copyright © 2012 r. r. dickerson & z.q. li 1 620 lecture10: dilution by entrainment lateral...

Copyright © 2012 R. R. Dickerson & Z.Q. Li

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620 Lecture10: Dilution by Entrainment

Lateral entrainment: mix cooler, drier air through cloud’s lateral boundaries. The cloud is warmer than surroundings and actively growing.

Effects: Reduce T – T’ Reduce w


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Cloudy Air of mass m consists of dry air, water vapor, and condensed water.

Assume that as cloudy air ascends a distance dz, a mass dm of environmental air is entrained. Condensed water in the cloud will evaporate in response to the entrainment of drier air.

Primes will denote properties of ambient (environmental) air.


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Heat Required to warm the entrained air from T’ to T:

(neglect heat content of vapor and liquid)

Assume that just enough condensate evaporates to saturate the mixture. Let


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Substituting in the values for each individual heat transfer and rearranging:

m

dmww

Tc

LB

Tc

dwLds

p

v

p

sv

)(

With no entrainment (dm = 0) we recover the parcel theory result:

Tc

dwLd

p

sv

So for a bouyant parcel with entrainment, we see that the magnitude of d is larger than the pure parcel result.

Temperature falls off at a faster rate: buoyancy is impaired.


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If instead of solving for we solved for –dT/dz; we obtain

unstable.ly convective

be tocloud entrainingan for Then

TT and 0 if So

1

)()(1

s

2

2

dz

dm

Tw

RcL

wwcL

TT

dz

dm

mdz

dT

s

p

v

sp

v

s


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An Example from Hess

P = 700 mb; T’ = -1oC at cloud levelT = 0oC; f’ = 67% of f in the cloud.

125.01 km

dz

dm

m

kmC

kmCdz

dT

s

p

/8.5 whereas

/6.6


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Aircraft observations show T ~ T’ in many clouds. It is possible to integrate to find m(z) for specified p and f. Results show the cloud mass may easily double or triple in a few km of ascent. Lab measurements of man-made buoyant plumes bear out the theory.

But there’s a problem……


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Theory

z

Growth with lateral entrainment

Observed in Sky

The observations suggest downdrafts within cloud which dilute by entrainment of dry ambient air above cloud top.


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Moderate Gale with Heavy Clouds, a Pilot Boat Working its way out to a Waiting Brig

C. W. Eckersberg, 1831

Ny Carlsberg Glyptotek, Copenhagen


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Bubble Theory

Observations of cumuli indicate towers grow for a while, lose their impetus and are succeeded by new ones. This phenomena led Scorer (1958) to propose what is known as the “Bubble Theory” of convection.


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Life Cycle of a Cumulus Cloud

1. Initial Ascent

Buoyantbubble

Cumulusmass

Spherical cap

Bubble motion

Adiabaticdescent


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Cumulusmass

Turbulentwake

Erosion of cap

Lateral mixingand entrainment

2. Erosion of spherical cap and mixing of ambient and bubble air.


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3. Extension of Cumulus mass

Initial mass

Spherical cap completely eroded and no longer buoyant.

Cloud massevaporating


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Net Result of Bubble Cycle

The bubble has enriched the ambient air above the original cloud (moistened the environment). Thus the next bubble can penetrate further than the first. Successive bubbles extend the cloud further in the vertical direction.


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Micro-Pulse Lidar Network (MPLNET)

MPLNET Status E.J. Welton, NASA GSFC Code 613.1 02/01/08

Principal Investigator:Judd Welton, NASA GSFC Code 613.1

Data Processing & Analysis:Larry Belcher, UMBC GSFC Code 613.1

James Campbell, University of Alaska - Fairbanks

Instrumentation & Network Management:Tim Berkoff, UMBC GSFC Code 613.1

Sebastian Stewart, SSAI GSFC Code 613.1

GLAS Validation Activities:Jim Spinhirne, NASA GSFC Code 613.1

Judd Welton, Tim Berkoff

CALIPSO Validation Activities:Judd Welton, Tim Berkoff, James Campbell

AERONET & Synergy Tool Partnership:Brent Holben, NASA GSFC Code 614.4Dave Giles, NASA GSFC Code 614.4

NASA SMART-COMMIT Field Deployments:Si-Chee Tsay, 613.2

Jack Ji, 613.2

Site Operations & Science Investigations…. many network partners around the world

MPLNET is funded by the NASA Radiation SciencesProgram and the Earth Observing System

MPLNET information and results shown here are theresult of efforts by all of our network partners!



Lidar identifies the height, structure, and growth/decay of the planetary boundary layer (PBL)

• The concentration of pollutants in the PBL, and its height, dictate surface air quality

• The PBL controls the transfer of material and energy between the surface and troposphere.

1.0

0.5

0.0

MPLNET Level 1 Signals: GSFC May 3, 2001Uncalibrated Attenuated Backscatter (km sr)-1



1.0

0.5

0.0

From 500 m resolution WRF run (D-L Zhang)



MPLNET Data Products:

(new version 2 release)

Level 1: Lidar Signals

• 1 minute, 75 meters

• near real time - next day

Zoom in to 8 km

Level 1.5b: Layer Heights

• 1 minute gridded product

• near real time - next day

Focus on PBL & Aerosols

** 1.5 products are not quality assured

copyright © 2012 r. r. dickerson & z.q. li 1 620 lecture10: dilution by entrainment lateral...

Documents

cloud mass evaporating

copenhagen slide

w slide

problem slide

bubble air

cumulus cloud

cloudy air of mass

entrainment of drier