Earth’s Energy Balance
• The hydrologic cycle is fueled by energy from the sun.
• Planetary geometry creates areas of energy surpluses and
deficits which drive all active meteorological processes.
• Earth and the atmosphere are the media through which the
energy transport occurs
• Water transport and phase changes [i.e. liquid (oceans) 
vapor (humidity)  liquid (precipitation)] play a major
role energy transport
Earth’s Energy Balance
reflected from
particulates in air,
clouds and the
earth’s surface 30 %
longwave
radiation
emanated 70 %
longwave radiation
from clouds, vapor,
etc.
absorbed by atmosphere (water
vapor, dust, clouds) - 19 %
absorbed by
earth - 51%
earth heat entering
atmosphere - 0.002 %
(geothermal)
back radiation from
earth - 20%
Earth’s Energy Balance
• Short-wave energy from the sun moves through the atmosphere to the
earth more easily than longwave energy can move from earth through
the atmosphere. This keeps the planet warm
• Planetary geometry creates areas of energy surpluses and deficits.
– Incoming solar radiation is uneven because the earth is a sphere
which rotates on a tilted axis.
– Outgoing radiation is more uniform because the temperature of
earth’s atmosphere does not vary all that much from the equator to
the poles (~ 30 C).
• Energy gradients drive global energy transport processes such as wind
and ocean currents.
Earth’s Energy Balance
• Net radiation balance is positive for latitudes below 35 (receive more
radiation than is emitted), and negative for latitudes above 35.
• Therefore there is a net poleward transport of energy to maintain a
balance (2/3 of this transport occurs in atmosphere and 1/3 in the
oceans).
• Radiation (both short and longwave) is the energy source leading to
evaporation. Large quantities of energy are carried by water vapor.
(This is the energy absorbed by molecules during phase change from
liquid to vapor)
Radiation Physics
• All matter at a temperature above absolute zero radiates energy in the
form of electromagnetic waves that travel at the speed of light (lf=c ).
• The rate at which this energy is emitted is given by the Stefan Boltzmann law:
  ET 4
Stefan-Boltzmann constant
= 5.67 x 10-8 Watts/(m2K4)
= 1.38 x 10-12 cal/(cm2K4sec)
= 8.28 X 10-11 cal/(cm2 K4 min)
• The value of E ranges from 0 to 1 depending on the material and
texture of the surface.
• E = 1  Blackbody. Reflects no radiation. Absorbs and re-emits
radiation in proportion to surface area.
• E  1  Grey body. Radiates a fixed proportion (less) of blackbody
radiation at all wavelengths for a given temperature.
Radiation Physics
• Blackbody radiation intensity is distributed over various wavelengths.
• Spectrum of radiation of a black body:
Wiens Displacement Law -Tl
peak always at lT = 3000mK
Radiation
area under curve is 
wavelength
lT
temperature
• Blackbody radiation spectrum follows this curve at all temperatures.
Radiation Physics
• Sun radiates energy approximately as a black body at 6000
K  high temperature/short wavelengths.
• Not all this energy reaches the earths surface. Some is
absorbed by atmospheric gases (i.e. O2 and O3 absorb UV
radiation which can be harmful to biota).
• Depletion of O3 will increase UV incidence at earth’s
surface  concern about ozone hole.
Radiation Physics
• Earth radiates energy approximately as a black body at 290
K lower temperatures/ longer wavelengths.
• Some of this radiation is absorbed by atmospheric gases
(i.e. H2O and CO2 absorb infra-red (IR) radiation 
greenhouse effect).
• Without H2O and CO2, the earth’s surface would have a
temperature of ~ -18C  Concern that fossil fuel
combustion increases the CO2 levels which increases the
temperature of the earth  global warming.
Radiation Physics
• Based on the sun’s temperature and the Stefan - Boltzmann
law, the total energy emitted by the sun is:
  ( ET 4 )  (1)(8.28x1011
cal
cm 2  min  K 4
)(6000K ) 4  1x105
cal
cm 2  min

ly
min
• Because of the earth’s distance from the sun, only a small
fraction of this total energy is received at the outer edge of
the earth’s atmosphere.
• Intensity of solar radiation at a plane or the upper
atmosphere  to incoming solar radiation is called the solar
ly
J
 1350
constant:  o  2
2
min
m  sec
Solar Radiation
• Because the earth is a sphere which rotates on a tilted axis
the intensity of solar radiation on a plane perpendicular to
the earth’s atmosphere varies in space and time.


Solar radiation (o) spread over larger surface area
on the earth’s surface. Thus less radiation/(area
time)  lower temperatures
=
 - latitude
 - solar altitude - angle of incoming radiation
with plane tangent to earth-atmosphere surface
 - declination of the sun - latitude at which sun
is directly overhead - ranges from 23.17S to
23.17N
Solar Radiation
• Rs=insolation = effective radiation intensity incident at outer edge of
atmosphere
• Rs = osin
• If earth’s axis were perpendicular to plane of revolution,  would be a
function of latitude only (  90 - ).
• However, because of the angle of revolution,  varies with latitude,
declination (time of year), and longitude.
Solar Radiation
• Equation for total daily insolation is:
sin(Tsunset ) 

Rs  2 o Tsunset sin  sin   cos  cos



Tsunset = Number of hours after solar noon that sunset occurs (Note: sunrise
and sunset occur at equal times before and after solar noon)
Tsunset 
 cos1( tan  tan  )

Solar Radiation
• This equation gives radiation at outer edge of atmosphere. This solar
radiation is further reduced as it moves through the atmosphere by
scattering by molecules and particulates and absorption and scattering
by clouds.
• The net radiation received at the earth's surface is further reduced by
absorption by vegetation and reflection by earth materials.
• albedo - A - Reflectance of solar radiation by earth materials.
– Earth’s average albedo for shortwave radiation, As = 0.32. It ranges from
0.08 for black moist soil to 0.4 - 0.8 for snow.
– Longwave albedo is essentially zero for all earths surfaces except water.
For water, Al = 0.03
Net radiation received at earth
surface: