arXiv subjects

Christiane Jablonowski

Publications and source records attributed to Christiane Jablonowski.

4 recordsLinked to original sources

arXiv2025

Stability analyses of divergence and vorticity damping on gnomonic cubed-sphere grids

Divergence and vorticity damping, which operate upon horizontal divergence and relative vorticity, are explicit diffusion mechanisms used in dynamical cores to ensure stability. To avoid numerical blow-up from excessively strong diffusion, there are mesh-dependent upper bounds on the coefficients of the diffusion operators. This work considers such stability limits for three gnomonic cubed-sphere meshes: the 1) equidistant, 2) equiangular, and 3) equi-edge mappings. Stability limits are derived from a von Neumann analysis of damping with a simplified pseudo-Laplacian operator, as used in NOAA GFDL's finite-volume dynamical core on the cubed-sphere (FV3), and with the full curvilinear Laplacian. The resulting stability limits depend on the gnomonic mapping through the cubed-sphere cell areas, aspect ratios, and grid nonorthogonality. The analytical stability limits are compared to practical divergence and vorticity damping upper bounds in FV3, using idealised tests and the equiangular and equi-edge grids. For divergence damping, both the magnitude of maximum stable coefficients and the locations of instability agree with linear theory. Due to implicit vorticity diffusion in the FV3 transport scheme, practical limits for vorticity damping are lower than the explicit stability limits and depend on the choice of horizontal transport scheme.

math.NA↗

arXiv2024

Fast Summation on the Sphere with Applications to the Barotropic Vorticity Equation

Fast summation refers to a family of techniques for approximating $O(N^2)$ sums in $O(N\log{N})$ or $O(N)$ time. These techniques have traditionally found wide use in astrophysics and electrostatics in calculating the forces in a $N$-body problem. In this work, we present a spherical tree code, and apply it to the problem of efficiently solving the barotropic vorticity equation.

math.NA↗

arXiv2017

Recent progress and review of issues related to Physics Dynamics Coupling in geophysical models

Geophysical models of the atmosphere and ocean invariably involve parameterizations. These represent two distinct areas: Subgrid processes that the model cannot resolve, and diabatic sources in the equations, due to radiation for example. Hence, coupling between these physics parameterizations and the resolved fluid dynamics and also between the dynamics of the air and water, is necessary. In this paper weather and climate models are used to illustrate the problems. Nevertheless the same applies to other geophysical models. This coupling is an important aspect of geophysical models. However, often model development is strictly segregated into either physics or dynamics. As a consequence, this area has many unanswered questions. Recent developments in the design of dynamical cores, extended process physics and predicted future changes of the computational infrastructure are increasing complexity. This paper reviews the state-of-the-art of the physics-dynamics coupling in geophysical models, surveys the analysis techniques, and illustrates open questions in this field. This paper focuses on two objectives: To illustrate the phenomenology of the coupling problem with references to examples in the literature and to show how the problem can be analysed. Proposals are made on how to advance the understanding and upcoming challenges with emerging modeling strategies. This paper is of interest to model developers who aim to improve the models and have to make choices on and test new implementations, to users who have to understand choices presented to them and finally users of outputs, who have to distinguish physical features from numerical problems in the model data.

physics.ao-ph↗

arXiv2007

A Comparison of Two Shallow Water Models with Non-Conforming Adaptive Grids: classical tests

In an effort to study the applicability of adaptive mesh refinement (AMR) techniques to atmospheric models an interpolation-based spectral element shallow water model on a cubed-sphere grid is compared to a block-structured finite volume method in latitude-longitude geometry. Both models utilize a non-conforming adaptation approach which doubles the resolution at fine-coarse mesh interfaces. The underlying AMR libraries are quad-tree based and ensure that neighboring regions can only differ by one refinement level. The models are compared via selected test cases from a standard test suite for the shallow water equations. They include the advection of a cosine bell, a steady-state geostrophic flow, a flow over an idealized mountain and a Rossby-Haurwitz wave. Both static and dynamics adaptations are evaluated which reveal the strengths and weaknesses of the AMR techniques. Overall, the AMR simulations show that both models successfully place static and dynamic adaptations in local regions without requiring a fine grid in the global domain. The adaptive grids reliably track features of interests without visible distortions or noise at mesh interfaces. Simple threshold adaptation criteria for the geopotential height and the relative vorticity are assessed.

physics.comp-ph↗