Abstract

The influence of the sea surface temperature (SST) rise on extratropical baroclinic instability wave activity is investigated using an aquaplanet general circulation model (GCM). Two types of runs were performed: the High+3 run, in which the SST is increased by 3 K only at high latitudes, and the All+3 run, in which the SST is increased uniformly by 3 K all over the globe. These SST rises were intended to reproduce essential changes of the surface air temperature due to global warming. Wave activity changes are analyzed and discussed from the viewpoint of the energetics.

In the High+3 run, midlatitude meridional temperature gradient is decreased in the lower troposphere and the wave energy is suppressed in the extratropics. In the All+3 run, although the large tropical latent heat release greatly enhances the midlatitude meridional temperature gradient in the upper troposphere, global mean wave energy does not change significantly. These results suggest that the low-level baroclinicity is much more important for baroclinic instability wave activity than upper-level baroclinicity. A poleward shift of wave energy, seen in global warming simulations, is evident in the All+3 run. Wave energy generation analysis suggests that the poleward shift of wave activity may be caused by the enhanced and poleward-shifted baroclinicity in the higher latitudes and the increased static stability in the lower latitudes. Poleward expansion of the high-baroclinicity region is still an open question.

1. Introduction

Baroclinic instability wave activity is a key component of the general circulation in the extratropical troposphere. Transient waves in the extratropical troposphere are interpreted mainly as the baroclinic instability waves. Transient waves as well as stationary waves transport heat and angular momentum poleward and determine the mean meridional circulation and thermal structure of the troposphere. In addition, transient waves transport water vapor in the form of mean and eddy transports and influence precipitation. Moreover, transient waves govern midlatitude day-to-day weather system and sometimes cause disasters. Therefore, future projection of transient wave activity is of great concern.

Despite the importance of transient wave activity (i.e., storm track activity), projections of changes in hemispheric mean transient wave activity in future climate seem to depend strongly on global climate models, as can be seen in Fig. 3 of Yin (2005). One consistent result irrespective of models is a poleward shift of the storm track due to global warming (Fyfe 2003; Geng and Sugi 2003; Yin 2005; Fischer-Bruns et al. 2005; Bengtsson et al. 2006; Solomon et al. 2007; Lorenz and DeWeaver 2007). According to the study using reanalysis data, the poleward shift of the storm track is also evident during the last several decades (McCabe et al. 2001; Fyfe 2003). Additional significant changes due to global warming include a decrease in cyclone occurrence frequency and an increase in cyclone intensity (e.g., Geng and Sugi 2003). More recent studies on future projection of storm track activity are found in Solomon et al. (2007).

Considering the equator-to-pole temperature gradient, it is difficult to understand the mechanisms of the changes in transient wave activity due to global warming. According to climate model experiments in the troposphere, the temperature rise is expected to be great in the tropical upper troposphere and the Arctic lower troposphere (Solomon et al. 2007). Thus, the equator-to-pole temperature gradient is increased in the upper troposphere and is decreased in the Northern Hemisphere (NH) lower troposphere. In other words, zonal available potential energy and zonal kinetic energy of the whole troposphere are enhanced, at least in the Southern Hemisphere (SH). However, changes in hemispheric mean storm track activity are not consistent among the climate model experiments. Thus, the changes in equator-to-pole temperature gradient and hemispheric mean storm track activity are not intuitive.

According to the theory of the baroclinic instability wave, lower-tropospheric baroclinicity1 is very important for baroclinic instability wave activity in the troposphere (Hoskins and Valdes 1990; Iwasaki 1990). Therefore, some researchers suggested the importance of the lower-tropospheric baroclinicity for changes in storm track activity (e.g., the poleward shift of the storm track) due to global warming (e.g., Geng and Sugi 2003; Bengtsson et al. 2006). Geng and Sugi (2003) performed a global warming simulation with a high-resolution general circulation model (GCM) and found that in general the cyclone density, defined as the number of cyclones in a 4.5° × 4.5° area per season, is increased (decreased) downstream of the regions of the increased (decreased) maximum growth rate, although this linkage is not seen in some regions. Bengtsson et al. (2006) explained a poleward shift of the SH storm track as a poleward shift of the maximum sea surface temperature (SST) gradient position. Some studies emphasized the baroclinicity in the middle and/or upper troposphere (Fyfe 2003; Hall et al. 1994), whereas others discussed the baroclinicity in the whole troposphere (Lunkeit et al. 1996; Yin 2005). Other factors such as latent and sensible heat (Hall et al. 1994) and/or tropopause height (Lorenz and DeWeaver 2007) may also be important for changes in storm track activity.

