Salby M.L. Fundamentals of Atmospheric Physics

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300

Aerosol and Clouds

slant optical path. For

= 20, d c increases from 53% for overhead sun to

75% when the sun is on the horizon. The behavior of ~ is nearly comple-

mentary, decreasing from 32% for overhead sun to only 10% when the sun is

on the horizon. Shallower cloud depends even more strongly on solar zenith

angle because the slant optical path then varies between optically thin and

optically thick conditions.

The factor most strongly influencing cloud optical properties is liquid water

content, which determines

(Stephens, 1978b). The optical depth of a cloud

can be expressed in terms of the column abundance of liquid water,

Et - ~]o ~

pldZ

= Az c 9 47rPw [a3dn(a)

(9.44)

which is called the

liquid water path.

From (9.34) and the fact that &e -

QeTra 2 ~

2zra 2 for SW radiation, the optical depth can be expressed as

3Et

= ~, (9.45.1)

2Pwae

where

f a(Tra2)dn(a)

ae = f (Tra2)dn(a)

(9.45.2)

is a scattering-equivalent mean droplet radius. Because most water clouds

have liquid water contents greater than 0.1 g m -3 (Table 9.2), cloud layers

more than a kilometer thick have liquid water paths

of 100 g m -2 and

greater. Those clouds then have optical depths in the visible of several tens

and greater. Deep clouds with El > 1000 g m -2 have albedos exceeding 80%

(see the bright features in Fig. 1.24).

For given Et, clouds with smaller droplets have a higher albedo and smaller

absorptivity than clouds with larger droplets (Fig. 9.31). The increased reflec-

tivity of clouds containing smaller droplets follows from the increased number

densities in such clouds and reduced absorption by smaller droplets. Their

smaller droplets and greater number densities make continental clouds more

reflective than maritime clouds of the same type and liquid water path (see,

e.g., Twomey, 1977). For the same reason, precipitation (a > 100/xm) sharply

increases the absorptivity of cloud. Ice clouds, while more complex, are like-

wise highly reflective across the visible, where their dependence on microphys-

ical properties resembles that of water clouds. Thin cirrus with ice water paths

~i <

5 g m -2 have albedos of order 10% and absorptivities of only a couple

of percent (see, e.g., Paltridge and Platt, 1981).

According to Fig. 9.28b, scattering by cloud particles falls off at h > 4/xm,

where water absorbs strongly (Fig. 9.25b). Figure 9.32 illustrates that water

clouds 3 km thick, which are highly reflective at h < 1/xm, become fully ab-

sorbing at h > 4/xm. The interaction of cloud with LW radiation can be treated

9.4 Radiative Transfer in Aerosol and Cloud

CLOUD OPTICAL PROPERTIES

301

10o

.-. 80

(D 7 60~///4 / /

40~// /

..J

rr 20

0 , ,,,~,I I I I II''

10 102 103

Y'z

(g m21

20 t,b, ........ ....... I

o~" 16

UJ 16

o 12

< 8

i-.

13_ 4

rr 8

< 4

10 102 103

(g m -2)

Figure 9.31 SW (a) reflectance and (b) absorptance, as functions of liquid water path, for a

solar zenith angle of 60 ~ and for different scattering-equivalent droplet radii

ae.

Adapted from

Slingo (1989).

as in the foregoing development for SW radiation, but with the scattering of

direct solar in (9.37) replaced by emission of terrestrial radiation: (1 - ~o)B*[ T].

Inside a cloud layer of temperature

T c,

upwelling and downwelling LW fluxes

are then described by

dFt

dT*

dF+

d-r*

= Ft

- w

[fFt +

f)F +]

w)B*[Tc] ,

= F "~ - ~o [fF "~ +

(1 -

f)F t ] -

(1 -

w)B*[Tc],

(9.46.1)

(9.46.2)

0.9

0.8

0.7

0.6

0.5 ~t~~ Category I -

0.4 ~ C~176 2 1

0.1 ~ -

~s_/_Z_//Z~,

O i/ ~ J I

O 0.5

I.o

1.5 z.o 2.5

3 4

5 6.0

WAVELENGTH

(/.z m)

Figure 9.32 Reflectance and absorp-

tance of 3-km-thick stratus, as functions of

wavelength, for overhead sun and for a range

of microphysical properties bounded by cat-

egories 1 and 2. Category 1 is based on a

droplet distribution of characteristic radius 6

/xm, n=102 cm -3, and pl=0.30 gm -3. Cate-

gory 2 includes rain with a droplet distribu-

tion of characteristic radius 600/zm, n=0.001

cm -3, and p/=2.1 gm -3. Source: Cox (1981).

