## Friday, August 19, 2011

### Climate Change - The Tub Analogy

A reader has posted a claim about climate change that I have responded to in the past, but would like to respond to again.

It is a type of argument that, I hold, no rational person truly concerned with reaching a reasonable conclusion about climate change would offer.

The irrationality of the argument takes a little bit of demonstration, but the demonstration is solid.

The position under discussion is:

There is scientific models that show 2 ppm of CO2 is increasing in the environment each year. Are you aware that only 3% of this 2 ppm can be attributed to man?

I need to correct this a bit. It is actually 3.5 ppmv (parts per million by volume) per year. But this will not affect the logic of the objection.

Imagine that you own a tank partially filled with water. Each year, 210 gallons of water flow into the tank, and 210 gallons of water flow out of the tank. For 10,000 years, the level of water in the tank has stayed quite close to 270 gallons.

Note: For 10,000 years, atmospheric CO2 concentration has been hovering around 270 ppmv. Deviations from this have been small.

Now, somebody opens up a faucet that starts adding 7 gallons to the tub every year. After he turns on the faucet, you notice that the volume of water in the tub increases by 3.5 gallons per year.

Note: This corresponds to the 7 ppmv that humans are adding to the atmosphere each year, and the measured increase in atmospheric concentrations of 3.5 ppmv per year.

This happened quite a few years ago, and the volume of water in the tank is now 380 gallons rather than the traditional 270 gallons.

Corresponding to the current 380 ppmv concentration of CO2 in the atmosphere.

In this case, the 7 gallons of water entering the tub from the faucet represents only 3.3% of the total volume of water entering the tub.

Yet, given the following facts: (1) That the volume of water in the tub has been in equilibrium for 10000 years, (2) none of the other sources of water have changed their flow (the only source of increased volume of water entering the tub is what is coming out of the faucet), and (3) the increase in the volume of water (3.5 gallons per year) is half the volume that is coming out of the faucet (7 gallons per year) . . .

The only reasonable conclusion to draw is, of the 7 gallons going into the tub, half of it is flowing out again, and half of it is remining in the tub causing the volume of water in the tub to increase by 3.5 gallons per year.

Now, this is intuitive. In normal circumstances, people wouldn't even think twice about this. They open the faucet. They see a water volume that had been previously unchanged start to increase. They say that opening the faucet is causing the water volume to increase. It's a simple inference that nobody would find tricky.

However, when it serves a political or ideological purpose, we see that it is easy for a person to blind themselves (or intentionally attempt to blind others) to what would be a simple causal inference by making the totally irrelevant claim, "It is 3% of the volume of water flowing into the tub." It doesn't matter. The volume of water in the tub wasn't changing until the faucet was turned on and, if you turn off the faucet, the volume would return to normal. The faucet is 100% responsible for the change in volume in the tub.

Dana said...

....Yet, given the following facts: (1) That the volume of water in the tub has been in equilibrium for 10000 years, (2) none of the other sources of water have changed their flow (the only source of increased volume of water entering the tub is what is coming out of the faucet), and (3) the increase in the volume of water (3.5 gallons per year) is half the volume that is coming out of the faucet (7 gallons per year)

You make a good point if anything you state above was an actual fact.

Firstly, there is no CO2 balance in biomass input/output: CO2 is constantly being locked up/ released at varying rates so there is no dynamic equilibrium.
In (geologically)ancient times CO2 concentrations were as high as 6000ppm...for a long time high enough to preclude oxygen breathers evolving...until sufficent CO2 was locked up by plant life ( the oceans would have been more or less saturated) and O2 levels raised by algae and cyanobacteria.
There is no balance! Check out the Oxygen Cycle.

Secondly, there was changes in the input as temperature started to rise about 10,000 years ago, PRECEDED by CO2 increases. Lags of up to about 800 years has been documented. Meaning, that something else caused the temperature to rise which in turn released CO2 from sources.

Lastly, your tub analogy, while graphically pleasing, is nonetheless fallacious since a bathtub is a contained system (at least on 3 sides) while the atmosphere is an open system subject to the Stefan–Boltzmann law. Check out radiative forcing.

