Interannual variation of the tropopause is investigated by applying principal component analysis (PCA) to the zonal mean and eddy tropopause temperatures obtained from the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis. For the zonal mean tropopause temperatures, we find that the first PC represents the out-of-phase coherent variations between the tropics and the Northern Hemispheric (NH) polar region during NH late winter to early spring and the second PC represents the variations between the tropics and the Southern Hemispheric (SH) polar region during SH spring. The same analysis is applied to the zonal mean tropopause simulated in SUNYA Community Climate Model version 3 (CCM3), and the tropopause variations associated with the two PCs are reproduced, with about 74% of the NCEP/NCAR tropopause variability for the first PC and about 44% of the variability for the second PC. The model thermal budget indicates that the first PC is associated with the variation of dynamical heating in the NH polar region and the second PC is associated with the variation of O3 anomalies in the SH polar region. To investigate how the tropopause variation is modulated by the quasi-biennial oscillation (QBO), which is not simulated in the model, singular value decomposition (SVD) is applied to the NCEP/NCAR tropopause temperatures and zonal winds. The QBO accounts for about 16% of the zonal wind variability associated with the first PC and about 36% of the zonal wind variability associated with the second PC. For the eddy tropopause temperatures, the interannual variation associated with the El Niño–Southern Oscillation (ENSO) is evident. In the extratropics over the Pacific North American (PNA) sector, the anomalies are out of phase with the dumbbell-shaped anomalies located in the tropical eastern Pacific and are related to the anomalies in horizontal heat advection caused by the response of extratropical stationary waves. The model can simulate the ENSO-related tropopause variability close to the corresponding NCEP/NCAR's variability, although the model anomalies in the tropical western Pacific are too small.
 Temporal variation of the tropopause is essential for studying climate variability and chemistry in the lower stratosphere and upper troposphere (LSUT). The tropopause is a transition level where the static stability of the atmosphere undergoes a discontinuous change, from the low stability associated with rapid vertical mixing in the troposphere to the high stability associated with slow vertical transport in the stratosphere [Holton et al., 1995]. Below the tropopause, the diabatic heating that are caused by convection and the dynamical effects that are caused by the extratropical baroclinic eddies modulate the temperature and height of the tropopause [Haynes et al., 2001; Held, 1982; Thuburn and Craig, 1997; Wong and Wang, 2000]. Above the tropopause, temporal variation in dynamical heating that are caused by stratospheric planetary wave activity drives the tropopause variability [Wong and Wang, 2000]. Consequently variability of the tropopause can be an indicator of the climate variability in the LSUT.
 Steep vertical gradients of chemical constituents in the vicinity of the tropopause, as a result of the transition in static stability, are major factors causing different chemistry in the stratosphere and the troposphere. In the upper troposphere, the budgets of chemical constituents are affected by the variation in vertical mixing caused by convection. In the lower stratosphere, the budgets are related to the variations of the wave-induced meridional circulation and mixing. Therefore, chemical constituents exhibit not only sharper vertical gradients in the stratosphere [Mahlman, 1997], but also different seasonal variations above and below the tropopause (e.g., ozone) [Logan, 1999]. Because of the significant changes of background chemistry in the vicinity of the tropopause, the effects of anthropogenic emission of NOx on the ozone budget in the LSUT are related to the relative positions of the emission and the tropopause [Fuglestvedt et al., 1999; Gettleman and Baughcum, 1999]. Emission of NOx reduces ozone through the NOx catalytic cycle in the lower stratosphere, whereas it increases ozone through interaction with peroxide radicals in the upper troposphere. Consequently, the tropopause location is important for assessing tropospheric ozone budgets [Mickley et al., 1999; Shindell et al., 2001; Wang et al., 1998].
 Stratosphere–troposphere exchange (STE) of chemical constituents, which involves both large-scale air mass flux and turbulent mixing across the tropopause [Holton et al., 1995; Wong et al., 1999], is important to the study of the temporal and spatial variability of the constituents in the LSUT. In the tropics, air mass flux transports tracers upward across the tropopause into the stratosphere. Air parcels are desiccated during the process, resulting in low water vapor content in the stratosphere. Variation in tropopause temperature is essential to account for the variation of water vapor mixing ratios in the lower stratosphere [Highwood and Hoskins, 1998; Mote et al., 1996; Simmons et al., 1999]. Therefore, the cold point tropopause, defined as the level with the minimum temperature in the vertical profile, is more physically meaningful than the conventional lapse rate tropopause, defined as the lowest level at which lapse rate decreases to 2 K/km or less and the average lapse rate between this level and all higher levels within 2 km does not exceed 2 K/km. In the extratropics, large-scale downward motion and turbulent mixing across the tropopause play significant roles in ozone variability in the LSUT. As the cold point tropopause is only a reliable definition when the lower stratosphere is not close to isothermal, the lapse rate convention is often used for the definition of the extratropical tropopause. In the tropics, the two tropopauses have similar spatial pattern, with the cold point tropopause lying about 1 km above the lapse rate tropopause [Highwood and Hoskins, 1998].
 Reanalysis data have global spatial coverage and allow the study of global features of the tropopause [Appenzeller et al., 1996; Hoerling et al., 1991; Hoinka, 1998, 1999]. Randel et al.  compared the interannual tropopause variability from radiosonde observations in the tropics over the period 1957–1997 with that from the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis [Kalnay et al., 1996]. They found that the NCEP/NCAR reanalysis reasonably captures the seasonal and interannual tropopause variability, although there are temporally constant biases in the NCEP/NCAR tropopause temperatures and pressures. Zhou et al.  found that the European Centre of Medium-Range Weather Forecasts (ECMWF) reanalysis is suitable for investigating the interannual variability of the cold point tropopause in the tropics, despite an almost constant warm bias. The signatures of quasi-biennial oscillation (QBO) and El Niño–Southern Oscillation (ENSO) events are evident in the tropopause statistics [Randel et al., 2000; Zhou et al., 2001]. Variation of tropopause temperatures associated with the QBO is primarily zonally symmetric in character, with tropical positive anomalies and subtropical negative anomalies during the QBO westerly phase. Randel et al.  used the equatorial zonal wind at 50 hPa to define the QBO phase and found that the QBO effect on the monthly mean tropopause properties is instantaneous. Zhou et al.  used the equatorial zonal wind shear at 50 hPa to define the QBO phase and found that the tropopause anomalies lag behind the wind shear anomalies by about 6 months. Variation associated with ENSO events is zonally asymmetric in character and instantaneously responds to the SST anomalies in the eastern Pacific, exhibiting a dipole pattern that implies out-of-phase variations over the tropical eastern and western Pacific Ocean. The positive regression, with a dumbbell-shaped pattern located at the flanks of the equator over the eastern Pacific, indicates cooling of the local tropopause during ENSO warm episodes. Over the equator, an anomaly out of phase with the dumbbell-shaped anomaly is located in the west to central Pacific. The pattern of the ENSO-related tropopause temperature anomalies is consistent with that of the ENSO-related lower stratospheric temperature anomalies derived from the Microwave Sounding Unit (MSU) by Yulaeva and Wallace . As a result, the tropopause temperature variation in the tropics is highly correlated with the temperature variation in the tropical lower stratosphere. Randel et al.  further suggested that Brewer–Dobson circulation in the lower stratosphere links the interannual variation of the tropical tropopause to the extratropical lower stratospheric temperature.
