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The Lorenz Weather Model


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The Lorenz Weather Model

  1. 1. The Lorenz Weather Model<br />Abhranil Das<br />
  2. 2. One Question<br />Sunrise on 20 Sep 2031: 5:25 AM [1]<br />Weather on 20 Sep 2011:<br />?<br />[1] :<br />
  3. 3. Edward Norton Lorenz<br />Born in Connecticut<br />Studied Mathematics at Dartmouth and Harvard<br />Served as a forecaster in the US Army Air Corps from 1942-46<br />Returned to study meteorology at MIT, published good orthodox papers<br />
  4. 4. “The machine, a Royal McBee, […] broke down every week or so. It had neither the speed nor the memory to manage a realistic simulation of the earth’s atmosphere and oceans. Yet Lorenz created a toy weather in 1960… Every minute the machine marked the passing of a day by printing a row of numbers across a page… Digitized cyclones spun slowly around an idealized globe.”<br />- Chaos, James Gleick<br />
  5. 5. So, weather problem solved.<br />
  6. 6. Or not.<br />“One day in the winter of 1961, wanting to examine one sequence at greater length, Lorenz took a shortcut. Instead of starting the whole run over, he started midway through. To give the machine its initial conditions, he typed the numbers straight from the earlier printout.<br />“Then he walked down the hall to get away from the noise and drink a cup of coffee. When he returned an hour later, he saw something unexpected, something that planted a seed for a new science.”<br />
  7. 7.
  8. 8. But Nobody Cared<br />
  9. 9. The Logistic Equationa biological population growth model<br />𝑥𝑖+1=𝑟𝑥𝑖(1−𝑥𝑖)<br /> <br />
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  11. 11.
  12. 12. Sensitive dependence on initial conditions<br />(between 3.57 and 4)<br />.011<br />.0101<br />.01001<br />
  13. 13. .010001<br />.0100001<br />.01000001<br />
  14. 14. What will I study?<br />Simulate the Lorenz weather model (attractor) exhaustively, tweaking all parameters till I have a clear understanding.<br />Study and compare its Butterfly Effect against the variation of different parameters<br />Study the restoration to similarity following a period of complete deviation<br />Study how good it is as a model of the earth’s weather system<br />Latch on to anything else that interests me<br />
  15. 15. Like this one:<br />
  16. 16. References<br />Deterministic Nonperiodic Flow<br />Edward Lorenz, Journal of the Atmospheric Sciences, 1963<br />Chaos: the making of a new science<br />James Gleick<br />