Jacobson M.Z. Atmospheric Pollution
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THE GREENHOUSE
EFFECT AND GLOBAL
WARMING
12
T
he two major global-scale environmental issues of international concern since
the 1970s have been the threats of global stratospheric ozone reduction and
global warming. As discussed in Chapter 11, the threat to the global ozone
layer has been controlled to some degree because national and international regula-
tions have required the chemical industry to use alternatives to chlorocarbons and
bromocarbons, the chemicals primarily responsible for much of the ozone-layer reduc-
tions. Regulations are similarly responsible for improvements in air quality and acid
deposition problems in the United States and many western European countries since the
early 1970s (e.g., the U. S. Clean Air Act Amendments of 1970 motivated U.S. automo-
bile manufacturers to develop the catalytic converter in 1975, which led to improvements
in urban air quality; regulations through the Clean Air Act Amendments and the 1979
Geneva Convention on Long-Range Transboundary Air Pollution led to reductions in sul-
fur emissions and an amelioration of some acid deposition problem in the 1980s and
1990s). The second major issue of international concern, the threat of global warming, has
been addressed at international meetings, but progress in regulating emissions responsible
for the problem has been slow. In this chapter, global warming is discussed and distin-
guished from the natural greenhouse effect. Climate responses to enhanced gas and
aerosol particle concentrations are examined. Historical and recent temperature trends,
both in the lower and upper atmosphere, are described. National and international ef
forts
to curtail global warming are also discussed, as are potential effects of global warming.
12.1. THE TEMPERATURE ON THE EARTH IN THE ABSENCE OF A
GREENHOUSE EFFECT
The natural greenhouse effect is the warming of the Earth’s lower atmosphere due to
natural gases that transmit the sun’s visible radiation, but absorb and reemit the Earth’s
thermal-IR radiation. Greenhouse gases cause the air below them to warm like a glass
house causes a net warming of its interior. Because most incoming solar radiation can
penetrate a glass house but a portion of outgoing thermal-IR radiation cannot, air
inside a glass house warms during the day so long as mass (such as plant mass) is
present to absorb solar and reemits thermal-IR radiation. The surface of the Earth, like
plants, absorbs solar and reemits thermal-IR radiation. Greenhouse gases, like glass,
are transparent to most solar radiation but absorb a portion of thermal-IR. Global
warming is the increase in the Earth’s temperature above that from the natural green-
house effect due to the addition of anthropogenically emitted greenhouse gases and
particulate black carbon to the air.
In the absence of greenhouse gases, the temperature of the Earth can be estimated,
to first order, with a simple radiation balance model that considers incoming solar radi-
ation and outgoing thermal-IR radiation from the Earth. This model can be applied to
other planets as well. The difference between the temperature predicted by the energy
balance model and the real temperature observed at the surface of the Earth is hypoth-
esized to result from the greenhouse effect. The simple energy balance model is
described next.
12.1.1. Incoming Solar Radiation
In Chapter 2, it was shown that the sun emits radiation with an effective photosphere
temperature of about T
p
5,785 K. The energy flux (joules per second per square
310
meter or watts per square meter) emitted by the sun’s photosphere can be calculated
from the Stefan–Boltzmann law (Equation 2.2) as
F
p
p
B
T
p
4
(12.1)
where
p
is the emissivity of the photosphere. The emissivity is near unity because the
sun is essentially a blackbody (a perfect absorber and emitter of radiation).
Multiplying the energy flux by the spherical surface area of the photosphere, 4R
p
2
,
where R
p
6.96 10
8
m (696,000 km) is the effective radius of the sun (distance
from the center of the sun to the top of the photosphere), gives the total energy per unit
time (J s
1
or W) emitted by the photosphere as 4R
p
2
F
p
. Energy emitted from the pho-
tosphere propagates through space on the edge of an ever-expanding concentric sphere
originating from the photosphere. Because conservation of energy requires that the
total energy per unit time passing through a concentric sphere an
y distance from the
photosphere equals that originally emitted by the photosphere, it follows that the total
energy per unit time passing through a sphere with a radius corresponding to the
Earth–sun distance (R
es
) is
(12.2)
where F
s
is the solar energy flux (J s
1
m
2
or W m
2
) on a sphere with a radius corre-
sponding to the Earth–sun distance. Rearranging Equation 12.2 and combining the
result with Equation 12.1 gives
(12.3)
which indicates that the energy flux from the sun decreases proportionally to the
square of the distance away from the sun. This can be illustrated with a simple exam-
ple. If you put your hand over a lightbulb, you will feel the heat from the bulb, but as
you move your hand away from the bulb, the heat that you feel decreases proportional-
ly to the square of the distance away from the bulb.