 There are also a few modeling works studying the physical mechanisms underlying the tropopause variation [Houghton, 1997; Thuburn and Craig, 1997, 2000; Wong and Wang, 2000]. Wong and Wang  analyzed simulation results from an atmospheric general circulation model (AGCM) to understand the interhemispheric asymmetry in the seasonal variation of the zonal mean tropopause. The asymmetry is associated with the stronger stratospheric planetary wave activity in the Northern Hemisphere (NH) during winter to spring as well as the stronger tropospheric convective activity in the NH during summer. Both processes above and below the tropopause play essential roles in driving the seasonal variation of the tropopause. The simulated seasonal variation of the tropopause is in reasonable agreement with the NCEP/NCAR reanalysis and with radiosonde observations in the tropics [Randel et al., 2000; Reid and Gage, 1996; Seidel et al., 2001] and the extratropics [Hoinka and Reinhardt, 1993].
 This study is an extension of the work by Wong and Wang  to study the interannual variation of the global tropopause. We performed an AGCM simulation using SUNYA Community Climate Model version 3 (CCM3) forced by estimates of changes in observed O3 and SSTs. Temperature variation in the lower stratosphere, which is sensitive to the local ozone variation, is important for a proper simulation of the tropopause variation. In order to properly represent the spatial and temporal ozone variations in the lower stratosphere, the SUNYA 4D ozone archive [Liang et al., 1997; Wang et al., 1995] was modified by the observed stratospheric ozone trends [Randel and Wu, 1999] to give a relatively realistic vertical distribution in interannual ozone anomalies. Boundary SSTs are forced by the midmonth SSTs used in the Atmospheric Model Intercomparison Project 2 (AMIP 2) [Gates et al., 1999]. Same statistical analyses were applied to both the AGCM and NCEP/NCAR reanalysis results for comparison purposes. As the AGCM cannot reproduce the QBO, the effects of the QBO on the interannual variability of the tropopause are studied using the NCEP/NCAR winds and tropopause temperatures. Hereafter, we refer to SUNYA CCM3 as the “model” and the NCEP/NCAR reanalysis data as the “NCEP data.”
 Large-scale dynamical processes in the lower stratosphere connect the interannual variations of the tropical and extratropical tropopause. The dynamical connection involves the modulation of Brewer–Dobson circulation by stratospheric planetary wave activity through the suction pump mechanism [Holton et al., 1995; Rosenlof, 1995], as well as the response of extratropical stationary waves to the tropical diabatic heating anomalies [Hoerling et al., 1995, 1997]. In this study we concentrate on the tropical–extratropical tropopause connection diagnosed in the model simulation and the reanalysis data. Section 2 describes the reanalysis data, the model simulation, and the statistical analyses. Section 3 presents the diagnosed interannual variations in the model and NCEP zonal mean tropopause. The effects of the QBO are assessed and their relative importance is estimated. Section 4 presents the interannual variations in the model and NCEP eddy tropopause. The effects of the ENSO are illustrated. Section 5 includes conclusions and discussion.
2.1. Reanalysis and Model Data
 Monthly mean tropopause temperatures and pressures, with horizontal resolution of 2.5° × 2.5°, were already computed in the NCEP reanalysis [Kalnay et al., 1996]. The vertical resolution of the assimilation model used in the reanalysis is of order 2 km near the tropical tropopause. The tropopause pressures were obtained by the conventional lapse rate criterion. Tropopause temperatures were interpolated to these levels from the adjacent sigma levels [Randel et al., 2000]. Data from the period January 1979 to December 1994 were used to match the model-simulated period described in the next paragraph. This period is within the post satellite period so that the discontinuous behavior due to the introduction of satellite data into the assimilation is excluded [Randel et al., 2000]. Seasonal cycles of the temperature or pressure were computed as the climatological monthly averages over the period and subtracted from the original data to get the corresponding temperature or pressure anomalies. Before any analyses began, the anomalies were decomposed into the zonal mean and eddy components. Besides the NCEP tropopause variables, the NCEP and the ECMWF monthly averaged temperatures at the 100 hPa level were also used for reference purposes.
 The AGCM simulation covers the AMIP 2 period January 1979 to February 1996 [Gates et al., 1999]. The simulation was conducted using NCAR CCM3 [Kiehl et al., 1998] with SUNYA 4D ozone [Liang et al., 1997; Wang et al., 1995] and midmonth SSTs supplied for AMIP 2 as inputs. The model uses T-42 horizontal resolution (equivalent to 2.8° × 2.8°) with 18 layers in the vertical (about 2 km vertical resolution near the tropopause). The dynamical time step is 20 min, while shortwave and longwave fluxes are calculated every hour. The ozone archive was first constructed by the zonal and monthly mean climatology compiled from the 1984–1989 SAGE II data for the stratosphere [Cunnold et al., 1989], and from sonde data for the troposphere [Logan, 1985]. The zonal mean ozone climatology was then set as the zonal mean profile of ozone for the middle year of the period (i.e., 1986). Before and after the middle year, ozone trends computed by Randel and Wu  were used to linearly extrapolate the zonal mean ozone profiles from 1979 to 1994. The zonal mean profiles were then rescaled according to the 1979–1994 TOMS version 7 column ozone data [McPeters et al., 1996] to allow longitudinal and interannual variations with proper column ozone amount. For years after 1994 the O3 values repeated those in 1994. Before taking monthly averages, model diagnostics were interpolated onto the pressure levels commonly used by observations or model intercomparison. These pressure levels are 10, 20, 30, 50, 70, 100, 150, 200, 250, 300, 400, 500, 600, 700, 850, 920, and 1000 hPa. In this study only data from 1979 to 1994 were used for analyses.
