DFG
  1. Home
  2. Research
  3. Area M
  4. M3

M3: Towards Consistent Subgrid Momentum Closures

Principal investigators: Prof. Sergey Danilov (Alfred Wegener Institute for Polar and Marine Research), Dr. Janin Jäger (Catholic University of Eichstätt-Ingolstadt), Prof. Stephan Juricke (GEOMAR Helmholtz Centre for Ocean Research Kiel), Prof. Marcel Oliver (Catholic University of Eichstätt-Ingolstadt)

Computational models of atmosphere and ocean can only resolve a limited range of scales. Dynamical processes on scales smaller than the grid scale are parameterized or simply truncated.

When the grid scale lies within one of the classical turbulent inertial ranges, the use of viscous closures is well-understood, but in practice, simulations tend to be over-dissipative because of insufficient scale separation between numerical dissipation and the forcing scale. This problem is particularly severe when forcing occurs near the grid scale, for example through the process of baroclinic instability which converts available potential energy into kinetic energy in eddy-permitting or barely eddy-resolving simulations of the ocean. In general, momentum closures, as well as momentum advection, must aim at being minimally dissipative, which may require active reinjection of energy into the resolved kinetic energy range, a process termed in the context of oceanic momentum closures as kinetic energy backscatter.

This project will evaluate existing closure and advection schemes and develop new ones with a particular focus on (i) properly analysing their precise discrete behaviour, especially the energy budget near the resolution scale and the propagation of linear waves on unstructured meshes, (ii) developing closures that work on unstructured and variable grids (the B-grid in FESOM, the hexagonal and triangular C-grids in ICON-IAP and ICON-o), (iii) gaining physical understanding of numerically induced processes, and (iv) developing and assessing stochastic closures.

We will, first, continue the development of ocean kinetic energy backscatter which, as we demonstrated in the first project phase, is an effective means of improving energy consistency of eddy-permitting or barely eddy-resolving ocean simulations. Second, we will investigate the behaviour of models near the grid scale (i) top-down, by analysing the effective resolution of different choices of grids, discrete operators, and momentum closures empirically in the context of realistic model runs, and (ii) bottom-up, by building physical and mathematical understanding of the explicit as well as implicit choices of momentum closures. The combination of these methods and the application to the two different main models of the TRR181 – i.e., FESOM and ICON – will ensure a holistic approach to the development of efficient, energetically consistent and optimal discretizations of the momentum equations.

Next phase outlook:

➢ Spurious interfacial waves on unstructured meshes

➢ Further development and adjustment of kinetic energy backscatter schemes in global ocean models

➢ Investigation of effective resolution of general circulation models on various grids

The union of different grids (B) and the local inclusions of refined mesh areas (C) imply the appearance of a new type of waves, namely guided waves propagating at the interface, and local waves. These types of waves, sometimes called Rayleigh-Stoneley waves, considered to be "spurious" in the current context and should be muffled, since there are no such waves in the original uniform grid (A) reflecting the homogeneity of real models.

Report - EGU General Assembly in Vienna by Hao Liang (May 26)

I travelled together with colleagues from MIDS (Mathematical Institute for Machine Learning and Data Science) from Catholic University Eichstätt-Ingolstadt and arrived in Vienna on a sunny Sunday afternoon. Even before the conference officially began, the city already felt connected to EGU. Around metro stations, cafés, and the conference venue, it was easy to spot participants wearing name badges or carrying poster tubes. Vienna itself provided a beautiful setting for the week, with its grand historical buildings, churches, parks, and opera houses creating a calm yet lively atmosphere.

The scale of the conference was impressive. Oral sessions, poster presentations, short courses, and networking events ran throughout the day. What impressed me most, however, was how much effort people put into presenting and discussing their work. Researchers from very different backgrounds were all eager to exchange ideas and explain their research in detail.
During the week, I mainly attended sessions related to ocean dynamics, turbulence, numerical modelling, and machine learning applications in geoscience, especially the OS1.11 and NP6.4 sessions organised by members of the TRR 181 project. The talks covered a wide range of topics, from physical ocean processes to modern computational and data-driven methods, and the discussions were often lively and inspiring. Researchers from the TRR 181 project also contributed several excellent talks and poster presentations throughout the week, and unexpectedly meeting familiar faces across different sessions added another enjoyable part to the conference experience.

My own poster presentation took place towards the end of the conference. It was my first time presenting a poster at such a large international meeting, and I really enjoyed the experience. Compared with oral presentations, the poster session allowed for more direct and relaxed discussions. I had several interesting conversations about possible applications of the method, which gave me useful ideas for future research.

Outside the sessions themselves, the conference had a very lively atmosphere. During breaks, many participants gathered outside in the sunshine, sitting on the grass and continuing scientific discussions. Others explored the exhibition area, where journals, scientific companies, and research organisations presented new projects, software, and publications. There were also quiet working areas filled with researchers preparing talks, answering emails, or making last-minute changes to posters.
Vienna itself also became an important part of the experience. After the conference sessions ended, colleagues and I often spent the evenings walking through the city centre while continuing discussions from the day. The architecture constantly changed from one street to another: monumental buildings, quiet courtyards, churches, statues, and elegant parks appeared almost everywhere.

