Physics of the Climate System

Learning Outcomes: Students know the basics of probability theory and the most important probability distribution functions. They are able to perform standard statistical analyses including hypothesis tests. The students are familiar with the basics of extreme value theory, time series analysis, and autoregressive processes.

Contents: Probability theory, probability density functions, parameter estimation, hypothesis testing, extreme value statistics, analysis of time series, stochastic processes.

Educational Concept: Lectures (2 SWS) including discussions, introduction to the statistical software R, practice in applications, problem solution in teams.

Course Lecturer: Christian Franzke 

Learning Outcomes: Students have a basic understanding of the meteorological and oceanographic processes relevant for the mean state and variability of the climate system. 

Contents: Description of oceanic and atmospheric mean state, and circulation. Ocean – atmosphere interaction. Radiation Balance. Global Energy Budget and Transports. Thermohaline Circulation. Climate Variability from Decadal to Paleoclimatic timescales. Observations and Modeling of the Climate System.

Educational Concept: Lectures (2 SWS) and exercises (2 SWS) 

Course Lecturers: J. Baehr, A. Düsterhus 

Learning Outcomes: Students are familiar with the fundamentals of numerical approaches used in geophysical and climate models. They know the underlying mathematical problem formulations, the principle of numerical discretization and understand the uncertainties of corresponding models. They know how to implement numerical methods in prototypical software.

Contents: Introduction to numerical methods and concepts of accuracy/ uncertainty evaluation, introduction to floating point numbers, condition and stability, solution of linear systems, interpolation and approximation, discretization of differential equations (finite differences), interpolation, linear approximation, numerical quadrature, trigonometric interpolation, programming introduction in MATLAB scripting.

Educational Concept: Lectures with practical parts (2 SWS) 

Course Lecturer: J. Behrens

Learning Outcomes: This course provides a hands-on introduction into the physics of sea ice and its interaction with the atmosphere and the ocean. The students will learn how sea-ice related processes are observed in situ and from satellite, and how these processes can be modeled numerically. They will gain experience in planning an observational campaign, analysing field and laboratory data, carrying out lab experiments, and presenting research findings. 

Contents: Overview of sea ice in the Earth System; the polar climate system; seaice dynamics and thermodynamics; snow on sea ice; techniques of in situ and remote sensing observations; modeling sea ice; analysing field and laboratory data.

Educational Concept: Lectures and tutorials (4 SWS)

 Course Lecturer: D. Notz

Learning Outcomes: Students have an overview of basic physical concepts and processes explaining the structure and dynamics of planetary atmospheres, as well as a deeper understanding of selected examples.

Contents: Important topics are: atmospheric environment, composition and structure; moist thermodynamics and the fluid parcel concept; circulation systems (waves, vortices and turbulence) in simple idealized atmospheres.

Educational Concept: Lectures including discussions (2 SWS); exercises and worked examples (1 SWS)

Course Lecturer: H. Borth

Learning Outcomes: Students have a thorough understanding of the theoretical basics of climate dynamics, and know the art and science of constructing conceptual models of the climate system.

Contents: Concepts and models are introduced that help us to understand fundamental aspects of the earth’s climate, such as global mean temperature, global-scale temperature differences, and what might cause these to vary on timescales of decades and longer. Particular emphasis will be placed on oceanic and coupled ocean atmosphere processes. While we cover observed elements of the climate system and a hierarchy of models ranging from the simplest models to general circulation models, the focus will be on the art and science of constructing simplified models that help us obtain conceptual understanding. Discussing what is not understood, and hence identifying areas of current and future research, will be a crucial element of the course.

Educational Concept: Lectures (2 SWS), homework assignments

Course Lecturer: J. Marotzke

Learning Outcomes: Students know the distinction between externally forced climate variability and internal climate variability at time scales of centuries and longer.

Contents: A brief overview of climate variations and climate change since the beginning of Earth some 4.6 billion years ago is given. Climate reconstructions from paleo records are physically interpreted by using conceptual and comprehensive climate system models. Precambrian: the snowball earth. Phanerozoic: effects of long- term plate tectonics and development of the biosphere. Mesozoic and early Cenozoic: greenhouse climate and Tertiary cooling. Quaternary: Ice ages, Milankovich cycles. Pleistocene: sub- Milankovich cycles. Holocene: interglacial climate, little ice age. Anthropocene: external greenhouse gas emissions, land-cover

Educational Concept: Lectures (2 SWS)

Course Lecturer: M. Claussen

Learning Outcomes: Students will have obtained knowledge about the physical theoretical foundations of the spectrum of variability in the ocean (from periodic processes to mesoscale eddies to turbulence). They understand the fundamental mechanisms, their mathematical description and their treatment in ocean general circulation models.

