Geoscience Reference
In-Depth Information
The first term on the right is the net TOA solar radiation flux, where S is the solar
constant (1361.5 W m
−2
at average earth-sun distance), A is the planetary albedo
(approximately 0.3), and R is the radius of the earth (6371 km). Note that about
99.9 percent of the radiation emitted by the sun is in wavelengths of 0.15 to 4 µm
with a peak intensity near 0.5 µm. Approximately 50 percent of the total emitted
energy is within the visible spectrum (approximately 0.4-0.7 µm). The planetary
albedo (A) differs from the surface albedo (α) (see
Chapter 5
) in that it includes the
effects of scattering and absorption by clouds, aerosols and atmospheric gases, as
well as the surface albedo. However, to a first order, absorbtion of solar radiation by
the atmosphere itself is relatively small. Put differently, most of the solar radiation
that is not scattered back to space by the atmosphere reaches the surface. Assuming
a planetary albedo of 0.3, the net solar flux at the top of the atmosphere is about
1.220 × 10
17
J per year of energy; division by the surface area of the planet (4πR
2
)
yields a radiation flux density of 239 Wm
−2
.
The second term on the right is the balancing longwave radiation emitted to
space, where σ is the Stefan-Boltzman constant (5.7 × 10-
8
W m
−2
K
−4
), and T
e
is the
effective radiation emission temperature of the earth, which is approximately 255
K. This longwave radiation is in wavelengths of about 4-300 µm, peaking at about
10 µm. In contrast to solar radiation, the atmosphere is semi-opaque with respect
to longwave radiation. This effect is included in T
e
. T
e
depends on both the physical
temperature and the longwave emissivity of the atmosphere and the surface consid-
ered as a whole. This emissivity is a measure of how efficiently the atmosphere and
surface both absorb and emit longwave radiation. The surface is heated primarily
through the absorption of solar radiation, and longwave radiation emitted toward
the surface from the lower atmosphere. The atmosphere is heated primarily from the
surface upward through vertical turbulent heat fluxes (sensible and latent heating)
and longwave radiation exchanges. These longwave exchanges can be understood
by considering an atmospheric column sliced into a series of thin slabs. Some of
the radiation emitted from the surface is absorbed by the first slab above the surface
(layer 1), heating that layer. Some of the radiation emitted by layer 1 is directed
downward to the surface, while some is directed upward, some heating the next
layer (layer 2), some heating higher layers (3,4,5, and so on) and some escaping to
space. These layers in turn radiate both downward (to heat lower layers as well as
the surface) or upward. Most of the longwave radiation emitted to space comes from
the atmosphere. Direct emission to space from the surface occurs through various
atmospheric “windows” (e.g., from 3-5 µm and from 8-14 µm, the former overlap-
ping with the solar spectrum), within which atmospheric absorption is small.
Although approximate radiative balance (R
top
= 0) holds for the earth as a whole,
when zonal averages are examined (averages for different latitude circles), we find
a strong latitudinal dependency of the net TOA solar flux: the equatorial regions
receive more while the polar regions receive less. This uneven distribution of solar
heating arises because the earth is a sphere. Solar radiation strikes the top of the
atmosphere at a shallower (more grazing) angle in higher latitudes compared to lower
latitudes. This basic pattern is in turn modified somewhat by latitudinal variations in
