It is shown that a quantitative relation exists between the stratospheric polar cap potential vorticity and the 100-hPa eddy heat flux. A difference in potential vorticity between years is found to be linearly related to the flux difference integrated over time, taking into account a decrease in relaxation time scale with height in the atmosphere.This relation (the PV-flux relation) is then applied to the 100-hPa flux difference between 2008/09 and the climatology (1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) to obtain a prediction of the polar cap potential vorticity difference between the 2008/09 winter and the climatology. A prediction of the 2008/09 polar cap potential vorticity is obtained by adding this potential vorticity difference to the climatological potential vorticity. The observed polar cap potential vorticity for 2008/09 shows a large and abrupt change in the potential vorticity in midwinter, related to the occurrence of a major sudden stratospheric warming in January 2009; this is also captured by the potential vorticity predicted from the 100-hPa flux and the PV-flux relation.The results of the mean PV-flux relation show that, on average, about 50% of the interannual variability in the state of the Northern Hemisphere stratosphere is determined by the variations in the 100-hPa heat flux. This explained variance can be as large as 80% for more severe events, as demonstrated for the 2009 major warming.

The zonal mean state of the atmosphere in the Northern Hemisphere in winter is determined by the temperature at the Earth's surface and by two potential vorticity (PV) anomalies (defined as that part of the PV field that induces a wind field) centred over the North Pole: one in the upper troposphere/lower stratosphere (UTLS), extending to the Subtropics, and the other over the polar cap in the lower to middle stratosphere. Isentropic PV inversion demonstrates that the UTLS PV anomaly induces the main part of the zonal mean wind in the troposphere, including the subtropical jet stream, while the stratospheric PV anomaly induces the polar night stratospheric jet. The stratospheric PV anomaly has a greater amplitude and extends further downwards if the Arctic Oscillation (AO) index is positive. Also, the UTLS PV anomaly has a slightly larger amplitude if the AO index is positive, but the meridional PV gradient in the Subtropics that is associated with this anomaly is greatest when the AO index is negative, resulting in a stronger subtropical jet when the AO index is negative. PV inversion translates the UTLS PV anomaly into a wind anomaly and a static stability anomaly. The resulting differences in the vertical wind shear and in the Brunt-Väisälä frequency between the two AO phases show a larger baroclinicity in the extratropics when the AO index is positive. This explains why more extratropical cyclones are observed when the AO index is positive. Copyright

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By defining the reference state as the state of rest, two distinct potential vorticity (PV) anomalies are identified: the upper troposphere/lower stratosphere (UTLS) PV anomaly and the stratospheric PV-anomaly (Hinssen et al., 2010). Together with the surface temperature anomaly these PV anomalies determine the zonal average wind in the atmosphere. Some of our results are obtained from piecewise PV inversion of these anomalies. We have discovered an error in the application of the lower boundary condition in the PV inversion code. The main findings of the paper are not affected, but the correction of the code has led to a different view regarding the coupling of the UTLS PV anomaly and the surface temperature anomaly. Figure 1, which is the corrected version of Figure 6, shows that the new inverted wind deviates somewhat more from the ERA-40 wind, and that the influence of the surface temperature anomaly is much stronger in the corrected inversion. As a consequence of this, it is not possible to examine separately the influence, on the zonal wind, of the UTLS PV anomaly and of the boundary temperature anomaly by applying piecewise PV inversion. In other words, the UTLS PV anomaly is inextricably connected to the lower boundary. It is therefore not possible to make a corrected version of Figure 9(c) of Hinssen et al. (2010).Subtracting the wind field that is shown in Figure 1(c) from the wind field that is obtained from the inversion of the stratospheric PV anomaly including the observed boundary temperature anomaly yields a wind that is nearly identical to the wind that is obtained from inversion of the stratospheric PV anomaly with no boundary temperature anomaly. Therefore, it remains possible to examine the influence of the stratospheric PV anomaly on the tropospheric wind using piecewise PV inversion. As was stated before, this linear superposition does not apply to the UTLS PV anomaly and the boundary temperature anomaly. et al. (2010), demonstrates that the difference in lower boundary temperature between positive and negative AO cases is of greater importance than was thought previously. In other words, in order to explain fully the observed zonal wind differences between positive and negative AO cases by means of PV inversion, the difference in surface temperature between the two cases needs to be taken into account.

The influence of a CO₂ doubling on the stratospheric potential vorticity (PV) is examined in two climate models. Subsequently, the influence of changes in the stratosphere on the tropospheric zonal wind response is investigated, by inverting the stratospheric PV.

Radiative effects dominate the stratospheric response to CO₂ doubling in the Southern Hemisphere. These lead to a stratospheric PV increase at the edge of the polar vortex, resulting in an increased westerly influence of the stratosphere on the tropospheric midlatitude winds in late winter.

In the Northern Hemisphere, dynamical effects are also important. Both models show a reduced polar PV and an enhanced midlatitude PV in the Northern Hemisphere winter stratosphere. These PV changes are related to an enhanced wave forcing of the winter stratosphere, as measured by an increase in the 100 hPa eddy heat flux, and result in a reduced westerly influence of the stratosphere on the high latitude tropospheric winds. In one model, the high latitude PV decreases are, however, restricted to higher altitudes, and the tropospheric response due to the stratospheric changes is dominated by an increased westerly influence in the midlatitudes, related to the increase in midlatitude PV in the lower stratosphere.

The tropospheric response in zonal wind due to the stratospheric PV changes is of the order of 0.5 to 1 m s⁻¹. The total tropospheric response has a somewhat different spatial structure, but is of similar magnitude. This indicates that the stratospheric influence is of importance in modifying the tropospheric zonal wind response to CO₂ doubling