The Misleading Math of Climate Activism (Updated)

Two big — and misleading — stories about the climate "crisis" came out this week. In one, CNN said:

The world's oceans are now heating at the same rate as if five Hiroshima atomic bombs were dropped into the water every second, scientists have said. @CNN

In another, the Independent in the UK came out with:

”The amount of heat being added to the oceans is equivalent to every person on the planet running 100 microwave ovens all day and all night.” @GretaThunberg

That was tweeted by St. Greta of Thunberg, so we know it's got to be right.

As I've written before, there's science and then there's press-release science. "Press-release science" is when someone writes a press release that isn't necessarily scientifically wrong but which is phrased to advance an agenda.

Both of these stories are press-release science.

Climate activism is especially prone to press-release science that sounds terrifying but turns out to be pretty trivial on examination, even if true.

So, let's examine. And yes, there will be math, or at least arithmetic. (If you don't want to walk through the arithmetic with me, jump to "The Moral of This Story" below.)

One of the ways you can tell when you're getting a press-release science story is when something is stated in exciting but unclear units. Here, we've got "five Hiroshima bombs a second."

Sounds exciting, but what does it even mean?

The "Little Boy" bomb dropped on Hiroshima had a yield of about 15 kilotons (kt), or by definition, the energy of exploding 15,000 metric tons of TNT. (Move the decimal point and that's 15 million kilograms or (multiply by 2.2) 33 million pounds.) But hell, even one pound of TNT is still an impressive explosion, so that's still not very informative. So let's go to real units.

"Five Hiroshima bombs a second" sounds like a really big number. But then the ocean is really, really big. I'm going to resort to scientific notation here: "valueexponent"  So 1 billion, 1,000,000,000, is 1e9. [Update: Strictly that's the computer-text version but typing "1 × 109" in HTML this many times would end me.]

According to Wikipedia, the total volume of the world's oceans is 1.335 billion cubic kilometers, 1.335e9.

There are 1 trillion liters, 1e12 liters, in 1 cubic kilometer, so there are 1.335e21 liters. (That's 1.335 sextillion.)

A "Hiroshima bomb" would be the Little Boy bomb, with a yield of about 15 kilotons, a kiloton by definition is 4.184e9 Joules, and a Joule is the amount of energy you need to raise the temperature of 1 kilogram of water (which is 1 liter) by 1°C.

So "Five Hiroshima bombs a second" is 15  5 4.184e9 Joules; a year is 60 seconds  60 minutes  24  365 days, or 31,536,000 seconds; and thus 5 Hiroshima bombs a second over a year is 9.896e18 Joules per year. In the immortal words of Leeloo, "big bada boom."

Finally, to get Joules per liter, we just divide.

Which gives us 0.007143 Joules per liter. A temperature increase of 0.007143°C. Or 0.01286°F

Look, this number is so unbelievable that I've redone the calculation about five times. But even if the numerical values are incorrect (and honestly, it's not like someone used a measuring cup to check the volume of the oceans) the orders of magnitude are correct: 1e18/1e21 = 1e-3, 0.001; we're in the neighborhood of 1/1000.

Update

Okay, the math went a little astray, so I went back when wide awake and redid it. Formatting this nicely is beyond our WordPress so here's an image. This time I made a Google Sheet, so you can look at the original as well.

Computing change in temperature of the oceans by 5 Hiroshima bombs a second

There were several errors, mostly counteracting, as I wound my way through a maze of little units, all mostly alike, but the upshot is I was off on the average temperature change by an order of magnitude.

Too high.

The revised — and I hope better — estimate is 0.0003543°C per year. Times 100 years per century and that's roughly 0.04°C per century.

The Moral of This Story

Now that we've looked at the arithmetic (twice) we see that "Five Hiroshima Bombs A Second" actually turns into "raising the temperature of the ocean less than 1°C  0.1°C a century," ignoring all the other feedbacks that will be involved — like the "enthalpy of fusion" involved in melting the ice caps. It turns this from an "OMG OMG OMG story" into yet another story about global warming making a nearly unmeasurable change. And what fun is that? The story is true but unsurprising. The headline is not meant to inform, it's meant to excite. Or incite.

What we've got here is press-release science at its "best": a really scary-sounding number that turns out to reflect a tiny actual outcome. We've seen it before, with misleading visualizations and NASA tweets based on misleading cartoons. Most reporters aren't what you'd call "numerate" and when they see the phrase "scientists say" they just copy what the scientists say into their story unquestioningly.

The moral is: trust but verify. A science story in the press is often a nothing result gussied up to make a headline.