Salby M.L. Fundamentals of Atmospheric Physics

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260

Aerosol and Clouds

Asia (see Fig. 9.40). Combustion and secondary aerosols originate chiefly in

the industrialized regions of Europe and North America. These continental

source regions give the Northern Hemisphere greater number densities than

the Southern Hemisphere. Carbonaceous aerosol has large sources in tropical

regions due to agricultural burning and, through reaction with other species,

to vegetative emissions.

Aerosol number density decreases vertically away from the surface

(Fig. 9.1), where particles and gaseous precursors originate. In the tro-

posphere, n has a characteristic height of only 2 km. This shallow depth

reflects the absolute concentration of water vapor (Fig. 1.14) and removal by

precipitation processes. In the stratosphere, n decreases more slowly.

Aerosol is characterized by its size distribution, n(a), which denotes the num-

ber density of particles with radii smaller than a [a monotonically increasing

function of a, with n(a) approaching n as a ~ c~]. The size spectrum, dn/da

(Fig. 9.2), represents the contribution to n = f(dn/da)da from particles with

F--

_ I I I

IIII I

~ t

- ?

_ /

/ I Illlllli i llllllli

10 1 10 0 101

I I I~Jllll

I I ItllLI

..................... Marine

Continental (Sept.

1979) _

Continental (Dec. 1982) --

i i lilili~J"~ IIIII

10 2 103

AEROSOL NUMBER DENSITY (cm 3)

Figure 9.1 Aerosol number density n as a function of height in continental and marine envi-

ronments. Profile of marine aerosol corresponds to particle radii a > 0.5/zm. The steep decrease

of n above the marine boundary layer mirrors a similar decrease in dew point temperature (not

shown). Profiles of continental aerosol correspond to a > 0.15 /zm and are shown before and

after the eruption of El Chichon. Sources: Patterson (1982) and WMO (1988).

9.1 Morphology

of Atmospheric Aerosol

261

102 102

101 101

1 0 ~ 1 0 ~

] 0 .2 ] 0 .2

102 101 10 ~ 101

a (pro)

10 -3

10 -2

(b) Marine

.....

N. "

Boundary lager

Free Troposphere

] I I I I II 11 I I I I I It II I I I I I II

10 1 100 101

a (pm)

Figure 9.2 Aerosol size spectra, as functions of particle radius a, inside the planetary bound-

ary layer and aloft for (a) continental environment and (b) marine environment. From Patterson

(1982). Copyright by Spectrum Press (A. Deepak Publishing).

radii between a and

a + da.

As before, plotting

dn/d(log a)

versus log a is area

preserving: Equal areas under the spectrum represent equal contributions to n

from different size ranges. Crustal aerosol, which is comprised chiefly of wind-

blown silicates, involves particles with radii a > 1 /zm. Secondary and com-

bustion aerosols, which form through condensation, contain submicron-scale

particles. These different production mechanisms give continental aerosol a

bimodal size spectrum (Fig. 9.2a), in which particles are concentrated in two

distinct ranges of a. The size spectrum diminishes sharply with increasing a,

the greatest contribution to n arriving from particles with a < 0.1 ~m--the

so-called

Aitken nuclei.

Despite their relative abundance, Aitken nuclei con-

stitute less than half of the surface area of aerosol (Fig. 1.22), which figures

centrally in thermodynamic and chemical processes, and only about 10% of

its mass.

Combustion and secondary aerosols form through several mechanisms: (1)

gas-to-particle conversion, wherein gaseous precursors undergo physical and

chemical changes that result in particle formation, (2) direct condensation of

combustion products, and (3) direct emission of liquid and solid particles. Gas-

to-particle conversion is responsible for much of the sulfate and nitrate that

dominate urban aerosol. That process is exemplified by a series of reactions

which begins with the gaseous pollutant sulfur dioxide

OH + SO 2 -+ HSO3,

(9.1)

followed by oxidation of HSO 3 to form H2SO 4 vapor. Owing to its low satu-

ration pressure, sulfuric acid vapor readily condenses, or

nucleates,

into liquid

particles---especially in the presence of water vapor. Once formed, nuclei grow

rapidly to radii of 0.01 to 0.1/xm. Larger aerosol can then develop through

coagulation of individual nuclei to form

accumulation panicles.

