The Nonhydrostatic Icosahedral NIM Model Description and Potential

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

X-section location Flow-followingfinite-volume Icosahedral Model FIM Temp at lowest level 2

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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. 5

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

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. 7

FIM/NIM model characteristics: • Horizontal discretization on Icosahedral grid. • Computations: Single loop, table described, indirect addressed (Scalable to 100, 000 CPUs). • Explicit 3 rd-order Adams-Bashforth (AB 3) time differencing. • Model variables defined on a non-staggered A-grid. • Finite-Volume line integration on local coordinate. • AB 3 -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, heightcoordinate, GFS physics, + …… Lee and Mac. Donald (2009): A Finite-Volume Icosahedral Shallow Water Model in Local Coordinate, MWR, 2009, in press (on-line early release)8

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

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

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

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

Graphic Processing Units: On a Steep Performance Curve 13

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2011: GPU 4 KM NIM 1 Day Forecast Projected Processors Points per Processor Time (hours) Percent of Real Time 1280 32768 1. 87 7. 8% 2560 16384 . 99 4. 1% 5120 8192 . 56 2. 3% 10240 4096 . 33 1. 3% 20480 2048 . 20 . 8% 40960 1024 . 15 . 6% 15

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. 16

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

Numerical experiment on mountain waves 18

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

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

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

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

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. 56

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

OLR Hovmoller showing MJO simulation NICAM dx=3. 5 km (Non-hydrostatic ICosahedral Atmospheric Model) 58 Courtesy of Prof. Satoh (Science, Dec. 7, 2007)

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. 59

NIM Development and Implementation Schedule • Model design complete Dec 2008 • Initial dynamic model coded Mar 2009 • Initial dynamic model test Jun 2009 • Initial full physics test Dec 2009 • Prediction test and debug 2010 • Continuous real-time runs 2011 • Full GPU NIM runs 2012 • Available for operations 2013 60

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