Lecture 11Lecture 11

Cloud MicrophysicsCloud Microphysics

Wallace and Hobbs – Ch. 6

Ignore most of the math – concentrate on descriptive conclusions and graphs

Cloud TypesCloud Types

OutlineOutline

Cooling

Supersaturation

Droplet Formation

Droplet Growth Precipitation Formation

NucleationNucleation

Usually refers to the initial formation of a Usually refers to the initial formation of a dropletdroplet More general definition: More general definition: AMS GlossaryAMS GlossaryHomogeneous nucleationHomogeneous nucleation Droplet spontaneously forms in pure airDroplet spontaneously forms in pure air No particles presentNo particles present

Heterogeneous nucleationHeterogeneous nucleation Droplets form on particles called cloud Droplets form on particles called cloud

condensation nuclei (CCN)condensation nuclei (CCN)

Homogeneous NucleationHomogeneous Nucleation

Formation of a curved water surface Formation of a curved water surface requires energyrequires energy maintenance of a small droplet requires large maintenance of a small droplet requires large

supersaturations supersaturations

RH to Form Droplet of Radius rRH to Form Droplet of Radius r

r (m)

RH

0.01

112%

W & H, Fig. 6.2

Such large RHs do not occur in nature.

Heterogeneous NucleationHeterogeneous NucleationHygroscopicHygroscopic CCN are particularly effective CCN are particularly effective condensation initiatorscondensation initiators Generally made of soluble saltsGenerally made of soluble salts

When droplet forms, solution has a much When droplet forms, solution has a much lower vapor pressure than pure waterlower vapor pressure than pure water Condensation begins when RH < 100%Condensation begins when RH < 100%

Droplet growth requires supersaturations of Droplet growth requires supersaturations of less than 1%less than 1% Such supersaturations are achieved in updraftsSuch supersaturations are achieved in updrafts

KKöhler Curvesöhler Curves

Give the equilibrium droplet size for a Give the equilibrium droplet size for a given RH.given RH.

Köhler Köhler CurvesCurves

Suppose RH = 100.1%

10-19 g

10-18g

10-17g

Numbers indicate mass of dissolved salt (NaCl)

“Saturation ratio” = RH/100

10-19 g

10-18g

10-17g

Droplets grow until they reach equilibrium radius

10-19 g

10-18g

10-17g

Droplets grow until they reach equilibrium radius

10-19 g

10-18g

10-17g

Droplets grow until they reach equilibrium radius

10-19 g

10-18g

10-17g

Droplets grow until they reach equilibrium radius

10-19 g

10-18g

10-17g

Droplets grow until they reach equilibrium radius

10-19 g

10-18g

10-17g

Droplets grow until they reach equilibrium radius

Typical cloud droplet radius

Droplet GrowthDroplet Growth

If ambient RH < value at peak of curve, If ambient RH < value at peak of curve, droplets stop growing when much smaller droplets stop growing when much smaller than typical cloud dropthan typical cloud drop

They are called They are called hazehaze droplets droplets

Suppose RH = 100.3%

10-19 g

10-18g

10-17g

Droplets growing on smaller nuclei behave as before

10-19 g

10-18g

10-17g

Look at largest nucleus

10-19 g

10-18g

10-17g

10-19 g

10-18g

10-17g

10-19 g

10-18g

10-17g

10-19 g

10-18g

10-17g

10-19 g

10-18g

10-17g

10-19 g

10-18g

10-17g

10-19 g

10-18g

10-17g

Droplet keeps growing!

Droplet “Activation”Droplet “Activation”

If ambient RH > peak value, droplet grows If ambient RH > peak value, droplet grows indefinitelyindefinitely

Once droplet has gotten “over the hump”, Once droplet has gotten “over the hump”, it is said to be it is said to be activated.activated.

