Convective cloud life cycles in a wavy stratified environment Brian Mapes University of Miami

1. Convective cloud life cycles in a wavy stratified environment Brian Mapes University of Miami

2. Life cycle: resemblances. why? MCS: Zipser 1969 MCS: Zipser et al. 1981 2-day: Takayabu et al. 1996 Kelvin: Straub & Kiladis 2004 MJO: Lin and Johnson 1996

3. Where to begin? THEY LOOK SO SOLID

4. BUOYANCY OF LIFTED AIR PARCELS FROM LOW LEVELS LESS DENSE THAN ENV. Really, more like a void

5. Outline • The obvious part of convection: white lumps • The invisible embedding flow: a specter. • Spectral laws of stratified flow • “Modes” of convection • The life cycle: why grow just to die?

6. Constrained cumuli • The white part of convection is physically complex (mixing, microphysics, etc.) • but bounded by a skin-tight, form-fitting outer surface ”the environment”

7. Even tighter: make sound speed infinite How are white cloud and clear env coupled? Mass continuity The shape and size of a cloud can change only as permitted by the massive (but responsive) clear air surrounding it.

8. Glimpses of invisible env. flow

9. Continutiy in mass coordinates (hydrostatic pressure)  = -gw vertical mass flux w, times gravity (‘weight flux’)

10. Vergence of horizontal wind from L. vergere "to bend, turn, tend toward, incline" convergence or negative divergence wind divergence

11. Interpreting a divergence profile Convection-centric: “Derivative of the vertical mass flux profile” Environment-centric: “Mass source at each pressure level within the ambient stratification”

12. Measuring divergence: exact area averaging by the divergence theorem Normal component of wind along perimeter Vn Some area A on a pressure surface Vn dl Perimeter length increment dl

13.     V dA = [Vr] x 2/R A Special case: a circular area with a Doppler radar in the middle A Vr Perimeter = 2R Area = R2 [Vr] = azimuthal mean of radial velocity

14. N E S W N Velocity vs. Azimuth Display (VAD)Example: 925 mb in deep convection Vr (m/s) [Vr] < 0 convergence Azimuth

15. Upward mass flux in between low-level con, upper level div [Vr] > 0 at125 mb [Vr] < 0 at925 mb N E S W N

16. Revisiting the outline • (Intro: white lumps, invisible environs) • will return to observations, I promise • Spectral laws of stratified flow • “Modes” of convection • The life cycle: why grow just to die?

17. Ghosts • specter, from Fr. spectre "image, figure, ghost" (16c.). Spectral from 1815 in the sense of "ghostly". • spectrum 1611, "apparition, specter, ghost," from L. spectrum. Online Etymology Dictionary the other OED

18. Ghosts in the laws of motion • Stratified flow: simplestcase • variables: • w - vertical wind • u - horizontal wind (x-z plane for now) • b - buoyancy •  - pressure perturbation • parameters: • N - buoyancy frequency (a measure of density stratification)

19. mass continuity (rarely put first!) horiz. momentum (Newton’s 2nd law) vertical momentum 1st law of thermodynamics Ghosts in the laws of motion • Stratified flow: simplestcase • linearized, Boussinesq, 2D

20. Ghosts in the laws of motion • Familiar game: assumeei(kx+mz-t)form of solution • diffeq’s yield algebraic dispersion eq. relating ,m,k

21. gravity or buoyancy or internal waves

22. Even simpler • Large-scale (hydrostatic) motions • k << m in dispersion relation, or • discard ∂w/∂t in vertical momentum equation:

23. Spectral laws of stratified flow • phase and group velocities • phase from Gk. ...phantasma "image, phantom". • group likely from P.Gmc. kruppaz "round mass, lump." cp = (/k, /m) speed of phantoms cg = (∂/∂k, ∂/∂m) speed of lumps

24. Speed of phantoms AND lumps • Horizontal phase and group speed same: cp = cg= N/m • horizontalsorting of waves according to their verticalwavelength • hyd. distortion: short waves (small k) go too fast

25. Longer vertical wavelengths travel faster horizontally early A complex convective event in a salt-stratified tank excites many vertical wavelengths in the surrounding fluid (photo inverted to resemble a cloud). Strobe-illuminated dye lines are displaced horizontally, initially in smooth, then more sharply with time. late Mapes 1993 JAS

26. Revisiting the outline • (Intro: white lumps, invisible environs) • will return to observations, I promise • Spectral laws of stratified flow • “Modes” of motion • “Modes” of convection • The life cycle: why grow just to die?