 The model simulates both monthly averaged temperature tendencies and diabatic heating rates, which include solar and thermal infrared heatings, heatings due to convective adjustment and latent heat release. Dynamical heating rates were calculated as the subtraction of the diabatic heating rates from the temperature tendencies. The model tropopause pressures were determined by the method described by Wong and Wang  using the model monthly averaged temperature. The lapse rate definition was first applied to obtain an upper bound for the troposphere. Then, the temperatures at this upper bound and the adjacent lower level were linearly extrapolated, according to the corresponding lapse rates at the two levels, for any altitude between the two levels. The tropopause location was simply estimated as the altitude at which the two temperature extrapolations intersected. We applied this method to every air column at every model's longitude and latitude, and a geographical distribution of tropopause pressures was therefore obtained for each month. Tropopause temperatures were obtained by linear interpolation of the model temperatures to the estimated tropopause locations.
2.2. Statistical Analyses
 Principal component analysis (PCA) [Bretherton et al., 1992; Peixoto and Oort, 1992] was applied to both NCEP and model data to decompose the major components of interannual variations in the zonal mean and eddy tropopause temperatures. Detailed description of PCA is included in Appendix A. Spatial and temporal distributions of each dominant PC allow one to investigate the coherent interannual variations between the tropics and extratropics. In Appendix B we describe in detail the mathematical reasoning behind a method, which can be used to analyze the model anomalies of temperature tendency to identify the physical mechanisms underlying the dominant PCs. The orthogonal property of the PC time series allows one to decompose the anomalies of temperature tendency into components that are associated with the corresponding PCs. Each component of the anomalies of temperature tendency can further be decomposed according to the budget terms representing the heating/cooling mechanisms. Therefore, the model-simulated thermal budget can be used to understand the physical mechanisms underlying the dominant PCs.
 The QBO is not simulated in any GCMs with coarse vertical resolution. In order to study how the QBO modulates the tropical–extratropical connection of the interannual tropopause variation, singular value decomposition (SVD) was applied to the NCEP zonal mean zonal winds and the NCEP zonal mean tropopause temperatures. SVD isolates the variations of the two fields that tend to be linearly related to each other, by optimally maximizing the covariance matrix of the two fields [Bretherton et al., 1992]. The detailed description of SVD is included in Appendix A. Investigations of the spatial and temporal distributions of each pair of linearly related components can give insights into the way the tropical and extratropical tropopause temperatures are linked through the coherent variation of the zonal winds, and the way the corresponding variations are related to the tropically confined QBO.
 Hereafter, we refer to the component from SVD as the “SVD component.” The statistical significance of each PC or SVD component can be simply realized by the fraction of variance or covariance explained by the component. Furthermore, the significance at a particular gird is estimated using the F test by considering how significant the component reduces the residual (see Appendix A for details). In the following sections, results over the 95% confidence level are discussed, unless it is mentioned in the text.
3. The Zonal Mean Tropopause
 Comparison with NCEP/NCAR reanalysis shows that the model can simulate reasonable amplitudes and phases of the climatological seasonal cycles of the zonal mean tropopause pressure and temperature in the tropics and middle latitudes. In polar regions, the model can provide the reasonable phases but underestimate the amplitudes. Detailed description about the model performance for the seasonal cycle of the tropopause properties was included in the study of Wong and Wang . In the following, our discussion will focus on the interannual variability of the tropopause.
3.1. Tropopause Pressures and Temperatures
 The interannual variation of the zonal mean tropopause is investigated. Figure 1 shows the NCEP zonal mean tropopause pressure and temperature anomalies as well as the 100 hPa level temperature anomalies averaged for both polar regions and the tropics. Also shown is the 100 hPa level temperature from the ECMWF reanalysis (thick solid line) for reference purpose. The corresponding standard deviations of the time series are shown in Table 1. Over the three regions, the variation of the tropopause pressure is positively correlated with that of the tropopause temperature (about 0.9 correlation in polar regions and 0.7 in the tropics). Furthermore, the tropopause temperature varies coherently with the 100 hPa level temperature (over 0.85 correlation for all three regions). Therefore, a warmer lower stratosphere implies a warmer tropopause with a lower altitude. Seidel et al.  presented a similar correlation computation for the tropical tropopause based on a longer period (1978–1997) of radiosonde records. Our results are in reasonable agreement with their findings, in which the correlation between the tropopause temperature and pressure is about 0.78 and that between the tropopause temperature and the 100 hPa level temperature is about 0.92. In the NH polar region (60°–90°N) large anomalies are seen during NH winter to early spring, in association with the period when large stratospheric planetary wave activity occurs in the NH extratropics. Standard deviations of the NH polar tropopause pressure and temperature anomalies are, respectively, 8.4 hPa and 1 K. The 100 hPa level temperature varies consistently with that shown in the ECMWF data (both with a standard deviation of about 1.8 K).
Table 1. Comparison of Tropopause and 100 hPa Temperature Interannual Variations (Standard Deviations of the Anomalies; Units are hPa for Pressure and K for Temperature) Between Different Data Sets
Tropopause P (hPa)
Tropopause T (K)
100 hPa T (K)
Tropopause P (hPa)
Tropopause T (K)
100 hPa T (K)
Tropopause P (hPa)
Tropopause T (K)
100 hPa T (K)
 In the tropics (20°S–20°N) a clear warming in 1982–1983, corresponding to the episode of El Chichón eruption, is seen for the NCEP data. The warming in 1989–1990 may be spurious because it was not observed in the radiosonde and ECMWF data [Randel et al., 2000]. Standard deviations of the tropical tropopause pressure and temperature anomalies are, respectively, 1.8 hPa and 0.8 K, smaller than those in the polar regions. Compared with the ECMWF data for the 100 hPa level temperature anomalies (with a standard deviation of about 0.4 K), NCEP data shows larger interannual variability (with a standard deviation of about 0.7 K). The warming caused by the El Chichón eruption seen in the NCEP data is stronger than that seen in the ECMWF data. These results about the tropical tropopause are in reasonable agreement with those reported by Randel et al. , in which the interannual variation of the tropopause pressure is about 2–4 hPa and that of the tropopause temperature is about 1–2 K.
