Figure 2showed trends in both the extratropical and subtropical components of the Austral jet. In this study the focus is on the extratropical jet, defined here as the first local maximum in zonal-mean zonal-wind at 500 hPa equatorward of 65°S where the zonal-mean wind speed is greater than 10 m s−1. Data are provided on a range of horizontal grids (Table 1). To locate the jet, zonal-mean monthly mean data are first linearly interpolated onto a 0.5° latitude grid. Local maxima are then identified using the first derivative of zonal-mean wind with respect to latitude. On the rare occasions when no local maxima can be identified between 65°S and 25°S, jet position is defined as the position of the minimum in the second derivative of zonal-mean monthly mean zonal-wind within this latitude range.
 Figure 3bshows that the mean position of the jet is more equatorward in the high-top models, compared to the low-top models. The high-top jet moves poleward more rapidly, especially under RCP8.5, and the difference between the position of the high- and low-top jets decreases with time. A decrease in the rate of change in the position of the jet is seen in both ensemble means and forcing scenarios in the first half of the 21st century, although it is more pronounced and more persistent in the high-top ensemble. There is a suggestion of a brief reversal of the trend in the high-top mean from 2000–2020. The jet then resumes its poleward migration under RCP8.5, with the high-top jet again moving more rapidly than the low-top. Jet position remains almost constant in the latter half of the 21st century under RCP4.5.
 Examination of the 1979–2006 zonal-mean zonal-winds showed that the latitude of the DJF jet in the CMIP5 models was generally too far equatorward compared to reanalyses (Figure 4). The mean latitude of the jet at 500 hPa is 46°S and 49°S in the high- and low-top models respectively. The mean latitude of the ERA-Interim and CFSR jets is 49°S, compared to 50°S in NCEP/NCAR. Mean jet latitudes in the individual models lie in the range 52°S (CCSM4) to 43°S (IPSL-CM5A-LR), with high-top models tending to have more equatorward jets (Figure 4).
 Linear least-squares trends (DJF, 1979–2006) in jet position are −0.51, −0.49, and −1.07°N/decade in ERA-Interim, CFSR, and NCEP/NCAR respectively, giving a reanalysis mean trend of −0.69 ± 0.30°N/decade. The CMIP5 multimodel mean is in good agreement with the reanalyses for this period: −0.60 ± 0.28°N/decade. The high-top models overestimate the trend (−0.94 ± 0.25°N/decade), while the low-top models underestimate the trend (−0.27 ± 0.12°N/decade). Two low-top models give slightly positive (equatorward) trends for this period in response to recovering stratospheric ozone concentrations, contributing to the underestimate of the trends in the low-top mean.
4.1. Temperature Trends as a Driver for Jet Changes
 Changes in the position of the extratropical jet are linked to changes in the meridional temperature gradient [Lee and Kim, 2003]. This relationship can be seen in Figure 5. Figure 5a shows the trend in jet position and meridional temperature gradient, under RCP8.5, for each model for 1960–2000 (black), 2000–2050 (blue) and 2050–2098 (red). Figure 5bshows the high- and low-top multimodel mean. Here, the meridional temperature gradient is defined as the difference between polar average lower-stratospheric temperature (150 hPa, 75–90°S) and tropical upper-tropospheric temperature (250 hPa, 0–25°S) (as shown inFigure 3).
Figure 5. (a) Meridional temperature gradient (K/decade) and 500 hPa jet position (°N/decade) trends for each model for 1960–2000 (black), 2000–2050 (blue), and 2050–2098 (red) for RCP8.5. Squares indicate high-top models. Error bars for individual models are one standard error. (b) Same as Figure 5a but for the low- and high-top multimodel mean. Error bars for multimodel means are two standard errors.
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 Figure 5a shows a largely compact linear relationship (discussed further in section 4.2) between meridional temperature gradient and jet shift. A least-squares fit for 1960–2000, when the linear relationship is strongest, shows that a temperature trend of +1 K/decade typically results in a poleward jet shift of °S. This relationship becomes slightly less well defined in future as the model spread increases.
