fields are shown in Figs. 2 and 3 for the 2D and 3D basic states, respectively. The passive tracer remains trapped within the troposphere for the 2D basic state, while for the 3D basic state it gradually rises through the TTL, crossing the tropopause (thick solid line) by day 12. Because the convective heating is confined to levels below 175 hPa, and also because convective overshooting is absent in this model, the upwelling is not a direct response to the heating, nor is it due to convective overshooting. Moreover, because the upwelling tracer crosses the isentropic

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surfaces, the rising motion cannot be explained by adiabatic wave motions. Instead, these characteristics are consistent with the BLN mechanism where the upwelling is a manifestation of a forced overturning circulation driven by Rossby wave momentum flux divergence. This wave momentum flux divergence field will be examined in the next section. The 3D case also shows the formation of a shallow cold layer (a negative temperature perturbation) in the upper part of the TTL, directly above the heating. As was analyzed in RLS, this cold layer comprises part of the vertically propagating Kelvin wave excited by the heating. RLS also showed that the Kelvin wave may attain its largest amplitude in this region because the wave is modulated by the zonal and vertical variations in the background state. It can be seen that the bulk of the upwelling tracer transits through this cold layer, supporting the hypothesis described in the introduction that both the upwelling and the cold trap may arise from waves excited by the heating. This picture also suggests that the occurrence of conjoined TTL upwelling and the cold trap is not a coincidence. Figure 3 also shows that by day 16, the tracer makes its appearance over the eastern Pacific, below 15-km level. The horizontal distribution of the tracer field (Fig. 4) shows that while the tracer rises through the TTL, it is also transported horizontally. Following the anticyclonic circulation of the Rossby wave pair, the tracer is first transported toward the extratropics over the western Pacific (day 8) and then back to the tropics in the eastern Pacific (days 12, 16, and 20). This tracer-field evolution resembles the adiabatic back trajectory pattern calculated by Pfister et al. (2001), who studied the origin of the moist air parcels that are necessary for the formation of the cirrus clouds observed over the central Pacific. Because their back trajectory was calculated along the 380-K isentropic surface, the distribution of the tracer at a constant height level (i.e., 17 km in this case) may not be directly compared with their result. During the NH winter, between 108S and 108N, the 380-K isentropic surface lies at a level close to 17 km. However, because the isentropic surface descends with latitude, northward (southward) of 208N (208S) the tracer is absent at the 17-km level (right column) but can instead be seen at the 14-km level (left column). The absence of TTL upwelling over the central Pacific (1808–1408W) in Fig. 3 further supports the impression that it is the horizontal transport from the western Pacific that is responsible for the increase in the tracer mixing ratio over the central Pacific (see day 20 of Fig. 4).

c. Tracer distributions: Eastern Pacific heating The finding that the TTL upwelling occurs in the 3D basic state but not in the 2D basic state implies that the background state plays an important role for generating

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FIG. 1. Perturbation pressure and horizontal wind fields at the 14-km level, for the (left) zonally symmetric basic state and (right) 3D western Pacific heating case. The contour interval is 25 Pa. The shaded area indicates the location of the heat source.

the upwelling. This result also suggests that the occurrence of the western Pacific TTL upwelling may not necessarily be due to the proximity of the convection but is rather due to the background flow, an indirect effect

of the convection. This possibility can be addressed by placing the convective heating elsewhere in the tropics (e.g., in the eastern Pacific). Figure 5 shows the horizontal response of the tropical waves to the eastern Pacific heat

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FIG. 2. Longitude–height cross section of the perturbation temperature (contours), wind vectors (arrows), and tracer mixing ratio (g kg21; shading) for the zonally symmetric basic state. The gray contours with labels indicate potential temperature and the thick solid horizontal line represents the tropopause. The contour interval is 0.3 K. The vertical wind is multiplied by 2.0 3 103 so that the slope of the wind vectors is consistent with the aspect ratio of the figure. All variables are averaged between 28N and 28S.

source. While this integration employed the 3D basic state, the Rossby wave signal to the west of the heat source more closely resembles that for the 2D basic state (see Fig. 1) than that for the 3D western Pacific heat source. In both cases (the 2D basic state and the 3D

eastern Pacific heat source cases), the two anticyclonic circulations form closer to the equator than those in the western Pacific case. Again similar to the 2D basic-state case, the vertical cross sections of the tracer (Fig. 6) exhibit no evidence of

