The Nonhydrostatic Icosahedral (NIM) Model: Description and Potential Use in Climate Prediction

1. The Nonhydrostatic Icosahedral (NIM) Model: Description and Potential Use in Climate Prediction Alexander E. MacDonald Earth System Research Lab Climate Test Bed Seminar June 3, 2009 World Weather Building NIM Design: Jin Luen Lee and Alexander E. MacDonald

2. X-section location Flow-following- finite-volume Icosahedral Model FIM Temp at lowest level

5. NIM Talk Summary 1. NIM equations. 2. NIM grid, numerical and computational formulation. 3. NIM test cases. 4. Cloud resolving global models and 100 day prediction. 3. NIM schedule.

6. NIM 3-D finite volume nonhydrostatic equations on Z-coordinate:

7. NIM Talk Summary 1. NIM equations. 2. NIM grid, numerical and computational formulation. 3. NIM test cases. 4. Cloud resolving global models and 100 day prediction. 5. NIM schedule.

8. FIM/NIM model characteristics: • Horizontal discretization on Icosahedral grid. • Computations: Single loop, table described, indirect addressed (Scalable to 100,000 CPUs). • Explicit 3rd-order Adams-Bashforth (AB3) time differencing. • Model variables defined on a non-staggered A-grid. • Finite-Volume line integration on local coordinate. • AB3-multistep Flux Conserving Transport: extend Zalesak’s (1979) two-time level to multiple time levels. • FIM: ALE in vertical (sigma-theta hybrid) GFS physics, GSI Initialization + ……. • NIM: 3-D finite-volume formulated on control volume, height-coordinate, GFS physics, + …… Lee and MacDonald (2009): A Finite-Volume Icosahedral Shallow Water Model in Local Coordinate, MWR, 2009, in press (on-line early release)

9. Icosahedral Grid Generation n=0 n=1 n=2 n=3 N=((2**n)**2)*10 + 2 ; 5th level – n=5  N=10242 ~ 240km; max(d)/min(d)~1.2 6th level – n=6 N=N=40962 ~ 120km; 7th level – n=7N=163842 ~60km 8th level – n=8N=655,362 ~30km; 9th level – n=9N=2,621,442 ~15km 10th level ~7.km; 11th level ~3.5km , 12th level ~1.7km

10. Finite Volume Numerical Weather Prediction: Represent fields as “total over volume”, using integral relations: Advantage over finite difference: Perfectly conservative.

11. Nonhydrostatic • Icosahedral • Model • Finite Volume • Control volume coordinate • Full conservative form • Characteristic vert. sound waves • Designed for GPU • Fourth order time accuracy • Piecewise Parabolic space (3rd order) 3-D finite volume

12. Local coordinate: Every point (and its neighbors) are mapped to a local stereographic coordinate.

13. Graphic Processing Units: On a Steep Performance Curve

15. 2011: GPU 4 KM NIM 1 Day Forecast Projected

16. NIM Talk Summary 1. NIM equations. 2. NIM grid, numerical and computational formulation. 3. NIM test cases. 4. Cloud resolving global models and 100 day prediction. 5. NIM schedule.

17. Preliminary NIM 2-D test cases:1. Mountain waves.2. Warm bubble.3. Heating forced vertically propagating acoustic waves.

18. Numerical experiment on mountain waves

19. Warm Bubble simulation: A rising thermal in an isentropic atmosphere.

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