 Figure 5bshows low- and high-top ensemble mean trends. The trend in meridional temperature gradient is larger in the high-top models (Figure 5b). The high-top and low-top values are significantly different at the 5% level (‘separable’) in all periods considered. Warming of the polar lower-stratosphere in the period 2000–2050 results in a near zero trend in both high- and low-top meridional temperature gradient.
 High-top models have a larger jet shift in 1960–2000 (Figure 5, black) and 2050–2098 (red), compared to the low-tops, as a result of the larger temperature trends. Variability in jet position is greater than that in temperature, so confidence intervals are larger, but jet responses are separable in 2050–2098 (red,Figure 5b). The mean position trend for 2050–2098 in high-top models is −0.59°N/decade compared to −0.21°N/decade for the low-top models. In 2000–2050 the magnitude of the jet shift is not significantly different from zero at the 5% level in either ensemble mean (Figure 5b). Small or zero trends in jet position in this period are the result of a near cancellation between the effects of increasing GHG and stratospheric ozone concentrations. Such a cancellation was also highlighted by Polvani et al. .
 Detailed examination of the mechanisms that drive changes in the position of the jets is beyond the scope of this study. There is a developing consensus in the literature that the changes are linked to the impact of the upper level pole-to-equator temperature gradient and the linked stratospheric wind shear on the type of non-linear wave-breaking in the troposphere [Wittman et al., 2007]. Increases in the pole-to-equator temperature gradient lead to increases in upper level baroclinicity and an increase in anticyclonic LC1 type wave-breaking linked to a shift in the mean eddy length scales toward longer wavelengths [Riviere, 2011]. As shown by McLandress et al. [2011b], this mechanism is consistent with the observed poleward shift in momentum flux convergence on the poleward side of the eddy driven jet. The recent analyses of Wang and Magnusdottir  and Ndarana et al. both point to a large increase in anticyclonic wave-breaking on the equatorward side of the SH jet, consistent both with this picture and the observed poleward shift of the jet.
 Meridional temperature gradient has been defined in this study as the difference between the polar average lower-stratospheric temperature and tropical upper-tropospheric temperature. To understand further the origin of the changes in meridional temperature gradient, the contribution to the gradient trend from each of these regions is shown inFigure 6, plotted against the total jet shift, as in Figure 5.
Figure 6. (a) Polar lower-stratospheric temperature (K/decade) and 500 hPa jet position (°N/decade) trends for each model for 1960–2000 (black), 2000–2050 (blue), and 2050–2098 (red) for RCP8.5. (b) Same as Figure 6a but for the low- and high-top multimodel mean. (c) Tropical upper tropospheric temperature (K/decade) and jet position (°N/decade) trends for each model. (d) Same as Figure 6c but for the low- and high-top multimodel mean. Squares indicate high-top models. Error bars for individual models (Figures 6a and 6c) are one standard error. Error bars for multimodel means (Figures 6b and 6d) are two standard errors.
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 Figure 6ashows polar lower-stratospheric temperature trends for each model for 1960–2000 (black), 2000–2050 (blue), and 2050–2098 (red). Polar lower stratospheric temperature trends are negative in all models for 1960–2000, ranging from −2.61 K/decade in GFDL-CM3 to −0.90 K/decade in HadGEM2-CC (the latter is not significantly different from zero at the 5% level). The multimodel means (Figure 6b) show greater lower-stratospheric cooling trends in high-top models compared to low-top models in 1960–2000 (black) and 2050–2098 (red): −1.64 K/decade compared to −1.40 K/decade for 1960–2000 and −0.41 K/decade compared to −0.12 K/decade for 2050–2098. Estimates from the two sets of models are separable in both periods. Opposite temperature trends in the region of +0.5 K/decade are found across all models during 2000–2050 (blue).
 In 2000–2050 stratospheric ozone recovery typically dominates the polar temperature trend, and all models predict a warming trend there. In this period, low-top models predict a warming of 0.38 K/decade, while high-top models predict a larger trend of +0.61 K/decade (Figure 6b). However, the trends from high- and low-top models are not separable. Some models predict an equatorward trend in jet position in this period, although only the GFDL-CM3 trend is significantly different from zero at the 5% level.
