Potter T.D., Colman B.R. (co-chief editors). The handbook of weather, climate, and water: dynamics, climate physical meteorology, weather systems, and measurements

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photographs of clouds with their classiﬁcations can be found in the International

Cloud Atlas (World Meteorological Organization, 1987).

Clouds are composed of ensembles of water and ice particles, most of which form

on aerosol particles that range in diameter from about 10

8

to 10

5

m. Raindrops

typically grow to diameters between 10

4

and 5 10

3

m, while large hailstones

reach diameters of about 5 10

2

m. Clouds typically have dimensions between 10

and 10

m, and individual particle paths through clouds may extend 10

to 10

m. As

water drops and ice particles follow these paths, they can encounter temperatures

that can range from 30 to 50



C, pressures from 1050 to 250 mb, and humidity

conditions from supersaturation with respect to water to nearly dry air. The complex-

ities of the ever-changing cloud environment and this enormous range of scales must

all be considered when investigating the physics governing cloud and preci pitation

processes.

This chapter explores the fundamental principles and key issues within the disci-

pline of cloud microphysics, a discipline speciﬁcally concerned with the formation,

growth, and fallout of cloud and precipitation particles. An extensive body of cloud

microphysics literature has been published over the last century. Limited references

are provided in this chapter. Readers who wish to explore individual topics in greater

depth, or quickly refer to the scientiﬁc literature summarized in this chapter, should

consult Pruppacher and Klett (1997), the most authoritative treatise on cloud micro-

physics currently available.

2 ATMOSPHERIC AEROSOL

The atmosphere consists of a mixture of gases that support a suspension of solid and

liquid particles called the atmospheric aerosol. Chemical react ions between gases,

aerosol, and cloud particles continually modify the chemical structure, concentra-

tion, and distribution of aerosol in the atmosphere. Cloud droplets and ice crystals

form on speciﬁc aerosol called cloud condensation nuclei and ice nuclei. Once

formed, cloud droplets and ice crystals scavenge atmospheric gases and aerosol

and provide an environment for additional chemical reactions.

Sources, Sinks, and Formation Mechanisms

Aerosol particles (AP) form during chemical react ions between gases (gas- to-

particle conversion), as droplets containing dissolved or solid material evaporate

(drop-to-par ticle conversion), and through mechanical or chemical interactions

between the earth or ocean surface and the atmosphere (bulk-to-particle conversion).

Gas-to-particle conversion primarily involves the transformation of sulfur oxides,

nitrogen oxides, and gaseous hydrocarbons to sulfates, nitrates, and solid hydrocar-

bon particles. These reactions typically involve water vapor, often require solar

radiation, and usually include intermediate states involving sulfuric, nitric, or

other acids. Drop-to-particle conversion occurs when cloud drops containing

dissolved or suspended material evaporate. Tiny droplets originating at the sea

256 MICROPHYSICAL PROCESSES IN THE ATMOSPHERE

surface when air bubbles break also produce AP when they evaporate. Bulk-to-

particle conversion involves wind erosion of rocks and soils and decay of biological

material.

Mineral dust from Earth’s land surfaces, salt particles from the ocean, organic

material and gas emissions from aquatic and terrestrial plants, combustion products

from human activities and natural ﬁres, volcanoes, and even meteor bombardment

all are sources of atmospheric aerosol. The continents are a much larger source than

the oceans, and urbanized areas are a larger source than rural areas. Consequently,

the highest concentration of aerosol in the lower atmosphere can normally be found

over cities and the lowest concentrations over the open ocean. The concentration of

AP decreases rapidly with height, with approximately 80% of AP contained in the

lowest kilometer of the atmosphere. Aerosol concentrations are reduced through

self-coagulation, precipitation processes, and gravitational settling. The residence

time of aerosol in the atmosphere depends on the size and composition of the

particles and the elevation where they reside (Fig. 1). Smaller particles (<0.01 mm

radius) collide rather quickly due to thermal diffusion and coagulate, while large

particles (>10 mm radius) fall out quickly due to their increased fall velocity. Parti -

cles with radii between 0.01 and 10 mm have the longest residence times, typically

from 1 to 10 days in the lower troposphere, weeks in the upper troposphere, and

months to years at altitudes above the tropopause.

