model-fictive temperature, T, sometimes called the 'equilibrium temperature of the Earth', that is to be found, and S is the solar constant – the incoming solar radiation per unit area—about 1367 W·m−2 is the Earth's average albedo, measured to be 0.3. r is Earth's radius—approximately 6.371×106m π is the mathematical constant (3.141...) is the Stefan–Boltzmann constant—approximately 5.67×10−8 J·K−4·m−2·s−1 is the effective emissivity of earth, about 0.612 The constant πr2 can be factored out, giving Solving for the temperature, This yields an apparent effective average Earth temperature of . This is because the above equation represents the effective radiative temperature of Earth's combined surface and atmosphere (including clouds). This very simple model is quite instructive. For example, it easily determines the change in the effective temperature caused by changes in solar constant, Earth albedo, or effective Earth emissivity. The average emissivity of the earth is readily estimated from available data. The emissivities of terrestrial surfaces are all in the range of 0.96 to 0.99 (except for some small desert areas which may be as low as 0.7). Clouds, however, which cover about half of the earth's surface, have an average emissivity of about 0.5 (which must be reduced by the fourth power of the ratio of cloud absolute temperature to average earth absolute temperature) and an average cloud temperature of about . Taking all this properly into account results in an effective earth emissivity of about 0.64 (earth average temperature ). Models with separated surface and atmospheric layers Dimensionless models have also been constructed with functionally separated atmospheric layers from the surface. The simplest of these is the zero-dimensional, one-layer model, which may be readily extended to an arbitrary number of atmospheric layers. The surface and atmospheric layer(s) are each characterized by a corresponding temperature and emissivity value, but no thickness. Applying radiative equilibrium (i.e conservation of energy) at the interfaces between layers produces a set of coupled equations which are solvable. Layered models produce temperatures that better estimate those observed for Earth's surface and atmospheric levels. They likewise illustrate the radiative heat transfer processes which underlie the greenhouse effect. Quantification of this phenomenon using a version of the one-layer model was first published by Svante Arrhenius in year 1896. Radiative-convective models The zero-dimensional model above, using the solar constant and given average earth temperature, determines the effective earth emissivity of long wave radiation emitted to space. This can be refined