1. Introduction
Because of increased amounts of greenhouse gases (GHGs), several changes in the atmospheric general circulation have been noted in future climate Intergovernmental Panel on Climate Change (IPCC) scenarios relative to the present climate. Among them, there is a rise in the height of the tropopause (Lorenz and DeWeaver 2007), an increase in the dry static stability (Yin 2005; Frierson 2006), and a poleward shift of the tropospheric jet streams and storm tracks. This is seen in both hemispheres but is more marked in the Southern Hemisphere (SH) (e.g., Yin 2005; Lorenz and DeWeaver 2007). Because of the key role played by the baroclinicity in storm-track dynamics, some authors (e.g., Hall et al. 1994; Yin 2005; Kodama and Iwasaki 2009) have related the poleward shift of the jets and storm tracks to changes in baroclinicity. The most drastic difference between present and future climates appears in upper-level baroclinicity. Because of stronger warming in the tropical upper troposphere resulting from an enhancement of latent heat release in these regions, a significant increase in upper-tropospheric horizontal temperature gradients occurs in midlatitudes in all seasons. Other changes in baroclinicity have been also noted depending on the season and hemisphere. During the Northern Hemisphere (NH) winter, the northern polar regions undergo an important increase in temperature at the surface, leading to a decrease in low-level horizontal temperature gradients in midlatitudes (Geng and Sugi 2003). The effect of the static stability increase is to decrease the baroclinicity in the whole troposphere but the anomalies of the horizontal temperature gradients generally dominate over those of the static stability in the baroclinicity field, as shown by Yin (2005). Finally, a poleward shift of the low-level baroclinicity has been emphasized in various studies (e.g., Hall et al. 1994; Yin 2005), which is consistent with the poleward shift of the storm tracks and eddy-driven jets. However, the dynamical interpretation of this poleward shift is still an issue under debate.
Simulations of coupled climate models are not enough to determine a clear explanation for the poleward shift of the jet streams and simpler numerical experiments are necessary. Several factors have been recently highlighted as playing a role in this shift. Lorenz and DeWeaver (2007) have shown that when the height of the tropopause is raised in a simple dry atmospheric general circulation model (GCM), zonal winds move poleward and are accompanied by a strengthening of the poleward eddy momentum fluxes. However, no interpretation that may explain the positive eddy feedback is proposed in that study. Kodama and Iwasaki (2009) have also presented evidence of positive eddy feedback by uniformly increasing the SSTs in an aquaplanet GCM. An additional experiment shows that an increase in SSTs in the polar regions alone has the reverse effect. The eddy kinetic energy (EKE) decreases because of the decrease in low-level baroclinicity. The analysis reveals also that the eddy momentum flux anomalies are essentially equatorward. The authors conclude that the reduction in low-level baroclinicity cannot favor the poleward shift of the jets, but the increased and poleward-shifted upper-level baroclinicity in concert with the increased static stability can do so. Different mechanistic arguments have been also proposed to interpret the poleward shift of the eddy-driven jets. The strengthening of the midlatitude upper-tropospheric wind may increase the eastward phase speed of the eddies, leading to a poleward shift of the subtropical wave-breaking region (Chen et al. 2008; Lu et al. 2008). Note that the role played by increased eddy phase speeds in pushing the jet poleward has been already discussed in other circumstances, using both idealized simulations (Chen et al. 2007) and reanalysis data (Chen and Held 2007). Another potential mechanism is that the increase in subtropical static stability reduces the eddy generation on the equatorward side of the storm track, shifting the eddy source region and thus the eddy-driven jet poleward (Lu et al. 2008, 2010). However, since the more drastic change in baroclinicity in such scenarios is the increase in upper-level baroclinicity, the present study will carefully analyze, theoretically and numerically, the effect of upper-level baroclinicity on synoptic waves.
More direct effects of increased water vapor in global warming scenarios may occur in eddy life cycles. A few studies (Orlanski 2003; Rivière and Orlanski 2007; Laîné et al. 2011) indicate that the increase in humidity favors the occurrence of cyclonic wave-breaking (CWB or LC2) events to the detriment of anticyclonic wave-breaking (AWB or LC1) events. As explained by Orlanski (2003), more latent heat release increases the cyclone–anticyclone asymmetries, cyclones become more intense than anticyclones, and therefore more CWB events occur. Since AWB and CWB respectively push the jet more poleward and equatorward (Thorncroft et al. 1993), an increase in CWB will tend to move the jets equatorward. However, this feedback is opposite to that diagnosed in future climate scenarios. Furthermore, Laîné et al. (2009) found that the direct effect of latent heat release changes in the eddy energy budget in simulations with fourfold CO2 increase was of second order compared to baroclinic conversion. In the present study, the effect of water vapor on storm-track dynamics will not be investigated and only dry dynamics will be analyzed.
One possibility is that the poleward shift of the jet streams in the future climate may come from the increased eddy length scale as suggested by Kidston et al. (2010). Very recently, Kidston et al. (2011) have provided an explanation in terms of the dissipation and source latitudes of eddy activity. The increased eddy length scale shifts the dissipation regions farther from the jet core. There is therefore a broadening of the net eddy source region, but more importantly on the poleward side of the jet since dissipation and source regions are close to each other on this side of the jet. It results in a poleward shift of the zonal acceleration region. A more classical argument to understand the impact of the eddy length scale on the latitudinal vacillation of the jet is based on the nature of the breaking. Numerous numerical idealized studies (e.g., Simmons and Hoskins 1978; Balasubramanian and Garner 1997a; Hartmann and Zuercher 1998; Orlanski 2003; Rivière 2009, hereafter R09) have noted that the sign of the eddy momentum fluxes, or equivalently the type of the wave breaking, depends largely on the spatial scales of the waves. Long (short) waves tend to break anticyclonically (cyclonically), leading to a poleward (equatorward) shift of the jet. The transition from one type of breaking to another usually occurs at intermediate wavenumbers 7 or 8 depending on the background flow (Wittman et al. 2007; R09). However, despite this well-known scale effect on wave breaking, there is no well-established consensus in the literature to explain it. The anticyclonic breaking for long waves is usually explained by effective beta asymmetries (e.g., Balasubramanian and Garner 1997a; Orlanski 2003; R09) but the cyclonic breaking for short waves leads to various interpretations. Balasubramanian and Garner (1997a) involves linear non-quasigeostrophic effects that already exist in Cartesian geometry, while the argument of R09 points out the role played by the latitudinal variations of the Coriolis parameter in the stretching term of the potential vorticity (PV) gradient. Orlanski (2003) put forward a vortex interaction mechanism. Because of non-quasigeostrophic effects, cyclones are much more intense than anticyclones for short waves, which makes CWB more probable. Observational evidences support the previous numerical studies concerning the relationship among the eddy length scale, the nature of the breaking, and the latitudinal vacillation of the jet. For instance, the positive (negative) phase of the North Atlantic Oscillation is shown to be accompanied by more AWB (CWB) than usual and longer (shorter) waves (Rivière and Orlanski 2007). Following all these studies, the purpose of the present paper is to investigate the effect of enhanced upper-level baroclinicity on the growth rates and spatial scales of baroclinic waves and consequently on the behavior of their breaking. It will provide a new dynamical interpretation for the poleward shift of the jet streams in global warming scenarios.
Section 2 is dedicated to the results of the twentieth- and twenty-first-century simulations of two IPCC models, with particular emphasis on changes in the eddy length scale. In section 3, the baroclinic instability in a three-level quasigeostrophic (QG) model on an f plane is analyzed. We compare different growth rates by modifying the intensity of the upper-level baroclinicity. This provides a simple dynamical interpretation for the eddy length scales differences between present and future climates. Section 4 confirms the results of section 3 using a global dry primitive equation model of the atmosphere and two numerical methods: a normal-mode study and long-term simulations forced by different restoration-temperature profiles. A rationale for the poleward shift of the jet streams is given in terms of an eddy length scale selection. Finally, concluding remarks and a discussion are presented in section 5.