 Figure 6cshows tropical upper-tropospheric temperature trends, plotted against the trend in jet position. The high- and low-top multimodel means are shown inFigure 6d. All models have warming trends in all periods. The magnitude of the trends increases with time, as expected from the increasing GHG concentration gradients shown in Figure 1, and the tropical temperature response shown in Figure 3a. Multimodel means (Figure 6d) show larger temperature trends in the high-top models compared to the low-top models. The trends are separable in each period, and the difference between them increases with time. The difference between the warming trends in the high- and low-top models is especially pronounced in 2050–2098, with a mean trend of +1.07 K/decade predicted in the high-top models, compared to +0.79 K/decade in the low-top models.
 Enhanced warming in the tropical upper-troposphere in the high-top models compared to the low-tops could be the result of differing parameterizations of moist processes, different tropical tropopause layer processes, or differences in stratospheric upwelling. The very limited number of direct, single model, high- and low-top comparisons available in CMIP5 make it difficult to determine whether the representation of the stratosphere plays an important role in this difference without further experiment.
4.2. Linearity in the Jet Response to Temperature Trends
 The mean ratio of trends in jet position to trends in temperature gives a measure of the sensitivity of the jet response to the temperature trend. The sensitivity of jet position trends to meridional temperature gradient trends, and polar and tropical temperature trends, is shown in Figure 7 for RCP8.5 (red) and RCP4.5 (blue). Negative sensitivity indicates a poleward movement in response to positive temperature trends, positive sensitivity indicates a poleward movement in response to negative temperature trends.
Figure 7. Sensitivity (°N/K) of the position of the 500 hPa jet to trends in polar lower-stratosphere temperature (dashed), tropical upper-troposphere temperature (dotted), and meridional temperature gradient (solid), in the ozone depletion (1960–2000), ozone recovery (2000–2050), and GHG dominated (2050–2098) periods. Historical data are shown in black, RCP4.5 in blue, and RCP8.5 in red. Error bars are two standard errors.
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 The sensitivity of the jet to each of the three temperature trends is invariant across all the time periods and forcing scenarios considered. The sensitivity of the jet to meridional temperature gradient changes (solid lines) remains in the region of −0.3°N/K across all periods, and both forcing scenarios. However, there are larger error bars in 2050–2098 in the RCP8.5 case. The sensitivity of the jet to polar lower-stratospheric temperature trends is 0.4°N/K, with no significant differences between the two forcing scenarios considered.
 The relationship between tropical upper-tropospheric temperature trends and jet position trends is weaker than those in the temperature gradient and polar lower-stratospheric temperature cases, and the errors intersect zero in the 2000–2050 case under both RCP4.5 and RCP8.5 (Figure 7). However, there is insufficient evidence to suggest that the sensitivity of the jet to tropical upper-tropospheric temperature trends changes with forcing.
 Analysis of the latitude of jet in the individual models considered showed a decrease in the rate of change of jet position in some individual models, and also in the low-top mean, after 2080 in the RCP8.5 scenario (Figure 3c). This change was apparent in IPSL-CM5A, HadGEM2-CC, NorESM1-M, and CSIRO-Mk3.6, hinting at a possible deviation from a linear jet response to temperature trends in these models. However, this change can only be seen over a short period. As such, it cannot be demonstrated to be significantly different to the 50-year trends considered inFigure 7.
 A decrease in the rate of change of jet position as the jets are located closer to the pole would be consistent with the findings of Barnes and Hartmann . They suggest that the jet shift lessens as it moves poleward because the positive feedback between eddies and the mean flow is reduced due to the inhibition of polar wave-breaking for jets positioned at high latitudes. Despite some evidence in time series from individual models, there is no clear evidence of an approach to a geometric limit on the absolute shift of the jet in the ensemble mean by the end of the 21st century, even under the large forcing RCP8.5 scenario.