Literature/1972/Lorenz


 * http://eapsweb.mit.edu/research/Lorenz/Butterfly_1972.pdf

Description

 * American Association for the Advancement of Science, 139th Meeting
 * Subject : "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?"
 * Author : Edward N. Lorenz, Sc.D. Professor of Meteorology
 * Address : Massachusetts Institute of Technology Cambridge, Mass. 02139
 * Time : 10:10 a.m., December 29, 1972
 * Place : Sheraton Park Hotel, Wilmington Room
 * Program : AAAS Section on Environmental Sciences New Approaches to Global Weather: GARP (The Global Atmospheric Research Program)
 * Convention Address : Sheraton Park Hotel

Excerpts
Regardless of what any theoretical study may imply, conclusive proof that good day-to-day forecasts can be made at a range of two weeks or more would be afforded by any valid demonstration that any particular forecasting scheme generally yields good results at that range. To the best of our knowledge, no such demonstration has ever been offered. Of course, even pure guesses will be correct a certain percentage of the time.

Returning now the the question as originally posed, we notice some additional points not yet considered. First of all, the influence of a single butterfly is not only a fine detail -- it is confined to a small volume. Some of the numerical methods which seem to be well adapted for examining the intensification of errors care not suitable for studying the dispersion of errors from restricted to unrestricted regions. One hypothesis, unconfirmed, is that the influence of a butterfly's wings will spread in turbulent air, but on in calm air.

A second point is that Brazil and Texas lie in opposite hemispheres. The dynamical properties of the tropical atmosphere differ considerably from those of the atmosphere in temperate and polar latitudes. It is almost as if the tropical atmosphere were a different fluid. It seems entirely possible that an error might be able to spread many thousands of miles within the temperate latitudes of either hemisphere, while yet being unable to cross the equator.

We must therefore leave our original question unanswered for a few more years, even while affirming our faith in the instability of the atmosphere. Meanwhile, today's errors in weather forecasting cannot be blamed entirely nor even primarily upon the finer structure of weather patterns. They arise mainly from our failure to observe even the coarser structure with near completeness, our somewhat incomplete knowledge of the governing physical principles, and the inevitable approximations which must be introduced in formulating these principles as procedures which the human brain or the computer can carry out. These shortcomings cannot be entirely eliminated, but they can be greatly reduced by an expanded observing systems and intensive research. It is to the ultimate purpose of making not exact forecasts but the best forecasts which the atmosphere is willing to have us make that the Global Atmospheric Research Program is dedicated.

Wikimedia

 * Lorenz attractor

Chronology

 * Strogatz, Steven H. (1994). Nonlinear Systems and Chaos. Perseus publishing.
 * Frøyland, J. & K. H. Alfsen (1984). "Lyapunov-exponent Spectra for the Lorenz Model". Phys. Rev. A 29 (5): 2928-2931.
 * Grassberger, P. & I. Procaccia (1983). "Measuring the Strangeness of Strange Attractors". Physica D 9 (1-2): 189-208.
 * Knobloch, Edgar (1981). "Chaos in the Segmented Disc Dynamo". Physics Letters A 82 (9): 439-440.
 * Lorenz, Edward Norton (1976). "Nondeterministic Theories of Climate Change." Quaternary Research. Vol.6
 * Haken, H. (1975). "Analogy between Higher Instabilities in Fluids and Lasers." Physics Letters A 53 (1): 77-78.
 * Edward N. Lorenz (1969). "Atmospheric Predictability as Revealed by Naturally Occurring Analogues." Journal of the Atmospheric Sciences 26: 636-646.
 * Edward Norton Lorenz Publications
 * http://eapsweb.mit.edu/research/Lorenz/publications.htm
 * Edward Norton Lorenz Publications
 * http://eapsweb.mit.edu/research/Lorenz/publications.htm