## What on Earth is Mathematics of Planet Earth?

Until recently I had no troubles to explain what I was studying; I was just an average Maths student. I could predict the reaction of a person informed about this fact: “How can you do that? I’ve always been hopeless at Maths. And I think teaching is boring.” Things got much more complicated since I have started PhD studies at Mathematics of Planet Earth (just to clarify: not all mathematicians end up teaching in schools!). First reaction is usually the question used as a title to this article. After a brief explanation that I am learning how to use Maths in climate and weather predictions, I just get a reassuring statement: “I know that this whole climate change thing is very dangerous/rubbish”. And a question: “So why did you resign from doing Maths”?

Actually, I am more involved in studying Mathematics than anytime before. No Science would exist without Mathematics, in particular Climatology or Meteorology. Some people can predict the rain by feeling it in their bones. Well, I can “predict” the rain more or less based on the fact that we are in UK. But do we really want to base our life on someone’s shooting pains in their bones? No, I do not exaggerate. Our life really can depend on it. Do not forget that a bad weather prediction not only will get you wet, but also farmers will not prepare for the drought (hence the crops will get extremely expensive next year), local authorities will not decide to grit ice-covered roads (so you will get stuck in traffic or even have an accident) or a dangerous storm will hit citizens completely not ready for it. The game is worth a candle, is it not?

To get more reliable predictions about the state of atmosphere in the next couple of hours, days or even centuries (the latter is a big simplification which I do not have a space to explain it), 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.

• Chaos Theory

You will have heard of a 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 as follows: When the present determines the future, but the approximate present does not approximately determine the future.[1] 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, eg. due to flawed 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 in development.

• Numerical Analysis

There would be no weather forecast without very advanced computers we are using. Some of them are even called supercomputers, such as the one used by Met Office. It costed a trifling 97 million£[2]. 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, i.e. checking properties of the system.

I 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 him to study Maths. Just in case.

[1]Danforth, Christopher M. (April 2013). “Chaos in an Atmosphere Hanging on a Wall”. Mathematics of Planet Earth 2013. Retrieved 27 January 2016.

[2]Met Office (October 2014). “£97m supercomputer makes UK world-leader in weather and climate science“. Retrived 27 January 2016.

## One comment for “What on Earth is Mathematics of Planet Earth?”

1. Vijay K Vijayaratnam says:

Looks like you are trying to apply most of the latest mathematical theories like Fractals chaos Theory,complexity science,stochastic dynamical process,wavelets and so on.Best wishes to you whatever your research is.