M5: Reducing spurious diapycnal mixing in ocean models

Principal investigators: Prof. Armin Iske (Universität Hamburg), Prof. Hans Burchard (Institute for Baltic Research Rostock), Dr. Sergey Danilov (Alfred Wegener Institute of Polar and Marine Research Bremerhaven)

Objectives

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

Challenges

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

Invited Guests

No guests available.

Reports

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.

Publications

Banerjee, T., Danilov, S., Klingbeil, K. & Campin, J.-M. (2024). Discrete variance decay analysis of spurious mixing. Ocean Modelling, Volume 192, December 2024, 102460. doi: https://doi.org/10.1016/j.ocemod.2024.102460
Banerjee, T., Scholz, P., Danilov, S., Klingbeil, K. & Sidorenko, D. (2024). Split-explicit external mode solver in the finite volume sea ice–ocean model FESOM2. Geosci. Model Dev., 17, 7051-7065, doi: https://doi.org/10.5194/gmd-17-7051-2024.
Li, X., Chrysagi, E., Klingbeil, K., & Burchard, H. (2024). Impact of islands on tidally dominated river plumes: A high-resolution modeling study. Journal of Geophysical Research: Oceans, 129, e2023JC020272. doi: https://doi.org/10.1029/2023JC020272.
Brüggemann, N., Losch, M., Scholz, P., Pollmann, F., Danilov, S., Gutjahr, O., Jungclaus, J., Koldunov, N., Korn, P., Olbers, D., Eden, C. (2024). Parameterized Internal Wave Mixing in Three Ocean General Circulation Models. Journal of Advances in Modeling Earth Systems, 16, e2023MS003768. doi: https://doi.org/10.1029/2023MS003768
Chang, Y., Li, X., Wang, Y.P., Klingbeil, K., Li, W., Zhang, F. & Burchard, H. (2024). Salinity mixing in a tidal multi-branched estuary with huge and variable runoff. Journal of Hydrology 634, 1-16, doi: https://doi.org/10.1016/j.jhydrol.2024.131094.
Li, X., [...], Danilov, S., Koldunov, N., [...] & Jung, T. (2024). Eddy activity in the Arctic Ocean projected to surge in a warming world. Nat. Clim. Chang., doi: https://doi.org/10.1038/s41558-023-01908-w.
Henell, E., Burchard, H., Gräwe, U. & Klingbeil, K. (2023). Spatial composition of the diahaline overturning circulation in a fjord-type, non-tidal estuarine system. J. Geophys. Res. - Oceans 128, e2023JC019862, doi: https://doi.org/10.1029/2023JC019862.
Reese, L., Gräwe, U., Klingbeil, K., Li, X., Lorenz, M. & Burchard, H. (2023). Local mixing determines spatial structure of diahaline exchange flow in a mesotidal estuary – a study of extreme runoff conditions. J. Phys. Oceanogr. 54(1), e2019JC015527, doi: https://doi.org/10.1175/JPO-D-23-0052.1.
Reinert, M., Lorenz, M., Klingbeil, K., Büchmann, B., & Burchard, H. (2023). High-Resolution Simulations of the Plume Dynamics in an Idealized 79°N Glacier Cavity Using Adaptive Vertical Coordinates. J. Adv. Model Earth Sy. 15(10), e2023MS003721, doi: https://doi.org/10.1029/2023MS003721.
Klingbeil, K. & Henell, E. (2023). A rigorous derivation of the Water Mass Transformation framework, the relation between mixing and dia-surface exchange flow, and links to recent theories in estuarine research. J. Phys. Oceanogr. 53, 2953-2968, doi: https://doi.org/10.1175/JPO-D-23-0130.1.
Umlauf, L., Klingbeil K., Radke, H., Schwefel, R., Bruggeman, J. & Holtermann, P.L. (2023). Hydrodynamic control of sediment-water fluxes: Consistent parameterization and impact in coupled benthic-pelagic models. J. Geophys. Res. - Oceans 128, e2023JC019651, doi: https://doi.org/10.1029/2023JC019651.
