Weather prediction is part of every news service. Three, maybe four days ahead. And sometimes they're right! But what about a week ahead, or a month? Naturally, Chaos scientists have had a go at this one. They're conclusions are not going to be much use if you want to choose a fine day for your Church Fair in three months time! There are many variables associated with the weather: temperature, air pressure, wind speed, wind direction, humidity and many more. The equations which govern the weather involve all of these variables.

You can accurately put all these variables in an equation and calculate, with some degree of certainty the value of all the variables one second hence. These answers can be fed back in, and the values for the next second can be calculated. Leave the poor computer go for long enough to do the iterations and you will know the weather one month hence. Or will you?

Edward Lorenz tried this. The full story is given in the Lorenz Gets Lazy task, but basically, Lorenz decided to run the program for longer. To do so he entered the values for half way through the run and set the machine off again. BUT the results soon deviated from the previous run. Lorenz found the reason was that he had put the values in accurate to three decimal places. The computer had calculated to six places. So a difference of one in a thousand was enough to change the output significantly. We can't measure the variables accurately enough to avoid the effects of chaos.

One of the signatures of chaos is the sensitivity to initial conditions. In terms of weather, this means that if a butterfly flapping his wings in the forest of South America it can cause a hurricane in China. Lorenz coined the term The Butterfly Effect to describe this sensitivity to the state at the start of the process. For ten years, Lorenz's paper on this result was ignored, despite Lorenz being aware that this was a crucial discovery. When he plotted the three key variables in the differential equations in three dimensional space he gained a plot like that shown below.

The Lorenz Attractor This is now known as the Lorenz Attractor. Any single moment in time is represented by one point on the attractor. But differential equations can't merge, so Lorenz realised he had discovered a mathematical object which was in fact an infinitely complex set of surfaces, never intersecting. The trajectories of the weather variables follow the lines within the attractor, cycling around the lobes, with apparently random behaviour. This is a Strange Attractor having a non-integer dimension of about 2.06 On the attractor, mark one point to represent today. Mark another point close to the first point to represent another day of almost identical weather conditions. As the weather conditions progress from these two points they may: a. move together in one wing b. move together to the other wing or c. move apart, one into each wing. By examining the Attractor closely, it is possible to see that there are some conditions in which all the nearby points will follow similar paths and other areas where they diverge quickly. Imagining one wing to represent one weather pattern and the other to represent a very different pattern, this can lead to a reasonable degree of certainty in the future for some points and almost total unpredictability for others.

If you have Chaos: the Software, select Strange Attractors and you will be watching the Lorenz Attractor plot. To see it better, for our purposes, select Tweak and turn the Ribbon Erase off. This will ensure the paths stay on the screen. As you are watching the points plotting out the Lorenz Attractor, remember you are watching weather conditions change. Tweak the Flock Size to 1 and you will see the detail of this infinitely complex attractor emerge. To Zoom on this Strange Attractor, select Options and set the Cursor to Zoom. Examine its internal structure.

A Hypothetical Weather Pattern

The map labelled Start indicates the initial conditions from which a computer can then model what will happen to the weather. Five cases were taken, all very similar to the map labelled Start: westerlies over the west coast of Iteratia and the west coast of Mandeland. Note not only the wind direction but the closeness of the isobars. The closer these lines, the stronger the winds.

Computer modelling for the next week is performed for five slightly different variations of the Start weather pattern. These variations are within the uncertainties of the figures collected at weather stations.

2. Look at Iteratia. How does the wind direction and strength and possible temperature vary for Iteratia?

3. If you were a weather forecaster who was paid according to the accuracy of your forecasts, where would you rather work and what would you predict?

4. From what you know of world weather, can you suggest places which are on points in the attractor which stay with a fixed pattern? Can you suggest places whose points on the attractor are such that they lead to the possibility of such divergent paths the weather is much more difficult to predict? (Those from Melbourne, Australia, can now have some sympathy with the poor forecasters!)

A real example is given in Tim Palmer's Chapter  A Weather Eye on Unpredictability in The New Scientist Guide to Chaos, edited by Nina Hall and published by Penguin.

So is the climate difficult to predict, too? Not really. The climate can be imagined as the Attractor - only certain states are acceptable. Ice in the tropics, sweltering sands in Antarctica are not represented by points on the Attractor. So these weather positions will not occur, except if there is some catastrophic event.

 But the question for all environmentalists is: Is the Attractor slowly being changed? If it is, what is the long term effect on our weather, lifestyles and environment?