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

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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

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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

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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 )

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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)

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

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

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

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

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

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

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

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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

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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

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

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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

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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)

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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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