The average Earth–sun distance is about 1.5 10
11
m (150 million km), giving the
average energy flux at the top of the Earth’s atmosphere from Equation 12.3 as F
s
1,365 W m
2
, which is called the solar constant. Figure 12.1 shows that the
F
s
R
p
R
es
2
F
p
R
p
R
es
2
B
T
4
p
4R
2
es
F
s
4R
2
p
F
p
THE GREENHOUSE EFFECT AND GLOBAL WARMING 311
Obliquity
23.5°
Sun
Autumnal equinox
Sept. 23
Vernal equinox
Mar. 20
147 million km
152 million km
N.H. winter
S.H. summer
solstice
Dec. 22
N.H. summer
S.H. winter
solstice
June 22
Figure 12.1. Relationship between the sun and Earth at the times of solstices and equinoxes.
Earth–sun distance is 147 million km in December (Northern Hemisphere winter) and
152 million km in June (Northern Hemisphere summer) due to the fact that the Earth
rotates around the sun in an elliptical pattern with the sun at one focus. If these
distances are used in Equation 12.3, F
s
1,411 W m
2
in December and 1,321 W m
2
in June. Thus, a difference of 3.3 percent in Earth–sun distance between December
and June corresponds to a difference of 6.6 percent in solar radiation reaching the
Earth between these months. In other words, 6.6 percent more radiation falls on the
Earth in December than in June.
Despite the excess radiation reaching the top of the Earth’s atmosphere in
December, the Northern Hemisphere (N.H.) winter still starts in December because the
Southern Hemisphere (S.H.) is tilted toward the sun in December, as shown in
Fig. 12.1. The figure shows that the axis of rotation of the Earth is tilted all year 23.5
from a line perpendicular to the plane of the Earth’s orbit around the sun. This angle is
called the obliquity of the Earth’s axis of rotation. As a result of the Earth’s obliquity,
the sun’s direct rays hit their farthest point south, 23.5S latitude, on December 22
(N.H. winter, S.H. summer solstice) and their farthest point north, 23.5N latitude, on
June 22 (N.H. summer, S.H. winter solstice) (Fig. 12.1 and 12.2). The latitude at
23.5S is called the Tropic of Capricorn and that at 23.5N is the Tropic of Cancer.
The winter and summer solstices are the shortest and longest days of the year, respec-
tively. On March 20 (vernal equinox) and September 23 (autumnal equinox), the sun
is directly over the equator and the length of day equals that of night.
Because the sun’s rays are most intense over the Southern Hemisphere in
December and because Northern Hemisphere days are shorter in December than in
June, temperatures in the Northern Hemisphere are cooler in December than in June,
even though the Earth receives more radiation in December than in June.
From the sun’s point of view, the Earth is merely a circular disk (rather than a
sphere) absorbing some of its radiation. Thus, the quantity of incoming radiation
received by the Earth is the solar constant multiplied by the cross-sectional area of the
Earth, R
e
2
(m
2
), where R
e
6.378 10
6
m (6378 km) is the Earth’s radius. Not all
312 ATMOSPHERIC POLLUTION: HISTORY, SCIENCE, AND REGULATION
N.H. winter, S.H. summer
solstice, Dec. 22
23.5°
23.5°
Vernal equinox, Mar. 20
Autumnal equinox, Sept. 23
Tropic of
Cancer
Tropic of
Capricorn
Earth
Sun
Sun
Sun
Equator
Axis of
rotation
N.H. summer, S.H. winter
solstice, June 22
Figure 12.2. Positions of the sun relative to the Earth during solstices and equinoxes. Of the
four times shown,
the Earth
–sun distance is gr
eatest at the N.H. summer
, S.H. winter solstice.
incoming solar radiation is absorbed by the Earth. Some is reflected by snow, deserts,
and other light-colored ground surfaces. In the real atmosphere, clouds also reflect
incoming solar radiation. The fraction of incident energy reflected by a surface is the
albedo or reflectivity of the surface. Table 12.1 gives mean albedos in the visible
spectrum for several surface types. The table shows that the albedo of the Earth and
atmosphere together (planetary albedo) is about 30 percent. More than two-thirds of
the Earth’s surface is covered with water, which has an albedo of 5 to 20 percent (typ-
ical value of 8 percent), depending largely on the angle of the sun. Soils and forests
also have low albedos. Much of the Earth-atmosphere reflectivity is due to clouds and
snow, which have high albedos.
