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Area M: Mathematics, New Concepts and Methods

Area M represents the foundation of our project. The scientists in that area work on new mathematical concepts and numerical methods to be tested in the other project areas. Thus, it forms the basis for future work.

Interdisciplinary approach

Applied mathematicians and experts from geo sciences are working together in area M, to foster an exchange with the other research areas and to transfer knowledge between the different disciplines. By working on consistent model formulation, new and consistent parameterisations and numerics for both atmosphere and ocean, the mathematicians can help climate scientists improve their models and thus enhance climate projections.

Specific research questions in Research Area M are:

  • What is a mathematically and physically consistent model formulation for the different dynamical regimes and their interaction?
  • Can we formulate better and physically consistent sub-grid scale parameterisations for the interaction between different dynamical regimes?
  • Can we develop better numerical schemes?

  • Bagaeva, E., Danilov, S., Oliver, M. & Juricke, S. (2024). Advancing Eddy Parameterizations: Dynamic Energy Backscatter and the Role of Subgrid Energy Advection and Stochastic Forcing. J. Adv. Model Earth Sy. 16(4), doi: https://doi.org/10.1029/2023MS003972. 

  • 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. 

  • Brecht, R. & Bihlo, A. (2024). M-ENIAC: A Physics-Informed Machine Learning Recreation of the First Successful Numerical Weather Forecasts. Geophysical Research Letters, 51, e2023GL107718, doi: https://doi.org/10.1029/2023GL107718.

  • Holst, P., Rademacher, J.D.M. & Yang, J. (2024). Rotating Convection and Flows with Horizontal Kinetic Energy Backscatter. In: Henry, D. (eds) Nonlinear Dispersive Waves. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. doi: https://doi.org/10.1007/978-3-031-63512-0_7.

  • Kutsenko, A.A. (2024) Complete Left Tail Asymptotic for the Density of Branching Processes in the Schröder Case. J Fourier Anal Appl 30, 39. https://doi.org/10.1007/s00041-024-10096-w

  • 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

  • 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.

  • 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. 

  • Kutsenko, A. (2024). Closed-form solutions for Bernoulli and compound Poisson branching processes in random environments. J. Stat. Mech. doi: https://doi.org/10.1088/1742-5468/ad83c8

  • 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