1. Figures from http://www.ldeo.columbia.edu/NAO by Martin Visbeck Dynamics of extratropical jet shift Pablo Zurita Gotor Depto. Física de la Tierra I Universidad Complutense CLIVAR SPAIN 2/12/08

2. Outline of the talk 1.Zonal index, persistence and eddy-zonal mean feedback. 2.Diagnostics of jet position: the jet symmetry budget. 3.Eddy-driven shift in the two-layer QG model.

3. Internal variability of the jet: the zonal index Leading mode of variability of zonal-mean zonal wind Represents a meridional shift of the jet Has equivalent barotropic structure Lorenz and Hartmann (2001)

4. Zonal index and annular modes The zonal index variability is intimately related to the annular mode variability Geostrophic zonal wind Geopotential height (Thompson and Wallace 2000)

5. Forced annular response The annular mode response is ubiquitous for many types of climate perturbations Projected 21st century stormtrack shift in IPCC AR4 models (Yin 2005) Southern Hemisphere geopotential trend, partly attributed to ozone changes (Thompson and Solomon 2002) In many circumstances, the annular pattern dominates the forced response even when the external forcing has little projection on this pattern.

6. Zonal index persistence zonal wind autocorrelationmomentum flux autocorrelation lag (days) Taken from Lorenz and Hartmann (2001) The zonal index is much more persistent than the eddies that drive it: At long time scales, there might be a role for the stratosphere and/or ocean At subsynoptic time scales, eddy-zonal mean feedback is likely more important The eddy forcing is such that it tends to reinforce preexisting zonal wind anomalies

7. Likewise, models with more persistent internal variability show stronger annular trends From Gerber et al (2008) The short answer is predictability… There seems to exist a relation between the persistence of the mode and the percentage of variance that it explains (e.g., Yang and Chang 2007) Why is persistence important?

8. Diagnostics of jet position Start with zonal-mean zonal momentum equation: This is just a balance between the different accelerations. However, this tells us nothing about the position of the jet!

9. Diagnostics of jet position Start with zonal-mean zonal momentum equation: Multiply by latitude: Integrating in y and z: We refer to this equation as the jet symmetry budget A measure of the jet position (or asymmetry) Torque forcing Eddy forcingFriction

10. Two-layer QG model on the beta plane Eliassen-Palm fluxes Since this model is symmetric about midchannel, all terms independently vanish We break the symmetry adding an easterly torque F on one side only

11. Jet sensitivity to torque position Control run: no torque Jet is symmetric about midchannel Remote torque Easterly jet created on the side but the original jet remains symmetric > 0

12. Jet sensitivity to torque position Control run: no torque Jet is symmetric about midchannel Torque within eddy-dominated region When the eddies interact, they make the jet shift poleward

13. Jet sensitivity to torque position As the torque moves closer to the center of the channel, the jet shift increases… Eventually, the jet moves back to the center of the channel and symmetry is recovered

14. Jet symmetry budget Terms contributing to jet shift: For a remote torque, its forcing is simply balanced by friction As the torque approaches the eddy dominated region, there is a positive eddy feedback that amplifies the torque forcing This results in a shift of the jet Torque forcing Friction Eddy forcing

15. Jet sensitivity to torque strength At a given position, the jet shift increases with increasing torque

16. Jet sensitivity to torque strength This can again be explained using the jet symmetry budget

17. The eddies also shift…

18. Mechanisms of eddy-zonal mean feedback That’s the big question!!! And a very difficult question too… Some proposed mechanisms: Different eddy lifecycles (LC1 vs LC2) due to changes in barotropic shear/refractive index/eddy propagation Meridional displacement of critical layers due to differential acceleration Resilience of the jet to stay at its perturbed position due to the ‘negative viscosity’ effect (i.e., the eddy generation shifts with the jet) But we don’t really know… We just submitted a proposal to investigate these issues

19. Conclusions 1.The zonal index (jet shift) is the leading form of zonal-mean extratropical variability and a fundamental part of the forced response. 2.This mode varies on longer time scales than the driving eddies, which might be due to an eddy-mean flow feedback 3.Eddy reinforcement may explain why this mode dominates the internal variability and why this is a preferred response in the forced problem. 4.We have derived an evolution equation for the position of the jet, driven by asymmetry. The main forcing is the asymmetry in eddy momentum flux. 5.In an idealized model, we showed that the eddy momentum flux tends to amplify other sources of asymmetry, implying a positive feedback. 6.The dynamics of this feedback remains to be elucidated. Thank you for your attention!

20. Other variables also shift, including the eddies…

21. Gerber (2005) The NAO may be regarded as the regional manifestation of that annular pattern

22. From Lorenz and Hartmann (2001)

23. From Polvani and Esler (2008)

24. From Gerber et al (2008)