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.

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.

Erika Henell, PhD M5

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 ( 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.

Reducing spurious diapycnal mixing in ocean models

My part of work is studying the newly proposed methods of rotating the diffusive part of the advection schemes into the isoneutral plane.

Margarita Smolentseva, PhD M5

Hi everyone, my name is Margarita and I’m a PhD student of the subproject M5 “Reducing spurious diapycnal mixing in ocean models.” This project is about development and analysis of algorithms leading to reducing spurious mixing in ocean models.

Particularly my part of work is studying the newly proposed methods of rotating the diffusive part of the advection schemes into the isoneutral plane. I work in AWI under supervision of Sergey Danilov.

By the moment adapted to triangular meshes with vertex-based and cell-based placement of scalar variables algorithm described by Lemarie at al. (2012) was implemented on the sea-ice model FESOM2.0. I started doing reference potential energy (RPE) analysis of the implemented harmonic version of the algorithm. Also biharmonic version is to be implemented soon. RPE analysis will be held for both versions and also on dissorted meshes. This analysis allows to determine spurious mixing depending on advection schemes and meshes type.

The future work includes analysis of spurious mixing with variance decay technique (by Knut Klingbeil et al.), analysis of regular and irregular meshes, carrying of realistic ocean simulations and analysis of spurious mixing under real conditions.

Solving equations faster and more accurately

Designing high-order numerical methods needs a good understanding of the mathematical equations we want to solve.

Claus Götz, Postdoc in M5

Hi, I’m Claus and I am a PostDoc in Project M5. The focus of my research in this project is the development and analysis of high-order advection methods and high-oder flux evaluation techniques for ocean models. Our goal is to reduce spurious diapycnal mixing in ocean models and I’m working on the intersection between mathematical analysis and numerical methods to help with that.

High-order numerical methods for flow computations are becoming increasingly more popular in computational engineering, but may be not as widespread in climate and ocean science. So what’s the deal with high and low order?

Classical finite differences and finite volume methods for the discretization of partial differential equations use one piece of information in each cell (say, a function value at the cell-center or an integral average over the cell) and put this information into a discrete version of the PDE. This allows for fast and robust algorithms, but in order to resolve small scale features, we often need very fine grids. On the other hand, the high-order methods we are interested in, use higher degree polynomials or other nonlinear functions in each cell. This extra information allow us resolve more features of the solution, even on coarser girds. In many computational fluid dynamics applications this leads to a smaller overall computational time and we would like to show that this is also true for problems in ocean science.

However, carelessly throwing high-order polynomials at your problem is a sure recipe for failure. If we want to include more features of the analytical solution in our numerical solution, we need a good understanding of the analytical properties and how they can be translated into our numerical scheme. For our particular application, e.g., we want tight control over diffusion properties and need to tune our methods to avoid artificial diffusion without losing stability properties that numerical diffusion brings.

In short, designing high-order numerical methods needs a good understanding of the mathematical equations we want to solve. I’m happy to be involved with learning more about the equations in ocean science, so that we can solve them faster and more accurately.

Minimising spurious mixing in numerical ocean models

The possibility for direct application of newly developed model techniques within leading national climate model systems is very stimulating.

Knut Klingbeil, Postdoc in M5

Hi. Last month I started working as a postdoctoral researcher in subproject M5. After being involved already in the project's proposal and review process, I am very happy to finally participate in this exciting TRR. As a co-developer of the coastal ocean model GETM, I am strongly interested in the development of energy-consistent modelling techniques. In ocean models the advective transport of water masses is prone to energetic inconsistency. On the discrete model level this transport is associated with truncation errors causing spurious diapycnal mixing, which artificially increases potential energy without any physical sources.

Recently, I developed (together with PI Hans Burchard) a new analysis method that can quantify spurious mixing locally in every single grid cell. In M5 this method will be applied now to assess the new adaptive grid techniques and advanced advection schemes, that will be developed at UHH (PI Armin Iske), AWI (PI Sergey Danilov) and IOW (PI Hans Burchard) in order to reduce spurious mixing. I will be responsible for the development of algorithms that during runtime adapt the discrete model layers to the fluid flow (in order to minimise vertical transports across the layer interfaces), to isopycnals (in order to minimise diapycnal transports along the model layers) as well as to regions where high vertical resolution is needed (in order to minimise truncation errors) in an optimal way.

Furthermore, I will successively implement all schemes and algorithms developed in M5 into GETM to identify promising combinations that should finally be included into FESOM (developed by Sergey Danilov), which is the ocean component of the state-of-the-art climate model system ECHAM6/FESOM. With Sergey Danilov and Armin Iske being also PIs in the synthesis project S2, this possibility for direct application of newly developed model techniques within leading national climate model systems is very stimulating.

In the frame of the TRR I am looking forward for the close collaboration with experienced oceanographers, meteorologists and mathematicians, which offers an optimal academic environment for me as a young scientist. To foster the internal collaboration within M5, I will be first employed at UHH for 1.5 years and afterwards at IOW.