Category Archives: Climate Change

What on Earth is Mathematics of Planet Earth?

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.

Chaos Theory

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 [1] 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.

Numerical Analysis

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.


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

Why bring maths into it?

To thrive on planet Earth, knowing what it’s going to throw at us is key. We need to know what crops can be grown where and what time of year to plant and harvest them. We need to know whether the mosquito that’s about to bite us is likely to be carrying malaria. We need to know how to manage flooding, and how much snow or wind our structures have to withstand.

So how do we know these things? Experience, first. The security that what will happen tomorrow will probably not be too much different from things that have happened before. But more and more, we are profiting from a delicate and precise understanding of the “why” and “how” of the system encoded in mathematical models to deduce more exactly what tomorrow will bring: how much light will shine on the solar panels or even when to shut the roof on Wimbledon to avoid the rain.

With climate change, the need for strong predictive structures become even more dire. Humanity is taking a complex, intricate system and dramatically altering a key component – greenhouse gases. We really are putting a cat amongst the pigeons, and, without doubt, things are going to change. The future is not going to be like the past: how it will change and how we can best avoid the worst–those are questions that require a mathematical and physical mastery of the system.

And of course, this is desperately important. While we in Britain might have enough resources and padding to quickly adapt to these changes, a lot of the people who share the earth with us are in a much more precarious position. Think of what famine does to a country with ethnic tensions, what water shortages in a country with a strong military imply for its neighbors and how a poor country deals with a new set of diseases traveling in with the weather.

Realizing the patterns, quantifying the interactions and building models is not a fix by itself. We still have the problem of wanting ever more growth and energy at as low a price as possible, of prioritizing today over generations from now.

But what we, as mathematical and physical thinkers, can contribute is a demystification: revealing the behavior of the complex Planet Earth so that as a society, a species, we can make the large ethical decisions facing us with more determination and confidence.

Mathematics, physical, geological, biological, ecological and chemical sciences don’t offer a pre-packaged answers: they’re ways of thinking to be drawn on depending on the question at hand. In this rest of this blog, we’ll be talking about some of the puzzles important in a responsible response to climate change and what tricks and elegant techniques from the mathematical world especially we can use. Expect calculus in the form of Partial Differential Equations used to describe a system changing over time, linear algebra to make those equations approximately solvable by a computer, dynamical systems thinking to try to simplify the complicated evolution and understand the butterfly effect and finally statistics and probability to express what we know and don’t know after all of that.