We start with a very brief review of tropopause theories, for a better understanding of the results presented below. The formation and maintenance mechanisms of pt and Tt are relatively well understood. The climatological pt and Tt in the tropics are, to a first order, determined by radiative and convective processes [Manabe and Strickler, 1964; Held, 1982]. In the extratropics, baroclinic eddies largely set the climatological pt and Tt [Held, 1982; Lindzen, 1993; Schneider, 2004]. Both the tropical and extratropical tropopause properties are also modified by stratospheric processes such as the Brewer-Dobson circulation and the polar vortices [Gabriel et al., 1999; Kirk-Davidoff and Lindzen, 2000; Thuburn and Craig, 2000; Birner, 2010b]. It is also known that short-term variability of pt and Tt is primarily controlled by organized deep convection and equatorial waves in the tropics [Randel et al., 2003; Son and Lee, 2007; Ryu et al., 2008] and baroclinic eddies in the extratropics [Zängl and Wirth, 2002; Son et al., 2007].
 The sharpness of the tropopause, Nt2, is a relatively new subject. It has been often examined in the context of the TIL, whose strength (NLS2) is qualitatively similar to Nt2 in both space and time. Observational studies have shown that TIL is sharp in the tropics year-round [Grise et al., 2010] and in the extratropics during the summer [Birner, 2006; Randel et al., 2007a; Grise et al., 2010]. Different theories have been proposed for the formation of the extratropical TIL. Using potential vorticity inversion, Wirth  has attributed the midlatitude TIL to synoptic-scale weather systems. He has shown that a sharp temperature inversion forms right above the tropopause at the center of anticyclonic vortices, resulting in strong NLS2. Although cyclonic vortices do not produce strong NLS2, the composite of anticyclonic and cyclonic vortices still shows a distinct NLS2 due to significantly strong NLS2 in association with anticyclonic vortices. This argument has subsequently been confirmed by Son and Polvani  from simple general circulation model integrations, and by Randel et al. [2007a] from observations. Birner [2010b] proposed that the midlatitude TIL is also affected by the stratospheric circulation. He showed that adiabatic warming in the descending branch of the Brewer-Dobson circulation could enhance the temperature inversion in the LS, strengthening NLS2 in the midlatitudes. In addition to dynamical considerations, Randel et al. [2007a], Kunz et al. , and Randel and Wu  have proposed that strong Nt2 in the summer hemisphere high latitudes could result from radiative processes in the UTLS. Observations show a substantial amount of water vapor near the polar tropopause in the summer hemisphere [e.g., Randel and Wu, 2010]. The resulting radiative cooling at the tropopause level can generate a sharp temperature inversion layer in the LS (high NLS2). This radiative process has recently been confirmed by climate model simulations [Birner, 2010b].
 With the above theoretical background in hand, we next examine the spatiotemporal structure of the global tropopause. The climatology, seasonal cycle and intraseasonal variability of three tropopause properties (pt, Tt, and Nt2) are described in detail.
 The climatology of each tropopause property is presented in Figures 2a–2c. In general, the overall structure is qualitatively similar to the one obtained from CHAMP [e.g., Schmidt et al., 2005; Grise et al., 2010] and reanalysis data [e.g., Hoerling et al., 1991; Hoinka, 1998, 1999]. To ensure the capability of COSMIC observations in tropopause detection, pt and Tt shown in Figures 2a and 2b are quantitatively compared with radiosonde observations. The climatological differences in pt and Tt between COSMIC and radiosonde observations are illustrated in Figure 3. They are computed by simply subtracting climatological pt and Tt of radiosonde observations from those of COSMIC measurements at the nearest grid point. In other words, pointwise radiosonde observations are compared with area-integrated (5° × 5°) COSMIC observations. It is found that the difference is reasonably small in most areas, typically less than a few percent of the climatological value. The seasonal mean and intraseasonal variability also exhibit reasonably small and unorganized differences (not shown). Nonnegligible biases are, however, found around at 30–40° in both hemispheres. These regions largely coincide with the regions where tropopause properties change abruptly with latitude (see Figures 2a–2c), suggesting that higher spatial resolution is needed there. Although significant differences are also found near the South Pole, these are likely caused by sampling error. As shown in Figure 1, only a limited number of soundings are available at the pole.