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FIG. 3. As in Fig. 2, but for the 3D western Pacific heating case.

upward TTL transport over the eastern Pacific where the heat source was placed. Most of the tracer is trapped below 13 km over the eastern Pacific where it was released. However, by day 16, an upward transport starts to occur over the western Pacific. During the same time

period, between days 4 and 16, Fig. 5 shows that the tropical Rossby waves propagate from the eastern Pacific to the western Pacific. Over the western Pacific, the Rossby waves are displaced more poleward than they were over the eastern Pacific. This poleward displacement

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FIG. 4. The horizontal distribution of the tracer mixing ratio (g kg21) and horizontal wind vectors (arrows) at the (left) 14-km and (right) 17-km levels for the 3D western Pacific heating case. The contour interval is 0.2 g kg21. At right, two additional contour levels, 0.05 and 0.1 g kg21, are included.

somewhat resembles the response seen for the western Pacific case (right column in Fig. 1). These results, taken together, suggest that the western Pacific upwelling may hinge on Rossby waves taking on the particular structure, more clearly shown in Fig. 1, where the waves tilt so as to transport westerly momentum toward the equatorial

region. This again supports the BLN mechanism. As such, in the next section, we will examine the momentum flux convergence of the simulated Rossby waves and discern whether the flux divergence and vertical motion fields are consistent with the picture predicted by BLN (see Fig. 1 of Boehm and Lee 2003).

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4. Mechanisms for the TTL upwelling a. Rossby wave driving

FIG. 5. As in Fig. 1, but for the 3D eastern Pacific heating case. A box is drawn over the westward-propagating Rossby wave in the NH.

As was motivated in the previous sections, we examine here whether the simulated TTL upwelling is consistent with the BLN mechanism. Figure 7 shows the vertical cross section of the anomalous meridional convergence of the eddy zonal momentum flux, 2[›(u* y*)/ ›y 2 ›(u0*y 0*)/›y], averaged zonally between 1208E and 1808, where the asterisk denotes the deviation from the zonal mean and zero in the subscript denotes the basic state. This zonal interval is chosen because it covers approximately one wavelength of the Rossby wave over the western Pacific and also because the bulk of the passive tracer was released over this region (see Fig. 3). As was expected from the horizontal structure of the Rossby waves (northwest–southeast tilt in the NH and northeast–southwest tilt in the SH), when the heating is turned on (prior to day 10) there is a region of eddy momentum flux convergence between approximately 10 and 18 km. This convergence region is flanked by two centers of divergence, with the NH center being more pronounced. After the heating is turned off, during the period between days 8 and 12, the SH divergence center disappears, while the remaining pair of equatorial convergence and NH divergence moves northward and weakens. This northward shift is consistent with the poleward Rossby wave propagation shown by Fig. 1. Because an overturning circulation can also be driven by other eddy fluxes, namely the vertical convergence of zonal momentum and the meridional convergence of heat (KerrMunslow and Norton 2006), the impact of these fluxes were also examined. However, these fluxes are found to play a minor role in our calculation (not shown). To examine the relationship between 2[›(u*y*)/›y 2 ›(u0*y 0*)/›y] and the TTL upwelling, perturbation vertical velocity fields, averaged over the same zonal interval, are shown in the right column of Fig. 7. For the first 10 days, when the heating is turned on, the perturbation vertical velocity is defined as the total response on that day minus the day-3 response. By day 3, the total vertical velocity, averaged over the western Pacific region, is observed to asymptote to a constant value. The day-3 response is thus subtracted so as to isolate the vertical velocity field driven by the wave momentum flux. Beyond day 10, after the heating is turned off, the perturbation vertical velocity is defined as the total response on that day minus the basic state. The perturbation vertical velocity fields between days 3 and 12 are consistent with the expected thermal wind adjustment driven by the corresponding eddy momentum flux convergence fields, with rising (sinking) motion above (below) the level of maximum flux convergence, conforming to the BLN mechanism. For

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FIG. 6. As in Fig. 2, but for the 3D eastern Pacific heating case only.

