ICON Ocean and a New Numerical Approach in Ocean Modelling

ICON-Ozeanmodell (Peter Korn)

The Max Planck Institute for Meteorology (MPI-M) has a long tradition in creating atmosphere and ocean general circulation models in order to pursue its scientific goals. The ICON project provides the framework in which this tradition is continued and in which MPI-M's modelling strategy is adapted to new emerging technologies in High-Performance Computing. This task comprises manifold challenges in computational engineering and in scientific modelling; it commands us to revisit the fundamental physical laws of atmosphere and ocean dynamics underlying our models and to transform them sensibly to computer codes that are capable of running efficiently on massively parallel computing architectures.

The two papers by Peter Korn (and co-author) describe the conceptual foundation of the ICON-Ocean model and analyse how it translates essential properties of geophysical fluid dynamics such as conservation and wave propagation properties to the discrete grid. The grid that is used by all ICON models constitutes the fundamental challenge: the grid consists of triangular cells on which the variables are placed following a so-called Arakawa C-type staggering (variables such as temperature or pressure are located at the centre of a triangular cell, while the normal component of the velocity vector is positioned at the midpoint of a triangle edge). This choice of grid geometry and variable placement implies already and without any further specifications the existence of a computational mode, i.e. an undesirable mode that has no physical justification and that contaminates the physical solution with an unpleasant noisy component. A computational cure to control this computational mode without degrading the physical mode was not known in ocean modelling, as a consequence various modelling groups have abandoned the triangular C-grid, because of the severe impact of computational noise and have favoured different grid and variable layouts such as hexagonal grids with a C-staggering or triangular cells with an Arakawa A- or B-type staggering.

The first of the two paper (see [1] below) introduces a new computational method for the solution of the dynamic equations of the ocean that is able to control the above mentioned computational mode of the triangular C-grid and that is, at the same time, compatible with the conservation laws. This is substantiated by a theoretical and an experimental analysis. The numerical experiments cover a range of simulations from idealized setups that demonstrate the models skill to suppress the computational mode, to a global eddy-permitting simulation, that shows that the noise control does not come at the expense of the models capability to create eddies. The representation of eddies is essential, because global ocean modelling tends towards high-resolution and eddy-resolving simulations with grid spacings of 10km and less, and the investigation of the impact of eddies constitutes a focus of the department "The Ocean in the Earth System" at MPI-M. Finally the paper shows that the model results compare favourable with observations.

Global map of flow speed at 100 m depth. The scale is logarithmic.

The second of the two papers, written in collaboration with S. Danilov from the Alfred-Wegener-Institute for polar and marine research, supplements the previous study with an investigation of the wave propagation properties of the ICON-Ocean model. A sensible wave propagation is for obvious reasons important for any ocean model. Less obvious is the fact, that the wave propagation, described by so-called dispersion relations, is directly influenced by the grid staggering. Favourable dispersion relations at high-resolutions are one of important arguments to choose the C-type staggering and not other options such as the A- or B-type staggering. This prompts the question whether the new numerical approach of [1] does affect the C-grid-dispersion relations or not. For Poincaré, Rossby and Kelvin waves that were studied in [2] the answer is that the dispersion relations remain intact. This confirms the discretization approach of ICON-Ocean also from a wave propagation viewpoint.

Original publications
[1] P. Korn, Formulation of an Unstructured Grid Model for Global Ocean Dynamics, Journal of Computational Physics 339 (2017) 525-552. doi.org/10.1016/j.jcp.2017.03.009
[2] P. Korn, S. Danilov, Elementary Dispersion analysis of some mimetic discretizations on triangular C-grid, Journal of Computational Physics 330 (2017) 156-172. doi.org/10.1016/j.jcp.2016.10.059


Dr Peter Korn
Max Planck Institute for Meteorology
Phone: +49 (0) 40 41173 470
Email: peter.korn@we dont want spammpimet.mpg.de