2. Simulations of the twentieth- and twenty-first-century climates
a. Description of models and diagnostics
The two coupled IPCC models used in this study are the Centre National de Recherches Météorologiques Coupled Global Climate Model, version 3.3 (CNRM-CM3.3) and the Institut Pierre et Simon Laplace Coupled Model, version 4 (IPSL-CM4). The simulations studied in this paper consist of runs performed within the framework of the multimodel ENSEMBLES project (http://ensembles-eu.metoffice.com/), which follows the recommendations of the IPCC Fourth Assessment Report. We compare the outputs of the twentieth (20C)- and twenty-first-century (A1B) simulations. Experiment 20C consists of initializing the run under a preindustrial condition and forcing it with historical GHG, aerosol, volcanic, and solar forcing from the twentieth century. Experiment A1B is forced with specified GHGs for the period 2001–2100 according to the A1B scenario of the IPCC report. Only daily-mean datasets during 20 consecutive years are used, from 1980 to 1999 for 20C and from 2080 to 2099 for A1B.
A high-pass filter (periods less than 10 days) is applied to the daily fields to analyze storm-track properties. A wave-breaking detection method is also used to estimate the frequency of CWB and AWB events. The purpose of the algorithm is to detect, at each day, all the regions where there is a local reversal of the absolute vorticity gradient on each isobaric surface. Then, it identifies the type of breaking (AWB or CWB). More details on the algorithm can be found in R09 and Rivière et al. (2010). It allows us to define a frequency of occurrence for each breaking at each grid point (denoted hereafter as fa and fc for AWB and CWB events, respectively). To look at the changes in the nature of each breaking, the high-frequency eddy momentum fluxes will be averaged in AWB and CWB regions (i.e., at all grid points where there is an anticyclonic and cyclonic reversal of the absolute-vorticity gradient) and will be denoted as (uυ)a and (uυ)c, respectively. The averaged high-frequency eddy momentum fluxes over all the wave-breaking regions will be therefore (uυ)a fa/(fa + fc) + (uυ)c fc/(fa + fc).
b. Results
1) Zonal-mean climatologies
Figure 1 depicts zonal-mean and annual climatologies for CNRM and IPSL. There is a maximum increase in temperature from 20C to A1B in the tropical upper-level troposphere with larger anomalies for IPSL (see the black contours in Figs. 1a,b). The CNRM temperature anomalies are slightly less than those of the multimodel ensemble mean computed by Yin (2005), who found an increase of about 5°C in these regions. Zonal winds increase in the upper troposphere and move poleward except for the IPSL NH, where no significant anomalies can be detected (Figs. 1c,d). In most cases, eddy-driven jets, which can be diagnosed from the low-level zonal winds (e.g., at 800 hPa) are shifted poleward. Note that the less robust poleward shift in the NH compared to the SH is accompanied by smaller differences in the upper-tropospheric horizontal temperature gradients. The high-frequency kinetic energy (EKE) shows a global increase and a poleward shift as already noted by Yin (2005) for all seasons (Figs. 1e,f). The summer NH case is the one that has the less obvious increase in EKE (not shown). There is also a significant increase in poleward high-frequency momentum fluxes, which is larger for cases where the eddy-driven jet is displaced more poleward (see, e.g., the SH IPSL case in Fig. 1h). In contrast, anomalous momentum fluxes are weak and even slightly equatorward for the NH IPSL case where the jet does not move poleward. As expected, there is a close relationship between the poleward shift of the jets and the increase in poleward eddy momentum fluxes.
Zonal-mean climatology for the 1980–99 period (shading) and the difference between the 2080–99 and 1980–99 periods (black contours, negative and positive values in dashed and solid lines, respectively) for the (left) CNRM and (right) IPSL models: (a),(b) mean temperature [interval (hereafter int): 10°C] and anomalies (int: 1°C); (c),(d) mean zonal wind (int: 5 m s−1) and anomalies (int: 1 m s−1); (e),(f) mean of the high-frequency kinetic energy (int: 10 m2 s−2) and anomalies (int: 2 m2 s−2); and (g),(h) mean of the high-frequency momentum fluxes (int: 5 m2 s−2) and anomalies (int: 1 m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Zonal-mean climatology for the 1980–99 period (shading) and the difference between the 2080–99 and 1980–99 periods (black contours, negative and positive values in dashed and solid lines, respectively) for the (left) CNRM and (right) IPSL models: (a),(b) mean temperature [interval (hereafter int): 10°C] and anomalies (int: 1°C); (c),(d) mean zonal wind (int: 5 m s−1) and anomalies (int: 1 m s−1); (e),(f) mean of the high-frequency kinetic energy (int: 10 m2 s−2) and anomalies (int: 2 m2 s−2); and (g),(h) mean of the high-frequency momentum fluxes (int: 5 m2 s−2) and anomalies (int: 1 m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Zonal-mean climatology for the 1980–99 period (shading) and the difference between the 2080–99 and 1980–99 periods (black contours, negative and positive values in dashed and solid lines, respectively) for the (left) CNRM and (right) IPSL models: (a),(b) mean temperature [interval (hereafter int): 10°C] and anomalies (int: 1°C); (c),(d) mean zonal wind (int: 5 m s−1) and anomalies (int: 1 m s−1); (e),(f) mean of the high-frequency kinetic energy (int: 10 m2 s−2) and anomalies (int: 2 m2 s−2); and (g),(h) mean of the high-frequency momentum fluxes (int: 5 m2 s−2) and anomalies (int: 1 m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Figure 2 depicts changes in wave-breaking statistics. AWB events usually occur on the equatorward side of the jets and CWB more on the poleward side (Figs. 2a,b). For CNRM, the differences in wave-breaking frequencies of occurrence between 20C and A1B are very slight, except for the SH where the number of CWB events significantly decreases (Fig. 2a). For IPSL, there is a slight increase in frequency and a poleward shift of AWB from 20C to A1B in the SH, which is accompanied by a decrease in CWB events. The reverse happens in the NH with an important decrease in AWB events (Fig. 2b). The high-frequency eddy momentum fluxes averaged in AWB and CWB regions show respectively an increase in amplitude of both poleward and equatorward fluxes, except for the NH IPSL case (Figs. 2c,d). This is consistent with the global increase in EKE shown in Figs. 1e,f. However, the percentage of increase in poleward fluxes is significantly greater than that in equatorward fluxes when these fluxes are multiplied by the frequencies of occurrence of their respective breaking regions [i.e., when comparing (uυ)a fa/(fa + fc) to (uυ)c fc/(fa + fc); Figs. 2e,f]. The decrease in CWB events in the SH in both models compensates in large part the increase in intensity of the equatorward fluxes in these regions as shown by comparing fc (Figs. 2a,b), (uυ)c (Figs. 2c,d), and (uυ)c fc/(fa + fc) (Figs. 2e,f). Therefore, in cases where the jet moves poleward (i.e., in the NH and SH for CNRM and in the SH for IPSL), the anomalous eddy momentum fluxes averaged over all the wave-breaking regions are mainly poleward because the poleward fluxes in AWB regions increase in intensity and there is a relative decrease of CWB events compared to AWB events. Note, finally, that for the NH IPSL case, where there is no displacement of the jet, the anomalous eddy momentum fluxes averaged over all the wave-breaking regions are almost unchanged (Fig. 2h).