Figure 2. Annual mean (a) tropopause pressure pt, (b) temperature Tt, and (c) sharpness Nt2 derived from COSMIC observations. The shading interval is 8.3 hPa for pt, 1.2 K for Tt, and 0.09 × 10−4 s−2 for Nt2. Background flow derived from NNR data is also shown: (d) 300 hPa zonal wind (contours, with 25 m s−1 contour thick) and standard deviation of 300 hPa meridional wind (shaded only for local maxima) and (e) 500 hPa geopotential height deviated from the zonal mean (contours) and NOAA OLR (shaded only for local minima).
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 Returning to Figure 2, it can be seen that the climatological pt reaches its minimum (∼80 hPa) over the equator and stays homogeneous in latitude within ∼20° of the equator. It sharply increases around 35°, settling to values of ∼250–300 hPa in the extratropics. A qualitatively similar structure is also evident in Tt (Figure 2b). In contrast to pt and Tt, Nt2 shows a very different structure (Figure 2c): although it is inversely correlated with Tt in the tropics (i.e., cooling at the tropopause level would increase γUT but decrease γLS, resulting in stronger Nt2 (equation (1)), there is essentially no correlation in the extratropics. This result suggests that extratropical Nt2 may be driven by mechanisms different from those maintaining pt and Tt. We discuss this in section 3.2.
 The latitudinal distribution of tropopause properties exhibits an abrupt transition across the subtropical jet (see the subtropical wind speed maxima in Figure 2d). This can be attributed to the occurrence of a double tropopause in this region. Randel et al. [2007b], among others, have shown that in the subtropics a double tropopause is often present, i.e., a high (or tropical) tropopause height aligned with the top of the subtropical jet and a low (or extratropical) tropopause height aligned with its bottom. The tropical tropopause is often detectable up to 40–50°, whereas the extratropical tropopause starts to appear around 30°. As described in section 2.2, the WMO  definition of the tropopause captures only the first, or lowest, tropopause. Hence, pt changes abruptly at the lowest latitude where the extratropical tropopause appears.
 The subtropical transition however occurs at different latitudes for each tropopause property. For instance, the maximum Tt gradient is found about 5–10° equatorward of the maximum pt gradient (compare Figures 2a and 2b). This difference results from the temperature distribution in the UTLS. Figure 4a illustrates the zonal mean temperature and its latitudinal gradient from the COSMIC observations. The maximum temperature gradient is found on the poleward side of the tropical cold point at ∼35°. This is the latitude where the maximum pt gradient is also found (Figure 4b). Along the tropopause, however, the temperature gradient rapidly decreases as pt increases with latitude. Thus, the maximum Tt gradient is slightly equatorward of the maximum pt gradient (Figure 4b). Unlike pt and Tt, Nt2 shows a transition at a much lower latitude with minimum Nt2 at 25–40° in both hemispheres (Figure 2c). These subtropical minima are collocated with the subtropical jet [see also Grise et al., 2010], and likely caused by the fact that the tropopause is not well defined in this region and temperature keeps decreasing with height across the tropopause (e.g., Figure 4a).
Figure 4. (a) Annual mean zonal mean temperature (contours) and its latitudinal gradient (shading) and (b) latitudinal gradient of pt (solid line) and Tt (dashed line) derived from COSMIC observations. The thick line in Figure 4a denotes the climatological tropopause pressure.
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 Figures 2a–2c also show that the latitudinal distribution of tropopause properties is not symmetric about the equator. In fact, a strong hemispheric difference is present in the extratropics. Unlike in the Northern Hemisphere (NH), all tropopause properties in the Southern Hemisphere (SH) decrease from the midlatitudes (∼45°S) to the South Pole. As discussed by Zängl and Hoinka , this is largely caused by the stratospheric polar vortex which is colder in the SH than in the NH.
 Next we consider the longitudinal structure of tropopause properties. Figures 2a–2c show that all three tropopause properties are largely symmetric in the zonal direction. A considerable asymmetry is found only in the deep tropics and in the NH extratropics. In the tropics, all tropopause properties show extrema in three regions. These regions largely coincide with the regions of strong convection (shading in Figure 2e), and suggest that the spatial distribution of the tropical tropopause is significantly influenced by localized deep convection and related UTLS processes [Highwood and Hoskins, 1998; Seidel et al., 2001]. In the NH extratropics, pt exhibits maxima around 70°W and 150°E. These two local maxima reflect an influence of stationary waves (Figure 2e). For instance the maximum pt over northeastern Canada and western Greenland is collocated with a negative geopotential height anomaly at 500 hPa.
