The only thing we can be sure of about the future is that it will be absolutely fantastic. So if what I say now seems to you to be very reasonable, then I have failed completely. Only if what I tell you appears absolutely unbelievable, have we any chance of visualizing the future as it really will happen.

- Arthur C. Clarke (h/t Brin)

Wednesday, November 18, 2009

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.

20 comments:

The Cunctator said...

From MT's post, world's daily oil production produces CO2 that traps enough heat to melt 55,000 square miles of ice of a depth of a meter = 142 km^3.

Admittedly, these are kind of silly calculations, but...

http://www.ipcc.ch/ipccreports/tar/wg1/412.htm#tab113
Total ice volume in the world's glaciers is 80,000 km^3.

That's 56 days.

Total ice volume on the planet - 28.56 * 10^6 km^3.

That's 550 years, so that's good. If we weren't fiddling with the earth's albedo and melting the permafrost, I'd be less concerned about Greenland and Antarctica.

(Again, I recognize this is a silly way of going about it.)

Michael Tobis said...

Not silly at all. That is pretty much what we thought about the ice sheets about 15 years ago.

It turns out it's wrong, though. That's not how ice sheets fail.

They fail mechanically. As they warm, they crack and slip, and eventually fall into the ocean. The good news (sort of) is that this cools the ocean a bit. The bad news is that the ocean gets a little bit bigger...

There's paleclimate evidence at 14Ka of a big chunk of Antarctica falling off in the space of a century or so.

The West Antarctic looks poised to fall into the ocean first. The main part of Antarctica looks safe.

King of the Road said...

I tried hard to resist, but failed. A ton for Enco in 1962 would surely have been a short ton, or about 907 kilograms. Clearly it doesn't defeat your point.

Also, it's a bit of a shame you used Wikipedia for your latent heat source, you have found something which WolframAlpha could actually have supplied, a feat of which I'm rarely capable.

King of the Road said...

Sigh. I feel bad about this nitpicking but an American football field is 120 yards by 160 feet. See here (by the way, WoframAlpha gives the useless answer of "100 yards" when queried about this). This actually does make a difference to your calculations, though not an order of magnitude.

Michael Tobis said...

Thanks and aargh.

Michael Tobis said...

Corrected. Fortunately the error does not cascade.

I appreciate people checking up on this. Part of the point of this sort of exercise is getting people to play along.

Anyway my fallibility is part of my charm...

skanky said...

" could melt an area of meter-thick ice covering a mid-sized state."

To use UK standard measurements, that's about 14 times the area of Wales (880 square miles), to the depth of a double decker bus (4.38m).

rustneversleeps said...

Nice bit.

One minor nit, which also does not "cascade". Following your calculations to paragraph 5, I get one barrel of oil "melts" ~ 18 tons of ice, not 3 tons? I.e. 7*10^6 / 3.9*10^5 ? Did I miss a step?

Hank Roberts said...

Now here's an optimistic take.
Maybe the iceberg will melt before we hit it ...
http://www.seattlepi.com/dayart/20091118/cartoon20091118.jpg

Michael Tobis said...

Rust, not sure what you are saying. The 7e6 is Humble's 1962 number, not a physical constant.

Nosmo said...

Hank,
Looks like a rock not an iceburg.

Michael Tobis said...
This comment has been removed by the author.
rpauli said...

Where is the modern photograph of the same scene?

Michael Tobis said...

What a strange question!

rpauli said...

Oh, I dunno. I could envisage an article written, say 5 years from now... on the subject of denialism that might describe what message Enco was going for...even back then. A modern picture next to this - is or will be showing a scene greatly diminished.

http://www.theboywhodeniedwolf.com/2009/04/google-timeline-reveals-triumph-of-denialism.html

http://news.google.com/newspapers?id=xQAOAAAAIBAJ&sjid=_HsDAAAAIBAJ&pg=7244,4365891&dq=global+warming

Pelto said...

I will disagree with your interpretation of what we knew about ice sheets 15 years ago. Twenty five years ago I spent a lot of time modelling ice sheets and it was the calving losses and changes in bed conditions that were the key. We have know this is the weakness and the problem of the WAIS for sometime just as an example look at the history of the idea of the Pine Island Glacier as a weak underbelly, Realclimate review a term I knew 25 years ago.

WAG said...

My great-grandfather worked for Humble Oil in the Texas Panhandle...

Steve Bloom said...

Sure, Mauri, but look at the AR4. Jim Hansen wasn't calling Richard Alley and others reticent for nothing. Speaking of Richard, he continues to push back on this stuff, e.g. at the Oregon PAGES conference when he mischaracterized as a prediction Jim's remark about multi-meter SLR being more likely than the AR4 number. As Richard continues to be seen as the most prominent voice among U.S. glaciologists, it seems to me that he needs to get some squawks when he does stuff like that. Otherwise the entire field will be seen as in agreement.

Michael Tobis said...

Thanks to Dr Pelto for reading and commenting.

I would point out that this is another instance of the difference between "what is known" in the three major senses: 1) what somebody knows 2) what the field accepts and 3) what the public believes. (Many additional finer variants can easily be constructed, but these are the main classes.)

I was aware of the theory that the WAIS might collapse early in my student career around 1994. I would not go so far as to say I believed it, deferring to the common wisdom within the climatological field (as opposed to the glaciological subfield).

Even AR4 was unwilling to take a position on how ice sheets behave under warming, though by then I had some exposure to glaciology which turned out vastly more interesting than I had suspected, as many things do. So my expertise climbed a little and the acceptance of the idea spread a little, so now I take it as "known".

It's a very interesting question in the face of new developments in "agnotology": the science of cultivation of popular ignorance. The gap between class 2 and class 3 of "what is known" has drastically widened.

Pelto said...

Thank you for the good post, and the prompting to go back and read AR$ again. If you read the details of AR4 on glaciers and ice sheets it reads pretty well. However, there are some odd statements.."Until recently (including IPCC,2001), it was assumed that velocities of these outlet glaciers and ice streams cannot change rapidly, and impacts of climate change were estimated primarily as changes in snowfall and surface melting. Recent observations show that outlet glacier and ice stream speeds can change rapidly, for reasons that are still under investigation. Consequently, this assessment will not adequately quantify such effects."
Attending a meeting on Fast Glacier flow in 1986 the focus was on this topic how fast changes in the flow in some of the ice streams had occurred. Working on Pine Island Glacier and Jakobshavn at the time with T.Hughes of U Maine, we were trying to model how to apply the Jakobshavn model to other glaciers. The problem was accurate data on the thickness and bottom profile of the glaciers. The community did realize that some ice streams had turned on and off so to speak. So here we are 20 years later and I read an assumption that was viewed as not true in the mid-1980's. ice streams do respond fast, that was why we were studying them, we were trying to learn how, since there was more than one mechanism. Alley was there as a doctoral, focussed. on the speed of Antarctic Ice Stream B- now Whillans Ice Stream- Whillans was there too. The other odd statement is .."Enhanced flow in ice streams arises either from higher gravitational stress linked to thicker ice in bedrock troughs, or from increased basal lubrication." Since it is has been well documented that it is the thinning in the lower reaches of the calving tidewater glaciers resulting in reduced frictional stresses that leads to the acceleration. The gravitational stresses are not as important. This again was a point that has been recognized for some time. However, was lost by some, which led to the over emphasis of the silly notion that moulins were the key to GIS acceleration.
RC article
We have all been surprised not that this can happen, but that it is on so many ice stream and glaciers. I know that when I selected some of the glaciers I did to work in, I expected them to disappear, just not so fast. Milk Lake Glacier Thanks