Internal Interannual Variability of the Troposphere ... - AMS Journals

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Internal Interannual Variability of the Troposphere–Stratosphere Coupled System in a Simple Global Circulation Model. Part I: Parameter Sweep Experiment MASAKAZU TAGUCHI

AND

SHIGEO YODEN

Department of Geophysics, Kyoto University, Kyoto, Japan (Manuscript received 14 August 2001, in final form 23 April 2002) ABSTRACT Internal variations of the troposphere–stratosphere coupled system with intraseasonal and interannual timescales are investigated in a parameter sweep experiment with a simple global circulation model under a periodic annual forcing. In order to examine the role of forced planetary waves in the variations, the amplitude of a sinusoidal surface topography is chosen as an experimental parameter; 100-yr integrations are performed for each of 10 topographic amplitudes from 0 to 3000 m. The extratropical stratospheric circulation depends on the topographic amplitude in its mean seasonal march and intraseasonal and interannual variations. In the run without the topography, the stratospheric circulation is basically driven thermally and hardly shows interannual variation in any seasons. In the runs in which the topography is included, on the other hand, the stratospheric circulation is dynamically active and shows large interannual variation in different seasons, that is, spring for small topographic amplitudes (around 500 m) and winter for large amplitudes (around 1000 m). The mean seasonal march and interannual variation in these runs of small and large amplitudes resemble those in the Southern and Northern Hemispheres, respectively. In this study, the annual forcing is introduced only in the stratosphere while the tropospheric condition is kept constant in time, in order to investigate downward influence from the stratosphere to the troposphere in the seasonal march. The annual response of the atmosphere can significantly penetrate into the troposphere, depending on the topographic amplitude. The downward penetration is significant for the amplitudes of planetary and synoptic-scale waves, while it is negligible for zonal mean quantities. The empirical orthogonal function and lag correlation analyses show that a sequence of variability associated with stratospheric sudden warmings (SSWs) in the run of the topographic amplitude of 1000 m is characterized by poleward and downward propagation of anomalies of the zonal mean zonal wind and the planetary wave amplitude. Preconditioning for and the aftereffect of SSWs extend through both the stratosphere and troposphere. One month before SSWs, the polar night jet and the tropospheric jet shift poleward while planetary waves amplify in the troposphere and stratosphere. The anomalies of the zonal wind and wave amplitude further propagate poleward and downward for several months after SSWs.

1. Introduction The extratropical stratospheric circulation is different between the Northern and Southern Hemispheres in its seasonal march as well as interannual and intraseasonal variations (e.g., Randel 1992; Randel and Newman 1998). The interannual variation is a year-to-year variation defined as a deviation from the climatological annual cycle, while the intraseasonal variation is a lowfrequency variation within a season. Figures 1a and 1b display annual variations of frequency distributions of the monthly mean temperature in the middle stratosphere at the South Pole (SP) and the North Pole (NP), respectively, drawn with National Centers for Environmental Prediction (NCEP)–National Center for Atmo-

Corresponding author address: Dr. Masakazu Taguchi, Department of Atmospheric Sciences, Box 351640, University of Washington, Seattle, Washington, 98195-1640. E-mail: [email protected]

q 2002 American Meteorological Society

spheric Research (NCAR) reanalysis data for 1979–97 (Yoden et al. 2002). The interannual variation is large in October and November at the SP, while large in January, February, and March at the NP. If such frequency distributions are drawn with a longer dataset over 45 yr compiled at Free University Berlin (Fig. 1c), they present some hints of detailed distributions, such as positive skewness for winter months. An observational analysis of the stratospheric circulation from a dynamical viewpoint of wave–mean flow interaction shows interhemispheric differences too (Shiotani and Hirota 1985). The seasonal march of the stratospheric circulation in the NH is characterized by intermittent enhancement of planetary wave activity with a timescale of about 2 weeks during winter. Such enhanced wave activity dramatically reverses the polar night jet at times to replace it by the easterlies, that is, causes stratospheric sudden warming (SSW). Major SSW events take place about every 2 or 3 yr and their timing is at random during winter, which results in the

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FIG. 1. Frequency distributions of the monthly mean temperature at p 5 30 hPa (Yoden et al. 2002): (a) the South Pole and (b) the North Pole drawn with NCEP–NCAR reanalysis data for 1979–97, as well as (c) the North Pole with a longer dataset from Jul 1955 to Oct 2000, compiled at Free University Berlin (through the courtesy of Prof. K. Labitzke). Broken line denotes climatological seasonal march, and shade shows the variable range. Two numbers for each month denote (top) the climatological mean and (bottom) the standard deviation of the monthly mean temperature. Frequency distributions for a seasonal mean are also displayed in the bottom: spring mean for the South Pole and winter mean for the North Pole.

extremely large intraseasonal and interannual variations during the season (Labitzke 1982; see also Fig. 1). In the SH, on the other hand, planetary wave activity is suppressed in midwinter corresponding to the strong polar night jet. After the polar night jet shifts poleward and downward in late winter, planetary wave activity increases and persists during spring. The shift of the jet occurs at different timing in different years so that the interannual variation is large in late winter (Shiotani et al. 1993). Such differences of the intraseasonal and interannual variations between the two hemispheres can be extracted by empirical orthogonal function (EOF) analyses. Kodera (1995) and Kuroda and Kodera (1998) investigated interannual variability of the tropospheric and stratospheric circulations in the NH and the SH by means of extended and multiple EOF analyses. Common to both hemispheres, the extracted dominant modes of variability exhibit poleward and downward propagation of anomalous zonal mean zonal wind. It takes about 2 or 3 months for the propagation from the subtropical upper stratosphere to the polar region of the lower stratosphere and the troposphere. They call the slow mean zonal wind

variation the polar night jet oscillation (PJO). They also note that time coefficients of the mode in the SH show a clear biennial oscillation in the 1980s. A difference between the two hemispheres is that the sequence of the propagation is locked more closely to the seasonal cycle in the SH; the shift of the polar night jet occurs only in late winter in the SH, while SSW events occur at random during winter in the NH. Some part of these interannual variations is considered as a response to time variations of external forcings or boundary conditions of the stratosphere. The troposphere is one of such external forcings of the stratosphere, as shown in Matsuno’s (1971) theory on SSW in which he assumed impulsive initiation of a wave forcing in the troposphere. Other examples of the external forcings or boundary conditions, such as 11-yr solar cycle and intermittent eruptions of volcanos, are described in Yoden et al. (2002). On the other hand, some interannual variations may be generated internally within the stratosphere. Recent numerical studies with a hierarchy of stratosphere-only models having a timeconstant lower boundary near the tropopause argued the importance of internal processes in the stratosphere in