 In the Southern Hemispheric (SH) polar region (60°–90°S) large anomalies are seen during SH winter and spring, in association with the period when the SH extratropical planetary wave activity is strong and the polar lower stratospheric O3 has large interannual variability. Standard deviations of the SH polar tropopause pressure and temperature anomalies are, respectively, about 10 hPa and 1 K, slightly larger than those of the NH polar tropopause. The 100 hPa level temperature also varies consistently with that of the ECMWF data (both with a standard deviation of about 1.7–1.8 K).
 Similar regionally averaged time series are plotted (Figure 2) for the model tropopause pressure, the model tropopause temperature, and the model 100 hPa level temperature. The corresponding standard deviations are shown in Table 1. These three variables vary coherently over the three regions in the model as they do in the NCEP reanalysis. Correlations between the tropopause pressure and temperature anomalies are about 0.8 in polar regions and 0.65 in the tropics. Correlations between the tropopause temperature and the 100 hPa level temperature anomalies are within 0.87–0.94 in the three regions. In the NH polar region large anomalies are seen during NH late winter to early spring, consistent with both NCEP and ECMWF data. Standard deviations of the tropopause pressure and temperature anomalies are, respectively, 6.7 hPa and 1.2 K, about the same magnitude as those of the NCEP tropopause. In the tropics the model tropopause has much less interannual variability than the NCEP tropopause. Standard deviations of the tropical tropopause pressure and temperature anomalies are, respectively, 0.6 hPa and 0.3 K, about one-third to one-half of the NCEP variability. At 100 hPa the model temperature variability (0.3 K) is also smaller than the corresponding NCEP variability but closer to the corresponding ECMWF variability, which captures smaller volcanic aerosol effects compared to the NCEP reanalysis. This smaller model variability at the tropical tropopause is related to the missing natural variations in the model (e.g., effects due to volcanic aerosol absorption and the QBO). In the SH polar region large anomalies are seen during SH late spring to early summer, later than the period of large anomalies seen in the NCEP SH polar tropopause. Interannual variability of the model tropopause is also smaller than that of the NCEP tropopause in the SH polar region. Standard deviations of the model tropopause pressure and temperature anomalies are, respectively, 5 hPa and 0.8 K, smaller than the corresponding values of the NCEP tropopause. At 100 hPa the model temperature anomalies has a standard deviation (1.6 K) close to those of the NCEP and ECMWF data. In conclusion, the model simulates about the same magnitude of variability for the NH polar tropopause but underestimates the variability for the tropical and the SH polar tropopause.
Figure 3 shows the correlation between the tropical tropopause temperature and the 100 hPa temperature for both NCEP and model anomalies. For the NCEP data, significant positive correlations span an area from the tropics to middle latitudes for all seasons. In the NH polar region, significant negative correlations (reaching −0.7) span from the NH winter to early spring. In the SH polar region, significant negative correlations are seen during May, and SH winter to spring (August and September). These results are consistent with those of Randel et al. , in which a longer time period of NCEP data was used. As indicated by Randel et al. , the out-of-phase variation of the tropical–polar temperatures implies stronger polar jet intensity when the tropical tropopause is warmer, and the seasonal dependence of the meridional structures seen in Figure 3 is associated with the variation of the mean stratospheric circulation [Holton et al., 1995]. The model can simulate the qualitative behavior of the correlation pattern. The area of positive correlation in the model spans a narrower band from the tropics to middle latitudes. The significant negative correlation in the NH polar region during winter exists for a shorter period. In the SH polar region the model simulates a slightly larger negative correlation, especially in SH midwinter (July) and late spring (November). Around 30°–40°S, the model simulates a large negative correlation during June–October that is not seen in the NCEP data.
 In most of the discussion in this study, the tropopause temperature anomalies are used to represent the interannual tropopause variation. In the next two subsections, PCA is used for both NCEP and model data to diagnose the relationship between the tropical and the polar tropopause variations. SVD is used for the NCEP data to further diagnose the relationship between the zonal mean zonal wind and the zonal mean tropopause.
3.2. Tropical–Polar Tropopause Connection
 The two leading empirical orthogonal functions (EOFs) are shown in Figure 4. The NCEP EOFs are plotted with solid lines and the model EOFs with dashed lines. For the first EOF (Figure 4, EOF1), both NCEP and model data have similar latitudinal distributions, with the maximum located in the NH polar region. In the tropics the NCEP data indicate small negative values (about −6 × 10−2), implying out-of-phase coherent tropopause variation between the tropics and the NH polar region. The model tropical EOF values are close to zero owing to the small model variability in the tropics. The NCEP first PC has a time series with a standard deviation of about 5.8 K, about 35% of the total variability and contributing about 2 K to the standard deviation of the tropopause temperature in the Northern Polar region. The model first PC has a time series with a standard deviation of about 5 K, about 40% of the total variability and contributing about 2.5 K to the standard deviation of the tropopause temperature in the Northern Polar region. The model variability is about 74% of the NCEP's (square of 5/5.8).
 For the second EOF, the NCEP and the model latitudinal distributions are in qualitative agreement (Figure 4, EOF2), with maximum positive values in the SH polar region and negative values in the tropics, implying out-of-phase coherent variation between the tropics and the SH polar region. The model EOF has two distinct discontinuities around 30°S and 50°–60°S that are not seen in the NCEP EOF. These discontinuities may be an artifact of the coarse vertical resolution because the model second EOF for the 100 hPa level temperature anomalies (not shown) does not show the corresponding discontinuities. The standard deviations of the time series for the second PCs are 4.78 K for the NCEP data, contributing about 24% to the total variability and 1.4 K to the standard deviation of the tropopause temperature in the Southern Polar region, and 3.2 K for the model data, contributing about 16% to the total variability and 1.2 K to the standard deviation of the tropopause temperature in the Southern Polar region. The model variability is about 44% of the NCEP's.
 To investigate the thermal budget associated with the variation of tropopause temperature, the time series of the PCs for the 100 hPa temperatures are used to expand the anomalies of the zonal mean temperature tendency at the same pressure level with a 1-month time lag (Figure 5 and Appendix B). The NCEP and the model data show similar patterns for the first and second components of temperature tendency anomalies (thick solid lines). For the first component, significant positive values are located in the NH polar region, and for the second component, the positive values are located in the SH polar region. The patterns also resemble those of the corresponding EOFs for the tropopause or 100 hPa level temperature anomalies, indicating that the components of temperature tendency anomalies can be used to explain the physical mechanisms underlying the corresponding PCs.