Zonal and vertical averages of different wave breaking–related quantities for the 1980–99 (black line) and 2080–99 (red line) periods of the (left) CNRM and (right) IPSL simulations. (a),(b) Cyclonic (dashed) and anticyclonic (solid) frequencies of occurrence (i.e., fc and fa) (day−1). (c),(d) Average of the high-frequency eddy momentum fluxes in cyclonic (dashed) and anticyclonic (solid) wave-breaking regions [i.e., (uυ)a and (uυ)c] (m2 s−2). (e),(f) Product between the wave-breaking frequencies of occurrence and the averaged momentum fluxes [i.e., (uυ)c fc/(fa + fc) (dashed) and (uυ)a fa/(fa + fc) (solid)] (m2 s−2). (g),(h) Average of the high-frequency eddy momentum fluxes in all wave-breaking regions {i.e., the sum [(uυ)c fc + (uυ)a fa]/(fa + fc)} (m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Zonal and vertical averages of different wave breaking–related quantities for the 1980–99 (black line) and 2080–99 (red line) periods of the (left) CNRM and (right) IPSL simulations. (a),(b) Cyclonic (dashed) and anticyclonic (solid) frequencies of occurrence (i.e., fc and fa) (day−1). (c),(d) Average of the high-frequency eddy momentum fluxes in cyclonic (dashed) and anticyclonic (solid) wave-breaking regions [i.e., (uυ)a and (uυ)c] (m2 s−2). (e),(f) Product between the wave-breaking frequencies of occurrence and the averaged momentum fluxes [i.e., (uυ)c fc/(fa + fc) (dashed) and (uυ)a fa/(fa + fc) (solid)] (m2 s−2). (g),(h) Average of the high-frequency eddy momentum fluxes in all wave-breaking regions {i.e., the sum [(uυ)c fc + (uυ)a fa]/(fa + fc)} (m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Zonal and vertical averages of different wave breaking–related quantities for the 1980–99 (black line) and 2080–99 (red line) periods of the (left) CNRM and (right) IPSL simulations. (a),(b) Cyclonic (dashed) and anticyclonic (solid) frequencies of occurrence (i.e., fc and fa) (day−1). (c),(d) Average of the high-frequency eddy momentum fluxes in cyclonic (dashed) and anticyclonic (solid) wave-breaking regions [i.e., (uυ)a and (uυ)c] (m2 s−2). (e),(f) Product between the wave-breaking frequencies of occurrence and the averaged momentum fluxes [i.e., (uυ)c fc/(fa + fc) (dashed) and (uυ)a fa/(fa + fc) (solid)] (m2 s−2). (g),(h) Average of the high-frequency eddy momentum fluxes in all wave-breaking regions {i.e., the sum [(uυ)c fc + (uυ)a fa]/(fa + fc)} (m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
These results are confirmed in Table 1 where all the regions are taken into account and not only the wave-breaking regions. For CNRM, the global averages of the poleward momentum fluxes in the SH and NH increase respectively by 11% and 9% from 20C to A1B while those of the equatorward fluxes increase by 6% and 5% only. For IPSL, in the SH, the poleward and equatorward fluxes increase by 17% and 7%, respectively. It indicates that the poleward shift of the jet streams, when it occurs, is not simply due to a global increase in EKE. Indeed, in that case, we would expect a similar increase in the intensity of the equatorward and poleward fluxes.
Time and spatial averages in the two hemispheres of the high-frequency eddy momentum fluxes for the CNRM and IPSL simulations (m2 s−2).
2) Spatial scales
Following the hypothesis that changes in the eddy length scale play a role in the shift of the jet streams, the high-frequency meridional wind amplitude is plotted as a function of the latitude and zonal wavelength in Figs. 3a,b. At 40°N, for CNRM (Fig. 3a), there is usually an important increase in their amplitude for wavelengths longer than 4000 km and a weaker decrease for shorter wavelengths. The respective increase and decrease in intensity of the long and short wavelengths are obvious at all midlatitudes. For IPSL (Fig. 3b), the same tendency appears in the SH with stronger dipolar anomalies. In contrast, the dipolar anomaly and the scale selection are much less obvious in the NH. In particular, the increase in intensity for long wavelengths is weak between 20° and 45°N. These results are robust when looking at the total meridional wind amplitude (Figs. 3c,d). The fact that the difference in eddy length scales appears more clearly in the SH, precisely in the regions where the poleward shift of the jets is obvious, supports the idea that the length scale plays a role in this shift. This aspect is investigated further in section 4.
High-frequency meridional wind amplitude vertically averaged between 200 and 500 hPa as a function of the latitude and zonal wavelength for the 1980–99 period (shading; int: 1 m s−1) and the difference between the 2080–99 and 1980–99 periods (black contours; int: 0.2 m s−1) for the (a) CNRM and (b) IPSL models.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
High-frequency meridional wind amplitude vertically averaged between 200 and 500 hPa as a function of the latitude and zonal wavelength for the 1980–99 period (shading; int: 1 m s−1) and the difference between the 2080–99 and 1980–99 periods (black contours; int: 0.2 m s−1) for the (a) CNRM and (b) IPSL models.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
High-frequency meridional wind amplitude vertically averaged between 200 and 500 hPa as a function of the latitude and zonal wavelength for the 1980–99 period (shading; int: 1 m s−1) and the difference between the 2080–99 and 1980–99 periods (black contours; int: 0.2 m s−1) for the (a) CNRM and (b) IPSL models.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
3. Baroclinic instability in a three-level quasigeostrophic model on an f plane
a. Model description
Equation (1) can be viewed as a linearized, Cartesian version of the three-level QG model on the sphere of Marshall and Molteni (1993) that does not include dissipative and forcing terms. In their model, levels 1, 2, and 3 typically correspond to 200, 500, and 800 hPa, respectively and R1 = 700 km and R2 = 450 km are Rossby radii of deformation appropriate respectively to the 200–500-hPa and 500–800-hPa layers. In what follows, cases with equal Rossby radii of deformation are investigated together with cases using the previous, more realistic values.
b. Growth rates
Baroclinic instability in a three-layer context has already been investigated by several authors (e.g., Davey 1977; Smeed 1988). The curvature in the vertical profile of the horizontal velocity has been shown to have an effect on the normal-mode growth rates and the range of unstable wavelengths. The purpose of the present section is to underline this effect in the context of climate change scenarios.
The complex phase velocities of the normal modes c and their growth rates kci are obtained by solving a cubic equation [see Eq. (10) of Smeed (1988) or the appendix of the present study] analytically. It is shown to depend only on three key parameters: 
1) Equal Rossby radii of deformation
As is well known in such simple baroclinic models, there is a high-wavenumber cutoff beyond which there is no instability (see, e.g., the bold solid line in Fig. 4). This is classically interpreted in the context of the two-level model (Hoskins et al. 1985; Vallis 2006): the upper and lower waves are able to interact with each other for sufficiently long wavelengths, otherwise it is commonly said that they “do not see each other.” Indeed, the larger the spatial scale of a PV anomaly of given strength located at a given level the stronger the induced velocity field at the other level. Because of its short vertical decay scale, a short wave is not able to induce a sufficiently strong meridional velocity to advect the basic-state PV gradient and to reinforce its companion wave at the opposite level.
(a) Growth rate in nondimensional units kci/(UR−1) as a function of the nondimensional wavenumber kR in the three-level model for ϵ = 1.0; (U1, U3) = (U, −U) (thick solid), (U1, U3) = (0, −U) (dashed), (U1, U3) = (U/2−U) (dashed–dotted) and (U1, U3) = (U, −2U) (thin solid). (b) As in (a), but for meridional PV gradient in nondimensional units ∂yQ/(UR−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
(a) Growth rate in nondimensional units kci/(UR−1) as a function of the nondimensional wavenumber kR in the three-level model for ϵ = 1.0; (U1, U3) = (U, −U) (thick solid), (U1, U3) = (0, −U) (dashed), (U1, U3) = (U/2−U) (dashed–dotted) and (U1, U3) = (U, −2U) (thin solid). (b) As in (a), but for meridional PV gradient in nondimensional units ∂yQ/(UR−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
(a) Growth rate in nondimensional units kci/(UR−1) as a function of the nondimensional wavenumber kR in the three-level model for ϵ = 1.0; (U1, U3) = (U, −U) (thick solid), (U1, U3) = (0, −U) (dashed), (U1, U3) = (U/2−U) (dashed–dotted) and (U1, U3) = (U, −2U) (thin solid). (b) As in (a), but for meridional PV gradient in nondimensional units ∂yQ/(UR−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Let us first look at the effect of decreasing the upper-level baroclinicity U1 while keeping the lower one U3 constant. As can be seen by comparing cases for (U1, U3) = (U, −U) (thick solid line), (U1, U3) = (U/2, −U) (dashed–dotted line), and (U1, U3) = (0, −U) (dashed line) in Fig. 4a, decreasing U1 leads to an increase in the high-wavenumber cutoff and, therefore, a destabilization of the smaller scales as well as a decrease in the growth rates of the largest scales. This can be easily interpreted in terms of the basic-state PV gradient (Fig. 4b). For (U1, U3) = (U, −U) (thick solid line), the PV gradient increases from −UR−2 at level 3 to +UR−2 at level 1 and is exactly zero at level 2, whereas for (U1, U3) = (0, −U) (dashed line), the same change in PV gradient occurs in a thinner layer from levels 3 to 2. Therefore, when the upper-level baroclinicity decreases, the vertical distance between the PV gradient of opposite signs (i.e., between potentially unstable baroclinic waves) decreases, which tends to destabilize short waves. Why do long waves become less unstable? Since such waves have a large vertical extent, the vertical distance between PV gradients of opposite signs is not a limiting factor for them. But as the upper-level baroclinicity decreases, its vertical mean also decreases and the available potential energy that the waves can extract from their environment is reduced. The appendix (section b) easily shows that growth rates for very long wavelengths (K ≫ R−1) are halved for (U1, U3) = (0, −U) relative to (U1, U3) = (U, −U).