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causing intraseasonal and interannual variations. These studies are also reviewed in Yoden et al. (2002). The stratosphere-only models, either ‘‘slave-stratospheric-variation’’ models or ‘‘independent-stratospheric-variation’’ models, assume no downward influence from the stratosphere to the troposphere. The stratospheric variations are caused by the variations of bottom boundary, that is, the troposphere, without any stratospheric influence on the troposphere in the slave-stratospheric-variation models, while the stratospheric variations are possible for a time-constant bottom boundary condition in the independent-stratospheric-variation models. However, some recent reviews (e.g., Baldwin 2000; Hartmann et al. 2000) have pointed out the coupled variability of the troposphere and the stratosphere at intraseasonal and interannual timescales in the contexts of SSWs and the Arctic Oscillation. These studies indicate that the troposphere and the stratosphere should be considered as a dynamically coupled system. Taguchi et al. (2001, hereafter referred to as TYY) demonstrated the usefulness of parameter sweep experiments with a simple global circulation model to understand the dynamical nature of the troposphere–stratosphere (T–S) coupled system. TYY investigated internal intraseasonal variation of the T–S system, such as SSWs, in a series of numerical experiments under a perpetual-winter condition. They changed the amplitude of a sinusoidal surface topography to examine the role of forced planetary waves in the T–S coupled system, and clarified highly nonlinear dependence on the parameter. Although the framework of a perpetual-winter condition is useful to isolate the intraseasonal variation in winter, the seasonal march and interannual variation that are vital to the T–S system are excluded. In this study, we introduce an annual thermal forcing (i.e., seasonal cycle) to TYY’s experiment to investigate not only the seasonal march but also internal intraseasonal and interannual variations of the T–S coupled system. The intraseasonal and interannual variations in this experiment are purely internally generated in the T–S system because they are obtained under a purely periodic annual forcing that excludes the time variations of the external conditions or boundary conditions mentioned above. It should be noted that the annual forcing is included only in the stratosphere but not in the troposphere to elucidate downward influence from the stratosphere to the troposphere, which is one of the open questions on the T–S coupling. External conditions in the troposphere are held constant in time, so that any annual response in the troposphere is result of the downward influence. We choose 10 representative values of the topographic amplitude from a series of TYY’s experiment, and perform 100-yr integrations for each of them. In this paper, we describe the seasonal march and internal intraseasonal and interannual variations, which are dependent on the topographic amplitude, or forced planetary waves. Some statistical analyses are also made to

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investigate the T–S coupling associated with SSWs. Furthermore, we carry out millennium (1000 yr) integrations for two selected runs under the same conditions to obtain more statistically reliable results, which will be reported in a separate paper (Taguchi and Yoden 2002). The present paper is organized as follows. The model is documented in section 2. Results of the parameter sweep experiment are described in section 3 from the viewpoints of seasonal march and interannual variability of the stratospheric circulation. A sequence of low-frequency variability associated with SSWs is analyzed in section 4. Discussion is in section 5, and conclusions in section 6. 2. Model The model used in this study is basically the same as in TYY, and the details are documented there. The model is a three-dimensional global primitive equation model (Swamp Project 1998), which explicitly describes large-scale motions with a horizontal resolution of T21 spherical harmonics truncation and 42 levels from the surface to the mesosphere. The horizontal resolution is validated from Christiansen (2000a), who obtained qualitatively similar T–S variability in GCM calculations with T21 and T42. Time integration is performed with Dt 5 1200 s 5 20 min for 100 yr in each run, after 1 yr of spinup period from an initial state of an isothermal atmosphere (240 K) at rest. Small perturbations are added to the initial state for efficient spinup. The seasonal cycle is included by Newtonian-type radiative relaxation toward a prescribed temperature field T* (f, z, t) that varies in time t with an annual cycle. Here, f is latitude and z geometric height. The temperature field is a sinusoidal superposition between NH winter [December, January, February (DJF)] and summer [June, July, August (JJA)] temperature fields T*w (f, z) and T*s (f, z), respectively, following Scott and Haynes (1998): T*(f, z, t) 5 r(t)T*( w f, z) 1 [1 2 r(t)]T*( s f, z).

(1)

The temperature field T*w (f, z) is the standard basic temperature field used in TYY for the perpetual-winter integrations, which mimics a radiative equilibrium state in NH winter, while T*s (f, z) 5 T*w (2f, z) and r(t) 5 [1 1 cos(2pt/T)]/2. Here, T is 1 yr (360 days 5 30 days 3 12 months). The radiative relaxation rate is given as a function of height, a(z) 5 {1.5 1 tanh[(z 2 35 km)/7 km]} 3 10 26 s 21 , as in Holton and Mass (1976). In order to clarify downward influence from the stratosphere to the troposphere, T* is held constant in time in the troposphere. This is based on the fact that T*w (f, z) is symmetric with respect to the equator. Some other physical processes are also simplified in the model; dry atmosphere with no moist processes, dry convective adjustment, and Rayleigh friction at the bottom level with a relaxation rate of 0.5 days. A sinusoidal

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FIG. 2. Time–latitude sections of mean seasonal march in the upper stratosphere in the run of h 0 5 1000 m: (a) zonal mean temperature [T ] (K) at p 5 2.6 hPa, (b) zonal mean zonal wind [U ] (m s 21 ) at p 5 1.2 hPa, and (c) wave amplitude of zonal wavenumber-1 geopotential height (wave 1) | Z1 | (m) at p 5 1.2 hPa. Each is averaged for each calendar day in the 100 yr. Contour intervals are (a) 5 K, (b) 10 m s 21 , and (c) 200 m. Broken lines in (a) denote contours of 252.5 K.