Sulfate aerosol

is also produced through reaction of sulfur dioxide with ammonia inside cloud

262

Aerosol and Clouds

droplets, which, upon evaporating, leave behind sulfate particles. In the tro-

posphere, (NH4)2SO4, NHnHSO4, and H2SO 4 are all present, whereas super-

cooled H2SO 4 droplets are the prevalent form of sulfate in the stratosphere.

Nitrogen emissions from combustion and natural sources lead to analogous

products. Sulfate and nitrate are both important in the troposphere, but nitrate

is especially prevalent in urban areas because it is an inevitable by-product of

combustion.

Carbonaceous aerosols like soot consist of submicron-size particles. Natural

sources include pollen and spores, as well as complex hydrocarbon vapors, like

isoprene. Emitted via plant transportation, those vapors react with oxides of

nitrogen and subsequently nucleate.

Once formed, aerosol nuclei interact strongly with water vapor. Through

condensation (Fig. 9.3), liquid particles like H2SO 4 enlarge steadily with in-

creasing relative humidity

(RH).

Conversely, hygroscopic solids like NaC1 and

(NH4)2SO 4 remain dry below a threshold of

RH ~-

80%. Particles then dis-

solve, undergo a discontinuous enlargement, and thereafter exhibit depen-

dence on

similar to liquid aerosol.

Anthropogenic sources account for about 30% of aerosol production. The

anthropogenic component of sulfate, which plays a key role in cloud forma-

tion, exceeds 60% over urban areas. The distribution of continental aerosol

is strongly affected by sedimentation, especially for large crustal species. Fall

speeds range from 50 cm s -1 for large silicates (a ~ 50/zm) to 0.03 cm s -1 for

smaller (a -~ 1/xm) particles. As a result, larger particles tend to be confined

to a neighborhood of their source regions.

I | I

| /

2.4

__ H2SO 4

--- (NH4)2SO 4 .."

2.2,- ..... NaCI .. --

2.0 "'"'""

,,'1

i /'

i ,

1.0

0 0.2 0.4 0.6 0.8

RELATIVE HUMIDITY

Figure 9.3 Aerosol particle radius as a function of relative humidity for liquid droplets and

hygroscopic solids. Adapted from Patterson (1982). Copyright by Spectrum Press (A. Deepak

Publishing).

9.1 Morphology of Atmospheric Aerosol

263

Top Jet Drop

O t 5 cm Ejection Height

50 IJm Diameter

9 9 9 O 9 9 Film Drops

9 9 9 9

9 15-20 Produced

o~.... ~e

9 9

/ ~ \

9 9 Submicronto

Film Cap r.ea-~ i i / ! T 101JmDiameter

5x10 IJm A

1 to 3 IJm Thlck~ /..~//5 00 IJm Diameter

Rise

Velocity

3.5 cm/sec

Figure 9.4 Formation of marine aerosol

particles from a bursting ocean bubble.

Adapted from Patterson (1982). Copyright by

Spectrum Press (A. Deepak Publishing).

9.1.2 Marine Aerosol

Composed primarily of sea salt, marine aerosol has a smaller overall concentra-

tion. Its number density drops sharply above the boundary layer (Fig. 9.1), re-

sembling the distribution of moisture. Like continental aerosol, marine aerosol

has a size spectrum that is bimodal (Fig. 9.2b), which reflects two classes of

droplets that form when ocean bubbles burst (Fig. 9.4). Water entrained into

a bubble is ejected vertically in a stream of drops (a --- 25/zm). Upon evap-

orating, those drops leave behind large (a > 1/xm) particles of sea salt. The

thin film comprising the bubble's surface shatters to release droplets of 1 ~m

and smaller, which evaporate and produce smaller particles of sea salt.

9.1.3 Stratospheric Aerosol

Aerosol is introduced into the stratosphere through penetrative convection

and volcanic eruptions. It also forms

in situ

through gas-to-particle conver-

sion from precursors like SO2, which maintains a background level of H2SO 4

droplets. Its long residence time makes stratospheric aerosol fundamentally

different from tropospheric aerosol. Small particulates with slow fall speeds

are dynamically isolated by strong static stability. Sequestered from removal

processes associated with precipitation, aerosol can survive in the stratosphere

long after it is introduced. This feature enables stratospheric aerosol to alter

SW absorption at the earth's surface for long durations. The great eruption of

Krakatoa in 1883, which destroyed the Indonesian island of the same name, al-

tered SW transmission and sunsets for 3 years afterward (see, e.g., Humphreys,

1964).

