A cell-integrated semi-Lagrangian dynamical scheme based on a step- function representation Eigil Kaas, Bennert Machenhauer and Peter Hjort Lauritzen Danish Meteorological Institute Lyngbyvej 100, DK-2100 Copenhagen, Denmark SRNWP-NT mini workshop in Toulouse 12-13 December 2002
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A cell-integrated semi-Lagrangian dynamical scheme based on a step-function representation Eigil Kaas, Bennert Machenhauer and Peter Hjort Lauritzen Danish.
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A cell-integrated semi-Lagrangian dynamical scheme based on a step-function representation
Eigil Kaas, Bennert Machenhauer and Peter Hjort Lauritzen
Interpolating semi-Lagrangian (IPSL) model:2 time level scheme based on bi-cubic interpolation Semi-implicit formulation (Coriolis implicit)No additional horizontal diffusion
SF-CISL model: 2 time level scheme based on step-function representation Semi-implicit formulation (Coriolis implicit)No additional horizontal diffusion
Four different model formulatoins
Spectral Eulerian modelEulerian grid-point model
Interpol. semi Lagrangian model SF-CISL model
48 hour ”forecasts” at low resolution.Parameter: height field
Spectral Eulerian modelEulerian grid-point model
Interpol. semi Lagrangian model SF-CISL model
48 hour ”forecasts” at high resolution.Parameter: height field
Spectral Eulerian modelEulerian grid-point model
Interpol. semi Lagrangian model SF-CISL model
48 hour ”forecasts” at low resolution.Parameter: passive tracer
Spectral Eulerian modelEulerian grid-point model
Interpol. semi Lagrangian model SF-CISL model
48 hour ”forecasts” at high resolution.Parameter: passive tracer
Interpol. semi Lagrangian model
SF-CISL model
10 day ”forecasts” at high resolution.Parameter: passive tracer
Discussion and conclusion
• Cost Passive advection 1.7 times IPSL.
• Truncation/horizontal diffusion This is a critical point
• Memory consumption When step function geometries are defined from the total mass field they could in principle be used for all prognostic variables (i.e. only one prognostic variable per tracer variable)
• The passive advection tests in realistic flow demonstrate the monotonicity, mass conservation and positive definiteness
• The shallow-model works with the new scheme !No noise due to step functions
”Bad”
”Good”
Discussion and conclusion
• Other possible formulations“horizontal diffusion/truncation”Choice of step-functions.
• Generalisation to 3-DCascade interpolation (Nair et al. 1999) for the vertical problem.Prognostic variables: 3-D cell averages, horizontal averages at model levels, vertical averages at grid points, grid point values.
• Spherical geometryNo real problem (reduced lat-lon (or Gaussian) grid).