surface topography (Yamane and Yoden 1998) is included: h(l, f ) 5

5

4h0 m 2 (1 2 m 2 ) sin(ml) 0

(m $ 0), (m , 0),

(2)

where l is longitude, m 5 sinf, and m is the zonal wavenumber. Note that the surface topography is the only difference between the NH and the SH in the model, and the surface is flat in the SH. The amplitude h 0 of the topography is chosen as an experimental parameter, with m 5 1; 100-yr integrations are performed for each of 10 topographic amplitudes from 0 to 3000 m after the spinup. Dependence of internal variations of the troposphere and stratosphere in the NH on h 0 is described in the parameter sweep experiment. The variations in the NH are mainly determined there; interhemispheric influence is unlikely from the ‘‘downward control’’ principle (Haynes et al. 1991) that planetary wave drag basically drives diabatic motions in each

hemisphere, in addition to little planetary waves in the SH due to the flat surface. 3. Parameter sweep a. Seasonal march Before showing results of the parameter sweep experiment, we examine model performance in terms of mean seasonal march in the run of h 0 5 1000 m. This run is regarded as a control run, in which some SSW events are simulated during winter to lead to the seasonal march and interannual variability that generally look like those in the real NH. Figure 2 displays time– latitude sections of mean seasonal march in the upper stratosphere averaged for each calendar day in the 100 yr, the zonal mean temperature [T], the zonal mean zonal wind [U], and wave amplitude of zonal wavenumber-1 component of geopotential height (wave 1) | Z1 | . Here, square brackets denote the zonal mean, and absolute

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value symbols wave amplitude. Each quantity is displayed at a level where it shows strong features of the seasonal march. Common to both hemispheres, these quantities exhibit general features of the seasonal march in the real stratosphere (e.g., Randel 1992); the maximum (minimum) zonal mean temperature at the summer (winter) pole (Fig. 2a) and the zonal mean easterly (westerly) wind in the extratropics of the summer (winter) hemisphere (Fig. 2b). Planetary wave amplitude is large around winter when the zonal mean wind is westerly (Fig. 2c). The zonal wind for summer is not as strongly easterly in both hemispheres for the model as for the real atmosphere (e.g., Randel 1992), which results from the prescribed basic temperature field T*. However, the seasonal march of the stratospheric circulation is qualitatively well simulated enough to examine its dependence on h 0 in the cold seasons from autumn to spring. Some interhemispheric differences of the seasonal march are also noticeable in Fig. 2, indicating that the seasonal march depends on the surface topography. The winter polar temperature is higher in the NH than in the SH, while the polar night jet is much weaker. The higher polar temperature and weaker polar night jet are dynamically consistent with the wave 1 of larger amplitude in NH winter. Note that wave 1 in the SH winter arises from nonlinear interaction of baroclinic eddies in the troposphere as in the situation studied by Scinocca and Haynes (1998). In the tropical upper stratosphere, the zonal mean temperature and zonal wind exhibit remarkable annual responses in spite of the semiannual cycle of the thermal forcing there; the zonal mean temperature is lower in NH winter than in SH winter while the mean easterly wind is stronger. The annual cycle of the tropical temperature in this model is analogous to that in the real atmosphere (Yulaeva et al. 1994) in the sense that both result from the interhemispheric difference of the extratropical planetary wave amplitude; the wave driving, or the ‘‘extratropical pump,’’ is stronger in NH winter for both of the model and the real atmosphere. In order to show the dependence of the mean seasonal march on h 0 , mean annual variations of [T], [U], and | Z1 | in the extratropical upper stratosphere are plotted for each run in Fig. 3. The annual variations exhibit strong dependence on h 0 from autumn to spring. For the runs of small h 0 (h 0 5 0 and 300 m), the polar temperature shows almost a sinusoidal seasonal march (Fig. 3a), following the annually varying prescribed temperature T* (denoted by a broken line) with a time lag of several days. As h 0 increased to h 0 5 600 m, the polar temperature comes to depart from the prescribed temperature toward the warm side in spring. The timing of the maximum departure becomes earlier with increasing h 0 . The temperature in early and midwinter is as low as the radiatively determined state. As h 0 is further increased up to h 0 5 3000 m, the polar temperature de-

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parts more largely in a longer period during winter and the maximum departure appears earlier. The seasonal march of the polar night jet and planetary wave amplitude also has corresponding dependence on h 0 (Figs. 3b,c). The maximum value of [U] becomes smaller while it appears earlier from midwinter to late autumn, with increasing h 0 through the whole range. The maximum value of | Z1 | becomes larger while its timing becomes earlier from late spring to midwinter, as h 0 is increased from 300 to 1000 m. For the runs of larger h 0 , the mean seasonal march of wave1 amplitude is not so dependent on h 0 . The run of h 0 5 3000 m is exceptional, where the amplitude is small in winter. Note another maximum of wave-1 amplitude in autumn for the run of h 0 5 300 m. In summer, the stratospheric circulation is relatively independent of h 0 through the whole range except for runs of small h 0 , in which the polar temperature departs from the prescribed temperature and the zonal wind is westerly corresponding to the situation in the SH of Fig. 1. A key feature of the present model is that the annual thermal forcing is included only in the stratosphere while not in the troposphere. Thus, it is possible to quantitatively clarify downward influence from the stratosphere to the troposphere by examining vertical profiles of annual cycle response of the atmosphere measured by power spectrum density (PSD) with a period of 1 yr (Fig. 4). For each quantity, the PSD is calculated for the period at each meridional grid point and then averaged over latitudes where the PSD is large. This way of examining the downward influence is validated from the fact that, for each quantity, the tropospheric mean PSD has a peak at the period and the PSD at the period in this seasonal cycle experiment is much larger by orders than that in TYY’s perpetual-winter experiment (not displayed). The downward penetration of the PSD has strong dependence on h 0 as well as on quantity, although the thermal relaxation works for both the zonal mean and waves with the same timescale at each pressure level. The PSDs of the zonal mean temperature and the zonal mean zonal wind in the extratropics (Figs. 4a,b) sharply decrease with decreasing height from the stratosphere to the troposphere for all the runs; their PSDs are much smaller in the troposphere than in the stratosphere, by a factor of O(10 23;24 ). On the contrary, the annual cycle response of wave-1 amplitude (Fig. 4c) can significantly penetrate from the stratosphere down to the surface depending on h 0 , while the response in the stratosphere itself depends on h 0 . The downward penetration is most significant for the runs of h 0 5 300 and 400 m, in which the PSDs in the troposphere are comparable to those in the stratosphere. The downward penetration is significant even in other runs of 600 m # h 0 # 1000 m, with a factor that is as large as about O(10 21 ). Downward penetration of the annual cycle response of wave-5 amplitude (Fig. 4d) is also significantly dependent on h 0 . The PSDs in the troposphere are larger than those in

