Salby M.L. Fundamentals of Atmospheric Physics

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310 9

Aerosol and Clouds

(a) Longwave Cloud Forcing

..... L.,..., .'"

" i

9 , " ~ "

(b) Shortwave Cloud Forcing

~,~--. ...... :..- ....

Figure 9.37 Cloud radiative forcing during northern winter derived from ERBE measure-

ments on board the satellites ERBS and NOAA-9 for the (a) LW energy budget, (b) SW energy

budget.

(continues).

radiative forcing depends importantly on the vertical distribution of cloud.

For instance, deep cumulonimbus and comparatively shallow cirrus with the

same cloud-top temperature yield identical LW forcing, yet imply very dif-

ferent optical depths. The strong correlation between water vapor and cloud

cover introduces another source of uncertainty because it biases CLW toward

higher values (Hartmann and Doelling, 1991).

Clouds introduce heating through the release of latent heat. Precipitation

leads to a net transfer of heat from the oceans to the atmosphere. Latent

heating is particularly important for organized deep cumulus clouds, which

produce large volumes of precipitation in the tropics. The column-integrated

9.5 Roles of Clouds and Aerosol in Climate

311

Figure

9.37

(Continued).

ington).

latent heating rate follows from the specific heat 1 and precipitation rate P as

Q = lp w [,. (9.54)

A counterpart of TOA radiative fluxes in (9.48), (9.54) gives approximately 25

W m -2 for each mm day -1 of precipitation.

Figure 9.38 illustrates the geographical distribution of precipitation. Large

precipitation is found inside the ITCZ, where P ~ 10 mmday -1. Thus, la-

tent heating contributes of order 250 W m -2 to the energy budget of the

atmospheric column. These are the same regions implied by cloud forcing to

experience strong radiative heating and cooling. But latent heating of the col-

umn is three times greater than SW or LW forcing individually and an order

of magnitude greater than net cloud radiative forcing in those regions. Fur-

ther, whereas cloud radiative forcing is sharply concentrated in the vertical,

latent heating inside deep cumulus affects much of the tropical troposphere.

Latent heat release inside tropical convection leads to a specific heating rate

(t/Cp

of order 10 K day -1 (Fig. 9.39). Radiative heating and cooling can ex-

ceed this value near cloud boundaries, but the deep distribution of latent heat

release makes it a key source of energy for the tropical troposphere.

INFLUENCE OF AEROSOL

Atmospheric aerosol introduces similar, albeit weaker, effects. Like cloud,

aerosol is an efficient scatterer of SW radiation, one that alters optical prop-

erties following major volcanic eruptions (Fig. 9.5). Depending on its com-

312

9 Aerosol and Clouds

100

125

150

9 .Q 200

0') 300

(/')

I.U

13.. 400

5OO

600

700

800

900

1000

CONVECTIVE HEATING

i | | | | i | |

0 1 2 3 4 5 6 7

~ (K day -1)

-14

10-1-

LLI

8 n-

Figure 9.39 Vertical profile of the heat-

ing rate inside tropical convection, normal-

ized by that accompanying a precipitation

rate of 10 mmday -1. Source: Webster and

Lukas (1992); adapted from data in Yanai

et al.

(1973).

position and the underlying surface, aerosol can either enhance or diminish

albedo. Aerosol increases the albedo over otherwise dark oceans to introduce

cooling in the SW energy budget. However, arctic haze (which is comprised

of anthropogenic pollutants) reduces the albedo over bright polar ice (Ack-

erman, 1988). Aerosol also contributes significantly to SW absorption in the

tropical troposphere (Fig. 8.26). To illustrate how these factors determine the

net effect of aerosol, we consider a natural species: desert dust.

During disturbed periods, Saharan dust has optical depths exceeding 2 (Fig.

