Effective temperature A given flux of thermal radiation has an associated
effective radiating temperature or
effective temperature. Effective temperature is the temperature that a
black body (a perfect absorber/emitter) would need to be to emit that much thermal radiation. Thus, the overall effective temperature of a planet is given by :T_\mathrm{eff} = (\mathrm{OLR}/\sigma)^{1/4} where OLR is the average flux (power per unit area) of outgoing longwave radiation emitted to space and \sigma is the
Stefan-Boltzmann constant. Similarly, the effective temperature of the surface is given by :T_\mathrm{surface,eff} = (\mathrm{SLR}/\sigma)^{1/4} where SLR is the average flux of longwave radiation emitted by the surface. (OLR is a conventional abbreviation. SLR is used here to denote the flux of surface-emitted longwave radiation, although there is no standard abbreviation for this.) Sometimes the greenhouse effect is quantified as a temperature difference. This temperature difference is closely related to the quantities above. When the greenhouse effect is expressed as a temperature difference, \Delta T_\mathrm{GHE}, this refers to the effective temperature associated with thermal radiation emissions from the surface minus the effective temperature associated with emissions to space: :\Delta T_\mathrm{GHE} = T_\mathrm{surface,eff} - T_\mathrm{eff} :\Delta T_\mathrm{GHE} = \left(\mathrm{SLR}/\sigma\right)^{1/4} - \left(\mathrm{OLR}/\sigma\right)^{1/4} Informal discussions of the greenhouse effect often compare the actual surface temperature to the temperature that the planet would have if there were no greenhouse gases. However, in formal technical discussions, when the size of the greenhouse effect is quantified as a temperature, this is generally done using the above formula. The formula refers to the effective surface temperature rather than the actual surface temperature, and compares the surface with the top of the atmosphere, rather than comparing reality to a hypothetical situation. The temperature difference, \Delta T_\mathrm{GHE}, indicates how much warmer a planet's surface is than the planet's overall effective temperature.
Radiative balance . Evaporation and convection partially compensate for this reduction in surface cooling. Low temperatures at high altitudes limit the rate of thermal emissions to space. Earth's top-of-atmosphere (TOA)
energy imbalance (EEI) is the amount by which the power of incoming radiation exceeds the power of outgoing radiation: :\mathrm{EEI} = \mathrm{ASR} -\mathrm{OLR} where ASR is the mean flux of absorbed solar radiation. ASR may be expanded as :\mathrm{ASR} = (1-A) \,\mathrm{MSI} where A is the
albedo (reflectivity) of the planet and MSI is the
mean solar irradiance incoming at the top of the atmosphere. The
radiative equilibrium temperature of a planet can be expressed as :T_\mathrm{radeq} = (\mathrm{ASR}/\sigma)^{1/4} = \left[(1-A)\,\mathrm{MSI}/\sigma \right]^{1/4} \;. A planet's temperature will tend to shift towards a state of radiative equilibrium, in which the TOA energy imbalance is zero, i.e., \mathrm{EEI} = 0. When the planet is in radiative equilibrium, the overall effective temperature of the planet is given by :T_\mathrm{eff} = T_\mathrm{radeq}\;. Thus, the concept of radiative equilibrium is important because it indicates what effective temperature a planet will tend towards having. If, in addition to knowing the effective temperature, T_\mathrm{eff}, we know the value of the greenhouse effect, then we know the mean (average) surface temperature of the planet. This is why the quantity known as the greenhouse effect is important: it is one of the few quantities that go into determining the planet's mean surface temperature.
Greenhouse effect and temperature Typically, a planet will be close to radiative equilibrium, with the rates of incoming and outgoing energy being well-balanced. Under such conditions, the planet's equilibrium temperature is determined by the mean solar irradiance and the planetary albedo (how much sunlight is reflected back to space instead of being absorbed). The greenhouse effect measures how much warmer the surface is than the overall effective temperature of the planet. So, the effective surface temperature, T_\mathrm{surface,eff}, is, using the definition of \Delta T_\mathrm{GHE}, :T_\mathrm{surface,eff} = T_\mathrm{eff} + \Delta T_\mathrm{GHE} \;. One could also express the relationship between T_\mathrm{surface,eff} and T_\mathrm{eff} using or . So, the principle that a larger greenhouse effect corresponds to a higher surface temperature, if everything else (i.e., the factors that determine T_\mathrm{eff}) is held fixed, is true as a matter of definition. Note that the greenhouse effect influences the temperature of the planet as a whole, in tandem with the planet's tendency to move toward radiative equilibrium. == Misconceptions ==