A locally mass Conserving semi-implicit semi-Lagrangian scheme with Lagrangian vertical coordinates – Niels Bohr Institute - University of Copenhagen

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Niels Bohr Institute > Calendar > 2009 > Conserving semi-implic...

A locally mass Conserving semi-implicit semi-Lagrangian scheme with Lagrangian vertical coordinates

Master Thesis: Brian Sørensen

The talk will be in Danish

In traditional 3-dimensional semi-Lagrangian schemes with quasi-Lagrangian vertical coordinates, the vertical Lagrangian levels are remapped to Eulerian model levels at the end of each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates numerical diffusion in the vertical distribution. This can be reduced by conserving the Lagrangian levels, and only interpolate the tendencies between the Lagrangian levels and Eulerian levels. Because tendencies are small compared to the full values, their interpolation errors are correspondingly small. At each time step the Lagrangian levels are used as model levels for the following time step. After several time steps, which can be either dynamically calculated or a fixed number, the Lagrangian levels are remapped to Eulerian model levels to ensure the stability of the model.

The implementation is done using the locally mass conserving semi-Lagrangian (LMCSL) scheme developed by Kaas. The LMCSL scheme combined with a monotonic filter is among the schemes that fulfills most, if not all of the desirable properties for advection schemes. The LMCSL scheme is implemented into the Enviro-HIRLAM model, an online integrated chemical transport version of the High Resolution Limited Area Model (HIRLAM), used for operational weather forecasting at the Danish Meteorological Institute (DMI).

A new mass conserving vertical interpolation method, based on weighted weights and irregular cubic interpolation is implemented as well. This method is both accurate, mass conserving and is shown to be highly efficient compared to the traditional routines. The tests performed using the ETEX-1 scenario, shows that the scheme reduces the vertical diffusion and alters precipitation patterns and cloud development, but is hampered by limitations in the underlying model.

Supervisor: Eigil Kaas, Niels Bohr Institute, University of Copenhagen