When the lower-level baroclinicity increases (i.e., U3 decreases), all wavenumbers become more unstable (cf. the bold and thin solid lines in Fig. 4). Short waves are more unstable for (U1, U3) = (U, −2U) than for (U1, U3) = (U, −U) because the vertical distance between PV gradients of opposite signs having equivalent amplitude is reduced. Long waves are more unstable because the total available potential energy is increased. Furthermore, (U1, U3) = (U, −2U) and (U1, U3) = (U/2, −U) have exactly the same high-wavenumber cutoff because, in both cases, the parameter S is equal to ½ (see appendix for more details), but they do not have the same growth rates. Note, finally, that the distinct effect of the lower- and upper-level baroclinicity shown in Fig. 4 comes from our choice of changing the sign of the PV gradient at or below the midlevel. If the PV gradient changes its sign above the midlevel, all the previous results are reversed.
2) A more realistic case
In the real atmosphere, stratification being stronger in the upper troposphere, a more adequate choice for Rossby radii of deformation is R1 = 700 km and R2 = 450 km as in Marshall and Molteni (1993) (i.e., ϵ = 0.4 approximately). Furthermore, since vertical shears in the upper and lower troposphere are roughly the same, the PV gradient at 500 hPa (or equivalently level 2) is positive [see Eq. (2)] and the critical (or steering) level is usually located at 700 hPa between the two lower levels. For that reason, the effect of the upper-level baroclinicity should be the same as that shown in the cases of Fig. 4. Figure 5 does indeed exhibit the same behavior when (U1, U3) = (1.25U, −U) (thick solid line) is compared with (U1, U3) = (U, −U) (dashed line). The difference between the two cases corresponds approximately to the observed increase in zonal winds as diagnosed from climate change scenarios between the twentieth and twenty-first centuries. There is a slight increase (decrease) in the growth rates of long (short) wavelengths from (U1, U3) = (U, −U) to (U1, U3) = (1.25U, −U). Note that this simple baroclinic model brings some similarities with that of Wittman et al. (2007; see their section 2), who found a similar scale selection with increasing stratospheric shear.
Growth rate in nondimensional units kci/(UR−1) as a function of the nondimensional wavenumber kR in the three-level model for ϵ = 0.4; (U1, U3) = (1.25U, −U) (thick solid) and (U1, U3) = (U, −U) (dashed).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Growth rate in nondimensional units kci/(UR−1) as a function of the nondimensional wavenumber kR in the three-level model for ϵ = 0.4; (U1, U3) = (1.25U, −U) (thick solid) and (U1, U3) = (U, −U) (dashed).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Growth rate in nondimensional units kci/(UR−1) as a function of the nondimensional wavenumber kR in the three-level model for ϵ = 0.4; (U1, U3) = (1.25U, −U) (thick solid) and (U1, U3) = (U, −U) (dashed).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
This simple normal-mode analysis supports therefore the idea that the enhanced upper-level baroclinicity could be responsible for the increase in the eddy length scale in the future climate as well as for the increased amplitude of long waves. The decrease in lower-level baroclinicity, which appears in global warming scenarios for some seasons, may also participate in the global increase in the eddy length scale since it decreases the most unstable wavenumber (see Fig. 4a). However, in contrast with the upper-level baroclinicity, changes in the lower-level baroclinicity cannot provide an explanation for the increase in amplitude of long waves since the decrease in lower-level baroclinicity diminishes the amplitude of all the wavelengths.
4. Simulations of a dry atmospheric general circulation model
a. Model description
The global atmospheric circulation model known as the Portable University Model of the Atmosphere (PUMA; Fraedrich et al. 2005) is used in this section. It consists of a primitive equation spectral model on the sphere. Our results have been obtained from a dry version not including orography and having 10 equally spaced sigma levels in the vertical direction. A T42 truncation is used but it has been checked that the results are similar at T21 resolution as well. Rayleigh friction is applied to the two lowest levels with a time scale of about 1 day at σ = 0.9. Hyperdiffusion has a damping time scale of 0.1 days.
b. Normal-mode study
The normal-mode structures and their nonlinear evolution are now investigated for different basic-state zonal flows and wavenumbers.
1) The eddy length scale effect on wave breaking
To capture the different asymmetries leading to the different types of breaking in the real atmosphere, spherical geometry is a necessary ingredient as shown, for instance, by Balasubramanian and Garner (1997b) and R09. The f-plane case of the previous section is not sufficient to reproduce these subtle effects. As explained in R09, the full variations of the Coriolis parameter with latitude create PV gradient asymmetries that are responsible for the preferential tilt of the baroclinic waves. In the upper troposphere, PV gradient asymmetries are dominated by those of the absolute vorticity term, which favor the anticyclonic tilt of the waves. In contrast, in the lower troposphere, the stretching term of the PV gradient becomes large and its asymmetries render the cyclonic tilt of the waves more probable. Since waves reach larger amplitudes in the upper troposphere, they feel the preferential anticyclonic tilt more and break anticyclonically in most cases, leading to the well-known domination of the poleward eddy momentum fluxes over the equatorward fluxes in climatological studies. However, as already mentioned in section 2, the eddy length scale exerts a strong influence on the way the waves break. This is recalled in Fig. 6, which compares the structure and the evolution of two normal modes for zonal wavenumbers 6 (left column) and 9 (right column) embedded in the same background zonal flow. As expected from the above discussion, the normal-mode tilts are mainly anticyclonic and cyclonic in the upper and lower troposphere, respectively (Figs. 6a,b). A major difference appears in the vertical distribution of the two wavenumbers. Wavenumber 9 is confined much more to low levels than wavenumber 6, which expands more in the upper troposphere as shown in Figs. 6a,b (cf. the thin and heavy contours) and Figs. 6e,f (thin contours). This can be understood by the values reached by the refractive index for high wavenumbers, which decreases rapidly below 0 in the upper troposphere, preventing wave propagation in that region (not shown). Because of this difference, the anticyclonic tilt appears more clearly for wavenumber 6 than wavenumber 9, leading to a major difference in their nonlinear evolution. Wavenumber 6 mainly breaks anticyclonically (Fig. 6c) whereas wavenumber 9 breaks mainly cyclonically (Fig. 6d). After 10 days, the former pushes the jet poleward and the latter equatorward (see the shadings in Figs. 6e,f), confirming the eddy length scale effect on wave breaking.
