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PHYS-575/CSI-655PHYS-575/CSI-655Introduction to Atmospheric Physics and Introduction to Atmospheric Physics and

ChemistryChemistryLecture Notes #6Lecture Notes #6

Cloud Microphysics – Part 1Cloud Microphysics – Part 1Overview of Clouds1. Nucleation of Water Vapor2. Warm Clouds3. Water Content and Entrainment4. Droplet Growth (Warm Clouds)5. Microphysics of Cold Clouds6. Artificial Modification of Clouds7. Thunderstorm Electrification8. Cloud and Precipitation Chemistry

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Announcements: April 2, 2007Announcements: April 2, 2007 Office Hours: Monday-3:00-5:00 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 TravelApril 3-6April 19-20April 24-26

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Overview of CloudsOverview of CloudsWhen the temperature in the Earth’s 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:(1) Reflect and absorb solar radiation(2) Reflect and absorb terrestrial radiation(3) Latent heat release atmospheric heating

04/22/23 4 http://www.weatherquestions.com/cloud_types.jpg

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.

Cloud Types

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Earth’s Highest Clouds: Noctilucent Earth’s Highest Clouds: Noctilucent CloudsClouds

From “Observing Noctilucent Clouds” by M. Gadsden and P. ParviainenIAGA, 1995

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Noctilucent CloudsNoctilucent Clouds

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AIM: Aeronomy of Ice in the MesosphereAIM: Aeronomy of Ice in the MesosphereAre Noctilucent Clouds the “miner’s canary” of Are Noctilucent Clouds the “miner’s canary” of

Global Change?Global Change?

http://aim.hamptonu.edu/

Launch Date: 3/29/07

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Clouds on Other PlanetsClouds on Other Planets

Sulfuric Acid (H2SO4) Water, Carbon DioxideMethane (CH4) &Hydrocarbons

CH4, Ammonia (NH3),Ammonium Sulfate (NH4SH), He

CH4 + variousHydrocarbons,Carbon vapor

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Formation of Water Vapor Clouds on EarthFormation of Water Vapor Clouds on Earth

http://www.tonya.me.uk/Marine/graphics/clouds/clouds1.gif

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1. Nucleation and Water Vapor 1. Nucleation and Water Vapor CondensationCondensation

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Vertical Motion and CondensationVertical Motion and Condensation

Upward motion leads to cooling, via the FLT. Cooling increases therelative humidity. When the relative humidity exceeds 100%, thencondensation will occur.

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Homogeneous Nucleation TheoryHomogeneous Nucleation TheoryStart 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 areformed by chance collisions of water molecules. Sticking tends to stabilizethe embryos, but thermal motion tends to disrupt them. To form an embryo thatis stable, the drop must be a critical size which is more energetically stable thanthe 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 Gwill simultaneously minimize energy and maximize entropy – just what isrequired for a stable system. Enthalpy (U + PV) is a thermodynamic variable.

G = H – TS = U + PV – TS dG = dU – TdS – SdT + PdV + VdPFLT: TdS = dU + PdV

dG = - SdT + VdP

In equilibrium dG = 0The key is to write dG in terms of the properties of the drop embryo.

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Homogeneous Nucleation - continuedHomogeneous Nucleation - continueddG = - 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 = VvdeLiquid: dGl = Vlde

V is the specific volume; Vv >> 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 Pressure:Saturation Vapor Pressure:Clausius-Clapeyron Equation of StateClausius-Clapeyron Equation of State

es(T) = CL e-Ls/RT

es(T) = Saturation vapor pressure at temperature TCL = constant (depends upon condensable)Ls = Latent HeatR = Gas constant

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Homogeneous Nucleation - ContinuedHomogeneous 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 πR3ρl

The total G of the system, including energy in the form of surface tensionσ (surface energy per unit area), is:

G = Gv(T,e)Mv + Gl(T,e)Ml + σ 4πR2

By conservation of mass, Mv = M0 – Ml, so the change in Gibbs Free Energy

G – G0 = (Gl – Gv) Ml + σ 4πa2

Finally we get G – G0 = - 4/3 πR3 ρl RvT ln [e/es(T)] + σ 4πR2

Or as in the text: ΔE = ΔG = σ 4πR2 – 4/3 πR3 nkT ln(e/es)

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Homogeneous Nucleation - ContinuedHomogeneous Nucleation - Continued

ΔE = σ 4πR2 - 4/3 πR3 nkT ln(e/es)

Thus the change in Gibbs Free Energy in the formation of a droplet ofradius R, is given by:

For unsaturated conditions, droplets aren’t 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 Homogeneous Nucleation – Critical Size for GrowthGrowth

ΔE = σ 4πR2 - 4/3 πR3 nkT ln(e/es)

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 forwhich growth is possible.

To find the critical size for which growth is more stable than evaporation:

Set d(ΔE)/dR = 0 and solve for the value of R*

The Critical Radius: Kelvin’s Equation)/ln(

2*seenkT

R

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Size of Stable Drop EmbryosSize of Stable Drop EmbryosTypical super-saturation in the atmosphere is only about 101% relativehumidity. 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 isthe dominant source of water droplets in the atmosphere.

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Supersaturation Near DropletsSupersaturation Near Droplets

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Cloud Condensation NucleiCloud Condensation Nuclei

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Cloud Condensation Nuclei (CCN)Cloud Condensation Nuclei (CCN)CCN are pre-existing atmosphericparticles that come from a largevariety of sources:

DustVolcanoesFactory smokeFires and sootSea SaltDi-methyl Sulfate (Phytoplankton)

Abundance ranges from 103-105

per cubic centimeter, larger overcontinents and urban areas.

Two Types:Hydrophilic/Hydroscopic: water sticks readilyHydrophobic: repels water

http://apollo.lsc.vsc.edu/classes/met130/notes/chapter6/ccn.html

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Aerosol Particle Sizes – Bi-modal DistributionsAerosol 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 Clouds2. 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 3. Cloud Liquid Water Content and EntrainmentEntrainment

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Cumulus Cloud Entrainment

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Model Simulation of Entrainment

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Questions for DiscussionQuestions for Discussion(1)(1) Is precipitation possible without Is precipitation possible without

CCN?CCN?(2)(2) Why does the relative humidity rarely Why does the relative humidity rarely

exceed 101%?exceed 101%?(3)(3) If precipitation did not occur, how If precipitation did not occur, how

would vapor be lost from the would vapor be lost from the atmosphere?atmosphere?

(4)(4) Is growth of an ice particle the same Is growth of an ice particle the same as growth of a liquid water droplet?as growth of a liquid water droplet?