Abstract

A composite analysis is made of 132 stratospheric sudden warming (SSW) events obtained in a 10 000-day integration with a simple global circulation model under a perpetual-winter condition. The analysis confirms general features of the SSWs, such as enhanced upward propagation of planetary wave activity from the troposphere to the stratosphere before the SSWs and downward propagation of warming signals to the lower stratosphere after the events.

A further dynamical diagnosis shows that the tropospheric circulation is quite different between pre-SSW and post-SSW periods in terms of the zonal mean zonal wind, planetary wave, and synoptic-scale waves. In the pre-SSW period, the planetary wave is more active than normal in relation to the tropospheric westerly jet that shifts poleward. In the post-SSW period, on the other hand, the planetary wave is less active, while the mean zonal wind is close to the climatology. Synoptic-scale waves also exhibit anomalous features in both periods corresponding to the anomalous planetary-scale flow. The less active planetary wave in the post-SSW period is a return signal of the SSWs, or a tropospheric response to the SSWs, since the signal disappears as SSWs are absent by increased thermal damping in the stratosphere.

1. Introduction

The dynamical coupling between the troposphere and stratosphere has recently received increasing attention (e.g., Baldwin 2000; Hartmann et al. 2000). Stratospheric sudden warming (SSW) is a most spectacular phenomenon that may involve two-way vertical coupling. It was theoretically demonstrated by Matsuno (1971) that SSWs can be caused by planetary waves that amplify in the troposphere and propagate to the stratosphere to interact with the zonal mean zonal flow there. Such upward propagation of planetary waves has been well documented for SSWs observed in the real atmosphere or simulated in general circulation models (Andrews et al. 1987, sections 6.2 and 11.3). It has been assumed that the increased planetary wave forcing is related in some way to low-frequency, large-scale disturbances in the troposphere, such as blocking events (e.g., Quiroz 1986).

On the other hand, there is increasing interest in possible effects of the stratosphere on the troposphere. In the context of SSWs, much attention has been paid to downward propagation of circulation anomalies from the stratosphere to the troposphere in observations (e.g., Baldwin and Dunkerton 1999; Zhou et al. 2002) as well as in numerical simulations (e.g., Yoden et al. 1999; Taguchi et al. 2001). Baldwin and Dunkerton (1999) found downward propagation of Arctic Oscillation (AO) anomalies from the stratosphere to the surface with a time lag of about three weeks. Negative AO anomalies in the stratosphere correspond well to SSWs. Baldwin and Dunkerton (2001) further showed that the downward-propagating stratospheric anomalies tend to be followed by anomalous tropospheric weather regimes, characterized by meridional displacement of storm tracks.

One approach to test stratospheric effects on the troposphere is numerical experimentation in which experimental conditions in the stratosphere are changed while those in the troposphere are held identical. Such numerical experiments can be classified into two groups depending on the complexity of the models used, and there is a remarkable difference of results between the two groups. In the first group using linear models, it is shown that stratospheric changes do not affect the troposphere significantly; response of planetary waves in the troposphere is quite insensitive to changes of the basic state in the stratosphere (Jacqmin and Lindzen 1985). On the contrary, studies with full nonlinear models (second group) found significant tropospheric response to stratospheric changes introduced in some ways (e.g., Boville 1984; Polvani and Kushner 2002; Taguchi 2003). Such full nonlinear models can be divided into general circulation models (GCMs) and mechanistic circulation models (MCMs). GCMs and MCMs are common in that both simulate large-scale (synoptic scale and larger) motions, but they are different in representations of physical processes; the representations are relatively sophisticated in GCMs while highly idealized in MCMs. Yoden et al. (2002) argued that the idealization of physical processes in MCMs helps us to understand dynamical essence and to perform long integrations while GCMs are necessary for quantitative arguments. The difference of the tropospheric response between the two groups suggests that the linear models are inadequate when one tries to understand stratospheric effects on the troposphere.

The purpose of this study is to explore the vertical dynamical coupling related to SSWs by a composite analysis of a number of samples (132) simulated in a long integration (10 000 days) with an MCM under a perpetual-winter condition. We not only confirm general features of SSWs as seen in observations and GCMs, but also diagnose the tropospheric circulation before and after the SSWs in terms of the zonal mean zonal wind, planetary waves, and synoptic-scale waves. We further examine relationship between the occurrence of SSWs and subsequent tropospheric circulation anomalies. By comparing the tropospheric evolution in the baseline simulation and additional simulations in which SSWs are absent due to stronger thermal relaxation in the stratosphere, we demonstrate that the tropospheric anomalies after SSWs in the baseline simulation take place only when SSWs happen. Extracting a statistically robust image of a typical sequence of SSWs in the idealized situation as above, this study aims to give an insight to the dynamical coupling in the real atmosphere. Yoden et al. (1999) made a composite analysis of 64 SSWs in a 7200-day integration with a GCM under a perpetual-winter condition. This study is different from Yoden et al. (1999) in that this study makes the diagnosis of the tropospheric circulation and the comparison between the baseline and additional simulations.