 It is noteworthy that while the spatial distribution of Tt is qualitatively similar to that of pt in the NH, the regions of maximum Tt are more zonally elongated over the northeastern Pacific and North Atlantic. This elongation is partly due to the storm tracks. Son et al.  have shown that transient eddies tend to increase Tt on the poleward side of the storm track. Consistent with their findings, the regions of maximum Tt are located on the poleward side of the storm tracks (shading in Figure 2d). No storm track signal is, however, found in the annual mean NH Nt2 (Figure 2c). This does not imply that Nt2 is insensitive to storm track eddies: in fact, it simply results from the strong cancellation between warm and cold seasons, as shown in section 3.2.
3.2. Seasonal Cycle
 Figure 5 presents the seasonal mean tropopause properties during DJF and JJA. They are again quite similar to the ones derived from the coarser resolution GPS RO observations [e.g., Schmidt et al., 2005] but show much richer structure. Since pt and Tt share qualitatively similar features, we first discuss them. The characteristics of Nt2 are then discussed separately.
 The tropical pt and Tt exhibit a relatively weak seasonality (Figures 5a, 5b, 5d, and 5e). Maximum differences between DJF and JJA are only about 10 hPa in pt and 10 K in Tt, much smaller than those in the extratropics. But the tropics still show a clear seasonal contrast: the nonzonal feature in the boreal winter disappears in the summer. This indicates that the longitudinal structure evident in the climatological tropopause properties (Figures 2a and 2b) is mostly due to boreal winter conditions. Convection alone does not appear to account for this behavior. Climatological OLR exhibits localized maxima over Africa, Southeast Asia and Central America year round, but the tropopause properties show little sensitivity to this in JJA. Even in DJF, the locations of deep convection and the minima of Tt and pt do not match exactly: the pt and Tt minima are located at the equator although OLR minima are located around 10°S. This suggests that the tropical tropopause is not solely controlled by localized deep convection. Other processes, such as convectively driven waves, may also play a role in setting the tropical tropopause [Highwood and Hoskins, 1998].
 In the extratropics, tropopause properties show a significant zonal asymmetry in NH DJF. This nonzonal structure is largely due to the stationary waves and storm track activity (Figures 5a–5c), and essentially disappears during JJA (Figures 5d–5f). This again indicates that the longitudinal structure of the climatological tropopause properties, shown in Figures 2a and 2b, results largely from boreal winter conditions. From this, one may expect that the seasonal cycle of the extratropical tropopause is primarily controlled by stationary waves and the storm tracks. While this is partly true in the midlatitudes, it appears not to be the case in the high latitudes. For instance, the high-latitude Tt is lower than the midlatitude Tt in cold seasons in both hemispheres. Furthermore, the high-latitude tropopause in the SH, where stationary waves and storm tracks are relatively weak, has a stronger seasonality than in the NH. This strong seasonality in the high latitudes is instead associated with the stratospheric polar vortex. Zängl and Hoinka  showed that extremely cold air extending downward from the stratosphere can cause pt and Tt to decrease in the polar regions in cold seasons. The colder Tt in the SH than in the NH high latitudes also simply results from the greater strength and stability of the Antarctic polar vortex compared to the Arctic vortex. This suggests that the seasonal cycle of the extratropical tropopause is more sensitive to stratospheric processes than tropospheric processes.
 Figures 5c–5f present the Nt2 distribution during DJF and JJA. Nt2 undergoes a strong seasonal cycle (compare Figures 2c, 5c, and 5f). Although not shown, overall spatial structure of Nt2 is remarkably similar to NLS2 distribution [see Grise et al., 2010, Figure 6], suggesting that Nt2 is dominated by NLS2. It is again found that, while the spatial structure and seasonality of Nt2 are negatively correlated with those of Tt in the tropics (compare Figures 5a and 5e with Figures 5c and 5f), they are not well matched in the extratropics. For instance, subtropical maxima in Tt, especially those over the Tibetan plateau during JJA, are absent in Nt2. Maximum Nt2 is simply observed in the storm track regions where synoptic-scale weather systems are active. This result suggests that midlatitude Nt2 is strongly constrained by baroclinic eddies, supporting the hypothesis that midlatitude TIL is primarily driven by tropospheric dynamics [Wirth, 2003] although other processes [e.g., Birner, 2010b; Randel and Wu, 2010] might still contribute.