 The model temperature tendency anomalies are decomposed into thermal budget terms corresponding to dynamical heating rates, and heating rates due to absorption or emission of shortwave and longwave radiation. For the first PC the model indicates that the dominant term is the dynamical heating/cooling, implying that the large variability of the tropopause in the NH polar region during NH late winter to early spring is associated with the interannual variation of dynamical heating. Since dynamical heating in the stratosphere is mainly driven by the adiabatic heating of the Brewer–Dobson circulation, which is modulated by stratospheric planetary wave activity [Holton et al., 1995; Rosenlof, 1995; Wong and Wang, 2000], the interannual variation of the tropopause in the NH polar region during NH late winter to spring is related to the variation in stratospheric planetary wave activity. Radiative cooling/heating associated with emission/absorption of longwave radiation responds in a way opposite to the dynamical heating/cooling. Shortwave radiation plays almost no role in driving the NH polar tropopause variability. For the second component the dominant term is the heating/cooling caused by absorption of shortwave radiation, implying that the large variability of the tropopause temperature in the SH polar region during SH spring and early summer is associated with the interannual polar O3 variation. Again, the term caused by longwave radiation responds in a way opposite to the shortwave radiative effect. The dynamical heating/cooling term varies in phase with the solar heating/cooling term, implying that a deep (shallow) O3 depletion is associated with dynamical cooling (heating) anomalies occurring 1 month earlier. This is consistent with the modeling results by Shindell et al.  in which a deeper O3 hole is associated with a quiescent dynamic year, although in our model the O3 variation is prescribed instead of being interactively calculated with the model meteorology. In Figure 1, the NCEP/ECMWF time series in the SH polar region indicate that the variations of the tropopause and the 100 hPa level temperatures resemble the observed variation of SH polar O3 anomalies [WMO, 1994].
 In the model the variability in the tropics is too small. Since the model does not simulate the QBO, which drives significant variability in the tropics, it is interesting to investigate how the QBO affects the tropical tropopause and how it modulates the extratropical tropopause variation.
3.3. QBO Effects
 The QBO has significant influences on both tropical and extratropical circulation and temperature [Baldwin et al., 2001]. In the tropics during the QBO westerly phase (defined as the wind anomalies over the equator at 50 hPa), equatorial downward wind anomalies are associated with the subtropical upward wind anomalies. The lower stratosphere is, therefore, warmed over the equator and cooled at the subtropics [Andrews et al., 1987; Baldwin et al., 2001; Zhou et al., 2001]. In the extratropics, the QBO modulates the planetary wave propagation and, hence, the winter polar vortex strength as well as the temperature in the polar lower stratosphere. During the QBO westerly phase, it is more likely to have a more stable polar vortex and colder polar lower stratosphere [Balachandran and Rind, 1995; Baldwin et al., 2001; Holton and Tan, 1982]. These QBO effects on the lower stratospheric temperature can induce an interannual variability in the tropopause temperature.
 SVD was applied to NCEP data for studying the relationship between the zonal mean wind and the tropopause temperature anomalies. The results are shown in Figure 6 for the leading four SVD patterns of the zonal mean tropopause temperature anomalies, and Figure 7 for the leading four SVD patterns of the zonal mean wind anomalies. Fractions of total covariance as well as the correlations of the expansion coefficients are measures of the strength of the coupling between the tropopause temperature and the zonal mean wind. They are shown in the titles of Figure 8 along with the corresponding temperature and zonal mean wind time series of the SVD components. The patterns shown in Figures 6 and 7 are consistent with mechanisms stated in the last paragraph and the thermal wind relation in the extratropics.
Here ϕ represents latitude; Ω, the angular frequency of the Earth's rotation; a, the radius of the Earth; R, the ideal gas constant; H, the scale height of the atmosphere density; u, the zonal mean wind anomalies; and T, the zonal mean temperature anomalies. This relation implies that large positive vertical wind shear in the extratropical stratosphere is associated with large negative meridional temperature gradient at the tropopause level. For example, a vertical westerly shear seen in the extratropical stratosphere is associated with a poleward decrease of tropopause temperatures. In the tropics during westerly phase of the QBO, the equatorial lower stratosphere is warmer than the climatology because of the local sinking motion, and the subtropical lower stratosphere is cooler because of the local rising motion [Andrews et al., 1987; Baldwin et al., 2001; Zhou et al., 2001].
 The first SVD component contributes about 64% of the total covariance and the correlation of the wind and temperature time series is 0.82 (Figure 8, SVD1). The pattern of the first SVD component for the tropopause temperature anomalies (Figure 6, SVD1) resembles that of the first PC (Figure 4, EOF1) with maximum weight in the NH polar region. The large meridional temperature gradient at the NH subpolar tropopause is associated with a strong vertical wind shear around 60°–80°N (Figure 7, SVD1). In the tropics the weight of the SVD component (Figure 6, SVD1) is of opposite sign to that in the NH polar region, indicating an out-of-phase coherent variation between the tropical and the NH polar tropopause temperatures. This can be explained by the adiabatic heating/cooling mechanism driven by the Brewer–Dobson circulation (see section 3.2). The associated zonal mean wind anomalies in the tropics have the same direction as that in the NH subpolar to polar region, and the maximum is located above 10 hPa (Figure 7, SVD1). Over 20°–40°N the wind anomalies are in direction opposite to those in the tropics and the NH subpolar to polar region, the well-known dipole pattern discussed in the literature [Baldwin et al., 2001]. The activity represented by the first SVD component occurs mainly in the NH winter to early spring (December–March), as indicated in the time series shown in Figure 8, SVD1. The standard deviation of the temperature series is 5.7 K, about the same magnitude as that of the first PC (see section 3.2). The standard deviation of the wind time series is 44 m/s, contributing a standard deviation of about 6.6 m/s to the zonal wind variability around 10 hPa and 70°N.
