Reports Area M

Research Stay in Texas by Paul Holst (April 23)

In April this year, I had the unique opportunity to enjoy a 2-week stay in College Station, USA, at Texas A&M University to visit Edriss Titi, who is a professor of nonlinear mathematical science. Professor Edriss Titi is a worldwide renowned applied mathematician who specializes in the mathematical study of problems from fluid dynamics, nonlinear partial differential equations, and in a dynamical systems approach to turbulence. His contributions to these areas are of the highest calibre and practical impact.

After hearing about Edriss Titi's expertise a few months before my research stay and after a simple email to him in which I briefly introduced myself and my research work, a good exchange of information with him developed, I was already very excited to do research together with him and learn from him during the research stay planned shortly thereafter in April. When I arrived in Texas shortly after Easter in April, we started working together on my research topic almost immediately. We talked daily at selected times from then on and made good progress. I greatly benefited from the conversations with him and learned new methods and aspects of my research topic and, even more generally, of the topics in my research area. The conversations I had with Xin Liu, one of the postdocs in Edriss Titi's research group at Texas A&M University, were also very helpful. At the end of my time in Texas, our conversations even resulted in a meaningful outcome regarding my research topic.

In between the meetings I had with Edriss Titi, I worked a lot on the exercises he gave me as well as a lot on my research topic. Away from my research work, I mostly explored the town of College Station on a bicycle in my scarce free time. During these explorations, I especially remembered a couple of beautiful green parks that College Station has to offer, as well as the impressive mansion district. There were also long distances that I had to travel to get from one place to another in College Station. This then gave me a sense, in those moments when I was out of breath, of why even many local people thought you needed a car to get from A to B in Texas.

After my return, I was very happy with the experience, knowledge, and results I was able to gain in Texas. The whole experience I had there has advanced me both scientifically and personally. I am very grateful for this and can therefore only recommend that everyone take advantage of the opportunity of a research stay.

Screening The Coupled Atmosphere-Ocean System Based On Covariant Lyapunov Vectors

I use the tangent linear version of the coupled atmosphere-ocean quasi-geostrophic model MAOOAM, and calculate the CLVs based on the so-called Ginelli method.
Melinda Galfi, Postdoc in M1

Covariant Lyapunov vectors (CLVs) reveal the local geometrical structure of the systems‘s attractor, thus providing valuable information about the basic dynamics. They are physically meaningful since they point into the directions of linear perturbations applied to the trajectory of the system. CLVs are linked to Lyapunov exponents, which describe the growth or decay rate of linear perturbations.

My name is Melinda Galfi, and I am a postdoc in the M1 subproject. I am continuing the work on CLV analysis started by Sebastian Schubert. I use the tangent linear version of the coupled atmosphere-ocean quasi-geostrophic model MAOOAM, and calculate the CLVs based on the so-called Ginelli method. I compute the CLVs in the phase space of the model, spanned by the spectral model variables, which can be grouped into four different categories: atmospheric dynamic and thermodynamic variables, as well as oceanic dynamic and thermodynamic variables.

The spectrum of Lyapunov exponents of our systems reveals the existence of a central or slow manifold. This is a basic property of coupled ocean-atmosphere models, and has to do with the multiscale character of this type of chaotic system. Based on the CLVs, we hope to understand more deeply the dynamical properties of the system itself, and especially of the slow manifold. To achieve this, one can use several CLV based indicators. One of these indicators is the variance of CLVs, showing the contribution of each model variable to the growth or decay of perturbations. By computing the variance of the CLVs in MAOOAM, we see that the atmospheric variables have the strongest contribution to the evolution of perturbations in our system. However, we detect an exception in case of instabilities growing or decaying on long time scales, where the contribution of the oceanic thermodynamic variables is approximately as strong as the one of the atmosphere. This shows that the d y n a m i c s of the slow manifold is governed by interactions between atmosphere and ocean, with the main coupling taking place through the ocean thermodynamics. The contribution of the ocean is the strongest in case of perturbations decaying over long time scales. Another useful indicator is the angle between CLVs, revealing the local structure of the attractor. Our results show that the angle between the CLVs corresponding to the slow manifold is dominantly very near zero, hinting to multiscale instabilities and geometrical degeneracies.