Number Concentration, Mass, and Size Distribution

Aerosol particles range in size from molecular clusters consisting of a few mol ecules

to about 100 mm. Aerosol spectra fall into four size groups: Aitken particles (dry

radii r < 0.1 mm), large particles (0.1 < r < 1 mm), giant particles (1 < r < 10 mm),

and ultragiant particles (r > 10 mm). Whitby (1978) showed that the aerosol size

distribution is comprised of three modes, each related to different physical processes

(Fig. 2). The nuclei mode, which consists of the smallest particles, develops during

chemical reactions associated with gas-to-par ticle conversion. This mode is large in

polluted regions and essentially absent in pristine environments. The larger accu-

mulation mode forms through coagulation of smaller particles and continued g rowth

of existing particles during vapor condensation and chemical reactions. The accu-

mulation mode develops as a result of aging of the aerosol population. The largest

mode, the coarse particle mode, is comprised of particles that originate at Earth’s

surface, either through mechanical disintegration of the solid earth or through

evaporation of tiny droplets produced during bubble breakup at the ocean surface.

These aerosols differ in chemical composition from those comprising the accumula-

tion mode.

The number concent ration of aerosol in the troposphere varies substantially from

location to location. In very polluted air over cities, the number concentration may

approach 10

3

. Over land, average concentrations range from 10

to 10

3

while over the oceans, average concentrations typically range from a few hundred to

3

. The mass concentration varies in a similar way. Over cities, the mass

concentration of aerosol typically ranges from about 100 to 200 mg=m

3

, while over

2 ATMOSPHERIC AEROSOL 257

the oceans, mass concentrations are nearly an order of magnitude smaller (15 to

30 mg=m

3

). The number concentration of Aitken particles decreases exponentially

with height between the surface and 5 km with a scale height of about 1 km

(Fig. 3). Between 5 km and the tropopause, the Aitken par ticle concentration is

nearly constant. In the lower stratosphere, to a height of about 20 km, the Aitken

particle concentration decreases slowly with a scale height of about 7 km. The

number concentration of ‘‘large’’ particles decreases by about 3 orders of magnitude

over the 4 lowest kilometers of the atmosphere, and reaches a minimum near the

tropopause. Unlike Aitken particles, the concent ration of large particles increases

Figure 1 Residence time of aerosol particles as a function of their radius and altitude. I,

small ions; A, Aitken particles; C, from thermal diffusion of aerosol particles; R, based on

radioactivity data; P, removal by precipitation; F, removal by sedimentation. Solid lines are

empirical ﬁts for three atmospheric levels (Jaenicke, 1988).

258

MICROPHYSICAL PROCESSES IN THE ATMOSPHERE

with height in the stratosphere, with maximum concentrations occurring at an alti-

tude of about 20 km. This stratospheric aerosol layer, called the Junge layer after its

discoverer, consi sts primarily of sulfate particles. The number concentration of giant

particles, such as sea salt particles, decreases rapid ly with height above the surface.

The effects of gravitational settling and cloud scavenging reduce the concentration of

sea salt aerosol to near insigniﬁcance above about 3 km.

Figure 2 Number size distribution of aerosol particles in urban conditions. N, number of

particles; D

, diameter of particles; V

, total volume concentration; r, correlation coefﬁcient

between the power law in the ﬁgure and experimental data (Whitby, 1978).

2 ATMOSPHERIC AEROSOL 259

Because of the wide range of sizes of aeroso l particles, it has been customary to

use logarithmic size intervals to characterize the aerosol particle size distribution. If

we express the total concentration of aerosol particles with sizes greater than r as

NðrÞ¼

logðrÞ

nðrÞ d logðrÞð1Þ

then the number of particles in the size range r, r þ d log r is given by

nðrÞ¼

d logð rÞ

ð2Þ

Figure 3 Vertical proﬁles of Aitken particles: (1) Average concentration per reciprocal cubic

centimeter from seven ﬂights over Sioux Falls, South Dakota (44



N); (2) average concentra-

tion per cubic centimeter from four ﬂights over Hyderabad, India (17



N); (3) average

concentration per cubic centimeter based on ﬂights over the Northeast United States. (Adapted

from Junge, 1963.)

