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The Lorenz Weather Model
- 1. The Lorenz Weather Model Abhranil Das
- 2. One Question Sunrise on 20 Sep 2031: 5:25 AM [1] Weather on 20 Sep 2011: ? [1] : timeanddate.com
- 3. Edward Norton Lorenz Born in Connecticut Studied Mathematics at Dartmouth and Harvard Served as a forecaster in the US Army Air Corps from 1942-46 Returned to study meteorology at MIT, published good orthodox papers
- 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.” - Chaos, James Gleick
- 5. So, weather problem solved.
- 6. Or not. “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. “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.”
- 9. The Logistic Equationa biological population growth model 𝑥𝑖+1=𝑟𝑥𝑖(1−𝑥𝑖)
- 12. Sensitive dependence on initial conditions (between 3.57 and 4) .011 .0101 .01001
- 14. What will I study? Simulate the Lorenz weather model (attractor) exhaustively, tweaking all parameters till I have a clear understanding. Study and compare its Butterfly Effect against the variation of different parameters Study the restoration to similarity following a period of complete deviation Study how good it is as a model of the earth’s weather system Latch on to anything else that interests me
- 15. Like this one:
- 16. References Deterministic Nonperiodic Flow Edward Lorenz, Journal of the Atmospheric Sciences, 1963 Chaos: the making of a new science James Gleick