 It is evident from Figures 5c and 5f that the seasonal cycle of extratropical Nt2 is not solely controlled by storm track eddies. In fact, as with pt and Tt, Nt2 shows the strongest seasonality in the high latitudes. In both hemispheres, the polar summer (winter) exhibits maximum (minimum) Nt2 (Figures 5c and 5f). Randel et al. [2007a], Kunz et al.  and Randel and Wu  have related these summertime maxima in high-latitude Nt2 to the water vapor concentration in the UTLS. Water vapor concentrations near the polar tropopause reach their maximum during the summer because of warmer tropospheric temperatures. This increased water vapor causes radiative cooling near the tropopause, generating a strong temperature inversion layer right above the tropopause. Randel and Wu  further argued that this radiative process can also explain the hemispheric difference in high-latitude Nt2: the Arctic Nt2 is higher than the Antarctic Nt2 during the summer (compare Figures 5c and 5f) as water vapor concentrations near the tropopause are higher in the Arctic than in the Antarctic.
 Since tropopause properties are, to a first order, uniform in the zonal direction (except in the deep tropics and NH extratropics during DJF), it is informative to look at the seasonal evolution of the zonal mean tropopause properties (Figures 6a–6c). In the tropics both pt and Tt show minimum values in the boreal winter. They gradually increase until August then decrease (Figures 6a and 6b). This is consistent with the seasonality of tropical upwelling driven by the Brewer-Dobson circulation [e.g., Yulaeva et al., 1994; Randel et al., 2002]. Previous studies have shown that strong upwelling during the boreal winter tends to push the tropopause height upward, lowering both pt and Tt [Reid and Gage, 1996; Highwood and Hoskins, 1998; Randel et al., 2000]. This suggests that, while the longitudinal structure of the tropical tropopause properties is largely controlled by localized deep convection and the related UTLS processes, the zonal mean properties and their seasonal cycles are primarily determined by stratospheric processes as proposed by Highwood and Hoskins  and Seidel et al. .
Figure 6. Monthly evolution of (a–c) zonal mean tropopause properties and (d–f) zonal mean temperature at 70, 150, and 500 hPa.
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 In the extratropics, tropopause properties generally reach their maxima in the warm season and minima in the cold season. One exception is pt in the Arctic, which shows a primary maximum in April and a secondary maximum in October (Figure 6a). This is not an artifact of sampling errors, as similar results are also found in radiosonde [Highwood et al., 2000] and reanalysis data [Zängl and Hoinka, 2001]. Although not fully understood, this behavior shows partial correspondence to the Brewer-Dobson circulation. It is well known that high-latitude downwelling reaches its maximum intensity in March–April, a few months later than the maximum upwelling in the deep tropics [e.g., Appenzeller et al., 1996; Randel et al., 2002]. As discussed in the work of Highwood et al. , this likely pushes the polar tropopause height downward, increasing pt. It however remains unclear why Arctic pt behaves so differently from Tt (compare Figures 6a and 6b), and what causes the secondary maximum of pt in October. Although there is no reason to expect a linear relationship between pt and Tt, this puzzling relationship between Arctic pt and Tt, which does not occur in the Antarctic, deserves further analysis.
 The seasonal cycle of Nt2 is qualitatively similar to that of Tt except in subtropical minima (Figures 6b and 6c). However they are not exactly matched. In particular, the maximum Nt2 in the polar regions is delayed by about a month compared to the maximum Tt. In the Arctic, the maximum Nt2 is found in July–August, whereas maximum Tt occurs in June–July. Similarly in the Antarctic, maximum Nt2 is observed in February–March, about a month after the Tt maximum. This delay has again a closer correspondence to water vapor concentrations as shown by Randel and Wu [2010, Figures 9a and 13a].
