PHYS575CSI655 Introduction to Atmospheric Physics and Chemistry Lecture Notes

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PHYS-575/CSI-655Introduction to Atmospheric
Physics and ChemistryLecture Notes 6Cloud
Microphysics Part 1
Overview of Clouds 1. Nucleation of Water
Vapor 2. Warm Clouds 3. Water Content and
Entrainment 4. Droplet Growth (Warm Clouds) 5.
Microphysics of Cold Clouds 6. Artificial
Modification of Clouds 7. Thunderstorm
Electrification 8. Cloud and Precipitation
Chemistry
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Announcements April 2, 2007

• Office Hours Monday-300-500 pm, by
  appointment
• (other times possible)
• Homework 4
• 5.12, 5.14, 5.18 (make table, show work),
  5.19, 5.24
• Due April 2
• Homework 5 (Assigned early due to second exam)
• Part 1 6.8 a, b, d, f, I, k, n, r, s,
  t, x, bb
• Part 2 Clouds Homework Clouds in a
  Glass of Beer (Bohren
• article) and Physics Today article.
• Due April 16
• Exam 2 April 16
• Instructor Travel
• April 3-6
• April 19-20
• April 24-26

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Overview of Clouds
When the temperature in the Earths atmosphere
drops below the condensation temperature, water
vapor condenses or freezes out the numerous
water droplets and/or ice crystals make up clouds.

• Influences of Clouds
• Reflect and absorb solar radiation
• Reflect and absorb terrestrial radiation
• Latent heat release ? atmospheric heating