Contents: Sound, internal and planetary waves, propagation in variable environment, instability of waves. Three- and two-dimensional turbulence, generation and dissipation, energy and entropy cascades, relationship between turbulence and mixing, parameterization of turbulence in models.

Educational Concept: Lectures (4 SWS)

Course Lecturer: C. Eden

Learning Outcomes: Students will have obtained in depth practical experience of solving common theoretical problems. They will understand the fundamental mechanisms and the mathematical description of ocean theory. They will gain experience about ocean general circulation models.

Contents: Various wave solutions and their practical application of internal and planetary waves. Common problems of linear stability analysis and instability of waves. Mixing and parameterizations in ocean models

Educational Concept: Exercises (2 SWS)

Course Lecturers: L. Czeschel, A. Griesel

Learning Outcomes: Students have gained insight in advanced numerical methods for climate modeling, especially for conservation laws, efficient parallel solvers for large linear systems of equations, multi-level methods, etc.

Contents: Introduction to numerical methods for the implementation of conservation laws: introduction to structure of conservation laws, finite volume methods, discontinuous Galerkin methods, finite element methods, advanced time integration schemes, issues in high performance computing. Parallel solution of large systems of linear equations: introduction to parallel architectures and HPC systems, iterative solution of large systems of equations: Krylov subspace methods, multi-level methods, efficient pre-conditioners.

Educational Concept: Lectures, practical exercises (2 SWS)

Course Lecturer: J. Behrens

Learning Outcomes: Students will have a basic understanding of the advantages and limitations of climate models, and their use to enhance our understanding of the climate system.

Contents: Investigate the use of (components of) climate models. The analysis will be guided by questions posed by the instructor as well as the students themselves.

Educational Concept: Lectures (2 SWS)

Course Lecturer: J. Baehr

Learning Outcomes: Students will have a basic understanding of the advantages and limitations of climate models, and their use to enhance our understanding of the climate system.

Contents: Investigate the use of (components of) climate models. The analysis will be guided by questions posed by the instructor as well as the students themselves.

Educational Concept: Seminar (2 SWS)

Course Lecturer: J. Baehr

Learning Outcomes: Students have learned physical processes related to weather and climate extremes and various statistical methods for analyzing extremes in observations and climate model simulations. They will have an overview of how weather and climate extremes have been assessed by the Intergovernmental Panel on Climate Change (IPCC). Students have developed an understanding of how weather and climate extremes contribute to societal risks.

Contents: The course covers physics and statistics of extreme weather and climate events, scenario development for climate change projections, insights in the assessment reports of the IPCC, and socio-economic aspects of climate-related risks.

Educational Concept: Lectures (2 SWS)

Course Lecturer: Prof. Dr. Jana Sillmann

Learning Outcomes: Students have gained a deeper insight into selected atmospheric circulation systems and acquire basic knowledge on global atmospheric circulation modeling.

Contents: Important topics are: moist entropy and tropical circulation systems; potential vorticity and mid-latitude dynamics; atmospheric global circulation modeling; atmospheric transport.

Educational Concept: Lectures including discussions (2 SWS); exercises and worked examples (1 SWS)

Course Lecturer: H. Borth

Learning Outcomes: The course will provide basic description and practical exercises with simplified models of different complexity of numerical weather prediction (NWP) as an initial value problem, coupled to the ocean. Knowledge and understanding include atmospheric and ocean observations, data assimilation methods in theory and practice, formulation of numerical forecast models, predictability, ensemble forecasting, interpretation of outputs of forecast models. Students develop an understanding of various components of the numerical prediction model and how they contribute to the model outputs.

Contents: Numerical weather and ocean prediction as an initial value problem: general introduction. Components of the global observing system. Types of observations. Observation errors. Relative importance of various observations Data assimilation for numerical weather prediction (NWP) and for the ocean: probability calculus, function fitting, early methods of data assimilation, method of successive corrections, background state, statistical interpolation, variational methods, (3D-Var, 4D-Var), background-error covariance modelling, Kalman filter and assimilation methods based on ensembles of forecasts and analyses. Initialization of numerical models: balance issues and the process of geostrophic adjustment, nonlinear normal-mode initialization, and digital filter initialization. Formulation of NWP models: global and limited-area models, initial and lateral boundary conditions, nesting. Bottom and top boundary conditions. Issues in mesoscale modelling. Lateral boundary problem and methods for coupling the regional and global models. One-way and two-way nesting. Atmospheric predictability: fundaments of theory of chaotic systems, forecast error growth and predictability limits. Ensemble forecasting: sources of uncertainties, formulation of initial conditions for ensemble forecast, interpretation and application of ensemble products. Monthly, seasonal and long-range forecasts.