As stated above, the mechanisms of the changes in extratropical storm track activity due to global warming are not yet fully understood. Analysis of the energetics is a powerful approach to investigate the mechanisms, since energy is a conserved quantity. Boer (1995) diagnosed the Lorenz energy cycle to interpret results of the global warming simulation. He found that available potential energy of the atmosphere is suppressed because of global warming, which is consistent with the decreased meridional temperature gradient in the lower troposphere. However, he did not pay much attention to the increased meridional temperature gradient in the upper troposphere, because his results showed smaller changes in meridional temperature gradient in the upper troposphere compared with that in the lower troposphere. The complexity of the results, especially the existence of the stationary ultralong waves, is one of the challenges to understanding the mechanisms. Transient waves and stationary ultralong waves seem to interact with each other. Thus, it may be inappropriate to apply the theory of the baroclinic instability wave to storm track activity under the existence of the stationary ultralong waves. In addition, results of the global warming are sometimes significantly different among models (e.g., the magnitude of the temperature rise in the Arctic lower troposphere; Houghton et al. 2001), which makes it more difficult to understand the mechanisms.

In this paper, the influence of the global-warming-like idealized SST rise on extratropical baroclinic instability wave activity (i.e., transient wave activity and storm track activity) is investigated under an aquaplanet condition. Two types of the SST rise are prescribed for the model: warming only at high latitudes and warming uniformly all over the globe. These two types of the SST rise are intended to reproduce essential changes of the surface air temperature due to global warming and to control separately the lower- and upper-tropospheric equator-to-pole temperature gradients (section 2b). Similar aquaplanet experiments were done by Caballero and Langen (2005), whose main focus was on a discrepancy in the meridional temperature gradients between the geological proxy record and numerical simulations in the past warm periods. Alexeev et al. (2005) also performed similar aquaplanet experiments to investigate polar amplification of surface warming without ice–albedo feedbacks. Using a simple aquaplanet condition, stationary wave activity is expected to be negligible. Therefore, interpretations of the results from the aquaplanet experiments are expected to be simple compared with those from the more realistic global warming experiments.

The model description, experimental design, and analysis method are given in section 2. Results for temperature, zonal wind, wave energy, global mean energy cycle, and wave energy generation rates are shown in section 3. A discussion and conclusions are provided in section 4 and 5, respectively.

2. Model and experiments

a. Model description

The atmospheric GCM used in this study is MJ98 (Shibata et al. 1999; Yukimoto et al. 2006), developed at the Meteorological Research Institute (MRI) and the Japan Meteorological Agency (JMA). The horizontal truncation wavenumber is set to T63 (equivalent longitude–latitude grid of 1.875° × 1.875°), which is reasonable to simulate storm track activity (e.g., Boville 1991; Dong and Valdes 2000). There are 45 vertical levels from the surface to 0.01 hPa (around the mesopause). The parameterization schemes used here are the same as in Kodama et al. (2007) except that no orographic gravity wave drag is exerted because of the lack of the topography in this study.

b. Experimental design

In this study, the atmospheric GCM is run under an aquaplanet condition; that is, the lower boundary condition is a zonally symmetric sea surface without mountains all over the globe. At the beginning, the control SST, which is similar to the observed SST, is prescribed for the model (control run). Then, the control SST is increased in two ways to reproduce essential changes in surface air temperature due to global warming. First, High+3 SST, which is 3K warmer than the control SST only at high latitudes, is prescribed for the model (High+3 run). This corresponds to the warming local maximum at NH high latitudes commonly seen in the global warming simulations. The High+3 SST is expected to decrease the equator-to-pole temperature gradient in the lower troposphere without significantly changing that in the upper troposphere. Second, All+3 SST, which is 3K warmer than the control SST all over the globe, is prescribed for the model (All+3 run). Such a uniform SST rise is expected to enhance the latent heat release due to cumulus convection in the tropical upper troposphere and therefore to warm there more than the other regions. Hence, the equator-to-pole temperature gradient is expected to increase in the upper troposphere without changing that in the lower troposphere. By performing two types of sensitivity experiments, we can independently control the equator-to-pole temperature gradient in the lower and upper troposphere.

The SST distributions prescribed for the model are derived from the Qobs SST proposed by Neale and Hoskins (2000a). The Qobs SST approximates the observed zonal mean SST distribution in a simple manner. The following equations are latitudinal distributions of the SST used in this study (in °C):

 
formula
 
formula

where ϕ is the latitude in radians, γ is a parameter of the SST rise at high latitudes (i.e., a decrease in equator-to-pole SST gradient), and δ is a parameter of the uniform SST rise. Parameters are set to (δ = 0, γ = 0) for the control run, (δ = 0, γ = 3) for the High+3 run, and (δ = 3, γ = 0) for the All+3 run. Figure 1 shows latitudinal distributions of the SST prescribed for the model in the series of the runs. For simplicity, all the SST distributions are uniform longitudinally and are symmetric against the equator.