The present paper is organized as follows. Section 2 outlines the numerical simulations used in this study and introduces a threshold of SSWs for a composite analysis. Section 3 describes general features of the SSWs obtained in the composite analysis. Dynamical features of the tropospheric circulation are analyzed in section 4. The relationship between the SSWs and following tropospheric circulation anomalies is also examined in section 4. Discussion is given in section 5 and conclusions in section 6.

2. Model and composite technique

We make a composite analysis of SSWs that are obtained in the 10 000-day control simulation (CS) with a simple global circulation model (Swamp Project 1998) under a perpetual-winter condition performed in Taguchi (2003). The details of the model are documented in Taguchi et al. (2001). The model is a three-dimensional global primitive-equation model, with a horizontal resolution of T21 and 42 levels from the surface to the mesosphere. The horizontal resolution can marginally capture key features of synoptic-scale waves. The model also includes simplified physical processes such as Newtonian heating/cooling to a perpetual-winter condition in the model Northern Hemisphere, Rayleigh friction at the surface, and so on, but does not include moist processes. A sinusoidal surface topography of zonal wavenumber 1 is included in the model Northern Hemisphere, with amplitude h0 of 1000 m. The results described below are for CS, unless noted otherwise explicitly.

We use four degraded stratosphere simulations (DS), performed in Taguchi (2003) with the same model, as well as CS. Each DS was carried out for 10 000 days. In DS, the thermal relaxation rate is increased only in the stratosphere (z ≥ 15 km) to suppress dynamical processes there. For example, the thermal relaxation time in the middle stratosphere (p = 26 hPa) is about 18 days for CS, while 7.7, 4.6, 2.6, and 0.64 days for the four runs of DS. As a result of the change of the thermal damping, the extratropical stratosphere is colder, with the stronger polar night jet, in the time mean states for DS than for CS. As for stratospheric variability, SSWs are absent from the runs in which the relaxation rate is increased sufficiently. The climatological tropospheric westerly jet is located more poleward for DS than for CS, while the magnitude of tropospheric variability is similar between CS and DS.

The control run simulates reasonable tropospheric and stratospheric circulation as shown in Figs. 1 and 2 of Taguchi et al. (2001) for the zonal mean states and planetary wave properties. The climatological zonal mean zonal wind and wave activity flux are shown later in this paper. The stratospheric variability in CS is characterized by irregular, intermittent occurrence of SSWs as shown in Fig. 1, which displays time series of the zonal mean temperature [T] at ϕ = 86°N and p = 2.6 hPa for the first 1000 days. Here, square brackets denote the zonal mean. The grid point is where the standard deviation of [T] is largest so that the quantity can be used as a measure of dynamical condition of the extratropical winter stratosphere.

Fig. 1.

Time series of the zonal mean temperature [T] at ϕ = 86°N and p = 2.6 hPa for the first 1000 days. Shading indicates the SSW periods and crosses indicate the key days of the SSW events in the 1000 days. Horizontal line denotes the 10 000-day mean (240.5 K).

Fig. 1.

Time series of the zonal mean temperature [T] at ϕ = 86°N and p = 2.6 hPa for the first 1000 days. Shading indicates the SSW periods and crosses indicate the key days of the SSW events in the 1000 days. Horizontal line denotes the 10 000-day mean (240.5 K).

In order to make a composite analysis, we define SSW events using the time series with a reference to Yoden et al. (1999). First, we search periods in which the temperature remains higher than its 10 000-day mean value (240.5 K, denoted by horizontal line in Fig. 1) for any length. The temperature should cross the mean value just before and after each of the periods. Next, we judge whether the maximum temperature in each of the periods is higher than 270 K; if so, the period is defined as an SSW period. As a result of the procedure, 134 SSW periods are chosen in the 10 000 days. A key day for each of the SSW periods is the day of the maximum temperature. The key days are also referred to as lag = 0 day. The SSW periods and key days in the first 1000 days are denoted by shades and crosses in Fig. 1, respectively. The obtained results are robust, independently of the subjective values included in the criteria.

3. General features of SSWs

In this section, we extract general features of the SSWs by a composite analysis for the zonal mean fields (temperature and zonal wind) and planetary wave properties (amplitude and wave activity flux). Figure 2 displays time–height sections of the SSW composites for the four quantities. Each quantity is shown by anomalies (denoted by prime) from the climatological state (denoted by overbar). The anomalies are normalized with the standard deviation at each meridional grid point to remove the strong height dependence. If a latitudinal average is taken, the normalization is operated at each grid point before the average. The composites show general features of the SSWs simulated in this model, which basically agree with the results of Yoden et al. (1999). As a direct result of the definition of the SSWs, the zonal mean temperature [T] in the polar region (ϕ = 86°N) shows the strong warming, as manifested by its positive anomalies over 1.6 around lag = 0 day in the upper stratosphere (Fig. 2a). Correspondingly, the anomalies of the zonal mean zonal wind [U], averaged over latitudes 60°N ≤ ϕ ≤ 80°N, are negative exceeding −1.4, indicating the strong deceleration of the polar night jet. The signals of the zonal mean fields are accompanied by the positive anomalies of the amplitude |Z1| and vertical component of the Eliassen–Palm (E–P) flux Fz for planetary wave of zonal wavenumber 1 (wave 1), averaged over latitudes 50°N ≤ ϕ ≤ 70°N, in the upper stratosphere (Figs. 2c,d). In each of the SSWs, wave 1 dominates the stratospheric circulation due to the planetary wave forcing by the surface topography of the zonal wavenumber (not displayed).