302 9

Aerosol and Clouds

where the cloud is sufficiently thin for

to be treated as constant. The

blackbody spectrum B* is a particular solution of (9.46). Proceeding as in the

treatment of SW radiation leads to the general solution

F t - Ca+e ~* + Da_e -~* +

(1 -

oo)B*[Tc] ,

F + = Ca_e ~* + Da+e -~* +

(1 -

w)B*[Tc] ,

(9.47)

which applies inside the scattering layer.

To illustrate the influence of clouds on the LW energy budget, we consider

a statistically homogeneous scattering layer within the framework of radiative-

convective equilibrium (Sec. 8.5.2). Microphysical properties incorporated in

the treatment of SW radiation (Fig. 9.28) are used to define a cloud layer of

thickness

Azc

= 1 km and fractional coverage r/that is situated at a height

the troposphere--all under the conditions of radiative-convective equilibrium

(Fig. 8.21). In the spirit of a gray atmosphere, radiative characteristics at 10/zm

are used to define the broadband transmission properties for LW radiation,

whereas the fractional cloud cover is adjusted to give an albedo of 30%. The

fluxes F t and F+ are described by (8.70) outside the cloud layer and by (9.47)

inside the cloud layer. Matching fluxes across the scattering layer then leads

to behavior analogous to that under simple radiative-convective equilibrium

(Fig. 8.22), except for the addition of the cloud layer.

Figure 9.33a shows upwelling and downwelling fluxes in the presence of a

cloud layer of

"r c

= 20 that is situated at

= 8 km. The equilibrium tem-

perature structure (not shown) is identical to that in Fig. 8.21, except that

temperatures beneath the cloud layer are uniformly warmer. The surface tem-

perature T s has increased from its cloud-free value of 285 to 312 K. Below

the cloud layer, upwelling and downwelling fluxes resemble those under cloud-

free conditions (Fig. 8.22a), except likewise displaced to higher values. Inside

the cloud layer, the profiles of Ft and F+ undergo a sharp adjustment that

drives them nearly into coincidence. This behavior follows from the cloud be-

ing optically thick, so, away from its boundaries, the LW flux is approximately

isotropic and equal to

o'T 4.

Above the cloud layer, Ft and F~ recover the

cloud-free forms in Fig. 8.22a to satisfy boundary conditions at the top of the

atmosphere (8.63).

Sharp changes of Ft and F~ in Fig. 9.33a introduce strong LW warming and

cooling near the base and top of the cloud layer. The cloud-induced heating,

0 (q)

Cp Cp

where

(Q/r

is the clear-sky heating profile under radiative--convective equi-

librium (Fig. 8.22b), is shown in Fig. 9.33b. Absorption (warming) is concen-

trated within an optical depth of the cloud base, whereas emission (cooling) is

concentrated within an optical depth of the cloud top. These regions of net ab-

FLUX

m-*)

HEATING RATE

day-’)

Figure

9.33

Energetics inside a cloudy atmosphere that is in radiativexonvective equilibrium and contains a 1-h-thick scattering

layer with microphysical properties

cumulus

and downwelling

fluxes.

(b)

Cloud-induced

clear-sky conditions (Fig.

8.22).

304 9

Aerosol and Clouds

sorption and emission are shallow, analogous to Chapman layers (Sec. 8.5.3),

so they introduce substantial heating and cooling locally (8.72). The LW heat-

ing rate approaches 70 K day -1 near the cloud's base, whereas the LW cooling

rate approaches 50 K day -1 near its top. ~ By reemitting energy downward, the

cloud also introduces heating beneath its base, but much smaller than the

heating and cooling at the cloud's boundaries.