Boundary conditions except for SST are same in all the runs. The CO2 concentration is 348 ppmv all over the globe; O3 distribution is uniform longitudinally and symmetric against the equator. Following Neale and Hoskins (2000a), the initial conditions are obtained from extrapolating output of the realistic GCM simulation (with full orography and realistic SST) to sea level. After a spinup term of 1 yr, each run is integrated for 10 yr under the perpetual 20 March (approximately equinox) insolation condition. Results are averaged for 10 yr and further averaged over the NH and the SH.

c. Analysis method

The mass-weighted isentropic zonal mean (MIM; Iwasaki 1989, 2001; Tanaka et al. 2004; Uno and Iwasaki 2006) is used to diagnose zonal mean temperature, zonal wind, Eliassen–Palm (EP) flux, meridional circulation, wave energy, and wave energy generation rates. The MIM is similar to the transformed Eulerian mean (TEM; Andrews and McIntyre 1976) in the sense that both MIM meridional circulation and TEM residual circulation approximate Lagrangian mean meridional circulation. The most important advantage of the MIM is the conservation of mass, momentum, and energy owing much to the accurate treatments of the lower boundary. In addition, MIM equations are derived directly from the primitive equations and no geostrophic assumptions are used. It makes the MIM a more powerful and attractive method to analyze the general circulation. (The MIM analysis program is available online at http://wind.geophys.tohoku.ac.jp/mim/).

In this study, wave energy, which is a sum of the eddy kinetic energy and eddy available potential energy, is estimated as an index of extratropical wave activity. To discuss changes in wave energy, we estimate dynamic and diabatic wave energy generation rates using a four-box energy diagram (Iwasaki 2001). Detailed derivations of the MIM energy equations are found in Iwasaki (2001) and the global mean energy cycle of the climate is diagnosed by Uno and Iwasaki (2006).

The global mean wave energy ( budget equation is expressed as

 
formula

(see the list of symbols in appendix A). The first and second terms on the right are wave energy generation rates due to dynamic and diabatic processes, respectively. The last term on the right is dissipation by friction. The global mean dynamic wave energy generation rate is expressed in the form

 
formula
 
formula
 
formula

where is isentropic form drag, Fϕ is meridional EP flux, and 〈ε1〉 and 〈ε2〉 are secondary terms [see Eqs. (B1)(B7) for details]; is a major term of the vertical EP flux in the extratropics in the MIM framework (Tanaka et al. 2004). The term 〈GBaroclinic〉 involves baroclinic processes and is equal to 〈C(Kz, AE)〉, the global mean energy conversion rate from the zonal kinetic energy KZ to the eddy available potential energy AE. In contrast, 〈GBarotropic〉 involves barotropic processes and is equal to 〈C(Kz, KE)〉, the global mean energy conversion rate from KZ to the eddy kinetic energy KE. Wave energy budget equations in the latitudinally varying form are shown in appendix C.

3. Results

a. Basic state

Thermal and dynamical structures of the atmosphere are crucial for baroclinic instability wave activity. Figure 2 shows zonal mean temperature and zonal wind for each run. In the control run (Figs. 2a,d), zonal mean temperature in the lower and middle troposphere is highest near the equator; thus, the meridional temperature gradient is greatest at the midlatitudes. The westerly jet appears at midlatitudes in the upper troposphere, consistent with the temperature structure in the sense of thermal wind balance. These features of the basic state in the aquaplanet troposphere are qualitatively similar to those of observations. In a quantitative sense, however, the strength and width of the tropospheric westerly jet are somewhat different between aquaplanet and observations. In the aquaplanet control run, the westerly jet core located around 200 hPa, 33° has a peak value of about 50 m s−1, which is far stronger than that derived from National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric research (NCAR) reanalysis data (Kalnay et al. 1996). In addition, the strong westerly zone does not well expand latitudinally in the aquaplanet control run. Such differences between aquaplanet and observations are the same as those reported by Neale and Hoskins (2000b). In the aquaplanet stratosphere, the zonal mean temperature has minimum values in both the tropics and the poles, and strong westerlies are observed in the extratropics. Hence, the background thermal and dynamical structures of the stratosphere in the aquaplanet are qualitatively similar to those in the actual winter hemisphere.

In the High+3 run compared with the control run (Figs. 2b,e), the troposphere warms in the extratropics, especially at high latitudes in the lower troposphere. Therefore, the meridional temperature gradient is decreased and the vertical shear of westerlies is suppressed at the midlatitudes in the lower and middle troposphere. The westerly jet is suppressed and slightly shifted equatorward in the troposphere and the lower stratosphere.

In the All+3 run (Figs. 2c,f), warming occurs in the entire troposphere. The greatest warming of 7.4 K is found in the tropical upper troposphere and results from diabatic heating by cumulus convection (not shown). The meridional temperature gradient is increased and the vertical shear of westerlies is enhanced at midlatitudes in the middle and upper troposphere. Consequently, the westerly jet is remarkably enhanced in the upper troposphere and stratosphere. In addition, the westerly jet is shifted poleward in the troposphere, especially near the surface. In the stratosphere, there is small warming extending from the subtropical lower stratosphere to the extratropical middle stratosphere. Such warming in the stratosphere is associated with changes in mean meridional circulation, as will be shown in the next subsection.