Fig. 2.

Time–height sections of anomalies from the climatology composited with respect to the SSWs: (a) zonal mean temperature [T] at ϕ = 86°N, (b) zonal mean zonal wind [U] averaged over latitudes 60°N ≤ ϕ ≤ 80°N, (c) wave 1 amplitude |Z1| averaged over latitudes 50°N ≤ ϕ ≤ 70°N, and (d) vertical component of the E–P flux Fz of wave 1 averaged in the same latitudes as in |Z1|. All quantities are normalized by the std dev at each meridional grid point. The normalization is done before the latitudinal average for [U], |Z1|, and Fz. Contour interval is 0.2. Values greater than 0.4 (1.0) are lightly (heavily) shaded with dots. Values less than −0.4 (−1.0) are lightly (heavily) shaded with diagonal lines. Arrows below (d) denote pre-SSW (lag = −7 ± 5 days) and post-SSW periods (lag = 20 ± 5 days)

Fig. 2.

Time–height sections of anomalies from the climatology composited with respect to the SSWs: (a) zonal mean temperature [T] at ϕ = 86°N, (b) zonal mean zonal wind [U] averaged over latitudes 60°N ≤ ϕ ≤ 80°N, (c) wave 1 amplitude |Z1| averaged over latitudes 50°N ≤ ϕ ≤ 70°N, and (d) vertical component of the E–P flux Fz of wave 1 averaged in the same latitudes as in |Z1|. All quantities are normalized by the std dev at each meridional grid point. The normalization is done before the latitudinal average for [U], |Z1|, and Fz. Contour interval is 0.2. Values greater than 0.4 (1.0) are lightly (heavily) shaded with dots. Values less than −0.4 (−1.0) are lightly (heavily) shaded with diagonal lines. Arrows below (d) denote pre-SSW (lag = −7 ± 5 days) and post-SSW periods (lag = 20 ± 5 days)

The composites also show preceding signals in the lower stratosphere and troposphere. The zonal mean westerly wind is stronger than normal in the high latitudes, with values over 0.4 for lag ∼ −35 to −5 days. Note that the negative time lags mean the signals precede the SSWs. The enhancement of wave 1 can be traced back from the stratosphere down to the surface with a timescale of about one week or so in both of |Z1|′ and Fz. After the peak of the warming in the upper stratosphere, the signals of the SSWs, such as the positive anomalies of [T], |Z1|, and Fz and the negative anomalies of [U], propagate downward to the lower stratosphere and persist there for about 30 days or longer. Note that the negative wind anomalies do not extend to the troposphere, where the anomalies are generally positive but the magnitude is less than 0.2 after lag = 5 days or so. The amplitude and vertical component of the E–P flux of wave 1 are smaller than the climatology in the troposphere when the SSW signals descend to the lower stratosphere; for lag = 10–45 days for |Z1|′ and for lag = 15–30 days for Fz. These tropospheric features of the zonal wind and wave properties after the SSWs are different from the observation (Baldwin and Dunkerton 1999) and GCM results (Yoden et al. 1999). All of the signals in the stratosphere and troposphere exceeding ±0.2 are statistically significant according to Student's t test with a confidence level higher than 95% (not displayed).

Figure 3 displays latitude–height sections of the zonal mean zonal wind and E–P flux of wave 1 for the climatological state and SSW composites on four lag days. The SSW composites are shown by anomalies from the climatological state for both the zonal wind and E–P flux. The climatological state is characterized by the tropospheric jet and stratospheric polar night jet as well as by the equatorward and upward propagation of wave 1. On lag = −20 days, the zonal wind anomalies show a meridional dipole pattern in the lower stratosphere and troposphere, with positive values in high latitudes and negative values in midlatitudes. Note that the anomalous zonal wind is normalized with the standard deviation at each grid point. The E–P flux anomalies are relatively small on lag = −20 days. The wind anomalies proceed poleward and develop with time to form the SSW signal in the extratropical stratosphere on lag = 0 days. The E–P flux anomalies are largest in the troposphere and stratosphere on lag = −7 days. The pattern of the anomalous E–P flux is similar to that of the climatology, indicating that the upward and equatorward propagation of wave 1 is enhanced on this lag day. The anomalous E–P flux decreases from lag = −7 days to lag = 0 days in the troposphere while keeping the comparable magnitudes in the stratosphere for this period. After the peak of the stratospheric warming, the local maximum of the negative wind anomalies is located more downward on lag = 20 days than on lag = 0 days. Wave 1 goes through a remarkable change in the troposphere before and after the peak of the warming. The E–P flux anomalies point poleward and downward, or the opposite direction to the climatological E–P flux, on lag = 20 days. This means that the propagation of wave 1 is weaker than normal on this lag day.

