Goal: 400 words researched and written in half and hour. For me, for practice. Corrections welcome in the comments.

Why does the weather forecast only go a few days into the future, and why are they so often wrong about what will happen in a couple of days time? If they know where the weather systems – clouds and so on – are right now, and they have a good computer model for how things change over time, why can’t they predict the weather a fortnight from now, or a year?

The answer is that weather is a chaotic system. In everyday language, chaos means complete disorder without pattern but in mathematics the same word chaos refers to a particular phenomenon. Chaos theory studies the behaviour of systems that are very sensitive to small changes in initial conditions. This means slight differences in the starting point of a system can give very different results in the long term.

Because the system gives very different results when you run it twice with similar starting conditions, you might think that it involves some random elements that change each time you run the process. However, this mathematical chaos does not involve random elements. If you run the process twice with exactly the same starting conditions, it will give the same results. This is not like a random process – each time you run it you get a different outcome. We call such a process, in which running the system in the same way gives the same results every time, deterministic, because if we know everything about it we can determine in advance what will happen.

What makes chaotic systems interesting is that they are deterministic but so sensitive to initial conditions that they aren’t predictable. A slight difference in the initial conditions can give massively different outcomes.

For the weather forecast, the computer model is fed by initial data from weather monitoring stations. If some of that data is slightly off, or if the computer model doesn’t correctly guess what is happening between stations, the model can give radically different answers to what will actually happen. These differences mount up – if you got tomorrow’s weather forecast slightly wrong and used it as the initial conditions to forecast the next day, then that could be very wrong indeed.

This is why weather forecasts are continually updated and why forecasts are only made reliably for a short period in the future.

Time: 39 minutes. 388 words. Performance: took too long. I started without a clear idea and started writing as I was researching. At 25 minutes I gave up on one idea and started anew. Bad practice! I should try to remember to take some time to process before I start writing.

Explanation. More 400 words.