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

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

3. THEY LOOK SO SOLID Where to begin?

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

5. Outline white lumpsThe obvious part of convection: white lumps specter.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. How are white cloud and clear env coupled? Mass continuity Even tighter: make sound speed infinite 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 wind divergence convergence or negative divergence from L. vergere "to bend, turn, tend toward, incline"

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

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

14. Velocity vs. Azimuth Display (VAD) Example: 925 mb in deep convection V r (m/s) SN EW N Azimuth [V r ] < 0 convergence

15. low-level con, upper level div SN EW N [V r ] < 0 at 925 mb [V r ] > 0 at 125 mb Upward mass flux in between

16. Revisiting the outline white lumps, invisible environs(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".specter spectrum 1611, "apparition, specter, ghost," from L. spectrum.spectrum Online Etymology Dictionary the other OED

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

20. Ghosts in the laws of motion –Familiar game: assume e i(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".phase –group likely from P.Gmc. kruppaz "round mass, lump."group c p = (  /k,  /m) speed of phantoms c g = (∂  /∂k, ∂  /∂m) speed of lumps

24. Speed of phantoms AND lumps sameHorizontal phase and group speed same: c p = c g = N/m horizontal sorting of waves according to their vertical wavelengthhorizontal sorting of waves according to their vertical wavelength –hyd. distortion: short waves (small k) go too fast

25. vertical horizontally Longer vertical wavelengths travel faster horizontally 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. Mapes 1993 JAS early late

26. Revisiting the outline white lumps, invisible environs(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. Modes: ghosts with boundaries ??? Upward mass flux divergence(masssource) solid boundary how can this really exist?

28. The top lid 1.The tropopause is a lid –Clean discrete modes: show next –Not quite correct, but essence is clear 2.There isn’t one (radiation condition) –Continuum of vertical wavelengths 3.A higher lid (small p where  =0) –Vertically prop. waves reflect off the lid and create an interference pattern –Discretization artificial, bands are valid

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

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

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 vertical horizontally –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. discretizesbands –lid discretizes spectrum; bands robust

34. Revisiting the outline white lumps, invisible environs(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” Con Strat In pure simplest theory case Con: sin(z) Strat Strat: sin(2z) Houze 1997 BAMS

38. realistic? (or kinda kooky?) 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. Spectrum of average VAD divergence from many profiles in tropical rain different lid pressures -> different discretizations, bands robust Hey -- what’s this? Mapes 1998

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

41. Melting: forcing is localized in z, response is localized in wavenumber! Melting mode 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=1 m=3/2 Does this exist? m=1/2 Re: kookiness Are convective and stratiform really dynamical modes?

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

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

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

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

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

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

51. Modal (band) responses seen away from convection Yes, Convective and stratiform “modes” seen in T fluctuations, but ~15 m/s also prominent Fast ghosts zipping everywhere - only statistics are available reliably ?

52. A fundamental source for c ~ 15 m/s radiative cooling 12km moist adiabat runs dry 8km spectrum of square Qrad forcing obs. strat.

53. NO fundamental source for c ~ 25 m/s ("stratiform mode") Apparently excited by processes internal to convective cloudiness –half-troposphere depth cumulus congestus rainclouds –precipitating stratiform anvil clouds

54. No fundamental source -> GCMs fail Lack of stratiform processes, or of cumulus showers? GCM Deep convection heating in GCM Lee Kang Mapes 2001 20N-20S cooling Deep convection heating obs Earth Mapes 2000

55. Cloud resolving model has it... Tulich Randall Mapes 2006 shallow cu (SC) & stratiform (ST) opposed SC only in lower half of mode

56. Revisiting the outline white lumps, invisible environs(Intro: white lumps, invisible environs) Spectral laws of stratified flow “Modes” of convection The life cycle: why grow just to die? –A question of coupling between the 2 halves of convective circulations »(white part + spectral env.)

57. Bigger things have longer lives suggests a key velocity scale (not x or t) Mapes Tulich Lin Zuidema 2006

58. Clean: 4000 km rain waves in a 2D model (All the following work by Stefan Tulich) cc3

59. The life and death of cc3 a multicellular entity shallow deep strat.

60. Why die? Why do new cells fail? 1 km warm T’ BUOYANCY OF LIFTED AIR PARCELS FROM LOW LEVELS env warm (& dried)

61. cell-killing warm wedge: a downward displacement in a wave warm T’ cold pools slide under, but new cu fail

62. What does the LS wave look like? a larger version of cc3, of course! cu in front deep strat. LS wave motion to right Note T’ no bigger in heated areas - equilibrated wave

63. Front edge: wave forces cu clouds keeps falling cu heating nestled in low T’, which keeps falling

64. But why does the large scale wave exist? Must go back to origins (different model run - main wave went R->L) widening river of wave amplitude as events trigger next events

65. Key mechanism: short vertical wavelength mode change it via radiative cooling depth and/or lapse rate changed wavelength spectrum actual wave speed changes accordingly

66. Conclusions Illusion of clouds as substantial is visually compelling –Must be resisted with rationality Motions of embedding environment are inseparable, and spectral –Longer vert. waves travel faster –chromatography of outgoing signals –sloped destabilizing by incoming signals

67. Not kooky, but a little spooky Artifice of upper lid not too bad –believe bands not modes (but mode is a convenient word) Neglect of advection not too bad –wavefronts remain upright & coherent even in shear how ?? –secondary circs?

68. Where does wave-1 of troposphere activity come from? Precipitating stratiform anvils force it Cumulus congestus showers force it »lower half only These cancel on average - there is no physically fundamental source »large-scale models can miss it via parameterization errors

69. Convective & stratiform –Inevitable microphysical outcomes of bubble ascent (rain, ice, etc)? –Or dynamical modes of motion? What governs downdraft depth for example? »rain could just saturate air & stop evaporating if descent didn’t agree with the ambient airflow...

70. Leading edge of the life cycle Is this 2000 km / 20 hour wedge scale governed by the cumulus dynamics of moisture buildup? Or does wave cooling invite (by buoyancy) or demand (for balance) a certain heating? »Sensitivity to precipitation efficiency of cu? shallow cu heating

71. Is the MCS just another convectively coupled wave type? small scale, large amp., but qualitatatively...

72. What’s up with this? Substantial, very repeatable deviation from a moist adiabat. CRMs don’t get it. microphys (e.g. ice?) small cu effects? LS (trades) crucial?

73. Discussion welcomed mapes @ miami.edu Thank you!