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FIG. 3. Mean seasonal march in the upper stratosphere in each run: (a) [T ] (K) at f 5 868N and p 5 2.6 hPa, (b) [U] (m s 21 ) averaged over latitudes 508N # f # 708N at p 5 1.2 hPa, and (c) | Z1 | (m) averaged as in [U]. A broken line in (a) denotes the time change of the prescribed radiative equilibrium temperature T* at the grid point. Labels are h 0 (m) 3 10 22 .

the stratosphere in the runs of 0 m # h 0 # 1000 m, but comparable in the other runs. b. Interannual variability Figure 5 displays daily variations of the zonal mean temperature near the polar stratopause for the 100 yr in each run. For the run of h 0 5 0 m, the polar temperature shows little interannual variations throughout the year. As h 0 is increased to h 0 5 500 m, interannual variations become large in spring; their timing becomes earlier from late spring to early spring. For the run of h 0 5 500 m, the polar temperature is anomalously high in some winters for the 100 yr, reflecting the occurrence of large SSW events in these years. For the runs of 600 m # h 0 # 3000 m, interannual variations become extremely large in midwinter. In order to address the change of interannual variability with h 0 , Fig. 6 displays annual variation of frequency distributions of monthly mean polar temperature in three particular runs of h 0 5 0, 500, and 1000 m. The frequency distribution in the run of h 0 5 0 m (Fig.

6a) is hardly scattered in any seasons (i.e., small interannual variability in all the seasons), as the variable range is denoted by shade. The standard deviation is always small. In the run of h 0 5 500 m (Fig. 6b), the interannual variability is large in spring, especially in March and April, while small in the other seasons. The polar temperature in winter is low in most of the 100 yr but extremely high in a few exceptions. In the run of h 0 5 1000 m (Fig. 6c), the variability is large from late autumn (November) to early spring (March); especially large during winter from December to February. The variability becomes small after April. These two types of interannual variations in the runs of h 0 5 500 and 1000 m correspond to those in the real SH and NH, respectively, as seen in Fig. 1, although the pressure levels are different. 4. A sequence of low-frequency variability associated with SSWs in the run of h 0 5 1000 m The stratospheric interannual variability is large during winter in the run of h 0 5 1000 m reflecting the

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FIG. 4. Vertical profiles of the power spectrum density with a period of 1 yr in each run: (a) P[T] (K 2 day 21 ) averaged over latitudes 708N # f # 908N, (b) P[U] (m 2 s 22 day 21 ) over 508N # f # 708N, (c) P | Z1 | (m 2 day 21 ) over the same latitudes as in P[U] , and (d) P | z 5 | (m 2 day 21 ) over 358N # f # 558N. Labels are h 0 (m) 3 10 22 . The annual thermal forcing is included above the upper horizontal line, while it is not at all below the lower one.

occurrence of SSW events as shown in Figs. 5 and 6. In order to examine a sequence of low-frequency variability associated with SSWs in this run, EOF analyses and lag correlation analyses are made based on monthly mean fields.

Two kinds of EOF analysis are used to objectively extract a space–time sequence associated with SSW events. One is multiple EOF (MEOF) analysis, in which the usual EOF analysis is performed by combining a vector ui(m) for n consecutive months into a vector xi as

FIG. 5. Daily variations of [T ] (K) at f 5 868N and p 5 2.6 hPa for the 100 yr in each run.

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FIG. 6. Frequency distributions of monthly mean [T ] at f 5 868N and p 5 2.6 hPa in three runs: (a) h 0 5 0 m, (b) 500 m, and (c) 1000 m. Averages and standard deviations for the 100-yr data are written on the right-hand side of each month (upper and lower numbers, respectively).

x i 5 [u i (m), u i (m 1 1), . . . , u i (m 1 n 2 1)].

(3)

Here, u i (m) denotes an anomalous field for the mth month of the ith year. The other is extended EOF (EEOF) analysis, which further includes delayed signals of t months as independent ensembles: x ti 5 [u i (m 1 t), u i (m 1 t 1 1), . . . , u i (m 1 t 1 n 2 1)],

Thus, the MEOF analysis is useful to extract a sequence of variability that is locked to the calendar months, or the seasonal cycle, while the EEOF analysis is useful to extract a sequence that takes place at random, independent of the seasonal cycle. This is why the MEOF and EEOF analyses are used by Kuroda and Kodera (1998) and Kodera (1995) for the SH and NH variations, respectively, which are mentioned in section 1.

(4)

where t 5 0, 1, . . . , T 2 1 (Weare and Nasstrom 1982). Note that x i0 in the EEOF analysis is identical to x i in the MEOF analysis and that a special case of the EEOF analysis in which no delayed signal is introduced (i.e., T 5 1) is identical to the MEOF analysis. The EOFs in the MEOF analysis are defined as the eigenvectors of the covariance or correlation matrix calculated from x i , while those in the EEOF analysis are calculated from x it. The obtained eigenvectors in the MEOF and EEOF analyses represent space–month sequences of the u anomalies that are dominant in yearto-year variability. In the MEOF analysis without the delayed signals, sequences of SSW events occurring in different months can be extracted as different EOFs. In the EEOF analysis including the delayed signals, on the other hand, the sequences can be captured by an EOF.

a. Polar temperature First, the MEOF analysis based on the covariance matrix is applied to the monthly mean polar temperature from June to May (Fig. 6c). In this case, u i (m) is polar temperature anomaly for the mth month of the ith year, and n 5 12. The leading MEOF (Fig. 7a, top line) represents a sequence of variability in which polar temperature anomalies remain either positive or negative for the 4 months from November to February. The maximum anomaly appears in January, so that this mode captures a sequence associated with SSW events which take place in the month. No strong anomalies appear except for winter. The MEOF explains large fraction (44.2%) of the total variance. Next, the MEOF analysis is applied for two other

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FIG. 7. (a) The first MEOFs of monthly mean [T ] at f 5 868N and p 5 2.6 hPa in the run of h 0 5 1000 m. The MEOF analysis is applied for three different periods: (top line) Jun–May, (center) Sep– May, and (bottom) Nov–Mar. The center and bottom lines are offset. (b) The first EEOFs of monthly mean [T ] at the same grid point in the run: (thin line) Oct–Feb to Dec–Apr, and (thick line) Sep–Jan to Jan–May. The ordinate is arbitrary in both (a) and (b). See text for details of the MEOF and EEOF analyses.