Uchida, T., Danilov, S., Koldunov, N. et al. (2022). Cloud-based framework for inter-comparing submesoscale-permitting realistic ocean models. Geosci. Model Dev. 15, 5829–5856, doi: https://doi.org/10.5194/gmd-15-5829-2022.
Li, X., Lorenz M., Klingbeil, K., Chrysagi, E., Gräwe, U., Wu, J. & Burchard, H. (2022). Salinity Mixing and Diahaline Exchange Flow in A Large Multi-outlet Estuary with Islands. J. Phys. Oceanogr., doi: https://doi.org/10.1175/JPO-D-21-0292.1.
Scholz, P., Sidorenko, D., Danilov, S., Wang, Q., Koldunov, N., Sein, D., & Jung, T. (2022). Assessment of the Finite-VolumE Sea ice–Ocean Model (FESOM2.0) – Part 2: Partial bottom cells, embedded sea ice and vertical mixing library CVMix. Geosci. Model Dev. 15(2), 335–363, doi: https://doi.org/10.5194/gmd-15-335-2022.
Fofonova, V., Kärnä, T., Klingbeil, K., Danilov, S., Burchard, H. et al. (2021). Plume spreading test case for coastal ocean models. Geosci. Model Dev. 14(11), doi: https://doi.org/10.5194/gmd-14-6945-2021.
Bauer, T. P., Holtermann, P., Heinold, B., Radtke, H., Knoth, O. & Klingbeil, K. (2021). ICONGETM v1.0 – flexible NUOPC-driven two-way coupling via ESMF exchange grids between the unstructured-grid atmosphere model ICON and the structured-grid coastal ocean model GETM. Geosci. Model Dev., 14, 4843–4863, doi: https://doi.org/10.5194/gmd-14-4843-2021.
Burchard, H., Klingbeil, K., Lorenz, M. et al. (2021). Effective Diahaline Diffusivities in Estuaries. J. Adv. Model Earth Sy. 13(2), doi: https://doi.org/10.1029/2020MS002307.
Osinski, R.D., Enders, K., Klingbeil, K. et al. (2020). Model uncertainties of a storm and their influence on microplastics and sediment transport in the Baltic Sea. Ocean Sci. 16(6), 1491–1507, doi: https://doi.org/10.5194/os-16-1491-2020.
Kerimoglu, M., Voynova, Y.G., Klingbeil, K. et al. (2020). Interactive impacts of meteorological and hydrological conditions on the physical and biogeochemical structure of a coastal system. Biogeosciences 17(20), doi: https://doi.org/10.5194/bg-17-5097-2020.
Schulz, K., Klingbeil, K., Morys, C., & Gerkema, T. (2020). The fate of mud nourishment in response to short-term wind forcing. Estuar. Coast 44, doi: https://doi.org/10.1007/s12237-020-00767-4.
Chegini, F., Klingbeil, K., Burchard, H., Winter, C. et al. (2020). Processes of Stratification and Destratification During An Extreme River Discharge Event in the German Bight ROFI. J. Geophys. Res.- Oceans 125(8), doi: https://doi.org/10.1029/2019JC015987.
Smolentseva, M., & Danilov, S. (2020). Comparison of several high-order advection schemes for vertex-based triangular discretization. Ocean Dyn., 70(4), 463-479, https://doi.org/10.1007/s10236-019-01337-4 .
Lorenz, M., Klingbeil, K., & Burchard, H. (2020). Numerical study of the exchange flow of the Persian Gulf using an extended Total Exchange Flow analysis framework. J. Geophys. Res.: Oceans 125(2), e2019JC015527, doi: https://doi.org/10.1029/2019JC015527.
Scholz, P., Sidorenko, D., Gurses, O., Danilov, S., Koldunov, N., Wang, Q., Sein, D., Smolentseva, M., Rakowsky, N. & Jung, T. (2019). Assessment of the Finite VolumE Sea Ice Ocean Model (FESOM2.0), Part I: Description of selected key model elements and comparison to its predecessor version, Geosci. Model Dev., https://doi.org/10.5194/gmd-2018-329.
Klingbeil, K., J. Becherer, E. Schulz, H. E. de Swart, H. M. Schuttelaars, A. Valle-Levinson and H. Burchard (2019). Thickness-weighted averaging in tidal estuaries and the vertical distribution of the Eulerian residual transport. J. Phys. Oceanogr., doi: https://doi.org/10.1175/JPO-D-18-0083.1.