Fig. 3.

Latitude–height sections of [U] (contours and shades) and F of wave 1 (arrows). Leftmost panel is for the climatology, and the others show SSW composites on lag days indicated. The SSW composites are shown by anomalies from the climatology averaged over 5 days between lag ± 2 days. The wind anomalies are normalized with the std dev at each meridional grid point. Contour interval is 10 m s−1 for [U] and 0.2 for normalized [U]′. Negative values are shaded. The E–P flux is divided by the square root of pressure in both F and F′. The composited E–P flux is multiplied by 2

Fig. 3.

Latitude–height sections of [U] (contours and shades) and F of wave 1 (arrows). Leftmost panel is for the climatology, and the others show SSW composites on lag days indicated. The SSW composites are shown by anomalies from the climatology averaged over 5 days between lag ± 2 days. The wind anomalies are normalized with the std dev at each meridional grid point. Contour interval is 10 m s−1 for [U] and 0.2 for normalized [U]′. Negative values are shaded. The E–P flux is divided by the square root of pressure in both F and F′. The composited E–P flux is multiplied by 2

4. Tropospheric circulation changes

The composite analysis in section 3 has shown that the tropospheric circulation is quite different before and after the SSWs (Figs. 2 and 3). The period before the SSWs is characterized by the positive anomalies of the amplitude and vertical component of the E–P flux of wave 1 while wave 1 has the negative anomalies of the quantities after the SSWs. In this section, the tropospheric circulation in the two periods is examined through composites of some properties of the zonal wind, wave 1, and synoptic-scale waves. The lag = −7 ± 5 days of all the SSWs are collected to make composites of the pre-SSW period, and the lag = 20 ± 5 days are selected for the post-SSW period. The two periods are denoted by horizontal arrows below Fig. 2d. Synoptic-scale waves are extracted using zonal wavenumbers 4–10 (waves 4–10). This corresponds to the definition of the planetary wave as wave 1. Another extraction of planetary- and synoptic-scale waves is also possible based on frequency. The two ways of separating the waves closely correspond to each other, because wave 1 is basically stationary and waves 4–10 have much shorter timescales than wave 1. Waves 2 and 3 are of less importance in this model.

Figure 4 displays latitude–height sections of the zonal mean zonal wind [U] (top) and the E–P flux F and its divergence DF of wave 1 (bottom) for the climatology, the pre-SSW period, and the post-SSW period in the troposphere. The composites in the two periods are shown by anomalies from the climatology. Figure 4 is a similar plot to Fig. 3, but it focuses on the troposphere in the two periods and includes the E–P flux divergence. The composites show that wave 1 is generated, propagates, and interacts with the mean zonal wind quite differently between the two periods. In the pre-SSW period, the mean zonal wind shows positive anomalies poleward of the climatological jet axis, indicating poleward shift of the jet. It is confirmed that the upward and equatorward propagation of wave 1 is enhanced as seen in Fig. 3. Note that wave 1 has positive anomalies of the E–P flux divergence in the high-latitude lower troposphere, where the climatological E–P flux diverges. This means that wave 1 is generated more strongly in the pre-SSW period there, which may be related to the wind anomalies. In the extratropical mid- and upper troposphere, the anomalous E–P flux converges, acting to reduce the westerly wind anomalies in high latitudes. On the other hand, the magnitude of the wind anomalies in the post-SSW period is much smaller than that in the pre-SSW period, while the patterns are broadly similar between the two periods. The upward and equatorward propagation of wave 1 is weaker than normal in the post-SSW period as seen in Fig. 3. The negative anomalies of the E–P flux divergence of wave 1 in the high-latitude lower troposphere indicate weaker generation of the planetary wave. The anomalous E–P flux of wave 1 diverges in the mid- and upper troposphere, which maintains the westerly wind anomalies in high latitudes.

Fig. 4.

Latitude–height sections of [U] in top row, and F (arrows) and its divergence DF (contours and shades) of wave 1 in bottom row: (a) climatology, (b) pre-SSW composites, and (c) post-SSW composites. The SSW composites are shown by anomalies from the climatology. Contour interval is 10 m s−1 for [U] and 0.5 m s−1 for [U]′. The E–P flux is divided by the square root of pressure in both F and F′. The composited E–P flux is multiplied by 2. Contour interval is 2 m s−1 day−1 for DF and 0.5 m s−1 day−1 for DF. Shades indicate negative values of [U] and DF in both the climatology and SSW composites

Fig. 4.