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Cloud Types
Cloud types are usually classified grouped into
"low", "middle", and "high" clouds, referring to
the altitudes they occur at. "Low" clouds are
generally below about 6,500 ft. "Middle" clouds
range from about 6,500 ft to 20,000 ft, and high
clouds range between 20,000 and 40,000 feet in
altitude. As seen in the photos above, low clouds
include cumulus, stratus, and stratocumulus
middle clouds include altocumulus and
altostratus and high clouds include cirrus,
cirrocumulus, and cirrostratus. If low stratus
clouds are raining, they are usually called
nimbostratus. Cumulonimbus clouds (thunderstorms)
often span all three cloud heights, with bases
from 1,000 to 5,000 feet and tops sometimes
reaching 60,000 feet.
http//www.weatherquestions.com/cloud_types.jpg
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Earths Highest Clouds Noctilucent Clouds
From Observing Noctilucent Clouds by M. Gadsden
and P. Parviainen IAGA, 1995
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Noctilucent Clouds
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AIM Aeronomy of Ice in the MesosphereAre
Noctilucent Clouds the miners canary of Global
Change?
Launch Date 3/29/07
http//aim.hamptonu.edu/
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Clouds on Other Planets
Methane (CH4) Hydrocarbons
Sulfuric Acid (H2SO4)
Water, Carbon Dioxide
CH4 various Hydrocarbons, Carbon vapor
CH4, Ammonia (NH3), Ammonium Sulfate (NH4SH), He
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Formation of Water Vapor Clouds on Earth
http//www.tonya.me.uk/Marine/graphics/clouds/clou
ds1.gif
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1. Nucleation and Water Vapor Condensation
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Vertical Motion and Condensation
Upward motion leads to cooling, via the FLT.
Cooling increases the relative humidity. When
the relative humidity exceeds 100,
then condensation will occur.
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Homogeneous Nucleation Theory
Start with a moist parcel of clean air and let it
cool (say, by moving it vertically). Drops do not
form immediately upon super-saturation, but drop
embryos are formed by chance collisions of water
molecules. Sticking tends to stabilize the
embryos, but thermal motion tends to disrupt
them. To form an embryo that is stable, the drop
must be a critical size which is more
energetically stable than the same amount of
water in the vapor phase, otherwise the embryo
will re-evaporate and disappear due to thermal
agitation. Gibbs Free Energy (G) is a measure of
both energy and entropy. Minimizing G will
simultaneously minimize energy and maximize
entropy just what is required for a stable
system. Enthalpy (U PV) is a thermodynamic
variable. G H TS U PV TS
? dG dU TdS SdT
PdV VdP FLT TdS dU PdV
? dG - SdT VdP In equilibrium dG 0 The
key is to write dG in terms of the properties of
the drop embryo.
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Homogeneous Nucleation - continued
dG - SdT VdP
Consider a constant temperature system (liquid
vapor) where the partial pressure of the liquid
varies from e to e de. IGL ?
eVv RvT Vapor dGv Vvde Liquid
dGl Vlde V is the specific volume Vv gtgt
Vl, and the IDL for the vapor Vv RvT/e, so
d(Gv - Gl) (Vv Vl) de Vvde
RvT (de/e) RvT d(ln e) Integration (fixed T)
gives Gv(T,e) Gl(T,e)
RvT (ln e) constant At equilibrium, e es(T),
so the constant - RvT (ln es)
Gv(T,e) Gl(T,e) RvT ln (e/es)
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Saturation Vapor PressureClausius-Clapeyron
Equation of State
es(T) CL e-Ls/RT
es(T) Saturation vapor pressure at
temperature T CL constant (depends upon
condensable) Ls Latent Heat R Gas constant
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Homogeneous Nucleation - Continued
Initially, before a drop forms, the total G0
Gv(T,e)M0 where M0 total mass At some time
later we have a droplet of radius R and mass Ml
4/3 pR3?l The total G of the system, including
energy in the form of surface tension s (surface
energy per unit area), is G Gv(T,e)Mv
Gl(T,e)Ml s 4pR2 By conservation of mass, Mv
M0 Ml, so the change in Gibbs Free Energy G
G0 (Gl Gv) Ml s 4pa2 Finally we get
G G0 - 4/3 pR3 ?l RvT ln e/es(T) s
4pR2 Or as in the text ?E ?G s 4pR2
4/3 pR3 nkT ln(e/es)
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Homogeneous Nucleation - Continued
Thus the change in Gibbs Free Energy in the
formation of a droplet of radius R, is given by
?E s 4pR2 - 4/3 pR3 nkT ln(e/es)
For unsaturated conditions, droplets arent
stable and thus evaporate. For saturated and
supersaturated conditions, droplets above a
critical radius r, are stable and subsequently
grow.
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Homogeneous Nucleation Critical Size for Growth
?E s 4pR2 - 4/3 pR3 nkT ln(e/es)
To find the critical size for which growth is
more stable than evaporation Set d(?E)/dR 0
and solve for the value of R The Critical
Radius
Kelvins Equation
For saturated and supersaturated conditions,
droplets above the critical radius R, are
stable and subsequently grow. Given a radius r,
we can calculate the vapor pressure of water
vapor for which growth is possible.
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Size of Stable Drop Embryos
Typical super-saturation in the atmosphere is
only about 101 relative humidity. Thus droplets
must be about 0.1 microns in size to be
stable. This requires about 106 water molecules.
However, the critical radius can be arbitrarily
small for a pre-existing, hydrophilic,
atmospheric particle. Thus heterogeneous
nucleation is the dominant source of water
droplets in the atmosphere.
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Supersaturation Near Droplets
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Cloud Condensation Nuclei
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Cloud Condensation Nuclei (CCN)
CCN are pre-existing atmospheric particles that
come from a large variety of sources Dust Volcan
oes Factory smoke Fires and soot Sea
Salt Di-methyl Sulfate (Phytoplankton) Abundance
ranges from 103-105 per cubic centimeter, larger
over continents and urban areas. Two
Types Hydrophilic/Hydroscopic water sticks
readily Hydrophobic repels water
http//apollo.lsc.vsc.edu/classes/met130/notes/cha
pter6/ccn.html

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Aerosol Particle Sizes Bi-modal Distributions
http//www.defra.gov.uk/environment/airquality/aqs
/air_measure/images/02.gif
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2. Microstructures of Warm Clouds
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Cloud Optical Thickness
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Ship Tracks
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3. Cloud Liquid Water Content and Entrainment
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Cumulus Cloud Entrainment
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Model Simulation of Entrainment
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Questions for Discussion

• Is precipitation possible without CCN?
• Why does the relative humidity rarely exceed
  101?
• If precipitation did not occur, how would vapor
  be lost from the atmosphere?
• Is growth of an ice particle the same as growth
  of a liquid water droplet?