Note that our experiments may suppress the effects of meridional heat transport change on the basic state, especially near the surface, because of the fixed SST. Alexeev et al. (2005) and Cai (2005) suggested the dynamical amplification of the polar warming without ice–albedo feedbacks, which may be underestimated in this study.

b. EP flux and mean meridional circulation

The baroclinic instability wave in the troposphere is characterized as the upward EP flux and the thermally direct circulation in the extratropics. Figures 3 and 4 show EP flux and mean meridional circulation, respectively. In the control run, the EP flux diverges in the extratropical lower troposphere and converges in the extratropical mid to upper troposphere (Fig. 3a). In conjunction with the EP flux convergence (divergence), poleward (equatorward) flows are seen in the extratropical upper (lower) troposphere (Fig. 4a). This is consistent with the view that the extratropical direct circulation in the troposphere is mainly driven by the EP flux divergence and convergence related to the baroclinic instability waves (Iwasaki 1990; Tanaka et al. 2004). The equatorward component of EP flux is also significant in the subtropical upper troposphere. In addition to the extratropical direct circulation, there is another direct circulation in the tropics, namely, the Hadley circulation. The Hadley circulation is closely related to the diabatic heating due to cumulus convection in the upper troposphere. In the stratosphere, the mean meridional circulation, namely, the Brewer–Dobson circulation, is driven by the EP flux convergence in the extratropics. The strength of the Brewer–Dobson circulation is weaker in the aquaplanet than in the actual climate (not shown) because the aquaplanet has almost no stationary waves propagating into the stratosphere.

In the High+3 run, upward EP flux is suppressed in the extratropical lower troposphere and the EP flux divergence (convergence) is suppressed in the extratropical lower (middle) troposphere (Fig. 3b); hence, baroclinic instability wave activity is weakened in the troposphere. At the same time, EP flux convergence is enhanced in the extratropical upper troposphere and lower stratosphere, indicating an upward shift of the EP flux convergence zone. Equatorward EP flux is suppressed around the westerly jet core, consistent with the equatorward shift of the westerly jet. Changes in the extratropical mean meridional circulation are balanced by the changes in the EP flux divergence and convergence. The mean meridional circulation becomes slower in the lower troposphere and slightly faster in the polar upper troposphere (Fig. 4b).

In the All+3 run, upward EP flux is suppressed at midlatitudes in the lower and middle troposphere (Fig. 3c). Thus, EP flux divergence (convergence) is suppressed at midlatitudes in the lower (upper) troposphere. At higher latitudes, on the other hand, upward EP flux is enhanced in the middle and upper troposphere, and the EP flux convergence is enhanced in the upper troposphere. These changes indicate that baroclinic instability wave activity is suppressed on the equatorial side of the extratropics and enhanced on the polar and upper sides of the extratropics. As in the High+3 run, changes in the extratropical mean meridional circulation are balanced by the changes in EP flux divergence and convergence in the All+3 run. The mean meridional circulation becomes slower at midlatitudes and faster in the middle-to-upper troposphere at higher latitudes (Fig. 4c). Note that the downwelling is enhanced in the subtropical lower stratosphere to the extratropical upper stratosphere, which is consistent with the warming maximum as shown in Fig. 2c.

c. Wave energy

Wave energy is diagnosed as an index of baroclinic instability wave activity. Figure 5 shows the latitude–pressure cross section of eddy kinetic energy KE. We confirmed by 1 month time filtering that KE is almost determined by transient waves (not shown). In the control run (Fig. 5a), KE is greatest in the midlatitude upper troposphere (around 35°, 250 hPa), corresponding to baroclinic instability wave activity. The area where KE is greater than 100 m2 s−2 extends meridionally between the subtropics and extratropics and vertically between the troposphere and lowermost stratosphere. Compared with NCEP–NCAR reanalysis data (not shown), KE is located more equatorward and concentrates latitudinally in the control run. Figure 6 shows vertically integrated KE, eddy available potential energy AE, and W (=KE + AE; wave energy). All the values are multiplied by cosϕ (ϕ: latitude) to show the latitudinal contributions to the global means. Both AE and KE have maximum values at midlatitudes, corresponding to baroclinic instability wave activity. Note that AE is smaller than KE at most of the latitudes, although the contribution of AE to the wave energy is increased at higher latitudes. As a result, the global mean value of AE is about half that of KE in the control run.

In the High+3 run (Fig. 6, center) extratropical wave activity is suppressed at all latitudes. Both the vertically integrated KE and AE are suppressed by around 10% and contribute to the reduction of W. As shown in Fig. 5b, reduction of KE occurs almost everywhere in the troposphere, especially in the midlatitude upper troposphere, although no significant changes are seen in the stratosphere.

