Lecture: July 19, Monday, 10-12;

Exercises within and after the lecture

Prof. Dr. Gerrit Lohmann, University of Bremen & AWI


This course is part of the introductory course on “mathematical modeling for climate and environment” at the University of Bayreuth, held and organized by Prof. Dr. Vadym Aizinger. The course introduces the main physical concepts and mathematical descriptions underlying modern climate and environmental models. The fundamental concepts of the climate system are explored. Exercises complement the lesson.




pdf will be available here


Learning outcome

Dynamics of the ocean and atmosphere:
  • Applications in the fields of climate dynamics and fluid mechanics,
  • Theoretical concepts in physics of climate
  • Temporal and spatial scales of climate dynamics

    Energy balance and sea ice model:
  • key approximations
  • Effects of albedo

    Earth System Models:
  • Examples of Resolution (global spectral model)
  • Ocean circulation models and boundary conditions
  • Coupling between model components
  • Carbon, Radiocarbon, Tracers in the Sea
  • Climate sensitivity, Paleoclimate dynamics
  • Vegetation & Ecosystem models, e.g. Daisyworld Model



  • Exercises



  • Holton, J.R., Introduction to Dynamical Meteorology, Academic Press
  • Gill, A., Atmosphere-Ocean Dynamics, Academic Press
  • Dutton, J.A., The Ceaseless Wind, Dover
  • Olbers, D.J., Ocean Dynamics, Springer
  • Cushman-Roisin, B. & Beckers, J.-M., Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects
  • Marchal, J., Plumb, R. A., 2008. Atmosphere, Ocean and Climate Dynamics: An Introductory Text. Academic Press, 344 pp; videos pdf
  • Stewart, R. H., 2008: Introduction To Physical Oceanography, online Version:  http://oceanworld.tamu.edu/home/course_book.htm
  • Stocker, T. F., 2011. Introduction to Climate Modelling. Springer. SBN 978-3-642-00773-6
  • Saltzman, B., Dynamical Paleoclimatology - A generalized theory of global climate change, Academic Press, San Diego, 2002, 354 pp.
  • Goose, H., Climate system dynamics and modelling, Cambridge University Press, Cambridge, 2015, 358 pp.
  • Pruscha, H., 2013: Statistical Analysis of Climate Series Analyzing, Plotting, Modeling, and Predicting with R, VIII, 176 p. (link)
  • Kämpf, J., 2009: Ocean Modelling for Beginners Using Open-Source Software. Springer. (link)
  • Kaper, H.G., Engler, H., 2013: Mathematics and Climate. SIAM. Includes bibliographical references and index. ISBN 978-1-611972-60-3
  • Hantel, M., 2013: Einführung Theoretische Meteorologie. ISBN 978-3-8274-3055-7 DOI 10.1007/978-3-8274-3056-4 Springer, Heidelberg.
  • Lohmann, G., 2020: Climate Dynamics: Concepts, Scaling and Multiple Equilibria. Lecture Notes 2020, Bremen, Germany. (pdf of the script)
  • Gershenfeld, N. The nature of mathematical modeling, Cambridge University Press, Cambridge, 2003, 344 pp. 
  • Chirila, D., and G. Lohmann, 2015: Introduction to Modern Fortran for Earth System Sciences. 2015, XXII, 250 pages. 15 illus., 10 illus. in color. ISBN: 978-3-642-37008-3; Springer, Berlin Heidelberg. link, link to source code, link to source
  • Press, W. H., S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, “Numerical Recipes: The Art of Scientific Computing, 3rd Edition” Cambridge University Press, 2007, 1235 pp. http://www.nr.com/
  • R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. An Introduction to R
  • Paul Torfs, P., and & Claudia Brauer, C., 2014: A (very) short introduction to R