9.40). Convection carries desert aerosol as high as 500 mb. Dust absorbs SW

radiation, so it reduces the albedo over a highly reflective surface, like desert

or shallow stratus, to introduce warming in the SW energy budget of the

column (9.48). However, dust changes the albedo over a dark surface like

ocean only slightly--because both absorb strongly. The LW energy budget is

influenced by desert aerosol in a manner similar to clouds. When convected

Figure 9.38 Annual-mean precipitation rate inferred from convective clouds colder than

230 K in global cloud imagery (Fig. 1.25) between August 1983 and July 1984 [see Hendon

and Woodberry (1993) for details]. Deep convection in the maritime ITCZ and over tropical

landmasses leads to mean precipitation rates exceeding 10 mm day -1. Note also the North Atlantic

and North Pacific storm tracks, which lie east of North America and Asia, respectively.

9.5

Roles of Clouds and Aerosol in Climate

313

Figure

9.40 Visible image from Meteosat on March 25, 1991, which reveals a tongue of

Saharan dust that is drawn northward from the African coast ahead of a cold front. Courtesy of

D. Rosenfeld and Y. Levi (Hebrew University).

to great heights, desert aerosol can reduce the effective emission temperature

significantly, with a commensurate warming in the column energy budget. 6

SW effects dominate the energy budget for desert aerosol and produce

net warming of the column, at least over surfaces with appreciable albedo.

The same is true for the atmosphere alone, but LW and SW components

both determine the vertical distribution of heating. Figure 9.41 shows the net

heating rate for Saharan dust that is distributed between the surface and 500

mb. Over cloud-free ocean (Fig. 9.41a), absorption of upwelling LW radiation

introduces significant heating near the surface, where

gl/Cp

> 2 K day -a. For

optical depths greater than 1, SW absorption introduces a second heating max-

imum near the middle of the dust layer. Over cloud-free desert (Fig. 9.41b),

higher surface albedo backscatters much of the transmitted SW radiation,

which is then absorbed inside the dust layer. Net heating is then dominated

by SW absorption, which leads to

gl/Cp

of order 1 to 2 K day -1 across much

of the dust layer. Because it heats the atmosphere and cools the underlying

surface, the net effect in both cases is to stabilize the stratification.

Aerosols are central to cloud formation, a role that is even more important

than their direct radiative effect. Outbreaks of Saharan dust alter both the

6The

reduction of effective emission temperature can exceed that of cloud occupying the

same volume because the temperature at the top of the dust layer decreases with height "dry

adiabatically."

314

Aerosol and Clouds

300

400

~, 500

LU 600

co 700

o_ 800

900

1000

300

(a) Cloud-Free Ocean

........ ~d = 0.2

..... 0.5

--- 1.0

1.5

..... 2.0

~;~.,~.~ .......... 2.5

',~ ~.~

400

,~ 500

I-

27~176 I

8oo I

900 I

1000]

Desert

-~~"1; d = 0.2

0.5

1.0

1.5

2.0

~~,~:,~ .... 2.5

t: ! i '

/_///: /

/: / //

//,;///

I .~ II |

0 1 2 3 4 5

-2

0 1 2 3 4

i (K day 1) ~ (K day 1)

Cp Cp

Figure 9.41 Vertical profiles of heating rate for Saharan dust that is distributed between 1000

and 500 mb and has optical depths

z d

over (a) cloud-free ocean and (b) desert. Adapted from

Carlson and Benjamin (1982). Copyright by Spectrum Press (A. Deepak Publishing).

amount and type of cloud, with stratiform being favored. Therefore, changes

in the concentration, size, or composition of atmospheric aerosol can introduce

important changes in cloud cover and radiative energetics.

9.5.2 Involvement in Chemical Processes

Clouds also support important interactions with chemical species. Precipita-

tion is the primary removal mechanism for atmospheric pollutants. By serving

as CCN, aerosol particles are incorporated into cloud droplets and precip-

itated to the earth's surface. This process scavenges air of most nuclei ac-

tivated and others absorbed through collision with cloud droplets. The effi-

ciency of washout accounts for the short residence time of tropospheric aerosol

(~1 day). Washout also operates on gaseous pollutants that are water soluble.

Aerosol particles support heterogeneous chemistry, which requires the pres-

ence of multiple phases. Cloud particles comprising PSCs are directly in-

volved in the formation of the Antarctic ozone hole (Chapter 17). Beyond

that role, PSCs introduce an important transport mechanism that can also in-

fluence ozone depletion. If they attain sufficient size, PSC particles undergo

sedimentation~like cirrus ice particles. Water vapor and nitrogen are then

removed from the lower stratosphere.

