2005 September 22 | Random Fate

I end many of my posts with the sentence, “Do the math.”

I write this phrase for many reasons. It recalls what I have read in several science textbooks, where “the solution is left as an exercise for the reader,” (a huge pain in the ass to do 99% of the time, and pointlessly trivial the remaining 1%), but in the same way as the old books did it also calls upon those who actually finish reading some of my longer posts to consider further the points I have raised.

There is some real math that needs to be done, in this case to show those who reveal their profound ignorance of science when they say, “What does it matter if the temperature goes up 2 degrees? I wouldn’t even notice that!”

Oh, really?

Let’s do the math, in the case of a hurricane, an “on the napkin” calculation over dinner, as it were.

Before I get started, though, I want to be well understood: I am NOT saying that global warming caused Katrina (or Rita). Hurricanes have occurred on this planet for millenia at least.

My aim is to make clear one simple thing to those who dismiss immediately what is said by people who know what they are talking about: you should do the math first before you reject out of hand claims of ANY type, scientific or other. If you are not an expert, through exactly what arrogance do YOU think you know better than those who study a problem for most of their adult lives?

First, let’s see how much energy is added to seawater if the temperature of the seawater goes up two degrees Fahrenheit (roughly one degree Celsius).

The specific heat capacity of water is 1 calorie per gram of water for each degree Celsius of temperature increase. The “calorie” here is actually only 1/1000 that of the calories you read about on food labels, which are actually kilocalories. In metric units, the specific heat capacity of water is 4.186 Joules per gram for each degree Celsius.

The density of seawater is roughly 1,020 kilograms per cubic meter, so let’s make the math easy and assume that energy that feeds a hurricane is taken only from the top meter of seawater (in other words, to a depth of roughly three feet).

So, each cubic meter of water has roughly 1000 calories of energy added for each degree Celsius of increased temperature (using the calories you read on food labels; it has roughly 500 calories per degree Fahrenheit of temperature increase).

For comparison, a healthy adult man uses roughly 2000 calories a day.

Pretty small numbers, huh? So, all this worry about a two degree Fahrenheit temperature increase is nothing but hype, right?

We haven’t finished doing the math yet.

Suppose you have a hurricane the size of Dennis (in 1999), which has been estimated to have covered an area of approximately 122,852 square miles.

The volume of water (to one meter of depth) beneath that storm was 3.18E11 cubic meters (E11 means “times 10 raised to the 11th power, or times 100,000,000,000″… count the number of zeros).

So, the total amount of energy increase in that volume of water for a one degree Celsius temperature increase (or two degree Fahrenheit increase) is 3.24E17 calories, or 1.36E18 Joules (the metric measure of energy).

Whoa, all of a sudden the numbers got frigging big, didn’t they?

Now, suppose only 0.1% of that additional energy actually is absorbed by the storm.

That works out to be 3.24E14 calories, or 1.36E15 Joules of additional energy in the storm.

For comparison, the amounts of energy (in Joules) for:

The Hiroshima bomb - 1E14

Energy used in the US in one year - 2.7E20

Electricity for an average US home for one year - 1E10

100 megaton fusion bomb - 1E17

Fission of 1 ton of uranium - 1E17

Energy in the average hurricane - 1E15

Look at that last number carefully, the energy of the average hurricane is 1E15 Joules (ten times as much as the total energy released, including the radiation, heat, and light, along with the blast wave that flattened the city, of the Hiroshima bomb). A two degree Fahrenheit increase in water temperature could DOUBLE the energy of a weak hurricane even if only 0.1% of the additional energy available is absorbed by the tempest.

All of a sudden, that two degree increase ain’t looking so inconsequential any more, is it?

What else might you have missed in immediately saying something is inconsequential because on the face of it the change appeared to negligible?

Think about it. In other words, do the math.

Again, I am NOT saying that the recent spate of powerful hurricanes was caused by “global warming” or any other specific, attributable origin.

What I AM saying is that immediately dismissing things because at first glance it appears trivial is NOT wise.

Systems that change in large ways with only small variations in the initial conditions are referred to as “chaotic” in Physics. The “butterfly effect” is used as a crude way of describing this characteristic, where the flaps of the wings of a butterfly in China can result in a hurricane in the Atlantic.

Sounds far fetched?

Why do you think they did multiple course corrections on the trips to the moon? It wasn’t because they were unable to see their destination, which was hugely obvious in their windows.

It was because small errors early in the voyage could create large offsets at the end of the journey.

Just as a seemingly small, two degree Fahrenheit temperature increase in seawater could result in a doubling of energy available for a hurricane.

What other apparently minute shifts could have large effects?

Do the math.

Always do the math.

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