Stephen Ogden November 6, 2013

1. Finding Energy Pathways from a Tropical Energy Bubble to a Mid-Latitude Jet Using Wave Activity Flux Vectors Stephen Ogden November 6, 2013

2. Motivation • Finding a way to quantify and track energy from an energy bubble in the tropics to the mid-latitude Rossby wave train and the jets associated with it • Finding a better way to describe downstream development in the mid-latitude wave train • Explaining the connection between seemingly unconnected events in the tropical upper levels and mid-latitude low levels • Quantifying the energy provided by the bubble

3. What's The Energy Bubble? • Convection in the tropics lifts high theta air to the tropopause • This inflates the space between isentropes, creating an area of low static stability • This is also a density anomaly compared to areas in the mid-latitudes, creating a potential energy difference (measured as Jet Available Potential Energy, JAPE) • On maps, it is an anomalously high tropopause height and ridging in the tropics • Energy is accumulated above the equilibrium level, the straight isentropeabove the polar jet and below the subtropical jet

4. Physical Reasoning • Pieces of the tropical energy bubble can break off and move towards the mid-latitudes, creating a potential energy gradient above the equilibrium level • When this gradient is tapped, energy is provided for the mid-latitude wave train • The amplified upper-level wave pattern that results is associated with stronger jet streaks • Stronger or new jet streaks are tied to enhanced kinetic energy conversion and an enhanced Sawyer-Eliassen circulation

5. More on Jet Streaks • The Sawyer-Eliassencirculations can be enhanced by providing low static stability air to the right entrance region of the jet (Lang, 2011) • This enhances the ability to have vertical motion in the circulations, allowing for an increase in the wind speed and extraction of energy from the bubble due to enhanced geopotential height gradients From Tripoli (2013)

6. More on Jet Streaks II • In addition, the vertical motion caused by non-zonal jets serves to push the bubble along into the mid-latitude wave train • Vertical motions in the jet core squeeze the bubble (and energy) into the jet in SW flow and pull it out (and across the jet) in NW flow Height patterns and anomalies. SW (NW) flow represented by arrows is geostrophic warm (cold) advection.

7. Downstream Energy Propagation in the Mid-Latitudes • After the bubble potential energy is converted to kinetic energy entering the mid-latitude jet, it must be converted back to potential energy to terminate the jet • That potential energy will develop a new trough below the equilibrium level in the wave pattern • The energy in the trough then creates a new jet streak afterwards, continuing the cycle

8. Not Always Directly Downstream Modified from Orlanskiand Sheldon (1995) • Geostrophic wind rules seem to partially contradict previous downstream work (Orlanski and Sheldon, 1995) • Why wouldn't a supergeostrophic area produce an enhanced jet over the top of a ridge? • And how would you shove energy into a jet exit region downstream of a ridge? • Does this also lead to recycling of bubble/ridge energy?

9. The Equations • A set of equations describing vectors will show where the energy is going • Kinoshita and Sato (2013): A Formulation of Three-Dimensional Residual Mean Flow Applicable Both to Inertia–Gravity Waves and to Rossby Waves • Describes wave activity flux vector components (equations 2.21a-f) in 3D compared to a time-mean flow • Does not use a specific dispersion relation to derive the flux, making it equally applicable to inertia–gravity and Rossbywaves • The equations assume the following: • Wave amplitudes are small and consistent • There is no time mean derivative of any value • Time mean vertical velocity is neglected

10. Wave Activity Flux • Does not account for energy movement from simple undisturbed wave propagation • Wave activity flux is a measure of wave forcing • Wave activity flux vector convergence implies wave development/amplification and accumulation of energy • Vector divergence implies wave decay and loss of energy

11. Modifications/Adaptations • Vertical (x3) components are ignored here, due to their small magnitude • The analysis is done on one level between the tropical tropopause/subtropical jet and the polar tropopause/jet (250mb) • The assumption of small wave amplitudes is stretched, if not broken due to the depth of the waves depicted