LW cooling in upper portions of a cloud is offset by SW heating, but

only partially (see, e.g., Stephens

et al.,

1978). Anvil cirrus experience net

radiative cooling at their tops of several tens of K day -1 (see, e.g., Webster

and Stephens, 1980) and heating at their bases as large as 100

K day -1

(Platt

et al.,

1984a). Radiative cooling at its top and heating at its base destabilize a

cloud layer, introducing convection that entrains drier environmental air and

tends to dissolve the cloud (Fig. 9.19). Radiative heating also tends to dissolve

cloud by elevating its saturation mixing ratio.

The cloud layer in Fig. 9.33 is optically thick. Therefore, it influences the

LW energy budget chiefly through cloud-top emission, which decreases with

the cloud's temperature and elevation. Figure 9.34 shows the dependence on

cloud height of surface temperature under radiative-convective equilibrium.

,~ 7

-1-

(.9

"1-"

..j 5

285 290 295 300 305 310 315 320 325

T s

(K)

Figure 9.34 Surface temperature for the cloudy atmosphere in Fig. 9.33, as a function of the

cloud layer's height.

9.5

Roles of Clouds and Aerosol in

Climate 305

Situating the cloud below 2 km recovers nearly the same surface temperature

as under cloud-free conditions. The scattering layer is then embedded inside

the optically thick layer of water vapor, so the cloud does not alter the effective

emission temperature of the atmosphere. However,

> 2 km leads to warmer

surface temperature, which increases steadily with the cloud's height. By

Zc = 8

km, T s has increased 27 K to maintain the cloud at the equivalent blackbody

temperature of the earth (Problem 9.40).

Water clouds become optically thick to LW radiation for liquid water paths

~t greater than about 20 g

m -2

(see, e.g., Stephens, 1984), wherein they behave

as blackbodies. The LW characteristics of ice clouds are more complex, at

least for those that are optically thin. The emissivity (LW absorptivity) of thin

cirrus with ice water paths less than 10 g m -2 (which is typical of cirrus 1 km

thick) is 0.5 or smaller and may vary diurnally with convection (Platt

et aL,

1984b). However, even cirrus emits approximately as a blackbody for

Azc

sufficiently large. Figure 9.35 shows spectra of outgoing LW radiation (OLR)

in the tropics over a clear-sky region and several neighboring cirrus-covered

regions of different optical depths. Cirrus reduces the radiation emitted to

space throughout the LW, except near 15/xm, where radiation emitted by the

surface has already been absorbed by underlying CO2. By an optical depth

of ~'c = 5, OLR has approached the blackbody spectrum with a temperature

equal to the cirrus temperature of 230 K. The effect of cirrus is to remove

the layer emitting to space to a higher level and colder temperature. Outgoing

radiation is most reduced in the atmospheric window between 8 and 12/xm,

where radiation emitted by the surface passes relatively freely through the

atmosphere under cloud-free conditions.

Contrary to the preceding treatment, real clouds have only finite horizontal

extent. A finite cloud scatters energy out its sides, which allows neighbor-

ing clouds to interact. Energy lost through the sides of a cloud exceeds SW

absorption for aspect ratios as small as 1/20 (Cox, 1981), so finite extent is im-

portant for all but extensive stratiform decks. Optical characteristics are then

sensitive to the vertical distribution of microphysical properties. A cloud hav-

ing the smallest droplets near its base will be less reflective than one having

the smallest droplets near its top because, in the former case, much of the SW

energy will have already been scattered out the sides before the highly reflec-

tive droplets are encountered. Finite cloud can also increase SW absorption

by reducing the effective solar zenith angle.

9.5 Roles of Clouds and Aerosol in Climate

Clouds modify the global energy balance by altering the absorption and scat-

tering characteristics of the atmosphere. The largest variations of albedo and

OLR in Fig. 1.29 are associated with clouds (see, e.g., Ramanathan

et al.,

1989). Convection also supports large transfers of sensible and latent heat

306 9

Aerosol and Clouds

WAVELENGTH (IJm)

100 20 16.7 14.2 12.5 I0 9 8 7 6 5

200 ........ i .......... J ! ............... I ~ I ............. ......... i ............... I l 1 ~ ..................