Aerosol number density decreases vertically in the stratosphere more slowly

than in the troposphere (Fig. 9.1). Following major volcanic eruptions, aerosol

number density actually increases into the stratosphere, as was evident follow-

ing the eruption of E1 Chichon in 1982. A clear signature of E1 Chichon was

registered in SW transmission (Fig. 9.5), which decreased sharply in 1982. In-

264

Aerosol and

Clouds

.01

0 - .02

or)

0') - .03

.04

< - .05

n-"

I--

.06

or)

.07

-J - 08

- .09

.10

-.11

.12

I I I I I I I I I I I I

58 60 62 64 66 68 70 72 74 76 78 80 82 84 86

YEAR

Figure 9.5 Change of direct solar transmission through the atmosphere, as observed over

Hawaii by ground-based instruments.

Note:

Reduction of direct transmission is offset by an in-

crease of diffuse transmission (see, e.g., Hoffman, 1988). After WMO (1988).

creased extinction in volcanic debris can increase radiative heating, which, in

turn, can produce ascent of air in which the debris is suspended.

A characteristic vertical scale of 7 km for n in the stratosphere resembles

the scale height of air density, which suggests that the relative concentration

of aerosol (e.g.,

n/nd)

is approximately conserved for individual air parcels.

Owing to the absence of removal processes, stratospheric aerosol behaves as a

tracer. Figure 9.6 shows the cloud of volcanic debris introduced by the eruption

of Mount St. Helens. Two months after the eruption, the cloud has dispersed

zonally but not meridionally. Its confinement to high latitudes of the summer

hemisphere follows from certain characteristics of the stratospheric circulation

(Chapter 17).

9.2 Microphysics of Clouds

Large particles (a > 1/zm) are vulnerable to sedimentation, which accounts

for 10 to 20% of the overall removal of atmospheric aerosol. A more efficient

removal mechanism is

washout,

which occurs when cloud droplets that form

on aerosol particles carry them back to the earth's surface. This removal

mechanism is closely related to cloud formation.

9.2.1 Droplet Growth by Condensation

The simplest means of forming cloud is through

homogeneous nucleation,

wherein pure vapor condenses to form droplets. Suppose a small embryonic

9.2

Microphysics of Clouds

265

~., . : . . -r .x~. :~-.-~..-.-.... :...:.:.:.:d+:.:.::

173 ~0 . i/::- " " - ..... ! ~'::'::~.

" : :- ::t ::: ""i::: :::::::::::::::::::::::::: - ::

I-- -~o - " ........ -.i :iii-liiii~iiiiii:~:i~:~-:.::i:~: 9 :.:..i .........

.... .. -. :, ========================== :. :.:

-30 -- . 9 .. :-.":: ::-:::i.i::::::.?...: . .- "

. :-..--.. ::.....: ============================== :...:.:.:.:.:::~ :.

.......... ii

_40 _ . :i:.~::iiiiiii:i:~i~ii~!:ii~:~

" . ....... :.i+:-i.)i~i~i.ii!:i

.)i. :

-4rdO ~ " : ~~~.t~..~.,.f:'" "" """ " """" " '

...... : i:~i~ i:.i::

i iii

i! :::: i~i iii; ~i~iii::iiiii! i:~:i!i.~...:!:/:ii~ .. :::i ..... +i~:-i:ii:i:~i:~::i::!~.!~i.r

:... : ....:...:..::.:.:.: :::::...:.....::-: .::.:.::.:.:.:.:-::.:.:.:.:-::.. 9 :..:..:-:~:...... ......:::.:.:. ..

.... . : ..:.. :::::::::::::::::::::::::::::::

.............................. :.:! ......,

================================================================================================= : _-L.:~.-~.:~:i~

~o SHADING OPTICAL SI-IADING OPTICAL -'!

