Lorenz attractor used in meteorology

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Ed Lorenz not only opened our eyes to the ever-present chaos in nature but also founded its governing principles. He changed 20th century meteorology with a discovery that would change our view of the world. It is ironic that chaos theory which is a landmark discovery in modern science was in fact developed in meteorology. Lorenz's discoveries in chaos are built on the foundations of numerical forecasting techniques, which in fact were formulated by great meteorologists trying to make sense of the unpredictability of weather.

Weather forecasting made very little use of advances in mathematics and physics until late into the 20th century. The old technique was to use past situations that resembled the current situation, and then assumed that the weather following will be similar to the weather in the past situation. The analogue method proved to be both simple and modestly successful, one reason for its continued use as a forecasting aid by meteorologists today. Despite its successes, the analogue method was frustrating. The weather is so diverse that it seems to never repeat. And even when meteorologists did find a decent match, the two scenarios evolved quite differently after a day or two.

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Edward Lorenz stumbled on chaotic behaviour accidently through his work in predicting the weather in 1961. Lorenz was using a simple digital computer to run his weather simulation, the desired outcome to this was to see a sequence of data. However due to time restrains he started his simulation at the middle of the previous simulation which he had the calculations for. Lorenz was confused that this time the computer produced a different result to what was previously calculated. He started looking back at the data and he noticed that a 6 decimal number was rounded up to a 3 decimal number. This small and almost insignificant change caused the big change in the results. This discovery which gave its name Lorenz attractors proved that meteorology could not predict the weather beyond a weekly period.

The matrix of the attractor appears as two disks wrapped together, their actual structure is far more complex. What appear to be disks in the Lorenz attractor turn out to be layers of disks. A geometric figure of this sort with an infinite level of detail is called a fractal.

The butterfly effect occurs because the weather depends on a number of different factors theses include temperature, humidity and air flow to name a few. These factors are to a certain degree interdependent. However the way the temperature changes depends on the humidity, but this depends on temperature. Consequently, equations relating these factors are nonlinear. This nonlinearity is what causes the sensitive dependence on initial conditions. The weather is a system that repeats itself, giving periods of dry weather and periods of wet, but it repeats itself in an unpredictable way.

        The weather predictions that are being forecasted today used dynamical-empirical approach. The state of the atmosphere is represented by a numerical values of the weather elements. Theses are then put into a system of equations which used Lorenz equations, to predict the weather.

References

  • Lorenz equation, http://planetmath.org/encyclopedia/LorenzEquation.html, date accessed 11/03/2010
  • Development of meteorology http://www.infoplease.com/ce6/weather/A0859595.html, date accessed 20/03/2010
  • Edward N Lorenz, (1969), Three Approaches to Atmospheric predictability,
  • http://eapsweb.mit.edu/research/Lorenz/Three_approaches_1969.pdf, date accessed 09/03/2010.
  • Lisa Alter, Meteorology, http://yale.edu/ynhti/curriculum/units/1994/5/94.05.01.x.html date accessed 09/03/2010
  • Bulletin of the American Meteorological Society, Vol. 50, No. 5, May 1969, pp. 345-351