example, at day 8, equatorial upwelling (downwelling) occurs above (below) the 13-km level, the equatorial center of the eddy momentum flux convergence. However, on days 16 and 20, the perturbation vertical velocity

fields do not entirely match with the BLN mechanism. This is because the eddy momentum flux convergence decreases significantly from day 12 to 16, yet the TTL upwelling becomes stronger at day 16. Instead, the wind

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FIG. 7. Zonally averaged (between 1208E and 1808) meridional convergence of the (left) eddy momentum flux, 2[›(u*y*)/›y 2 ›(u*0 y*)/›y], and (right) perturbation vertical velocity for the western 0 Pacific heating case. The contour intervals are (left) 1025 m s22 and (right) 50 m day21. In the right column, shading indicates basic-state static stability (1024 s22), averaged between 1208E and 1808.

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vectors shown in Figs. 1 and 3 suggest that the Kelvin wave, which reenters the western Pacific region, may also contribute to this upwelling. For the case of the eastern Pacific heating, the perturbation vertical motion is characterized by a muted TTL response and a relatively strong response below the TTL. As will be described below, it appears that these characteristics are attributable both to a stronger TTL static stability and to a more complex eddy flux structure than the western Pacific case. The basic-state static stability field, shown with shading in the right columns in Figs. 7 and 8, exhibits a stark contrast in the TTL region between the western and eastern Pacific, with the former being much weaker than the latter. For example, the basic-state static stability between 13 and 15 km (the lower TTL region just above the heat source) is about 5 3 1025 to 1 3 1024 s22 over the western Pacific, while it is as high as 1 3 1024 to 2 3 1024 s22 over the eastern Pacific. In the eastern Pacific, the weakest static stability occurs between ;8 and ;12 km, below the TTL. Accordingly, the vertical motion is also confined to this layer and is very weak in the TTL. Except at day 4, sinking motion prevails at the equator. On day 12, in particular, strong equatorial sinking motion develops below the level of maximum convergence. This again conforms to the expectation based on thermal wind adjustment. However, above the level of maximum convergence, the expected upward motion is absent, again presumably due to the large static stability in that region (see Fig. 8). The analysis presented in this section suggests that the presence of the TTL upwelling in the western Pacific can be ascribed both to a weak static stability in that region and to the eddy momentum flux convergence field taking on a favorable structure. Conversely, the lack of TTL upwelling for the eastern Pacific heating case can be attributed to the absence of these two features. In the next subsection, by comparing the Rossby wave response in the western and eastern Pacific, we will address the question of why the eddy momentum flux takes on its particular spatial structure.

b. Rossby wave source Figure 9 shows the barotropic and baroclinic components of the response for the (left) western and (right) eastern Pacific heating cases, where the barotropic and baroclinic components of a field F are respectively defined as F barotropic 5 ½[F (200 hPa) 1 F (850 hPa)] and F baroclinic 5 ½[F (200 hPa) F (850 hPa)]. In both cases, the baroclinic flow is composed of equatorially trapped Rossby and Kelvin waves, the hallmark of the Gill-type near-field response. In contrast, the barotropic component of the Rossby waves, shown in Fig. 9, freely

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propagates into the extratropics, generating a far-field response. As discussed earlier, it is these meridionally propagating Rossby waves that generate the eddy momentum flux convergence in the tropics, which in turn spawn the TTL rising motion. Therefore, in the rest of this subsection, the analysis will be focused on the upper troposphere, which dominates the barotropic component of the response. Because the Rossby wave response can be interpreted using the concept of the Rossby wave source (RWS) formulated by Sardeshmukh and Hoskins (1988), we next examine the RWS fields generated by the heating. The Rossby wave source is defined as 2$ (Vx z), where z is the absolute vorticity and Vx is the irrotational (divergent) wind. The Rossby wave source can be partitioned into tropical and extratropical components (Qin and Robinson 1993), 2Vx $z and 2z$ Vx, respectively. The tropical component of the perturbation RWS is shown in Figs. 10a and 10b for the western and eastern Pacific heating cases, respectively. Here, the perturbation RWS is defined as the deviation from the climatological RWS and thus represents the RWS associated with the imposed heating (Jin and Hoskins 1995). The extratropical component is not shown because this component is weak in the tropics and also because it often reflects the Rossby wave response itself, rather than the source. The tropical RWS provides insight as to why the equatorial eddy momentum flux convergence is large in the western Pacific but not in the eastern Pacific. It can be seen that there is a strong anticyclonic RWS center at 308N, 1208E, and a secondary anticyclonic center near 58N, 1508E. The barotropic response (Fig. 9a) is consistent with this RWS field, with an anticyclonic circulation centered at 308N, 1208E, and a hint of a weak anticyclonic circulation centered at 58N, 1508E. Figure 9a shows a cyclonic circulation that forms to the south of the first anticyclone and to the west of the second anticyclone. The generation of this cyclonic circulation is consistent with Rossby wave dispersion that would result from these two centers of negative RWS. Because this cyclone is associated with the equatorial westerly patch over the western Pacific, it can be inferred that the eddy momentum flux convergence into the equatorial region is carried out by this cyclonic circulation and that this cyclone in turn owes its existence to the two centers of negative RWS. Over the eastern Pacific (Fig. 10b), there is a single negative RWS center spanning the latitude belt between the equator and 308. This RWS thus generates equatorial easterlies, as can be seen in Fig. 9b. It is worth noting that the Kelvin wave generates a patch of equatorial westerlies between 908 and 608W. In principle, this westerly pulse can also generate TTL upwelling,

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FIG. 8. As in Fig. 7, but for the eastern Pacific heating case. All variables are averaged over the longitudes between 1508 and 908W.

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FIG. 9. The day-4 (top) barotropic and (bottom) baroclinic perturbation geopotential (contours) and the horizontal wind vectors (arrows) for the (left) western and (right) eastern Pacific heating cases. The contour interval is 20 m2 s22.

but such upwelling is absent, presumably because the static stability in this part of the equatorial region is too strong. In interpreting the wave field (Fig. 9), however, it is important to recall that the perturbation eddy momentum flux convergence (Figs. 7 and 8) includes interactions between the background and perturbation eddy fields. 5 2›(u*y*9)/›y 2 That is, 2[›(u*y*)/›y 2 ›(u*y 0 *)/›y] 0 0 2 ›(u*9y*9)/›y. The momentum flux inferred ›(u*9y *)/›y 0 from Fig. 9 only represents the 2[›(u*9y*9)/›y] contribution to the full perturbation flux. Although not shown for the western Pacific heating case, the back2 ground–perturbation interaction terms, 2›(u*y*9)/›y 0 contribute significantly to the perturbation ›(u*9y *)/›y, 0 eddy momentum flux convergence, and their structure closely resembles the 2›(u*9y*9)/›y term. The above RWS analysis indicates that the latitude of the RWS plays an important role in ultimately generating the equatorial eddy momentum flux convergence over the western Pacific. Figure 10c displays V9x (vectors)

and z0 (contours). As was shown by Qin and Robinson (1993), because the resulting advection term, 2V9x $z0, dominates the tropical RWS field, other fields are not shown. It can be seen from Fig. 10c that the western Pacific heating generates a RWS center at 308N, 1208E because the meridional gradient of z0 is large at 308N. This large absolute vorticity gradient is associated with the strong subtropical jet, which in large part is driven by climatological western Pacific heating. In comparison, the absolute vorticity gradient over the eastern Pacific is weaker and spread evenly throughout the tropics and subtropics. The eastern Pacific RWS (Fig. 10b) is consistent with this z0 field. The analyses in this subsection collectively suggest that the occurrence of eddy momentum flux convergence can ultimately be attributed to the strong climatological heating in the western Pacific, since the resulting climatological subtropical jet determines the latitudinal position of the RWS. Likewise, it can be inferred that the lack of eddy momentum flux convergence over the

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FIG. 10. (a),(b) The 200-hPa perturbation tropical RWS (10211 s22) at day 4 from the (a) western and (b) eastern Pacific heating cases. (c),(d) The day-4 climatological mean absolute vorticity (1025 s21, contours) and the perturbation divergent wind (m s21, arrow) for the (c) western and (d) eastern Pacific heating cases.

eastern Pacific can be ultimately ascribed to the weak climatological heating in that region.