periods of September to May (m 5 9, n 5 9) and November to March (m 5 11, n 5 5). The leading modes in these two cases (Fig. 7a, center and bottom lines) exhibit very similar sequences as in the first case. The percentages of the variance explained by the leading modes are as large (44.2% and 47.1%) as in the first case. It is a robust feature that large temperature variations are seasonally locked to winter. Since SSW events take place not only in January but also in other months (Fig. 6c), it is necessary to employ the EEOF analysis so as to extract a common sequence of SSW events. Two cases of the EEOF analysis that include delayed signals are performed, with n 5 5. One is for m 5 10 and T 5 3 (October–February to December–April), as shown by thin solid line in Fig. 7b, while the other is for m 5 9 and T 5 5 (September–January to January–May), as shown by thick solid line in the same figure. A common feature of the leading EEOF between the two cases is that the leading EEOF exhibits temperature anomalies that remain in one sign for 4 months around the maximum anomalies. This indicates that SSW events accompany strong positive temperature anomalies that last for several months. The percentage of the leading EEOF is substantial (58.8% and 51.4%). Time series of the EEOF analysis are examined below, which is important to understand the procedure of the EEOF analysis. In the latter case of the EEOF analysis, there are five periods (i.e., T 5 5) for which temperature anomalies in each year are projected onto the leading EEOF. The projection produces five year-to-year time series of the EEOF, shown by solid lines in the five panels of Fig. 8, with each projection period denoted at the top left in each panel. The values of time series are large in magnitude for the periods starting from September, October, or November.

FIG. 8. (solid lines) Time series of the first EEOF of monthly mean [T ] from Sep–Jan to Jan–May (latter case in Fig. 7b) in the run of h 0 5 1000 m as functions of year. The five panels represent the five different periods for which [T ] anomalies are projected onto the first EEOF (denoted at the top left in each): (top) Sep–Jan, to (bottom) Jan–May. (broken lines) Monthly mean [T ] anomalies in months (denoted at the right top) when the correlations with the EEOF time series are maximum (denoted at the right bottom) at f 5 868N, and p 5 2.6 hPa.

In order to examine the contribution of each month to the leading EEOF, correlation coefficients of the EEOF time series for each period with the polar temperature of each month are calculated (Fig. 9). The sequence of the correlations in the first four periods resemble that of the leading EEOF; the correlations remain positive for 3 or 4 months, with the maximum in the third or fourth month of each period. The maximum correlations are very high, which are larger than or close to 0.8. The resemblance indicates that the four periods make substantial contribution to the leading EEOF. The last period starting from January is exceptional in which the sign of the correlations reverses with a shorter timescale; significant correlations with the opposite signs appear in January and in March. Year-to-year variations of the polar temperature anomalies are also plotted by broken lines in Fig. 8, for the month when the correlation is maximum for each period. As expected from the very high correlations, the interannual variations of the EEOF time series are quite similar to those of the temperature anomalies, particularly for the first three periods starting from September, October, or November. b. Zonal mean zonal wind in the troposphere and stratosphere In order to examine a sequence of low-frequency variability of some important physical properties in the

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FIG. 9. Correlation coefficients of the EEOF time series with monthly mean [T ] in each of the 12 months. The five panels represent the five different periods of projection (denoted by vertical lines), as in Fig. 8.

troposphere and stratosphere, a lag correlation analysis is made by using the polar temperature at p 5 2.6 hPa; a lag correlation coefficient r A (where A is a physical property) is calculated between the polar temperature (key variable) on either of some months (key month) and A(f, p) at all grid points in the meridional plane for each month. The key month corresponds to lag 5 0 month. Regarding statistical significance of the correlation coefficients, a Monte Carlo simulation indicates that a pair of data, each of which consists of 100 random numbers, has a correlation coefficient over 60.083 with a probability of occurrence by chance of 5%. Therefore, the correlation coefficients that exceed the range show correlated relationship of statistical significance. Figure 10 displays latitude–height sections of the lag correlation coefficients for a case in which the key month is January. In lag 5 0 month, the autocorrelation coefficient r[T ] exhibits a quadrupole structure of SSWs in the stratosphere and mesosphere; the correlation is

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positive (negative) in the stratosphere (mesosphere) in the high latitudes, and opposite in the midlatitudes. The positive correlation in the polar stratosphere extends down to the troposphere, where the maximum correlation appears more equatorward around f ; 508N. This means that the troposphere in the latitudes is also warmer than climatology in January when SSWs take place. The correlation of the zonal mean zonal wind r[U ] is negative in most of the extratropical stratosphere; the polar night jet weakens in the months when SSWs take place. The negative correlation in the stratosphere extends down to the midlatitude troposphere. The correlation in the high latitudes is positive below the middle stratosphere. Wave-1 amplitude has positive correlation (r | z1 | . 0) in the high-latitude stratosphere; wave 1 amplifies and the polar vortex shifts off from the pole in the months of SSWs. The correlation of wave-5 amplitude r | z 5 | is positive in most of the stratosphere and mesosphere, which suggests that wave-5 disturbances appear as a result of nonlinear interactions in SSW events. In lag 5 21 month, a ‘‘preconditioning’’ pattern of the zonal mean zonal wind and wave-1 amplitude for SSWs is remarkable in both of the stratosphere and the troposphere. The zonal mean zonal wind shows an equivalent barotropic dipole pattern consisting of positive correlation in the high latitudes and negative one in midlatitudes in the troposphere and lower stratosphere. The correlation is stronger in the troposphere, with the maximum ( | r[U ] | . 0.6) near f 5 658 and 358N. This correlation pattern indicates that both of the tropospheric jet and the polar night jet are located more poleward than their climatological positions 1 month before SSW events; in synoptic terms, the polar vortex is tighter than usual. The correlation of wave-1 amplitude is positive in the extratropical stratosphere and troposphere, showing the amplification of wave 1 at 1 month before SSWs. The correlation in the troposphere is as strong as that in the stratosphere, and the maximum in the troposphere (r | z1 | . 0.6) appears near f 5 458N. Note that the correlations in lag 5 22 months are not so significant. After the month of SSWs (lag 5 1 and 2 months), strong correlation regions of the zonal mean zonal wind and wave-1 amplitude generally propagate poleward and downward in the stratosphere, although detailed features of the propagation depend on month and location. Significant correlation is noticeable even in the troposphere after the month of SSWs; r | z1 | , 20.4 in lag 5 1 month near f 5 358 and 708N, indicating wave-1 amplitude is smaller than climatology. Note that the correlations r[U ] and r | z1 | are more significant in lag 5 2 months than in lag 5 22 months, which means that the timescale of the preconditioning for SSWs is shorter than that of the aftereffects. A similar sequence of the lag correlations is obtained in cases in which the key month is changed from November to February of the large interannual variability (not displayed).

