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 subgrid 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. Journal of Fluid Mechanics, 822, 689716.

Kutsenko, A. A. (2017). Application of matrixvalued integral continued fractions to spectral problems on periodic graphs with defect. Journal of Mathematical Physics 58, 063516 (2017), doi: 10.1063/1.4989987

Graves, T., Gramacy, R., Watkins, N., and Franzke, C. (2017). A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA, 1951–1980. Entropy, 19(9), 437.

Bódai, T., and Franzke, C. (2017). Predictability of fattailed extremes. Physical Review E, 96(3), 032120.

Conti, G., & Badin, G. (2017). Hyperbolic Covariant Coherent Structures in Two Dimensional Flows. Fluids 2017, 2(4), 50. doi: 10.3390/fluids2040050

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 largescale effect of macrofauna on the suspended sediment concentration in a shallow shelf sea Estuarine, Coastal and Shelf Science, Geoscientific Model Development, https://doi.org/10.1016/j.ecss.2017.11.002 .

Oliver, M. (2017). Lagrangian averaging with geodesic mean. Proceedings of the Royal Society of London, doi.org/10.1098/rspa.2017.0558

Gao, M., and Franzke, C. L. (2017). Quantile Regression–Based Spatiotemporal Analysis of Extreme Temperature Change in China. Journal of Climate, 30(24), 98979914.

A. Kutsenko (2017). Mixed multidimensional integral operators with piecewise constant kernels and their representations. Linear and Multilinear Algebra, 110.