cumulus clouds. what goes on inside a cumulus cloud?

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Cumulus Clouds

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Page 1: Cumulus Clouds. What goes on inside a cumulus cloud?

Cumulus Clouds

Page 2: Cumulus Clouds. What goes on inside a cumulus cloud?

What goes on inside a cumulus cloud?

Page 3: Cumulus Clouds. What goes on inside a cumulus cloud?

Conceptual Model

• Series of convective plumes rising to form individual turrets comprising cloud

• Each rising pulse a toroidal circulation

• Successive toroids give rise to mean upward current called updraft

• Sustained downward current between toroids, if existing, would be downdraft

Page 4: Cumulus Clouds. What goes on inside a cumulus cloud?
Page 5: Cumulus Clouds. What goes on inside a cumulus cloud?

Liquid Water Content

Page 6: Cumulus Clouds. What goes on inside a cumulus cloud?

What causes liquid water content to be below adiabatic LWC?

• Lateral entrainment– Neutral mixing– Dynamic entrainment

• Cloud Top Entrainment

Page 7: Cumulus Clouds. What goes on inside a cumulus cloud?

Bubble and JetModels of Convection

<= mixing lateral entrainment

Page 8: Cumulus Clouds. What goes on inside a cumulus cloud?

Dynamic Lateral Entrainment

Page 9: Cumulus Clouds. What goes on inside a cumulus cloud?

Dynamic Entrainment

Page 10: Cumulus Clouds. What goes on inside a cumulus cloud?

Effects of Dynamic Lateral Entrainment

Page 11: Cumulus Clouds. What goes on inside a cumulus cloud?

Effects of Dynamic Lateral Entrainment

Page 12: Cumulus Clouds. What goes on inside a cumulus cloud?

Cloud Top entrainment

Page 13: Cumulus Clouds. What goes on inside a cumulus cloud?

Deep Cumulus

• Must consider impact of precipitation on cumulus circulation

• Must consider pressure effects because of cloud depth– Thermodynamic pressure, ie hydrostatic pressure

– Dynamic pressure due to inertia of air motions

• Friction layer small compared to cloud and we generally ignore friction

Page 14: Cumulus Clouds. What goes on inside a cumulus cloud?

Vertical Acceleration(using Pressure)

31 1 2 2 2 1

'

3

'

( ) ( )

1

i

o

u kf u f u

t x

p

x

g

Inertia

Pressure

Buoyancy

Page 15: Cumulus Clouds. What goes on inside a cumulus cloud?

Vertical Acceleration(Using Total Pressure)

31 1 2 2 2 1

3

( ) ( )

1i

u kf u f u

t x

p

x

g

Inertia

Pressure

Buoyancy

Page 16: Cumulus Clouds. What goes on inside a cumulus cloud?

Vertical Acceleration(using Exner function)

31 1 2 2 2 1

'

3

'

( ) ( )i

o

vv

o

u kf u f u

t x

x

g

Inertia

Pressure

Buoyancy

Page 17: Cumulus Clouds. What goes on inside a cumulus cloud?

Traditional Buoyancy

'

1 0.61 1vvv l i o

o o

gg q q q

| | | |

Warm/Cold air rises/sinks

Vapor less dense than dry air

Liquid water loading

Ice water loading

Page 18: Cumulus Clouds. What goes on inside a cumulus cloud?

Anelastic Approximation• Neglect frequencies higher than those

associated with meteorological phenomena such as sound wave frequencies

• Similar to incompressible assumption, but for a compressible system

0 (anelastic approximation)

or

0

i

i

i i

i

i

u

x

u ux tt x

Page 19: Cumulus Clouds. What goes on inside a cumulus cloud?

Continuity Equation

t

j

j

j jj

j j j

ud

dt x

u uu

x x x

Page 20: Cumulus Clouds. What goes on inside a cumulus cloud?

Multiply momentum equation (momentum form) by density:

3

3

3

1( )

1

hence,

ji i ii i

j

ijk j j k ii i

ij ijk j k i

j i

i jiijk j k i

i j

uu u uu u

t t t t x

k pf u g

x x

u pu f u g

x x

u uu pf u g

t x x

Page 21: Cumulus Clouds. What goes on inside a cumulus cloud?

Multiply momentum equation (vorticity form) by density:

3

1( )

hence,

ji i ii i

j

ijk j j k ii i

jii

j

uu u uu u

t t t t x

k pf u g

x x

uuu

t x

3

3

( )

( )

ijk j j k ii i

ijk j j k ii i

k pf u g

x x

k pf u g

x x

Page 22: Cumulus Clouds. What goes on inside a cumulus cloud?

Decomposition of Pressure into Dynamic and Buoyancy Pressure

u

v

w w

u pDynamic

t x

v pDynamic

t y

w pDynamic Buoyancy

t z

Page 23: Cumulus Clouds. What goes on inside a cumulus cloud?

Dynamics (or inertia) Terms

2 2 3 3 3 21

1 1 3 3 3 12

1 1 2 2 2 13

( ) ( )

( ) ( )

( ) ( )

u

v

w

kDynamic f u f u

x

kDynamic f u f u

x

kDynamic f u f u

x

Page 24: Cumulus Clouds. What goes on inside a cumulus cloud?

