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

Copyright © 2012 R. R. Dickerson & Z.Q. Li 2 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.

Copyright © 2013 R. R. Dickerson & Z.Q. Li 3 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

Copyright © 2012 R. R. Dickerson & Z.Q. Li 4

Copyright © 2013 R. R. Dickerson & Z.Q. Li 5 Substituting in the values for each individual heat transfer and rearranging: With no entrainment (dm = 0) we recover the parcel theory result: 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.

Copyright © 2013 R. R. Dickerson & Z.Q. Li 6 If instead of solving for  we solved for –dT/dz; we obtain

Copyright © 2013 R. R. Dickerson & Z.Q. Li 7 An Example from Hess P = 700 mb; T ’ = -1 o C at cloud level T = 0 o C; f’ = 67% of f in the cloud.

Copyright © 2013 R. R. Dickerson & Z.Q. Li 8 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……

Copyright © 2013 R. R. Dickerson & Z.Q. Li 9 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.

Copyright © 2013 R. R. Dickerson & Z.Q. Li 10

Copyright © 2013 R. R. Dickerson & Z.Q. Li 11

Copyright © 2013 R. R. Dickerson & Z.Q. Li 12 Moderate Gale with Heavy Clouds, a Pilot Boat Working its way out to a Waiting Brig C. W. Eckersberg, 1831 Ny Carlsberg Glyptotek, Copenhagen

Copyright © 2013 R. R. Dickerson & Z.Q. Li 13 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.

Copyright © 2013 R. R. Dickerson & Z.Q. Li 14 Life Cycle of a Cumulus Cloud 1. Initial Ascent Buoyant bubble Cumulus mass Spherical cap Bubble motion Adiabatic descent

Copyright © 2013 R. R. Dickerson & Z.Q. Li 15 Cumulus mass Turbulent wake Erosion of cap Lateral mixing and entrainment 2. Erosion of spherical cap and mixing of ambient and bubble air.

Copyright © 2013 R. R. Dickerson & Z.Q. Li Extension of Cumulus mass Initial mass Spherical cap completely eroded and no longer buoyant. Cloud mass evaporating

Copyright © 2013 R. R. Dickerson & Z.Q. Li 17 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.

Copyright © 2012 R. R. Dickerson & Z.Q. Li 18 Cumuli and Horizontal Winds z z wind Wake carried downstream Greatest vertical growth is on down-shear side. ~ Verified by observation ~

Copyright © 2013 R. R. Dickerson & Z.Q. Li 19

Micro-Pulse Lidar Network (MPLNET) MPLNET Status E.J. Welton, NASA GSFC Code /01/08 Principal Investigator: Judd Welton, NASA GSFC Code Data Processing & Analysis: Larry Belcher, UMBC GSFC Code James Campbell, University of Alaska - Fairbanks Instrumentation & Network Management: Tim Berkoff, UMBC GSFC Code Sebastian Stewart, SSAI GSFC Code GLAS Validation Activities: Jim Spinhirne, NASA GSFC Code Judd Welton, Tim Berkoff CALIPSO Validation Activities: Judd Welton, Tim Berkoff, James Campbell AERONET & Synergy Tool Partnership: Brent Holben, NASA GSFC Code Dave Giles, NASA GSFC Code NASA SMART-COMMIT Field Deployments: Si-Chee Tsay, Jack Ji, Site Operations & Science Investigations …. many network partners around the world MPLNET is funded by the NASA Radiation Sciences Program and the Earth Observing System MPLNET information and results shown here are the result of efforts by all of our network partners!

Micro-Pulse Lidar Network (MPLNET) MPLNET Status E.J. Welton, NASA GSFC Code /01/08 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 MPLNET Level 1 Signals: GSFC May 3, 2001 Uncalibrated Attenuated Backscatter (km sr)-1

Micro-Pulse Lidar Network (MPLNET) MPLNET Status E.J. Welton, NASA GSFC Code /01/ MPLNET Level 1 Signals: GSFC May 3, 2001 Uncalibrated Attenuated Backscatter (km sr)-1

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

Micro-Pulse Lidar Network (MPLNET) MPLNET Status E.J. Welton, NASA GSFC Code /01/08 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