| Véronique Fuller | Novembre 2019 |

Prof. Colin Cotter, professeur de Mathématiques à Imperial College, explique comment l’analyse numérique permet de prédire le temps et mesurer les évolutions du climat, et évoque l’impact des progrès récents en intelligence artificielle dans ce domaine.

How do Mathematics help measure climate change? Are AI and deep learning improving weather predictions? Will it be sunny on Sunday? Will flights be delayed at Heathrow tomorrow? How much energy will wind farms be able to produce this week? Will Cornwall become the New Rivera?

Behind all these questions hides exciting Mathematics.

Prof. Colin Cotter, Mathematics Professor at Imperial College, works on weather and climate predictions, i.e. on mathematical approximations of the motion of the atmosphere and ocean, and their implementation as algorithms within models to predict weather and climate under different greenhouse gas scenarios to inform the Intergovernmental Panel on Climate Change. Weather forecasts, developed by operational centres like the Met Office and Météo France, have impacts on many parts of industry and society: governments (e.g. flood/storm response), businesses (stock control), insurers, the energy sector (to predict energy production from wind/solar and domestic/industrial energy consumption), as well as the general public.

Climate is indeed different from weather: as defined in the dictionary, climate is “the composite or generally prevailing weather conditions of a region, as temperature, air pressure, humidity, precipitation, sunshine, cloudiness, and winds, throughout the year, averaged over a series of years.“

“Creative” springs to Prof. Cotter’s mind to characterise his numerical analysis field, as knowledge of how supercomputers work needs to be combined with Mathematics.

Principles of Calculus (which students will know as integration and differentiation) are involved but these equations are very hard to solve. “Thanks to work by Euler, Gauss, Laplace, Liouville, fundamental laws of motion for parcels of fluid in the atmosphere can be described in the language of calculus. Yet, as a computer can only compute a finite number of values of temperature/velocity/pressure/density/moisture at a finite number of points in time, these equations need to be approximated to be solved.

Numerical weather prediction is the pioneer in combining large datasets with computer models to produce verifiable forecasts, a process called « data assimilation » insists Prof. Cotter. The Met Office model has grid points that are as much as 16km apart, i.e. where the temperature/velocity/pressure/etc. are represented. Certain processes, including clouds, tropical convection, air flow close to mountains or urban canopies are too small to be captured by the grid. Machine learning could help to improve the parameterisations of these unresolved processes, yet, Prof. Cotter believes “the best progress will be made by combining physics-based and data-driven approaches. Maybe we should give our field a name related to AI to receive more attention”, he jokes.

Sensing and physical measuring have improved the quality of input data.

“In the atmosphere and ocean, satellite observations have revolutionised our forecasting skills and understanding of circulation patterns. More recently, automated floating devices with GPS transmitters in the ocean have also led to huge improvements in forecasting and physical understanding.”

In recent decades, forecasts have become faster and more accurate thanks to the increase in capacity and speed of new generation Supercomputers, “models are put on the line with predictions every few hours. Today’s 6 day forecast is as accurate as the 5 day forecast ten years ago” says Prof. Cotter.

Recently, the Met Office chose to adopt Prof. Cotter’s mathematical approximations (known as compatible finite element methods) for the dynamical core (the part of the model that predicts winds, pressures, temperatures) of their next generation weather and climate model. Developed as part of a consortium between the Met Office, the STFC laboratory and the Natural Environment Research Council, the model is being designed for new supercomputers which achieve high processing speed through performing computations across hundreds of thousands of chips at the same time.

Beyond technology, this achievement is due to “fantastic international and interdisciplinary collaboration between meteorologists, engineers, computer scientists, mathematicians and statisticians”. Through the World Meteorological Organisation, under the umbrella of the United Nations, international agreements allow sharing of observational data from satellites or weather stations as inputs to the model forecast, as well as forecast comparisons.

#### Which advice would you give to a student who would be interested in studying (applied) maths?

“Be curious about all areas of mathematics, and stay persistent because understanding mathematics takes time – don’t give up because it seems complicated to start with. Make sure that you speak to mathematical researchers about the creative aspects of their work which are often under-emphasised in school and even in undergraduate studies. Especially make sure that you hear from researchers who are not male, or who identify as LGBT+ or are from diverse ethnic backgrounds, who will have great additional perspectives to learn from.”

Mathematical approximations and computational science techniques are developed across the whole of science, including applications in finance. Modelling of the motion of fluids has strong links to other disciplines: vehicle and aircraft aerodynamics, chemical engineering, physiological flows, hydrology, oil and gas exploration, carbon sequestration, etc., and a lot of people move into weather modelling from these fields (although there are some special aspects such as the rotation of the Earth, and the thinness of the atmosphere relative to the Earth’s surface area).

Propos recueillis par Véronique Fuller

Prof. Collin Cotter

After a Bachelor degree in Mathematics in Cambridge and a PhD on wave-vortex interaction in atmosphere and ocean flows in the Department of Mathematics at Imperial College, Prof. Collin Cotter stayed at Imperial College, first in the Earth Science and Engineering, then Aeronautics and finally returning to the Mathematics Department where he is now a Professor. Prof. Cotter is the co-author of a textbook on data assimilation, and a co-Director for an EPSRC doctoral training programme on Mathematics of Planet Earth.