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
De Cruz, L., Schubert, S., Demaeyer, J., Lucarini, V. & Vannitsem, S. (2018). Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models, Nonlin. Proc. Geo., 25, 387-412, doi.org/10.5194/npg-25-387-2018.
Mohamad, H. and Oliver, M. (2018). H s-class construction of an almost invariant slow subspace for the Klein-Gordon equation in the non-relativistic limit, J. Math. Phys., 59, 051509, https://doi.org/10.1063/1.5027040.
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.
Vissio, G. and Lucarini, V. (2018). Evaluating a stochastic parametrization for a fast--slow system using the Wasserstein distance. Nonlinear Proc. Geoph., 25(2), 413-427, doi.org/10.5194/npg-25-413-2018.
Biferale, L., Cencini, M., De Pietro, M., Gallavotti, G., & Lucarini, V. (2018). Equivalence of nonequilibrium ensembles in turbulence models. Phys. Rev. E, 98(1), 012202, doi.org/10.1103/PhysRevE.98.012202.
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.
Blender, R., Gohlke, D., & Lunkeit, F. (2018). Fluctuation Analysis of the Atmospheric Energy Cycle. Phys. Rev. E, 98(2), 023101, doi: 10.1103/PhysRevE.98.023101.
Juricke, S., MacLeod, D., Weisheimer, A., Zanna, L., & Palmer, T. (2018). Seasonal to annual ocean forecasting skill and the role of model and observational uncertainty. Q. J. Roy. Meteor. Soc., doi: https://doi.org/10.1002/qj.3394.
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.
Mohamad, H., and Oliver, M. (2019). A direct construction of a slow manifold for a semilinear wave equation of Klein–Gordon type. J. Differ. Eq., doi: https://doi.org/10.1016/j.jde.2019.01.001.