Stähler, S. C., Panning, M. P., Hadziioannou, C., Lorenz, R. D., Vance, S., Klingbeil, K., & Kedar, S. (2019). Seismic signal from waves on Titan's seas. Earth Planet Sc. Lett., 520, 250-259, doi: https://doi.org/10.1016/j.epsl.2019.05.043.
Lorenz, M., K. Klingbeil, P. MacCready, and H. Burchard (2019). Numerical issues of the Total Exchange Flow (TEF) analysis framework for quantifying estuarine circulation, Ocean Sci., 15, 601-614.
Gräwe, U., K. Klingbeil, J. Kelln, and S. Dangendorf (2019). Decomposing mean sea level rise in a semi-enclosed basin, the Baltic Sea. J. Climate, doi: https://doi.org/10.1175/JCLI-D-18-0174.1.
Burchard, H., X. Lange, K. Klingbeil, and P. MacCready (2019) Mixing estimates for estuaries, J. Phys. Oceanogr., 49, 631-648, doi: https://doi.org/10.1175/JPO-D-18-0147.1.
Iske, A. (2019). Approximation Theory and Algorithms for Data Analysis. Texts App. Math., 68, Springer, doi: 10.1007/978-3-030-05228-7.
Klingbeil, K., Burchard, H., Danilov, S., Goetz, C. & Iske, A. (2019). Reducing spurious diapycnal mixing in ocean models. In Energy Transfers in Atmosphere and Ocean (pp. 245-286). Springer, Cham., doi: https://doi.org/10.1007/978-3-030-05704-6_8.
Rybicki, M., Moldaenke, C., Rinke, K., Dahlhaus, H., Klingbeil, K., Holtermann, P. L. ... & J. Zhu (2019). WP-C: A Step Towards Secured Drinking Water: Development of an Early Warning System for Lakes. In Chinese Water Systems (pp. 159-205). Springer, Cham, doi: https://doi.org/10.1007/978-3-319-97568-9_5.
Burchard, H., Bolding, K., Feistel, R., Gräwe, U., MacCready, P., Klingbeil, K., Mohrholz, V., Umlauf, L., & van der Lee, E. M. , (2018). The Knudsen theorem and the Total Exchange Flow analysis framework applied to the Baltic Sea, Prog. Oceanogr., 165, 268-286, doi: https://doi.org/10.1016/j.pocean.2018.04.004.
Slavik, K., Lemmen, C., Zhang, W., Kerimoglu, O., Klingbeil, K. & Wirtz, K. W. (2018). The large-scale impact of offshore wind farm structures on pelagic primary productivity in the southern North Sea. Hydrobiologia, 1-19, doi: 10.1175/JAS-D-17-0114.1.
Klingbeil, K., Debreu, L., Lemarié, F. & Burchard, H. (2018). The numerics of hydrostatic structured-grid coastal ocean models: state of the art and future perspectives. Ocean Model., Vol. 125, 80-105, doi: https://doi.org/10.1016/j.ocemod.2018.01.007.
Frassl, M., B. Boehrer, P. Holtermann, W. Hu, K. Klingbeil, Z. Peng, ... & K. Rinke (2018). Opportunities and Limits of Using Meteorological Reanalysis Data for Simulating Seasonal to Sub-Daily Water Temperature Dynamics in a Large Shallow Lake. Water-Sui., 10(5), 594, doi: https://doi.org/10.3390/w10050594.
Lemmen, C., Hofmeister, R., Klingbeil, K., Nasermoaddeli, M. H., Kerimoglu, O., Burchard, H., Kösters, F. & Wirtz, K. W. (2018). Modular System for Shelves and Coasts (MOSSCO v1.0) – a flexible and multi-component framework for coupled coastal ocean ecosystem modelling, Geosci. Model Dev., 10.5194/gmd-2017-138 .
Nasermoaddeli, M. H., Lemmen, C., Stigge, G., Kerimoglu, O., Burchard, H., Klingbeil, K., Hofmeister, R., Kreus, M., Wirtz, K. W. & Kösters, F. A (2018). A model study on the large-scale effect of macrofauna on the suspended sediment concentration in a shallow shelf sea Estuarine, Coastal and Shelf Science, Geosci. Model Dev., https://doi.org/10.1016/j.ecss.2017.11.002.