Aside from the endless stream of Cantor cranks, the next biggest category of emails I get is from climate “skeptics”. They all ask pretty much the same question. For example, here’s one I received today:
My personal analysis, and natural sceptisism tells me, that there are something fundamentally wrong with the entire warming theory when it comes to the CO2.
If a gas in the atmosphere increase from 0.03 to 0.04… that just cant be a significant parameter, can it?
I generally ignore it, because… let’s face it, the majority of people who ask this question aren’t looking for a real answer. But this one was much more polite and reasonable than most, so I decided to answer it. And once I went to the trouble of writing a response, I figured that I might as well turn it into a post as well.
The current figures – you can find them in a variety of places from wikipedia to the US NOAA – are that the atmosphere CO2 has changed from around 280 parts per million in 1850 to 400 parts per million today.
Why can’t that be a significant parameter?
There’s a couple of things to understand to grasp global warming: how much energy carbon dioxide can trap in the atmosphere, and hom much carbon dioxide there actually is in the atmosphere. Put those two facts together, and you realize that we’re talking about a massive quantity of carbon dioxide trapping a massive amount of energy.
The problem is scale. Humans notoriously have a really hard time wrapping our heads around scale. When numbers get big enough, we aren’t able to really grasp them intuitively and understand what they mean. The difference between two numbers like 300 and 400ppm is tiny, we can’t really grasp how in could be significant, because we aren’t good at taking that small difference, and realizing just how ridiculously large it actually is.
If you actually look at the math behind the greenhouse effect, you find that some gasses are very effective at trapping heat. The earth is only habitable because of the carbon dioxide in the atmosphere – without it, earth would be too cold for life. Small amounts of it provide enough heat-trapping effect to move us from a frozen rock to the world we have. Increasing the quantity of it increases the amount of heat it can trap.
Let’s think about what the difference between 280 and 400 parts per million actually means at the scale of earth’s atmosphere. You hear a number like 400ppm – that’s 4 one-hundreds of one percent – that seems like nothing, right? How could that have such a massive effect?!
But like so many other mathematical things, you need to put that number into the appropriate scale. The earths atmosphere masses roughly 5 times 10^21 grams. 400ppm of that scales to 2 times 10^18 grams of carbon dioxide. That’s 2 billion trillion kilograms of CO2. Compared to 100 years ago, that’s about 800 million trillion kilograms of carbon dioxide added to the atmosphere over the last hundred years. That’s a really, really massive quantity of carbon dioxide! scaled to the number of particles, that’s something around 10^40th (plus or minus a couple of powers of ten – at this scale, who cares?) additional molecules of carbon dioxide in the atmosphere. It’s a very small percentage, but it’s a huge quantity.
When you talk about trapping heat, you also have to remember that there’s scaling issues there, too. We’re not talking about adding 100 degrees to the earths temperature. It’s a massive increase in the quantity of energy in the atmosphere, but because the atmosphere is so large, it doesn’t look like much: just a couple of degrees. That can be very deceptive – 5 degrees celsius isn’t a huge temperature difference. But if you think of the quantity of extra energy that’s being absorbed by the atmosphere to produce that difference, it’s pretty damned huge. It doesn’t necessarily look like all that much when you see it stated at 2 degrees celsius – but if you think of it terms of the quantity of additional energy being trapped by the atmosphere, it’s very significant.
Calculating just how much energy a molecule of CO2 can absorb is a lot trickier than calculating the mass-change of the quantity of CO2 in the atmosphere. It’s a complicated phenomenon which involves a lot of different factors – how much infrared is absorbed by an atom, how quickly that energy gets distributed into the other molecules that it interacts with… I’m not going to go into detail on that. There’s a ton of places, like here, where you can look up a detailed explanation. But when you consider the scale issues, it should be clear that there’s a pretty damned massive increase in the capacity to absorb energy in a small percentage-wise increase in the quantity of CO2.
