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Analysis of the performance of the two-way nesting version of LM on idealized test cases

Analysis of the performance of the two-way nesting version of LM on idealized test cases. M. Milelli (*), N. Loglisci (*) and L. Bonaventura (**) (*) ARPA Piedmont, Turin (**) Max Planck Institut fuer Meteorologie, Hamburg. 5 th COSMO Meeting, 24-26 September 2003, Langen, Germany.

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Analysis of the performance of the two-way nesting version of LM on idealized test cases

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  1. Analysis of the performance of the two-way nesting version of LMon idealized test cases M. Milelli (*), N. Loglisci (*) and L. Bonaventura (**) (*) ARPA Piedmont, Turin (**) Max Planck Institut fuer Meteorologie, Hamburg 5th COSMO Meeting, 24-26 September 2003, Langen, Germany

  2. Outline of the talk • Motivations and background • Idealized 3D lee wave test cases • Analysis of the results • Proposed improvements for a multiscale model

  3. Motivations and background • Winter Olympic Games Torino 2006 • Use of LMnest for high resolution local forecast • Assessment of the accuracy of present nesting strategies and implementation of possible improvements

  4. LMnest dynamical core • LM dynamical core applied on each grid • Hierarchies of Cartesian grids with refinement ratio 1:3 • Options for various possible feedbacks from finer to coarser grids

  5. Types of feedback • Fbk = 0 No feedback • Fbk = 1 Xi,j=0.25xi,j+0.125(xi,j+1+xi,j-1+xi+1,j+xi-1,j)+ 0.0625(xi+1,j+1+xi-1,j-1+xi-1,j+1+xi+1,j-1) • Fbk = 2 Xi,j=xi,j • Fbk = 3, 4 Shapiro smoother: Xi,j=xi,j-y(1-y)(xi,j+1+xi,j-1+xi+1,j+xi-1,j-4xi,j)/2+ y2(xi+1,j+1+xi-1,j-1+xi-1,j+1+xi+1,j-1 -4xi,j)/4 • Fbk = 5 Xi,j=0.111111(xi,j+xi,j+1+xi,j-1+xi+1,j+xi-1,j+xi+1,j+1+ xi-1,j-1+xi-1,j+1+xi+1,j-1)

  6. Idealized 3D lee wave test cases U=10 m/s U=25 m/s Grid 2 Grid 2 Grid 1 Grid 1 • grid1: 60x60, grid2: 25x20 • 20 vertical levels • 100 m high mountain (pseudo-Gaussian shape) • +6h runs • tests in two different flow regimes: Fr > 1 and Fr  1 • all feedback tested (not all shown) • slices of U and T at z  3400 m (10th model level) CASE 1 CASE 2

  7. Vertical velocity profiles Case 1 Fr = 2.18 Case 2 Fr = 0.87

  8. Grid 1 Fr> 1 T(K) Feedback 0 Feedback 1 Grid 2

  9. Grid 1 Fr> 1 U(m/s) Feedback 0 Feedback 1 Grid 2

  10. Grid 1 Fr> 1 T(K) Feedback 0 Feedback 3 Grid 2

  11. Grid 1 Fr> 1 U(m/s) Feedback 0 Feedback 3 Grid 2

  12. Grid 1 Fr 1 T(K) Feedback 0 Feedback 1 Grid 2

  13. Grid 1 Fr 1 U(m/s) Feedback 0 Feedback 1 Grid 2

  14. Analysis of the results • Spurious reflections of the waves in the finer grid • Corruption of the solution in the coarser grid in case of feedback > 0 • Cases with feedback 3/4 need a more careful study

  15. 1 A 2 3 Nestingvsmultiresolution modelling • Nesting: no dynamical link between the different grids B C • Multiresolution modelling: prognostic degrees of freedom at grid interface, accurate discretization D

  16. Formulation Knowing the slow terms fu,p the equations to be solved are: Eq. 1

  17. Approximation of p at point 1 (p’ perturbation from the reference profile): at the right side  Eq.1 at the left side  Eq.1 Continuity of mass flux at the interface (from Eq. 1) p’1,... become functions of p’A,...  calculation of p and u

  18. Proposed improvements • Finite volume treatment of divergence on hybrid coarse/fine grid • Accurate discretization of pressure gradient at coarse/fine grid interface (Edwards 1996, Bonaventura and Rosatti 2002)

  19. Conclusions • Major errors detected in LMnest dynamics on idealized lee wave cases • The feedback options can be grouped into two categories with similar results: 1, 2, 5 and 3, 4 • Proposed plans for future work on an improved multiscale model with “minimal” adjustments

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