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Goal Oriented Adaptivity for Tropical Cyclones

Aims & Objectives

Forecasting the development and motion of tropical cyclones presents a severe challenge for numerical weather prediction. A major roadblock to progress in this area is the large range of scales that must be considered. Tropical cyclone motion is determined by the environmental flow on scales of several thousand kilometres whereas the genesis is particularly sensitive to inner-core convection on scales below several kilometres. The structure and intensification are influenced by the large-scale and the convective scale. In the project “Goal Oriented Adaptivity for Tropical Cyclones” such multi-scale problems are investigated and adaptive techniques such as local mesh refinement and model adaption are developed and analyzed.

For this project the following fields are relevant:

  • Dynamics of tropical cyclones and their evolution in vertical shear flows
  • Interaction of tropical cyclones with the midlatitude flow
  • Modelling tropical cyclones using a hierarchy of numerical models
  • Numerical solution of PDEs
  • Goal oriented adaptive finite element methods
  • Optimization, optimal control and parameter identification
  • High performance computing and optimization on parallel platforms
  • Designing the dynamical core of a general circulation model
  • Structure preserving numerical schemes by employing Hamiltonian methods
  • Working with unstructured grids

The project belongs to the DFG priority program 1276 MetStröm  “Multiple Scales in Fluid Mechanics and Meteorology“.

Research Topics

Numerical modelling of tropical cyclones requires a careful balance in the choice of appropriate model, discretization methods as well as an efficient methodology for the solution process. A main emphasis of this project is put on the design of goal oriented adaptive techniques towards automatic mesh adaptation both in time and space. A key issue is the ability to determine the influence of uncertainties in the initial conditions as well as the model and discretization error with respect to arbitrary physical quantities of interest. Important aspects are

  • Definition of adequate goal functionals
  • Analysis of the evaluation of the error estimator for time-varying problems
  • Singular value decomposition (SVD)
  • Efficient numerical methods
  • Full adjoint-based sensitivity analysis in space and time
  • Application of the multipleadaptivity methodologies (local mesh refinement, r-adaptivity)
  • Role of tropical-cyclone asymmetries and dynamical instabilities that influence both the intensity and motion of tropical cyclones


The project is partly funded by the DFG in the framework of the priority program 1276 MetStröm “Multiple Scales in Fluid Mechanics and Meteorology ”.


Engineering Mathematics and Computing Lab (EMCL)

The Engineering Mathematics and Computing Lab (EMCL) headed by Prof. Dr. Vincent Heuveline is working on analysis, development and implementation of efficient numerical methods in scientific computing. Main focus is set to computational fluid dynamics (CFD), reactive flow problems, optimization and optimal control for partial differential equations, adaptive finite element methods, visualization and high performance computing.

Institute for Meteorology and Climate Research (IMK)

The Institute for Meteorology and Climate Research  consists of four divisions. They work on atmospheric processes of the troposphere (IMK-TRO) as well as of atmospheric trace gases and remote sensing (IMK-ASD). A third division, the Atmospheric Aerosol Research (IMK-AAD) is jointly operated with the Institut für Umweltphysik of the University of Heidelberg. Since January 2002 the Institute of the research of the atmospheric environment, former part of the Fraunhofer Gesellschaft, has been a division of the IMK as IMK-IFU.

Max Planck Institute for Meteorology (MPI-M)

The Max Planck Institute for Meteorology  in Hamburg is an internationally renowned institute for climate research. The major objective is to understand how physical, chemical and biological processes, as well as human behaviour contribute to the dynamics of the Earth system, and specifically how they relate to global and regional climate changes. They develop models and measurement techniques to analyze the natural variability in the atmosphere, the ocean and the biosphere, and to assess how the system is affected by changes in land-use, industrial development, urbanization, and other human-induced perturbations. Advanced numerical Earth system models are used to simulate the behaviour of the atmosphere, the ocean, the cryosphere and the biosphere, and the interaction between these different components of the Earth´s system.


  • Dipl.-Phys. Werner Bauer  (MPI-M)
  • Dr. Martin Baumann  (EMCL)
  • Dr. Almut Gassmann  (MPI-M)
  • Prof. Dr. Vincent Heuveline  (EMCL)
  • Prof. Dr. Sarah Jones  (IMK)
  • Dr. Leonhard Scheck  (IMK)


  • Dr. Martin Baumann  (EMCL)


Baumann, M., Heuveline, V., Scheck, L. & Jones, S.C.
Goal-oriented adaptivity for idealised tropical cyclones:  A binary interaction scenario
Meteorologische Zeitschrift, doi: 10.1127/metz/2015/0591, 2015

Vincze, M., Borchert, S., Achatz, U., von Larcher, T., Baumann, M., Liersch, C., Remmler, S., Beck, T., Alexandrov, K.D., Egbers, C., Fröhlich, J., Heuveline, V., Hickel, S. & Harlander, U.
Benchmarking in a Rotating Annulus: A Comparative Experimental and Numerical Study of Baroclinic Wave Dynamics
Meteorologische Zeitschrift, doi: 10.1127/metz/2014/0600, 2015

Bauer, W. & Baumann, M. & Scheck, L. & Gassmann, A. & Heuveline, V. & Jones, S. C.
Simulation of tropical-cyclone-like vortices in shallow-water ICON-hex using goal-oriented r-adaptivity
Theoretical and Computational Fluid Dynamics, doi: 10.1007/s00162-013-0303-4, 2013

Scheck, Jones, Juckes
The Resonant Interaction of a Tropical Cyclone and and a Tropopause Front in a Barotropic Model Part I: Zonally-oriented front
J. Atmos. Sci., 68, 3, p. 405-419, 2011

Scheck, Jones, Juckes
The Resonant Interaction of a Tropical Cyclone and a Tropopause Front in a Barotropic Model Part II: Frontal waves
J. Atmos. Sci., 68, 3, p. 420-429, 2011

Numerical Simulation of Tropical Cyclones using Goal-Oriented Adaptivity
Phd thesis, Karlsruhe Institute of Technology (KIT), 2011

Baumann, Heuveline
Evaluation of different strategies for goal oriented adaptivity in CFD - Part I: The stationary case
Preprint Series EMCL, No. 2010-06, 2010; submitted in GEM