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FIG. 10. Latitude–height sections of the lag correlation coefficients with [T ] in Jan at f 5 868N and p 5 2.6 hPa (denoted by 3) in the run of h 0 5 1000 m: (top to bottom) [T ], [U ], | Z1 | , and | Z 5 | in (from left to right) Nov (lag 5 22 months) to Mar (lag 5 2 months). Contour interval is 0.2, and correlations over 60.4 are hatched.

Although the lag correlation analysis shows the sequence of low-frequency variability associated with SSW events (Fig. 10), the polar temperature in the upper stratosphere was prechosen as the key variable in the analysis, so that it is not evident whether or not the sequence is dominant in the whole interannual variability. The EOF analysis is a statistical way to extract a dominant mode of variability more objectively. The

EEOF analysis, based on the correlation matrix, is applied to the zonal mean zonal wind from September– January to January–May (m 5 9, n 5 5, T 5 5). The period corresponds to the latter case of the EEOF analysis for the polar temperature (thick solid line in Fig. 7b). The sequence of the extracted leading EEOF (Fig. 11a), which explains 18.3% of the total variance, resembles that of the lag correlation r[U ] with the key

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FIG. 11. (a) Latitude–height sections of the first EEOF of [U ] in the run of h 0 5 1000 m. The EEOF analysis is applied to monthly mean [U ] in the whole troposphere and stratosphere of the Northern Hemisphere for Sep–Jan to Jan–May. Panels are for the first month (left) to the fifth (right). Magnitude is arbitrary and contour interval is 5. Values over 610 are hatched. (b) Time series of the first EEOF for the 5 months from Oct to Feb (solid line). Time series of [T ] anomalies in Dec at f 5 868N and p 5 2.6 hPa are also drawn by a broken line.

month of January (Fig. 10). The anomalies of the zonal mean zonal wind show a dipole pattern throughout the extratropical troposphere and lower stratosphere in the first and second months. They have larger amplitude in the troposphere, which corresponds to the stronger correlation in the troposphere shown in Fig. 10. As the anomalies proceed poleward, they develop to the SSW pattern in the third month, with strong negative anomalies dominating the extratropical stratosphere. In the fourth and fifth months, the anomalies further propagate poleward and downward while they attenuate with time. Figure 11b displays time series of the leading EEOF for October–February (denoted by solid line) and those of the polar temperature anomalies in December (denoted by broken line), as in Fig. 8. The combination of the time series is the case that produces the strongest correlation (0.82), so that the time variations are very similar. Such strong correlations over 0.7 are also obtained for other combinations, as in Fig. 8. The resemblance of the leading EEOF (Fig. 11a) to the lag correlations (Fig. 10) and the strong correlations of the EEOF time series with the polar temperature (Fig. 11b) show that the sequence of the leading EEOF captures the fundamental properties of the time variations obtained by the lag correlation analysis in which the polar temperature was used as the key variable. The leading EEOF of the zonal wind anomalies in the troposphere and stratosphere (Fig. 11a) are in accord with

that of the polar temperature anomalies (Fig. 7b, latter case) obtained with the same values of m, n, and T; each of the EEOFs captures a sequence of low-frequency variability associated with SSW events that occur in the third or fourth month of the 5 consecutive months, although the contribution is smaller (18.3%) for the zonal wind anomalies due to the larger degrees of freedom. In order to examine the dependence of such sequence of low-frequency variability on the external parameter h 0 , the leading EEOF of the zonal wind anomalies is extracted in the same way for each of the 10 runs (Fig. 12). The leading EEOF has two different features depending on h 0 . One is the poleward propagation of the wind anomalies. In the run of h 0 5 0 m, the wind anomalies hardly propagate poleward with time, or stay in the same latitudes. On the contrary, as h 0 is increased to h 0 5 1600 m, the anomalies propagate poleward and also downward. The poleward propagation speed is faster for larger h 0 . In the runs of h 0 5 2000 and 3000 m, the anomalies appear a little irregularly but basically propagate poleward and downward. The other difference is the vertical extension of the wind anomalies. The wind anomalies deeply extend from the stratosphere to the troposphere in the runs of h 0 5 0 and 700 m # h 0 # 1600 m. The preconditioning pattern in the second month for the latter three runs is an example of the deep extension, although there is only weak connection to the troposphere in the fourth and fifth months. On the other hand, the

FIG. 12. As in Fig. 11a, but for each of the 10 runs. Magnitude is arbitrary, and only contours of 610, 615, and 620 are drawn. Values over 610 are hatched.

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FIG. 13. Latitude–height sections of climatological differences between Jul and Jan in the three runs: (left to right) [T ] (K ), [U ] (m s 21 ), | Z1 | (m), and | Z 5 | (m) in the runs of (a) h 0 5 0, (b) 500, and (c) 1000 m. Horizontal line denotes p 5 276 hPa, below which the annual forcing is not included at all. Contour intervals are 0.5 K for [T ], 2 m s 21 for [U ], 20 m for | Z1 | , and 2 m for | Z 5 | . Value range of 210 to 10 is plotted for [T ]. Negative values are hatched.

