1. TITLE SUB SYNOPTIC SCALE INSTABILITY AND HURRICANE PRECURSORS Doug Sinton SJSU Meteorology Wednesday May 2, 2007 A PREFERRED SCALE FOR WARM CORE INSTABILITIES IN A MOIST BASIC STATE Brian H. Kahn JPLJPL Doug Sinton SJSU Meteorology Friday June 8, 2007

2. ABSTRACT Model –linear two-layer shallow water Orlanski (1968) –simple parameterized latent heat release Conditions –moderate to weakly baroclinic –near moist adiabatic Results –most unstable mode: warm-core –maximum growth rates ~ 0.46f –Ro of most unstable mode ~ 0.9 for 10 < Ri < 1000 –for given static stability preferred scale varies as Ri -1/2 Implications –organize convection in tropical cyclone precursors –account for tropical cyclone and polar low scale

3. OBSERVATIONS

4. Frank and Roundy 2006 O BS DET Statistical correlation – Tropical waves precede tropical cyclogenesis Four types of tropical cyclone precursors –Rossby-Gravity, Baroclinic, Equatorial Rossby, MJO –Produce favorable conditions for tropical cyclogenesis Common structure –Flow reversal aloft –Baroclinic first internal vertical mode Moore and Haar 2003 OBSERVATION DETAIL Polar Low – warm core structure OBSERVATION DETAILOBSERVATION DETAIL

5. POLAR LOW

6. THEORY

7. CISK FIGURE < 0 CISK C onditional I nstability of the S econd K ind CAPE

8. CISK Hypothesis Convective heating induces sub-synoptic circulation Circulation converges water vapor needed by convection Deficiencies Convective vs sub-synoptic scale mismatch CAPE redistributes moist static energy without replenishing it CAPE Ultra-violet catastrophe CISK CIFK

9. W ind I nduced S urface H eat E xchange WISHE > 0 WISHE FIGURE

10. WISHE Hypothesis SST source of sufficient moist static energy Wind enhances evaporative water vapor flux from ocean Saturated boundary layer aids/sustains convection Enhanced convective heating strengthens wind Deficiency Motivation SCALE of wind circulation NOT accounted for

11. TYPHOON SIZES

12. HYPOTHESIS METHODOLOGY LIMITATIONS

13. HYPOTHESIS DETAILSHYPOTHESIS DETAILS Hypothesis: test for linear instability –Is there a preferred scale? –If so, what is its structure? –If so, what are controlling processes and conditions? Methodology: simple model –Two layer shallow water model permits range of instabilities First internal vertical mode: feasibility of simple LHR scheme –Non quasi-geostrophic approach Short wave scale violation problem avoided Ageostrophic thickness advection permits warm core structure Caveats –Not a simulation –Not only explanation for development

14. G vs AG TEMP ADV warm core P2P2 T = P 2 – P 1 P1P1 C W AG GGEO vs AGEO TEMP ADV FOR WARM CORE z y x

15. MODEL

16. MODEL SCHEMATIC TWO LAYER SHALLOW WATER MODEL SCHEMATIC H1H1 H2H2 LxLx LyLy H WARM COLD

17. LINEARIZED MODEL EQUATIONS q q

18. LATENT HEAT SCHEMATICLATENT HEAT SCHEMATIC LATENT HEAT PARAMETERIZATION

19. -DIV -Q*DIV -(1-Q)DIV INITIAL Q = 0 AVG DENSITY INCREASES “COOLING” Q = 0.5 AVG DENSITY UNCHANGED “CONSTANT” DIV < 0 LATENT HEAT PARAMETERIZATION CASES Q > 0.5 AVG DENSITY DECREASES “WARMING”

20. ROSSBY NUMBERROSSBY NUMBER Ro

21. NON DIM MOMENTUM EQN Ro

22. MODEL ENERGETICS SCHEMATIC ZAPE EAPE W BC WQWQ EKE WKWK

23. MODEL ENERGETICS q

24. QG BAROCLINIC ENERGETICS q = 0 ZAPE EAPE W BC EKE WKWK Ro

25. QG SHORT WAVE CUTOFF q = 0 ZAPE EAPE W BC EKE WKWK Ro

26. CISK ENERGETICS q > 0.5 ZAPE EAPE W BC WQWQ EKE WKWK Ro

27. WISHE ENERGETICS q 0.5 ZAPE EAPE W BC WQWQ EKE WKWK Ro

28. Newton - Raphson confirms eigenvalues EIGENVALUE PROBLEM

29. PHASE LAGS T = P 2 – P 1 P2P2 P1P1 T 0° 90° 180° -90°

30. RESULTS

31. ENERGY VECTOR W BC G W BC AG -W BC G -W BC AG W BC > W Q W Q > W BC W BC AG W BC G

32. GROWTH RATES vs constant q Ri 10

33. q PROFILE

34. q PROFILE CLOSEUP

35. GROWTH RATES DRY vs MOIST for Ri WARM CORE MOST UNSTABLE

36. Ri 40 qc 0.496 E vectors

37. Ri 100 WARM CORE MOST UNSTABLE

38. LARGE R o X – Z CIRCULATION y x z WARM CORE CIRCULATION qc ~ 0.49 R o ~ 0.9 P2P2 T P1P1 C W C W WARM CORE CIRCULATIONWARM CORE CIRCULATION

