The Earth's Energy Balance
By Roger Aiken

(CLICK HERE to learn more about Roger's work at the CREED website.) 


We live in a thin envelope of air about five miles thick surrounding the surface of the earth known as the troposphere, or more commonly the atmosphere. Above the troposphere are other layers of gases known as the stratosphere and ionosphere, but it is in the troposphere where our weather takes place and where air pollution occurs. The troposphere is also where most of the energy interchange between the atmosphere and the earth's surface happens. 

The main gases of the atmosphere are nitrogen (about 80%), oxygen (about 19%) and argon (1%). However, it is the presence of small amounts of some other gases that have the most profound influence on the earth's energy balance and the purity of the air we breathe. The most important of these "minor" gasses are carbon dioxide (CO2), methane (CH4), sulfur dioxide (SO2), nitrogen oxides (NOx), ozone (O3) and water vapor. 

Solar radiant energy is continually streaming in from the sun. The earth-atmosphere system absorbs a portion of this energy and, in turn, radiates this energy back to space establishing an energy balance. In addition to the energy received from the sun, the surface of the earth is warmed by: 

  • A geothermal heat flux, Eg, from the interior of the earth that results primarily from the decay of radioactive isotopes in the earth's core. 
  • The tides which are a consequence of the sun-earth-moon gravitational system. Tidal friction dissipates a minute fraction of the energy in this system, Et. 
  • The heat generated by man through the use of fossil and nuclear fuels, Em. 
  • Referring to the figure (above, right) we see that a fraction, r, of the total short wave solar radiation reaching the vicinity of the earth, S, is reflected back into space. This amount, rS, is known as the earth's albedo. The remainder of the incident solar energy, (1-r)S, is absorbed by the earth and its atmosphere. Compared to (1-r)S the geothermal, tidal and man-made contributions are very small. If the earth and its atmosphere did not lose any of the energy received in these ways it would get hotter and hotter and very soon the Earth would become uninhabitable. 

    An energy balance is achieved as a result of the fact that the earth and its atmosphere also emit radiant energy back to space. Whereas the energy received from the sun is radiant energy in the short infra-red, visible and near ultra-violet bands, the reradiated energy is in the longer infra-red, corresponding to the mean absolute temperature of the earth, TE, which is about 286 Kelvin (i.e. 55°F). 

    For balance to occur, the reradiated energy, must be equal to the sum of the inputs, i.e. 4ea(TE)4 = (1-r)S+Eg+Et+Em. The factor 4 is present because the total area of the earth is four times the area which intercepts solar radiation, e is an emissivity coefficient which depends on the nature of the atmosphere and the earth's surface, a is a physical constant and r, as we mentioned before, is the fraction reflected back to space as the earth's albedo. 

    A change in any one of the factors in this equation will alter the energy balance of the earth and consequently the mean temperature, TE , of the earth's surface

    Energy Balance & Global Warming

    Most people erroneously think that it is the term, Em--i.e. the extra heat discharged into the atmosphere from fossil fuel and nuclear plants--which is the main culprit in contributing to global warming. This term is very small indeed compared to the solar radiant input from the sun, only about 0.005%. (See figure on the link page.)

    It is the factors r and e which are primarily responsible for controlling the energy balance. It can be shown that changes of only about 1.0% in the values of either r or e will result in a temperature change of about 2°F!! These factors are greatly influenced by the gaseous composition of the atmosphere and by the nature of the earth's surface. 

    Let me give you a couple of examples. 

    1. For the earth as a whole the values of r and e are about 0.35 and 0.58 respectively. These values of course vary with the type of terrain, oceans and tropical rain forests having values of r much less than 0.35 and ice caps and deserts values much greater. It is easy to see that human activities such as the burning of forests, the paving over of large tracts of land and natural events such as the melting of ice caps will have a profound effect on these coefficient factors. 

    2. Since most of the albedo and infra-red radiation back to space occurs from the atmosphere rather than the surface of the earth, the gaseous composition of the atmosphere will be an even greater determinant of the energy balance than the earth's surface. It is the presence of the "minor" gases that determines the values of r and e for the atmosphere rather than that of oxygen and nitrogen which are both largely transparent to both solar radiation and the long wave reradiated energy. CO2, CH4, SO2, NOX and water vapor, the so-called green house gases contribute to global warming by virtue of their great ability to absorb the reradiated long wave infra-red energy from the earth's surface. 

    What this means is that the atmosphere's emissivity coefficient, e, is reduced, less energy is radiated back to space and the earth warms up. To compound the problem, as the earth and its oceans warm up, more evaporation takes place from the oceans, more water vapor enters the earth's atmosphere and e is reduced even further since water vapor itself is a green house gas. 

    The burning of fossil fuels, which produce SO2 and NOX as well as CO2, is also the main contributor to the formation of acid rain in the atmosphere. The two greatest sources of these acid rain producing gases are coal fired electric power plants and the internal combustion engine. So every time we turn on the light switch or fill our automobile tanks up with gas at the pump we incrementally contribute to both the global warming and acid rain problems. 

    What must we do to prevent these problems from stifling life as we know it on planet earth? The answer is we must find ways to intercept and use the abundant energy flowing to us from the sun before it ends up as low grade heat and is reradiated to space. There are many ways of doing this. Here in Minnesota we are already harnessing the wind, growing crops for energy, converting the sun's rays to electricity using solar cells and trapping the sun's heat directly for space and water heating. We need to employ the ingenuity of our people to accelerate this task.

    Learn more about Roger Aiken's

    Center for Global Environmental Education
    Hamline University Graduate School of Education
    1536 Hewitt Avenue, St. Paul, MN 55104-1284
    Phone: 651-523-2480 Fax: 651-523-2987
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