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

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

MT 454 Class Slide Chapter 5 - PBL

MT 454 Class Slide Chapter 5 - PBL

MT 454 Class Slide Chapter 5 - PBL

5.1 Turbulence - 1 MT 454 Class Slide

5.1 Turbulence - 2 MT 454 Class Slide

MT 454 Class Slide 5.1 Turbulence - 3

MT 454 Class Slide 5.1 Turbulence - 4

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

MT 454 Class Slide 5.1 Turbulence - 6

MT 454 Class Slide 5.1 Turbulence - 7

MT 454 Class Slide 5.1 Turbulence - 8

MT 454 Class Slide 5.1 Turbulence - 9

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

MT 454 Class Slide 5.1 Turbulence - 11

MT 454 Class Slide 5.1 Turbulence - 12

MT 454 Class Slide 5.1 Turbulence - 13

MT 454 Class Slide 5.2 TKE - 1

MT 454 Class Slide 5.2 TKE - 2

MT 454 Class Slide 5.2 TKE - 3

MT 454 Class Slide 5.2 TKE - 4

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

MT 454 Class Slide 5.2 TKE - 6

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

MT 454 Class Slide 5.2 TKE - 8

MT 454 Class Slide 5.2 TKE - 9

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

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

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

MT 454 Class Slide 5.2 TKE - 13

MT 454 Class Slide 5.2 TKE - 14

MT 454 Class Slide 5.2 TKE - 15

MT 454 Class Slide 5.2 TKE - 16

MT 454 Class Slide 5.2 TKE - 17

MT 454 Class Slide 5.2 TKE - 18

MT 454 Class Slide 5.2 TKE - 19

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide (See figures) 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

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

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

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

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

MT 454 Class Slide 5.3 PBL momentum

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

MT 454 Class Slide 5.4 Spin Down

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

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

Class Slide 5.4 Spin Down

MT 454 Class Slide 5.4 Spin Down

MT 454 Class Slide 5.4 Spin Down

MT 454 Class Slide 5.4 Spin Down

MT 454 Class Slide 5.4 Spin Down

MT 454 Class Slide 5.4 Spin Down

MT 454 Class Slide 5.4 Spin Down

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

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

Class Slide 5.4 Spin Down

MT 454 Class Slide 5.4 Spin Down

MT 454 Class Slide 5.4 Spin Down

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

Class Slide 5.4 Spin Down

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

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

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

Chapter 5 – Planetary Boundary Layer MT 454 END