Taking into account the cross-sectional area of the Earth and the Earth’s albedo
(A
e
, fraction), the total energy per unit time (W) absorbed by the Earth in the simple
energy balance model is
E
in
F
s
(1 A
e
)(R
e
2
) (12.4)
This incoming radiation must be equated with radiation emitted by the Earth to derive
an equilibrium temperature.
12.1.2. Outgoing Thermal-IR Radiation
The Earth emits radiation as a sphere, not a cross section. The energy flux emitted by
the Earth can be estimated with the Stefan–Boltzmann law, given in Equation 2.2.
Applying this law to the Earth and multiplying through by the surface area of the
Earth, 4R
e
2
(m
2
), gives the energy per unit time (W) emitted by the Earth as
E
out
e
B
T
e
4
(4R
e
2
) (12.5)
where
e
is the globally averaged thermal-IR emissivity of the Earth (dimensionless)
and T
e
is the equilibrium temperature (K) of the Earth’s surface. Table 12.1 gives thermal-
IR emissivities for different surfaces. The actual globally averaged emissivity of the
Earth is about 0.9 to 0.98, but for the basic calculation presented here, it is assumed to
equal 1.0.
THE GREENHOUSE EFFECT AND GLOBAL WARMING 313
Table 12.1. Solar Albedos and Ther
mal-IR Emissivities for Se
veral Surface Types
Earth and atmosphere 0.3 0.90–0.98
Liquid water 0.05–0.2 0.92–0.96
Fresh snow 0.7–0.9 0.82–0.995
Old snow 0.35–0.65 0.82
Thick clouds 0.3–0.9 0.25–1.0
Thin clouds 0.2–0.7 0.1–0.9
Sea ice 0.25–0.4 0.96
Soil 0.05–0.2 0.9–0.98
Grass 0.16–0.26 0.9–0.95
Desert 0.20–0.40 0.84–0.91
Forest 0.10–0.25 0.95–0.97
Concrete 0.1–0.35 0.71–0.9
Surface Type Albedo (Fraction) Emissivity (Fraction)
Estimates from Liou (1992), Hartmann (1994), Oke (1978), and Sellers (1965).
12.1.3. Equilibrium Temperature of the Earth
Equating the incoming solar radiation from Equation 12.4 with the outgoing thermal-
IR radiation from Equation 12.5 and solving for the equilibrium temperature of the
Earth’s surface in the absence of an atmosphere gives
314 ATMOSPHERIC POLLUTION: HISTORY, SCIENCE, AND REGULATION
(12.6)T
e
F
s
(1A
e
)
4
e
B
14
EXAMPLE 12.1
Estimate the equilibrium temperature of the Earth given F
s
1,365 W m
2
, A
e
0.3, and
e
1.0.
Solution
From Equation 12.6, the equilibrium temperature of the Earth is T
e
254.8 K, which would be the
temperature of the Earth in the absence of an atmosphere.
Data compiled from Lide et al. (1998), except that equilibrium temperatures were calculated from Equation 12.6.
Table 12.2. Equilibrium and Actual Temperatures of the Surfaces of Planets and the Moon
Mercury 57.9 2.44 2 10
15
He(0.98), H(0.02) 0.11 436 440
Venus 108 6.05 90 CO
2
(0.96), N
2
(0.034), H
2
O(0.001) 0.65 252 730
Earth 150 6.38 1 N
2
(0.77), O
2
(0.21), Ar (0.0093) 0.30 255 288
Moon 150 1.74 2 10
14
Ne(0.4), Ar(0.4), He(0.2) 0.12 270 274
Mars 228 3.39 0.007 CO
2
(0.95), N
2
(0.027), Ar(0.016) 0.15 217 218
Jupiter 778 71.4 100 H
2
(0.86), He(0.14) 0.52 102 129
Saturn 1,427 60.3 100 H
2
(0.92), He(0.74) 0.47 77 97
Uranus 2,870 26.2 100 H
2
(0.89), He(0.11) 0.51 53 58
Neptune 4,497 25.2 100 H
2
(0.89), He(0.11) 0.41 45 56
Pluto 5,900 1.5 1 10
5
? 0.30 41 50
Equili-
brium Actual
Distance Equatorial Surface Tempe- Tempe-
from Sun Radius Pressure Major Atmospheric Gases (Volume rature rature
Object (10
9
m) (10
6
m) (Bars) Mixing Ratios) Albedo (K) (K)
Example 12.1 shows that the equilibrium temperature of the Earth,
255 K, is about
18 K below the freezing temperature of water and would not support most life on
Earth. Fortunately, the actual globally averaged near-surface air temperature is about
288 K. The 33 K difference between the predicted equilibrium temperature and the
actual temperature of the Earth results from the fact that the Earth has an atmosphere
that is transparent to most incoming solar radiation but selectively absorbs a portion of
outgoing thermal-IR radiation. Some of the absorbed radiation is reemitted back to the
surface, warming the surface. The resulting 33 K increase in temperature over the
equilibrium temperature of the Earth is called the natural greenhouse effect.
