Research Statement

My research centres around computational geophysical fluid dynamics in general and numerical ocean modelling in particular and is located at the interface between applied mathematics, physics and high-performance computing. It has always fascinated me how natural phenomena such as the movement of fluids can be captured by comparably simple mathematical equations and that the apparent beauty of the physical phenomena is reflected by numerical simulations that are build upon these mathematical equations. I am deeply convinced that research in atmosphere/ocean modelling requires us to combine mathematical theory, numerical methods and physical reasoning in a shameless cross-disciplinary fashion. In my general approach I am guided by Henri Poincare’s remark:

"The combinations that can be formed with numbers and symbols are an infinite multitude. In this thicket how shall we choose those that are worthy of our attention? Shall we be guided only by whimsy... [This] would undoubtedly carry us far from each other and we would rapidly cease to understand each other. But that is only the minor side of the problem. Not only will physics perhaps prevent us from getting lost but it will also protect us from a more fearsome danger... turning around forever in circles. History [shows that] physics has not only forced us to choose [from the multitude of problems which arise, but it has also imposed on us directions that would never have been dreamed of otherwise  What could be more useful !"


Numerical Ocean Modelling - ICON-O

Focus of my work is the general ocean circulation model ICON-O whose main architect I am and which contains many of my ideas. ICON-O is part of MPI-M’s new Earth System Model MPI-ESM-2. For ICON-O I have developed a “mimetic” or "structure-preserving" discretization method of the partial differential equations of ocean dynamics on unstructured C-grids. The mimetic discretization of ICON-O offers a conservative discretization of the equations of ocean dynamics on unstructured grids, it includes new transport algorithms and it shares with the general mimetic methods the property of great flexibility with respect to the grid. The discretization of physical ocean parametrizations such as the mesoscale eddy parametrization constitutes another fascinating field for physically-compatible numerical modelling. In ICON-O we treat these parametrizations also via a mimetic discretization approach. This results in an elegant model design in which the dynamical core and the parametrizations are handled in a coherent fashion. A distinguishing property of ICON-O's mimetic discretization is its ability to incorporate interpolations/reconstructions in an energetic consistent way. In summary I have created a whole class of ocean discretizations of the ocean equations that share the same conservation properties but may differ in other properties such as accuracy, wave propagation or the representation of eddies. 

 

My research interests comprise methodological aspects as well as model applications. Methodological aspects deal with the further refinement and extension of mimetic methods and their numerical analysis, investigating for example their relation to the continuous dynamical equations. Applying the ICON-O model in eddy-resolving high-resolution ocean simulations on modern supercomputers allows to increase our understanding of ocean dynamics and at the same time provides invaluable information about the model itself that is inaccessible to theoretical analysis. The progress towards eddying regimes is accompanied by the emergent need to adapt techniques of computational fluid dynamics, such as the field of large-eddy simulations (LES), to ocean modelling.   

 

 

Data Assimilation, Adjoint Equations and Error Estimation

I am also active in the area of data assimilation and error estimation. Together with Phd Students and postdocs I have studied adjoint equations as a means to develop fundamental algorithms that allow to estimate errors such as the discretization error or the assimilation error. Adjoint equations are also directly linked to variational data assimilation.