Chemical reactions similar to those occurring inside PSCs take place on

natural aerosol, the concentration of which increases sharply following ma-

jor volcanic eruptions (Fig. 9.1). Enhanced aerosol surface area, which figures

Problems

315

centrally in heterogeneous chemistry, is then comparable to that normally ob-

served over the Antarctic in connection with PSCs. This mechanism may have

been at least partly responsible for anomalously low ozone abundances that

were observed following the eruption of E1 Chichon (Hoffmon and Solomon,

1989).

Suggested Reading

Atmospheric Science: An Introductory Survey

(1977) by Wallace and Hobbs

contains a nice overview of cloud formation. Advanced treatments of cloud

microphysics are given in

Microphysical Processes in Clouds

(1993) by Young

and in

Microphysics of Clouds and Precipitation

(1978) by Pruppacher and

Klett, which also includes observations of macrophysical cloud properties.

Production of atmospheric aerosol is discussed in the monograph

Atmospheric

Aerosols: Their Formation, Optical Properties, and Effects

(1982), edited by

Deepak.

Aerosol and Climate (1988)

edited by Hobbs and McCormick discusses

possible impacts of increased aerosol. Stratospheric aerosol is reviewed jointly

with polar stratospheric clouds in

Report of the International Ozone Trends

Panel: 1988

(WMO, 1988).

International Cloud Atlas

(WMO, 1969) presents a complete classification of

clouds and a photographic survey.

Cloud Dynamics

(1993) by Houze is a comprehensive treatment of the subject

that includes numerous illustrations of cloud formation and structure. An

advanced treatment of the fluid dynamics surrounding cloud formation and of

laboratory simulations is presented in

Environmental Aerodynamics

(1978) by

Scorer.

Classical Electrodynamics

(1975) by Jackson provides a rigorous development

of Rayleigh scattering. Mie scattering is formally discussed in

An Introduction

to Atmospheric Radiation

(1980) by Liou.

Radiation and Cloud Processes in the Atmosphere

(1990) by Liou is a com-

prehensive treatment of cloud radiative processes and their roles in global

energetics. The radiative properties of water clouds and their parameteriza-

tion are developed in Stephens (1978a,b).

Hartmann

et al.

(1986) contains a nice overview of how cloud and surface

effects figure in the Earth's energy budget.

Climate Change: The IPCC Scientific Assessment

(Houghton

et al.,

1990) dis-

cusses historical variations of climate, surveying trends in atmospheric aerosols

and trace gases and their possible involvement in climate feedback mecha-

nisms.

Problems

9.1. Contrast the characteristic vertical scale of aerosol in the troposphere

with that in the stratosphere, in light of removal processes.

316 9

Aerosol and Clouds

9.2. Why is nitrate an inevitable by-product of combustion?

9.3. In terms of the size distribution

n(a),

derive an expression for the size

spectrum of (a) aerosol surface area

S(a)

and (b) aerosol mass

M(a),

particles have uniform density p.

9.4. A population of cloud droplets has the log-normal size spectrum

dn- no

[ ln2(~)]

d(log a) - cr~/2--~ exp - 20.2

where n o = 300 cm -3,

a m

5 Ixm is the median droplet radius, and

~r = 4 Ixm is the rms deviation of ln(a). (a) Plot the size spectrum

dn/d(log a),

the surface area spectrum

dS/d(log a),

and the mass spec-

trum

dM/d(log a).

(b) Contrast the distributions of those properties over

droplet radius a.

9.5. Discuss how the introduction of volcanic dust can affect the mean surface

temperature of the earth.

9.6. Derive expression (9.11) for the growth rate of a droplet through con-

densation.

9.7. Show that the rate a droplet's mass increases via coalescence is described

by (9.13).

9.8. Provide an expression for the potential barrier that must be overcome

for a water droplet to be activated.

9.9. (a) Determine the critical radius at 0.2% supersaturation for a droplet of

pure water. (b) How large must a droplet containing

10 -16

g of sodium

chloride become to grow spontaneously?