Normal-mode structure and evolution using the PUMA model for a disturbance with a zonal wavenumber (left) 6 and (right) 9 embedded in the control basic state (CTRL). (a),(b) Basic-state zonal winds at 200 hPa (shading; int: 10 m s−1) and normal-mode meridional velocities at 200 (heavy contours) and 800 hPa (light contours) normalized by maximum amplitude (int: 0.2 m s−1). (c),(d) Absolute vorticity after 6 days (int: 2 × 10−5 s−1). (e),(f) zonal-mean zonal winds at the initial time (thick black contours; int: 10 m s−1), after 10 days (shading; int: 10 m s−1) and zonal mean of the normal-mode meridional wind variance normalized by its maximum amplitude (int: 0.2 m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Normal-mode structure and evolution using the PUMA model for a disturbance with a zonal wavenumber (left) 6 and (right) 9 embedded in the control basic state (CTRL). (a),(b) Basic-state zonal winds at 200 hPa (shading; int: 10 m s−1) and normal-mode meridional velocities at 200 (heavy contours) and 800 hPa (light contours) normalized by maximum amplitude (int: 0.2 m s−1). (c),(d) Absolute vorticity after 6 days (int: 2 × 10−5 s−1). (e),(f) zonal-mean zonal winds at the initial time (thick black contours; int: 10 m s−1), after 10 days (shading; int: 10 m s−1) and zonal mean of the normal-mode meridional wind variance normalized by its maximum amplitude (int: 0.2 m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Normal-mode structure and evolution using the PUMA model for a disturbance with a zonal wavenumber (left) 6 and (right) 9 embedded in the control basic state (CTRL). (a),(b) Basic-state zonal winds at 200 hPa (shading; int: 10 m s−1) and normal-mode meridional velocities at 200 (heavy contours) and 800 hPa (light contours) normalized by maximum amplitude (int: 0.2 m s−1). (c),(d) Absolute vorticity after 6 days (int: 2 × 10−5 s−1). (e),(f) zonal-mean zonal winds at the initial time (thick black contours; int: 10 m s−1), after 10 days (shading; int: 10 m s−1) and zonal mean of the normal-mode meridional wind variance normalized by its maximum amplitude (int: 0.2 m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
2) The effect of upper-level baroclinicity
To investigate the effect of increasing the upper-level baroclinicity on normal modes, two distinct basic states are considered. One is the control background flow (CTRL hereafter in this section) and the other (UB+) is the CTRL flow plus an anomaly that increases the upper-level baroclinicity in the jet-core region. The temperature anomaly is close to the multimodel ensemble difference between the twentieth- and twenty-first-century simulations (see Fig. 1 of Lorenz and DeWeaver 2007) in the upper troposphere. It has a maximum of 6°C for σ = 0.3 at the equator and decreases to 0°C at the poles (see the dashed line in Fig. 7f). This corresponds to an increase of around 4 m s−1 in the zonal wind maximum at 300 hPa.
(left) As in the left column of Fig. 6, but for zonal wavenumber 8. (right) As at left, but for a basic state characterized by stronger upper-level baroclinicity (denoted UB+; see more details in the text). The dashed line in (f) corresponds to the temperature anomaly between UB+ and CTRL (int: 1 K).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
(left) As in the left column of Fig. 6, but for zonal wavenumber 8. (right) As at left, but for a basic state characterized by stronger upper-level baroclinicity (denoted UB+; see more details in the text). The dashed line in (f) corresponds to the temperature anomaly between UB+ and CTRL (int: 1 K).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
(left) As in the left column of Fig. 6, but for zonal wavenumber 8. (right) As at left, but for a basic state characterized by stronger upper-level baroclinicity (denoted UB+; see more details in the text). The dashed line in (f) corresponds to the temperature anomaly between UB+ and CTRL (int: 1 K).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Figure 7 shows the difference between CTRL (left column) and UB+ (right column) for wavenumber 8. Slight differences appear in the normal-mode structure. It is more confined to low levels for UB+ and meridional wind isolines at 200 hPa extend slightly less on the southern side of the jet (Figs. 7a,b). These differences will favor the cyclonic tilt of the waves. This is in agreement with R09’s findings since an increase in baroclinicity reinforces the asymmetry of the stretching part of the basic-state PV gradient. During their nonlinear stage, these structural differences increase. For instance, the anticyclonic overturning of the absolute vorticity contour in Fig. 7c is missing in Fig. 7d. After 10 days, the jet is pushed poleward in CTRL (Fig. 7e) and equatorward in UB+ (Fig. 7f). Therefore, for wavenumber 8, the increased upper-level baroclinicity leads to an equatorward shift of the jet (i.e., it has the reverse effect to what was expected).
However, we should look at the growth rates according to wavenumber to anticipate the total response of the waves on the jet (Fig. 8). As expected from section 3, growth rates are weaker in UB+ than in CTRL in the high-wavenumber range (zonal wavenumbers > 7) and are slightly greater in the low-wavenumber range. Since the growth rates of low wavenumbers, such as 5 or 6, increase slightly, an increase in poleward momentum fluxes can be observed (see the black and red curves in Figs. 9c,d), leading to a stronger northward acceleration of the zonal winds (see the black and red curves in Figs. 9a,b). Despite the normal-mode structural changes discussed previously, low wavenumbers still break anticyclonically in UB+ and even more strongly than in CTRL because of the increase in their growth rates. Note that this cannot be simply explained by a poleward shift of the subtropical critical latitude as proposed in Chen et al. (2008) since all the normal-mode phase speeds slightly decrease from CTRL to UB+. In the high-wavenumber range, the opposite effect is diagnosed. Wavenumber 10 breaks cyclonically in both CTRL and UB+ (see the negative momentum fluxes in Fig. 9c) but, because of a reduction in its growth rate in UB+, the negative momentum fluxes in this integration are weaker in amplitude (Fig. 9d). Its impact on the southward shift of the jet is slightly less strong (cf. the difference in zonal winds at 45°N between the dashed black and magenta lines in Figs. 9a,b). For intermediate wavenumbers (7 and 8), the differences can be explained by the normal-mode structural changes rather than their growth rates. The amplitude of the positive momentum fluxes decreases significantly for both wavenumbers from CTRL to UB+. This leads to a reduction in the poleward shift of the jet for wavenumber 7 (green curve in Figs. 9a,b) and even a reverse tendency for wavenumber 8 with a transition from poleward to equatorward shifted jets (blue curve in Figs. 9a,b).
Normal-mode growth rate as a function of the zonal wavenumber for the control basic state (CTRL; squares) and a basic state with enhanced upper-level baroclinicity (UB+; triangles).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Normal-mode growth rate as a function of the zonal wavenumber for the control basic state (CTRL; squares) and a basic state with enhanced upper-level baroclinicity (UB+; triangles).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Normal-mode growth rate as a function of the zonal wavenumber for the control basic state (CTRL; squares) and a basic state with enhanced upper-level baroclinicity (UB+; triangles).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
(a),(b) Vertically averaged zonal-mean zonal wind at the initial time (black dashed line) and after 10 days for different wavenumbers (colored lines) for (a) the control basic state (CTRL) and (b) the basic state having a stronger upper-level baroclinicity (UB+). (c),(d) As in (a),(b), but for the vertically averaged zonal-mean eddy momentum fluxes averaged from the initial time to 10 days. The eddies are defined here as deviations from the zonal mean.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
(a),(b) Vertically averaged zonal-mean zonal wind at the initial time (black dashed line) and after 10 days for different wavenumbers (colored lines) for (a) the control basic state (CTRL) and (b) the basic state having a stronger upper-level baroclinicity (UB+). (c),(d) As in (a),(b), but for the vertically averaged zonal-mean eddy momentum fluxes averaged from the initial time to 10 days. The eddies are defined here as deviations from the zonal mean.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
(a),(b) Vertically averaged zonal-mean zonal wind at the initial time (black dashed line) and after 10 days for different wavenumbers (colored lines) for (a) the control basic state (CTRL) and (b) the basic state having a stronger upper-level baroclinicity (UB+). (c),(d) As in (a),(b), but for the vertically averaged zonal-mean eddy momentum fluxes averaged from the initial time to 10 days. The eddies are defined here as deviations from the zonal mean.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
To summarize, when the upper-level baroclinicity is increased, low wavenumbers become more unstable and push the jet more poleward while high wavenumbers are less unstable and are less efficient in pushing the jet equatorward. However, for intermediate wavenumbers, a transition toward less AWB and more CWB occurs due to their initial structural changes. Therefore, from this normal-mode perspective, it is not obvious what the impact of increasing the upper-level baroclinicity will be when all the wavenumbers interact with each other. The purpose of the next section is to investigate this aspect.