Slowing of GrowthSlowing of Growth

Rate of droplet growth decreases as Rate of droplet growth decreases as droplets growdroplets grow

Let r = droplet radiusLet r = droplet radius

It can be shown thatIt can be shown that

rdt

dr 1

Depletion of Water VaporDepletion of Water Vapor

Also, growth of large number of droplets Also, growth of large number of droplets reduces supersaturationreduces supersaturation

Result: Droplet radius tends to level off at Result: Droplet radius tends to level off at about 10about 10mm

Fall velocity of such a droplet is < 1 cmFall velocity of such a droplet is < 1 cm-1-1

droplets tend to be carried droplets tend to be carried upwardupward

Droplets must be much larger to actually Droplets must be much larger to actually fallfall

Microphysical ParametersMicrophysical Parameters

Liquid water content (LWC)Liquid water content (LWC) grams of liquid water per mgrams of liquid water per m33 of cloud of cloud

Droplet concentration, NDroplet concentration, N Number of droplets per cmNumber of droplets per cm33

Mean droplet size, Mean droplet size, Usually given in Usually given in mm

Not independent – knowledge of any two Not independent – knowledge of any two determines the thirddetermines the third

r

Relationship Between Relationship Between Microphysical ParametersMicrophysical Parameters

,3

4 3rNLWC L

where L is the density of liquid water.

See W & H, p. 217 for typical values of microphysical parametersSee W & H, p. 217 for typical values of microphysical parameters

Supercooled WaterSupercooled Water

Definition: Liquid water with T < 0Definition: Liquid water with T < 0CCFreezing Freezing Homogeneous nucleation occurs at -40Homogeneous nucleation occurs at -40C!C! Heterogeneous nucleation occurs in presence Heterogeneous nucleation occurs in presence

of a of a freezing nucleusfreezing nucleus(Typically occurs at temps much higher than -40(Typically occurs at temps much higher than -40C)C)

Freezing PointFreezing Point

Common experience: Water freezes at 0Common experience: Water freezes at 0CCThis works when mass of water >> cloud dropletThis works when mass of water >> cloud droplet Only one nucleation event is required to freeze entire Only one nucleation event is required to freeze entire

massmass Such an event is virtually certain for masses of water Such an event is virtually certain for masses of water

normally encounterednormally encountered

Cloud droplets very smallCloud droplets very small Probability of a nucleation event at 0Probability of a nucleation event at 0C is smallC is small Probability increases as temperature fallsProbability increases as temperature falls

Ice CrystalsIce Crystals

When T < 0When T < 0C, ice crystals can form C, ice crystals can form directly from vapordirectly from vapor

Homogeneous nucleation requires Homogeneous nucleation requires unrealistically large super-saturationsunrealistically large super-saturations

Heterogeneous nucleation occurs on Heterogeneous nucleation occurs on particles called particles called deposition nucleideposition nuclei

Ice NucleiIce Nuclei

General name for various types of nucleiGeneral name for various types of nuclei e.g., freezing nuclei, deposition nucleie.g., freezing nuclei, deposition nuclei

Relatively rareRelatively rare 1 particle in 101 particle in 1088 suitable! suitable!

Nucleation TempsNucleation Temps

-3-3Bacteria!Bacteria!

-4-4Silver IodideSilver Iodide

-9-9KaoliniteKaolinite

Temp. (Temp. (C)C)SubstanceSubstance

Source: Table 9.1 in A Short Course in Cloud Physics, 3rd Ed. Rogers, R. and M. Yau. Pergamon Press, 293 pp.

Supercooled Water and IceSupercooled Water and Ice

Let eLet es,ws,w(T) be the saturation vapor pressure (T) be the saturation vapor pressure

over liquid water at temperature Tover liquid water at temperature T

Let eLet es,is,i(T) be the saturation vapor pressure (T) be the saturation vapor pressure

over ice at temperature Tover ice at temperature T

ees,is,i(T) < e(T) < es,ws,w(T) for T < 0(T) for T < 0CC

T (T (C)C) ees,is,i(hPa)(hPa) ees,ws,w(hPa)(hPa)

00 6.116.11 6.116.11

-5-5 4.024.02 4.214.21

-10-10 2.602.60 2.872.87

-15-15 1.651.65 1.911.91

-20-20 1.031.03 1.251.25

-25-25 0.630.63 0.810.81

-30-30 0.380.38 0.510.51

-35-35 0.220.22 0.310.31

-40-40 0.130.13 0.190.19

ees,is,i vs. e vs. es,w s,w

(Source: (Source: Smithsonian Meteorological Tables, 6th EdSmithsonian Meteorological Tables, 6th Ed.).)