 The second SVD component contributes about 21% of the total covariance and the correlation of the wind and temperature time series is 0.6 (Figure 8, SVD2). The pattern of the second SVD component (Figure 6, SVD2) for the tropopause temperature anomalies resembles that of the second PC (Figure 4, EOF2) with maximum weight in the SH polar region (noticing that we have reversed the sign in the SVD component so that the weight for the wind anomalies is positive in the tropics). The large meridional temperature gradient at the SH midlatitude to subpolar tropopause is associated with the large vertical wind shear around 40°–70°S (Figure 7, SVD 2, confidence level over 90%). In the tropics the tropopause temperature variation is out of phase with that in the SH polar region. The maximum weight for the tropical zonal wind anomalies is located over 10 hPa. The activity represented by the second SVD tends to occur in SH spring to early summer (October–December), as indicated in the time series shown in Figure 8, SVD2. The standard deviation of the temperature series is about 4.7 K, in agreement with that of the second PC (see section 3.2). The standard deviation of the wind series is about 42 m/s, contributing a standard deviation of about 5 m/s to the zonal wind variability near 10 hPa and 50°–60°S. The time series in Figure 8, SVD2, show an evident signal of the QBO, implying the modulation of the SH polar lower stratospheric temperature by the QBO.
 The third SVD component contributes about 6% of the total covariance and the correlation of the wind and temperature time series is 0.5 (Figure 8, SVD3). For the third SVD component, there are significant variations in the tropopause temperature (Figure 6, SVD3) at the equator (confidence level about 90%) and the subtropics (30° of both hemispheres). The subtropical temperature variation is out of phase with that over the equator. A strong vertical wind shear, with the same sign as the temperature anomalies, is located right above the equatorial tropopause (Figure 7, SVD3), with the maximum weight for the wind anomalies at about 40 hPa. The reverse of wind shear locates at about 20 hPa. The bell-shaped pattern of the tropical temperature anomalies (Figure 6, SVD3) is consistent with the meridional structure of the QBO effect, which is strongest over the equator and decaying poleward with a half-width of about 12° in latitude [Baldwin et al., 2001; Randel et al., 2000]. In the extratropics, significant tropopause temperature anomalies are over the SH polar region, with a sign opposite to that of the equatorial anomalies. The SH polar temperature anomalies are associated with a significant vertical wind shear, which has the same sign as the wind shear over the equatorial tropopause, at about 60°S. In Figure 8, SVD3, the peaks of the wind series seem to be more likely to occur during SH late spring to early summer (November and December). The standard deviation of the temperature series is about 3.3 K, implying standard deviations of about 0.3 K for the equatorial tropopause temperature anomalies and about 0.8 K for the SH polar tropopause temperature anomalies. The standard deviation of the wind series is about 37.2 m/s, implying standard deviations of about 3.7 m/s around 40 hPa over the equator, and of about 1.9 m/s around 10 hPa over 50°–60°S.
 The fourth SVD component contributes about 4% of the total covariance and the correlation of the wind and temperature time series is 0.5 (Figure 8, SVD4). In the tropics to subtropics the tropopause temperature and the zonal wind patterns corresponding to the fourth SVD component are very similar to those corresponding to the third SVD component. However, the equatorial and the 30°S weights for the temperature anomalies are larger in magnitudes in the fourth SVD component, associated with the stronger equatorial vertical wind shear. The maximum weight of the tropical wind anomalies is located higher in altitude (about 30 hPa). In the SH polar region the third and fourth SVD components show opposite effects on the tropopause temperatures, associated with the opposite wind anomalies over 60°S. The time series shown in Figure 8, SVD4, indicate no distinct seasonal preference. The standard deviation of the temperature series is about 2.6 K, implying standard deviations of about 0.6 K for the tropical and the SH polar tropopause temperature anomalies. The standard deviation of the wind series is about 37.1 m/s, implying standard deviations of about 5.6 m/s around 30 hPa over the equator and of about 1.9 m/s around 40 hPa over 60°S.
Figure 9 shows the time lag correlations between the wind time series (dashed lines) shown in Figure 8 and the anomalies of a conventional QBO index, the observed zonal wind over Singapore at 50 hPa [Naujokat, 1986]. For 192 time samples, correlations over 0.2 are over the 99% confidence level. The first SVD wind time series has a maximum correlation of about 0.4 with the QBO index. The other three SVD wind time series have maximum correlations of about 0.6–0.8 with the QBO index. For the first (thin solid) and second (thin dashed) SVD components, the peaks occur, respectively, about 5 and 8 months before the 50 hPa QBO signal. This is reasonable because the cores of activity for these two components are located at or above 10 hPa (Figure 7, SVD1 and SVD2), and the QBO signal propagates downward at the equator. The peak of the third SVD component occurs about 2 months after the 50 hPa QBO signal because the core of activity is closer to the 50 hPa altitude (Figure 7, SVD3). Finally, the peak of the fourth SVD component occurs about 3 months before the 50 hPa QBO signal as the core of activity is located at 30 hPa (Figure 7, SVD4). The peak-to-peak time differences shown in Figure 9 span a range of 26–30 months, consistent with the cycle of the QBO that varies from 22 to 34 months (with an average slightly longer than 28 months) [Baldwin et al., 2001]. If instantaneous linear regression (with zero time lag) is carried out for the anomalies of the tropopause temperature and the QBO index, the signals associated with the third and fourth SVD components are most likely to be picked up because of their highest correlations with the QBO index. At the equator, the temperature–wind slope associated with the linear combinations of the third and fourth components is about 0.68 K/(10 m/s). The standard deviation of the similar linear combination for the zonal wind is about 5.34 m/s, 2.4 times smaller than that of the QBO index, which is of about 13 m/s. Therefore, the regression of the equatorial tropopause temperature to the QBO index is estimated to be about 0.28 K/(10 m/s), consistent with the estimation given by Randel et al. [2000, Figure 13a].
 In conclusion, the correlations shown in Figure 9 imply that the QBO accounts for about 16% of the NH zonal wind variability associated with the pattern in Figure 7, SVD1, which gives rise to the tropical NH polar connection of tropopause temperature seen in Figure 4, EOF1. In the SH the QBO accounts for about 36% of the variability associated with the pattern shown in Figure 7, SVD2, which gives rise to the tropical SH polar connection of tropopause temperature shown in Figure 4, EOF2. The QBO accounts for over 60% of the wind variability represented by the third and fourth SVD components (Figure 7, SVD3 and SVD4); however, these components give rise to relatively small coherent variation in tropopause temperature between the tropics and polar regions.