In the All+3 run (Fig. 6, right) global mean wave activity is rather unchanged. Global mean KE is slightly enhanced by about 2.6% in the All+3 run. The change in AE is smaller and less obvious than the change in KE. The resulting change in the global mean W is very small (only 1.4%). In the All+3 run, a poleward shift of wave activity is evident, which results primarily from the changes in the KE. From Fig. 5c, the positions of KE maxima are shifted poleward and upward. Such a poleward and upward shift of KE is also seen in the future climate simulations under realistic conditions (Yin 2005). In the stratosphere, KE is enhanced at midlatitude, whereas it is suppressed at high latitudes. As a result, about a quarter of the increase in global mean KE is contributed from changes in KE above 100 hPa.

d. Global mean energy cycle

Global mean energy cycles proposed by Iwasaki (2001) are shown in Fig. 7 to get an insight into the wave energy changes. In the control run, zonal available potential energy AZ is generated by the meridional differential heating QZ. Then AZ is converted to zonal kinetic energy KZ through mean meridional circulation. Some of the zonal kinetic energy is dissipated by friction and the rest is converted to W through wave–mean flow interactions. Energy conversions between KZ and W have two paths: one is 〈C(KZ, AE)〉, conversion from KZ to AE, and the other is 〈C(KZ, KE)〉, conversion from KZ to KE. The former involves baroclinic process and the latter involves barotropic one, as stated in section 2c. In the control run (Fig. 7, left) 〈C(KZ, AE)〉 > 0 and 〈C(KZ, KE)〉 < 0; that is, KZ is converted to W through baroclinic processes and some is converted back to KZ through barotropic processes. The fact that 〈C(KZ, KE)〉 < 0 is related to the poleward eddy angular momentum transport from the subtropics to the westerly jets in the upper troposphere. In this paper, barotropic energy conversion is often represented as 〈C(KE, KZ)〉 (>0) instead of 〈C(KZ, KE)〉. In addition to these dynamic energy conversions, W is generated by the eddy component of diabatic heating QE and is dissipated by friction.

In the High+3 run (Fig. 7, center) all the energy and energy conversion rates except for QE are clearly suppressed; that is, the energy cycle is decelerated. Changes in AZ and KZ are consistent with decreased equator-to-pole temperature gradients in the lower troposphere and suppressed westerly jets in the entire troposphere. Both 〈C(KZ, AE)〉 and 〈C(KE, KZ)〉 are suppressed by 14%, indicating less interaction between wave and mean flow. In contrast, QE is enhanced by around 7% and partly offsets suppression of the dynamical wave energy generation rate.

In the All+3 run (Fig. 7, right) both AZ and KZ are enhanced, consistent with the increased equator-to-pole temperature gradient and westerly jets. Nevertheless, changes in 〈C(KZ, AE)〉 and 〈C(KE, KZ)〉 are less than 5%; 〈C(KZ, AE)〉 is slightly suppressed and 〈C(KE, KZ)〉 is slightly enhanced. Therefore, both the changes in dynamical energy conversion rates tend to suppress the wave energy. On the other hand, QE is enhanced by more than 15%, consistent with the overall temperature rise in the troposphere.

e. Latitudinal variations of wave energy generation

Figure 8 shows latitudinal variations of the wave energy generation rates contributed from QE, GBaroclinic (baroclinic processes), GBarotropic (barotropic processes), and horizontal advection of KE. Global mean wave energy generation rates due to baroclinic and barotropic processes (〈GBaroclinic〉 and 〈GBarotropic〉) are equivalent to 〈C(KZ, AE)〉 and 〈C(KZ, KE)〉, respectively, as mentioned in section 2c. In the control run (Fig. 8, left) baroclinic processes and QE enhance wave energy, and barotropic processes (and dissipation) suppress it at midlatitudes. The position of the barotropic wave energy reduction is located equatorward by about 10° latitude compared with that of the baroclinic wave energy generation. Advection of KE is small enough to be neglected.

In the High+3 run (Fig. 8, center) both the baroclinic wave energy generation rate and the barotropic wave energy reduction rate are suppressed, indicating that the energy cycle is decelerated in the extratropics. In the All+3 run (Fig. 8, right) enhancement of W at higher latitudes is contributed primarily from baroclinic processes and secondarily from QE, and suppression of W at lower latitudes occurs through both baroclinic and barotropic processes. The baroclinic wave energy generation rate is suppressed around 30° in latitude and is enhanced around 40° (i.e., there is a poleward shift of the baroclinic wave energy generation). Around 30° latitude, the barotropic wave energy reduction rate is enhanced, leading to the suppression of W in concert with the suppressed baroclinic wave energy generation rate there. At mid to higher latitudes, both QE and the baroclinic wave energy generation rate are enhanced, leading to the enhancement of W.