Table 12.2 compares the equilibrium temperatures, calculated from Equation 12.6
with actual temperatures for several planets. The table indicates that the planet with the
largest difference between its actual and equilibrium temperatures is Venus [Fig. 12.3(a)].
The surface temperature of Venus is more than 470 K wa
rmer than is its equilibrium
temperature. Because Venus is closer to the sun than is the Earth, Venus receives more
incident solar radiation than does the Earth, and Venus’s temperature, early in its evo-
lution, was higher than was that of the Earth. As a result, liquid water and ice on the
surface of Venus, if ever present, melted and evaporated, respectively. The resulting
water vapor, exposed to intense far-UV radiation from the sun,
photolyzed to atomic
hydrogen [H(g)] and the hydroxyl radical [OH(g)]. Over time, atomic hydrogen escaped
Venus’s gravitational field to space, depleting the atmosphere of its ability to reform
water vapor. Because the surface of Venus lost all liquid water from evaporation, there
was no mechanism to dissolve and convert CO
2
(g), which was building up in the
atmosphere due to volcanic outgassing, back to carbonate rock. As its mixing ratio
increased, CO
2
(g) absorbed more thermal-IR radiation, heating the atmosphere, pre-
venting condensation of water, preventing further removal of CO
2
(g). The nearly
endless positive feedback cycle that occurred on Venus is called the runaway green-
house effect. Today, Venus has a surface air pressure ninety times that of the Earth,
and its major atmospheric constituent is CO
2
(g).
Table 12.2 shows that Mercury, the Moon, Mars, and Pluto have thin atmospheres
and little greenhouse effect. Their atmospheres are thin because light gases have
escaped their weak gravitational fields. Although Mars’ surface pressure is less than
one percent that of the Earth, Mars’ CO
2
(g) partial pressure is about 20 times that of
the Earth. Because CO
2
(g) is relatively heavy, it has not entirely escaped Mars’ atmos-
phere, and because Mars has no oceans, CO
2
(g) cannot be removed by dissolution.
Some CO
2
(g) deposits seasonally over Mars’s poles as dry ice (solid carbon dioxide)
[Figure 12.3(c)], which forms from the gas phase when the temperature cools to
194.65K. Despite its abundance of CO
2
(g), Mars has only a small greenhouse effect
because it emits little thermal-IR due to its low surface temperature and its atmosphere
contains no water vapor.
The main gases on Jupiter, Saturn, Uranus, and Neptune are molecular hydrogen
and helium. These planets are so large that their gravitation prevents the escape of
even light gases. Because neither hydrogen nor helium is a strong absorber of thermal-
IR radiation, the greenhouse effect on these planets is small. The high surface pressure on
these planets compresses hydrogen into oceans of liquid hydrogen. High pressures in the
interior of Jupiter cause solid hydrogen, and possibly metallic solid hydrogen, to form.
THE GREENHOUSE EFFECT AND GLOBAL WARMING 315
(a) (b) (c)
Figure 12.3. (a) Ultraviolet image of Venus’s clouds as seen by the Pioneer Venus Orbiter,
February 26, 1979. (b) Earth, as seen from the Apollo 17 spacecraft on December 7, 1972.
(c) Sharpest image to date of Mars, taken by Hubble telescope on March 10, 1997. The
North Pole dry-ice cap is rapidly sublimating during the Martian Northern Hemisphere spring.
Courtesy of the National Space Science Data Center.
12.1.4. The Goldilox Hypothesis
Figure 12.3 shows images of Venus, Earth, and Mars. At the surface temperature of
Venus (730 K), water is in the form of vapor. At the surface temperature of Mars
(218 K), water, if ever present, would be in the form of ice. At the surface temperature
of the Earth (288 K), water is in the form of liquid. Whereas Venus is too hot and Mars
is too cold, the Earth is ideal for supporting liquid water. The presence of liquid water
and amiable temperatures have allowed life on Earth to flourish.
If Earth did not have an atmosphere that absorbed thermal-IR radiation, its equilib-
rium temperature (255 K) would be too cold to support liquid water or much life.
Fortunately, Earth’s atmosphere contains water vapor, initially outgassed from volcanos
but now evaporated from the oceans as well, that absorbs thermal-IR radiation, keep-
ing the planet warm. The atmosphere also contains carbon dioxide gas, which
contributes to the Earth’s natural warmth.