DEPTH DEPTH _

-70 ~E"---I <,.Oxl() 3 I~ 3.O-4.0xl(~3_~f--~~~'~ d

-,o ~ ,.o-z.o,,o -~ m, 4.o-~o,tq-' ~'--!

z,.o,3.o~,o -~ ,R", ,>~oi,,~,~,,,,,,,, , ,--I

-9q I I I I I I I I I I ~ I I _ I I ,

-180"lTO'll~-If~O-14O-130-l'20-IK)i:)O-90-1~O-'rO-60~~-~ 0 I0 20 ~ 40 ~1060 70 80 90 I00110 1201~0 IdlOlSO 160 I'/0180

LONGITUDE

Figure 9.6 Mean aerosol optical depth at 1 /xm two months after the eruption of Mt. St.

Helens. Constructed by averaging satellite measurements from the Stratospheric Aerosol and Gas

Experiment (SAGE) between July and August 1980. After Kent and McCormick (1984). Copyright

by the American Geophysical Union.

droplet forms through chance collisions of vapor molecules. The survival of

that droplet is determined by a balance between condensation and evapora-

tion. The equilibrium between the droplet and surrounding vapor is described

by the Gibbs free energy (3.16.2), but with one modification. In addition to

expansion work, a spherical droplet performs work in association with its sur-

face tension cr, which has dimensions of energy/area. Thus,

odA

represents

the work to form the incremental area

of interface between vapor and

liquid.

For a heterogeneous system comprised of the droplet and surrounding

vapor, the fundamental relation for the Gibbs free energy (4.13) becomes

where

dG --SdT + Vdp + (tz v - p,w)dmv + ordA,

(9.2.1)

dmv - -dmw

= -nwdV w,

(9.2.2)

266 9 Aerosol and Clouds

and

n w

and Vw denote the number density and volume of the droplet,

respectively. ~

The difference of chemical potential between the vapor and liquid phases

can be expressed in terms of the vapor and saturation vapor pressures by

appealing to the fundamental relation (3.16) for the individual phases. 2 Under

an isothermal and reversible change of pressure

de,

for the vapor and

d~v - v,,de

(9.3.1)

dtzw - vwde

(9.3.2)

for the liquid. Subtracting gives

d(t~ - l~w) - (v~- vw)de

~- vvde.

(9.4)

Then applying the gas law for an individual molecule of vapor

ev o = KT

(9.5)

(e.g., Lee

et al.,

1973), where K is the Boltzmann constant, gives

d(i~o - tZw) - KTdln e,

which upon integrating from the saturation pressure (at which /z o - ~w)

obtains

/zv -/z w - KT ln(e-~). (9.6)

Incorporating (9.6) into (9.2) and integrating from a reference state of pure

vapor (with the vapor pressure maintained) yields the change of Gibbs free

energy

AG=

-VwnwKTln(-~w)+OrA.

Thus, forming a spherical droplet of radius a corresponds to the change of

Gibbs free energy

4 (~w)

AG =--47ra2o - -

-~Tra3nwKTln .

(9.7)

In phase transformations away from saturation, the system is out of chemical equilibrium, so

the chemical potentials in (9.2) need not be equal.

2 Surface tension introduces a pressure difference between the droplet and surrounding vapor,

which makes the pressure during a phase transformation variable. Strictly, that process should

be treated as isothermal and isochoric, for which F is the appropriate free energy. However,

discrepancies with G under isothermal and isobaric conditions are small enough to be ignored

(see, e.g., Pruppacher and Klett, 1978).

9.2 Microphysics of Clouds

267

1.6

1.4

1.2

1.0

v 0.8

,I.--

(.9 0.6

0.4

0.2

-0.2

e w

- 0.999

/ e

~ = 1.u

/ / e w

- 1.002

e w

i I i I i I t I t I t I i I I I t I I

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

a (pm)

Figure 9.7 Gibbs free energy of a pure-water droplet produced through homogeneous nucle-

ation, as a function of droplet radius. Shown for subsaturation (e/ew < 1), saturation (e/e w = 1),

and supersaturation (e/ew > 1).