5. Role of tropical waves for the stratospheric water fountain In this section, we test the hypothesis that the upwelling tracer, examined in earlier sections, passes through the Kelvin wave cold trap that occurs at the CPT. Figure 11 displays latitude–height cross sections of the tracer and perturbation temperature fields, averaged over the longitudes between 1208E and 1808. For the western Pacific heating case (left column of Fig. 11), longitude–height cross sections were also shown (Fig. 3) where it was noted that the path of the upwelling tracer intersects with the Kelvin wave cold trap. The time evolution of the tracer field, shown in the left column of Fig. 11, reveals that the upwelling tracer (forced by the Rossby wave momentum flux), as it continues to ascend, enters the cold trap between days 16 and 20. These figures also show that once the tracer reaches the cold trap, it is transported poleward and

downward, following the isentropes. If this tracer was water vapor, enhanced dehydration would be expected to occur as it passes through this cold region. [Although the minimum temperature perturbation is 21.2 K (see day 16), Fig. 3 shows that the minimum can be as low as 22.0 K.] As such, the poleward and downward air that enters the extratropics is expected to be drier than the upwelling air in the tropics. Although this model calculation utilized an idealized setting, the above conjoined feature between the tracer and the cold pocket is reminiscent of the satellite observations shown in Fig. 6 of Randel et al. (2001). In addition, at days 16 and 20, it can also be seen that a thin layer of tracer forms between 17 and 18 km. Such a layer, if it also forms in the atmosphere, may help explain the formation of the observed thin cirrus clouds (Wang et al. 1996; Pfister et al. 2001). It was suggested in the previous sections that the presence (absence) of TTL upwelling in the western (eastern) Pacific can be ascribed to the western Pacific background state having favorite characteristics in terms of both the static stability and the RWS. To further test this

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FIG. 11. Latitude–height cross section of the perturbation temperature (contours), wind vectors (arrows), and tracer mixing ratio (shading) for (left) the western Pacific heating case and (right) the case in which the heating is placed in the eastern Pacific, but the initial tracer distribution is zonally uniform. The contour interval for temperature is 0.3 K. The vertical wind is multiplied by 1.5 3 103 so that the slope of the wind vectors is consistent with the aspect ratio of the figure. The thick solid contours indicate potential temperature (K). All variables are averaged between 1208E and 1808.

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possibility, an additional experiment was performed wherein the heating was placed in the eastern Pacific but the initial tracer mixing ratio was set to be zonally uniform between 58S and 58N. The result is presented in the right column of Fig. 11. During the first 10 days, while the heating was turned on, there is no evidence of TTL upwelling (not shown in Fig. 11, but this can be expected from the day-4 and day-8 snapshots in Fig. 6). However, by day 12, upward transport starts to occur (see also the wind vectors). The subsequent tracer evolution on days 16 and 20 resembles that of the western Pacific case. This result once again underscores the earlier impression that the prevalence of TTL upwelling is not necessarily due to direct effect of the convection but rather to the properties of the background state over the region. To the extent that the CPT cold trap can be ascribed to the Kelvin wave, as was analyzed by RLS, the same conclusion can be drawn for the formation of the cold trap.

6. Conclusions The impact of convectively driven Rossby and Kelvin waves is investigated with an idealized global general circulation model. With the DJF climatological flow as the basic state, TTL upwelling is found to occur over the western tropical Pacific. The upwelling is stronger and penetrates to a higher altitude when the heating is placed in the western Pacific, but substantial western Pacific TTL upwelling still occurs even when the heating is placed in the eastern Pacific. In the latter experiment, in spite of the proximity to the heating, TTL upwelling does not occur over the eastern Pacific. TTL rising motion is also absent in a run where the zonally averaged DJF climatological flow is used as the basic state. These results imply that the background state plays an important role for the occurrence of western Pacific TTL upwelling. We identify two properties of the background state that are important for this upwelling. First, the TTL static stability over the western Pacific is much weaker than that over the eastern Pacific. Second, the results from a Rossby wave source analysis suggest that the occurrence of eddy momentum flux convergence, which drives the TTL upwelling in our calculation, hinges on the strong absolute vorticity gradient associated with the Asian subtropical jet. Because both of these properties can be ascribed to the climatological convective heating over the western tropical Pacific, it can be concluded that the western tropical Pacific heating is ultimately responsible for the TTL upwelling, but that it is realized indirectly through its impact on the background flow and the convectively driven Rossby waves. The analysis presented in this study supports the BLN hypothesis

