The Greenhouse Effect and Global Warming - Air Pollution and Global Warming: History, Science, and Solutions - page 264

collectively referred to as brown carbon (BrC) .BC
absorbs across the entire solar spectrum. BrC strongly
absorbs UV and short visible wavelengths of light, but
not solar-IR wavelengths (Chapter 7). Because parti-
cles containing BC and BrC contain some nonwarming
components but predominantly cause warming, they are
referred to as warming particles .
Whereas BC and BrC warm the climate, most
other aerosol constituents - sulfate, nitrate, ammonium,
sodium, potassium, calcium, magnesium, nonabsorb-
ing organic material, and liquid water attached to these
ions and molecules - reflect solar radiation and reduce
near-surface temperatures. The sources of the cooling
components generally differ from the sources of warm-
ing components, so particles containing predominantly
cooling components are referred to as cooling parti-
cles .Cooling particles offset part of the warming due
to greenhouse gases and warming particles (Section
12.2.3).
In the absence of greenhouse gases or warming par-
ticles, the temperature of the Earth can be estimated, to
first order, with a simple radiation balance model that
considers solar radiation coming into and thermal-IR
radiation leaving 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
before anthropogenic emissions is caused primarily by
the greenhouse effect. The simple energy balance model
is described next.

on the edge of an ever-expanding concentric sphere
originating from the photosphere. Because conserva-
tion of energy requires that the total energy per unit
time passing through a concentric sphere any distance
from the photosphere equals that originally emitted by
the spherical photosphere, the total energy per unit time
passing through a sphere with a radius corresponding
to the Earth-sun distance ( R es )mustbe

R es F s = R p F p 4 4 (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 corresponding to the Earth-sun
distance. Rearranging Equation 12.2 and combining the
result with Equation 12.1 gives

R p
R es

2 R p

R es

2

B T p F s = F p = (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 by putting
your hand over a light bulb. Close to the bulb, you
will feel the heat from the bulb; however, as you move
your hand away from the bulb, the heat that you feel
decreases proportionally to the square of the distance
away from the bulb.
The average Earth-sun distance is about 1.49598

×
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 the solar constant .
Figure 12.1 shows that the Earth-sun distance is 147.1
million km in December (Northern Hemisphere winter)
and 152.1 million km in June (Northern Hemisphere
summer) due to the fact that the Earth rotates around
the sun in an elliptical orbit with the sun at one focus.
If these distances are used in Equation 12.3, F s =

=

12.1.1. Incoming Solar Radiation
The sun emits radiation with an effective photosphere
temperature of about T p = 5,785 K (Chapter 2). Thus,

the energy flux (joules per second per square meter
or watts per square meter) emitted by the sun's pho-
tosphere can be calculated from the Stefan-Boltzmann
law (Equation 2.2) as

1,411
Wm − 2 in December and 1,321 W m − 2 in June. Thus, a
difference of 3.4 percent in Earth-sun distance between

Autumnal equinox
Sept. 23

F p = ε p B T p

N.H. summer
S.H. winter
solstice
June 22

(12.1)

Obliquity
23.5 o

where ε p is the emissivity of the photosphere. The emis-

sivity 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, 4

1 47 million km 1 52 million km

Sun

N.H. winter
S.H. summer
solstice
Dec. 22

R p 2 ,where R p ×

10 8 m(696,000 km) is the effective radius of the sun
(the 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 4

= 6.96

Vernal equinox
Mar. 20

Figure 12.1. Relationship between sun and Earth at
the times of solstices and equinoxes. The sun is
positioned at one focus of the ellipse.

R p 2 F p .Energy
emitted from the photosphere propagates through space