Latitude–height sections of [U] in top row, and F (arrows) and its divergence DF (contours and shades) of wave 1 in bottom row: (a) climatology, (b) pre-SSW composites, and (c) post-SSW composites. The SSW composites are shown by anomalies from the climatology. Contour interval is 10 m s−1 for [U] and 0.5 m s−1 for [U]′. The E–P flux is divided by the square root of pressure in both F and F′. The composited E–P flux is multiplied by 2. Contour interval is 2 m s−1 day−1 for DF and 0.5 m s−1 day−1 for DF. Shades indicate negative values of [U] and DF in both the climatology and SSW composites

Equation (5.2.6) of Andrews et al. (1987) states that the vertical component of the E–P flux of a particular zonal wavenumber component is proportional to its amplitude squared and vertical phase tilt, where the amplitude and phase are defined in geopotential height. Changes of wave 1 patterns are examined in Fig. 5, which displays geopotential height fields of wave 1, Z1, at p = 254 hPa for the climatology and the two periods. The composites in the two periods are shown by anomalies Z1 from the climatology Z1, as in Fig. 4. The composited pattern Z1 in the pre-SSW period is very similar to the climatological state Z1, with positive (negative) anomalies centered near λ = 30°W (150°E) at ϕ = 60°N. The superposition of the composite on the climatology produces the amplification of wave 1, which is seen in Fig. 2c and is responsible for the Fz anomalies in Figs. 2d, 3, and 4. An examination of the longitude–height structure of wave 1 reveals that the structure in the pre-SSW period is close to that in the climatology. In the post-SSW period, the height anomalies have the opposite signs as the climatology at most grid points, which results in smaller wave amplitude. The Z1 pattern is not exactly in the antiphase relationship to the Z1 pattern, indicating that wave 1 changes in the vertical structure as well as in the amplitude.

Fig. 5.

Synoptic fields of geopotential height Z of wave 1 at p = 254 hPa: (a) climatology, (b) pre-SSW composite, and (c) post-SSW composite. The SSW composites are shown by anomalies from the climatology. Contour interval is 50 m in (a) and 10 m in (b) and (c). Negative values are shaded in all the panels. Latitudinal circles denoted by broken lines are 60° and 30°N, and the outermost solid circle is 20°N

Fig. 5.

Synoptic fields of geopotential height Z of wave 1 at p = 254 hPa: (a) climatology, (b) pre-SSW composite, and (c) post-SSW composite. The SSW composites are shown by anomalies from the climatology. Contour interval is 50 m in (a) and 10 m in (b) and (c). Negative values are shaded in all the panels. Latitudinal circles denoted by broken lines are 60° and 30°N, and the outermost solid circle is 20°N

Since the zonal wind is more relevant to synoptic-scale wave activity, the geopotential height fields in Fig. 5 are related to the zonal wind fields at the same level (p = 254 hPa) in Fig. 6, where all zonal wavenumbers are retained as well as the zonal mean. The zonal wind fields primarily reflect the features of the zonal mean state and wave 1 for both the climatological state and the composites. In addition to the latitudinal peak of the climatological zonal mean westerly wind near ϕ = 45°N as seen in Fig. 4a, there is a strong westerly wind maximum (jet) in a region of λ = 150°E–120°W (Fig. 6a). From the geostrophic wind relationship, this region corresponds to where the climatological height of wave 1 has strong negative meridional gradients (Fig. 5a). The anomalous zonal wind field in the pre-SSW period shows a meridional dipole centered near λ = 90°W, with positive (negative) values in high (mid-) latitudes (Fig. 6b). The dipole is broadly explained by synchronization of the zonal mean and wave 1 components. As seen in Fig. 4b, the zonal mean component exhibits positive (negative) anomalies in high (mid-) latitudes. The Z1 field in Fig. 5b shows that the anomalous wave 1 component in the zonal wind has a similar latitudinal structure to the anomalous zonal mean component near the longitude. The U′ field in the post-SSW period also corresponds well to the Z1 field.

Fig. 6.

Same as in Fig. 5, but for U at p = 254 hPa. All zonal wavenumbers are included as well as the zonal mean. Contour interval is 10 m s−1 in (a) and 2 m s−1 in (b) and (c). Light (dark) shading denotes values over 30 (40) m s−1 in (a). Negative values are shaded in (b) and (c)

Fig. 6.

Same as in Fig. 5, but for U at p = 254 hPa. All zonal wavenumbers are included as well as the zonal mean. Contour interval is 10 m s−1 in (a) and 2 m s−1 in (b) and (c). Light (dark) shading denotes values over 30 (40) m s−1 in (a). Negative values are shaded in (b) and (c)

Synoptic-scale wave activity, simply measured by variance of geopotential height of waves 4–10 at p = 254 hPa, fluctuates in its spatial distribution with the related jet displacement (Fig. 7). If the whole 10 000 days are taken into account (Fig. 7a), synoptic-scale waves have their largest variance (storm track) in a region of λ = 150°E–90°W near ϕ = 50°N, as well as the latitudinal peak in terms of the zonal mean. The zonally localized region of the storm track roughly accords with that of the climatological westerly jet (Fig. 6a). In the pre-SSW period, the variance is larger than normal in longitudes of λ = 30°E–180° through the Western Hemisphere near ϕ = 60°N (Fig. 7b), corresponding to the poleward displacement of the local westerly jet. A similar relationship of synoptic-scale waves to the zonal wind is also found for the post-SSW period (Fig. 7c), for example, in longitudes of λ = 0°–180° through the Eastern Hemisphere, where the variance is larger (smaller) than normal in high (mid-) latitudes associated with the positive (negative) zonal wind anomalies. Such correspondence between the zonal wind and synoptic-scale waves is consistent with the observed fact in the real Northern Hemisphere that the waves tend to develop in the regions of maximum time mean zonal wind and to propagate downstream along the storm tracks that approximately follow the jet axes (e.g., Blackmon et al. 1977).

