Foucault's Pendulum; small forces extended over space and time can have large effects.
Even if the Paris Agreement were implemented in full, with total compliance from all nations, it is estimated it would only produce a two-tenths of one degree — think of that, this much — Celsius reduction in global temperature by the year 2100. Tiny, tiny amount.
— Donald Trump [source]
Figures like “0.2 Degrees Celsius” convey a powerful false impression. Powerful, because you can easily imagine yourself walking out your front door and finding that the only change is that it’s 0.2C warmer — e.g. 71.53 F instead of 70 F. That particular effect would indeed be tiny.
But that’s not what scientists are saying will happen. What they’re saying is the entire globe will be 0.2 degrees warmer on average, and if you add up all the energy that represents, the sum is vast.
And it turns out it’s not that hard get a rough estimate. I’ll show you how.
Stretch out your right arm. If you’re a man, on average the length from your left shoulder to right finger tip is about a meter. If you’re a woman it’s a bit less. Now mentally mark off a cube of air in front of you 1 m on a side. How much energy do you think would it take to raise that cube of air by, say, 1 degree?
We’re in luck here, because engineers have figured this out: it takes almost exactly 1 joule of energy to raise 1 gram of dry air by 1 degree. So all we need to do is figure out what the air in that cube weighs, and here we’re in for our first big surprise:
One cubic meter of dry air weighs 1225 grams (2.7 pounds).
You probably had no idea air was so heavy, but this is why balloons can lift heavy objects with lifting gas that’s just a little bit lighter than the ambient air. This also means we need quite a bit of energy to raise that cube’s temperature by 1 degree:
It takes 1225 joules to raise the temperature of 1 cubic meter of air by 1 degree.
Joules aren’t familiar to most people, we’re much more familiar with watts which is the rate of energy use per time. So you can think of it this way: to raise the temperature of a cubic meter of air by 1 degree in 1 minute would take about 20 watts. To raise the temperature of a 10 foot by 20 foot room by 1 degree in 1 minute takes 924 watts, or 1.24 horsepower.
The point is that even though you can’t feel 1 degree of warming, it amounts to a significant amount of energy.
And we’re still talking about small volumes. The 0.2 degrees Trump is talking about applies to the entire lower layer of the atmosphere, called the troposphere. Just how big is that?
Well, the Earth is a sphere 6.3 million meters in radius, and the troposphere is about 11000 meters thick on average, so multiplying the surface area of the sphere (4*pi*r2) by 11000 we get:
The volume of the troposphere is about 6 x 10^18 cubic meters, and it weighs about eight million billion pounds (3.7 trillion metric tons).
So there’s a lot of air out there, and raising it by a degree will take an astonishing amount of energy. Multiplying 1225 joules/m3 by 6 * 10^18 m3 :
The lower bound of energy needed to raise the troposphere by 1 degrees is 7 * 10^18 joules.
Why “lower bound”? Remember how I used “dry air” above as my starting point? Humid air has a much higher specific heat. I also have left out interactions with the atmosphere and the ocean, which is huge: most of the excess energy captured by the atmosphere goes into the ocean. So overall what I just laid out is a gross underestimate of the amount of energy we are adding into the climate system. But we have at least a lower bound.
So the amount of energy Trump is talking about is 20% of that, or 1.4 x 10^18 joules. But it’s another number that’s so big it seems almost meaningless. What can we compare it to? Well, the bomb dropped on Hiroshima yielded 15 kt, or roughly 6.3×1013 joules. So working out the math:
A 0.2 C temperature increase globally corresponds to the energy that would be released by detonating over 20,000 Hiroshima-sized nuclear bombs.
And yet that doesn’t change the undeniable fact that you simply can’t feel 0.2 degrees of difference. It is an immensely significant change that when looked at on familiar scales seems insignificant.
That is why I illustrated this essay with an image of Foucault’s Pendulum. It’s a kind of clock that many of us have seen in museums, a heavy weight on a long wire that swings freely. As the weight swings back and forth the rotation of the Earth deflects the pendulum in its path a little bit so that the pendulum eventually makes its way around the entire perimeter of the circle beneath it. (If you’ve never seen one, you can see a video here)
The force that deflects the pendulum is called the Coriolis force, and it is very tiny. So tiny that no human has ever felt it. And yet, this same force can bend the winds of a hurricane and deflect its path, something that is utterly beyond any human agency. A tiny force reproduced on a global scale can be mighty.
Palm trees in southwest Britain.
Likewise the energy represented by 0.2 C spread across the entire globe is mighty. It can change man of the patterns of wind, rain and temperature we are familiar with. Some places that are warm might actually get cooler; many places will see both more heat in the summer and cold in the winter.
Did you know that palm trees grow in southwest Britain? Check the map and you’ll see that Cornwall is about the same latitude as Winnipeg. That shows how the the way the atmosphere distributes energy and matter is complicated.
It’s as if our local climate conditions are a hand of cards we’ve been dealt. Adding 10^18 joules into the atmosphere isn’t like changing the deck, it’s more like reshuffling it and dealing everyone a new hand. Even though the deck hasn’t changed much it will be a completely different game for the players.