27. ? ? ? divergence (mass source) Upward mass flux solid boundary Modes: ghosts with boundaries how can this really exist?

28. The top • The tropopause is a lid • Clean discrete modes: show next • Not quite correct, but essence is clear • There isn’t one (radiation condition) • Continuum of vertical wavelengths • A higher lid (small p where =0) • Vertically prop. waves reflect off the lid and create an interference pattern • Discretization artificial, bandsarevalid

29. D (stratified) Tropopause as lid: a pure mode Response to specified deep convection-like sin(mz) heating, with m =/D Nicholls Pielke Cotton 1991; graphics courtesy S. Tulich

30. Response to heating Vertical velocity w -c c = N/m ~50 m/s

31. Environment feels mass source (upper) & sink (lower) Horizontal velocity u -c c

32. Heat radiation Temperature T -c c Warm

33. Summary of wave/mode background • The flow of stratified clear air outside convective clouds is dispersive • longer vertical wavelength components expand faster/farther away from source horizontally • Any vertical profile, e. g. divergence, can be expressed as a spectrum, w/ axis labeled by phase speed. • lid discretizes spectrum; bands robust

34. Revisiting the outline • (Intro: white lumps, invisible environs) • Spectral laws of stratified flow • “Modes” of motion • “Modes” of convection • The life cycle: why grow just to die?

35. What kinds of vertical structure are observed in deep convection? many field obs sources - Houze, Zipser, Johnson,... Top-heavy heating profile in net deep heating

36. “Modes”? Convective and Stratiform Example: 2 radar echo (rain) maps (w/ VAD circles) 200 km

37. Convective & stratiform “modes” In pure simplest theory case Con: sin(z) Strat: sin(2z) Strat Con Strat Con Houze 1997 BAMS

38. Is all this sin(z) ghost/mode stuff realistic? (or kinda kooky?) • Need: modes of a realistic atmosphere (actual  stratification profiles) • Ready: Fulton and Schubert 1985 • Need: realistic heating (divergence) profiles • Ready: many many VAD measurements

39. Hey -- what’s this? Spectrum of average VAD divergencefrom many profiles in tropical rain different lid pressures -> different discretizations, bands robust Mapes 1998

40. Top-heavy C+S: spectrum & response Mapes and Houze 1995 T response when observed mean VAD divergence is used as a mass source in observed mean stratification

41. Melting mode Melting: forcing is localized in z, response is localized in wavenumber! Mapes and Houze 1995

42. Raw data:Snow melts, whole troposphere shivers(wavelength set by melting layer thickness?) spectral view not quite so kooky?

43. m=3/2 Does this exist? Re: kookinessAre convective and stratiform really dynamical modes? m=1 m=1/2

44. (great data quality) Rare, but compelling Jialin Lin

45. (5h of data, from front to back of storm) Rare, but compelling Aboard the R/V Brown JASMINE project considerable front-back cancellation

46. diurnal May 22, 1999 (figs from U. of Washington web pages on JASMINE) In a storm notable for fast, long-distance propagation ~15 m/s ship Webster et al. 2003, Zuidema 2003 Kousky - Janowiak - Joyce (NOAA CPC)

47. u u later Pandya and Durran 1996 Re: kookinessnumerical modeling, with advection

48. Re: kookiness Wavefront 2 stays vertical and coherent despite advection by sheared winds nearly half the wave speed! Pandya and Durran 1996

49. Re: kookinessmore numerical modeling Yang and Houze 1995 Even convective cells appear to be gravity waves!? This stuff hasn't totally sunk in to the convection community (myself included!)

50. Spectral questions • Where do the observed modes come from ultimately?