1. Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer

2. MT 454 Class Slide The Planetary Boundary Layer Chapter 5 - PBL

3. MT 454 Class Slide Chapter 5 - PBL

4. MT 454 Class Slide Chapter 5 - PBL

5. MT 454 Class Slide Chapter 5 - PBL

6. 5.1 Turbulence - 1 MT 454 Class Slide

7. 5.1 Turbulence - 2 MT 454 Class Slide

8. MT 454 Class Slide 5.1 Turbulence - 3

9. MT 454 Class Slide 5.1 Turbulence - 4

10. MT 454 Class Slide Red = w’(t) Blue =  ’(t) 5.1 Turbulence - 5

11. MT 454 Class Slide 5.1 Turbulence - 6

12. MT 454 Class Slide 5.1 Turbulence - 7

13. MT 454 Class Slide 5.1 Turbulence - 8

14. MT 454 Class Slide 5.1 Turbulence - 9

15. MT 454 Class Slide 5.1 Turbulence - 10 is the radiative heating rate. Note:

16. MT 454 Class Slide 5.1 Turbulence - 11

17. MT 454 Class Slide 5.1 Turbulence - 12

18. MT 454 Class Slide 5.1 Turbulence - 13

19. MT 454 Class Slide 5.2 TKE - 1

20. MT 454 Class Slide 5.2 TKE - 2

21. MT 454 Class Slide 5.2 TKE - 3

22. MT 454 Class Slide 5.2 TKE - 4

23. Derive TKE Equation Similarly for v’ and w’ 5.2 TKE - 5

24. MT 454 Class Slide 5.2 TKE - 6

25. MT 454 Class Slide 5.2 TKE - 7  = Frictional dissipation (molecular diffusion)  > 0 TR = Redistribution by transport & pressure forces (no new TKE created)

26. MT 454 Class Slide 5.2 TKE - 8

27. MT 454 Class Slide 5.2 TKE - 9

28. MT 454 Class Slide Analogue in large-scale flow: How does this circulation lower center of mass? 5.2 TKE - 10

29. BPL - TKE increase for unstable PBL w’ < 0  ’ < 0 w’ > 0  ’ > 0  z If PBL heated from below, then  (z): BPL > 0 Primary energy source for unstable PBL (In stable PBL, BPL term gives energy loss) 5.2 TKE - 11

30. BPL - Side Note  z More precise  (z) when well-mixed PBL is fully developed. Homogeneous, well- mixed layer Unstable layer maintained near surface by surface heating 5.2 TKE - 12

