Mathematics and Meteorology

Mathematical modelling in Finance and Meteorology

Mathematics, being the "language of science" is being used increasingly to model the most diverse phenomena. In this project, we'll look at a small sample of these applications.

Geometric Brownian Motion
Mathematical finance is one of the most recent in a long list of successes of mathematical modelling. In the most prominent model used today to describe the random behaviour of stock prices, it is assumed the stock price acts in a certain sense like a particle being constantly bombarded with other very small particles.

In this project we'll discuss the assumptions behind the model, its precise mathematical statement, some of the counter-intuitive mathematical properties, the approximation by simpler mathematical structures, try to find out why it works, and conduct computer simulations to get a feel of what it says. The model will also be tested against real world data.

Numerical Weather Prediction
Weather forecasting is not a new science (or art), it has a long history because of the importance of weather in human activity. How is it possible to predict the futuristic behaviour of the atmosphere, despite the existence of sayings such as “as unpredictable as the weather”? It turns out that even the atmosphere must obey the laws of nature. More precisely, the conservation laws of energy, mass and momentum must be obeyed. The mathematical expression of these laws results in a complex set of partial differential equations. The exact solution of these equations is not known, but it can be approximated using numerical techniques. Today powerful supercomputers are used to find these approximated solutions (and thereby the future state of the atmosphere). This is known as numerical weather prediction.

The aim of this part of the project is to establish our own weather forecasting office. We will study and use a sophisticated numerical weather prediction model in combination with satellite pictures and radar images. Our final goal will be to timely predict the occurrence of a severe storm, and then to chase and observe it using a mobile automatic weather station.
 

Participants