Flow, deformation, and transport - Physical Processes in Earth and Environmental Sciences - page 195

4.18.5 Fourier's famous law of heat conduction

where conduction or molecular diffusion depends upon
time. In the latter case, some mathematical development
leads to a relationship in which the temperature of a
cooling body varies as the square root of time elapsed
(see Cookie 20).

Illustrated (Fig. 4.148) are the two cases of heat
conduction and molecular diffusion for (1) steady state,
with no variation in time and (2) the more complex case

4.19 Heat transport by radiation

4.19.1 Solar radiation: Ultimate fuel for the
climate machine

distance traveled. The fraction of monochromatic energy
transmitted is given by the Lambert-Bouguer absorption law
stated opposite (Box 4.4). Further latitude dependence of
incoming solar energy received by Earth's surface arises
from the simple fact that oblique incident light must warm
a larger surface area that can be warmed by normally inci-
dent light. In addition to mean absorption of energy by
atmospheric gases, radiative energy is also reflected, scat-
tered, and absorbed by wind-blown and volcanic dust and
natural and pollutant aerosol particles in the atmosphere.
The amount of dust varies over time (by up to 20 percent
or more), exerting a strong control on the magnitude of
incoming solar radiation. Because of scattering, absorp-
tion, and reflection, it is usual to distinguish the direct
radiation received by any surface perpendicular to the Sun
from the diffuse radiation received from the remainder of
the atmospheric hemisphere surrounding it. Continuous
cloud cover reduces direct radiation to zero, but some
radiation is still received as a diffuse component.

Solar energy is transmitted throughout the Solar System as
electromagnetic waves of a range of wavelengths, from
x -rays to radio waves, all traveling at the speed of light.
The Sun's maximum energy comes in at a short wave-
length of about 0.5

m in the visible range. Much shorter
wavelengths in the ultraviolet range are absorbed by ozone
and oxygen in the atmosphere. The magnitude of incom-
ing radiation is represented by the solar constant , defined
as the average quantity of solar energy received from normal-
incidence rays just outside the atmosphere. It currently
has a value of about 1,366 W m 2 , a value which has fluc-
tuated by about 0.2 percent over the past 25 years. As

discussed below it is possible that over longer periods
the irradiance might vary by up to three times historical
variation.
Although the outer reaches of the atmosphere receive
equal amounts of solar radiative energy, specific portions
of the atmosphere and Earth's surface receive variable
energy levels (Fig. 4.149). One reason is that solar radia-
tive energy is progressively dissipated by scattering and
absorption en route from the top of the atmosphere
downward. Since light has to travel further to reach all
surface latitudes north and south of a line of normal
incidence, it is naturally weaker in proportion to the

4.19.2 Sunspot cycles: Variations in solar
irradiance and global temperature fluctuations

The extraordinary dark patches on the face of the
otherwise bright sun are visible when a telescopic image is
projected onto a screen and viewed. The dark blemishes

1,36 6 W m -2
on perpendicular
surface

x

Solar constant = incoming solar irradiance
outside earth´s atmosphere

Local
path
length

Thickness
of atmosphere

1,366 W m -2
on perpendicular
surface

Fig. 4.149 Higher latitude radiation travels further through the atmosphere and is thus attenuated and scattered more. The more attenuated
higher latitude radiance must also act upon a larger earth surface area.