1. The Mean Meridional Circulation: A New Potential-Vorticity, Potential- Temperature Perspective Cristiana Stan Colorado State University March 11, 2005 http://dennou-k.gaia.h.kyoto.u.ac.jp/library/gfd_exp /exp_e/doc/bc/guide07.htm

2. Acknowledgements  Thanks to my advisor, Dr. Dave Randall, for challenging me with the idea that lies at the heart of this thesis.  Thanks to all my committee members: Dr. Wayne Schubert, Dr. Dave Thompson and Dr. Richard Eykholt.  Thanks to Dr. Ross Heikes for providing his isentropic model.  Thanks to all “rabbits” and people in this department who helped, both emotionally and technically.  Thanks to my husband who kept our life going and wonderful.

3. Motivation The main objective of the present work is to study the general circulation of the Earth’s atmosphere in a the general circulation of the Earth’s atmosphere in a new system of coordinates that consists of longitude, potential vorticity, and potential temperature (PVPT), and to give a new interpretation of the eddy momentum transport, one of the processes that determines the structure of the mean meridional circulation (MMC) in the midlatitudes, in terms of the form drag.

4. Outline  Review of theories explaining the MMC  Review of the eddy flux parameterizations  PVPT coordinates  MMC in PVPT coordinates  Conclusions and Perspectives

5. http://atschool.eduweb.co.uk/ Adapted from http://atschool.eduweb.co.uk/kingworc/departments/geography/nottingham/atmosphere/pages/pressureandwindsalevel.html

6. Cross-sections of monthly streamfunction in the NCAR- NCEP reanalysis. Contour interval is 2x10 10 kg s -1. Solid contours are positive, dashed contours are negative and the zero contour is gray. From Dima and Wallace, 2003.

7. Monthly mean zonally averaged wind in ECMWF reanalysis for the period 1985-94. Contour interval is 5 m s -1. Negative contours are dashed. From Hartmann and Lo, 1998.

8. Parameterization In the AMS-Glossary of Meteorology, parameterization is defined as “the representation in a dynamical model of physical effects in terms of admittedly oversimplified parameters, rather than realistically requiring such effects to be consequences of the dynamics of the system.”

9. Parameterization of Eddy Fluxes

18. Why Potential Vorticity, Potential Temperature ? 350K

19.  e ee e ee ee The Geometry of PVPT Coordinates       ee

20. y y Transformation to PVPT Coordinates q PV-thickness (Kushner and Held 1999)

21. The Continuity Equation Isentropic coordinates PVPT coordinates

22.  q    The flow through a PVPT tube 0 0

23. Mass distribution on potential temperature and potential vorticity. Northern Hemisphere, January (a) and Northern Hemisphere, July (b) in NCEP- NCAR reanalysis Mass Distribution in PVPT Coordinates a b

24. The Angular Momentum Equation Isentropic coordinatesPVPT coordinates Adiabatic, frictionless conditions

25. Constraints on the PVPT coordinates  Potential temperature varies monotonically with height/pressure.  Potential vorticity varies monotonically with latitude.

27. p  coordinates  coordinates PVPT  coordinates

28. No Dry Convective Adjustment

29. What happens?  in p-coordinates potential temperature is predicted by an ODE, which can be analytically integrated and gives  in  coordinates the pseudo-density  is predicted by an advection equation, which is a PDE, and the pressure is diagnosed from the top to the bottom by adding the mass from the isentropic layers above.

30. Dry Convective Adjustment

31. time convective/ baroclinic instability p/   0 time     convective/ baroclinic instability 0

32. Hemispherical statistical distribution of regions where the PV gradient on  =350K in ERA-40 reanalysis is negative for more than three consecutive days January 350KNH From Schubert et al., 1991

33. Momentum transport acting on the zonal mean flow

35. Eliassen-Palm Flux Isentropic Coordinates Andrews et al., 1987

36. Residual Circulation in PVPT Data used in these plots are simulated with Ross Heikes isentropic model

37. Conclusions 1.) Introduction of potential vorticity as meridional coordinate.  The merdional advection is zero for an adiabatic, frictionless flow.  In connection with the potential temperature the newly created system of coordinates allows to divide the atmosphere into undulating tubes bounded by isentropic and constant PV surfaces, and the air moves through these tubes without penetrating through the walls.  A numerical model that uses the PVPT system has the advantage of incorporating as “built-in” dry convective and baroclinic adjustment processes.

38. Conclusions 2.) Develop a framework adequate for parameterization of the eddy momentum transport.  When applied to the study of the mean meridional circulation the PVPT system of coordinates reveals a residual circulation driven by the Lagrangian time rate of change of the PV and   The momentum exchange that affects the zonal mean flow - zonal component of the pressure forces exerted by the eddies on a thin zonal tube bounded by surfaces of constant PV as lateral sides and undulating bottom and top isentropes.

39. Perspectives What could be the applications of the PVPT system of coordinates in climate studies?  PVPT framework emerges at the same time with the ERA 40 reanalysis products, which provide direct model outputs on the PV surface 2PVU.  As model resolution changes the need for parameterization does not simply go away. Simple zonally averaged models provide test beds for understanding hypothesized mechanisms.