Mathematical modeling in weather and climate research
Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.
Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.
This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.
The course will cover a selection from the following topics
1. Conservation laws and governing equations,
2. Numerical methods for geophysical flow simulations,
3. Dynamical systems and bifurcation theory,
4. Data-based characterization of atmospheric flows
Reading material will be provided depending on the choice of topics
for the semester.
Good starting points for items 1. through 4. are,
Hans Kaper and Hans Engler,
Mathematics and Climate, Society for Industrial and Applied Mathematics (SIAM) (2013)
Numerical Methods for Fluid Dynamics with Applications to Geophysics,
Springer, Computational Science and Engineering Series, (2010)
Metzner Ph., Putzig L., Horenko I.,
Analysis of persistent nonstationary time series and applications
Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)