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.
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 visit to “The University of New South Wales” (UNSW) in Sydney, Australia from September to October 2018
Arriving back in Hamburg, I am filled with new motivation and ideas on how to continue my PhD. Without a doubt, I will always remember the impressions of my research stay in Sydney. Thank you MINGS for making this experience possible!
Being halfway done with my PhD, I felt the need to talk to other mathematicians working on the same topic as me: the analysis of algorithms for covariant Lyapunov vectors. However, with such an exotic topic, it is hard to find experts to discuss with. Thus, I had to search outside of local conferences and workshops. Looking into literature, I found an author whose work is closely related to mine. After speaking to him and my supervisors, we were convinced that a research stay would be perfect. The stay should not only serve as a means to communicate my recent findings, but the primary goal was to obtain new research questions and contacts to help advance the second half of my PhD.
When organizing the trip, I applied for visa well in advance and even got a next-day response. Everything else was planned on more short notice. Hence, I did not find a place to stay near university and ended up booking a hotel a bit farther away but with a good connection via public transport. My hotel was located near Green Square Station, which has a train running to the airport, the central station, and the inner city. The university can be reached by bus in about 15 minutes. Unfortunately, there is no train connection as of yet. However, constructions on a new line stopping at the university are expected to finish in 2019. My relatively short visit of three weeks did not require any prior arrangements with the university itself, although for longer stays I recommend filling out the visit request form online to gain access to special rooms, such as printer rooms. The visitor's room provided basis necessities like desks and computers. After preparing the assigned workspace on my first day, I had lunch with my host at a café on campus.
Following lunch, I presented my recent work as a basis for discussions, which ensued the next weeks. Sadly, one of my host's students, whom I wished to meet, was no longer at the institute. Nevertheless, the discussions were very fruitful. Besides the helpful comments on my presentation, I got to ask questions that always bugged me and talked about various research ideas. Some turned out to be worth pursuing, while others seemed no more than an interesting thought. This kind of feedback was exactly what I was hoping for. Even more so, we came up with new ideas during the stay. It left me with the impression that there is still much to discover about my topic. Moreover, my host told me of applications that were previously unknown to me. In particular, the computation of long-time coherent sets in ocean dynamics is an application that I find fascinating. One topic we initially planned to collaborate in turned out to be already well-answered. Nevertheless, we agreed upon keeping in touch for further exchange.
Next to the exchange with my host, I was lucky to meet a lot of friendly and interesting people inside and outside of university. For one, a professor staying with me in the visitor's room gave me useful tips on leisure activities. Although in spring the ocean is still a bit cold, a trip to Coogee Beach is a must, as it is only a 15-minute walk from university. A bit farther away, but still reachable with Sydney's Opal card for public transport, is the Blue Mountains National Park. From the heritage center near Blackheath Station there are several hiking trails leading through the beautiful nature. Another nice place is the Royal National Park south of Sydney. It boasts a long walk along the coast that occasionally passes by sandy beaches. However, watch out for blue bottle jellyfish and bring enough sun screen to protect yourself from the strong sun of Australia.
All in all, I had a wonderful time in Sydney that has been enriching on both a professional and personal level. Sydney is a modern city, where people are welcoming and always glad to help. Countless possible activities make it hard deciding on where to spend your free time. The three weeks were over so fast that I still wonder how I managed to explore Sydney and reach my goals. Arriving back in Hamburg, I am filled with new motivation and ideas on how to continue my PhD. Without a doubt, I will always remember the impressions of my research stay in Sydney. Thank you MINGS for making this experience possible!
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.
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.
Subgrid-scale processes of geophysical flows using machine learning
I am working on applying machine learning tasks such as image super resolution to geophysical data.
I am a postdoc at Universität Bremen and I work on new sub-grid methods as part of the project M2. My research focuses on applying machine learning algorithms to geophysical fluid dynamics. Moreover, I organize the TRR Machine Learning Seminar, which takes place Tuesdays at 13:00 (everyone is welcome to join). Here, experts and newcomers meet to discuss project ideas or research results related to machine learning.
When a numerical simulation or data for a numerical simulation does not resolve the full dynamical scales, we need to simulate these missing dynamics. Unlike landscape or face pictures, geophysical data follows self-similarity such that learning the unresolved dynamics from data is a reasonable task. Especially for geophysical flow simulations an enormous amount of data has been stored in the last decades. Moreover, machine learning performs well when there is enough data available. Thus, I am working on applying machine learning tasks such as image super resolution to geophysical data.
Last year, I completed my PhD at Memorial University of Newfoundland, Canada. For my thesis, I used the shallow water equations to develop structure preserving discretization methods and a stochastic sub-grid model for efficient ensemble forecasting.
First Steps in Stochastic Ocean Modelling
To find a good stochastic kinetic energy backscatter parameterization is my local aim so far.
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.
Stochastic superparametrization (SSP) for ocean models
We are working on adapting SSP for applying it to ocean primitive equations (PE).
Please download Anton's report here, since we cannot display his equations with our CMS.
Coarse-graining, Entropy and the Unseen
Our goal is to unify two approaches currently taken to formulate closures for climate and weather simulations.
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.
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.
Reducing Spurious Mixing in Ocean Models
Every simulation ever done in human history includes some compromise.
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.
Analyzing Diapycnal Mixing in Ocean Models
The part of my supervisors and I in the M5, is to develop analysis tools to evaluate whether the new methods succeed in reducing the spurious mixing.
Hi! My name is Erika and I work as a PhD student at the Leibniz-Institute for Baltic Sea Research Warnemünde (IOW) in Warnemünde, Rostock. I am supervised by Dr. Knut Klingbeil (IOW) and Prof. Dr. Hans Burchard (IOW) and am part of the TRR subproject M5 entitled “Reducing Spurious Mixing and Energetic Inconsistencies in Realistic Ocean-Modelling Applications”.
Before I joined the TRR, I pursued a Bachelor in Physics/Meteorology at the University of Stockholm (Sweden) and a Master in Atmosphere – Climate – Continental surfaces at the University Grenoble Alpes (France). My first connection with physical oceanography was made possible through two internships, during which I worked with the NEMO-eNATL60 model to (a) assess meddies (Mediterranean eddies) and Mediterranean overflow water, and (b) describe the dynamical interaction of internal tides and eddies.
The broad goal of the work in M5 is to implement new methods to reduce errors due to the so called spurious numerical mixing in current ocean models. The part of my supervisors and I in the M5 is to develop analysis tools to evaluate whether the new methods succeed in reducing the spurious mixing. The way we will go about this, is to extend existing tools and ideas about diahaline mixing to diapycnal mixing (mixing across isohalines to mixing across isopycnals).
I will work in particular with the GETM model (https://getm.eu/) which was developed in the working group at IOW that I am a part of. The analysis tools will thus be developed in GETM for idealized cases, extended to the Baltic Sea, and are later to be implemented and applied to global ocean models in collaboration with the Synthesis projects S1 and S2.
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.
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.
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.