c. Long-term simulations using different restoration-temperature fields
1) Experimental design
Long-term PUMA simulations forced by a relaxation toward a prescribed temperature field are performed. The control run (CTRL in the present section) is obtained with the same restoration temperature as that of Held and Suarez (1994) (see shading in Fig. 10a). Three additional simulations are made by adding different anomalies to the CTRL restoration temperature. First, a positive temperature anomaly centered in the tropical upper troposphere (see black contours in Fig. 10a) is added to the CTRL restoration temperature similarly to the normal-mode section (called UB+ hereafter). It leads to an increase in upper-level baroclinicity in midlatitudes. The second experiment corresponds to a weakening of the lower baroclinicity by increasing the surface temperature at the poles (called LB− hereafter). This anomaly corresponds to the stronger warming that appears in the northern pole in winter in climate change scenarios. Third, an increase in tropical temperatures over the whole troposphere is implemented to reinforce the baroclinicity in both the lower and upper troposphere but with larger amplitudes at upper levels (called B+ hereafter). The definitions of these sensitivity experiments are included in Table 2. They are similar to those performed by Haigh et al. (2005). However, our anomalies are all located below the tropopause while they are above it in the latter study.
Zonal-mean climatology of the CTRL run (shading) and the difference between the UB+ and CTRL runs (black contours; negative and positive values in dashed and solid lines, respectively) using the PUMA model. (a),(b) Mean restoration temperature (int: 10 K) and anomalies (int: 1 K); (c),(d) CTRL zonal wind (int: 5 m s−1) and anomalies (int: 1 m s−1); (e),(f) CTRL high-frequency kinetic energy (int: 25 m2 s−2) and anomalies (int: 5 m2 s−2); (g),(h) CTRL high-frequency momentum fluxes (int: 15 m2 s−2) and anomalies (int: 3 m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Zonal-mean climatology of the CTRL run (shading) and the difference between the UB+ and CTRL runs (black contours; negative and positive values in dashed and solid lines, respectively) using the PUMA model. (a),(b) Mean restoration temperature (int: 10 K) and anomalies (int: 1 K); (c),(d) CTRL zonal wind (int: 5 m s−1) and anomalies (int: 1 m s−1); (e),(f) CTRL high-frequency kinetic energy (int: 25 m2 s−2) and anomalies (int: 5 m2 s−2); (g),(h) CTRL high-frequency momentum fluxes (int: 15 m2 s−2) and anomalies (int: 3 m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Zonal-mean climatology of the CTRL run (shading) and the difference between the UB+ and CTRL runs (black contours; negative and positive values in dashed and solid lines, respectively) using the PUMA model. (a),(b) Mean restoration temperature (int: 10 K) and anomalies (int: 1 K); (c),(d) CTRL zonal wind (int: 5 m s−1) and anomalies (int: 1 m s−1); (e),(f) CTRL high-frequency kinetic energy (int: 25 m2 s−2) and anomalies (int: 5 m2 s−2); (g),(h) CTRL high-frequency momentum fluxes (int: 15 m2 s−2) and anomalies (int: 3 m2 s−2).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Time and spatial averages of the high-frequency eddy momentum fluxes for the simple GCM simulations (m2 s−2). Since the forcing is symmetric between the two hemispheres, the amplitude of the NH poleward (equatorward) fluxes has been averaged with that of the SH poleward (equatorward) fluxes. The sign of the fluxes has been arbitrary chosen to correspond to the NH.
For all these simulations, the restoration time scale is 5 days at all levels. This differs from the Held and Suarez (1994) and Frisius et al. (1998) frameworks where the vertical levels have distinct restoration time scales. But with the focus of the present study being on the impact of the baroclinicity located at different levels, larger time scales at upper levels would have significantly diminished the impact of the upper-level baroclinicity. However, we checked that similar results to those described below could be found by implementing different restoration time scales at different levels and by increasing the temperature restoration anomalies. Each simulation is initialized with a random perturbation and run for six years. The time averages are computed for the last five years only. A daily dataset is extracted from each run and the same high-pass filter as that of section 2 is used to obtain the high-frequency eddy signal.
2) Results
Shadings in Fig. 10 represent the CTRL zonal-mean climatologies. High-frequency EKE anomalies are at least twice as strong as those found in the climatologies of the present-day climate simulations shown in Fig. 1. Compared to CTRL, UB+ has stronger zonal winds in the upper troposphere due to an enhanced upper-level baroclinicity. Zonal winds are also shifted poleward (Fig. 10b), with the node of the zonal wind anomalies centered at the maximum of the CTRL zonal wind below 500 hPa. EKE increases slightly from CTRL to UB+ since the amplitudes of the positive anomalies are greater than those of the negative anomalies but the major feature is a poleward and upward shift of EKE (Fig. 10c). Furthermore, high-frequency momentum flux anomalies are essentially poleward (Fig. 10d). All these characteristics are also present in the difference between the twentieth- and twenty-first-century simulations of section 2 in the SH.
Let us look at the spectrum of the high-frequency meridional wind amplitude (Fig. 11). In CTRL (shading in Fig. 11), the maximum amplitude is reached for wavelengths equal to 4000–5000 km at 40°N and 40°S, which is roughly similar to what happens in climate runs (shading in Fig. 3). From CTRL to UB+ (black contours in Fig. 11), a poleward shift as well as a displacement toward longer wavelengths is obvious. For instance, at a given latitude (40°N or 40°S), amplitude anomalies are positive and negative on the longer- and shorter-wavelength sides of the CTRL maximum and the node of the anomalies is very close to the CTRL maximum. The enhanced upper-level baroclinicity as simulated in UB+ thus leads to the main differences found between the present and future climates.
High-frequency meridional wind amplitude vertically averaged between 200 and 500 hPa as a function of the latitude and zonal wavelength for the CTRL run (shading; int: 2 m s−1) and the difference between the UB+ and CTRL runs (black contours; negative and positive values in dashed and solid lines, respectively, int: 0.5 m s−1).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
High-frequency meridional wind amplitude vertically averaged between 200 and 500 hPa as a function of the latitude and zonal wavelength for the CTRL run (shading; int: 2 m s−1) and the difference between the UB+ and CTRL runs (black contours; negative and positive values in dashed and solid lines, respectively, int: 0.5 m s−1).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
High-frequency meridional wind amplitude vertically averaged between 200 and 500 hPa as a function of the latitude and zonal wavelength for the CTRL run (shading; int: 2 m s−1) and the difference between the UB+ and CTRL runs (black contours; negative and positive values in dashed and solid lines, respectively, int: 0.5 m s−1).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
Figure 12 presents the difference in wave-breaking between CTRL and UB+. There is a global decrease in both AWB and CWB frequencies from CTRL to UB+ (Fig. 12a). But at the latitudes of the storm tracks (i.e., about 40°N and 40°S), only the CWB frequency decreases. Furthermore, there is a significant increase in averaged poleward fluxes in AWB regions (solid lines in Fig. 12b) while the averaged equatorward fluxes in CWB regions do not change so much in intensity but rather show a slight poleward shift (dashed lines in Fig. 12b). When the averaged fluxes are multiplied by the frequency of occurrence of each breaking (Fig. 12c), the percentage of increase in poleward fluxes from CTRL to UB+ becomes larger. There is also a slight decrease in amplitude of the equatorward fluxes on the equatorward sides of the CWB regions from CTRL to UB+ in Fig. 12c. Therefore, both the increase in intensity of the poleward fluxes in AWB regions and the relative increase of AWB compared to CWB frequencies in storm-track regions explain the anomalous poleward eddy momentum fluxes averaged over all the wave-breaking regions (Fig. 12d). Table 2 confirms the above results by globally averaging the poleward and equatorward fluxes separately. The amplitude of the averaged poleward fluxes increases by 8% whereas that of the equatorward fluxes decreases slightly by 2%. It is consistent with the scale effect on wave breaking: when long (short) waves increase (decrease) in amplitude, they break more (less) strongly anticyclonically (cyclonically).
