The main source of energy for the Earth system is solar radiation. The Sun emits radiation as a blackbody of effective temperature TS = 5800 K. The corresponding blackbody energy flux is
(1)
where σ = 5.67 × 10–8 W m–2 K–4 is the Stefan-Boltzmann constant. This radiation extends over all wavelengths but peaks in the visible at 0.5 μm. The solar energy flux intercepted by the Earth’s disk (surface perpendicular to the incoming radiation) is 1365 W m–2. This quantity is called the solar constant and is denoted S. Thus, the mean solar radiation flux received by the terrestrial sphere is S/4 = 341 W m–2. A fraction α = 30% of this energy is reflected back to space by clouds and the Earth’s surface; this is called the planetary albedo. The remaining energy is absorbed by the Earth–atmosphere system. This energy input is compensated by blackbody emission of radiation by the Earth at an effective temperature TE. At steady state, the balance between solar heating and terrestrial cooling is given by
(2)
The mean effective temperature deduced from this equation is TE = 255 K. It is the temperature of the Earth that would be deduced by an observer in space from measurement of the emitted terrestrial radiation. The corresponding wavelengths of terrestrial emission are in the infrared (IR), peaking at 10 μm. The effective temperature is 33 K lower than the observed mean surface temperature, because most of the terrestrial radiation emitted to space originates from the atmosphere aloft where clouds and greenhouse gases such as water vapor and CO2 absorb IR radiation emitted from below and re-emit it at a colder temperature. This is the essence of the greenhouse effect.
Figure 2 presents a more detailed description of the energy exchanges in the atmosphere. Of the energy emitted by the Earth’s surface (396 W m–2), only 40 W m–2 is directly radiated to space, while the difference (356 W m–2) is absorbed by atmospheric constituents. Thus, the global heat budget of the atmosphere must include the energy inputs resulting from (1) the absorption of infrared radiation by clouds and greenhouse gases (356 W m–2), (2) the latent heat released in the atmosphere by condensation of water (80 W m–2), (3) the sensible heat from vertical transport of air heated by the surface (17 W m–2), and (4) the absorption of solar radiation by clouds, aerosols, and atmospheric gases (78 W m–2). Of this total atmospheric heat input (532 W m–2), 199 W m–2 is radiated to space by greenhouse gases and clouds, while 333 W m–2 is radiated to the surface and absorbed. This greenhouse heating of the surface (333 W m–2) is larger than the heating from direct solar radiation (161 W m–2). At the top of the atmosphere, the incoming solar energy of 341 W m–2 is balanced by the reflected solar radiation of 102 W m–2 (corresponding to a planetary albedo of 0.30 with 23 W m–2 reflected by the surface and 79 W m–2 by clouds, aerosols and atmospheric gases) and by the IR terrestrial emission of 239 W m–2. Note that the system as described here for the 2000–2004 period is slightly out of balance because of anthropogenic greenhouse gases: A net energy per unit area of 0.9 W m–2 is absorbed by the surface, producing a gradual warming.