Educational Concept: Lectures and Exercises (2 SWS)

Course Lecturer: Prof. Dr. Nedjeljka Žagar

Learning Outcomes: n.a.

Contents: n.a.

Educational Concept: Seminar, 2 SWS

Course Lecturer: Prof. Dr. Corinna Schrum

Learning Outcomes: Students will develop a structured way of thinking about climate model errors in general, will become familiar with typical model deficiencies, and basic concepts of climate science related to them.

Contents: Current global climate models agree well on several aspects of the climate system, but they also show disconcerting biases in other areas that put into question their ability to predict climate changes with sufficient regional detail for reliable impact studies and the planning of adaptation measures. These model biases challenge our understanding of the functioning of the climate system, which should be represented in the models. Inspired by biases in the climate models developed and operated at the Max Planck Institute for Meteorology we will focus, in this lecture, on roughly six different areas where models have biases or disagree in their responses to forcings, among them stability in the tropical upper troposphere, boundary layer clouds, sea surface temperatures in the tropics, the high latitude lower stratosphere, the oceanic meridional overturning circulation, and the surface pressure distribution. We will review the theory behind phenomena relevant for these issues, potential consequences for global circulation, and approaches to improve the model performance.

Educational Concept: Lecture

Course Lecturers: B. Stevens, H. Schmidt 

Learning Outcomes: Students will be familiar with the techniques used to investigate predictability and the methods used to make predictions of climate variability at seasonal to decadal timescales with a focus on coupled ocean-atmosphere processes.

Contents: Introduction to predictability of climate; Lorenz model; determination of predictability; ensemble forecasting; forecast initialization; ensemble initialization; error propagation and assessment of forecast reliability/ quality; present understanding of the processes that determine predictability; seasonal to decadal predictions of the climate system.

Educational Concept: Lectures and research seminar (2 SWS)

Course Lecturer: J. Baehr

Learning Outcomes: Students participating in this course will learn the factors that influence climate in the urban area and can assess the potential of adaptation strategies for climate change on the urban scale. After attending this course, students have acquired solid specialist knowledge which improves their employability and facilitates the choice of a topic for the master thesis.

Contents: The lecture teaches micro-meteorological specialist knowledge using practical questions of the field of urban climatology as examples. The course explains the special features of the urban boundary layer and of the urban micro climate as well as transport processes within and above the roughness sublayer. Urban modifications of the fluxes of momentum, energy, humidity and trace gases are illustrated. The lecture further conveys the meteorological assessment of possible adaptation strategies to climate change.

Educational Concept: Lecture with exercises

Course Lecturers: Prof. Heinke Schlünzen, David Grawe 

Learning Outcomes: Students have developed an understanding of characteristics of the Asian monsoon and the related dynamical systems and mechanisms. Specifically, they have developed a holistic view of the monsoon system in the context of global climate systems, in particular, regarding its interaction with other large-scale climate modes (ENSO, MJO). Students are able to calculate various monsoon indices and identify the related characteristic circulation patterns from reanalysis data or numerical model outputs.

Contents: Monsoon definitions; circulation characteristics, centers of action, and related thermal-dynamical processes of the Asian (summer and winter) monsoon systems; key elements of the Asian Monsoon (AM) systems such as the Tibetan Plateau topographic forcing; literature review on the AM and the Tibetan uplift; interaction of the AM with climate modes like ENSO and MJO (Madden-Julian Oscillation) and its evolution in a warmer climate.

Educational Concept: Lectures (2 SWS)

Course Lecturer: X. Zhu

Learning Outcomes: The students hold experiences with tracer transport modeling, including knowledge about the numerical schemes, hands-on experience with passive transport algorithms, programming and visualization.

Contents: Lecture chapters on: • introduction to the underlying equations and short recapitulation of corresponding numerical schemes • mathematization and discretization of passive geophysical tracer transport • introduction to reacting tracer transport (advection-reactiondiffusion-equation) and corresponding numerical schemes • introduction to the time-discretization of stiff systems of differential equations • practical implementation of simple 1D and 2D methods for tracer transport • issues in data acquisition, simulation management, and visualization • advanced issues: conservation properties, adaptive methods for multi-scale phenomena, including adaptive mesh refinement.

Educational Concept: Lectures and practical training (2 SWS)

Course Lecturer: J. Behrens