 In order to identify the relative importance of UT and LS processes in the seasonal march of the zonal mean tropopause properties, the seasonal cycle of Tt (Figure 6b) is further compared with that of temperature at three pressure levels: 70, 150 and 500 hPa (Figures 6d–6f). These three levels are chosen to represent temperature in the tropical LS, the tropical UT and extratropical LS, and the extratropical UT, respectively. In the tropics, the seasonal cycle of Tt closely resembles that of LS temperature (compare Figures 6b and 6d). Even in the extratropics, Tt evolves in accordance with LS temperature although tropospheric processes are nonnegligible in the NH midlatitudes (e.g., maximum Tt in July–August around 45°N) and in the polar regions (e.g., minimum Tt in August at the South Pole). This, once more, suggests that the seasonal cycle of the global tropopause is strongly influenced by stratospheric processes.
3.3. Intraseasonal Variability
 The intraseasonal variability of each tropopause property is defined by means of the standard deviation, σ. Submonthly anomalies are first defined by subtracting instantaneous tropopause properties from their monthly mean value in a given month; they are then squared and averaged for each month. The resulting variance is square-rooted to obtain σ. This approach, which differs from conventional method based on daily climatology, is introduced here because COSMIC GPS radio occultations typically occur less than once a day within each grid box (see Figure 1). In many grid boxes in the tropics and high latitudes, occultations occur only once or never in each calendar day for 3 years. This leaves many missing data and makes daily climatology impossible to be defined. To test the robustness of σ, a similar analysis is also performed by defining anomalies with respect to the seasonal mean value. The results are found to be qualitatively similar to the ones presented in this section (not shown).
 Figure 7 shows intraseasonal variabilities of all three tropopause properties for the two seasons. While σ(pt) and σ(Tt) have qualitatively similar structures,σ(Nt2) again stands apart. Given this contrast, we first discuss σ(pt) and σ(Tt). In the tropics, both σ(pt) and σ(Tt) exhibit small amplitude and strong homogeneity (Figures 7a, 7b, 7d, and 7e). Although a weak hint of a local maximum is observed in σ(Tt) over the western Pacific (Figure 7b), localized σ(Tt) is generally not found over the three regions of strong convection (Figure 2e). This result suggests, surprisingly, that the short-term variability of the tropical tropopause is not directly linked to deep convection. This contrasts with the climatological tropical tropopause, which is largely controlled by deep convection and the related UTLS processes.
 In the extratropics, σ(pt) and σ(Tt) are relatively strong. The maximum variability is found primarily in the subtropics year-round and over the Tibetan plateau during JJA. Although localized maxima are also found over the storm track regions, they are relatively weaker than the ones in the subtropics. The subtropical maxima largely result from the frequent occurrence of double tropopauses in these regions. Figure 8a presents the probability density function (pdf) of pt during DJF over subtropical Asia, covering 25°N ≤ ϕ ≤ 35°N and 60°E ≤ λ ≤ 120°E. The pdf shows a distinct bimodal distribution with one peak around 100 hPa, tropical pt values, and the other peak around 250 hPa, extratropical pt values (see Figure 8d for individual temperature profiles). Together with σ(pt) shown in Figure 7, this depicts a tropopause that is switching between tropical and extratropical values on intraseasonal time scales. During JJA, extremely high values of σ(pt) and σ(Tt) are also observed over the Tibetan plateau. The pdf of pt and instantaneous temperature profiles are displayed in Figures 8b and 8e. As in Figure 8a, a bimodality of pt is evident, but, in contrast, the secondary peak is not well defined. Instead, there is a relatively high occurrence of tropopauses around 300–350 hPa that serve to flatten the overall pt distribution (Figure 8b). The lack of a secondary peak is associated with temperature inversion layers around 350 hPa (Figure 8e). Although detailed analyses are needed, these inversion layers are likely caused by elevated heating as well as monsoon convection over the Tibetan plateau.
Figure 8. (a–c) The pdfs of pt and (d–f) vertical temperature profiles from three regions: subtropical Asia over 25°N–35°N and 60°E–120°E during boreal winter (Figures 8a and 8d), Tibetan plateau over 34°N–44°N and 72°E–100°E during boreal summer (Figures 8b and 8e), and Antarctica over 70°S–90°S during austral winter (Figures 8c and 8f). For clarity, temperature profiles include only a subset of soundings, as indicated in each plot.
