ICON
ICON is probably the largest model development project within Germany. It has started more than 10 years ago as joint project between the Max-Planck Institute for Meteorology, German Weather Service DWD, the German Climate Computing Centre with the goal to develop a new model for Numerical Weather Prediction and Climate Science. It involves now national and international partners. ICON is a central element of Germany's national climate modelling strategy and it is used in national and International projects.
Within the ICON-project I designed the ocean general circulation model ICON-O and together with C. Mehlmann its sea-ice component. This involves the complete workflow from the design of new numerical methods, to implementing or overseeing the implementation of HPC code and finally to simulations of the biggest available supercomputers.
Numerics
The success of ICON-O is due to its underlying numerical method. I develope structure-preserving numerics for rotating, stratified flows that resolves a problem of the approximation space on triangular grids and that at the same time preserves essential conservation laws of atmosphere and ocean dynamics. My insight in the mathematical structure of the dynamical equations was instrumental. During this development I learned that mathematical beauty does also lead to highly efficient codes. I am currently working on the extension of these methods to non-hydrostatic compressible and incompressible equations.
Mathematical Analysis
I always tried to keep a strong connection to the mathematical analysis of fluid dynamical equations. This inspired much of my work on numerical methods. The problems I am interested in are classical questions of well-posedness and regularity properties for equations of geophysical fluid dynamics. I do also study the problem of combining models and observations in data assimilation for the purpose of model initialisation and state estimation. I proved that the hydrostatic Boussinesq equations with nonlinear thermodynamics are well-posed. I showed also that the data assimilation problem of initialising the hydrostatic Boussinesq equations such that the models trajectory minimises the difference to given time-distributed observations, provided one use a notion of distance that captures the regularity of the model solutions. I suggested also an idealised coupled atmosphere-ocean model for which I investigated the data stimulation problem. For this idealised coupled model together with colleagues from Imperial College London we formulated a stochastic version and studied the properties of the resulting SPDE.
Submesoscale Telescope: Upper Ocean Dynamics and HPC
ICON-O is one of the fastest ocean models worldwide. This is the result of its numerical properties, of a careful code design and of advanced optimization techniques. This performance allows us to approach unpre-cedented spatial resolutions. In an attempt to push the envelope we designed an experiment where ICON-O’s horizontal resolution ap-proaches locally 500m and where we have subkilometer resolution over large parts of the North Atlantic. With this experimental configuration we could represent submesoscale dynamics, a class of phenomena with a spatial extend of 100m-10 km spatially and a lifetime of days to weeks that is supposed to play an important role in the ocean’s route to dissipation. With our experiment we are analysing and quantifying the oceanic dissipation mechanism
Coastal Dynamics and Marine Biogeochemistry
The Hamburg Excelencecluster "Climate, Climatic Change, and Society" ("CLICCS" https://www.cliccs.uni-hamburg.de/) assess the question which climate futures are possible and which are plausible. As part of this cluster we modelled the physical and biogeochemical dynamics of the global land-ocean transition zone and its role in the Earth system using a coastal telescope configuration of the ICON-O and the integrated marine biogeochemistry model HAMOCC in global configuration. See also the EOS highlight: https://eos.org/editor-highlights/substantial-advance-towards-a-global-coastal-carbon-model. In order to handle the enormous computational costs that arise by including biogeochemistry models we implemented the concept of "concurrency" into ICON-O that allows us -on sufficiently large computers- to run the marine biogeochemistry at high resolution.
Forthcoming Projects
I. Machine Learning
In the project ExaOcean we aim to integrate ML-techniques into the numerics of ICON-O to improve the models performance and scalability on Exascale Computers. This project is funded by the German Federal Ministry of Education and Research. Started October 2022.
II. Convex Integration
Convex integration is a constructive method that was introduced by C. De Ellis and L. Szekelyhidi in the analysis of hydrodynamic equations. The application of convex integration culminated in the completion of the proof of Onsager’s conjecture. Convex integration is a promising tool that opens new direction in turbulence and in fundamental question on hydrodynamic equations such as uniqueness and regularity. In a collaboration with L. Szekelyhidi and R. Klein we aim to formulate and implement a computational version of convex integration and use it in cutting-edge turbulence simulations.
