Towards a dynamics core program Steven Caluwaerts ..., Exercises of Dynamics

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Towards a dynamics core program

Steven Caluwaerts

ALADIN-Hirlam Workshop

I finished my PhD about horizontal spatial discretization

in April 2016

In the next slides I will clarify this conclusion.

Why should we care about local horizontal spatial

discretization methods?

Strength spectral method:

Combining a spectral spatial approach with a SISL time discretization permits stable, long timestep integrations while solving efficiently the implicit Helmholtz problem.

But:

→ not very flexible (e.g. impossible to get horizontally inhomogeneous terms in SI solver) → needs global communication but what on massively parallel computer architectures?

We should investigate local spatial discretization alternatives (e.g. finite differences) but modularity is crucial. We need to keep as many building blocks as possible! Not only for practical reasons but also to permit ‘scientifically clean’ tests.

Why should we care about local horizontal spatial

discretization methods?

Stay on a collocation grid

In fact this is what is used currently with the spectral spatial discretization

Dispersion analysis on the SWE shows that the FD A-grid approach results in negative group velocity for the shortest waves.

No option, due to modularity

Conclusion: go for FD Z-grid

But analysis reveals two drawbacks of FD Z-grid

Introduction of asymmetries distorts the appropriate Z-grid geostrophic adjustment behaviour. A solution consists of constructing symmetric Z- grid schemes but they come at an extra cost...

Z-grid eigenvectors are different from the analytical eigenvectors at the short scale end of the spectrum. This is a fundamental property of Z-grid schemes and spoils even symmetric SI Z-grid schemes.

We can mimic a FD spatial discretization in the spectral

ALADIN model by changing the responses.

The scientific impact of local schemes can be tested by replacing the spectral responses by finite differences responses.

Different response functions for 1st order derivative

Implementation is trivial but the approach is very powerful and ‘scientifically clean’. ALADIN provides a unique testbed!

Real model ALADIN tests of FD and spectral method

Specifications experiments

Domain

• 2 different horizontal grid resolutions; 12km and 4km
• 46 vertical levels
• consider both linear as well as quadratic truncation

Finite difference parameters:

Simulated finite difference methods: A grid and Z grid Orders of accuracy: 2,4,6 and 8

Other parameters considered:

with DFI/without DFI

Forecast periods:

Investigate 2 periods of 7 consecutive days in different seasons (January 2016, June 2016)

domain used for the study

… in all experiments.

Back to the conclusion of my PhD

What’s next? : - publish these results

- go to real FD solvers within ALADIN context