4. ENSO Effect
 The zonally symmetric effects of the stratospheric wave activity and the QBO on the tropopause temperatures are much stronger than the effects of the ENSO. Since the ENSO effects are primarily associated with longitudinal variation [Gage and Reid, 1987], the ENSO signal in tropopause temperatures was found by analyses of the eddy tropopause temperatures (after the zonal mean values were removed) [Randel et al., 2000; Yulaeva and Wallace, 1994]. In this study, PCA was performed to the eddy tropopause temperatures for both NCEP and model data. After the zonal mean temperature is removed, the fraction of total variance explained by each PC becomes relatively small (smaller than 10%). Therefore, we applied an additional criterion to pick up the ENSO signal. Among the resolved PCs' time series for each data set, the one with the largest correlation with the Southern Oscillation Index (SOI), a conventional ENSO index, is used for our study. Figure 10 shows the time series of the PCs corresponding to the ENSO signal for the NCEP (solid) and model (dashed) data. For the NCEP data, the ENSO-related signal is the third PC and explains about 5.5% of the total variance. For the model data, the ENSO-related signal is the first PC and explains about 5.4% of the total variance. The model can reasonably reproduce the interannual variation indicated in the NCEP data. Both time series show distinct ENSO warm episodes during the winters of 1982/1983, 1986/1987, and 1991/1992. The model standard deviation is about 11 K, close to the NCEP's of about 10.6 K. Both time series significantly correlate with the SOI (correlation of about −0.4 to −0.5).
Figure 11 shows the EOFs corresponding to the ENSO signal for the NCEP and model data. In the tropics the model can simulate the dumbbell-shaped minima located at both flanks of the equator (around 10°–30° latitudes) in the eastern Pacific (around 140°W), indicating cooling of the local tropopause during ENSO warm episodes (El Niño) or warming of the local tropopause during ENSO cold episodes (La Niña). This dumbbell-shaped pattern is consistent with previous observational findings [Randel et al., 2000; Yulaeva and Wallace, 1994; Zhou et al., 2001]. The pattern is a response to the tropospheric diabatic heating anomalies in the central Pacific [Highwood and Hoskins, 1998; Hoerling et al., 1997]. For example, during warm episodes in the troposphere a dumbbell-shaped pair of dynamical warmings is induced to the east of the international dateline. In the stratosphere the associated rising motion aloft of the warming pairs causes the dynamical cooling seen in the tropopause temperature anomalies. This mechanism can be verified by analyzing the model temperature budget using the method described in the Appendix B. The model time series (Figure 10) is regressed on the anomalies of eddy dynamical heating rates and the anomalies of vertical velocity at 100 hPa. The results are shown in Figure 12. The pattern for the anomalies of eddy dynamical heating rates (Figure 12, upper panel) resembles that for the EOF of temperature anomalies (Figure 11, lower panel), indicating that the dynamical processes in the lower stratosphere drive the interannual tropopause variation related to the ENSO. In Figure 12, lower panel, during ENSO warm episodes regions of negative (positive) values represent regions of rising (sinking) motion, which is associated with adiabatic cooling (warming). It can be verified that the dumbbell-shaped pattern seen in tropopause temperature in the eastern tropical Pacific is related to the variation in vertical motion in the lower stratosphere.
 In the tropical to subtropical western Pacific, the significant anomalies out of phase with that of the eastern Pacific, as seen in the NCEP data, are too small in the model (Figure 11). Regression analysis done by Randel et al.  using NCEP data for 1979–1997 and by Zhou et al.  using ECMWF data for 1979–1993 also showed the anomalies located in the western Pacific. This model discrepancy is likely attributed to the weak dynamical warming simulated over the western Pacific. Reasons underlying this discrepancy need further investigation.
 In the extratropics the model can reasonably capture the teleconnection pattern seen in the NCEP tropopause temperature (Figure 11). The anomalies, located off the west coast of North America, over north Canada, and over Greenland, are well simulated in the model. Over northern Europe and Asia, the anomalies are out of phase with those over the northern American continent. However, these anomalies are significant in the model but not significant in the NCEP data. The extratropical temperature anomalies are again related to the interannual variation of dynamical heating in the lower stratosphere (Figure 12, upper panel). Since the pattern for the anomalies of vertical velocity does not match the pattern for the anomalies of dynamical heating rates in the extratropics, it suggests that the horizontal heat advection instead of the adiabatic process provides the anomalies of dynamical heating rates over the extratropical region. Time series of the ENSO-related PC (Figure 10) are regressed on the 100 hPa level geopotential height for both NCEP and model data. The results are shown in Figure 13. The EOF patterns in Figure 11 over the Pacific North American (PNA) sector are associated with the stationary waves shown in Figure 13. For example, during ENSO warm episodes the tropopause warming off the west coast of North America and over north Canada is associated with the northward eddy transport of warm air from the NE Pacific. The cooling in the North Atlantic and Europe is associated with the SE eddy transport of cold air from the polar region.
 The pattern of the extratropical stationary waves is a response to the tropical diabatic heating anomalies in the troposphere [Hoerling et al., 1997]. If this is the case, model simulations of the tropical–extratropical tropopause connection related to the ENSO depend on how well the model can simulate the response of the extratropical stationary waves. As seen in Figure 13, the NCEP and model results are in general agreement. In the tropics the model reproduces the upper tropospheric anticyclones associated with the dumbbell-shaped cooling pattern during ENSO warm episodes. In the extratropics the model can simulate the geopotential height anomalies associated with the stationary waves over the PNA sector [Hoerling et al., 1995, 1997], with strengthening of the cyclone over the NE Pacific and the anticyclone over North America during ENSO warm episodes. Major departures of the model pattern from the NCEP pattern include the more northward extension of the positive signal located over North America, and the more westward extension of the negative signal located in the extratropical Pacific (even to NE Asia).
5. Conclusions and Discussion
 The interannual variation of the tropopause is studied by analyzing data from NCEP reanalysis and a simulation using SUNYA CCM3 for the period 1979–1994. Both the NCEP and model data show the coherent variation between the tropical and extratropical tropopause that is mainly driven by large-scale dynamical processes in the lower stratosphere.
 Interannual variation of the meridional circulation, caused by the interannual variation in planetary wave propagation through a downward control mechanism [Holton et al., 1995], plays an essential role for the variation of the zonal mean tropopause. In the NH during winter, when stratospheric planetary wave activity is stronger than that in other seasons, interannual variation of the polar tropopause is mainly driven by the variation of dynamical heating rates. The related response of the tropical tropopause is to vary in phase opposite to that of the polar tropopause, consistent with the pattern of Brewer–Dobson circulation in the lower stratosphere. This tropical NH polar connection of the tropopause is the leading component in the global tropopause variation. Associated with the change in polar tropopause is the change in the polar night vortex, as indicated in the first SVD component. The vortex is strengthened for a colder polar tropopause temperature. In the SH during winter to spring, the polar O3 variation is the dominant factor driving the SH polar tropopause variation. Again, the tropical tropopause varies out of phase with the polar tropopause as a result of the dynamical response.