Changes in the baroclinic wave energy generation rate can be decomposed into contributions from isentropic form drag (a major term of the vertical EP flux), vertical shear of westerlies, and ε1 (other terms) as follows [see Eq. (B2) for details]:

 
formula

Figure 9 shows results of the decomposition. In the High+3 run, both the weaker vertical shear of westerlies and the isentropic form drag contribute to the suppression of the baroclinic wave energy generation rate. In the All+3 run, the baroclinic wave energy generation rate is enhanced primarily by the stronger vertical shear of westerlies at higher latitudes, and it is suppressed by the weaker isentropic form drag at lower latitudes. Changes in the isentropic form drag also have minor contributions to the enhancement of the baroclinic wave energy generation rate at higher latitudes; ε1 has a smaller influence on the total changes.

Changes in the barotropic wave energy generation rate can also be decomposed into contributions from the meridional EP flux, the meridional shear of westerlies, and ε2 [see Eq. (B3) for details], as shown in Fig. 10:

 
formula

In the All+3 run, changes in the meridional shear of westerlies are responsible for about half the total changes around 30° in latitude, although meridional EP flux and ε2 also make some contributions to the total changes.

4. Discussion

In the first half of this section, we discuss mechanisms of the changes in wave activity in each run. First, as a preliminary to discussion, the maximum growth rate of the baroclinic instability wave proposed by Lindzen and Farrell (1980) is introduced in the form

 
formula

Figures 11a–c show the zonal mean maximum growth rate; Figs. 11d–f show zonal mean static stability (N2). In the control run (Fig. 11a), the maximum growth rate between the subtropics and midlatitudes corresponds well to large wave activity (e.g., Fig. 5a). In the High+3 run (Fig. 11b), maximum growth rate is decreased in the lower and middle troposphere, especially between 30° and 40° latitude, due primarily to a smaller meridional temperature gradient. In the All+3 run (Fig. 11c), the maximum growth rate is remarkably increased in the upper troposphere because of the greater meridional temperature gradient (i.e., the greater vertical shear of the westerly jet). However, it is slightly decreased in the lower troposphere and subtropics, mainly because of increased static stability (Fig. 11f).

Results of the High+3 run show that meridional temperature gradient is decreased in the extratropical lower troposphere, and vertical shear of westerlies is suppressed there. In other words, the maximum growth rate is decreased in the lower troposphere, which considerably suppresses the dynamic wave energy generation rate and results in the suppression of the wave energy. These results indicate the importance of the low-level baroclinicity in global mean wave energy, which is consistent with past studies (e.g., Hoskins and Valdes 1990; Iwasaki 1990).

In the All+3 run, the meridional temperature gradient is increased in the upper troposphere and the vertical shear of the westerlies is enhanced there. In other words, the maximum growth rate is increased in the upper troposphere. Therefore, zonal available potential energy and zonal kinetic energy are clearly enhanced. However, changes in global mean wave energy are rather small. Specifically, why is the tropospheric wave energy suppressed in the lower latitude in the All+3 run? One possible mechanism is that the increased static stability (Fig. 11f), which occurs especially at lower latitudes, may suppress the development of the baroclinic instability waves. From the perspective of Rossby wave interaction (Hoskins et al. 1985), increased static stability means smaller Rossby height (=fL/N), which represents the height scale of potential vorticity anomaly influence. It leads to the suppression of the interaction between two waves trapped near the tropopause and lower boundary, respectively, and may suppress baroclinic instability wave activity. Another possible mechanism is that a decrease in the meridional temperature gradient in the subtropical lower troposphere may suppress wave activity in the lower latitudes. In fact, the contribution of the meridional temperature gradient to the decrease in the maximum growth rate is comparable to that of the static stability in the subtropical lower troposphere (not shown).

The poleward shift of wave activity is evident in the All+3 run. Analysis of the wave energy generation rate indicates that the enhanced vertical shear of westerlies primarily contributes to the enhanced wave energy at higher latitudes. In addition, the pattern of the changes in eddy kinetic energy (Fig. 5c) resembles that in the maximum growth rate (Fig. 11c). Therefore, the poleward shift of wave activity in the All+3 run may be caused by the increased upper-level baroclinicity in the higher latitudes in concert with the increased static stability in the lower latitudes. The region of the increased upper-level baroclinicity extends poleward of the high-baroclinicity region in the control run (i.e., the westerly jet is shifted poleward in the upper troposphere). The mechanism of this poleward jet shift is still an open question. Lorenz and DeWeaver (2007) suggested the possibility that the tropopause height rise causes a poleward shift of westerly jet.

