Temperatures Related to the Greenhouse Effect

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 definition1I 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 G = \SLR-\OLR\approx 158.2 W/m2 or \nghe=1-\OLR/\SLR\approx 0.40.2Values 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 T_{p,\mathrm{ef}} = (\OLR/\sigma)^\frac{1}{4} \approx 255.2 W/m2 where \OLR is the flux of outgoing longwave radiation that reaches space.
  • In thermal equilibrium, it would be the case that \OLR=\mathrm{ASR}, where \mathrm{ASR} is the flux of absorbed solar/shortwave radiation. So, the planetary effective temperature is often calculated as (\mathrm{ASR}/\sigma)^\frac{1}{4}. The problem is, that when a planet is not in equilibrium, this yields a different answer than the calculation in terms of \OLR. For Earth, at present, a calculation using \mathrm{ASR} yields 255.4 W/m2.

Surface temperature

  1. T_{s,a} = T_{s,s} - T_h \approx 288 K : The near-surface air temperature. This is, on average, less than the surface skin temperature, T_{s,s}, by some amount T_h. A positive value of T_h is required for conduction and convection to cause heat to flow from the surface into the air, as we know happens. T_{s,a} is sometimes used in informal reporting of the GHE.
  2. T_\mathrm{L-OTI} : The NASA Land-Ocean Temperature index is one a number of metrics for estimating changes in surface temperature. This is a blend of T_{s,a} for land surfaces and something between T_{s,s} and T_{s,b} for ocean surfaces. T_\mathrm{L-OTI} 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.)
  3. T_{s,r} = \left<(\underline\SLR/\sigma)^\frac{1}{4}\right> = T_{s,\mathrm{ef}} - T_v \approx 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, \underline\SLR. This is lower than the global surface effective temperature by an amount T_v\approx1.3 K as a result of the surface temperature being non-uniform.
  4. T_{s,\mathrm{ef}} = (\SLR/\sigma)^\frac{1}{4} \approx 289.6 K : The surface effective temperature. Here \SLR is the global mean surface-emitted longwave radiation flux. This is what should be used in rigorous discussions of the GHE.
  5. T_{s,b} : The surface bulk temperature. Given that Earth is in a warming phase, this must, on average, be somewhat lower than the surface skin temperature, T_{s,s}, 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 T_{p,\mathrm{ef}} by an amount T_g\approx34.4 K.
  6. T_{s,s} = T_{s,r} + T_\epsilon\approx 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 T_{s,r} because the surface has an emissivity, \epsilon, less than 1. For an emissivity \epsilon\approx 0.94, T_\epsilon\approx4.5 K and T_{s,s} \approx 292.8 K. However, the mean global value of \epsilon is not as well-established as one might expect, despite extensive satellite measurements. Fortunately, T_{s,s} 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 T_{s,r}.


So, in rigorous work, when defining the greenhouse effect temperature difference, one should define the greenhouse effect temperature difference using

(1)   \begin{equation*} T_g = T_{p,\mathrm{ef}} - T_{s,\mathrm{ef}} = (\SLR/\sigma)^\frac{1}{4} - (\OLR/\sigma)^\frac{1}{4} \approx 34.4\;\mathrm{K} \end{equation*}

However, in informal reporting, you might see the temperature difference calculated using something like as something like T_{s,a} or T_\mathrm{L-OTI} for the surface temperature, and (\ASR/\sigma)^\frac{1}{4} for the effective temperature. Such calculations yield a temperature difference value vaguely in the neighborhood of T_g, 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.

  • 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.
  • 2
    Values quoted here are generally based on my analysis of NASA CERES EBAF v4.2 data for the period 2001-2023.