Buoyancy Terms

1

where

w

d v l i

m l i

m d v

ll

m

ii

m

Buoyancy g

g

g q q

q

q

Page 25: Cumulus Clouds. What goes on inside a cumulus cloud?

Take divergence of density multiplied by three momentum equations and then result set to zero and

solve for pressure:

2 u v u wDynamic Dynamic Dynamic Buoyancyp

x y z z

or

2

2

''

u v ud

wb

o o d b

Dynamic Dynamic Dynamicp

x y z

Buoyancyp

z

p p p p p p

Where pressure is divided into dynamic and buoyancy pressure contributions

Page 26: Cumulus Clouds. What goes on inside a cumulus cloud?

Buoyancy vs. Dynamic Pressure

• Dynamic pressure, , is zero if flow is at rest.• Buoyancy pressure, , is hydrostatic pressure for flow

at rest.• Dynamic pressure results from inertia such as:

– Rotation (cyclostrophic pressure)– Straight line accelerations – Coordinate system accelerations (coriolis)

• Buoyancy pressure results from:– Moisture anomalies– Thermal anomalies– Condensate (precipitation drag)

dpbp

Page 27: Cumulus Clouds. What goes on inside a cumulus cloud?

Real Buoyancy Acceleration

• True buoyancy acceleration is :

• Where we see the acceleration is caused by thermal, moisture or precipitation drag anomalies

'1true buoyancy acceleration = b

o

p

z

Page 28: Cumulus Clouds. What goes on inside a cumulus cloud?

Dynamic Pressure Acceleratrion

• True dynamic pressure gradient acceleration is :

• Where we see the acceleration is caused by inertial effects of rotation, straight line movement and coordinate system movement

1dynamic pressure acceleration = d

o

p

z

Page 29: Cumulus Clouds. What goes on inside a cumulus cloud?

Conditional Instability of the First Kind

• Occurs when a parcel is statically unstable when saturated but stable when dry

• Results in the formation of moist convective thermal plumes, ie cumulus clouds

• Instability favors horizontal scales ~ vertical scale of overturning, i.e. meso-gamma scale for deep convection

Page 30: Cumulus Clouds. What goes on inside a cumulus cloud?

Three Stages of a Deep Convective Thermal

• Simplest Case:– Conditionally unstable for deep convection– No environmental wind– Dry middle layers– Moist unstable boundary layer

Page 31: Cumulus Clouds. What goes on inside a cumulus cloud?

Stage 1 : Cumulus Stage

• Updraft only• Cloud droplets only (no precipitation)• Level of Non-divergence (LND) near top of moist Planetary Boundary

Layer (PBL) • Cloud positively buoyant throughout:

• Environment neutrally buoyant• Low pressure under updraft• High pressure throughout cloud

'' 1

>0 or more precisely, 0bvv

p

z

Page 32: Cumulus Clouds. What goes on inside a cumulus cloud?
Page 33: Cumulus Clouds. What goes on inside a cumulus cloud?

Stage 2 : Mature Stage

• Updraft and downdraft• Precipitation and cloud droplets throughout cloud• Level of Non-divergence (LND) at middle levels • Cloud positively buoyant at middle levels,

negatively buoyant in lower part• Cold air dome (density current) at surface• Environment neutrally buoyant but warming• Low pressure at middle levels• High pressure at surface and top of cloud

Page 34: Cumulus Clouds. What goes on inside a cumulus cloud?
Page 35: Cumulus Clouds. What goes on inside a cumulus cloud?

Stage 3 : Dissipating Stage

• Downdraft only• Precipitation only throughout cloud• Level of Non-divergence (LND) at upper levels • Cloud negatively buoyant throughout• Environment positively buoyant• Low pressure at middle levels and above in cloud• High pressure at surface• Low pressure at surface of environment

Page 36: Cumulus Clouds. What goes on inside a cumulus cloud?
Page 37: Cumulus Clouds. What goes on inside a cumulus cloud?

Reasons for Breakdown

• Water loading of updraft from precipitation drag

• Cooling due to dynamic entrainment of mid level dry air

Page 38: Cumulus Clouds. What goes on inside a cumulus cloud?

Introduce Environmental Wind Shear to Prevent Breakdown

• Assume:– two-dimensions, i.e. infinitely long convective

line– Straight-line shear with height, I.e. wind speed

change with without direction change

Page 39: Cumulus Clouds. What goes on inside a cumulus cloud?
Page 40: Cumulus Clouds. What goes on inside a cumulus cloud?

Three-Dimensional Effect of Wind Shear

• As before but now assume convective plume is initially circular rather than infinitely long

• Also start by assuming a straight line shear profile again

• Assume westerly shear and veering winds in lowest 6 km

Page 41: Cumulus Clouds. What goes on inside a cumulus cloud?

View from South

Page 42: Cumulus Clouds. What goes on inside a cumulus cloud?

View from East

Page 43: Cumulus Clouds. What goes on inside a cumulus cloud?

Helicity

j jH u

Page 44: Cumulus Clouds. What goes on inside a cumulus cloud?

Convective Richardson Number

212 i

CAPER

u

Page 45: Cumulus Clouds. What goes on inside a cumulus cloud?

CAPE

( ) ( )

( )

z zCAPE g dz

a

Page 46: Cumulus Clouds. What goes on inside a cumulus cloud?

Wind Shear

6

06

0

km

i

i km

u dz

u

dz