There are a variety of technically-distinct temperatures that might be referenced in discussions of Earth’s temperature.
In some cases, referring to a different technical definition might alter precisely what temperature difference is associated with the greenhouse effect. This is a factor in why the greenhouse effect is widely described as being 33℃, while, applying a rigorous definition^{1}I agree with the definition in: Robert M. Haberle. Estimating the power of Mars’ greenhouse effect. In: Icarus 223.1 (2013), pp. 619–620. issn: 0019-1035. doi: 10 . 1016 / j . icarus.2012.12.022., the value is 34℃.
In serious scientific work, scientists typically quantify the greenhouse effect use the metric 158.2 W/m^{2} or 0.40.^{2}Values quoted here are generally based on my analysis of NASA CERES EBAF v4.2 data for the period 2001-2023. However, many people find describing the greenhouse effect as a temperature difference to be more meaningful. So, let’s look into the sort of temperatures that might show up in discussions of that temperature difference.
[Warning: the notation I use here to represent specific temperatures may or may not be consistent with notation elsewhere on this site.]
Planetary effective temperature
The planetary effective temperature, is the temperature a black-body would need to have in order to emit the same amount of radiation as the planet (where the atmosphere is included as part of the planet).
Confusingly, this is often simply called the planet’s “effective temperature” or “black-body temperature”; this terminology is unfortunate, because the term “effective temperature” can also appropriately be used to refer to other quantities, such as the effective temperature of the surface.
There are different definitions of the planetary effective temperature you might encounter:
- In rigorous usage, the planetary effective temperature is defined as 255.2 W/m^{2} where is the flux of outgoing longwave radiation that reaches space.
- In thermal equilibrium, it would be the case that , where is the flux of absorbed solar/shortwave radiation. So, the planetary effective temperature is often calculated as . The problem is, that when a planet is not in equilibrium, this yields a different answer than the calculation in terms of . For Earth, at present, a calculation using yields 255.4 W/m^{2}.
Surface temperature
- 288 K : The near-surface air temperature. This is, on average, less than the surface skin temperature, , by some amount . A positive value of is required for conduction and convection to cause heat to flow from the surface into the air, as we know happens. is sometimes used in informal reporting of the GHE.
- : The NASA Land-Ocean Temperature index is one a number of metrics for estimating changes in surface temperature. This is a blend of for land surfaces and something between and for ocean surfaces. or something like it may be used in informal reporting of the greenhouse effect. (Technically, the L-OTI index only reports temperature changes, not the actual baseline temperature.)
- 288.2 K : The surface radiating temperature. This is my name for the global mean of the local surface effective temperature, defined in terms of the local surface-emited longwave radiation flux, . This is lower than the global surface effective temperature by an amount K as a result of the surface temperature being non-uniform.
- 289.6 K : The surface effective temperature. Here is the global mean surface-emitted longwave radiation flux. This is what should be used in rigorous discussions of the GHE.
- : The surface bulk temperature. Given that Earth is in a warming phase, this must, on average, be somewhat lower than the surface skin temperature, , so that heat can flow from the skin layer into the bulk material below the surface. The surface bulk temperature is not typically used in GHE calculations. This is warmer than the planetary effective temperature by an amount K.
- 293(?) K : The surface skin temperature. This is the temperature of a thin (perhaps 10 microns thick) layer of material at the interface with the atmosphere. This temperature is higher than because the surface has an emissivity, , less than 1. For an emissivity , K and K. However, the mean global value of is not as well-established as one might expect, despite extensive satellite measurements. Fortunately, isn’t as central to the theory as one might imagine. It’s not typically referred to in GHE calculations. Warning: In informal writing (even mine), the term “skin temperature” might be used to refer to .
Conclusion
So, in rigorous work, when defining the greenhouse effect temperature difference, one should define the greenhouse effect temperature difference using
(1)
However, in informal reporting, you might see the temperature difference calculated using something like as something like or for the surface temperature, and for the effective temperature. Such calculations yield a temperature difference value vaguely in the neighborhood of , but not necessarily the same. Such calculations are likely the source of the 33℃ value that is widely circulated as being the size of the greenhouse effect.
Alternatively, the 33℃ value might be due to (a) an outdated vale of the temperature difference, or (b) combining the 34℃ atmospheric greenhouse effect with the -1℃ temperature-variation-emissions-boost surface effect.
- 1I agree with the definition in: Robert M. Haberle. Estimating the power of Mars’ greenhouse effect. In: Icarus 223.1 (2013), pp. 619–620. issn: 0019-1035. doi: 10 . 1016 / j . icarus.2012.12.022.
- 2Values quoted here are generally based on my analysis of NASA CERES EBAF v4.2 data for the period 2001-2023.