 The QBO accounts for a larger portion of the climate variability in the SH lower stratosphere than in the NH lower stratosphere. This interhemispheric asymmetry of the QBO effect is evident in the results of our SVD analysis. The QBO accounts for about 16% of the variability of zonal wind associated with the NH polar tropopause variation, and about 36% of the variability of zonal wind associated with the SH polar tropopause variation. Although the model cannot simulate the QBO, it reproduces about 74% of the NCEP variability for the NH tropopause temperature and about 45% of the NCEP's variability for the SH tropopause temperature. The model reproduces a smaller portion of the NCEP's variability in the SH, and this may be partially related to the larger QBO signal found in the SH lower stratosphere. One possible reason for the interhemispheric asymmetry is that the total climate variability in the SH stratosphere is smaller than that in the NH stratosphere, so that the QBO effect is more evident in the SH stratosphere. The detailed mechanism causing this interhemispheric asymmetry requires further model and observational studies about the QBO effects on both hemispheres. The zonal wind pattern shown in the first SVD component (Figure 7, SVD1) resembles the dipole pattern associated with the NH annular mode [Thompson and Wallace, 2000], which is modulated by the QBO through altering the stratospheric waveguide of planetary wave propagation, as discussed by Balachandran and Rind , Baldwin and Dunkerton , and Baldwin et al. . The zonal wind patterns shown in the second to fourth SVD components (Figure 7, SVD2–SVD4) capture some features of the QBO zonal wind composites for the SH [Baldwin and Dunkerton, 1998]. It therefore suggests that SVD can be a useful tool of statistical analysis for stratospheric dynamics as well as a tool to validate GCM simulations.
 The ENSO contributes a significant portion of natural variability in the troposphere. It also affects the interannual variation of dynamical processes in the lower stratosphere, driving the interannual variation of the eddy tropopause. Although the responses of the atmosphere to ENSO warm and cold episodes do not mirror each other [Hoerling et al., 1997], our study applying linear statistical analysis should obtain the linear portion of the response (i.e., anomalies in warm episodes minus those in cold episodes). During ENSO warm episodes, the rising motion induced above the dumbbell-shaped warming pattern in the tropical eastern Pacific cools the local tropopause. In the extratropics over the PNA sector, the warming of the tropopause over the NE Pacific and North Canada is associated with the response of stationary waves at 100 hPa, which is similar to the surface to 200 hPa PNA patterns found in previous studies [Hoerling et al., 1995, 1997; Livezey et al., 1997]. The model can well simulate the tropopause variation associated with the ENSO, capturing the warming/cooling patterns seen in the tropical eastern Pacific and in the PNA sector. The model variability is also close to the NCEP's variability. However, further study is necessary to investigate the underestimation of the anomalies in the tropical western Pacific.
 The covariance matrices for the PCA were directly constructed from the temperature anomalies (no normalization performed to the anomalies) as follows:
where cov(xi, xj) represents the matrix's element of the ith row and jth column, i and j represent the grid indices ranging from 1 to the maximum number of grid points, n represents the month index ranging from 1 to N (equals to 192), and T represents the temperature anomalies. The anomalies were decomposed into PCs as follows:
where cm(tn) is the associated time series for the mth principal component, and em(x) is the corresponding eigenvector (or EOF) of the covariance matrix. The eigenvectors (EOFs) of the covariance matrix are normalized to unity, and the eigenvalues, , represent the variance associated with the corresponding EOFs. The EOFs then represent the weight distribution of the PCs' standard deviations. The variance of the interannual variation contributed by the mth PC at any grid can be simply computed as λm · em2(x), and its root is the corresponding standard deviation at the gird.
 The covariance matrix for the SVD is constructed with an equation similar to (A1), from the zonal mean zonal wind anomalies and zonal mean tropopause temperature anomalies (no normalization performed to the anomalies). Since the numbers of spatial grids of the two anomalies are different (73 × 17 for the zonal mean zonal wind, and 73 for the zonal mean tropopause temperature), the matrix has different row and column dimensions. The singular vectors are obtained by solving the eigenvalue problem of a matrix constructed by the product of the covariance matrix and its transpose [Bretherton et al., 1992]. Again, the singular vectors were normalized to unity and the singular values represent the covariance of the pair of time series associated with the corresponding pair of singular vectors.
F test was performed to estimate the statistical significance of a PC or SVD component at any grid. The F value for the component at a grid is calculated by the ratio of χ2 before and after the component is included. For example, the F value for the Mth component at a grid x is calculated as follows:
The statistical significance at the grid of the Mth component is then estimated using the F distribution. This calculation was applied for both PCA and SVD expansions.
 Temperature anomalies are the results of heating/cooling mechanisms, which can be diagnosed according to the thermodynamic equation
 For simplicity we write only two terms in the right side of the equation. The left side represents the anomalies of the net temperature tendencies. The first and second terms in the right side are, respectively, the anomalies of the dynamical and diabatic heating rates. All terms in (A3) can be decomposed using the PC time series of the temperature anomalies in (A2). The spatial pattern of the temperature anomalies resembles that of the net temperature tendency anomalies of 1 month earlier. This is reasonable because the temperature is the integrated result of the temperature tendency. Therefore, in this study the temperature tendencies were projected onto the PC time series with 1-month time lag.
where hm(x), dm(x), and bm(x) are, respectively, the corresponding spatial patterns of the net temperature tendency, dynamical, and diabatic heating anomalies for each PC. The orthogonal property of cm(tn) and (A4) yield the following result for each PC:
(A5) allows one to decompose the temperature tendency anomalies associated with each PC into dynamical and diabatic heating terms. Consequently it can give insights into the underlying mechanisms associated with each dominant PC of the temperature anomalies, if the pattern hm(x) in (A5) is similar to the pattern em(x) in (A2). This condition is satisfied if the temperature tendency anomalies are projected with a 1-month time lag as indicated in (A4).
 We thank William J. Randel for supplying the O3 trends used in our construction of the O3 archive. We also thank two anonymous reviewers for their constructive suggestions of clarifying the presentation of the manuscript. Model simulations were conducted at NCAR computing facility. This work is supported by the Programs of Climate Dynamics and Atmospheric Chemistry of the National Science Foundation and the Office of Biological and Environmental Research, Office of Science Department of Energy.