1. 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

2. Outline of the talk Motivations and background Idealized 3D lee wave test cases Analysis of the results Proposed improvementsProposed 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 X i,j =0.25x i,j +0.125(x i,j+1 +x i,j-1 +x i+1,j +x i-1,j )+ 0.0625(x i+1,j+1 +x i-1,j-1 +x i-1,j+1 +x i+1,j-1 ) Fbk = 2 X i,j =x i,j Fbk = 3, 4 Shapiro smoother: X i,j =x i,j -y(1-y)(x i,j+1 +x i,j-1 +x i+1,j +x i-1,j -4x i,j )/2+ y 2 (x i+1,j+1 +x i-1,j-1 +x i-1,j+1 +x i+1,j-1 -4x i,j )/4 Fbk = 5 X i,j =0.111111(x i,j +x i,j+1 +x i,j-1 +x i+1,j +x i-1,j +x i+1,j+1 + x i-1,j-1 +x i-1,j+1 +x i+1,j-1 )

6. U=10 m/s Grid 2 Grid 1 U=25 m/s Grid 2 Grid 1 CASE 1 CASE 2 Idealized 3D lee wave test cases 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 (10 th model level)

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

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

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

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

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

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

13. Feedback 0Feedback 1 Fr 1 U(m/s) Grid 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. Nesting vs multiresolution modelling Nesting: no dynamical link between the different grids Multiresolution modelling: prognostic degrees of freedom at grid interface, accurate discretization B C D A 2 3 1

16. Formulation Knowing the slow terms f u,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