strong anomalies are confined in the stratosphere for the runs around h 0 ; 500 m. The percentage of the leading EEOF decreases with increasing h 0 . 5. Discussion It has been shown that the stratospheric circulation changes with the topographic amplitude h 0 , or forced planetary waves, in its seasonal march and interannual variability (Figs. 3, 5, and 6). Such change of the stratospheric circulation with forced planetary waves has been investigated in a hierarchy of stratosphere-only models (see Yoden et al. 2002 for references). The results in this study qualitatively agree with those of Yoden (1990), Christiansen (2000b), and Scott and Haynes (1998) among others, who used wave–mean flow interaction models for the extratropical channel or the spherical geometry, respectively. It is common between the three studies that, as wave forcing is increased, the climatological polar night jet becomes weaker and interannual variability becomes larger in winter. As for the seasonal march of planetary wave amplitude, the double-peak development obtained for small h 0 in this study (Fig. 3c) is analogous to the observation in the SH (e.g., Randel 1992) and the model results for small wave forcings (Plumb 1989; Yoden 1990). Since this study employs the T–S coupled model,

however, it has also presented some evidences of the T–S coupling. One interesting point is the downward influence from the stratosphere to the troposphere. Even if the annual thermal forcing is excluded in the troposphere, the annual response in the stratosphere can significantly penetrate down to the troposphere (Fig. 4). The annual response in the troposphere can be examined by taking the climatological differences between the opposite extremes of July and January for the three particular runs (Fig. 13). The climatological differences show that the troposphere also has substantial changes influenced by the stratospheric seasonal cycle, with some h 0 dependence of the changes. A common feature between the three runs of h 0 5 0, 500, and 1000 m is that the zonal mean zonal wind shows a negative (positive) difference in high- (mid-) latitude troposphere while the zonal mean temperature shows a negative difference in the extratropical troposphere. In the runs of h 0 5 500 and 1000 m, the planetary wave amplitude is smaller in July than in January. Baroclinic disturbances also show similar difference as the zonal wind in the troposphere. Another evidence of the T–S coupling is a sequence of low-frequency variability associated with SSW events for h 0 5 1000 m, which is characterized by poleward and downward propagation of anomalies of the zonal mean zonal wind and planetary wave amplitude

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(Figs. 10 and 11a). It was remarkable in the preconditioning stage for SSW events that the zonal wind anomalies extend through the troposphere and stratosphere to form a dipole pattern while the planetary wave amplifies in the troposphere and stratosphere. The wave amplification in the troposphere indicates that the large interannual variability in the stratosphere, mainly contributed by the occurrence of SSW events, is caused by the planetary wave variability in the troposphere. Such poleward and downward propagation of zonal wind anomalies in the NH, or PJO, has been investigated in many studies with observations (e.g., Baldwin and Dunkerton 1999; Christiansen 2001; Kodera 1995; Kuroda and Kodera 1998) as well as with a hierarchy of numerical models from the b-channel model to GCMs (e.g., Christiansen 2001; Kodera and Kuroda 2000; Scaife and James 2000; TYY; Yamazaki and Shinya 1999). Comparing the poleward and downward propagation of the wind anomalies between this model and the real NH, the dipole pattern extending down to the surface is a unique feature in this model result, which is related to the simplified surface condition. In the real NH, on the other hand, the surface condition is much more complicated, which can result in the subtle tropospheric signal of the PJO. All the results in this paper are based on the 100-yr datasets, which are long enough to obtain the statistically significant results. However, the datasets are not sufficiently long for some purposes. In Fig. 6, for example, even the 100-yr datasets cannot lead to statistically reliable results on higher moments, such as skewness, of the frequency distributions. Therefore, a pair of millennium (1000 yr) integrations are performed for h 0 5 500 and 1000 m, the results of which are described in Part II of this paper (Taguchi and Yoden 2002). 6. Conclusions A parameter sweep experiment with a simple global circulation model under a periodic annual forcing was performed to investigate internal intraseasonal and interannual variations of the troposphere–stratosphere coupled system. The amplitude h 0 of a sinusoidal surface topography of zonal wavenumber 1 was changed as an experimental parameter to examine the role of forced planetary waves in the internal variations; 100yr integrations were carried out for each of the 10 topographic amplitudes from h 0 5 0 to 3000 m. The parameter sweep experiment revealed that the extratropical stratospheric circulation depends on h 0 in its mean seasonal march and interannual variability. In the run of h 0 5 0 m without the topography, the extratropical stratospheric circulation is basically driven thermally all through the year; it only follows the annually varying radiative forcing with a time lag of the thermal inertia. From autumn to spring, the polar temperature is low, the polar night jet is strong westerly, while plan-

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etary wave amplitude is very small. The interannual variability is slight in all the seasons. As h 0 is increased from h 0 5 0 up to 3000 m, the stratosphere departs from the radiatively determined state, and becomes dynamically active in different seasons; mainly in spring for 300 m & h 0 & 600m, while in winter for 700 m & h 0 . In the dynamically active seasons, vertically propagating planetary waves occasionally cause stratospheric sudden warming (SSW) events, which lead to large interannual variability in the stratosphere. The occurrence of SSW events is also reflected in the mean seasonal march of the stratosphere; the polar temperature is higher and the polar night jet is weaker than the radiatively determined state while planetary wave amplitude is large. The two types of the mean seasonal march and interannual variability for the small and large amplitudes of the topography remind us of those in the real atmosphere; the run of h 0 5 500 m corresponds to the real SH stratosphere, in which the polar night jet is strong in winter and interannual variability is large in spring, while the run of h 0 5 1000 m does to the NH stratosphere, in which the polar night jet is weak and interannual variability is very large in winter. An evidence of downward influence from the stratosphere to the troposphere was found in the annual response of the troposphere, because the annual thermal forcing is included only in the stratosphere but not in the troposphere in the present experimental framework. The annual response of the model atmosphere, measured by the power spectrum density, significantly exists in the troposphere depending on h 0 and physical quantities. The downward penetration is most significant in the amplitude of planetary waves; the annual response in the troposphere is comparable to that in the stratosphere for the runs of h 0 5 300 and 400 m, while the former is smaller by about one order in the other runs. The downward penetration is also significant for synopticscale waves in all the runs. On the other hand, the downward penetration is negligible by two or three orders for the zonal mean temperature and zonal wind. A sequence of low-frequency variability associated with SSW events in the run of h 0 5 1000 m was examined with the EOF and lag correlation analyses. The sequence of variability is characterized by the poleward and downward propagation of anomalies of the zonal mean zonal wind and planetary wave amplitude for some months before and after SSWs. One month before SSWs, their anomalies exhibit preconditioning patterns for SSWs; the mean zonal wind anomalies form a dipole pattern throughout the extratropical troposphere and stratosphere indicating poleward shift of the tropospheric jet and the polar night jet, while planetary waves amplify in the troposphere and stratosphere. Their anomalies further propagate poleward and downward for a couple of months after SSWs. The aftereffects of SSWs is significant even in the troposphere; planetary wave amplitude is smaller than climatology in the mid-

