Climate science / Mathematics of Planet Earth

Can earthworms save the planet?

What is a climate scientist doing in the Ecology Department? Yes, they serve decent coffee but it is not the only reason why I visit this place. I actually work there too. One of the supervisors of my project has nothing to do with climate or weather. How can my work be relevant for the Mathematics of Planet Earth research?

Surprisingly, it is. Sometimes similar research methods work for scientists in various areas, e.g. geophysicists, sociologists or ecologists. This is because in principle their job is the same, no matter which topic is their area of expertise. First, they observe some phenomenon such as a rainfall, an epidemic or a life cycle of E. coli. If it arouses their interest, they want to describe this process. First step would be to collect observations. But in order to be able to do something useful with them, they cannot avoid mathematics.

Mathematicians like to use numbers and symbols instead of words; we want to depict the world in equations. From school you might remember equations describing some phenomena: E = mc2 probably rings a bell. Did you ever wonder how Albert Einstein1 came up with such an equation? This is our everyday problem. We try to develop a system of equations relying on our experience and observations but how can we be sure that our idea was right?

This is the case in the model I am currently working on. It describes the energy budget of earthworms, i.e. what they do with the food (energy) available. We observe how quickly the food is eaten, how its energy content influences the worm population size, what their reproduction rate is, etc.2 The problem is that the model contains 14 parameters, i.e. the constants we cannot measure exactly but need to estimate. In this case parameters would measure things such as worms’ mass at birth or the speed of their movement. However, sometimes we just cannot find their real value – or even if we could, the measurements would not be accurate enough. So what can we do?

Let us assume that I have some parameter k in my equation and that I take a guess such as k=100. Then I transfer my model into a computer program, run it and get some results. Meanwhile ecologists get the data from the worms playing in the laboratory so that we can compare the output of the model with the true experimental values. And they say: “You are a terrible mathematician, your result is completely wrong!” (although they tend to be nicer). But I do not give up and try k=10. Ecologists say: “A bit closer but still not close enough!” And we play like that many, many times, to find out which model would fit the reality most.

However, the nature is not so simple. Thus we usually need many parameters: not only k but the whole alphabet! And we can change all of them. I am actually quite lucky having to deal with “only” 14 parameters. Climate models include hundreds, even thousands such values!

A big number of parameters means that the computers must work very, very hard. It can even take a couple of years to run a complicated climate model! Not exactly ideal… So I am trying to develop a more efficient method of evaluating the parameters. In practice a quite simple algorithm allows me to reject values of parameters that make no sense according to previous computations. Thanks to that we need much less time (and money!) to establish the right model. And models are crucial for any science – they can predict the future!

As you can see, sometimes it does not really matter to which area of science we apply our mathematical skills. Essentially, maths stays the same. If we develop some good methods to help study worms, after smaller or bigger modifications we can use this approach to other problems. Worm model had been waiting for me so I took up the challenge. However, I have not forgotten about why I am here, that my main goal is to improve weather forecasts and tackle climate change.

Trust me, I will worm my way in using my methods in climate science!

Image from: http://www.uclan.ac.uk/research/explore/groups/earthworm_research_group.php.

2A little bit more about this model can be found here: http://www.sciencedirect.com/science/article/pii/S0304380015002173.

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