39. WARM CORE WINDS LOWER

40. WARM CORE WINDS UPPER

41. WARM CORE PRESSURES 2D

42. WARM CORE THICKNESS 2D

43. WARM CORE PRESSURES 3D

44. WARM CORE THICKNESS 3D

45. PHASE DIFF P2 – P1

46. PHASE DIFF THK – W

47. QG DRY CASE q = 0

48. P1P1 T P2P2 z y x QG CIRCULATION C W C W QG CIRCULATIONQG CIRCULATION

49. DRY MOST UNSTABLE LOWER WINDS

50. DRY MOST UNSTABLE UPPER WINDS

51. DRY MOST UNSTABLE PRESSURES 2D

52. DRY MOST UNSTABLE THICKNESS 2D

53. DRY MOST UNSTABLE PRESSURES 3D

54. DRY MOST UNSTABLE THICKNESS 3D

55. PHASE DIFF P2 – P1

56. PHASE DIFF THK – W

57. QG EADY Ri 10 DRY CASE q = 0

58. DRY EADY Ri 10 LOWER WINDS

59. DRY EADY Ri 10 UPPER WINDS

60. DRY EADY Ri 10 PRESSURES 2D

61. DRY EADY Ri 10 THICKNESS 2D

62. DRY EADY Ri 10 PRESSURES 3D

63. DRY EADY Ri 10 THICKNESS 3D

64. PHASE DIFF P2 – P1

65. PHASE DIFF THK – W

66. SUMMARY

67. CONCLUSIONSCONCLUSIONS Model –linear two-layer shallow water –simple parameterized latent heat release Conditions –weakly baroclinic –near moist adiabatic Results –warm-core: most unstable mode for nearly saturated conditions –growth rate sensitive to saturation not Ri –instabilities limited to Ro < 1.5 –preferred scale determined by (vertical shear) 1/2 Implications –Organize and pre-condition convection associated with hurricane and polar low development –account for hurricane and polar low scale –weaker shears favor development as smaller preferred scales more likely to be saturated –stronger shears stabilize shorter scales

68. WHAT’S NEXT? Make model non-frontal Add horizontal shear Nonlinear with random initial perturbation

69. ACKNOWLEDGMENT Professor C. R. Mechoso and Professor A. Arakawa Once a UCLA Atmos Science grad student Always a UCLA Atmos Science grad student

70. Ri 10 WARM CORE MOST UNSTABLE

71. WARM CORE WINDS LOWER

72. WARM CORE WINDS UPPER

73. WARM CORE PRESSURES 2D

74. WARM CORE PRESSURES 3D

75. WARM CORE THICKNESS 2D

76. WARM CORE THICKNESS 3D

77. W vs THICKNESS PHASE

78. W WARM CORE

79. W DRY CASE

80. W DRY EADY CASE

81. Ri 40 WARM CORE MOST UNSTABLE

82. WARM CORE WINDS LOWER

83. WARM CORE WINDS UPPER

84. WARM CORE PRESSURES 2D

85. WARM CORE PRESSURES 3D

86. WARM CORE THICKNESS 2D

87. WARM CORE THICKNESS 3D

88. Ri 1000 WARM CORE MOST UNSTABLE

89. WARM CORE WINDS LOWER

90. WARM CORE WINDS UPPER

91. WARM CORE PRESSURES 3D

93. WARM CORE THICKNESS 2D

94. WARM CORE THICKNESS 3D

95. MOST UNSTABLE q= 0.495 R o = 1.52

96. QG DRY CASE PRESSURES 3D X – Z CROSS SECTION

97. QG DRY CASE THICKNESS 3D X – Z CROSS SECTION

98. MOST UNSTABLE CIRUCLATION q.495MOST UNSTABLE CIRUCLATION q.495 P2P2 T P1P1 CC W W MOST UNSTABLE MODE CIRCULATION q = 0.495 R o = 1.52 z y x

99. MOST UNSTABLE WINDS LOWER q = 0.495

100. MOST UNSTABLE WINDS UPPER q = 0.495

101. MOST UNSTABLE PRESSURES 2D q = 0.495

102. MOST UNSTABLE PRESSURES 3D q = 0.495

103. MOST UNSTABLE THICKNESS 2D q = 0.495

104. MOST UNSTABLE THICKNESS 3D q = 0.495

105. MOST UNSTABLE PRESSURES q = 0.495 3D X – Z CROSS SECTION

106. MOST UNSTABLE THICKNESS q = 0.495 3D X – Z CROSS SECTION

107. CIRCULATION q = 0.495 R o = 3.0 z y x P1P1 T P2P2 wwcc cc HIGH Ro CIRCULATIONHIGH Ro CIRCULATION

108. NON DIM MOMENTUM EQN LARGE R o CASE RoRo RoRo RoRo