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latitude troposphere one month after SSWs. The sequence extending in both the stratosphere and the troposphere shows that the vertical coupling is inevitably two way in this run. The poleward and downward propagation of the zonal wind anomalies also depends on h 0. The wind anomalies do not propagate poleward for h 0 5 0 m, while they do as h 0 is increased. The wind anomalies are confined in the stratosphere for h 0 ; 500 m, while they extend from the stratosphere down to the troposphere for h 0 ; 1000 m. Acknowledgments. The present graphic tools were based on the codes in the GFD-DENNOU Library (SGKS Group 1999). Calculations were performed on VPP800 of the Kyoto University Data Processing Center. The authors express sincere thanks to Professor K. Labitzke of Free University Berlin for providing the data used in Fig. 1. This work was supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Culture, Science, and Technology of Japan and by the Grant-in-Aid for the Research for the Future Program ‘‘Computational Science and Engineering’’ of the Japan Society for the Promotion of Science. REFERENCES Baldwin, M. P., 2000: The Arctic Oscillation and its role in stratosphere–troposphere coupling. SPARC Newsl., 14, 10–14. ——, and T. J. Dunkerton, 1999: Propagation of the Arctic Oscillation from the stratosphere to the troposphere. J. Geophys. Res., 104, 30 937–30 946. Christiansen, B., 2000a: A model study of the dynamical connection between the Arctic Oscillation and stratospheric vacillations. J. Geophys. Res., 105, 29 461–29 474. ——, 2000b: Chaos, quasiperiodicity, and interannual variability: Studies of a stratospheric vacillation model. J. Atmos. Sci., 57, 3161–3173. ——, 2001: Downward propagation of zonal mean zonal wind anomalies from the stratosphere to the troposphere: Model and reanalysis. J. Geophys. Res., 106, 27 307–27 322. Hartmann, D. L., J. M. Wallace, V. Limpasuvan, D. W. J. Thompson, and J. R. Holton, 2000: Can ozone depletion and global warming interact to produce rapid climate change? Proc. Natl. Acad. Sci. USA, 97, 1412–1417. Haynes, P. H., C. J. Marks, M. E. McIntyre, T. G. Shepherd, and K. P. Shine, 1991: On the ‘‘downward control’’ of extratropical diabatic circulation by eddy-induced mean zonal forces. J. Atmos. Sci., 48, 651–678. Holton, J. R., and C. Mass, 1976: Stratospheric vacillation cycles. J. Atmos. Sci., 33, 2218–2225. Kodera, K., 1995: On the origin and nature of the interannual variability of the winter stratospheric circulation in the Northern Hemisphere. J. Geophys. Res., 100, 14 077–14 087. ——, and Y. Kuroda, 2000: A mechanistic model study of slowly

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propagating stratosphere–troposphere coupled variability. J. Geophys. Res., 105, 12 361–12 370. Kuroda, Y., and K. Kodera, 1998: Interannual variability in the troposphere and stratosphere of the Southern Hemisphere winter. J. Geophys. Res., 103, 13 787–13 799. Labitzke, K., 1982: On the interannual variability of the middle stratosphere during the northern winters. J. Meteor. Soc. Japan, 60, 124–139. Matsuno, T., 1971: A dynamical model of the stratospheric sudden warming. J. Atmos. Sci., 28, 1479–1494. Plumb, R. A., 1989: On the seasonal cycle of stratospheric planetary waves. Pure Appl. Geophys., 130, 233–242. Randel, W. J., 1992: Global atmospheric circulation statistics, 1000– 1 mb. NCAR Tech. Note 366, 256 pp. ——, and P. A. Newman, 1998: The stratosphere in the Southern Hemisphere. Meteorology of the Southern Hemisphere, Meteor. Monogr., No. 49, Amer. Meteor. Soc., 243–282. Scaife, A. A., and I. N. James, 2000: Response of the stratosphere to interannual variability of tropospheric planetary waves. Quart. J. Roy. Meteor. Soc., 126, 275–297. Scinocca, J. F., and P. H. Haynes, 1998: Dynamical forcing of stratospheric planetary waves by tropospheric baroclinic eddies. J. Atmos. Sci., 55, 2361–2392. Scott, R. K., and P. H. Haynes, 1998: Interannual variability of the extratropical stratospheric circulation: The low-latitude flywheel. Quart. J. Roy. Meteor. Soc., 124, 2149–2173. SGKS Group, cited 1999: DCL-5.1 (in Japanese). GFD-DENNOU Club. [Available online at http://www.gfd-dennou.org/library/ dcl/.] Shiotani, M., and I. Hirota, 1985: Planetary wave–mean flow interaction in the stratosphere: A comparison between Northern and Southern Hemispheres. Quart. J. Roy. Meteor. Soc., 111, 309– 334. ——, N. Shimoda, and I. Hirota, 1993: Interannual variability of the stratospheric circulation in the Southern Hemisphere. Quart. J. Roy. Meteor. Soc., 119, 531–546. Swamp Project, cited 1998: AGCM5 (in Japanese). GFD-DENNOU Club. [Available online at http://www.gfd-dennou.org/arch/ agcm5/.] Taguchi, M., and S. Yoden, 2002: Internal interannual variability of the troposphere–stratosphere coupled system in a simple global circulation model. Part II: Millennium integrations. J. Atmos. Sci., 59, 3037–3050. ——, T. Yamaga, and S. Yoden, 2001: Internal variability of the troposphere–stratosphere coupled system simulated in a simple global circulation model. J. Atmos. Sci., 58, 3184–3203. Weare, B. C., and J. S. Nasstrom, 1982: Examples of extended empirical orthogonal function analyses. Mon. Wea. Rev., 110, 481– 485. Yamane, S., and S. Yoden, 1998: Low-frequency variations and optimal excitation in a simple barotropic model with zonal asymmetry. J. Meteor. Soc. Japan, 76, 561–580. Yamazaki, K., and Y. Shinya, 1999: Analysis of the Arctic Oscillation simulated by AGCM. J. Meteor. Soc. Japan, 77, 1287–1297. Yoden, S., 1990: An illustrative model of seasonal and interannual variations of the stratospheric circulation. J. Atmos. Sci., 47, 1845–1853. ——, M. Taguchi, and Y. Naito, 2002: A review on numerical studies on time variations of the troposphere–stratosphere coupled system. J. Meteor. Soc. Japan, in press. Yulaeva, E., J. R. Holton, and J. M. Wallace, 1994: On the cause of the annual cycle in the tropical lower-stratospheric temperatures. J. Atmos. Sci., 51, 169–174.