Research I

I am an applied mathematician and computational physicist. One ambition runs through my work: to advance Earth science by computing what previously had to be prescribed — each new process or scale won by physics, cast into numerics, and turned into production code.

The arc that serves this ambition runs from the mathematical analysis of the fluid-dynamical and oceanic equations, through structure-preserving numerical methods, to extreme-scale computing — and into the ocean, where the resulting simulations answer questions that were previously out of reach. The recurring pattern is the same each time: identify what makes a physical process uncomputable, remove the obstruction by mathematics, transform the result into numerics, and carry it into production code.

The underlying theme is the enlargement of the computable spectrum of scales — from the millimetres at which the ocean turns motion into heat to the planetary circulation, from convective minutes to climatic centuries — one instrument, one budget. Beyond the Earth, the same theme continues toward planetary oceans and, further out, toward computational astronomy at galactic scales.

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Research II

• Mathematical analysis of the fluid-dynamical equations. Well-posedness of the ocean primitive equations with nonlinear thermodynamics and with the Gent–McWilliams–Redi eddy closure; analysis of variational data assimilation; stochastic climate modelling in Hasselmann's paradigm; and the theorem-level foundation of AC/DC — a no-go theorem for discrete compressible dynamics and its resolution. The standard throughout: the equations that models solve, and the methods that solve them, held to the standard of proof.

• Structure-preserving numerics for ocean and atmosphere. Mimetic discretisation of the ocean and atmosphere equations on unstructured grids using discrete exterior calculus. The discrete operators and their conservation properties are the key to robustness and reliability: a budget is trustworthy because one can prove what its operators do.

• Extreme-scale computing as an experimental facility. Code that runs on Europe's largest machines and the experiments it makes possible — global ocean simulation at 500 m, and telescoping into the circulation to resolve new scales inside the global flow. Every simulation is held against observations, from satellite altimetry to the global microstructure record.

• Current direction: from mathematics to climate — dissipation, mixing, and regional climate. For fifty years global ocean models have rested on the same convention: hydrostatic balance and prescribed convection, the small scales set by the modeller's hand rather than by physics. AC/DC — non-hydrostatic ocean dynamics at essentially the cost of hydrostatic dynamics — ends that convention. With it, the ocean's convection, dissipation and mixing become computable at global climate scale.​

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Research III: ICON

The arc's principal product is ICON-O, the ocean and sea-ice component of the ICON Earth System Model. I designed the model and its numerical method, which rests on a sole-author mathematical foundation, and I have written large parts of its roughly 50,000 lines of production code. ICON-O is the ocean of Germany's national Earth system model, of the coupled kilometre-scale simulations awarded the 2025 ACM Gordon Bell Prize for Climate Modelling, and of the highest-resolution global ocean simulation run to date, global at 500 m. The next stage of the arc is AC/DC: a new computational method that makes the ocean slightly compressible and thereby bypasses the global pressure solve — a cost structure no other global ocean model possesses.

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Further information: ICON model · my group at MPI-M.

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