The basic physics involved in the greenhouse effect are the same as heating a burrito in a microwave oven. Both carbon dioxide and water have absorption spectra. In the case of the microwave oven, the wavelength is about 12 cm. In the case of carbon dioxide the wavelength is about 15 microns. The radiation in both cases excite energetic quantized molecular states and is thereby absorbed. With the water molecule in the microwave spectrum we are talking rotational states. With the carbon dioxide molecule we are talking about a bending mode where the normally linear molecule (one positively charged carbon atom with one negatively charged oxygen atom at each end) vibrates by bending.

In isolation, such an excited molecule would undergo spontaneous decay. However, the more crowded things get the more likely that some collision will take place whereby some of the energy gets transferred to surrounding molecules. At 1/50th of the atmospheric pressure of sea level (20 mb out of 1015 mb) we are still talking about over a million collisions over the lifetime of the excited state. So even though oxygen and nitrogen can't absorb the Earth's thermal radiation they will get some of that energy, causing the atmosphere to heat up.

Carbon dioxide molecules will also acquire energy through collisions, and a certain percentage will be in an excited state at any given moment. Since the molecules don't remember how long they have been in an excited state, some percentage will undergo spontaneous decay over any given length of time, emitting photons. And when the photons finally escape to space rather than being absorbed they permit the climate system to cool off. Pretty much the same thing as with that burrito.

As we add carbon dioxide to the atmosphere this increases absorption, particularly where thermal radiation consists of photons that would have previously escaped to space, this increases absorption, raising the average altitude at which photons will finally escape to space. But the atmosphere will be cooler at that higher altitude and therefore will emit less radiation. This results in a radiation imbalance where the rate at which energy entering the climate system will exceed the rate at which energy leaves the climate system. At that point energy accumulates in the system and things warm up.

Now with a burrito it heats up and warms up from the outside in. This is because the microwave radiation can penetrate only so far. A bit like the photons travelling in the direction of space can travel only so far without being absorbed, although the infrared photons are headed out rather than in.

For the rate at which the planet is warming to decrease so that the planet warms more slowly, it is the upper part of the atmosphere where the photon energy finally escapes to space that has to heat up. When it heats up this reduces the rate at which heat is transferred (by convection as well as radiation) from the layers below. Reducing the rate at which heat is transferred from below means that the lower layers are going to warm. So like a burrito the atmosphere warms up from the outside in.

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Now that we know the basic physics behind an enhanced greenhouse effect it might be worthwhile to get some idea of the magnitudes involved.

In radiation balance theory, what matters is the deficit or surplus rate at which energy is entering the climate system. Reducing the amount of energy entering the leaving the climate system is that equivalent to raising the amount of energy energy entering the system. And if you "measure" at "Top Of Atmosphere", this is what is referred to as radiative forcing.

With this in mind, you could compare the forcing due to anthropogenic carbon dioxide to a doubling of solar radiance or to sticks of dynamite per hour. Or since the dimensions of this measure is energy per time, you could compare it to the average rate at which energy gets used in London.

So where do we stand?

A fellow by the name of Mike Sandiford has already run the calculations using a unit of measure he calls a "Hiro" which he has set equal to 1 Hiroshima bomb every second, or 60 trillion watts.

He states:

In these terms, our human energy system operates at a rate of 0.25 Hiros, or one Hiroshima bomb every four seconds. That is the equivalent of more than eight million Hiroshima bombs going off each year.

And we are on a trajectory towards the one Hiro mark by 2100, equivalent to the energy release of one bomb each year for every five-square kilometre patch of land on the planet.

The ocean heating is at 5 Hiros over the last few decades – the energy equivalent of detonating more than a 150 million Hiroshima bombs in our oceans each year.

And the radiative forcing of the CO2 we have already put in the atmosphere in the last century is a staggering 13 Hiros. The equivalent in energy terms to almost half a billion Hiroshima bombs each year.

Our effect on the earth is real: how we're geo-engineering the planet
Mike Sandiford, 16 June 2011, 6.02am AEST
http://theconversation.edu.au/our-effect-on-the-earth-is-real-how-were-geo-engineering-the-planet-1544

Little Boy was 15 kilotons. The largest nuclear weapon ever detonated was the Tsar Bomba a Soviet bomb weighing in at 50 megatons. So the forcing due to anthropogenic carbon dioxide is roughly equal to 14 Tsar Bombas per hour or 123,000 per year.

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For a more in depth discussion of the greenhouse effect, please see:

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