31. MT 454 Class Slide 5.2 TKE - 13

32. MT 454 Class Slide 5.2 TKE - 14

33. MT 454 Class Slide 5.2 TKE - 15

34. MT 454 Class Slide 5.2 TKE - 16

35. MT 454 Class Slide 5.2 TKE - 17

36. MT 454 Class Slide 5.2 TKE - 18

37. MT 454 Class Slide 5.2 TKE - 19

38. MT 454 Class Slide 5.3 PBL momentum

39. MT 454 Class Slide 5.3 PBL momentum

40. MT 454 Class Slide 5.3 PBL momentum

41. MT 454 Class Slide 5.3 PBL momentum

42. MT 454 Class Slide (See figures) 5.3 PBL momentum

43. MT 454 Class Slide 5.3 PBL momentum

44. MT 454 Class Slide 5.3 PBL momentum

45. MT 454 Class Slide 5.3 PBL momentum

46. MT 454 Class Slide 5.3 PBL momentum

47. MT 454 Class Slide 5.3 PBL momentum

48. MT 454 Class Slide 5.3 PBL momentum

49. MT 454 Class Slide 5.3 PBL momentum

50. MT 454 Class Slide (Add friction? See Figure 5.3 in Holton.) 5.3 PBL momentum

51. MT 454 Class Slide 5.3 PBL momentum

52. MT 454 Class Slide 5.3 PBL momentum

53. MT 454 Class Slide 5.3 PBL momentum

54. MT 454 Class Slide 5.3 PBL momentum

55. MT 454 Class Slide 5.3 PBL momentum

56. MT 454 Class Slide 5.3 PBL momentum

57. MT 454 Class Slide 5.3 PBL momentum

58. MT 454 Class Slide 5.3 PBL momentum

59. MT 454 Class Slide 5.3 PBL momentum

60. MT 454 Class Slide 5.3 PBL momentum

61. MT 454 Class Slide 5.3 PBL momentum

62. MT 454 Class Slide 5.3 PBL momentum

63. MT 454 Class Slide 5.3 PBL momentum

64. MT 454 Class Slide 5.3 PBL momentum

65. MT 454 Class Slide 5.3 PBL momentum

66. MT 454 Class Slide 5.3 PBL momentum

67. MT 454 Class Slide (See Figures 5.4 and 5.5 in Holton.) 5.3 PBL momentum

68. MT 454 Class Slide 5.3 PBL momentum

69. MT 454 Class Slide 5.3 PBL momentum

70. MT 454 Class Slide 5.3 PBL momentum

71. MT 454 Class Slide 5.3 PBL momentum

72. MT 454 Class Slide 5.3 PBL momentum

73. MT 454 Class Slide 5.3 PBL momentum

74. MT 454 Class Slide 5.3 PBL momentum

75. MT 454 Class Slide 5.3 PBL momentum

76. MT 454 Class Slide 5.3 PBL momentum

77. MT 454 Class Slide (See Fig. 5.5 in Holton + additional figures.) 5.3 PBL momentum

78. MT 454 Class Slide 5.4 Spin Down

79. Horizontal Wind in PBL In PBL, wind component toward lower pressure … L … giving horizontal convergence around low center 5.4 Spin Down MT 454

80. Vertical Wind in PBL Mass convergence around low pressure … L … gives upward motion over low. Effect on vortex? PBL top 5.4 Spin Down MT 454

81. Class Slide 5.4 Spin Down

82. MT 454 Class Slide 5.4 Spin Down

83. MT 454 Class Slide 5.4 Spin Down

84. MT 454 Class Slide 5.4 Spin Down

85. MT 454 Class Slide 5.4 Spin Down

86. MT 454 Class Slide 5.4 Spin Down

87. MT 454 Class Slide 5.4 Spin Down

88. Slowing Vortex: Vortex Compression Ekman pumping reduces vorticity in free troposphere by vortex compression: L PBL top Tropopause (w ≈ 0) 5.4 Spin Down MT 454

89. Slowing Vortex: Conservation of Angular Momentum Alternatively, outward secondary circulation in free troposphere slows vortex by conservation of angular momentum L PBL top 5.4 Spin Down MT 454

90. Class Slide 5.4 Spin Down

91. MT 454 Class Slide 5.4 Spin Down

92. MT 454 Class Slide 5.4 Spin Down

93. Spin-Down Time Use H = 10 km and previous values for other constants: Then,  e ~ 7 days Longer than synoptic time scale A reason why PBL was ignored when introducing quasi-geostrophic motion  e = H | 2/(fK m ) | 1/2 5.4 Spin Down MT 454

94. Class Slide 5.4 Spin Down

95. Ekman-Pumping: Torque Outward (secondary ) flow gives torque against primary flow by Coriolis force. L 5.4 Spin Down MT 454

96. Ekman-Pumping Effectiveness Ekman pumping more effective than diffusion: Works not by mixing high/low vorticity air Rather by forcing mass divergence in free troposphere Angular momentum = (moment of intertia) x (rotation rate) Outward mass movement => increased moment of inertia => reduced rotation to conserve angular mom. 5.4 Spin Down MT 454

97. Baroclinic Atmosphere? If atmosphere baroclinic (not barotropic): Circulation confined closer to surface Shear created in vortex => more damping closer to surface Shear balanced by induced  T: uplifted air at center cooler than air at vortex edge Final note: all rests on Ekman PBL Qualitatively OK Gives correct approximate physics (cross isobar flow) 5.4 Spin Down MT 454

98. Chapter 5 – Planetary Boundary Layer MT 454 END