Climate Change

Greenhouse gases make up about a percent of all of the molecules in the atmosphere, and CO2 makes up about .038% by volume. That is an increase from .028% from pre-industrial time (fixed– comments). That means that today, if you went through the atmosphere sifting through molecules and collected one million of them, you should only find 380 that were CO2. There are often remarks which read like “how can such a small amount make such a large difference?”

Of course, one needs to be familiar with what exactly the greenhouse effect does, and how the planet’s temperature is maintained. This was discussed in much more detail in my set of posts on “basic radiative models and Earth’s climate system.” An earth-like planet with no atmosphere would be roughly 33 K (33 C, 59 F) degrees cooler than it is now. The way the global mean temperature is maintained is very much determined by a concept called “radiative equilibrium” which is a condition where the net solar radiation coming in is equaled by the infrared (heat) radiation going out of the top of the atmosphere. A planet which took in solar radiation without getting rid of heat back to space would heat up without bound and approach sun-like conditions, but all bodies emit radiation at a magnitude proportional to the fourth power of its temperature. The presence of greenhouse gases help to delay that infrared radiation back to space, thereby making the planet warmer– the gases make the atmosphere harder to radiate infrared energy; for the same temperature, you lose energy less quickly than if the planet was greenhouse free.

As it turns out, most of the atmosphere (Nitrogen, Oxygen, Argon) in fact do not interact with the infrared radiation (IR), and so it is easier to visualize how such a small concentration of greenhouse gases can have such a disproportionate impact on climate. In reality, gases absorb IR selectively, and different gases at different concentrations will effect the outgoing IR differently, but the important point so far is that most of the atmosphere has no effect on this. In this post, I want to illustrate visually what happens as one adds a few molecules of, say, CO2 to the atmosphere.

Here, I use David Archer’s MODTRAN radiation model to illustrate the idea of band saturation. Here, I assume the atmosphere has no CO2 or other greenhouse gases, no water vapor, and no cloud cover. Temperature follows the 1976 US standard atmosphere, and the model computes the outgoing longwave (infrared) radiation (OLR) at 70 km above the Earth’s surface. The CO2 concentration will be varied.

Here is the spectrum with no CO2

Now let us introduce just 10 parts per million of CO2 into the atmosphere

Now let us enter modern day 380 parts per million of CO2

You can see that the small changes from no CO2 make a large difference, and as one enters 380 ppmv the “bite” in the spectrum appears. As one adds more and more CO2 to the atmosphere, the outgoing longwave radiation decreases, and it is as though one is putting more insulation around the atmosphere. Is this relationship linear?? In fact, it is not, as the OLR will drop like the log of the changing CO2 concentration. That is, going from 300 ppmv to 310 ppmv will not produce the same effect as going from 600 to 610 ppmv. Fortunately for us, each doubling of CO2 will produce roughly the same amount (e.g., going from 300 to 600 gives as much effect as going from 600 to 1200). If the OLR dropped in the other fashion, the planet would be too hot to support life as any small change in CO2 would produce extreme effects. Please note that this does not mean the changing CO2 concentration will have no effects, as the temperature changes that follow will certainly matter for us. However, you can see this “bite” does not change much as we go to 1000 ppmv.

In this model, with no water vapor or CO2 or other GHG’s, 347 W/m2 of longwave radiation is allowed to escape to space. If we toss up just 10 ppmv of CO2 into the atmosphere, 331.5 W/m2 is now allowed to leave. That number goes to 313 W/m2 for 380 ppmv, and drops to just 308 W/m2 at 1000 ppmv. Now, I will throw in realistic values for water vapor, tropospheric and stratospheric ozone, and methane with 380 ppmv for CO2. This produces an image like this:

Alright, so what’s going on here? What is quite clear is that the radiative forcing of carbon dioxide per unit ppmv decreases with increasing CO2 concentrations. This is due to the fact that center bands of CO2 effectively become “saturated.” The CO2 mainly absorbs in a spectral band around 667 cm-1. The radiation over the area here is emitted by the ground to the lower atmosphere, but very little in the upper atmosphere since the temperature decreases with altitude. The parts of the spectra that follow the colder blackbody curve come from greenhouse gases in the upper atmosphere. The primary bands centered around 667 cm-1 can become quickly saturated. So can we say that CO2 will continue to have only small effects and then suddenly stop having an effect on the OLR as our center band becomes saturated? In fact, no such conclusion can be made. Even though the center of the CO2 band is saturated, the edges of the band are not saturated, and these will continue to be radiatively important. The “bite” CO2 takes out of the spectrum may not get deeper, but it will in fact continue to get broader, and there is always absorption continuing to wait at the “wings” of the CO2 band. Because the flanks of the band are not very effective now (but they have the potential to be as you add CO2), continuing to add carbon dioxide will further have effects on the radiative forcing even as one approaches Venus-like conditions. However, because the bands get saturated as one moves progressively toward the wings, adding CO2 at high background levels will have less impact than adding CO2 at low background levels. This can be seen on the following curve of OLR vs. CO2 concentration, with water vapor in the atmosphere at constant relative humidity (click images to enhance them).

As you can see, this will continue to progress even at much higher CO2 levels, though the OLR can drop a bit quicker than the logarithm as the bands at the edges become much more active (not really relevant for today or anything in the future)

As one adds CO2, you make the outer bands relevant for that concentration, temperature, pressure, etc “optically thick” and you enhance the absorption there, and reduce transmission through one more layer of the atmosphere. In fact, as one continues to add CO2, the level at which the planet’s heat balance is determined moves up and so areas lower than this (or pressure > pressure (rad)) will warm up as a new radiative equilibrium is reached. By making the band wider, you replace some of the hotter surface emission with emission in the higher, colder, thinner layers of the atmosphere and thereby delay more radiation escape to space.

What is good to know is that the transmission does not decay exponentially. If this happened, a doubling of CO2 could raise temperatures by some hellish 50 degrees C, rather than the ~3 C cited today. But, that 3 C per doubling is significant, and doubling or tripling CO2 in the atmosphere could have extreme effects on life today. Ice ages can be given by just a reduction of several degrees, and hothouse climates from the past can be given with just several degrees hotter. Climate modelers use around 4x the pre-industrial CO2 to give you the steamy, hot Cretaceous when the dinosaurs were around. A rise of a doubling to a tripling of carbon dioxide is easily possible under “business-as-usual” socio-economic scenarios by the end of the century, especially as carbon sinks are now in decline.

What does this mean now?? The planet will warm by about another half a degree even if everything stopped today and CO2 concentrations were kept at 380 ppmv. We have already seen 0.8 degrees C, and a bit more is in the pipeline. Glaciers and oceans have not yet equilibrated to the new atmosphere, so it will be several decades for the climate to catch up to today’s greenhouse levels. It is still possible to avoid 2 C, which is where a threshold probably is for significant disruption on the climate system. However, the longer it takes to act, the larger the impact on climate–and if we allow CO2 to rise for many more decades before significant action is taken, the consequences can be severe.