As a next step, we would like to repeat the CLV analysis for a substantially higher model resolution. The currently used resolution consists of 5x5 atmospheric and 5x5 oceanic modes. Our final goal is to study the energy transfers between atmosphere and ocean based on CLVs.

Research Stay in Douai by Mouhanned Gabsi (Oct 23)

After completing a 1-month research stay at the Centre for Materials & Processes (CERI MP)- IMT Nord Europe in Douai, I feel it is an important moment to reflect on how the stay has informed my work, including key research findings, implications and emerging questions.
My intention in working in Douai as a visiting researcher was to experience another academic reality, build a professional network and identify possibilities for future research collaborations.

From October 2nd to October 31st, I had the great opportunity to visit Prof. Modesar shakoor at the IMT Nord Europe’s Centre for Education, Research and Innovation in Materials and Processes. The IMT (Institut Mines Télécom) Nord Europe is a French graduate school of engineering. It is located in the Hauts-de-France region, shared between 2 campuses: the science campus of the University of Lille (Villeneuve-d'Ascq, European Metropolis of Lille); and the city of Douai. The school trains high-level engineers and scientists (Master and PhD level) in various technological fields including Digital Sciences, Energy and Environment Eco-Materials, Industry and Civil Engineering.

The working environment in the research center was very vivid and enabled a productive exchange of knowledge. I received a lot of useful input regarding my PhD topic and was supported in any possible way. This leads me to clarify some doubts related to my current work. I have been able to further develop and improve a big part of my PhD.

I shared the office with Sarabilou, a Phd Student who is working in the same field of interest. This provided me an opportunity to have some interesting discussions with him on various topics.

During my research stay, Prof. Modesar recommended that I learn and experience some deep learning tools and for this, he proposed some online tutorials related to specific class of artificial recurrent neural network (RNN) architecture called the Long Short-Term Memory (LSTM) neural networks implemented in Python with the TensorFlow library. I used the LSTM to solve the 1D wave equation and 2D heat equation. Our regular meeting and discussions lead to a possibility for future research collaborations in this direction.

Although my stay abroad was shortened, the experience was still great and the journey was worthwhile. I got to know interesting personalities. The people I met in the Student Residence were extremely welcoming, supportive and easy to talk with.

Lastly, I believe the networking I have done throughout this experience will become valuable in the future and am very grateful to have made so many valuable contacts.

I would like to thank the TRR181 for enabling and financially supporting this research stay abroad.

Combining the multi-scale finite element with stochastic  subgrid informations

I defined my PhD reaserch project within the goal  to  combine Multi scale numerics with stochastic subgrid informations.
Mouhanned Gabsi, PhD M2

My name is Mouhanned Gabsi and I work as a PhD student at the  University of Hamburg under the supervision of Prof. Dr. Jörn Behrens   (University of Hamburg). I am part of the TRR subproject M2:   Systematic Multi-Scale Modelling and Analysis for Geophysical Flows.   M2 aims at systematically deriving new numerical and stochastic  methods for the energyconsistent representation of subgrid-scale  processes of geophysical flows. Beginning with a bit about myself, I got a bachelor degree in  Mathematics and Applications at the University of Monastir (Tunisia),   after that I persued a Master degree in Applied Analysis and  Mathematical Physics at the University of Toulon (France) that I  acquired with an internship of 6 months at the University of Paris  Saclay under the supervision of Danielle Hilhorst and Ludovic  Goudenège. The goal was to present numerical studies of iterative  coupling for solving flow and geomechanics  in a porous Medium. I started my work as part of TRR in April 2021. At the beginning, I  spent more time in literature and reading papers to dicover the new  environment that I am working on. Within this, I started to understand new scientific terms, phenomena and mechanisms related to Oceans, Atmosphere and Climate models and I found  RTG course that I took in  Mathematics, Oceanography, Meteorology and TRR meeting  very helpful  to me to acquire new knowledge and skills. After that, I defined my PhD reaserch project within the goal  to  combine Multi scale numerics with stochastic subgrid informations.   Multi-scale numerical methods will address the research questions by  providing a framework for coupling small-scale processes to the  large-scale. Subgrid-scale parametrization is the mathematical procedure describing  the statistical effect of sub-grid- scale processes on the mean flow  that is expressed in terms of the resolved-scale parameters. In global  atmospheric models, the range of processes which have to be  parametrized is large and the characteristics of the different  parametrized processes vary, e.g., atmospheric convection, gravity wave drag,   vertical diffusion. The resolvedand the subgrid-scale processes in the Earth's atmosphere are the  response to mechanical andthermal forcing, associated with the distribution of solar incoming radiation, topography, continents and oceans. There are several methods to improve the process of transferring  information from the subgrid-scale to the coarse grid in a  mathematically consistent way such as numerical multi-scale methods  which are based on homogenization or the multi-scale finite element  approach. This method is well established in porous media. The second  method is stochastic, and in particular stochastic parametrization  exploit the time scale difference between the slow resolved scale and  the fast-unresolved scale to model the latter with random noise terms.   This has many advantages such gain in computational timecompared to higher resolved simulations, reduction of model errors and  systematic representation of uncertainties. A first task is to combine  these two methods and to see  if this combination inherently address conservation properties, or  it pose an unnecessary overhead.

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 1^st, 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.

First Steps in Stochastic Ocean Modelling

To find a good stochastic kinetic energy backscatter parameterization is my local aim so far.
Ekaterina Bagaeva, PhD M3

My name is Ekaterina and I’m a PhD Student of project M3 “Towards Consistent Subgrid Momentum Closures”. I work at Jacobs University in Bremen and at AWI in Bremerhaven as well. Due to Corona pandemic the personal contacts are quite limited, but I was lucky enough to meet already my colleagues in AWI and also regularly meet the colleagues in Jacobs University.

Before joining to TRR I’ve got a master degree in Mathematical Modelling following an Erasmus Program in Europe. My master thesis was related to stochastic modelling of the evolution of an epidemic. The stochastic area of my thesis brings me to the current work in TRR.

My global aim in the projects is to improve the representation of ocean variability that represents by ocean eddies. Some ocean eddies are already resolved for certain degrees of resolution, but still there are variations where explicit simulation is not possible. Some of these variabilities could be resolved by bringing back to the model kinetic energy, so called kinetic energy backscatter, obtained through the stochastic parametrization. And to find a good stochastic kinetic energy backscatter parameterization is my local aim so far.

To date, we are on the second stage of the project, so the first months of my work were devoted to acquaintance with the FESOM model, its configurations and code itself. The other significant part was related to understanding of papers which were published by members of M3 during the first stage of the project. Currently I start to implement the idea of identifying the process based on EOF (Empirical Orthogonal Functions) analysis of kinetics energy difference between realization of the model on the fine and coarse grids.

I see the evolution of my work in the application of smarter and more sophisticated approached of stochastic parametrization, preserving the model intuitively understandable and available for computation.

Coarse-graining, Entropy and the Unseen

Our goal is to unify two approaches currently taken to formulate closures for climate and weather simulations.
Bastian Sommerfeld, PhD M4

My name is Bastian and I’m currently a PhD student at the IAP, working in the subproject M4 “Entropy Production in turbulence parameterisations”. Our goal is to unify two approaches currently taken to formulate closures for climate and weather simulations.

The nature of weather and climate is such that their equations may not directly be solved mathematically. This forces us to use computer models. In these models we define the necessary equations on grids. Each grid-box represents one set of values associated with the volume that grid-box covers. This usually affords us horizontal resolutions between 10 and 100 km and vertical resolutions between several hundred down to a kilometer.

Not unlike the picture of a tree, which from far enough away seems convincing enough, but from close up lacks the details to show the little squirrel on that branch, we struggle with small scale contributions to the motions in our simulations. Namely such that would be small enough not to be resolved in our model, but large enough to have a significant effect on the model dynamics. We try to account for these using mathematical and physical models to incorporate the effects of what we cannot resolve on what we resolve, in order to get the dynamics right, thus correctly predicting the rain on your granny’s birthday party – or how quickly the polar caps melt. These models are called parameterizations.

My particular task is to retrieve the statistics and distribution of fluxes of energy between the resolved and unresolved part of the simulated atmosphere, in order to learn how to better model said fluxes in a
physically stringent way. This means to find formulations which do not only improve our model data, but are in line with the fundamental laws of energy conservation and the second law of thermodynamics. I do this by programming informed routines, which effectively slice our model data into another poor resolution model and high resolution reality. Computing the fluxes between these two regimes I hope to be able to extrapolate into what we don’t know.

So far I’ve had some very exciting findings, which indicate that we have good reason to apply new types of parameterizations, called backscatter parameterizations in conjunction with our old approaches. In addition to that there are hints to how to find formulations which do not violate our understanding of physics, which will then afford us a better understanding of the processes in our atmosphere and climate.

Entropy production in turbulence parameterisations

The idea of M4 is the stochastic or counter-gradient parameterisation of momentum and heat fluxes in forced dissipative systems like the atmosphere and ocean.
Denny Gohlke, PhD student in M4

Dear Reader,

Yesterday I dropped my beloved teacup. Viewing the broken fragments from the perspective of an enthusiastic tea addict: hope for occurrence of the backward process called self-repair. From the sober viewpoint of a physicist: second law of thermodynamics and entropy.

Macroscopic (isolated) systems evolve in a one-way direction of time, towards states with increased entropy seeming to be in contradiction to the underlying microscopic equations that are needed for their description. For instance, Newton’s law of motion for classical systems is symmetric under time reversal; no preference of a certain time direction; no preference of neither the forward nor backward process. Then why is there a break of time symmetry at macroscopic level (irreversibility)?

The second law of thermodynamics is valid in a statistical sense for large system sizes (average statement in thermodynamic limit) within the frame of equilibrium thermodynamics and can be generalised by the Fluctuation Theorem (FT). Resulting from statistical physics this theorem with its different versions connects microscopic and macroscopic behaviour for time reversal systems of arbitrary size arbitrary far driven out of equilibrium in form of an analytical expression of probability ratio of observing a trajectory of a system (in phase space) to its time reversed counterpart.

The essential quantity of the FT is the dissipation function, an entropy-like quantity in non-equilibrium related to internal entropy production under specific conditions. The latter quantity is especially important in regard to our project M4. Here, ‘our’ consists of the Hamburg part, Richard Blender, Valerio Lucarini (Reading) and me (since October last year), and of the Rostock part (IAP) composed of Almut Gaßmann and Bastian Sommerfeld.

The idea of M4 is the stochastic or counter-gradient parameterisation of momentum and heat fluxes in forced dissipative systems like the atmosphere and ocean. These sub-scale fluxes are related to energy dissipation and backscatter; as well related to positive and negative entropy production. Is it possible to put more physics in these turbulence parameterisation schemes with the usage of the FT? However, it requires the applicability of FT for non-time reversal systems (Navier–Stokes equations). As a representative example for turbulence toy models I use the class of shell models (as a first step) to get a basic notion for the incorporation of the FT with the final aim of modification and improvement of climate prediction models. I am looking forward to this challenge. Thank you for your attention.

Research Stay in Boston by Tridib Banerjee (Oct 23)

Hi, my name is Tridib and this is a short report on my 2 months research stay at Massachusetts Institute of Technology, Boston, United States.

There is no way to begin this report without first thanking everyone involved in making it happen. I would like to express how grateful I am to everyone from TRR who helped me through the entire research stay. From planning to securing of funds. To the organizers and the Vorstand, thank you so much. I would also like to thank the responsible people from Constructor university for expediting the fund disbursement so that I could pursue the research at my desired dates. I would also like to thank my supervisor of the research stay Prof. Raffaele Ferrari, for being a terrific mentor (alongside postdoc Simone Silvestri) and sponsoring the discretionary funding to Massachusetts Institute of Technology. I would further like to thank Massachusetts Institute of Technology for making my immigration to US very easy. I would like to thank also my supervisor at TRR – Prof Sergey Danilov for always being available for consultations and helpful discussions and finally, also my current collaborators who kindly shared my workload so that I could focus on the research stay. Thank you all.

I joined the Climate Modelling Alliance to work in collaboration with California Institute of Technology and NASA, Jet Propulsion Laboratory. My role was to join the ocean modelling team at Massachusetts Institute of Technology and help them diagnose their new advection scheme using a diagnostic technique Me, Sergey Danilov, and Knut Klingbeil developed during my PhD. It was a great experience and I learned a lot during the process. Unlike the ocean model that I had worked with in Alfred Wegener Institute, the one I had to use during my research stay ran on GPUs instead of CPUs. This shift of compute architecture meant rethinking of even the fundamental mathematical operations. The work was initially planned to be concise but later, we realized it to be bigger and more important than expected. We ran several interesting experiments and, in the end, we began writing a new manuscript together. Currently, we are running more experiments and working towards finishing our manuscript. In summary, the stay in Boston impacted my career way more than I thought.

While I had my fair share of work to do in Boston, I also enjoyed my time there a lot. I fell in love with their research culture and found a family in my land-lady who was so generous and kind to me during my whole stay. I also went to Michigan to visit my actual family, watch my very first American Football, that too a classic Ohio versus Michigan which Michigan surprisingly won (it was a total pandemonium), and also have my very first American thanksgiving. I was extremely scared going to US but I had nothing but only fun during my entire stay. I would definitely do it again.

Reducing Spurious Mixing in Ocean Models

Every simulation ever done in human history includes some compromise.
Tridib Banerjee, PhD, M5

Hey everyone, I am Tridib, and I am a PhD student employed at Jacobs University but also working at the Alfred Wegener Institute. I am excited to share with you who I am and what my project is.

Beginning with a bit about myself, I did my Bachelor in Mechanical engineering, my Master in Aerospace Engineering, and currently, I am pursuing my PhD in Mathematics. Some of my proudest moments from academia include winning the gold medal and being the first ever in my Bachelor’s university from core engineering to score a perfect ten semester GPA, being the only one from my Master’s university in core engineering to win the prestigious DAAD scholarship for four semesters consecutively, and hopefully, being the first member of my family to ever get a PhD.
get a PhD. I am heavily invested outside academia as well. I love fine arts and landscape photography. My photograph of the Singapore National Museum was publicly voted as the third-best entry in a photography contest. I also love video editing and have worked on campaigns for business start-ups. I love digital painting too. Above all, my most prideful endeavour remains my involvement with nature conservation and animal rescue operations. Some of the significant differences that we were able to achieve include - preserving the rich biodiversity of nearly 130 acres of the Amazon forest in the Lorento and Ucayali regions of Peru vide the Rain Forest Trust, being part of the biggest ever Asian moon bear rescue operation from the bile farms in Vietnam and Nanning, southern China through the Animal Asia Foundation and being able to adopt countless abused and malnourished animals including an elephant named Yin Dee through the Save Elephant Foundation, which I am particularly fond of.
From bungee jumping to queuing for the next Dan Brown, I try not to miss out on good things in life.

Coming to my PhD project, I am working under the supervision of Dr. Sergey Danilov on the TRR subproject M5. Every simulation ever done in human history includes some compromise. Real world is infinitely complex, and whenever we try to model something mathematically, we can only pick our battles. We are limited by our computational resources, machine precisions, and of course, the discoveries we are yet to make. The same goes for the ocean. In such a case, our estimated solution approximates the realworld physical solution only to a certain level of accuracy. One of the consequences of this deviance is the “spurious mixing” or numerical mixing, which produces the same effect as real-world mixing, but has no physical reason to exist. These affect the ocean models greatly, reducing their prediction accuracy for phenomena like meridional overturning, overflows, and tracer transport. It impacts any numerical experiment reliant on density structures highly. They also affect our model parametrizations to an unknown extent, making them even more undesirable. My PhD includes exploring the reasons behind the spurious mixing in ocean models and finding ways to mitigate them. Currently, I am working with the ocean model FESOM 2.0. I am looking into different time-stepping schemes for the layer transport and barotropic sub-time stepping accuracy with a plan to look into layer motions within the true Arbitrary Lagrangian-Eulerian (ALE) framework by the end of this year.

Novel Measurements for Surface Waves

I recently developed a system to measure both ocean wave dynamics and turbulent motions in the airflow above the waves.
Marc Buckley, Postdoc M6

I’m Marc Buckley, a Postdoc in the Techniques subproject. My objective to measure and understand small-scale physics within the first few meters above and below the wavy ocean surface, and how they influence fluxes of energy between the atmosphere and the ocean. My main experimental approach is Particle Image Velocimetry (PIV), which consists in seeding a turbulent flow with particles and tracking the particles to retrieve information about the turbulent motions in the flow. I recently developed such a system to measure both ocean wave dynamics and turbulent motions in the airflow above the waves. I deployed it first from R/P FLIP in October 2017 off the coast of California, and more recently (September-October 2018) from a small platform in the Oder Lagoon (Baltic Sea lagoon).

We plan to use these novel measurements alongside laboratory wave tank measurements to test and validate a wind-wave coupling model developed at University of Hamburg by Michael Hinze and Nicolas Scharmacher. Additionally, we plan to use these high resolution measurements to better understand the complex physical processes that control air-sea energy fluxes, including airflow separation past steep surface waves, wave breaking, wave and current generation through the action of viscous and form (pressure) stresses. This will possibly lead to a novel physics-based air-sea energy and momentum flux parameterization, that may go beyond existing bulk parametrizations that are used in current atmospheric and oceanic models.

The making and breaking of waves

My job will be the numerical analysis and implementation of the Cahn-Hilliard/Navier-Stokes model.
Nicolas Scharmacher, PhD in M6

Hey, my name is Nicolas and I'm a PhD student currently working on the subproject M6: Techniques for atmosphere-ocean wave coupling, together with my supervisor Prof. Dr. Michael Hinze and also Dr. Jeff Carpenter and Dr. Marc Buckley from the HZG.

The energy transfer from the wind to the ocean surface and the energy dissipation caused by breaking waves accounts for the largest transfer of energy from the atmosphere to the ocean. However, despite the importance of the processes involved in surface wave generation and breaking, there are still fundamental gaps when it comes to modeling these processes.

We hope that the diffuse interface methods developed for the Cahn-Hilliard/Navier-Stokes model we are using will provide an improved method to deal with the current shortcomings of the simulation of the air-water interface. We believe that the method is well suited for that purpose due to its thermodynamical consistency, its mass-conserving property and its ability to handle topological changes, which might occur in breaking waves.

My job will be the numerical analysis and implementation of the model in order to be able to provide direct numerical simulations of the airwater interface in three dimensions, with focus on the formation and breaking of wind-generated surface waves. This requires, for example, the development and implementation of energystable time-integration schemes, efficient solvers and appropriate ways to incorporate the windforcing. Once finished, we will compare our simulations with measurements from laboratory experiments our colleagues at HZG have conducted.

No reports available.