Until recently I had no problem explaining what I was studying; I was just an average maths student. I could reliably predict the reaction of a person informed of this fact: “How can you do that? I’ve always been hopeless at maths. And anyway, what are you going to end up doing with that degree”? Things got much more complicated when I started a PhD at Mathematics of Planet Earth. The first reaction is now usually the question used as a title to this article: what on earth is mathematics of planet earth?! After a brief explanation that I am learning how to use and develop maths for climate and weather predictions, I just get a reassuring statement: “I know that this whole climate change thing is very dangerous/rubbish” (choose the option that applies to you) and a question: “But why did you resign from doing proper maths?”
Actually, I am more involved in studying mathematics than ever. No science would exist without mathematics, in particular climatology or meteorology. Some people can predict the rain by feeling it in their bones; I can “predict” the rain more or less based on the fact that we are in UK. But do we really want to risk our life on someone’s body niggles? No, I do not exaggerate. Our life really can depend on it. Do not forget that a bad weather prediction not only can get you wet, but also farmers might not prepare for a drought (and the crops would get extremely expensive next year), local authorities might not decide to grit ice-covered roads (so you might get stuck in traffic or even have an accident) or a dangerous storm might hit citizens completely not ready for it. It is something worth looking at, is it not?
To get more reliable predictions about the state of atmosphere in the next couple of hours, days or even centuries, we need… mathematics. No, not that boring multiplication table, but nearly every field of very advanced mathematics. Let us take a look at a couple of examples.
You will have heard of the “butterfly effect” which allegedly can provoke a hurricane. This is all about the chaos. The intuitive definition, given by E. Lorenz, the creator of chaos theory, is  when the present determines the future, but the approximate present does not approximately determine the future. It means that if we were given infinitely precise initial conditions (i.e. full description of the state of the weather now), we could predict the weather at any time in the future. So why do meteorologists sometimes get it wrong? Because this is just wishful thinking. In reality we are not able to get perfect measures of the weather components, for example due to the limitations of measuring devices. Thus mathematicians need to choose the most important measurements with the available precision and try to get the best prediction they can. However, chaos theory states that, under some conditions, starting from almost the same state we can get completely different results. It complicates weather prediction so chaos theory is still something we need to study.
There would be no weather forecast without very advanced computers we are using. Some of them are even supercomputers, such as the one used by Met Office. It costed a trifling £97 million. Why do governments invest such enormous sums into such equipment? Before we understand that, we have to see how the weather prediction works. As mentioned above, we cannot forecast it exactly. Hence mathematicians have to get rid of some parameters that seem to be less important (by the way, deciding which are those is far from obvious) and, using the ones that are left, build a model. This is a set of equations (sometimes thousands of them!) that describe the system. Do you remember solving systems of two equations at school? You might have struggled with it. So now imagine solving thousands of much more complicated ones. Yes, this is exactly why we need supercomputers; they make this job feasible. However, mathematicians still need to make sure that the result produced by a computer is sensible. They do it by carrying out a numerical analysis, checking the properties of the system.
I’ve mentioned only a tiny fraction of the whole range of mathematical tools used in the weather prediction. Next time when you listen to your favourite weather forecast, keep in mind that it would not make any sense without mathematics. And if you happen to have a child, encourage them to study maths. Just in case.
 Danforth, Christopher M. (April 2013). “Chaos in an Atmosphere Hanging on a Wall”. Mathematics of Planet Earth 2013. Retrieved 27 January 2016.