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Has anyone managed to read the (latest) full IPCC-report and do you know whether they have taken into account the Earth's core temperature in their models. Besides the IPCC-report, do we know how much the climate and temperature on Earth's surface is effected by it? As I'm guessing, the core temperature of the earth is an very important variable that the climate-models need to have.

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    $\begingroup$ The internal heat flux is, on average, about 0.1 W/m$^2$, while the incoming solar radiation is about 340 W/m$^2$. So internal heat is not an important variable for climate models. See for example this answer: earthscience.stackexchange.com/a/431/18081 $\endgroup$ Aug 22 at 20:57
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    $\begingroup$ @Jean-MariePrival It also does not change much in time, so it can be neglected in climate change calculations. I could not find an estimate of how many degrees warmer it makes the surface. Saturn is 32C warmer due to internal energy flux! $\endgroup$ Aug 22 at 21:40
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    $\begingroup$ To be an important variable it needs to be shown it is varying; it is not ignored or neglected - just known to be both relatively small in total amounts of heat flow and known that the rate of heat flow hasn't been increasing. And a whole lot of valid science would have to be ignored or neglected or overturned for the causes of global warming to still be considered an unexplained mystery. $\endgroup$
    – Ken Fabian
    Nov 17 at 21:27
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It's not the earth's core temperature per se that matters, but rather the amount of heat that flows from the core to the surface. Just like holding a cup of hot coffee - if the mug is insulated, it's fine, but if it's just thin metal, then your fingers will get burnt. The flux of heat through the surface of the solid earth is less than ~0.5 W/m$^{2}$. The sun heats the surface of the earth at an average rate of ~200 W/m$^{2}$ (which varies with latitude). We can therefore conclude that the heat coming from the centre of the earth isn't a big factor for the surface temperature of the land.

But, what about the ocean?

This paper from 2001 discusses the impact of the geothermal heat flux on the ocean. They use an approximation of the coupling between the atmosphere

$$\frac{\partial T_{ocean}}{\partial t} = \lambda (T_{ocean} - T_{0})$$

that relaxes the ocean temperature, $T_{ocean}$, back towards a set temperature, $T_{0}$, at a rat of $\lambda$ W m$^{-2}$ K$^{-1}$. They use a value of 32 W m$^{-2}$ K$^{-1}$, so an extra heat flux of 0.5 W m$^{-2}$ leads to a change in surface temperature of $1.5 \times 10^{-3}$ K. Not really noticeable.

If we look at the deep ocean, 3,000 m and below, then their results suggest that this heat flux can make a small but discernible difference; in their model the deep ocean is about 0.2-0.3°C warmer because of the heat flux coming through the sea floor.

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  • $\begingroup$ Rather than just passing it off by relative scale, I'd think the Stefan Boltzmann Law may offer a fair thought of what small factor 0.5 $\frac{W}{m^2}$ really has, given its 4th root relationship from radiation to temperature? $\endgroup$ Aug 23 at 11:47
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    $\begingroup$ This is a great answer. It's worth adding that the heat flux from core to surface is whatever it is. It doesn't lead to a heating or cooling of the atmosphere, it would simply contribute to keeping the temperature at the earth surface where it was historically. In other words, it's a constant contribution, unrelated to the climate change that the IPCC reports address. $\endgroup$ Aug 23 at 22:18
  • $\begingroup$ Thank you for the answer. Then what's the heat flux from a volcano since I guess molten lava comes from the core from there? Are these volcanic things implemented into the average-computation of the total heat that flows from core to surface? Thanks. $\endgroup$ Aug 23 at 22:24
  • $\begingroup$ @NaturalNumberGuy - estimates of geothermal heat flux includes heat from volcanic eruptions. $\endgroup$
    – Ken Fabian
    Nov 17 at 21:31
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This Skeptical Science article explains that geothermal is very small, $0.09W/m^2$, compared to radiant heat flows. It also does not change much in time, so it can be neglected in climate change calculations.

For an airless planet the equilibrium temperature $T$ can be calculated from $$ F=\sigma T^4$$where $F$ is the average absorbed heat flux at the surface and $\sigma$ is the Stefan-Boltzmann constant. If there is an additional internal flux $I$, the equilibrium temperature is increased by $\Delta$: $$F+I=\sigma(T+\Delta)^4$$ For small $I$ this leads to $$\Delta \approx \frac{TI}{4F}$$ Without the atmosphere, $I$ is three orders of magnitude smaller than $F$, so $\Delta$ is a fraction of a degree. I don't think the atmosphere would amplify this effect.

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