If the Earth were closer to or farther from the sun,
its temperature would be too
warm or cold, respectively, to support life. The hypothesis that the Earth is the ideal dis-
tance from the sun, in comparison with Venus or Mars, for sustaining life, is called the
Goldilox hypothesis. Venus is too hot because of its proximity to the sun; Mars is too
cold because of its distance from the sun; but the Earth is the ideal distance, so that the
addition of natural greenhouse gases into its atmosphere has put the Earth’s temperature
in a range that allowed water to exist as a gas, liquid, and solid and life to flourish.
12.2. THE GREENHOUSE EFFECT AND GLOBAL WARMING
Greenhouse gases are relatively transparent to incoming solar radiation but opaque to
certain wavelengths of IR radiation. The term relatively transparent is used because all
greenhouse gases absorb far-UV radiation (which is a trivial fraction of incoming solar
radiation). In addition, ozone strongly absorbs UV-B and UV-C radiation and weakly
absorbs visible radiation. Water vapor and carbon dioxide absorb solar near-IR radia-
tion. However, as shown in Fig. 11.5, gases affect only a fraction of total solar
radiation incident at the top of the Earth’s atmosphere.
12.2.1. Greenhouse Gases and Particles
The natural greenhouse effect is the warming of the Earth’s atmosphere due to the
presence of background greenhouse gases, primarily water vapor, carbon dioxide,
methane, ozone, nitrous oxide, and methyl chloride. The natural greenhouse effect is
responsible for about 33 K of the Earth’s average near-surface air temperature of 288 K.
Without the natural greenhouse effect, Earth’s average near-surface temperature would
be about 255 K, which is too cold to support most life. Thus, the presence of natural
greenhouse gases is beneficial. Anthropogenic emissions have increased the mixing
ratios of greenhouse gases and particulate black carbon (BC), causing global warming.
Whereas greenhouse gases transmit solar radiation and absorb thermal-IR radiation, BC
strongly absorbs solar radiation and weakly absorbs thermal-IR radiation. Thus, green-
house gases and particulate BC both warm the air, but by different mechanisms. Global
warming is the increase in the Earth’s temperature above the natural greenhouse effect
temperature as a result of the emission of anthropogenic greenhouses gases and BC.
Table 12.3 shows that the most important greenhouse gas is water vapor, which
accounts for approximately 89 percent of the 33 K temperature increase resulting from
316 ATMOSPHERIC POLLUTION: HISTORY, SCIENCE, AND REGULATION
THE GREENHOUSE EFFECT AND GLOBAL WARMING 317
Source: Derived from Jacobson (2001b).
Table 12.3. Estimated Percentages of Natural Greenhouse Effect and Global Warming
Temperature Changes Due to Greenhouse Gases and Particulate Black Carbon
since the mid-1800s
Water vapor H
2
O(g) 10,000 >99 <1 88.9 0
Carbon dioxide CO
2
(g) 370 75.7 24.3 7.5 46.6
Black carbon (BC) C(s) 0.15–0.3 Tg 10 90 0.2 16.4
Methane CH
4
(g) 1.8 39 61 0.5 14.0
Ozone O
3
(g) 0.02–0.07 50–100 0–50 1.1 11.9
Nitrous oxide N
2
O(g) 0.314 87.6 12.4 1.5 4.2
Methyl chloride CH
3
Cl(g) 0.0006 100 0 0.3 0
CFC-11 CFCl
3
(g) 0.00027 0 100 0 1.8
CFC-12 CF
2
Cl
2
(g) 0.00054 0 100 0 4.2
HCFC-22 CF
2
ClH(g) 0.00013 0 100 0 0.6
Carbon tetrachloride CCl
4
(g) 0.00010 0 100 0 0.3
Percentage
of Natural Percentage
Natural Greenhouse of Global
Current Total Percentage Anthropogenic Effect Warming
Tropospheric of Current Percentage of Temperature Temperature
Mixing Ratio Total Mixing Current Total Change Change
(ppmv) or Ratio or Mixing Ratio Due to Due to
Compound Name Formula Loading (Tg) Loading or Loading Component Component
CO
CH
4
N
2
O
O
3
CO
2
H
2
O
Total
0
100
0
100
0
100
0
100
0
100
0
100
0
100
2 4 6 8 10 12 14
Wavelength (μm)
Absorption (%)
Figure 12.4. Percentage absorption of radiation by greenhouse gases at infrared wavelengths.
Source: Valley (1965).