260

MICROPHYSICAL PROCESSES IN THE ATMOSPHERE

The cor responding volume, surface, and mass distributions, expressed in log radius,

are given respec tively by:

dV ðrÞ

d logðrÞ

4pr

d logð rÞ

ð3Þ

dSðrÞ

d logðrÞ

¼ 4pr

d logð rÞ

ð4Þ

dMðrÞ

d logðrÞ

4pr

rðrÞ

d logð rÞ

ð5Þ

where r(r) is the particle density. Figure 4 shows examples of aerosol number,

surface, and volume distributions from different environments. The accumulation

and course particle modes discussed by Whitby (1978) appear in many of the

volume distributions. The nuclei mode appears only in the number distributions

since these particles contribute negligibly to the volume because of their small

Figure 4 Number [n



(r) ¼dN=d log(r)], surface [s



(r) ¼dS=d log(r)], and volume



(r) ¼dV=d log(r)] size distributions for various aerosols (Jaenicke, 1988).

2 ATMOSPHERIC AEROSOL 261

radius. Note that the concentration of aerosol with r > 0.1 mm decreases with increas-

ing size such that the aerosol numbe r distribution can be approximated by:

d logðrÞ

¼ Cr

b

ð6Þ

where b generally falls between a value of 3 and 4.

3 FORMATION OF INDIVIDUAL CLOUD DROPLETS AND

ICE CRYSTALS IN THE ATMOSPHERE

Cloud droplets and ice crystals form in the atmospher e through a spontaneous

process called nucleation. Homogeneous nucleation is said to occur when a droplet

or ice crystal forms from water vapor in the absence of any foreign substance.

Homogeneous nucleation of ice crystals also occurs when water droplets freeze

without the action of an ice nucleus. The water droplets may be very highly diluted

solutions (cloud droplets) or concentrated solutions (haze droplets). Heterogeneous

nucleation is said to occur when a condensation nucleus is involved in the formation

of a water droplet or an ice nucleus is involved in the formation of an ice particle.

Homogeneous Nucleation of Water Droplets in Humid Air

The change in free energy during the homogeneous nucleation of a water droplet in

humid air has two contributions: a negative change per unit volume associated with

the creation of the new phase and a po sitive change associated with the creation of

the surface interface between the phases. The former is proportional to the volume,

while the latter is proportional to the surface area. Because the surface-to-volume

ratio is large for small droplets, the surface term dominates until the embryo

becomes sufﬁciently large. The thin surface layer of the drop has unique properties.

Molecules within this layer ﬁnd themselves in an asymmetric force ﬁeld, attracted

only to neighboring molecules located in the interior. This net attractive force causes

the surface of the drop to be in a state of tension described by the surface tension,

w,v

, which has units of energy=unit area. When humid air is cooled beyond satura-

tion, a metastable state develops where the water vapor becomes supersaturated

without condensing to form the new phase. The metastable state exists because

the path to the lower energy state (a water droplet) initially involves an increase

in free energy associated with the droplet surface. Homogeneous nucleation requires

the spontaneous collision and aggregation of a sufﬁcient number of water molecules

so that the embryonic droplet will be large enough to overcome this ‘‘energy

barrier.’’ Although statistical mechanics are required to strictly describe this process,

classical thermodynamic approaches that assume the embryos are distributed accord-

ing to the Boltzmann law and are water spheres that have macroscopic densities and

262 MICROPHYSICAL PROCESSES IN THE ATMOSPHERE

surface tensions provide an adequate description. With these assumptions, classical

thermodynamics predicts the energy barrier to be

DF ¼

4pr





T ln

s;1



þ 4pr

w;v

ð7Þ

where DF is the Helmholtz free energy change, e

is the water vapor pressure over a

spherically curved surface of radius r, e

s, 1

is the saturation vapor pressure over a

plane water surface, T is temperature, R



is the universal gas constant, M

is the

molecular weight of water, r

is the density of water, r is the radius of the embryo,

and s

w,v

is the surface tension at the water–vapor interface. The ratio e

s, 1

is the

saturation ratio, S

w,v

, over the droplet surface. The ﬁrst term on the right is the

decrease in free energy associated with the creation of the droplet, and the second

term is the increase in free energy associated with the creation of the droplet’s

surface. Taking the limit DF=Dr ¼0 to determine the equilibrium radius r

gives

the Kelvin equation:

w;v

¼ exp

w;v



ð8Þ

Substituting r

into (7) gives the height of the energy barrier:

max

16pM

w;v

3½R



lnðS

w;v

Þ

ð9Þ

The Kelvin equation relates the equilibrium radius of a droplet to the environmental

saturation ratio. A droplet must grow by chance collisions of water molecules to a

radius equal to r

to be stable. Numerical evaluation of the Kelvin equation shows

that an embryo consisting of 2.8 10

molecules would be in equilibrium at an

environmental supersaturation of 10% (S

v,w

¼1.10). A supersaturation of 500%

would be required for an embryo consisting of 58 molecules to be stable (Rogers

and Yau, 1989). The rate at which embryos of a critical radius form at a given

supersaturation, the nucleation rate, J, has been determined using statistical

mechanics to be

J ¼

w;v



1=2

s;1





w;v

exp

DF

max



 10

3

=s exp

DF

max



ð10Þ

where b is the condensation coefﬁcient, N

is Avogadro’s number, and k is the

Boltzmann constant. Numerical evaluations of J for different S

w,v

show that J

varies over 115 orders of magnitude as the cloud supersaturation increases from

3 FORMATION OF INDIVIDUAL CLOUD DROPLETS AND ICE CRYSTALS 263

200 to 600%. The threshold for nucleation is nominally considered to be J ¼1

droplet cm

3

=s. Supersaturations exceeding 550% are required before J ¼0.1

droplet cm

3

=s. Since supersaturations in natural clouds rarely exceed a few percent,

we conclude from consideration of J and the Kelvin equation that homogeneous

nucleation of water droplets does not occur in Earth’s atmosphere.

Heterogeneous Nucleation of Water Droplets

Homogeneous nucleation of cloud droplets directly from vapor cannot occur in

natural clouds because supersaturations in clouds rarely exceed a few percent.

Cloud droplets form through a heterogeneous nucleation process that involves aero-

sol particles. In cloud chambers, where supersaturations of several hundred percent

can be achieved, nearly all aerosol will initiate droplets. Aerosol that nucleate

droplets under these high supersaturation conditions are called condensation

nuclei. Aerosol that nucleate droplets in the low supersaturation conditions of natural

clouds are called cloud condensation nuclei (CCN). The number of CCN is a

function of cloud supersaturation (s

) as well as the mass, composition, and concen-

tration of the aerosol population in the region where the clouds are forming. The

supersaturation required to activate a cloud droplet is a strong inverse function of

particle mass, so only larger aerosol act as CCN. Figure 5 shows the concentration of

CCN as a function of supersaturation in maritime and continental environments

worldwide. The concentration of CCN typically varies from about 20 to 300 cm

3

in maritime air and from about 200 to 1000 cm

3

in continental air. Typically about

50% of maritime aerosol and 1% of continental aerosol act as CCN at s

¼1%. The

relationship between CCN concentrations and supersaturation (%) in Figure 5 can be

approximated as a power law of the for m

CCN

¼ CðS

ð11Þ

Measurements in unpolluted maritime environments have found values of C and k

ranging from 25 C 250 cm

3

and 0.3 k 1.4. Values of C and k measured in

continental environments are 600 C 5000 and 0.4 k 0.9.

Aerosols that act as CCN are normally hygroscopic and totally or partially water

soluble. The chemical co mposition of CCN depends on the proximity to sources.

The primary components of marine CCN are non-sea-salt sulfates (NSS). These

aerosols are produced from organic gases such as dimethylsulﬁde (DMS) and

methanesulfonate during gas-to-particle reactions. Measurements suggest that

DMS, which is produced primarily by marine algae, is emitted into the atmosphere

from the ocean at a global rate of 34 to 56 Tg=yr. The second component of the

marine CCN spectra is sea salt. Sea salt is injected into the atmosphere by bubble

bursting and spray. Studies suggest that submicron CCN in the marine atmosphere

are primarily NSS, while supermicron particles are sea salt, and that sea salt particles

contribute only about 1% to the total CCN concentration over the ocean.

The higher CCN concentrations found in continental air masses arise primarily

from natural sources rather than a nthropogenic activities. The production rate of

264 MICROPHYSICAL PROCESSES IN THE ATMOSPHERE

Figure 5 Median concentrations of CCN for (left) different oceanic regions, (center) different continents, and (right) all continents and oceans

(Twomey and Wojciechowski, 1969).

265