1 80 -- 316 K

.... -

.,"" "''4

160 -

,"'"

""',,

/ "'N

E " .... 296 K. ""

--,.. 140 -- /,-" "- "- --

20- 276,, "

"",,,

r-- "" """"

o ~ Itcc,b,,..

"",,, "",.,.

60 "'" " " "c~ 2"'" "'"'" --

4-0 ~'"" --

'~'"216K.'. ........... " .... 2

o i

....... t I ~ I ,,

[[7

.....

400 600 800 1 000 1 200 1 O0

Wavenumber

(cm -1 )

Figure 9.35 Spectrum of outgoing LW radiation observed by Nimbus-4 IRIS for a clear-sky

region

('r c

= 0) at (134~176 and neighboring cirrus-covered regions (zc > 0). Courtesy of

B. Carlson (NASA/Goddard Institute for Space Studies).

from the earth's surface (Fig. 1.27), which represent another important heat

source for the atmosphere. Similar radiative effects are introduced by aerosol,

which controls cloud formation through microphysical processes (Sec. 9.2).

9.5.1 Involvement in the Global Energy Budget

INFLUENCE OF CLOUD COVER

The role of clouds in global energetics can be interpreted as a forcing in

the radiative energy balance. For LW radiation, the large opacity of clouds in-

creases the optical depth of the atmosphere, which promotes increased surface

temperature by enhancing the greenhouse effect (8.81). Thus, clouds introduce

warming in the LW energy budget, and this warming is proportional to the

9.5 Roles of Clouds and Aerosol in Climate

307

cloud-top temperature and height (Fig. 9.34). Cold cirrus also cools the lower

stratosphere via exchange in the 9.6-~m band of ozone (Sec. 8.5.3). For SW ra-

diation, the high reflectivity of clouds decreases the incoming solar flux, which

favors reduced surface temperature (8.81). Thus, clouds introduce cooling in

the SW energy budget. Unlike the LW effect, cloud albedo is insensitive to

cloud height, so low clouds in visible imagery (Fig. 1.24) are almost as bright

as high clouds. The zenith angle dependence of scattering (Fig. 9.30b) en-

hances albedo at high latitudes. Clouds also introduce heating by absorbing

SW radiation.

Clouds routinely cover about 50% of the earth and account for about half

of its albedo. Marine stratocumulus (e.g., over the southeastern Atlantic in

Fig. 1.24) are particularly important because they cover a large fraction of the

globe and reflect much of the incident SW radiation. However, because their

cloud-top temperatures do not differ substantially from those of the surface,

marine stratocumulus do not appreciably modify OLR (refer to Fig. 1.23) and

hence the LW energy budget. In contrast, deep cumulus over Africa, South

America, and the maritime continent have cloud-top temperatures as much as

100 K colder than the underlying surface, so they sharply reduce OLR from

that under cloud-free conditions.

The SW and LW effects of clouds are both variable. Owing to the zenith an-

gle dependence of scattering (Fig. 9.30b) and to systematic variations in cloud

cover and type, the most important component of cloud variability is diurnal.

Figure 9.36 shows the daily variation of cloud properties over the southeast-

ern Pacific, which is populated by marine stratocumulus, and over the Amazon

basin, where deep continental convection prevails. Marine stratocumulus (Fig.

9.36a) is present throughout the day, but undergoes a 50% variation in albedo.

This resembles the variation of fractional cloud cover, which results from SW

heating during daylight hours. The corresponding variation of OLR is small.

Continental convection (Fig. 9.36b) undergoes a 25% variation of OLR, which

resembles the daily life cycle of cumulonimbus towers and anvil cirrus. The

corresponding variation of fractional cloud cover is small. Cirriform shields,

which are glaciated and markedly colder than the surface, persist several hours

after convection has dissipated (Houze, 1982; Platt

et al.,

1984a).

