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Lifting by cold pools (RKW theory)

Lifting by cold pools (RKW theory). A&OS C115/C228. Very rapid recap of CAPE & CIN (with some skewed, qualitative images). Environmental temperature profile. Average environmental lapse rate: 6.5˚C/km in tropopshere. Lift a parcel. Subsaturated parcel cools @ DALR, RH rises.

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Lifting by cold pools (RKW theory)

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  1. Lifting by cold pools(RKW theory) A&OS C115/C228

  2. Very rapid recap of CAPE & CIN(with some skewed, qualitative images)

  3. Environmental temperature profile Average environmental lapse rate: 6.5˚C/km in tropopshere

  4. Lift a parcel Subsaturated parcel cools @ DALR, RH rises

  5. Saturation reached (LCL) Note parcel negatively buoyant… a push needed

  6. Further lifting beyond LCL MALR varies with height Saturated parcel cools @ MALR

  7. Positively buoyant above LFC Parcel needed push to get to LFC

  8. Cloud top (TOC) where buoyancy vanishes Parcel runs out of vapor and/or reaches stratosphere

  9. Convective available potential energy (CAPE) Energy reservoir feeds strong storm updrafts; “positive area”

  10. Convective inhibition (CIN) Parcel must overcome inhibition to reach LFC -- needs a push

  11. Shear

  12. Midlatitudes: westerly wind increases with height in troposphere Principal reason: it’s colder to the north

  13. Vertical shear creates spin

  14. Vertical shear creates spin Storm moves faster than lower tropospheric winds

  15. Storm-relative view Storm moves faster than lower tropospheric winds

  16. Shear should force “downshear” tilt Storm would rain into its own inflow, not a good situation…

  17. A “better” storm configuration Storm avoids raining into its own inflow

  18. A “better” storm configuration Large amount of CAPE, low LFC, little CIN: A good recipe

  19. A downshear-tilting storm Storm rains into its own inflow, cooling it

  20. A downshear-tilting storm LFC rises, much less CAPE, much more CIN

  21. A downshear-tilting storm Unviable… and won’t live long…

  22. Shear == bad (for storm)… but it can be good thing too Cold pool == good (lifting)… but it can be bad thing too

  23. Spin in vertical plane Spin axis is horizontal “Right-hand rule” determines sign Positive horizontal vorticity illustrated Horizontal vorticity CW spin = positive CCW spin = negative

  24. Creating horizontal vorticity • Vertical wind shear • Horizontal temperature gradients

  25. Creating horizontal vorticity • Vertical wind shear • Horizontal temperature gradients

  26. Creating horizontal vorticity • Vertical wind shear • Horizontal temperature gradients

  27. Creating horizontal vorticity • Vertical wind shear • Horizontal temperature gradients Here: CCW spin & negative vorticity

  28. Horizontal vorticity  • Boussinesq equations, cross-derive to obtain • where

  29. An isolated warm bubble 8 km 16 km

  30. …with wind vectors Vorticity tendency largest here (largest horizontal B gradient) Vorticity largest here Temperature gradients = horizontal vorticity CCW, CW spins balanced

  31. Add on some shear? + Add shear to picture -- biased to CW spin; Thermal (cloud) would tilt downshear

  32. Storm cold pools make negative horizontal vorticity

  33. Effect of cold pool vorticity Air gets lifted… but not very well… By itself, cold pool vorticity bad for storm

  34. Now consider shear vorticity By itself, shear vorticity is also bad, forcing downshear tilt

  35. Now consider shear vorticity But two “wrongs” can make a “right”

  36. Vorticity balance Vorticities balanced - get deep lifting, strong storm

  37. The “optimal state” Optimal strength -- as close to vertical as possible, without raining into its own inflow

  38. RKW vorticity balance theory(Rotunno et al. 1988)

  39. RKW’s “optimal state” where: ∆u = wind speed difference over cold pool depth (proxy for vertical shear) c = storm speed (proxy for pool negative vorticity) Weisman and Rotunno (2004)

  40. Recap • Sources of horizontal vorticity: vertical shear & horizontal temperature gradients • By itself, CW shear vorticity weakens (multicell-type) storms… • Forces downshear tilt, rain into inflow • By itself, CCW cold pool vorticity weakens storms… • Provides lifting but its not very deep • Not an unalloyed good • Opposing vorticities can balance to produce optimal storm strength (Goldilocks!) • Cold pool vorticity stronger - leans upshear • Shear vorticity stronger - leans downshear

  41. Weisman and Rotunno (2004) RKW emphasized surface-based vertical shear over cold pool depth. WR2004 addresses objections to RKW theory by exploring (ii) Shear shifted above cold pool (iii) Shear extending above cold pool

  42. No shear case Observe vertical deformation of tracer lines

  43. Add some westerly shearover cold pool depth Max lifting case upshear side -- downshear side

  44. Same shear, but elevated A lot less total lift above x=+2

  45. Same shear, deeper layer Less total lifting - more downshear tilt

  46. Demonstration Nice multicell storm Sequence of short-lived updrafts; strong cold pool Storm leans upshear Cold pool vorticity stronger than shear vorticity

  47. Demonstration Take this storm and destroy its cold pool by turning off evaporation cooling Cold pool, its lifting and its vorticity go away What happens?

  48. Demonstration

  49. Another demonstration(cold pool collapse in very strong shear)

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