For the cloud described in Fig. 5.5, calculate the liquid water content at

650 mb, presuming adiabatic conditions.

A cumulus cloud forms inside a moist thermal. The base of the thermal is

at 1000 mb, where T O = 30~ and r 0 = 10 g kg -1. (a) If, at all elevations,

the thermal is 2~ warmer in its core than near its periphery (other

factors being equivalent), determine the height difference between the

cloud base at its center versus at its periphery. (b) How would mixing of

moisture with the environment modify this result?

Discuss why clouds often have bases at, not one, but several distinct

levels.

Convection is favored over elevated terrain. In terms of 0 and hydrostatic

stability, discuss why convection tends to form earlier during the day and

become more intense over mountains.

In relation to cloud dissipation, contrast entrainment of environmental

air from above versus below an established cumulus.

9.10.

9.11.

9.12.

9.13.

9.14.

Problems

317

9.15. The flow about a falling sphere of radius a and velocity w is

laminar

the dimensionless Reynolds number

paw

Re=

is less than 5000 (Chapter 13), where/z = 1.7 x 10 -5 kgm -1 s -1 is the

coefficient of viscosity for air. Under these circumstances, the sphere

experiences a viscous force

9.16.

9.17.

9.18.

9.19.

9.20.

9.21.

9.22.

9.23.

9.24.

9.25.

D = -6vrtzaw

known as

Stokes drag.

(a) Calculate the terminal velocity

w t

of a spherical

cloud droplet of radius a. (b) For what range of a does the preceding

result apply if the flow becomes turbulent for

> 5000? (c) If the flow

about them remains laminar, how large must droplets grow before they

can no longer be supported by an updraft of 1 rn s -1 ?

Consider a population of cloud droplets having size distribution

n(a)

un-

der the conditions of Problem 9.15. (a) Derive an expression for the spe-

cific drag force exerted on air by the falling droplet population. (b) What

is required to maintain an updraft in the presence of those droplets?

Estimate the time for volcanic dust particles of density 2.6 x 103 kg m -3

to reach the earth's surface from 50 mb if the tropopause is at 200 mb

and the particles are spherical with a mean radius of (a) 1.0/zm and

(b) 0.1/xm.

(a) Use typical observed values of

pl/p'~ a

to characterize the fractional

composition of a nonprecipitating cumulus by surface air. (b) Discuss the

thermodynamics of an air parcel inside the cloud and its interaction with

environmental air.

Estimate the entrainment height (Sec. 7.4.2) for a thermal of diameter

(a) 100 m and (b) 1 km.

Describe the evolution of a stack of lenticular clouds if they form from

moisture anomalies upstream that are sheared and advected through the

mountain wave by the prevailing flow.

Plot the saturation mixing ratio with respect to water and with respect to

ice as functions of temperature for cloud at 400 mb.

Why does the sky appear brighter when the ground is snow covered?

Discuss why the milky appearance of the sky, which is often observed

from the surface, disappears at an altitude of a kilometer or two.

Other factors identical, why does a nimbus cloud appear darker than

others?

Use the scattered intensity (9.19) to obtain the total scattered power

(9.20) for Rayleigh scattering.

318 9 Aerosol and Clouds

9.26.

9.27.

Transmission of diffuse SW radiation through a scattering layer is de-

scribed in terms of the phase function P(cos 19), where O is the three-

dimensional scattering angle. Express cos 19 in terms of the zenith angles

0 and 0' and the azimuthal angles ~b and ~b' of scattered and incident

radiation, respectively.

Calculate the atmospheric albedo due to Rayleigh scattering for overhead

sun and (a) h = 0.7/xm, (b) h = 0.5 /zm, and (c) h = 0.3 tzm. The

refractive index of air at 1000 mb and 273 K is approximated by

(m - 1)106 = 6.4328 101 +

2.94981

x 104

2.554 x 102

146- h -2 41 - h -2

with h in micrometers and m- 1 proportional to density.

9.28. Scattering of microwave radiation by cloud droplets and precipitation en-

ables cloud properties to be measured by radar. (a) Verify that Rayleigh

scattering is a valid description of such behavior. (b) The backscattering

coefficient (8.6), which measures the reflected power per unit length of

scattering medium, follows from the scattering cross section as

fl s ( "rr ) = n & s P ( 'rr ) ,

9.29.