A quantitative description of how clouds figure in the global energy budget

is complicated by their dependence on microphysical properties and inter-

actions with the surface. These complications are circumvented by comparing

radiative fluxes at the top of the atmosphere (TOA) under cloudy versus clear-

sky conditions. Over a given region, the column-integrated radiative heating

rate must equal the difference between the energy flux absorbed and that

emitted

Q - ~jn ~

pgtdz

= (1 -

d)F s -

FEW ,

(9.48)

308

9 Aerosol and Clouds

100

D 80

Z ~

<0~ 60

< 0 20

280

260

~. 240

200

180

160

(a) Southeastern Pacific (b) Amazon

Fractional |

k N ~%. Cloud Cover I IN,........._ Fractional /'~

..... Clear I

_ Cloud

9 Total ]

i i l i i l

6 12 18 6 12 18

LOCAL TIME (hr) LOCAL TIME (hr)

Figure 9.36 Top-of-the-atmosphere radiative properties, as functions of local time, over

(a) the southeastern Pacific, which is populated by marine stratocumulus, and (b) the Ama-

zon basin, which is populated by organized cumulonimbus and anvil cirrus. Adapted from Minnis

and Harrison (1984).

where d is the albedo of the region and FEW and F, denote the downward

SW and upward LW fluxes at the TOA. The

cloud radiative forcing

C - Q- 0 cs, (9.49)

where QCS is the heating rate under clear-sky conditions, then represents the

net radiative influence of clouds on the column energy budget of the region.

Incorporating (9.49) into (9.48) yields

C - (dcs -

ag)F s + (F cs -

FEW),

(9.50)

from which we identify the SW and LW components of cloud forcing

Csw - (d cs - d) F,

= FScW s - Fsw (9.51.1)

CLw = Fcs - FEW. (9.51.2)

9.5 Roles of Clouds and Aerosol in Climate

309

If the region has fractional cloud cover ?7, which refers to overcast subre-

gions, the outgoing SW and LW fluxes are given by

fsw = (1 - rl)f cs + tiE ~

FEW = (1 -- rt)F cs + rtF~ c,

(9.52)

where the superscripts refer to clear-sky and overcast subregions. Then the

SW and LW components of cloud radiative forcing can be written

Csw = ,(Fs - Fs%)

= ?TFs (d

cs - d ~

(9.53.1)

= s -

(9.53.2)

The components of cloud forcing (9.53) can be evaluated directly from

broadband fluxes of outgoing LW and SW radiation measured by satellite.

Figure 9.37 shows time-averaged distributions of Csw, CLw, and C. Long-

wave forcing (Fig. 9.37a) is large in centers of deep convection over tropical

Africa, South America, and the maritime continent, where CLW approaches

100 W m -2 (compare Fig. 1.25b). Secondary maxima appear in the maritime

Inter Tropical Convergence Zone (ITCZ) and in the North Pacific and North

Atlantic storm tracks. Shortwave forcing (Fig. 9.37b) maximizes in the same

regions, where Csw < -100 W m -2. Negative SW forcing over extensive ma-

rine stratocumulus is smaller but significant. Inside the centers of deep trop-

ical convection, SW and LW cloud forcing nearly cancel, leaving small values

of C (Fig. 9.37c) throughout the tropics. Negative Csw in the storm tracks

and over marine stratocumulus then dominate positive CLW to prevail in the

global-mean cloud forcing. Globally averaged values of CLw and Csw are

about 30 and -45 W m -2, respectively, which may be compared against the 90

W m -2 transfer of latent heat to the atmosphere (Fig. 1.27). The global-mean

cloud forcing is then -15 W m -2. This represents cooling about three times as

great the warming that would be introduced by a doubling of CO2. Thus, even

a small change of cloud radiative forcing could overshadow the direct effect

of increased greenhouse gases.

While circumventing many of the complications surrounding cloud behav-

ior, cloud forcing is limited in several respects. Foremost is the fact that C

gives only the column-integrated effect of clouds--it provides no information

on the vertical distribution of that heating. Shortwave cloud forcing (which

represents cooling) is concentrated near the surface, because the principal

effect of increased albedo is to shield the ground from incident solar radi-

ation. Longwave cloud forcing (which represents warming) is manifested in

heating near the base of a cloud and cooling near its top (Fig. 9.33b). That