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.
Objectives
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?
Publications
Blender, R. & Badin, G. (2017).Construction of Hamiltonian and Nambu Forms for the Shallow Water Equations. Fluids 2017, 2 (2), doi:10.3390/fluids2020024.
Dritschel, D. G., Gottwald, G. A. & Oliver, M. (2017). Comparison of variational balance models for the rotating shallow water equations. J. Fluid Mech., 822, 689-716, doi: https://doi.org/10.1017/jfm.2017.292.
Kutsenko, A. A. (2017). Application of matrix-valued integral continued fractions to spectral problems on periodic graphs with defect. J. Math. Phys. 58, 063516, doi:10.1063/1.4989987
Graves, T., Gramacy, R., Watkins, N. & Franzke, C. (2017). A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA, 1951–1980. Entropy, 19(9), 437, doi: https://doi.org/10.3390/e19090437.
Gálfi, V. M., Bódai, T. & Lucarini, V. (2017). Convergence of extreme value statistics in a two-layer quasi-geostrophic atmospheric model. Complexity, 2017, doi.org/10.1155/2017/5340858.
Bódai, T. and Franzke, C. (2017). Predictability of fat-tailed extremes. Phys. Rev. E, 96(3), 032120, doi.org/10.1103/PhysRevE.96.032120.
Conti, G. & Badin, G. (2017). Hyperbolic Covariant Coherent Structures in Two Dimensional Flows. Fluids, 2017, 2(4), 50., doi.org/10.3390/fluids2040050.
Vissio, G. & Lucarini, V. (2017). A proof of concept for scale‐adaptive parametrizations: the case of the Lorenz'96 model. Q. J. Roy. Meteor. Soc., 144(710), 63-75, doi.org/10.1002/qj.3184.
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.
Oliver, M. (2017). Lagrangian averaging with geodesic mean. P. R. Soc. London, https://doi.org/10.1098/rspa.2017.0558.