In the All+3 run, the wave energy generation rate due to diabatic heating, QE, is enhanced in the higher latitudes and secondarily contributes to the poleward shift of the wave energy. The tropospheric warming allows the air containing more water vapor everywhere in the troposphere. It can enhance QE and generate more wave energy. Conversely, enhanced (suppressed) wave energy can cause more (less) QE in the higher (lower) latitudes. In addition, tropospheric warming can make meridional transport of latent energy more efficient, as suggested by Boer (1995). As a result of these amplifying or compensating factors, QE is enhanced in the higher latitudes whereas it is almost unchanged in the lower latitudes.

Finally, we discuss similarities and differences between the aquaplanet and the realistic planet with emphasis on global warming projections. Solomon et al. (2007) suggested a poleward shift of the midlatitude storm track in both hemispheres due to global warming. In the global warming projections, the SST rise greatly warms the tropical upper troposphere and enhances midlatitude upper-tropospheric baroclinicity, as seen in our All+3 run. Yin (2005) suggested that the poleward shift and enhancement of storm track activity are accompanied by a poleward shift and upward expansion of baroclinicity associated with tropical upper-tropospheric warming and tropopause rise. Changes in the wave activity and basic state seem to be partly consistent with our aquaplanet experiment. The greater global mean wave energy, however, is not clearly found in our experiment. In the NH winter, attention must be paid to the interactions with stationary wave activity, which is suppressed due to global warming (T. Iwasaki et al. 2008, unpublished manuscript, hereafter IWA). Of course, our aquaplanet experiment is too simple to capture complex phenomena of the realistic global warming. Recently, SST fronts (locally confined SST gradient peaks) have been found to be important for storm track activity (Nakamura et al. 2008). In this study, no SST front exists, which may affect the results. In addition, dynamical amplification of the polar warming, as suggested by Alexeev et al. (2005) and Cai (2005), is not considered in this study. Moreover, the perpetual insolation condition may also affect the results. Further studies are needed to confirm the reason for the changes in storm track activity in the future projections.

5. Conclusions

We investigated the influence of SST rise on extratropical baroclinic instability wave activity using an aquaplanet general circulation model. Two types of sensitivity experiments were performed: the High+3 run, in which the SST is increased by 3 K only at high latitudes, and the All+3 run, in which the SST is increased uniformly by 3 K all over the globe. These two experiments were designed to reproduce the essential changes of the surface air temperature due to global warming. As an index of transient wave activity, wave energy, which is a sum of eddy kinetic energy and eddy available potential energy, is diagnosed based on the MIM. Wave energy generation rates due to dynamic and diabatic processes are estimated to explain changes in wave energy in each run.

Low-level baroclinicity is crucial to global mean wave activity. In the High+3 run, the baroclinicity in the lower troposphere is decreased, and the global mean wave energy is suppressed. In the All+3 run, although baroclinicity in the upper troposphere is increased, the global mean wave energy remains unchanged. These facts reveal that the low-level baroclinicity is essential for the global mean wave energy, whereas the upper-level baroclinicity is less important for it.

Increased and poleward-shifted upper-level baroclinicity, however, seems to influence the latitudinal variation of the wave energy in concert with the increased static stability in the lower latitudes. In the All+3 run, the temperature rise is greatest in the tropical upper troposphere as a result of the enhanced latent heat release. It leads to an increase in upper-level baroclinicity, although the poleward expansion of the baroclinicity increase (i.e., the poleward jet shift) is not understood in this study. These changes in upper-level baroclinicity enhance the energy conversion from the zonal kinetic energy to the eddy available potential energy at higher latitudes. It leads to the enhancement of the wave energy at higher latitudes. At the same time, the upper-level temperature rise enhances the static stability in the troposphere, suppresses the maximum growth rate of the baroclinic instability wave, and then suppresses the baroclinic instability wave. We suggested that these two effects of changed upper-level baroclinicity and increased static stability together may cause the poleward shift of the storm track without significantly changing the global mean wave energy in the All+3 run. The enhanced wave energy generation rate due to diabatic heating, QE, secondarily contributes to the poleward shift of the wave energy in the All+3 run.

The aquaplanet experiments provide us with the following implications in realistic storm track changes due to global warming. Polar warming observed in the NH lower troposphere suppresses baroclinic instability wave activity through a decrease in low-level baroclinicity. The tropical SST rise causes a maximum temperature rise in the tropical upper troposphere, enhances upper-level baroclinicity at midlatitudes, and shifts the storm track poleward. In the realistic global warming simulations, the magnitude of the polar warming depends strongly on the climate models (Houghton et al. 2001), and there are diverse future projections of global mean storm track activity. Finally, we emphasize the importance of stationary wave activity to the changes in global mean transient wave energy, as discussed in IWA.