As in each column of Fig. 2, but for the CTRL (black) and UB+ (red) simulations.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in each column of Fig. 2, but for the CTRL (black) and UB+ (red) simulations.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in each column of Fig. 2, but for the CTRL (black) and UB+ (red) simulations.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in Fig. 10, but for the LB− run (i.e., for an increase in temperature in the low-level polar troposphere).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in Fig. 10, but for the LB− run (i.e., for an increase in temperature in the low-level polar troposphere).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in Fig. 10, but for the LB− run (i.e., for an increase in temperature in the low-level polar troposphere).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
In LB−, the only difference from CTRL is the decrease in low-level baroclinicity. This simulation is similar to the aquaplanet GCM experiment of Kodama and Iwasaki (2009), where the authors increased the SST by 3 K at the poles. As in the previous study, there is a decrease in amplitude as well as a slight equatorward shift of the westerlies (Fig. 13b). This is accompanied by a decrease in EKE and an increase in equatorward momentum fluxes (Figs. 13c,d). The spectrum analysis of the high-frequency meridional winds shows that their amplitudes decrease for all the wavelengths and no scale selection appears for latitudes poleward of 40°N and 40°S (Fig. 14). Note that this is in good agreement with the three-level QG results where all the wavenumbers are shown to become more unstable when the low-level baroclinicity is increased. Only latitudes between 20° and 40°N and between 20° and 40°S exhibit a difference between the wavelengths with a slight increase in intensity for short waves. The fact that LB− is more characterized by a global decrease in EKE rather than by a scale selection process may explain why there is a decrease in intensity of both the equatorward and poleward fluxes by 2% and 6%, respectively (see Table 2).
As in Fig. 11, but for the LB− run.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in Fig. 11, but for the LB− run.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in Fig. 11, but for the LB− run.
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in Fig. 10, but for the B+ run (i.e., for an increase in temperature in the whole tropical troposphere).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in Fig. 10, but for the B+ run (i.e., for an increase in temperature in the whole tropical troposphere).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
As in Fig. 10, but for the B+ run (i.e., for an increase in temperature in the whole tropical troposphere).
Citation: Journal of the Atmospheric Sciences 68, 6; 10.1175/2011JAS3641.1
The above interpretation is confirmed by the B+ simulation (Fig. 15). The poleward shift of the jet streams and the increase in EKE and in poleward eddy momentum fluxes are even more impressive than in UB+. Note that there is an increase in intensity of both the poleward and equatorward fluxes by 18% and 7%, respectively (Table 2). This shows again that the increase in low-level baroclinicity reinforces the effect of the upper-level baroclinicity but their dynamical roles differ. The former increases the amplitude of all the wavelengths and, since AWB dominates when all the wavelengths are taken into account, an increase in EKE leads to a greater dominance of AWB over CWB. The latter induces a spatial scale selection that favors even more AWB than usual, leading to a stronger increase in the amplitude of the poleward fluxes compared to the equatorward fluxes.
5. Summary and discussion
A rationale for the poleward shift of the jet streams in global warming scenarios is provided in the present paper. Three distinct approaches have been followed to support our interpretation. First, the output of two state-of-the-art IPCC coupled models is analyzed to describe the main characteristics of the climate change. Second, an analytical study of baroclinic instability in the three-level quasigeostrophic model on an f plane offers a simple understanding of the distinct effects of the upper- and lower-level baroclinicity on synoptic waves. Third, a simple dry atmospheric general circulation model (GCM) is used to confirm the key role played by the upper-level baroclinicity. Two types of numerical experiments are employed: one is a normal-mode approach and the other consists of long-term simulations forced by relaxing the temperature toward different restoration fields.
The major characteristics of climate change scenarios can be summarized as follows. The temperature changes are mainly characterized by a stronger warming in the tropical upper troposphere leading to an increase in upper-level horizontal temperature gradients in midlatitudes. Yin (2005) has shown that this feature dominates in the Eady growth rate over other changes, and especially over the static stability changes. The poleward shift of the eddy-driven jets is obvious in the Southern Hemisphere while it is less marked in the Northern Hemisphere, as already shown by Lorenz and DeWeaver (2007) in a multimodel ensemble mean (see, e.g., their Figs. 3 and 4). For some models, the poleward shift can even be missing in the Northern Hemisphere. When the poleward shift occurs, it is accompanied by an increase and an upward, poleward shift of eddy kinetic energy as well as an increase in the eddy length scale, which is in agreement with the recent results of Kidston et al. (2010). Furthermore, a strengthening of the poleward eddy momentum fluxes is observed on the equatorward side of the storm tracks. It is accompanied by a relative decrease in cyclonic wave-breaking frequencies compared to anticyclonic wave breaking. These two changes may explain why anomalies of eddy momentum fluxes between the twentieth- to twenty-first-century simulations are mainly poleward. Note that the change in wave-breaking frequencies can also be viewed as a consequence of the poleward shift of the jet streams since AWB and CWB were shown to become respectively more and less probable with increasing the latitude of the jet in R09. However, the strengthening of the poleward eddy momentum fluxes, which is attributed to the enhancement of the upper-level baroclinicity in our analysis, can only be considered as a cause of the poleward shift.
The three-level QG model on an f plane is the simplest model that separates the effects of the upper- and lower-level baroclinicity. It is shown that, if the PV gradient changes its sign below the midlevel (i.e., if the critical level is located in the lower troposphere as in the real atmosphere), long and short wavelengths become respectively more and less unstable with an increased upper-tropospheric baroclinicity. The instability of short wavelengths is limited by the vertical distance between PV gradients of opposite signs because of their small vertical extent. When this distance increases with enhanced upper-level baroclinicity, the so-called high-wavenumber cutoff decreases. Since long wavelengths have a large vertical extent, they are able to extract the whole available potential energy, which is increased when the upper-level baroclinicity is enhanced. In contrast, when the low-level baroclinicity is enhanced, all the wavenumbers become more unstable. This analytical study provides a new interpretation for the increase in the eddy length scale, which differs from the static stability argument of Kidston et al. (2010) since the Rossby radii of deformation are constant in the model. It seems that both the increase in static stability and that in upper-level baroclinicity participate in the increase in the eddy length scale in global warming scenarios. Another potential factor is the Rhines scale, as also proposed in Kidston et al. (2010), since β is reduced toward the pole.
The normal-mode approach within the GCM framework shows that the eddy length scale is a key parameter determining the nature of the breaking and the eddy feedback onto the mean flow. Large (short) wavelengths break more anticyclonically (cyclonically). When the upper-tropospheric baroclinicity is reinforced, long wavelengths become more unstable, break more strongly anticyclonically, and push the jet more poleward. Short wavelengths, being less unstable, are less efficient in pushing the jet equatorward. However, intermediate wavenumbers have the opposite effect and the normal-mode analysis could not allow the eddy feedback to be anticipated when all wavenumbers were taken into account. Long-term GCM simulations were necessary to clarify this aspect. When the upper-tropospheric baroclinicity is increased in midlatitudes, the sensitivity experiment exhibits strong similarities with climate change scenarios: a poleward shift of the jet streams, an upward and poleward shift of the storm tracks, a slight increase in their global intensity, and, more importantly, an increase (decrease) in their amplitude for long (short) wavelengths. The latter property is considered to be a key one leading to the stronger poleward eddy momentum fluxes and the poleward shift of the jets. Another experiment shows that the diminution of the low-level baroclinicity reduces the intensity of all the wavenumbers. Since AWB dominates when all the wavenumbers are considered, this leads to a reduction in poleward momentum fluxes and a slight equatorward shift of the jet streams.