Fig. 7.

Same as in Fig. 5 but for variance of Z at p = 254 hPa, contributed by waves 4–10. Contour interval is 2000 m2 in (a) and 200 m2 in (b) and (c). Light (dark) shading denotes values over 8000 (10 000) m2 in (a). Negative values are shaded in (b) and (c)

Fig. 7.

Same as in Fig. 5 but for variance of Z at p = 254 hPa, contributed by waves 4–10. Contour interval is 2000 m2 in (a) and 200 m2 in (b) and (c). Light (dark) shading denotes values over 8000 (10 000) m2 in (a). Negative values are shaded in (b) and (c)

In order to examine role of synoptic wave activity in the planetary-scale flow shown in Fig. 6, the divergence of the three-dimensional localized E–P flux (Trenberth 1986) of waves 4–10, DE, is calculated for the climatology and the two periods (Fig. 8). The divergence approximates the local westerly wind acceleration. When calculating DE in each of the two periods, the period mean, which is mainly contributed by the zonal mean and wave 1 components, is first removed, because the timescales of these two components are as long as the defined period (Fig. 2). Then, departures from the period mean are obtained for waves 4–10 to calculate DE. The climatological three-dimensional E–P flux at p = 254 hPa converges throughout the hemisphere, with large values of the convergence in longitudes of λ = 30°E–150°W. There is a remarkable correspondence between DE (Fig. 8) and U′ (Fig. 6) for each of the pre-SSW and post-SSW periods. For the pre-SSW period, a dipole structure is noticeable for DE in high latitudes (ϕ ≳ 40°N) near λ = 120°W corresponding to the dipole of U′, although the two quantities have their local maxima in slightly different locations; the local maxima of DE are generally located more westward and poleward than those of U′. For the post-SSW period, a correspondence is discernible for the negative DE in λ = 0°–90°E near ϕ = 45°N, which is a more westward and poleward location to the local maximum of the negative U′. The correspondence in each of the two periods indicates that the anomalous synoptic wave activity acts to maintain the anomalous planetary-scale flow pattern, associated with the change of wave 1.

Fig. 8.

Same as in Fig. 5, but for the divergence of the three-dimensional localized E–P flux DE at p = 254 hPa, contributed by waves 4–10. Contour interval is 1 m s−1 day−1 for DE and 0.2 m s−1 day−1 for DE. Negative values are shaded in all the panels

Fig. 8.

Same as in Fig. 5, but for the divergence of the three-dimensional localized E–P flux DE at p = 254 hPa, contributed by waves 4–10. Contour interval is 1 m s−1 day−1 for DE and 0.2 m s−1 day−1 for DE. Negative values are shaded in all the panels

To examine the significance of the correspondence argued above, the spatial correlation coefficient is calculated between the U′ and DE fields for each of the two periods. In the calculation, the DE fields are shifted by one grid (5.6°) both eastward and equatorward to take account of the different locations of the local maxima of the two quantities. The domain for the calculation is poleward of ϕ = 20°N for U′. The obtained correlation coefficient is 0.34 for the pre-SSW period and 0.25 for the post-SSW period. These values are highly statistically significant, since the sample size (number of grid points) is more than 600 in the domain. This result supports the assertion that the correspondence is significant. A further question remains why the U′ and DE fields have their local maxima in the slightly different locations.

The preceding diagnosis has shown that the tropospheric circulation changes quite differently between the two periods separated by the peak of the SSWs (Figs. 48). However, the results do not necessarily mean that the changes of the tropospheric circulation arise from the SSWs. It is possible that the tropospheric circulation changes take place purely through tropospheric processes, independently of the happenings in the stratosphere. Here, the relationship between the tropospheric circulation changes and the occurrence of the SSWs is examined by a comparison between CS, where the SSW composite analysis has been done, and DS, where SSWs are absent due to the stronger thermal relaxation. We make a similar composite analysis using time series of the leading empirical orthogonal function (EOF) of low-frequency variability, defined in geopotential height at p = 549 hPa, in the extratropical troposphere for each run. Taguchi (2003) showed that the leading EOF is annular for each run independently of the representation of the stratosphere. The annular variability (AV) is a model counterpart of the AO in the real atmosphere. The time series of the AV (AV index) are useful to examine the SSWs and subsequent tropospheric anomalies in CS, since the AV is closely related to the SSWs for CS as shown next and the AV exists in the troposphere for both CS and DS.

