Sunday, January 17, 2010

CO2 Bathtub

A friend of mine, a retired aerospace engineer who helped send men to the Moon, tipped me off to this article and its simple, but effective analogy.

A recent National Geographic had a short article about an MIT professor who wrote a computer program he calls the "bathtub analogy." Very briefly, a bathtub has an inlet spigot and an outlet drain. If the spigot is letting in less than the drain can pass out, the tub will never fill up. If the spigot is flowing at exactly the same rate that the drain passes out, the tub won't fill up or if there's already an initial water level in the tub, that level will remain constant. And of course, if the spigot is flowing at a rate greater then the drain can pass out, the tub will eventually fill up and overflow.

The MIT professor uses this analogy for many scientific and economic systems. For example, with suitable adaptations, conversion parameters, input data, etc., his program will address how you can gain and/or lose weight, how your outstanding credit card balance will go up and down, and so forth. He recently applied this program to the level of CO2 in the atmosphere using input data from another professor at the University of Chicago and from the Carbon Project.

Without burdening you with a lot of analytical detail, his bathtub analogy program shows that in 2008, the latest year with adequate data, the "global spigot of everything" filled the Earth's CO2 Bathtub at a rate of 9.1 billion metric tons (bmt) per year. In that year the drain on our CO2 Bathtub drained out the following:
  • + 0.9 bmt were absorbed by sediments and rocks. They are a huge CO2"sink", but chemically work very slowly and would take centuries to absorb all the CO2 currently being emitted by all the natural and man-made processes on the planet.
  • + 2.8 bmt were absorbed by the oceans. This is also a huge CO2 "sink", but only absorbs CO2 on its surface. The CO2-laden surface sea water then sinks at various places defined by global sea circulations, and is replaced by new sea water. This also is a slow process, and physically isn't able to play catch-up at current CO2 emission rates.
  • + 2.7 bmt were absorbed by plants and soils. This is a more rapid process, but that reservoir is smaller (and will always be limited in size) and it will soon fill up, especially if global forests and agricultural land continue to be destroyed at current rates.
Obviously from simple arithmetic, the bottom line is that in 2008 our CO2 Bathtub spigot flowed at 9.1 bmt, but the drain only passed out 6.4 bmt. The difference stayed in the atmosphere.
So in order to keep the CO2 level constant in that year we would have had to reduce global CO2 emissions by (9.1 - 6.4) = 2.7 bmt, or by about 30%. Also, if we wanted to additionally decrease the CO2 level in the atmosphere, we would have had to turn the CO2 spigot down to a rate less than 2.7bmt, or more than 30%.

A very important conclusion from this arithmetic is that it's necessary to cut CO2 emissions below our current level of ~9.1bmt even to just keep the CO2 level in our bathtub constant! Just living with the current 9.1 bmt (or something a little less than that), or just stopping the annual growth in emissions that we've been experiencing, will not stop the CO2 level in the atmosphere from increasing! Just like water in the bathtub, the input spigot in our CO2 Bathtub has to be turned down to flow at a rate not more than the CO2 Bathtub drain can flow out to maintain a fixed level! This is a critical conclusion that most people don't comprehend. Accordingly, everybody must recognize that to keep the current CO2 level constant we need to talk about an annual CO2 emission reduction of 30% or more! Again, the spigot inflow has to be the same or less than the drain outflow (which is now ~6.4 bmt per year), for the level to remain constant.

Thinking about emission reductions of 10% or 20%isn't going to cut the mustard! And thinking about sequestering and other schemes to effectively increase the size of the drain in our CO2Bathtub is likely impractical - we're talking here of an excess of~3 billion metric tons per year! Therefore, as the MIT professor clearly implies, a 30% reduction goal should be the "magic number" for all scientific, economic, and political discussions.

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