1. 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. 2 Flow-following- finite-volume Icosahedral Model FIM X-section location Temp at lowest level

3. 3

4. 4

5. 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. 6 NIM 3-D finite volume nonhydrostatic equations on Z-coordinate:

7. 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. 8 Horizontal discretization on Icosahedral grid. Computations: Single loop, table described, indirect addressed (Scalable to 100,000 CPUs). Explicit 3 rd -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) FIM/NIM model characteristics:

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

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

11. 11 3-D finite volume 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)

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

13. 13 Graphic Processing Units: On a Steep Performance Curve

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15. 15 2011: GPU 4 KM NIM 1 Day Forecast Projected ProcessorsPoints per Processor Time (hours) Percent of Real Time 1280327681.877.8% 256016384.994.1% 51208192.562.3% 102404096.331.3% 204802048.20.8% 409601024.15.6%

16. 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. 17 Preliminary NIM 2-D test cases: 1. Mountain waves. 2. Warm bubble. 3. Heating forced vertically propagating acoustic waves.

18. 18 Numerical experiment on mountain waves

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

20. 20 t= 0.5 min

21. 21 t= 0.5 min

22. 22 t= 1.0 min

23. 23 t= 1.5 min

24. 24 t= 2.0 min

25. 25 t= 2.5 min

26. 26 t= 3.0 min

27. 27 t= 3.5 min

28. 28 t= 4.0 min

29. 29 t= 4.5 min

30. 30 t= 5.0 min

31. 31 t= 5.5 min

32. 32 t= 6.0 min

33. 33 t= 6.5 min

34. 34 t= 7.0 min

35. 35 t= 7.5 min

36. 36 t= 8.0 min

37. 37 t= 8.5 min

38. 38 t= 9.0 min

39. 39 t= 9.5 min

40. 40 t=10.0 min

41. 41 t=10.5 min

42. 42 t=11.0 min

43. 43 t=11.5 min

44. 44 t=12.0 min

45. 45 t=12.5 min

46. 46 t=13.0 min

47. 47 t=13.5 min

48. 48 t=14.0 min

49. 49 t=14.5 min

50. 50 t=15.0 min

51. 51 t=15.5 min

52. 52 t=16.0 min

53. 53 Test 3: Heating forced vertical acoustic waves to test upper boundary reflections.

54. 54 Explicit treatment of vertically propagated acoustic waves “Correct solution”: Explicit with top boundary at 80 km, 20 shown.

55. 55 Test of implicit form, vertical propagated acoustic waves Implicit (e.g. WRF tri-diaganol) vertical sound waves have reflection problems.

56. 56 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.

57. 57 Statements by Prof. J. Shukla at Hollingsworth Symposium: Proper numerical treatment of mid- latitude waves gives 10 day predictability. Proper numerical treatment of tropical deep convection gives predictability out to 100 days.

58. 58 OLR Hovmoller showing MJO simulation NICAM dx=3.5 km (Non-hydrostatic ICosahedral Atmospheric Model) Courtesy of Prof. Satoh (Science, Dec. 7, 2007)

59. 59 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.

60. 60 NIM Development and Implementation Schedule Model design completeDec 2008 Initial dynamic model codedMar 2009 Initial dynamic model testJun 2009 Initial full physics testDec 2009 Prediction test and debug2010 Continuous real-time runs2011 Full GPU NIM runs2012 Available for operations2013

61. 61 Questions.... alexander.e.macdonald@noaa.gov