After the conference, I stayed an extra day in Vienna and visited the Kunsthistorisches Museum. The museum’s collections span thousands of years of history, from Egyptian and Classical antiquities to Renaissance paintings and sculptures. One highlight for me was seeing Pieter Bruegel’s The Tower of Babel in person, part of the museum’s remarkable Bruegel collection.
Overall, EGU 2026 was a highly valuable experience for me. Beyond presenting my own work, the conference provided many opportunities for discussion, inspiration, and new perspectives on interdisciplinary research. At the same time, Vienna itself added a unique atmosphere to the week, combining science, history, art, and music in a memorable way.

At the beginning of May, I travelled to Vienna to participate in the EGU General Assembly 2026. The meeting brought together around 20,000 scientists from all over the world working across many areas of geoscience. Coming from a mathematical background and working on spectral recovery from sparse observations, it was exciting to experience such a large and interdisciplinary conference environment.

I travelled together with colleagues from MIDS (Mathematical Institute for Machine Learning and Data Science) from Catholic University Eichstätt-Ingolstadt and arrived in Vienna on a sunny Sunday afternoon. Even before the conference officially began, the city already felt connected to EGU. Around metro stations, cafés, and the conference venue, it was easy to spot participants wearing name badges or carrying poster tubes. Vienna itself provided a beautiful setting for the week, with its grand historical buildings, churches, parks, and opera houses creating a calm yet lively atmosphere.

The scale of the conference was impressive. Oral sessions, poster presentations, short courses, and networking events ran throughout the day. What impressed me most, however, was how much effort people put into presenting and discussing their work. Researchers from very different backgrounds were all eager to exchange ideas and explain their research in detail.

During the week, I mainly attended sessions related to ocean dynamics, turbulence, numerical modelling, and machine learning applications in geoscience, especially the OS1.11 and NP6.4 sessions organised by members of the TRR 181 project. The talks covered a wide range of topics, from physical ocean processes to modern computational and data-driven methods, and the discussions were often lively and inspiring. Researchers from the TRR 181 project also contributed several excellent talks and poster presentations throughout the week, and unexpectedly meeting familiar faces across different sessions added another enjoyable part to the conference experience.

My own poster presentation took place towards the end of the conference. It was my first time presenting a poster at such a large international meeting, and I really enjoyed the experience. Compared with oral presentations, the poster session allowed for more direct and relaxed discussions. I had several interesting conversations about possible applications of the method, which gave me useful ideas for future research.

Outside the sessions themselves, the conference had a very lively atmosphere. During breaks, many participants gathered outside in the sunshine, sitting on the grass and continuing scientific discussions. Others explored the exhibition area, where journals, scientific companies, and research organisations presented new projects, software, and publications. There were also quiet working areas filled with researchers preparing talks, answering emails, or making last-minute changes to posters.

Vienna itself also became an important part of the experience. After the conference sessions ended, colleagues and I often spent the evenings walking through the city centre while continuing discussions from the day. The architecture constantly changed from one street to another: monumental buildings, quiet courtyards, churches, statues, and elegant parks appeared almost everywhere.

After the conference, I stayed an extra day in Vienna and visited the Kunsthistorisches Museum. The museum’s collections span thousands of years of history, from Egyptian and Classical antiquities to Renaissance paintings and sculptures. One highlight for me was seeing Pieter Bruegel’s The Tower of Babel in person, part of the museum’s remarkable Bruegel collection.

Overall, EGU 2026 was a highly valuable experience for me. Beyond presenting my own work, the conference provided many opportunities for discussion, inspiration, and new perspectives on interdisciplinary research. At the same time, Vienna itself added a unique atmosphere to the week, combining science, history, art, and music in a memorable way.

Research Stay in Pusan by Ekaterina Bagaeva (Sep 23)

Since the end of 2022, the topic of research stay slowly began to appear in our discussions with my supervisor.  We were considering various research groups studying eddies' modeling but overall decided to contact Prof. Dr. Christian Franzke, an expert in atmospheric stochastic modeling. As I found out later during the research stay he has a broad range of scientific interests, but first things first. We reached out to Prof. Franzke, who confirmed his interest in hosting a guest PhD student. And I haven’t told you yet about the destination. South Korea, Pusan National University, what an exotic place for the research stay! 

I began preparations. Timing was settled (right after the summer break), duration was defined (3 weeks) and the tickets to cross the entire Eurasia  were bought. Pleasant little things have remained: to have online meetings to discuss the working plan for these 3 weeks, to find the perfect Airbnb near the university, to plan the weekend trips…  

On September 1st, when all the students in my home country started the new academic year, I  moved to the East. Everything went very smoothly and on Monday we were already having the meeting with Prof. Franzke. On the same day, I was introduced to the working group of young scientists, and we had lunch together in the Korean mensa. I think after these three weeks, the concentration of kimchi in my stomach reached a critical amount.

I am very grateful to Prof. Franzke, who found time to meet and discuss intermediate results every second day and also was always available by phone, despite the high workload. We ended up with the idea that I’m currently implementing in FESOM2. And what is also great is that we are in contact after the research stay and keep meeting biweekly. During the last week, I had the opportunity to give a talk about my PhD work in front of an ocean modelling group. I believe it went well, because there were quite some questions.  

It's time to come up with the summary. During this short time South Korea gave me a chance to get to know it. The working environment, the urban design, the Korean weather with sunny and rainy days, delicious food and the most important for me - people there. As a nice bonus I did weekend trips to Seoul, to the DMZ between two Koreas, did several hikes to the temples and around Pusan.