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 Figures 7a and 7d also show that σ(pt) is high over the winter pole, especially in the SH. This is not likely caused by the polar vortex as the vortex is very stable in the SH. As discussed by Highwood et al.  and Zängl and Hoinka , this is likely caused by the fact that the polar tropopause is not well defined during the cold seasons. Figures 8c and 8f present the pdf of pt and individual temperature profiles over 70°S poleward during the austral winter. Many profiles have no temperature inversion: temperatures keep decreasing with height well into the stratosphere.
 Unlike σ(pt) and σ(Tt), the latitude-longitude structure of σ(Nt2) is somewhat similar to that of the climatological Nt2 (compare Figures 7c and 7f with Figures 5c and 5f). In other words, σ(Nt2) is strong in the tropics and storm track regions but negligible in the subtropics. A notable exception is found in the summer hemisphere high latitudes: σ(Nt2) shows negligible values where the climatological Nt2 is maximum. Since the short-term variability associated with radiative processes is typically weaker than the one with dynamical processes in the LS, this result supports the hypothesis of a radiative (rather than dynamical) formation of the TIL in the high latitudes [Randel et al., 2007a; Kunz et al., 2009; Randel and Wu, 2010]. It is also noteworthy that σ(Nt2) is maximum in the tropics where σ(Tt) is minimum. A preliminary analysis has revealed that this is at least in part caused by equatorial waves which propagate vertically [Son and Lee, 2007; Ryu et al., 2008]. Son and Lee , for example, showed that temperature in the tropical UTLS is significantly modulated by convectively driven waves, particularly those associated with the Madden-Julian Oscillation on intraseasonal time scales. Details of this will be presented in a separate paper.
 Finally, the seasonal cycle of intraseasonal variability is examined with zonal mean σ(pt), σ(Tt) , and σ(Nt2) in Figure 9. Consistent with Figure 7, both σ(pt) and σ(Tt) exhibit weak seasonality in the deep tropics. In the extratropics, both σ(pt) and σ(Tt) show strong intraseasonal variability around the subtropical jet, where double tropopauses frequently occur. Strong variability is also evident in the SH high latitudes in July when the tropopause is not well defined. However, the intraseasonal variability associated with extratropical storm tracks does not stand out in the zonal mean fields. This result contrasts σ(Nt2) which shows strong seasonality in the midlatitudes only. Although σ(Nt2) shows maximum values in the tropics, its seasonal cycle is relatively weak. This suggests that extratropical storm tracks effectively modulate the vertical temperature gradient near the tropopause.
 From Figures 7 and 9, it might be concluded that the polar tropopause is relatively stable on intraseasonal time scales, especially in the Arctic. This is, however, not true during the boreal winter. As shown in the work of Zängl and Hoinka  and Grise et al. , Arctic tropopause properties can abruptly change as the stratospheric polar vortex suddenly breaks down. Such events, which are often referred to as sudden stratospheric warming (SSW) events, occurred once in the analysis period. Figure 10a shows time series of polar cap temperature at 50 hPa averaged over 60°N to the North Pole. In January 2009, polar cap temperature increases sharply by about 20 K in 10 days [see also Martineau and Son, 2010, Figure 3]. This temperature change is much larger than any short-term temperature changes observed during 2007 and 2008 boreal winters.
Figure 10. Time evolution of the Arctic tropopause properties taken using a cosine-weighted 3 day average from 60°N to the North Pole. Only January to March are shown for each of the 3 years.
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 The impact of the 2009 SSW event on Arctic tropopause properties is illustrated in Figures 10b–10d. Both pt and Tt abruptly increase (e.g., about 7 K warming of Tt and 60 hPa increase of pt in 10 days) and maintain their values for over a month (see thick black lines). Although the response of Nt2 is somewhat noisy, it also shows an increase with a time lag. This result suggests that SSW events can effectively modulate Arctic tropopause properties, confirming previous studies [Zängl and Hoinka, 2001; Grise et al., 2010]. Given this evidence, it is puzzling why Figures 7 and 9 do not show strong σ(pt) and σ(Tt) in the NH high latitudes during the boreal winter. This can be explained by the infrequent occurrence of SSW events, i.e., only one event in the analysis period.