Melting Ohio Daily

So this droll item, apparently unveiled by Jay Leno, is making the rounds, which makes it a perfect opportunity for an exercise with large numbers.

Let's start with what we can glean about Enco's production in 1962. We can then compare it with modern production of its more or less descendant corporation Exxon/Mobil.

Presumably the copywriter was trying to inflate the number in the first place, to make it more impressive. This would mean that all the ice was already at the freezing point, and all the energy was going to latent heat of fusion. The latent heat of fusion of water ice is 334 kJ/kg according to Wikipedia. Now a ton is a thousand kg, hence we are talking 334 MJ/ton, or for the 7 million tons, 334 x 7e6 MJ per day = 2.3 billion MJ. Now a barrel of oil contains about 6100 MJ, (confirmed here) so we are talking about production of 2.3e9/6.1e3 = 390 thousand barrels.

1962 world oil production was 23 million barrels per day. This is not that big a fraction for Humble/Enco, and perhaps refers only to energy sold in the US market.

And how much ice are we talking about? It's really hard to visualize "7 million tons". Let's use the standard metric of area, the American football field, (a bit under half the size of a typical professional soccer/euro-football field) which is 120 yards x 160 ft. I'll cheat and call yards meters, close enough for this kind of an exercise. OK, so we are covering the field in ice to a depth of hmm, 7,000,000/(120*(160/3)) = 1092 yards. (Update: Corrected; see comments.)

Or make it 1092 football fields to a depth of a yard. (Update: corrected too. My football fields were oversized. Shows how much attention I pay to football.)

Or, to make it easy, in 1962, Humble melted 3.5 km x 2 km or over two and a half square miles covered waist deep in solid ice. That was one company's modest contribution in 1962.

Consider, instead, total oil production today. That's 73 million barrels, or 220 times the number in the ad. If all that energy went into melting ice, it would melt 550 square miles to a depth of a meter daily, an area slightly larger than all the boroughs of New York City combined, or almost as large as London, or about twice the size of Toronto, or more than fifteen times the size of Paris.

But, of course, none of this takes into account the irony of the thing, which is that the side effect of the oil melts much more ice than the oil does itself. The exact multiplier is somewhat problematic, because carbon is forever. Some part of the CO2 you emit hangs around for millenia warming the earth. This can end up as a really scary quantity, a multiplier in the thousands. On the other hand, that heat is diluted, and what the distant future holds is hard to know. Let's stick to a planning horizon of a century, where the calculations are clearer.

I'll defer to Ray Pierrehumbert on this one. "by the time a hundred years have passed, the heat trapped each year from the CO2 emitted by using coal instead of solar energy to produce electricity is 125 times the effect of the fossil fuel waste heat." According to a neutral arbiter (a natural gas promotion site) oil has a 20% advantage over coal in carbon intensity. Which brings us neatly to a factor of 100.

So how much ice (assuming it were already at the freezing point) would that melt if it were all released at once? Well, the world's daily production of oil, with all the heat released at once, would melt 55,000 square miles of ice of a depth of a meter. This is larger than North Carolina or New York State, and a tiny bit smaller than Iowa, but I've fudged a few figures here and there so let's make it more like Ohio or Virginia to be on the safe side.

That is, the indirect warming associated with each day's production of petroleum could melt an area of meter-thick ice covering a mid-sized state.

A bit less than a tenth of this, or about the size of Connecticut, is directly attributable to Exxon/Mobil refineries. This is nearly 2000 times more than their proud claim of 1962 asserted.

Fortunately 1) not all the heat goes into melting ice 2) not all the ice is pre-warmed up to the melting point 3) the real ice sheets are thousands of times thicker than the one we imagined covering Ohio and 4) a lot of this warming is delayed decades into the future.

Unfortunately, we're not considering the coal, the natural gas, the direct methane releases, or the methane or CO2 feedbacks. What's more, the delay mentioned in point 4 above is going to come back to bite us later on. We are doing more damage than we perceive. Much more.

PS, Any Texans feeling smug should consider that a Texas sized portion of meter thick ice could be melted in a work week, leaving two more mid-sized states for the weekend. An area the size of the entire US could be thawed in less than three months by the contribution to anthropogenic warming over that same period.

PPS, Ken Caldeira as quoted by Joe Romm comes up with a factor of 100,000 rather than 100. In other words, a thousand times worse. My intuition is squawking about this multiplier being too high.