Global Warming

Rising CO2 concentration in the atmosphere leads to increased IR retention and hence global warming - this is a message hard to miss these days. But how does that work in detail?

It's generally fair to say that things are complicated -largely because it's not just CO2 that matters for the problem.

Out of the possible gases that can be specified for the atmosphere, diatomic molecules such as O2 or N2 have no significant IR absorption because they lack modes in the required energy range that could be excited. Molecules with three or more atoms such as CO2, O3, H2O or CH4 on the other hand show IR absorption, and the code computes for these four gases, so increasing the relative amount of any of them in the atmosphere will lead to increased IR retention.

Now, the complicated issue is that the concentration of some of them are temperature dependent - we have seen previously that during an Ice Age, moisture freezes out of the atmosphere, and the opposite is also true: a warmer atmosphere can hold a higher water content. Methane also may be released from the ground when Earth warms and e.g. perma-frost thaws. So the question we have to answer is how to treat these processes.

But does this matter much?

Computing the IR retention

We've seen before that specifying an atmosphere automatically makes the code suggest an IR retention coefficient. So a possible workflow is as follows:
  • start with the atmosphere declaration and increase CO2 content from the original 0.04%:

    h2o 0.5
    ch4 0.00018
    o3 0.00006
    n2 78.08
    o2 20.95
    ar 0.934
    co2 0.04
    surface_pressure 1.0

  • insert that value into the atmosphere_basic block as infrared_blocking
  • simulate an evolution for a year or two to get a stable reference temperature for the effect of only CO2
  • use this reference temperature in the Clausius-Clapeyron relation to compute how much more water the atmosphere can hold
  • increase the amount of H2O in the atmosphere by that factor and compute a new IR retention coefficient
  • insert that value into the atmosphere_basic block as infrared_blocking
  • re-run the simulation to find a new temperature including the effect of water
  • if you have a model of how methane is released, include that as well

The result is something like the following graph:

Temperature increase driven by CO2 concentration in the atmosphere, without (blue) and with (red) increasing water vapour with temperature.

So the effect of increasing CO2 by a factor 5 is not so bad, a warming of some 2.6 degrees, but including the higher water content in the atmosphere really makes things mich worse. Unfortunately this means we cannot neglect the fact that water and methane concentrations change with temperature. There are feedback loops that are driven by changing the CO2 concentration which make the problem harder to assess.

Indeed, if you've been paying attention to the suggested IR retention, you might have noticed that it changed a bit every time you changed the value of the coefficient to be actually used. This is because changing the actual coefficient changes Earth's temperature, that in turn changes the shape of the IR spectrum, so the same pattern of absorbing lines act differently on that changed shape - this is yet another feedback loop.

Most of what we've seen so far were positive feedback loops - a warmer atmosphere holds more water which absorbs more IR which makes the atmosphere yet warmer,... but there are also negative feedback loops: If there is more water in the atmosphere, cloud formation might be enhanced as well and so increase albedo. Higher temperatures might lead to more forest fires, bringing more aerosols into the stratosphere, again increasing albedo. It is assessing all these effects which makes precictions for global warming a complicated business.


The above workflow is somewhat inconsistent because there are two feedback loops which are computed automatically and don't need to be iterated by hand - precipitation is automatically tied to atmosphere temperature and the ability of the atmosphere to hold water, and the melting of snow and ice and the resulting effects on albedo are also included automatically. This is largely because simulating these effects is needed to get the yearly-averaged albedo of Earth even in the unperturbed state (and because - unlike e.g. the release of methane from the ground or cloud formation - they are fairly straightforward to compute).

But this means we can take a look at what the warming does to the snow cover in the simulation. The result (default vs. 7 deg warming) is shown here:

Snowcover [cm] for the default (blue) and hottest warming scenario (red)

The total amount of snow changes surprisingly little. True, snow melts faster in the hot scenario - but since precipitation is increased, there is more of it to begin with. So of anything, a trend for snow to be found more northward is observed, but in general here the increased ability of the atmosphere to hold water exemplifies a negative feedback loop as the increased amount of snow tends to bring albedo up.

Of course, as with the Ice Ages, it should be possible to drive Earth into a completely new state in which nearly all water is in the atmosphere which leads to a tremendous IR retention and prevents any snow or ice from ever forming. This is more or less the state Venus is in, but the required feedback loops would have to be iterated manually.

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