Acknowledgments

The authors wish to thank Dr. K. Shibata and Dr. S. Yukimoto of the Meteorological Research Institute for providing the MJ98 GCM and their support. We also thank Prof. H. Kanzawa, Dr. H. Nakamura, and Dr. M. Watanabe for their helpful comments and encouragement. This paper was improved thanks to the constructive comments and suggestions from two anonymous reviewers. The Grid Analysis and Display System (GrADS) was used to draw all the figures in this paper. This study was supported by the 21st Century Center of Excellence (COE) program “Earth Advanced Science Technology Center” and the global COE program “Global Education and Research Center for Earth and Planetary Dynamics” at Tohoku University. Part of this research was carried out using supercomputing resources at Cyberscience Center, Tohoku University.

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APPENDIX A

List of Symbols

  • a Earth radius

  •  Mass-weighted isentropic zonal mean

  • A′ Eddy (≡A)

    A〉 Global mean

  • AE Eddy available potential energy

  • AZ Zonal available potential energy

  • C(X, Y) Energy conversion rate from X to Y

  • Cp Heat capacity for a constant pressure process

  • δE Dissipation rate from KE by friction

  • Fϕ Meridional component of Eliassen–Palm (EP) flux

  •  Isentropic form drag

  • g Acceleration of gravity

  • G Dynamical wave energy generation rate (= GBaroclinic + GBarotropic)

  • GBaroclinic Wave energy generation rate due to baroclinic processes

  • GBarotropic Wave energy generation rate due to barotropic processes

  • H Scale height (≈7 km)

  • KE Eddy kinetic energy

  • KZ Zonal kinetic energy

  • κ ≡ R/Cp

  • λ Longitude

  • N Brunt–Väisälä frequency

  • p Pressure

  • p0 Reference pressure (≡ 1000 hPa)

  • p Isentropic zonal mean pressure

  • ps Zonal mean surface pressure

  • Φ Geopotential in the pressure coordinate

  • Φ Geopotential in the p coordinate [dΦ ≡ −(RT/p)dp]

  • ϕ Latitude

  • Q Diabatic heating

  • QE Wave energy generation rate due to diabatic heating

  • R Gas constant

  • ρ0 Reference density (≡ p/RT)

  • T Temperature

  • T ≡ θ(p/p0)R/Cp

  • θ Potential temperature

  • u Zonal wind

  • υ Meridional wind

  • W Wave energy (≡ AE + KE)

  • w Vertical wind (≡ dz/dt)

  • y =

  • z Log-p coordinate [≡ −H ln(p/p0)]

  • zs ≡ −H ln(ps/p0)

APPENDIX B

Global Mean Wave Energy Equation

A complete set of global mean wave energy budget equation is expressed as

 
formula

where the wave energy generation rates due to dynamic processes are

 
formula
 
formula
 
formula
 
formula
 
formula
 
formula

Note that is approximately equal to the vertical EP flux in the TEM framework [Tanaka et al. 2004, Eq. (A5)]. In other words, is approximately proportional to the eddy heat flux.

The wave energy generation rate due to diabatic heating is

 
formula
 
formula
 
formula

where Q is diabatic heating. Finally, is expressed in the form

 
formula

where X′ and Y′ are eddy components of the zonal and meridional frictional forcings, respectively.

APPENDIX C

Latitudinal Variations of Wave Energy Equation

Latitudinal variations of vertically integrated tendency equations for the eddy available potential energy and the eddy kinetic energy are expressed as follows:

 
formula
 
formula

where GBaroclinic, GBarotropic, , and are as in appendix B. The other terms are

 
formula
 
formula
 
formula

Note that GBaroclinic and GBarotropic indicate the local source of wave energy, not the local sink of zonal kinetic energy. In this study, wave energy generation and wave energy reduction mean the sources and sinks of wave energy, respectively. Of course, the global mean source of wave energy is equivalent to the global mean sink of zonal kinetic energy. Note further that a1 (advection of AE and its related term) is not considered in our analysis because it is difficult to estimate a1 due to lower boundary condition. Although a1 does not affect the global mean values, it may significantly shift the latitude of the wave energy generation rate.

Footnotes

* Current affiliation: Japan Agency for Marine-Earth Science and Technology (JAMSTEC).

Corresponding author address: Chihiro Kodama, JAMSTEC, 3173-25, Showa-Machi, Kanazawa-Ku, Yokahama, Kanagawa, 236-0001, Japan. Email: kodamac@jamstec.go.jp

1

According to the Glossary of Meteorology (Glickman 2000), the term baroclinicity is the state of stratification in a fluid in which surfaces of constant pressure intersect surfaces of constant density. In this sense, baroclinicity means R/p(∂T/∂y)p (i.e., meridional temperature gradient at constant pressure, if the longitudinal temperature variation is not considered). Some authors, however, use the term baroclinicity as a maximum growth rate of the baroclinic instability wave, in which not only meridional temperature gradient but also static stability are considered. These two concepts are similar but slightly different. In this paper, baroclinicity is defined as the former meaning, although, in this section, baroclinicity is also used as the latter meaning.