[ExI] Diminishing influence of increasing carbon dioxide on temperature

[Tomaz Kristan]

Anders:

> if it is geothermic dominated, then the planet will radiate way more
energy than it gets from the sun.

That is not true. Earth gets - let say 1000 W per square meter - from the
Sun and emits let say 1001 W per square meter out to the space.

This 1 W/m2 is relatively small compared to 1000 from the Sun. It comes
from the Earth's interior. Still the high temperatures deep down ARE
dominated by geothermic, not  "suntermic" factors.

High temperatures do not imply high energy per second.


On Fri, Aug 15, 2014 at 11:34 AM, Anders Sandberg <anders at aleph.se> wrote:

> Tomaz Kristan <protokol2020 at gmail.com> , 15/8/2014 9:26 AM:
>
> Venus "surface" is in fact deep down in the stuff. Sun has nearly nothing
> to do with the temperature there, it's geothermic.
>
>
>
> Hmm. Let's see: if it is geothermic dominated, then the planet will
> radiate way more energy than it gets from the sun. Assuming it to be a
> blackbody it will radiate A*sigma*T^4 Watts, where A is the total surface
> area (~5e14 m^2) , sigma is 5.67e-8 W/m^2K^4 and T is the average
> atmosphere temp (737 K). I get 7.85e18 Watts. The total solar input hitting
> it is I*a, where I is the solar irradiance (2613.9 W/m^2) and a is the
> cross sectional area (1.17e14 m^2): 3.07e17 W.
>
> That is a factor of 25. So clearly this is missing something. Or I made an
> error.
>
> But if we estimate the geothermal flux as what is missing, we get 15,000
> W/m^2! Earth has 0.087 W/m^2. Now, I can imagine more geothermal on Venus
> due to a bit stronger tidal forces, but most geothermal heat is due to
> radioactive decay and the compositions are not too different. But 5 orders
> of magnitude?15 kW/m^2 is not sustainable for long - if Venus was a lava
> ocean it would cool off within a geologically short timescale.
>
> What is going on? The most likely answer is that the naive blackbody model
> above is too simple. If we instead refine it so that there is an atmosphere
> layer that lets through sunlight to deep levels/the surface, and then acts
> opaque for infrared (which we do know is true for CO2 from lab
> experiments), then the thermal balance starts looking saner.
>
> Let Ts be the surface/troposphere temperature and Ta be the high altitude
> atmosphere temperature. Then energy balance requires S + sigma Ta^4 =sigma
> Ts^4 (solar + atmosphere downwards = surface upwards) and sigma Ts^4 = 2
> sigma Ta^4 (surface upwards = atmosphere up + down radiation). The last
> equation makes Ts = 2^(1/4) Ta = 1.19 Ta: adding the layer increases
> surface temperatures by nearly 20% *regardless of solar input*.
>
> And given that the optical depth of Venus' atmosphere is about 80, one
> could argue that there should be many such layers! If we have multiple
> layers, then the outermost could have the equilibrium Venusian blackbody
> temperature 238 K and energy balance would work, while the average
> temperature below could be way higher. Each layer would make the stuff
> beneath warmer. In practice the layers would be grey and there would be
> some messy interactions (i.e. time to write simulator code), but it is not
> hard to see that this kind of insulation could produce a high temperature
> at the surface/troposphere even for a modest solar influx.
>
> So I would be surprised if geothermal had a huge influence on Venusian
> surface temperatures. The solar input is on the order of 2613 W/m^2: to
> measure up you need a geothermal flow higher than Io's 2 W/m^2 - by a
> factor of a thousand! I think we would notice those eruptions. Also, that
> would assume an optically thin atmosphere, which we know is not true given
> observations. One can of course tone down the geothermal and make the
> atmosphere more opaque, but it seems that when we start to reach scenarios
> compatible with a solid surface we will already have added enough
> greenhouse to make geothermal rather moot.
>
>
> (Thanks Tomaz, this was fun to work through - at first I thought a mere
> paragraph would be enough to dismiss your idea, but it actually
> demonstrates just how quickly even fairly simple atmosphere models get
> nontrivial. )
>
>
>
> Anders Sandberg, Future of Humanity Institute Philosophy Faculty of Oxford
> University
>
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>


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