# Is weather a chaotic system?

#### Yoni

Many people consider the weather as a system which exhibits chaotic behaviors ('the butterfly effect' introduces weather as an example for chaos). But what are the reasons for that? Why are we so sure that weather is chaotic? Is it because people can't manage to predict it a long time in advance, or is there a deeper explanation for this?

As I understand a chaotic systems is a systems which exhibits dynamics that are highly sensitive to initial conditions. Which means that the ratio between initial uncertainty and the uncertainty after a period of time is very small (which also gives a possible measurable quantity for chaos, or rather the inverse of chaos). Does this definition seem valid?

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#### vanesch

Staff Emeritus
Gold Member
Many people consider the weather as a system which exhibits chaotic behaviors ('the butterfly effect' introduces weather as an example for chaos). But what are the reasons for that? Why are we so sure that weather is chaotic? Is it because people can't manage to predict it a long time in advance, or is there a deeper explanation for this?
One of the "typical chaotic systems", the Lorenz attractor was in fact a hugely simplified model of atmospheric dynamics:
http://en.wikipedia.org/wiki/Lorenz_attractor

That doesn't prove of course that the true dynamics of the atmosphere are so, but chances are big that it is.

As I understand a chaotic systems is a systems which exhibits dynamics that are highly sensitive to initial conditions. Which means that the ratio between initial uncertainty and the uncertainty after a period of time is very small (which also gives a possible measurable quantity for chaos, or rather the inverse of chaos). Does this definition seem valid?
Yes. This measure is precisely quantified by something that is called the Liapunov exponent(s): http://en.wikipedia.org/wiki/Lyapunov_exponent

#### Andy Resnick

The 'weather' (meaning the flow of various components to the air, heat flow, interactions with the oceans, land, and near-space, various phase transitions, etc. etc.) is certainly nonlinear.

Is the weather chaotic? I don't know- 'chaos' is a specifically defined term. Is the weather system even stable? Again, that's not clear either, especially given the current doomsday scenarios of 'runaway weather'.

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