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FIG. 12. A schematic of the convective heating, polewardpropagating Rossby wave (wavy arrows), TTL upwelling (thick arrow), and cold trap (shading) associated with the vertically propagating Kelvin wave. The letter ‘‘W’’ indicates westerly eddy momentum flux convergence, and the dashed ovals with arrows indicate the secondary circulation driven by the westerly momentum source. A similar schematic was shown by Boehm and Lee (2003), but their picture did not include the Kelvin wave cold trap.

that the TTL upwelling is part of a forced overturning circulation driven by Rossby wave momentum flux convergence. However, calculations in this study also raise the possibility that vertically propagating Kelvin wave may also contribute to the TTL upwelling. As was proposed by RLS, the background flow modulates the internal Kelvin waves in a manner that results in the coldest part of the Kelvin wave occurring at the CPT over the western tropical Pacific. Accordingly, the upwelling air, induced by the Rossby wave flux, passes through the Kelvin wave ‘‘cold trap.’’ These results are summarized schematically in Fig. 12, which illustrates that the convective heating drives both Rossby and Kelvin waves, the Rossby wave then drives the TTL upwelling, and finally the upwelling air enters the Kelvin wave cold trap. This air subsequently exits toward the extratropics along isentropic surfaces. This picture provides a self-consistent mechanism for both the stratospheric water fountain and the freeze drying (Newell and Gould-Stewart 1981). Our mechanism may also offer an explanation for the observed trend of tropical stratospheric cooling1 (Rosenlof and Reid 2008; Thompson and Solomon

1 Recently, Lanzante (2009) showed that the tropical lower stratospheric cooling during the last decade (1995–2005), as shown by Rosenlof and Reid (2008), is an artifact of the radiosonde instrument change. However, the adjusted temperature record, while weaker, still reveals a long-term cooling trend in the lower stratosphere.

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2005). Rosenlof and Reid (2008) provided evidence that the tropical stratospheric cooling is highly correlated with an increase in the sea surface temperature (SST). Because convective heating is expected to strengthen in response to a rising SST, the resulting tropical waves are likely to attain larger amplitudes. According to our mechanism, the intensified waves in turn would strengthen the TTL upwelling and the CPT cooling. Consistent with this expectation, Deckert and Dameris (2008) showed with a model that higher tropical SSTs strengthen TTL upwelling via upward propagating quasistationary waves generated by deep convection. This possibility can be tested, but doing so is beyond the scope of this study. Although this study presents a coherent mechanism for the TTL upwelling and the generation of the cold trap, the fact that this mechanism hinges on a particular background flow calls for additional discussion. If the transient wave response shown here is indeed prevalent in the tropics because the background state is the climatology of a reanalysis dataset, the key climatological features may reflect the aggregate effect of the convectively driven waves themselves. For example, the difference in the static stability between the western and the eastern Pacific may be, at least in part, caused by the convectively driven waves. Wirth (2004) and Wirth and Szabo (2007) have shown that vertical velocity divergence (convergence) reduces (enhances) the local static stability. Therefore, in the western Pacific UTLS region where upward motion increases with height (Fig. 7), this wavedriven motion itself may contribute to the low value of the climatological static stability. Although not shown, our calculation indeed indicates a slight decline in the static stability associated with the divergence of the upward motion. As such, at least in part, the background flow itself is forced by the convectively driven waves. An examination of the transient evolution in the reanalysis data may shed further light onto this potential caveat of the mechanism proposed in this study. Acknowledgments. This study was supported by the National Science Foundation under Grant ATM-0647776. The authors acknowledge valuable comments from anonymous reviewers and Steven Feldstein. We also acknowledge Seok-Woo Son for the transport code used in this study. REFERENCES Alcala, C. M., and A. E. Dessler, 2002: Observations of deep convection in the tropics using the Tropical Rainfall Measuring Mission (TRMM) precipitation radar. J. Geophys. Res., 107, 4792, doi:10.1029/2002JD002457. Boehm, M., and S. Lee, 2003: The implications of tropical Rossby waves for tropical tropopause cirrus formation and for the

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