Not to confuse this thread with math, but:

According to http://en.wikipedia.org/wiki/Carbon_dioxide 385 ppm corresponds to 3e12 tons of CO2 in the atmosphere, so we get:

year ppmV tons
1970 320 2.49E+12
2005 385 3.00E+12
5.06E+11 increase

Apparently the manmade carbon flux has risen from 4E+09 to 8E+09 tons from 1970 to 2005 so on average a flux of 6E+09 for 35 years is 2.10E+11 tons which is 42 % of the total increase and 7 % of the current total atmospheric CO2.

That begs the question, what is the cause of the other 48 % ? And how can a manmade increase of 7 % be the main reason for a global increase in temperature?

Respectfully,

Alonzo Fyfe said...

Firstly, there is no CO2 balance in biomass input/output: CO2 is constantly being locked up/ released at varying rates so there is no dynamic equilibrium.

There has been for the last 10,000 years. There had to have been, or the concentration of CO2 would not have been constant over that time.

If the water in the tub remains relatively constant for 10,000 years, there is no other conclusion that you can draw than to say the flow of water into the tub has quite closely matched the flow of water outside the tub for the past 10,000 years.

This is straight math.

In (geologically)ancient times CO2 concentrations were as high as 6000ppm...for a long time high enough to preclude oxygen breathers evolving...until sufficent CO2 was locked up by plant life ( the oceans would have been more or less saturated) and O2 levels raised by algae and cyanobacteria.

That would show that there are other potential causes for changes in CO2. It does not provide any evidence that there is some other change.

A man gets run over by a truck and dies. Somebody comes along and says, "My dad died when he fell down a mine shaft." That shows that there are other ways to die. It does not show that this person did not get run over by a truck.

If you start adding 7 gallons per year to the tub, and its volume increases by 3.5 gallons per year, this tells you that something else must have changed - there has been a 3.5 gallon per year increase in outflow - not inflow, but outflow. The 3.5 gallons is not evaporating into thin air.

If you want to argue that there is some other source of increased inflow . . . say, 10 gallons per year. First - where is it? Do you have any evidence for this? Second, NOW you also will need to account for 13.5 gallon increase in outflow (instead of 3.5).

It turns out, there is an explanation for the additional 3.5 gallons per year outflow. In the case of the atmosphere, it is CO2 being absorbed by the oceans - making the oceans more aciding. We put 7 ppmv CO2 into the atmosphere. 3.5 ppmv stays in the atmosphere, 3.5 ppmv gets absorbed by the ocean. And now our equations balance.

Again, straight math.

Lastly, your tub analogy, while graphically pleasing, is nonetheless fallacious since a bathtub is a contained system (at least on 3 sides) while the atmosphere is an open system subject to the Stefan–Boltzmann law. Check out radiative forcing.

We are not talking about radiative forcing here. We are talking about the volume of CO2 in the atmosphere.

Apparently the manmade carbon flux has risen from 4E+09 to 8E+09 tons from 1970 to 2005 so on average a flux of 6E+09 for 35 years is 2.10E+11 tons...

One has to be careful comparing tons Carbon to tons CO2. 1 ton of carbon = 3.6 tons CO2.

That is tons CARBON, not tons CO2. CO2 weighs over 3 times as much as carbon.

Alonzo Fyfe said...

Dana: I cannot help but notice that your "Math" point is, word for word, exactly the same as the comment made here:

http://www.skepticalscience.com/human-co2-smaller-than-natural-emissions.htm

Actually, two characters are different. Even the spaces around the units match.

In that instance (from 2007), a poster named Yves provided the same correction I did here.

I find this to be an odd coincidence.

curious cuber said...

Very interesting...ctrl-v.

dbonfitto said...

Hey, there could be a leak in the ceiling right above the tub, too. The neighbor could have put a hose in the window and it's filling the tub faster, too.

Why is 'fault' being addressed here as a prerequisite for mitigating the problem? It doesn't matter if CO2 levels are rising because of emissions, cosmic rays, solar flares, or fairy dust. They're rising.

The fact of the matter is that the only input we can stop right now is the faucet. We only control the man-made input. The longer we wait to close it, the more water damage we have to clean up later.

This isn't a liability issue. It's a survivability issue.