9.30.

9.31.

9.32.

9.33.

9.34.

9.35.

9.36.

where n is the particle number density and P(Tr) is the phase function

for backward scattering. Derive an expression for/3s(zr) in terms of the

radius a of scatterers and the fractional volume r/=

n. 47ra3

occupied

by them to show that the reflectivity is proportional to

a 6.

Derive the radiative transfer equation governing azimuthal-mean diffuse

radiation (9.36) from the full radiative transfer equation.

Sunsets were modified for several years following the eruption of Kraka-

toa. How small must particles have been?

Show that, for single scattering, the diffuse intensity I(/x, r) is propor-

tional to the phase function P(~; tz~).

Derive the system (9.37) governing upwelling and downwelling fluxes of

diffuse radiation.

Show that the blackbody function B*[T] is a particular solution of (9.46).

Show that transmission of diffuse SW radiation is governed by the system

(9.39).

For the cloud droplet population in Problem 9.4, compute (a) the

scattering-equivalent mean droplet radius, (b) the liquid water path for

a cloud 4 km deep, (c) the cloud's optical depth, and (d) the cloud's

absorptivity for A = 0.5/zm and a solar zenith angle of 30 ~

Calculate the optical depth posed to SW radiation by a 5-km cumulus

congestus (an organization of cumulus), which has an average liquid

Problems

319

9.37.

9.38.

9.39.

9.40.

9.41.

9.42.

9.43.

9.44.

9.45.

water content of 0.66 g m -3 and a scattering-equivalent mean droplet

radius of 12/zm.

Satellite measurements of SW radiation enable the albedo of clouds to be

determined, from which the cloud optical depth can be inferred. (a) Plot

cloud albedo as a function of optical depth for a solar zenith angle of

30 ~ presuming a homogeneous scattering layer and a black underlying

surface. (b) Discuss the sensitivity of cloud albedo to changes in optical

depth for ~'c > 50. What implications does this have for inferring optical

depth?

A satellite measuring backscattered SW radiation and LW radiation emit-

ted at 11 /xm observes a tropical cloud with an albedo of 0.9 and a

brightness temperature of 220 K. If the solar zenith angle is 30 ~ and

a scattering-equivalent radius of 5 /xm applies, use the result of Prob-

lem 9.37 to estimate (a) the liquid water path of the cloud and (b) the

cloud's average liquid water content if it is 1 km thick.

A homogeneous cloud layer of optical depth ~'c is illuminated by the

solar flux

at a zenith angle 0s - cos -a/Xs. If the surface is gray with

absorptivity a, (a) derive expressions for the upwelling and downwelling

diffuse fluxes inside the scattering layer and (b) plot the albedo and

transmissivity, as functions of a, for overhead sun and ~c - 20.

Consider the radiative-convective equilibrium for the cloudy atmosphere

in Fig. 9.33. (a) Explain why the surface temperature in Fig. 9.34 increases

linearly with the cloud's height once the cloud is elevated sufficiently

above the surface. (b) Nearly identical results are obtained for other

cloud optical depths. Why?

Satellite observations reveal the following scene properties for a region of

maritime convection in the tropics: a fractional cloud cover of 0.5, average

clear-sky and overcast albedos of 0.2 and 0.8, respectively, and average

clear-sky and overcast LW fluxes of 350 and 100 W m -2, respectively.

Calculate the average SW, LW, and net cloud forcing for the region.

Use the mean latent heat flux to the atmosphere, 90 W m -2 (Fig. 1.27),

to estimate the global-mean precipitation rate.

Estimate the fraction of the water vapor column in the tropics that is

processed by convection during one day. Reconcile this fraction with the

characteristic timescale and depth of individual convective cells.

Use the mean annual precipitation in Fig. 9.38 and a characteristic

tropopause height of 16 km to estimate the latent heating rate inside

the ITCZ.

Consider a horizontal interface separating two conservative media with

real refractive indices n l and n2. Use the condition that the horizontal

trace speed of electromagnetic waves (Sec. 14.1.2) must be identical on