# Applied mathematics and the modelling of uncertainties are the key to understanding climate change

Technological development has gotten to the point where practically an infinite amount of data can be collected on global phenomena. Connecting the data to reliable mathematical models enables solving a number of problems – also those related to climate change. LUT University recently received an addition to its highly skilled team of mathematical modelling experts.

"High school mathematics can be compared to a 100 metre sprint, whereas university mathematics is more like a marathon," describes **Tapio Helin**, LUT University's new Associate Professor of Applied Mathematics. Helin is passionate about mathematics and characterises it in colourful terms.

"Most people don't consider mathematics a creative field, but I most certainly do. Mathematics also involves much more collaboration between people than many may realise."

In fact, it is in collaboration with researchers from other fields and with representatives of the business world that LUT has crafted its expertise in computational science and applied mathematics over the past decades. "I've only worked at LUT for a few months, but I can already see that other research groups tend to challenge us computation people – in a positive sense. In other than technical universities, mathematicians are more of an isolated group," Helin relates.

LUT's other new mathematician, Associate Professor **Lassi Roininen**, confirms his colleagues observations.

"The cross-linking of disciplines and the depth of corporate collaboration at LUT are inspiring starting points for my own work. Even though my research is mostly connected to large infrastructures, such as large-scale radar systems in the Earth's upper atmosphere, the connection to the corporate world is still quite explicit," Roininen explains.

## **Inverse problems help to model uncertainties**

Heikki Haario has long been at the helm of inverse problems research at LUT. Haario's group has been part of a Centre of Excellence of the Academy of Finland over several programme seasons. Helin and Roininen have also worked on inverse problems throughout their careers.

What are inverse problems and what do they help us solve? The matter is not easy to explain in simple terms, but the two experts do their best to help the layperson understand.

"Inverse problems are a field of mathematics that goes against the typical everyday cause-and-effect chain of events. The methods of this field are able to model uncertainties and thus improve reliability in many areas of application. The modelling of uncertainties enables, for instance, medical imaging or understanding phenomena in the upper atmosphere – and nearly anything in between," says Helin.

"Tomography is a familiar word to many and a common inverse problem type. X-ray tomography aims to create a 3D image of a person by taking regular 2D x-rays from different directions," Helin continues.

All measurements include noise that distorts the results. In inverse problems, simple methods cause the noise to play a dominant role, making such approaches unusable for solving the problem at hand. Tailored numerical algorithms are needed for the development of reliable solutions despite errors in data.

LUT has come up with the unique idea of combining research in applied mathematics, statistics and machine learning.

Lassi Roininen, Associate Professor

"Finnish expertise in inverse problems is world-leading, and LUT's special strength lies in the modelling of uncertainties. This field is somewhere between mathematics and statistics and can also take advantage of machine learning. This combination at LUT is unique, and it's exciting to be involved in it," says Roininen.

## **Climate modelling high and low**

Combating climate change and securing clean air are key questions that humanity needs to solve. Climate modelling plays a significant role in tackling these issues. Forecasting climate change revolves around the modelling of uncertainties in extremely complicated systems. Also Roininen and Helin contribute to the development of new solutions that are based on mathematical methods, both at their own altitudes.

Roininen has figuratively soared 80–1000 kilometres above the Earth's surface for most of his academic career, as he has studied large-scale radar systems in the upper atmosphere. He has examined the structure of the upper atmosphere and the sun's effect on it, and how these effects reflect on the lower parts of the atmosphere.

In contrast, Helin has stayed closer to the ground – no higher than 20 kilometres above it. A large part of his research relates to optical telescopes that examine the atmosphere from the ground. "The vibration of the atmosphere greatly weakens the accuracy of large optical telescopes. The next generation of telescopes will aim to counteract the effects of the vibration in real time. We are developing related efficient algorithms with inverse mathematics," outlines Helin.

The two experts in advanced mathematical modelling say that even they are not aware of all of the ways in which their field of methodological science could improve the condition of the climate.

"A great deal remains to be uncovered about climate change especially if you view the matter from the perspective of upper atmospheric research. That's also what makes this work so interesting: finding new research avenues," concludes Roininen.

### Contact:

Tapio Helin, Associate Professor (tenure track), firstname.lastname@lut.fi, @**HelinTapio**

Lassi Roininen, Associate Professor (tenure track), firstname.lastname@lut.fi, @**LassiRoininen**

### Read more:

Uncertainty Quantification and Inverse problems - research group's site