12. Partitioning the Energy Transfer • The bubble provides some fraction of the mid-latitude Rossby wave train energy • That potential energy is converted to kinetic and then potential energies present in the wave train • The bubble can be quantified as JAPE, a density anomaly at a level in the tropics as compared to the mid-latitudes • Conversion can be isolated by defining a box and subtracting out KE fluxes in/out, leaving the KE change due to energy conversion

13. The Case • Cause: Hurricane Michelle (min. 934mb, late Oct-early Nov 2001) • Effect: An intense cyclone over Algeria and the Mediterranean Sea (min. 989mb, early to mid-Nov 2001) • Connection: Tracers released in the eyewall of Hurricane Michelle end up in a jet associated with the cyclone

14. The Tropopause Level View (0Z 5 Nov) A weak jet has formed on the north side of the bubble B

15. Putting the Vectors To Use (0Z 5 Nov) The Atlantic is mostly quiet as the bubble moves through the tropics B

16. The Tropopause Level View (12Z 5 Nov) T1 T1 C D B B As energy moves through the jet, some of it develops a trough to the north

17. Putting the Vectors To Use (12Z 5 Nov) T1 C D B Energy moves from a bubble associated with Michelle into the entrance region of a jet on its northern side, moving toward the exit region

18. The Tropopause Level View (0Z 7 Nov) T1 C C D B The bubble pushes northeast as its energy moves through the jet

19. Putting the Vectors To Use (0Z 7 Nov) T1 C C D B More energy exits the bubble into the entrance region

20. The Tropopause Level View (0Z 8 Nov) C C D D B C T1 An intense jet has wrapped around the north side of the bubble

21. Putting the Vectors To Use (0Z 8 Nov) C C D D B C T1 Energy is now moving en masse from the bubble through multiple jets

22. The Tropopause Level View (0Z 9 Nov) C B C D C T2 D C The jet is now 160kts, with the trough growing as well

23. Putting the Vectors To Use (0Z 9 Nov) C B C D C T2 D C Massive amounts of energy are pouring out of the bubble toward the west Energy is also pouring into the trough from the jet

24. The Tropopause Level View (0Z 10 Nov) C C B D C C D T2 D C The bubble is now rapidly deflating, seen in its lower tropopause The trough and jet are fully developed

25. Putting the Vectors To Use (0Z 10 Nov) C C B D C C D T2 D C Energy begins leaving the trough toward the south

26. The Tropopause Level View (0Z 11 Nov) C C D C B T2 C D The bubble is almost gone Downstream development has extended into northern Africa

27. Putting the Vectors To Use (0Z 11 Nov) C C D C B T2 C D The bubble has lost almost all of its energy

28. Statistics of the Energy Transfer • The amount of potential energy (as JAPE) in the bubble before interaction (calculated at 12Z 2 Nov) is 1.97x10^10J • Total energy converted from potential to kinetic in the mid-latitude wave train throughout the bubble interaction (12Z 2 Nov-18Z 8 Nov) is 2.11x10^10J • Based on this calculation, the bubble contributes a large fraction of the mid-latitude wave train energy!

29. Summary • The wave activity flux vectors show energy moving through a jet on the north side of the bubble, pulling the bubble into the mid-latitudes • The vectors show energy converging into jet entrance regions and diverging out of jet exit regions in the mid-latitudes, deflating the bubble and inflating troughs • The net effect is that energy moves into a trough and jet that lead to the surface cyclone, fueled by energy from a bubble associated with Hurricane Michelle as expected • But the energy must go through multiple other jets and build troughs before it can end up in the final trough and jet • Kinoshita and Sato's wave activity flux equations work well despite the stretching of the “small perturbation amplitude” assumption • The bubble provides much of the energy to the amplified mid-latitude wave train and associated jets

30. Potential Long-Term Future Work • See if the behavior/location of these bubbles can be related to things like the major oscillations, ENSO, etc. • Investigate how the global energy bubble would change in a changing climate • Quantify such changes as compared to energy extracted from baroclinicity • Model the effects of modifying the bubble (adding/subtracting energy, moving location, etc.)