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The Butterfly Effect

The Butterfly Effect is a term commonly used to describe the chaotic and non-linear nature of the atmosphere, where it is said that a butterfly may flap its wings in a Brazil and cause a tornado in Texas.

This paradigm describes how small differences in the initialisation of weather forecasts can lead to forecasts with very different predictions, this is due to the chaotic, non-linear nature of atmospheric dynamics.

The term "Butterfly Effect" has been attributed to the numerical work of Edward Lorenz (1963) (right (c) wikipedia), owing in part to the patterns produced by the numerical model.

However the concept of sensitivity to initial conditions was known much earlier. It was alluded to in the seminal work published by Bjerknes (1904) (left, (c) wikipedia), which stated that two necessary and sufficient conditions required to make a rational forecast (which remain true to this day):

1. to know with sufficient accuracy the state of the atmosphere at a given time.

2. to know with sufficient accuracy the laws according to which one state of the atmosphere

develops from another.

The former relates to the notion that forecasts are sensitive to their initialisation. This idea can be traced to the work of Henri Poincaré (right, (c) wikipedia), the page shown is page 68 taken from Poincaré's Science and Method published in 1914, and specifically relates sensitivity of initial conditions to meteorology. He states when discussing meteorology: "it may happen that small differences in the initial conditions produce very great ones in the final phenomena" (excerpt shown below).

Although the numerical work of Edward Lorenz brought much attention to the chaotic nature of the atmosphere the earlier work of Bjerkness and Poincaré must not be forgotten.



 Henri Poincaré (c) Wikipedia

References

Lorenz, E. N., 1963: Deterministic Non-periodic Flow. Journal of the Atmospheric Sciences, 20, 130–147

Bjerknes, V., 1904: Das Problem der Wettervorhersage, betrachtet vom Standpunkte der Mechanik und der Physik (The problem of weather prediction, considered from the view-points of mechanics and physics). Meteorol. Z., 21, 1–7, (translated and edited by Volkene E. and S. Bronnimann, 2009: Meteorol. Z., 18 663 - 667).