Figure 9 (top) displays time–height sections of [U]′ and |Z1|′ in CS, composited with respect to the high index state (exceeding 1.5 standard deviation) of the AV. The AV composites are shown by normalized anomalies as in the SSW composites (Fig. 2). A comparison of the AV composites (Fig. 9, top) to the SSW composites (Figs. 2b,c) reveals that the AV composites reproduce the SSW composites to a large degree. The high index state of the AV in the troposphere, characterized by the poleward shift of the jet and anomalous wave 1 amplification, leads to the SSW signals of the two quantities in the stratosphere, which then propagate downward to the lower stratosphere. Note that wave 1 amplitude has negative anomalies in the troposphere for the AV composite when the SSW signals propagate in the lower stratosphere. There is some time lag between the SSW and AV composites; the SSW signal of [U]′ appears around lag ∼ 25 days in the AV composite. The reproduction of the SSW composites by the AV composites is due to the fact that the high index state of the AV is essentially identical to the pre-SSW period. The relationship between the SSWs and AV (or AO) in the troposphere is different between the model run and the real atmosphere; the high index state of the AV in the troposphere leads to the SSWs in the model, while stratospheric AO anomalies tend to be followed by tropospheric AO anomalies of the same sign in the real atmosphere (e.g., Baldwin and Dunkerton 1999). In spite of the difference, the AV index is employed here as an arbitrary, useful index for the comparison between CS and DS; we do not intend to focus on the relationship between the SSWs and AV.

Fig. 9.

Time–height sections of composites with respect to AV index, or time series of the leading EOF of Z at p = 549 hPa in five simulations. Top panels are for CS, for which the SSW composite is made. Others are for DS1 to DS4 as indicated, in which the thermal relaxation rate is increased in the stratosphere. Left panels are for [U]′, and right panels for |Z1|′. Both quantities are normalized with the standard deviation at each meridional grid point and then averaged over latitudes. The latitudinal average is done in 60°N ≤ ϕ ≤ 80°N for [U]′ and in 50°N ≤ ϕ ≤ 70°N for |Z1|′. Values greater than 0.2 (0.6) are lightly (heavily) shaded with dots. Values less than −0.2 (−0.6) are lightly (heavily) shaded with diagonal lines

Fig. 9.

Time–height sections of composites with respect to AV index, or time series of the leading EOF of Z at p = 549 hPa in five simulations. Top panels are for CS, for which the SSW composite is made. Others are for DS1 to DS4 as indicated, in which the thermal relaxation rate is increased in the stratosphere. Left panels are for [U]′, and right panels for |Z1|′. Both quantities are normalized with the standard deviation at each meridional grid point and then averaged over latitudes. The latitudinal average is done in 60°N ≤ ϕ ≤ 80°N for [U]′ and in 50°N ≤ ϕ ≤ 70°N for |Z1|′. Values greater than 0.2 (0.6) are lightly (heavily) shaded with dots. Values less than −0.2 (−0.6) are lightly (heavily) shaded with diagonal lines

Even if the thermal relaxation rate is increased in the stratosphere, the zonal-mean zonal wind and wave 1 amplitude show similar features in the troposphere through lag = 0–20 days or so for DS as for CS (Fig. 9). This confirms the general existence of the AV and related wave amplification in CS and DS. If the sequence of the tropospheric circulation changes in CS (especially negative |Z1| anomalies after the SSWs) arises purely from tropospheric processes, then it should be reproduced after the high index state of the AV in DS. The following examination rejects this possibility, however. As the thermal damping is increased from DS1 to DS4, remarkable changes occur not only in the stratosphere but also in the troposphere; the SSW signal of the mean zonal wind becomes absent from the stratosphere, and correspondingly the negative anomalies of wave 1 amplitude disappear from the troposphere especially for DS3 and DS4. This demonstrates that the tropospheric circulation changes after the SSWs in CS results from the occurrence of the SSWs.

5. Discussion

One main point in this study is to argue possible effects of SSWs on the troposphere, or tropospheric response to SSWs. This study has shown that the planetary wave in the troposphere significantly responds to the occurrence of the SSWs in the present MCM. A possible mechanism for the tropospheric response is speculated on as follows. It is plausible that the planetary wave in the troposphere can change in response to the SSWs, or anomalous zonal mean zonal wind in the stratosphere, as inferred from the linear wave theory. However, the linear wave theory is inadequate alone to account for the response, since no significant response of tropospheric planetary wave to stratospheric wind changes was obtained in linear models, as mentioned in the introduction. The nonlinear interaction of planetary waves with synoptic-scale waves is a possible process that can exaggerate planetary wave response through the positive feedback. This mechanism is different from the conventional idea that the downward propagation of circulation anomalies from the stratosphere to the troposphere seen in the real atmosphere (e.g., Baldwin and Dunkerton 1999) may be a manifestation of stratospheric effects on the troposphere. It is possible that the proposed mechanism works in the real atmosphere, although the mechanism is suggested from the results under the idealized situation, where the modeled downward propagation of the SSW signals is different from the observed one.

