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Modeling Acts of God, Part 1


Hurricane structure. Click to enlarge.   

This post is the first in a series of the state of modeling very powerful, nasty natural phenomena such as hurricanes, earthquakes, and tsunami.

Depending on where you live you may have trouble acquiring or affording insurance protection form these so-called "acts of God. " Whatever these AOG’s might be, they are often home- and life-threatening. Can these AOG’s be modeled successfully, i.e. how well are they understood and can their generation, properties, and behavior be predicted with any accuracy?

Along with the understanding and prediction provided by standard models for these event, it is natural to wonder how global warming contributes to these phenomena. Do models for these AOG’s compensate for GW’s effect? This is a very pressing question. Anecdotally, many claim that the events are both more frequent and more severe, with natural tendency to assign blame to global warming.

Consider hurricanes. Hurricanes are pretty well "understood" in terms of how they start and move. Proto-hurricanes start as small tropical vortices , which themselves originate because of rotational effects of the earth on atmospheric gases. Kerry Emanuel, Professor of atmospheric sciences at MIT explains this in Hurricanes: Tempests in a Greenhouse:

In the part of the tropics where the sea surface is warm enough and the projection of Earth's angular velocity vector onto the local vertical axis is large enough, random small-scale convective currents sometimes organize into rotating vortices known as tropical cyclones. In computer models of the tropical atmosphere, such organization can happen spontaneously, but usually only if a combination of ocean temperature and rotation is somewhat higher than those observed in nature. In subcritical conditions, some trigger is necessary to initiate the vortices, and in the terrestrial atmosphere tropical cyclones only develop from preexisting disturbances of independent origin. In mathematical parlance, tropical cyclones may be said to result from a subcritical bifurcation of the radiative convective equilibrium state. About 10% of them develop in the Atlantic Ocean, where the disturbance is often a 100-km-scale "easterly wave" that forms over sub-Saharan Africa and then moves westward out over the Atlantic. When its maximum wind speed exceeds 32 m/s, it, by definition, becomes a hurricane.

Note the description of random small-scale convective currents organizing spontaneously. This description reminds me of the descriptions of the Great Red Spot of Jupiter - which is a classic case of order arising out of chaos, and which is featured in Gleick’s Chaos: Making a New Science

In addition to how hurricanes start, Emmanuel describes how hurricanes can be modeled thermodynamically using the idea of the Carnot cycle, i.e. a heat engine. (Click here for a nice Carnot Cycle applet).

The mature hurricane is an almost perfect example of a Carnot heat engine whose working fluid may be taken as a mixture of dry air, water vapor, and suspended condensed water, all in thermodynamic equilibrium. The engine is powered by the heat flow that is possible because the tropical ocean and atmosphere are not in thermal equilibrium. This disequilibrium arises because, thanks to the greenhouse effect, the ocean must lose heat by direct, non-radiative transfer to the atmosphere to balance the absorption of solar radiation and back radiation from the atmosphere and clouds. The heat transfer is accomplished mostly by evaporation of water, which has a large heat of vaporization. To maintain substantial evaporation rates, the air a short distance above the sea surface must be much drier than would be the case were it in equilibrium with the sea.

Modeling hurricanes as Carnot cycles is not a far extrapolation from Sadi Carnot ’s own views about the general atmosphere, and what drives it:

We must attribute to heat the great movements that we observe all about us on the Earth. Heat is the cause of currents in the atmosphere, of the rising motion of clouds, of the falling of rain and of other atmospheric phenomena ...


Carnot hurricane cycle. Click to enlarge.

The heat engine model for hurricanes is an excellent example of a model that has been extrapolated well beyond its original intent. While the Carnot model works very well for a very special system, in this case heat engines, it is quite amazing that it’s features and predictive power can be transferred to a totally different system - in this case a hurricane. This model transferability is an indication that Carnot’s model is more than robust - it is capturing a very real property of the universe. In this case it is the primacy of the 1st and 2nd Laws of Thermodynamics.

Any thermodynamic model must take entropy into account. The intensely rapid swirling of air near a hurricane’s eye, with trees, houses, and vehicles sucked off of the earth’s surface is the poster-child of the massive disorder that marks a literal entropic explosion:

In equilibrium, the planet must generate entropy, and the vast majority of that entropy is produced in the atmosphere, mainly through the mixing of the moist air inside clouds with the dry air outside them and through frictional dissipation by falling raindrops and snowflakes. Were it not for moisture in the atmosphere, the entropy would have to be produced by frictional dissipation of the kinetic energy of wind. The resulting air motion would be too violent to permit air travel.

Because the idea of entropy production at equilibrium may seem counter-intuitive, I recommend reading The Second Law of Thermodynamics and the Global Climate System: A Review of the Maximum Entropy Production Principle. This 2003 Geophysics Review by Ozawa, Ohmura, Lorenz, and Pujol does an excellent job of explaining the reasons and causes of entropy production. This paper also displays the excellent success of modeling the atmosphere in the Carnot fashion.

Now back to hurricanes. Emmanuel does indicate that the Carnot cycle model applied to hurricanes yields a pretty accurate prediction for maximum wind speed that depends on ocean and atmospheric temperatures. But what about global warming? How does it play a role? As described above, the greenhouse effect leads to a more pronounced thermal disequilibrium between the tropical oceans and atmosphere. The more the greenhouse effect, the higher the surface temperatures, and the greater the disequilibrium, with the net result that more entropy is produced. The hurricane vortices serve as big entropy channels, and thus these must grow more intense to handle the larger load. So there you have it - more global warming leads to more entropy which leads to bigger, nastier hurricanes.

So where are we? With a basic understanding of hurricanes as provided by a Carnot model, and the prediction of maximum wind speed, it would seem that not much more needs to be done.

Not so fast - can scientists predict WHERE and WHEN hurricanes will spontaneously generate? Or how severe they will be, and how fast they will move? Hurricane models are still frustratingly inexact, relying on many assumptions as well as statistical measurements. But the state of prediction is much better than it was in the past.

See the Feb. 2007 NOAA article on Predicting Hurricanes: Times Have Changed for much more on hurricane modeling and prediction.