M5: Reducing Spurious Mixing and Energetic Inconsistencies in Realistic Ocean-Modelling Applications

Principal investigators: Prof. Sergey Danilov (Alfred Wegener Institute for Polar and Marine Research Bremerhaven/Constructor University), Prof. Armin Iske (Universität Hamburg), Dr. Knut Klingbeil (Leibniz Institute for Baltic Sea Research Warnemünde)

The project investigates important aspects of the Arbitrary Lagrangian-Eulerian (ALE) layer motion framework and high-order weighted essentially non-oscillatory (WENO) advection schemes, in order to fully exploit the potential of these new concepts in realistic ocean climate modelling applications. During the first phase, these concepts have been identified as the most promising techniques to significantly reduce spurious mixing in ocean models. However, now the efforts in basic research have to be extended to address emerged challenges related to general robustness and efficiency as well as other further mandatory model adjustments. The main goals are:

  • Development of a robust generalized layer motion algorithm based on Lagrangian layer motion and a combination of different regridding strategies.
  • Adaptation and optimization of high-order numerical schemes for remapping, internal pressure gradient and WENO advection to the resulting unstructured mesh layout with sloping layers in FESOM.
  • Development of new diagnostics for diapycnal mixing and internal pressure gradient errors to assess the energetic consistency of the newly designed model components.

With these efforts, we aim for enabling a new era of energy-consistent climate simulations, which will not be dominated by spurious numerical mixing anymore, but by the advanced and wellcalibrated physically-motivated mixing parameterizations developed in other subprojects of this CRC.

The proposed project aims to further develop, assess and analyse numerical algorithms leading to reduction in spurious diapycnal mixing in ocean circulation models. This goal will be achieved by (i) the design and implementation of vertical mesh motion algorithms that reduce spurious mixing; (ii) use of advective schemes with isopycnal diffusion and special design of limiters; (iii) development and analysis of high-order advection algorithms relying on high-order flux evaluation.

Physical mixing (upper panels) and numerical mixing (lower panels) of temperature along a transect across the North Sea simulated with GETM using adaptive coordinates (left) and fixed (sigma in this case) coordinates (right). A reduction of numerical mixing and an according increase of physical mixing when using adaptive coordinates is clearly seen. This figure has been taken from Gräwe et al. (2015) (http://dx.doi.org/10.1016/j.ocemod.2015.05.008).

Reduction of spurious mixing by Lagrangian layer motion


  • realistic applications
  • with different dynamical regimes
  • combination of individual
  • layer motion techniques
  • triggering of regridding
  • efficient mesh regularization
  • analysis of diapycnal mixing
  • interpretation of mean
  • (thickness-weighted) quantities

Reduction of spurious mixing by new advection schemes and by stabilization with isoneutral dissipation


Improved understanding of solvers for generalized Riemann problems

Research gap:

Fast and robust solvers available, but only few rigorous analysis

Main questions:

What do approximate solvers

actually compute from an analytical perspective?

What is the common analytical structure of different solvers?


Our contribution:

Two new insights, important steps towards closing the gap

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.