This study has obtained the statistically robust image of the typical SSW sequence using the large number of samples in the long MCM integration. Due to the idealization of the MCM, however, not all the results may not be applied directly to the real atmosphere; the limitation comes from the moderate horizontal resolution, the sinusoidal topography at the surface, the highly simplified physical processes, and the exclusion of moist processes. Therefore, it will be beneficial to further investigate SSWs in the real atmosphere and more realistic GCMs from the viewpoints suggested in this study. First, it is helpful to describe a whole sequence around SSWs including both pre-SSW and post-SSW periods, since the tropospheric circulation can exhibit different features between the two periods as shown in this study. The interaction between planetary and synoptic waves will be also a useful viewpoint to understand tropospheric circulation changes in relation to SSWs. The changes of planetary and synoptic waves (including storm track) in the troposphere, found by Kodera and Chiba (1995) and Baldwin and Dunkerton (2001) in association with SSWs or strong stratospheric anomalies, may be interpreted from this point of view.

The composite analysis in sections 3 and 4 aimed to extract an average image of the SSWs. The extracted results were statistically significant. If the SSWs are examined individually, it is found that their sequence is highly variable from one event to another. For example, the relationship between strength of the SSWs in the upper stratosphere and preceding wave activity flux in the lower stratosphere is examined for each SSW in Fig. 10. The scatterplot confirms that most of the SSWs follow anomalously strong planetary wave forcing from the troposphere, as represented by the composites (denoted by broken lines). However, a close inspection reveals that stronger wave forcings do not always lead to stronger warmings. The correlation coefficient of the two quantities is positive, but is not so high (0.32). Such diversity of SSWs was also noticed in the composite analysis by Yoden et al. (1999), where the SSWs were divided into two groups according to the relative strength of planetary waves of zonal wavenumbers 1 and 2. These results suggest a complexity of the SSWs even in the simplified conditions, including possible importance of internal variability of the stratosphere, which can appear under time constant wave forcing from the troposphere (see Yoden et al. 2002 and references therein).

Fig. 10.

Scatterplot between wave 1 forcing from the troposphere and strength of the SSWs for all the 132 events. Abscissa is for the maximum of Fz of wave 1, averaged over latitudes 50°N ≤ ϕ ≤ 70°N at p = 120 hPa, in the 10-day period before the key day of each SSW. Ordinate is for [T] at ϕ = 86°N and p = 2.6 hPa on the key day of each SSW. Each quantity is shown by anomalies from the climatology normalized with the std dev. The latitudinal average is done after the normalization for Fz. Correlation coefficient of the two quantities is 0.32, as indicated. Solid lines denote the 10 000-day means, and broken lines the composites for the SSWs

Fig. 10.

Scatterplot between wave 1 forcing from the troposphere and strength of the SSWs for all the 132 events. Abscissa is for the maximum of Fz of wave 1, averaged over latitudes 50°N ≤ ϕ ≤ 70°N at p = 120 hPa, in the 10-day period before the key day of each SSW. Ordinate is for [T] at ϕ = 86°N and p = 2.6 hPa on the key day of each SSW. Each quantity is shown by anomalies from the climatology normalized with the std dev. The latitudinal average is done after the normalization for Fz. Correlation coefficient of the two quantities is 0.32, as indicated. Solid lines denote the 10 000-day means, and broken lines the composites for the SSWs

6. Conclusions

A sequence of intraseasonal variability in the troposphere and stratosphere has been investigated by a composite analysis of 132 SSWs simulated in a 10 000-day integration with a simple global circulation model under a perpetual-winter condition. The composite analysis confirmed the general features of the SSWs, as seen in the real atmosphere and realistic GCMs; such as the enhanced upward propagation of planetary wave from the troposphere to the stratosphere before the SSWs with a timescale of about 1 week, and the downward propagation of warming signals to the lower stratosphere after the events with a timescale of about 1 month.

The further dynamical diagnosis has shown that the tropospheric circulation is quite different between the pre-SSW and post-SSW periods in terms of the zonal mean zonal wind, wave 1, and synoptic-scale waves. In the pre-SSW period, wave 1 is more active than normal, related to the tropospheric westerly jet that shifts poleward. In the post-SSW period, on the other hand, wave 1 is less active than normal, while the zonal mean zonal wind is close to the climatological state. In each of the two periods, the anomalous planetary-scale flow regulates the spatial distribution of anomalous synoptic-scale wave activity. The anomalous synoptic-scale wave activity, in turn, appears to maintain the anomalous planetary wave pattern, suggesting the positive feedback between planetary and synoptic waves in both periods.

The comparison of the tropospheric circulation between CS and DS demonstrated that the less active wave 1 in the post-SSW period results from the occurrence of the SSWs. In other words, it is a return signal of the SSWs, or tropospheric response to the SSWs, since the signal disappears as SSWs become absent by the increased thermal damping in the stratosphere for DS. In summary, the planetary wave in the troposphere, which interacts with the zonal mean zonal wind and synoptic-scale waves, not only induces the SSWs, but also responds to the occurrence of the SSWs with an intraseasonal timescale (10 days to 1 month) in this model.

Acknowledgments

The author is grateful to D. L. Hartmann and J. Holton for their helpful comments and suggestions. The present graphic tools were based on the codes in the GFD-DENNOU Library (SGKS Group 1999). The author is supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. This work was supported in part by NSF Climate Dynamics Grant ATM-9873691.

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Footnotes

Corresponding author address: Dr. Masakazu Taguchi, Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195-1640. Email: taguchi@atmos.washington.edu