The Greenhouse Effect done correctly





This unfortunate term greenhouse effect comes from the physically incorrect analogy to a greenhouse maintaining heat by trapping warm air inside a structure and not letting that air exchange energy with the environment. As a result, most of the lay public is not aware of the natural greenhouse effect produced by atmospheric gases that maintains a habitable temperature on Earth and that the issue of global warming should be better termed as an enhanced greenhouse effect. A proper understanding of the "greenhouse effect" considers how shortwave length radiation emitted by the Sun and long wavelength radiation emitted by the finite temperature of the Earth, act in concert with atmospheric gases to control and regulate the average surface temperature of the Earth. The bulk of the molecules in the Earth's atmosphere are nitrogen (N2) and oxygen (O2) and these are small selective absorbers of optical light and do not absorb IR radiation at all. Therefore, they contribute very little to the temperature regulation of the Earth. Although water vapor and CO2 are trace gasses, as shown in Figure 1, they totally dominate the selective absorption of OLR. This overall energy balance of the Earth-atmosphere system is shown in Figure 2:

Figure 2: Qualitative balance between solar input radiation and Earth OLR



Figure 2 shows that out of the 100% of incoming solar energy that reaches the top of our atmosphere, almost 1/2 of it is lost before it reaches the ground. These losses occur via the following channels:

Reflection based losses:

  • Reflection by clouds (usually high cirrus clouds made of ice) dominates the loss channel at 20%
  • 6% reflects off atmospheric molecules (primarily N2) back to space
  • 4% bounces off the surface of the Earth (dirt is not highly reflective and neither are the oceans - only ice is highly reflective)
  • Total reflective losses are then 30% and this is called the planetary albedo, A. For Earth, A=0.3 Absorption losses:
  • 16% is of this optical radiation is absorbed by the atmosphere directly mostly by atmospheric dust (from pollution and natural sources) and trace amounts of ozone (O3).
  • Only 3% is directly absorbed by clouds (clouds/ water vapor are ineffective absorbers at short wavelengths)
  • Total absorption losses are therefore 19%


This leaves 51% of the incoming solar radiation to be absorbed by the Earth which uses this radiation (energy) to warm up to its characteristic temperature. To keep the Earth in thermal balance as much energyis emitted as is absorbed. The re-emitted energy is in the form of OLR.

The components of this OLR consist of:

  • 30% goes into mechanical energy associated with producing rising air (7%) and via the thermodynamic process that makes planetary water vapor (basically rising of surface air and subsequent cooling of that air into cloud formations- 23%)
  • Only 6% of this radiation is directly emitted by Earth back into space (in the 8-12 micron atmospheric window).
  • This leaves 64% to be absorbed and re-radiated by clouds and the atmosphere.


Any alteration of the absorption properties of the atmosphere (either short wavelength or long wavelength) will change the overall energy balance of the system. Our atmosphere can be effectively modelled as a thin slab of material at some characteristic temperature. This allows one to construct Figure 3 to show how the surface temperature is increased due to the existence of an atmosphere

Figure 3: Thin slab model of the Earth's Atmosphere and its modulation of incoming and outgoing fluxes



The total flux (energy input) of short wavelength solar radiation entering the top of the atmosphere , denoted as Fo, has to be equal to the total flux (energy output) of OLR, denoted as Fg.

The components and their interaction as shown in in Figure 3 are:

  • Incident flux from the sun on the top of our atmosphere (Fo) is filtered through the atmosphere by its short wavelength transmittance coefficient Ts, where 0 < Ts < 1.0. The flux that reaches the ground is then Fo * Ts.
  • That flux is absorbed by the ground and the ground heats up to some temperature (Tg). The ground (Earth) then re-radiates that heat as OLR (Fg). Some of that flux (Fg) is absorbed by the atmosphere through its long wavelength transmittance coefficient Tt, where 0 < Tt < 1.0.
  • The combination of absorption of short (s) and absorption of long (t) wavelength radiation causes the atmosphere to heat up to a temperature (Ta) and then radiate that temperature away as flux, Fa.


To derive the planetary equilibrium temperature we assume that, since the atmosphere is relatively thin (you can through it clearly on cloudless day) that 1/2 of Fa is emitted up into space while the other 1/2 is emitted down, back to the ground. In this way, the atmosphere remits some of the OLR that it absorbed back to the Earth so the Earth receives additional flux which causes it to warm more.

Because CO2 has a prominent absorption feature right at the peak of the blackbody emission of the Earth, it acts as a strong feedback mechanism to the Earth to increase its surface temperature. However, the re-heating effect remains dominated by water vapor. Since as much flux goes out of the system as comes into the system we can set up the following equilibrium conditions.

  • Flux entering the top of the atmosphere = flux leaving the atmosphere: Fo = Fa + Tt *Fg
  • Flux incident upon the ground = flux leaving the ground: Fg = Fa + Ts *Fo


In these two equations the common term Fa is present. Therefore, we can form a value for Fa in one equation and substitute into another.


For the Earth's atmosphere, most of the (s)hort wavelength emission is transmitted leading to a high value for Ts of 0.9. Most of the OLR (t) is not transmitted through the atmosphere leading to a low value for Trof 0.16. Thus,



As shown directly below, this extra factor of 1.63 times more flux will lead to a 30-35K increase in the nominal surface temperature of the Earth.

Human activities can then lead to surface temperature changes because of the artificial alterations of Ts and Tt. For example, sulphate aerosol pollution, primarily from burning coal but also from many other industrialized processes can reduce Ts because more incoming short wavelength light is scattered so that less reaches the surface. On the natural level, explosive volcanoes inject sulphate aerosols to high levels in the atmosphere which can result in temporary global cooling. For the case of the 1991 Pinatubo explosion, the equilibrium temperature of the Earth fell by about 1 degree F for a period of 18 months.

The increase of GHGS to the atmosphere necessarily makes the atmosphere opaquer to OLR which therefore lowers the value of Tt which directly leads to enhanced values for Fg and enhanced surface warming. The planetary equilibrium temperature depends on the amount of incoming solar flux which is determined by its distance from the sun and its albedo, A. If a planet with radius R is located at some distance D from a star with energy output L and radiates that absorbed energy as a blackbody of some temperature T then the equilibrium condition is:



The numerical value of A is subject to small fluctuations depending on its total snow and ice cover. The current observed value of A = 0.3 leads to T =254K. For A = 0.35 that would lead to T =250K. These temperatures are below the freezing point of what, making life on Earth relatively difficult to achieve. However, the observed temperature of earth is 288 K and that is due to the extra flux re-emitted by the atmosphere back to ground as previously described.

This is directly seen by multiplying 1370 by (1.63)0.25 so that the incoming flux is now 1548. This leads to T = 314 * (1- A)1/4 where for A= 0.3 the surface temperature becomes 287 K, in agreement with the observed value.

Hence the presence of the natural greenhouse effect due to naturally occuring concentratinos of CO2 and water vapor allow for a surface temperature range on the Earth to be conducive for the development of life.

Not also that, over geological time, there have been various "hot house" periods in the Earth where tectonically induced global vulcanism greatly elevates the CO2 Level to 4-5 times its baseline level.