AOM 4932 - 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.  These
processes originate to redistribute energy throughout the system.
Earth and the atmosphere are the media through which the energy transport occurs 
oceans and atmosphere are more active in this redistribution than land mass.
 Water transport and phase changes [i.e. liquid (oceans)  vapor (humidity)  liquid
(precipitation)] play a major role energy transport
Energy - flow for the earth as a whole
short-wave solar
radiation entering
atmosphere - 99.998%
longwave radiation
emanated - 70 %
reflected from particulates in
air, clouds and the earth’s
surface - 30 %
longwave radiation
from clouds, vapor,
etc.
absorbed by atmosphere
(water vapor, dust,
clouds) - 19 %
back radiation
from earth - 20%
earth heat entering
atmosphere - 0.002 %
(geothermal)
absorbed by earth 51%
N m (energy)
Radiation rate measured in
energy
Joules
calories
or
2
m  sec
cm2  sec
unit area
latent heat and sensible
heat flux - 30 %
time
Note:1
cal
= 1 langley (ly)
cm2
Radiation measured with a pyranometer or radiometer.
Important aspects of the earth's energy balance:
1. 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 (similar to greenhouse glass).
2. 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
1
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.
3. 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).
4. 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)
Brief Review of 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 ( f  c ). The rate at which this
energy is emitted is given by the Stefan - Boltzmann law:
  ET 4
absolute temperature of the
surface of the body (K)
rate of energy emission per
unit area per time
emissivity (dimensionless)
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.
Blackbody radiation intensity is distributed over various wavelengths.
Spectrum of radiation of a black body:
Radiation
Wiens Displacement Law -T
peak always at T = 3000mK
 B
area under curve is 
T5
wavelength
T
temperature
2
Blackbody radiation spectrum follows this curve at all temperatures.
Note:

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.

Earth radiates energy approximately as a black body at 290 K.  lower temperature
 longer wavelengths. Again 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.

Based on the sun’s temperature and the Stefan - Boltzmann law, the total energy
emitted by the sun is:
  ( ET 4 )  (1)(8.28 x10 11
cal
cm 2  min  K 4
)(6000 K ) 4  1x10 5
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 on the upper atmosphere  to incoming solar
radiation is called the solar constant:
o  2
ly
J
 1350 2
min
m  sec
solar constant
Since the earth is a sphere which rotates on a tilted axis while revolving around the sun,
the intensity of solar radiation at a plane  to earth’s atmosphere varies in space (due to
spherical earth) and time (due to tilted axis) which leads to variation of climate around
the earth and with time of year.


=

Solar radiation (o) spread over larger surface area  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
3
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 - ). This would mean there would be no seasons and all parts of the earth
would be illuminated 12 hours per day at all times. It would be colder at the poles than at
the equator, but temperatures would be uniform throughout the year.
23.17
N
~151 x
~145 x 106 km
106
km
sun
northern summer
southern winter
northern winter
southern summer
S
However, because of the angle of revolution,  varies with latitude, declination (time of
year), and longitude.
Equation for total daily insolation:
sin( Tsunset ) 

Rs  2 o Tsunset sin  sin   cos  cos 




angular velocity of the earth's
where:
rotation 0.2618 radians/hr
local latitude
= declination of the sun (latitude at which sun is directly overhead)

23.45
2
cos[
(172  D )]
180
365
declination
in radians
also tabulated in places like the CRC
Handbook
Julian Day
1-366
Tsunset = Number of hours after solar noon that sunset occurs (Note: sunrise and sunset
occur at equal times before and after solar noon)
4
Tsunset 
 cos 1 ( tan  tan  )

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:
short wave albedo
long wave albedo
dominant
Rn  Rs (1  As )  Rl (1  Al )  Rb
incident solar radiation at earth’s
surface after planetary geometry
and atmospherics reflection and
absorption are accounted for
longwave radiation emitted from
earth as a black body (EeTe4)
longwave radiation received from atmosphere emitting
as a black body
Rl  E aTa4
longwave
radiation received
from atmosphere
5