Reports

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. 

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.  

Hi, I am Federica and I am a PhD student in project M2. I studied mathematics and now I am working at the Meteorologic Institute of the University of Hamburg. Mathematics and physics are very intertwined one with the other: improvements in understanding the mathematics leads to physics advances to new realizations which in turn help developing more accurate mathematical models. The invention of the computer and the improvement of this technology, allowed more and more mathematical theories to find useful applications and one field for those applications is also climate (and ocean) modeling. Even though a lot has already been accomplished in this field, there is still room for development. There are material limitations (as computer processors, memory storage, computer precision, etc…) as well as theory limitations (not all the phenomena taking place are fully understood at the moment and the techniques used to model them are not always accurate enough) that have to be overcome.

This is where my work takes place. To be more specific most climate models include only the slow and most energetic modes since including also the fast modes would require too much computational time. However, in real atmosphere and ocean there is energy, enstrophy and momentum transfer between the resolved and the unresolved scales. Most current deterministic parameterisation schemes do not re-inject energy into the resolved scales; instead they are effectively an energy drain. Similarly, current stochastic parameterisations are operated mainly ad hoc without consideration of energy and momentum consistency. Recent studies showed that neglecting the fast unresolved modes induce also error growth, uncertainty and biases in the model therefore they should be included somehow. My work is focused on developing a stochastic parameterisation for the interaction between different flow regimes that will still preserve the total energy of the system and require not too much computational time.

Stochastic processes have some nice features that make them suitable in climate and ocean modeling. However, when dealing with stochastic processes, extra care should be employed. Their main feature is to have different realizations with same initial conditions. Therefore, if you find something worked fine once, you should be sure it was not just luck!

Hi, I am Gözde. I am a PhD student in the subproject M2 Systematic multi-scale modeling and analysis for geophysical flow at the Jacobs University with Marcel Oliver. This subproject is splitted into three parts. Our part is variational model reduction. The purpose is to look at balance, multi-scale phenomena and variational approaches.

We mainly focus on foundational aspects of the problem. Then, we expect to encounter a variety of models where fundamental mathematical questions, such as well-posedness, regularity of solutions, validity of limits, and the analysis of associated numerical schemes is open and possibly nontrivial to resolve. It is important to understand them for evaluating and improving numerical weather and climate prediction models.

We started to examine the well-posedness for balance models for stratified flow. We will compare some models such as L1 balance and classical semigeostrophic model from shocks. Both models are formally derived in the same distinguished scaling limit and to the same order of expansion. The shocks in semigeostrophic theory are thought to be representative of the frontal dynamics regime, but this has not been tested in direct comparison.

I am really happy to be part of this project. The best advantage of it is to contribute with the other groups.