Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.
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Transcript of Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.
![Page 1: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/1.jpg)
Chapter 5 - PBL MT 454
Material Based on Chapter 5
The Planetary Boundary Layer
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MT 454
Class Slide
The Planetary Boundary Layer
Chapter 5 - PBL
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MT 454
Class Slide
Chapter 5 - PBL
![Page 4: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/4.jpg)
MT 454
Class Slide
Chapter 5 - PBL
![Page 5: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/5.jpg)
MT 454
Class Slide
Chapter 5 - PBL
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5.1 Turbulence - 1
MT 454
Class Slide
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5.1 Turbulence - 2
MT 454
Class Slide
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MT 454
Class Slide
5.1 Turbulence - 3
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MT 454
Class Slide
5.1 Turbulence - 4
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MT 454
Class Slide
Red = w’(t)Blue = ’(t)
5.1 Turbulence - 5
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MT 454
Class Slide
5.1 Turbulence - 6
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MT 454
Class Slide
5.1 Turbulence - 7
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MT 454
Class Slide
5.1 Turbulence - 8
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MT 454
Class Slide
5.1 Turbulence - 9
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MT 454
Class Slide
5.1 Turbulence - 10
is the radiative heating rate.Note:
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MT 454
Class Slide
5.1 Turbulence - 11
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MT 454
Class Slide
5.1 Turbulence - 12
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MT 454
Class Slide
5.1 Turbulence - 13
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MT 454
Class Slide
5.2 TKE - 1
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MT 454
Class Slide
5.2 TKE - 2
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MT 454
Class Slide
5.2 TKE - 3
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MT 454
Class Slide
5.2 TKE - 4
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Derive TKE EquationDerive TKE Equation
Similarly for vSimilarly for v’’ and w and w’’Similarly for vSimilarly for v’’ and w and w’’5.2 TKE - 5
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MT 454
Class Slide
5.2 TKE - 6
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MT 454
Class Slide
5.2 TKE - 7
= Frictional dissipation (molecular diffusion) > 0
TR = Redistribution by transport & pressure forces(no new TKE created)
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MT 454
Class Slide
5.2 TKE - 8
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MT 454
Class Slide
5.2 TKE - 9
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MT 454
Class Slide
Analogue in large-scale flow:
How does this circulation lower center of mass?
5.2 TKE - 10
![Page 29: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/29.jpg)
BPL - TKE increase for unstable PBLBPL - 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
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BPL - Side NoteBPL - 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
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MT 454
Class Slide
5.2 TKE - 13
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MT 454
Class Slide
5.2 TKE - 14
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MT 454
Class Slide
5.2 TKE - 15
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MT 454
Class Slide
5.2 TKE - 16
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MT 454
Class Slide
5.2 TKE - 17
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MT 454
Class Slide
5.2 TKE - 18
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MT 454
Class Slide
5.2 TKE - 19
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
![Page 42: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/42.jpg)
MT 454
Class Slide
(See figures)
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
![Page 49: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/49.jpg)
MT 454
Class Slide
5.3 PBL momentum
![Page 50: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/50.jpg)
MT 454
Class Slide
(Add friction? See Figure 5.3 in Holton.)
5.3 PBL momentum
![Page 51: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/51.jpg)
MT 454
Class Slide
5.3 PBL momentum
![Page 52: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/52.jpg)
MT 454
Class Slide
5.3 PBL momentum
![Page 53: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/53.jpg)
MT 454
Class Slide
5.3 PBL momentum
![Page 54: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/54.jpg)
MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
![Page 58: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/58.jpg)
MT 454
Class Slide
5.3 PBL momentum
![Page 59: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/59.jpg)
MT 454
Class Slide
5.3 PBL momentum
![Page 60: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/60.jpg)
MT 454
Class Slide
5.3 PBL momentum
![Page 61: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/61.jpg)
MT 454
Class Slide
5.3 PBL momentum
![Page 62: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/62.jpg)
MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
![Page 66: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/66.jpg)
MT 454
Class Slide
5.3 PBL momentum
![Page 67: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/67.jpg)
MT 454
Class Slide
(See Figures 5.4 and 5.5 in Holton.)
5.3 PBL momentum
![Page 68: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/68.jpg)
MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
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MT 454
Class Slide
5.3 PBL momentum
![Page 77: Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697c00a1a28abf838cc7789/html5/thumbnails/77.jpg)
MT 454
Class Slide
(See Fig. 5.5 in Holton + additional figures.)
5.3 PBL momentum
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MT 454
Class Slide
5.4 Spin Down
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Horizontal Wind in PBLHorizontal Wind in PBL
In PBL, wind component toward lower pressure …
LL
v g
v
… giving horizontal convergence around low center
5.4 Spin Down MT 454
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Vertical Wind in PBLVertical Wind in PBL
Mass convergence around low pressure …
LL
… gives upward motion over low. Effect on vortex?
PBL top
5.4 Spin Down MT 454
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MT 454
Class Slide
5.4 Spin Down
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MT 454
Class Slide
5.4 Spin Down
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MT 454
Class Slide
5.4 Spin Down
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MT 454
Class Slide
5.4 Spin Down
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MT 454
Class Slide
5.4 Spin Down
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MT 454
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MT 454
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Slowing Vortex: Vortex CompressionSlowing Vortex: Vortex Compression
Ekman pumping reduces vorticity in free troposphere by vortex compression:
LLPBL top
Tropopause(w ≈ 0)
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Slowing Vortex: Conservation of Angular MomentumSlowing Vortex: Conservation of Angular Momentum
Alternatively, outward secondary circulation in free troposphere slows vortex by conservation of angular momentum
LLPBL top
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MT 454
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MT 454
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Spin-Down TimeSpin-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/(fKm) |1/2
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Ekman-Pumping: TorqueEkman-Pumping: Torque
Outward (secondary ) flow gives torque against primary flow by Coriolis force.
LL
v 1
v 2
fˆ k v 2
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Ekman-Pumping EffectivenessEkman-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.
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Baroclinic Atmosphere?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)
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Chapter 5 – Planetary Boundary Layer MT 454
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