To conclude, both the increase in EKE and the shift toward larger spatial scales participate in the poleward shift of the jet streams. It should be noted that, for some climate models, a poleward shift may occur in the NH summer without an increase in EKE (Yin 2005). This could be explained by the spatial-scale effect alone. The interpretation of the present paper is also consistent with the recent poleward shift that have undergone the SH jet streams during the late twentieth century (Polvani et al. 2011). The cooling caused by ozone depletion at high latitudes has reinforced the upper-tropospheric horizontal temperature gradients similarly to the global warming of the tropical upper troposphere. However, because of the future recovery of ozone hole, this cannot explain the difference between the SH and NH found in global warming scenarios.
Other changes could lead to effects similar to those created by an enhancement of the upper-level horizontal temperature gradients, such as the increase in the tropopause height (Lorenz and DeWeaver 2007) or in the subtropical static stability (Lu et al. 2010). Future studies should investigate the relative impact of these different components. Another interesting aspect to be analyzed in the future is the direct effect of moisture on wave breaking. As recalled in the introduction, several papers (e.g., Orlanski 2003) have shown that an increase in water vapor may favor CWB and the equatorward eddy momentum fluxes. This would have the opposite effect and may compensate that of increased upper-level baroclinicity in regions where this increase is weak. This could explain why some models in some regions do not show systematically a poleward shift of the jet streams.
Acknowledgments
The author would like to thank David Salas-Me´lia and Sophie Tyteca for providing the data of the CNRM model. Comments and suggestions of three anonymous reviewers have significantly improved the paper. The work was supported by a grant from the INSU/LEFE project entitled EPIGONE.
APPENDIX
Detailed Analysis in the Three-Level Quasigeostrophic Model
a. Normal-mode growth rates
b. The very-long-wavelength limit k ≪ R−1 for R1 = R2 = R
REFERENCES
Balasubramanian, G., and S. Garner, 1997a: The equilibration of short baroclinic waves. J. Atmos. Sci., 54, 2850–2871.
Balasubramanian, G., and S. Garner, 1997b: The role of momentum fluxes in shaping the life cycle of a baroclinic wave. J. Atmos. Sci., 54, 510–533.
Chen, G., and I. Held, 2007: Phase speed spectra and the recent poleward shift of southern hemisphere surface westerlies. Geophys. Res. Lett., 34, L21805, doi:10.1029/2007GL031200.
Chen, G., I. Held, and W. Robinson, 2007: Sensitivity of the latitude of the surface westerlies to surface friction. J. Atmos. Sci., 64, 2899–2915.
Chen, G., J. Lu, and D. Frierson, 2008: Phase speed spectra and the latitude of surface westerlies: Interannual variability and global warming trend. J. Climate, 21, 5942–5959.
Davey, M., 1977: Baroclinic instability in a fluid with three layers. J. Atmos. Sci., 34, 1224–1234.
Fraedrich, K., E. Kirk, U. Luksh, and F. Lunkeit, 2005: The Portable University Model of the Atmosphere (PUMA): Storm track dynamics and low-frequency variability. Meteor. Z., 14, 735–745.
Frierson, D. M. W., 2006: Robust increases in midlatitude static stability in simulations of global warming. Geophys. Res. Lett., 33, L24816, doi:10.1029/2006GL027504.
Frisius, T., F. Lunkeit, K. Fraedrich, and I. James, 1998: Storm-track organization and variability in a simplified atmospheric global circulation model. Quart. J. Roy. Meteor. Soc., 124, 1019–1043.
Geng, Q., and M. Sugi, 2003: Possible change of extratropical cyclone activity due to enhanced greenhouse gases and sulfate aerosols study with a high-resolution AGCM. J. Climate, 16, 2262–2274.
Haigh, J. D., M. Blackburn, and R. Day, 2005: The response of tropospheric circulation to perturbations in lower-stratospheric temperature. J. Climate, 18, 3672–3685.
Hall, N., B. J. Hoskins, P. Valdes, and C. A. Senior, 1994: Storm-tracks in a high-resolution GCM with doubled carbon dioxide. Quart. J. Roy. Meteor. Soc., 120, 1209–1230.
Hartmann, D., and P. Zuercher, 1998: Response of baroclinic life cycles to barotropic shear. J. Atmos. Sci., 55, 297–313.
Held, I., and M. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75, 1825–1830.
Hoskins, B. J., M. E. M. Intyre, and R. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877–946.
Kidston, J., S. Dean, J. Renwick, and G. K. Vallis, 2010: A robust increase in the eddy length scale in the simulation of future climates. Geophys. Res. Lett., 37, L03806, doi:10.1029/2009GL041615.
Kidston, J., G. K. Vallis, S. M. Dean, and J. A. Renwick, 2011: Can the increase in the eddy length scale under global warming cause the poleward shift of the jet streams? J. Climate, in press.
Kodama, C., and T. Iwasaki, 2009: Influence of the SST rise on baroclinic instability wave activity under an aquaplanet condition. J. Atmos. Sci., 66, 2272–2287.
Laîné, A., M. Kageyama, D. Salas-Mélia, G. Ramstein, S. Planton, S. Denvil, and S. Tyteca, 2009: An energetics study of wintertime Northern Hemisphere storm tracks under 4 × CO2 conditions in two ocean–atmosphere coupled models. J. Climate, 22, 819–839.
Laîné, A., G. Lapeyre, and G. Rivière, 2011: A quasigeostrophic model for moist storm tracks. J. Atmos. Sci., 68, 1307–1323.
Lorenz, D. J., and E. T. DeWeaver, 2007: Tropopause height and zonal wind response to global warming in the IPCC scenario integrations. J. Geophys. Res., 112, D10119, doi:10.1029/2006JD008087.
Lu, J., G. Chen, and D. Frierson, 2008: Response of the zonal mean atmospheric circulation to El Niño versus global warming. J. Climate, 21, 5835–5851.
Lu, J., G. Chen, and D. Frierson, 2010: The position of the midlatitude storm track and eddy-driven westerlies in aquaplanet AGCMs. J. Atmos. Sci., 67, 3984–4000.
Marshall, J., and F. Molteni, 1993: Toward a dynamical understanding of planetary-scale flow regimes. J. Atmos. Sci., 50, 1792–1818.
Orlanski, I., 2003: Bifurcation in eddy life cycles: Implication for storm track variability. J. Atmos. Sci., 60, 993–1023.
Polvani, L., D. Waugh, G. Correa, and S.-W. Son, 2011: Stratospheric ozone depletion: The main driver of twentieth-century atmospheric circulation changes in the Southern Hemisphere. J. Climate, 24, 795–812.
Rivière, G., 2009: Effect of latitudinal variations in low-level baroclinicity on eddy life cycles and upper-tropospheric wave-breaking processes. J. Atmos. Sci., 66, 1569–1592.
Rivière, G., and I. Orlanski, 2007: Characteristics of the Atlantic storm-track eddy activity and its relation with the North Atlantic Oscillation. J. Atmos. Sci., 64, 241–266.
Rivière, G., A. Laîné, G. Lapeyre, D. Salas-Mélia, and M. Kageyama, 2010: Links between Rossby wave breaking and the North Atlantic Oscillation–Arctic Oscillation in present-day and Last Glacial Maximum climate simulations. J. Climate, 23, 2987–3008.
Simmons, A. J., and B. J. Hoskins, 1978: The life cycles of some nonlinear baroclinic waves. J. Atmos. Sci., 35, 414–432.
Smeed, D., 1988: Baroclinic instability of three-layer flows. I: Linear stability. J. Fluid Mech., 194, 217–231.
Thorncroft, C. D., B. J. Hoskins, and M. McIntyre, 1993: Two paradigms of baroclinic-wave life-cycle behaviour. Quart. J. Roy. Meteor. Soc., 119, 17–55.
Vallis, G., 2006: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 745 pp.
Wittman, M., A. Charlton, and L. Polvani, 2007: The effect of lower stratospheric shear on baroclinic instability. J. Atmos. Sci., 64, 479–496.
Yin, J. H., 2005: A consistent poleward shift of the storm tracks in simulations of 21st century climate. Geophys. Res. Lett., 32, L18701, doi:10.1029/2005GL023684.
