MLA 31500

Natural Sciences Elective

Order and Chaos in the Natural World

Spring Quarter 2008

CLASS NOTES

FIFTH CLASS

April 26, 2008

I. STEWART, CHAPTER 7: THE WEATHER FACTORY

1. On page 117, Stewart indicates that the prediction of weather with the aid of a computer involves a “double approximation.” What are the two approximations that are meant here?

2. According to the Guardian article reproduced on pages 119-120, the Meteorological Office was to investigate the failure of Cyber 10 to predict the hurricane of October 15, 1987, in southern England and to “find out what went wrong.” What, if anything, did go wrong?

3. According to the same article, Cyber 10 did predict violent storms in the North Sea on the day of the hurricane in southern England. In what sense can we interpret the contrast between the weather predicted and the weather observed as a manifestation of chaos?

4. What is thermal convection? What is the arrangement of a system in which one would demonstrate thermal convection in a laboratory? What are the conditions under which convection would occur? What are the physical processes that govern the conditions under which convection occurs? Which of the physical processes inhibit convection and which drive convection? Under what conditions is convection chaotic?

5. On pages 122-126, Stewart describes Lorenz’s investigation of thermal convection. Is this description complete? What has been left out?

6. What is the butterfly effect? How does it differ from the prevailing expectations at the time of the discovery?

7. On pages 133 & 134, Stewart argues that the Lorenz attractor is similar to strange attractors described in Chapter 6. In what respects are these attractors similar?

II. LORENZ, CHAPTER 3: OUR CHAOTIC WEATHER

1. What was the basis for the belief that it would be possible to forecast the weather?

2. In what respects might the process of forecasting the weather be similar to predicting the motions of planets? Or similar to predicting ocean tides?

3. What is the distinction between dynamic meteorology and synoptic meteorology?

4. Why is it difficult to make use of direct observations of the weather in order to show that the terrestrial atmosphere is a chaotic system?

5. What is the role of laboratory experiments in meteorology? What are the implications of typical experimental results for our understanding of the terrestrial atmosphere?

6. How do dynamical meteorologists represent the behavior of weather with the aid of a computer?

7. Why does it improve a model of weather to solve the “filtered equations,” which are approximate, in place of the “primitive equations,” which are more nearly exact? What spurious effect is suppressed by using the filtered equations? (See page 118 in Stewart.)

8. Lorenz explains that, more recently, dynamical meteorologists have solved the primitive equations in their models, but they have suppressed unwanted spurious effects with the aid of “initialization.” This means that they adjust the initial conditions of the model so that the model starts from a state that is “on the attractor.” What does that really mean, and why is this the right approach?

9. By the end of Chapter 7 in Stewart and Chapter 3 in Lorenz, we understand that meteorologists now recognize that they cannot predict the weather reliably beyond several days. On the other hand, they talk about global warming, etc., as if they believe that climate models can be reliable in their long time predictions. Are these consistent propositions?

LINKS:

Return to Course Page: mla315spring2008.htm

Return to Peter Vandervoort's Home Page: pov.html

Go to the home page of the Department of Astronomy and Astrophysics

of the University of Chicago: http://astro.uchicago.edu/