Wednesday, March 14, 2007

Physics, Economics, Hurricanes and Mistakes

It recently occurred to me that one small part of the global warming discussion on this blog was interesting because it hinged on an error that I ought to have spotted twice, once as a physicist and once as an economist. In fact, someone else pointed it out.

The context was a discussion of whether global warming increased the frequency of hurricanes. Mike Huben pointed to an argument by a friend of his: that hurricanes were more common at times when sea water temperatures were higher. This was offered as evidence that global warming would increase hurricane frequency, in response to opinions by hurricane experts that there was so far no reason to think it did.

Consider first the physics. A hurricane is a heat engine; it converts thermal energy into work in the form of swirling winds. In principle one could use windmills to turn the hurricane into, say, electrical power, although I doubt it is a practical project. A heat engine that simply turns heat into work is a perpetual motion machine of the second kind, impossible because it violates the second law of thermodynamics. Actual heat engines take heat from a hot source, convert some of it into work, and dump some of it into a colder sink. They run not off the absolute temperature of the source but off the temperature difference between source and sink.

The ocean is a thermal buffer. Because its heat capacity is large it averages out atmospheric temperature changes; that's why San Jose, where I live, has a milder climate than Davis, where my sister lives. Seasons when the ocean is unusually warm are also times when the temperature difference between sea and air is unusually high, which fits the observation that they are when hurricanes are likely to be generated.

Global warming, however, as the second commenter pointed out, affects both air and sea. There is no reason to expect it to change the difference between air and sea temperature, so the evidence that warm seasons generate hurricanes is irrelevant to the question of whether global warming would.

Next consider the economics, where the argument is less rigorous but still suggestive. One of the most famous mistakes in mid-twentieth century economics was the Phillips Curve. A. W. Phillips observed, correctly, that higher rates of inflation historically correlated with lower rates of unemployment. Economists concluded that there existed a tradeoff, that if a country was willing to accept a somewhat higher rate of inflation it could get a somewhat lower rate of unemployment.

The actual relationship was not between inflation and unemployment but between unanticipated inflation and unemployment. For reasons I sketch in one chapter of my price theory text, when inflation is higher than expected unemployment is lower as a result. On average, high inflation correlates with higher than expected inflation, hence Phillips' statistical result. But if a country adopts a constant inflation rate of, say, 5%, pretty soon everyone anticipates a 5% inflation rate and unemployment goes back up to its long run level. Eventually, after observing the theoretical argument confirmed in the form of "stagflation," economists recognized the mistake; it is now generally agreed that the long run Phillips Curve is vertical, that anticipated inflation does not reduce unemployment.

The logic of the economic mistake and of the hurricane argument is identical. An effect that depends on a variable being higher or lower than its usual value is misidentified as an effect of its being absolutely high or low.

Incidentally, readers interested in the dispute over how large the costs of global warming are likely to be may want to take a look at the comments on the Blog "Backseat Driving," where I have been arguing with people. The argument started with a post quoting this blog and responding and went on to an interesting post about the ways in which our views are affected by our political bias. Brian, whose blog it is, seems like a nice fellow, somewhat more reasonable than his allies in the comment section, but none of them, so far, is willing to seriously consider the possibility that he might be wrong.


Brian said...

I'm never wrong!! Okay, so maybe I'm wrong in my predictions of political contests and the plot twists in Harry Potter books, but other than that...

Maybe next week I'll post a more substantive comment.

Anonymous said...

Climate of Fear by Richard Lindzen

If the models are correct, global warming reduces the temperature differences between the poles and the equator. When you have less difference in temperature, you have less excitation of extratropical storms, not more. And, in fact, model runs support this conclusion. Alarmists have drawn some support for increased claims of tropical storminess from a casual claim by Sir John Houghton of the U.N.'s Intergovernmental Panel on Climate Change (IPCC) that a warmer world would have more evaporation, with latent heat providing more energy for disturbances. The problem with this is that the ability of evaporation to drive tropical storms relies not only on temperature but humidity as well, and calls for drier, less humid air. Claims for starkly higher temperatures are based upon there being more humidity, not less--hardly a case for more storminess with global warming.

Brian said...

I don't think it's a productive use of your physics knowledge to attempt to reinvent, independently, hurricane climatology in a single blog post. I suggest you go instead to the WMO consensus statement on hurricanes prominently discussed on the Prometheus blog for now, and then look at the IPCC impacts analysis when it comes out. The issue is whether the Maximum Potential Intensity can change as a result of increased sea surface temp.

Anonymous said...

I'm not physicist or anything, but your argument seems to be based on the assumption that the % change in temp if the same for sea water and air. But is this true?

montestruc said...

David, I think you are missing a major point in your physics argument.

The heat engine of a hurricane is driven by a source and a sink, the source is indeed water vapor forming from hot water at the surface of the earth, however the sink is deep space where the water vapor gives up heat via radiation to space. So

1 -- The temperature of deep space is constant so a rise in temperature does indeed raise the ratio of source to sink temperature.

2 -- Higher fractions of greenhouse gasses in the atmosphere tend to make water vapor rise to a higher level before releasing heat to space due to the heat retention effects on radiation of greenhouse gasses. This second effect will tend to make storms more likely and stronger. The power of the storm is related to the difference in altitude from evaporation to condensation. IMHO but the physics seems obvious to me.

Anonymous said...

As a professional physicist, I would not like to comment on global warming. It is a an absolutely specialized discussion with huge amount of measurements, numerical models, and … political forces. Is not worth much time for professional physicists in different area (no strong arguments under hand) and for general public (to much political influence and manipulation).
There is an asymmetry between economist in physics and physicist in economics, however, arising from the difference between approaches in hard and soft sciences. Problems related to the discussion of inflation and unemployment can be described in some vague wording, like you can always hear from a macroeconomist, and some quantitative description with measurable, testable, verifiable, and falsifiable relationships between the studied parameters. I propose to check if I right with my quantitative model of inflation


With R**2 between 0.95 and 0.75, respectively, as described in my papers:

I would appreciate if somebody find a mistake in the relationships and related theory.