Figure 9.7 shows the free energy as a function of droplet radius for subsatu-

ration (e/ew < 1), saturation (e/ew - 1), and supersaturation

(e/e w

> 1). For

subsaturation as well as for saturation, G increases monotonically with droplet

radius a. Under isothermal isobaric conditions, a system approaches thermo-

dynamic equilibrium by reducing its free energy (3.23), so droplet formation

is not favored for e/ew _< 1. Those conditions characterize stable equilibrium

and

G(a)

an unbounded potential well. A droplet formed through chance

collision of vapor molecules will spontaneously evaporate (e.g., in association

with latent heat released during its formation). Under supersaturated condi-

tions,

G(a)

possesses a maximum at a critical radius

ac,

beyond which the free

energy decreases and condensation is more efficient than evaporation.

G(a)

then characterizes conditional equilibrium and a bounded potential well. A

droplet formed with a <

evaporates back to the initial state (G - 0). But

268

Aerosol and Clouds

one formed with a > a c grows spontaneously through condensation of vapor

and is said to be activated.

The critical radius for a given temperature and vapor pressure follows by

differentiating (9.7):

2tr

ac =

e "

(9.8)

nwKTln(~)

Known as Kelvin's formula, (9.8) can be rearranged for the critical or equilib-

rium supersaturation

(L)

e c = - 1, (9.9)

above which a droplet of radius a grows spontaneously through condensa-

tion. As shown in Fig. 9.8, small droplets have higher ec than large droplets,

with ec ~ 0 as a ~ c~. This behavior reflects the so-called curvature effect

of surface tension (9.2), which makes the equilibrium vapor pressure over a

spherical droplet higher than that over a plane surface.

The curve for ec describes an unstable equilibrium, which therefore can-

not be maintained. Adding a vapor molecule drives a droplet of radius a

above the equilibrium curve. The actual supersaturation e then lies above the

equilibrium value e c, so the droplet continues to grow through condensation.

Removing a water molecule has the reverse effect, wherein the droplet con-

tinues to evaporate. In either case, a perturbed droplet evolves away from the

equilibrium state. More importantly, values of ec implied by Kelvin's formula

pose a practical barrier to droplet formation via chance collection of vapor

molecules. An embryonic droplet as large as 0.01 /zm still requires a super-

saturation of 12% to be sustained. Yet, supersaturations exceeding 1% are

rarely observed, e = 0.1% being typical. Therefore, cloud formation cannot

be explained by homogeneous nucleation.

Instead, cloud droplets form through heterogeneous nucleation, when water

vapor condenses onto existing particles of atmospheric aerosol. Termed cloud

condensation nuclei (CCN), such particles support condensation at supersatu-

rations well below those required for homogeneous nucleation. Particles that

are wettable allow water to spread over their surfaces. Such particles pro-

vide ideal sites for condensation because they then resemble a droplet of

pure water, which, for observed supersaturations, could not attain that size

through homogeneous nucleation. According to Fig. 9.8, the larger such a nu-

cleus, the lower its equilibrium supersaturation and the more it favors droplet

growth through condensation. Other conditions equal, large nuclei then acti-

vate sooner than small nuclei.

Even more effective are hygroscopic particles, like sodium chloride and

ammonium sulfate. In the presence of moisture, NaC1 and (NH4)2SO 4 absorb

vapor and readily dissolve (Fig. 9.3). The resulting solution has a saturation

9.2 Microphysics of Clouds

EQUILIBRIUM SUPERSATURATION

12.0

11.0

10.0

9.O

! k

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

10 -2 10 -1 10 ~ 101 10 2

a (gm)

DROPLET RADIUS

269

Figure 9.8 Critical supersaturation ec = (e/ew)c - 1 at 278 K necessary to sustain a droplet

of radius a. The critical value of e describes an unstable equilibrium, wherein perturbations in a

are reinforced. A perturbed droplet then either evaporates or grows through condensation away

from the equilibrium state.

vapor pressure below that of pure water--because

e w

is proportional to the

absolute concentration of water molecules on the surface of the droplet. Con-

sequently, a droplet containing dissolved salt favors condensation more than

would a pure-water droplet of the same size. The so-called

K6hler curves

(Fig. 9.9) describe the equilibrium supersaturations for solutions containing

specified amounts of solute. Hence, a droplet which develops on a soluble nu-

cleus evolves along the curve corresponding to the fixed mass of that solute.

The presence of NaC1 sharply reduces the equilibrium supersaturation below

that for a pure-water droplet (homogeneous nucleation), which is superposed

on Fig. 9.9. For fixed a, e~ decreases with increasing solute and eventually