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ALADIN NH

ALADIN NH. Some side-results of the development effort for a stable and efficient semi-Lagrangian version of the ALADIN-NH code Radmila Brožková , Pierre Bénard, François Bouttier, Jean-François Geleyn & Alena Trojakov á. Introduction.

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ALADIN NH

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  1. ALADIN NH Some side-results of the development effort for a stable and efficient semi-Lagrangian version of the ALADIN-NH code Radmila Brožková, Pierre Bénard, François Bouttier, Jean-François Geleyn & Alena Trojaková SRNWP NH 5th Workshop, Bad-Orb

  2. Introduction • Three ‘side-questions’ for the developement of the adiabatic ALADIN-NH application (Laprise p-type coordinate, spectral, SI-SL-2tl, linear-grid): • A) Does the semi-Lagrangian efficiency indeed vanish at high resolution (Bartello & Thomas, MWR, 1996) ? • B) Are all the above-mentioned numerical choices reasonable and compatible ? • C) What about a dynamical test mimicking ‘strong diabatic’ conditions ? SRNWP NH 5th Workshop, Bad-Orb

  3. The ALPIA framework • Four ‘cascade-nested’ domains with the same centrer in a very ‘sharp’ location (near Grenoble): • A = 10 km mesh, 30 levels, 96 x 96 points • B = 5 km mesh, 42 levels, 108 x 108 points • C = 2.5 km mesh, 60 levels, 128 x 128 points • D = 1.25 km mesh, 85 levels, 160 x 160 points • Smolarkiewicz proposal for a semi-academic test-bed (real orography but equivalent barotropic situation with fixed N & U) • Tests done to search the maximum stable time steps in Eulerian or semi-Lagrangian 3tl mode while making diagnosis of respectively: • The maximum local Courant number in Eul. (not shown) • The maximum local Lipschwitz number in s.-Lag. (not shown) SRNWP NH 5th Workshop, Bad-Orb

  4. SRNWP NH 5th Workshop, Bad-Orb

  5. ALPIA CFL-results (U=24 m/s, N=0.01 s-1) CFL Mesh size (km) With 2tl-SL we can expect CFL 3 at high resolution (< 3 km mesh-size) SRNWP NH 5th Workshop, Bad-Orb

  6. A full comparison of options in the ALPIA framework • 4 domains (10, 5, 2.5, 1.25 km) with cascade coupling (like before but with a lower tropopause) • Non Hydrostatic (NH) vs. Hydrostatic Primitive Equations (HPE) • Semi-Implicit vs. Explicit • Linear grid vs. Quadratic grid • Semi-Lagrangian vs. Eulerian SRNWP NH 5th Workshop, Bad-Orb

  7. HPE NH Explicite Gr. quad. Gr. Lin. Eul. ad6A s.-L.(dt E) al6A «boum» ! s.-L. Semi-Implicite Gr. quad. Gr. Lin. Gr. quad. Gr. Lin. Eul. ad5 AB Eul. ad4 ABCD s.-L.(dt E) al5 ABC bl5 A s.-L.(dt E) al4 ABC bl4 ABC s.-L. s.-L. cl4 ABCD Studies of the NH dynamics (23 tests)

  8. The central role of the semi-implicittime stepping in ALADIN-NH • If one wants to be Spectral at high resolution one needs to use the Linear grid (~bijection sp. g.p.) • But Linear grid works only in Semi-Lagrangian advection mode • And Semi-Lagrangian computations need stabilisation by a time filter, preferably the Semi-implicit one in Spectral => S-I is the keyto this virtuous circle • Additional advantages: • No multiple trajectory problem and phys/dyn interface easier in A-grid • Far longer time-steps possible (if one can solve other problems => talks by P. Bénard and J. Vivoda) SRNWP NH 5th Workshop, Bad-Orb

  9. ALPIA intercomparison results • In HPE mode at 10 km (CPU-imposed experimental conditions), there is far more influence from the Eulerian to Semi-Lagrangian switch (at equal t) than from the Explicit to Semi-Implicit one, even despite using very short ts in the explicit case => • Very reassuring result for our basic choice SRNWP NH 5th Workshop, Bad-Orb

  10. Study of the NH dynamics (same t for Eul. & S-L) S-I Exp. Eul. S-L

  11. ALPIA intercomparison results (bis) • When compared to more expensive references: • The semi-Lagrangian advection is systematically (10 km => 1.25 km) better than the Eulerian one; this surprising result may be due to the higher order of precision (in the vertical on an irregular grid) of the s.-L. interpolators with respect to the grid-point-type Eul. discretisation (not shown) • The NH results are more regular and even more stable than the HPE ones at high resolution (’vertical escape’ effect of D3 vs. D) (not shown) SRNWP NH 5th Workshop, Bad-Orb

  12. Trapped lee waves’ test results • Reference prepared by Nance & Durran, 1998, JAS, 55, pp. 1429-1455 • Tough test: • 2 wave packets => interference => phase oscillations • Quite high vertical velocities (8 m/s) for a 40 m/s high level jet => adiabatic simulation of convective ascents’ conditions • Experiments: • 2D 500 m resolution (standard & ‘enlarged’ obstacle) • 2D 2000 m resolution (‘enlarged’ obstacle) • 3D 2000 m resolution (elliptic mountain) SRNWP NH 5th Workshop, Bad-Orb

  13. Aladin-NH vs Méso-NH 2D validationvertical wind and theta at 500m resolution Aladin Méso-NH SRNWP NH 5th Workshop, Bad-Orb

  14. Aladin-NH vs Méso-NH 3D validation at 2 km resolutionvertical wind at 2000 m Méso-NH SRNWP NH 5th Workshop, Bad-Orb

  15. Trapped lee waves’ test results (bis) • On the various declinations of this test ALADIN-NH does as well or better than a well-stabilised and fully-documented model • And this with time-steps potentially (in 2tl) 4 to 5 times longer • In high-resolution modelling where the cost of the integrations is dominated by the parameterisations, this is a strong advantage SRNWP NH 5th Workshop, Bad-Orb

  16. Conclusions • ALADIN NH is now a robust dynamical core at rather low cost (one iteration of the dry adiabatic 2tl step with a trivial solver); • The length of the maximum stable time-step reaches surprisingly high values; • The Spectral + SI-SL choice in p-type vertical coordinate is central to these good results; • The quality of simulations in controlled tough comparisons is rather good … SRNWP NH 5th Workshop, Bad-Orb

  17. SRNWP NH 5th Workshop, Bad-Orb

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