1 the nonhydrostatic icosahedral (nim) model: description and potential use in climate prediction...
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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
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Flow-following- finite-volume
Icosahedral Model FIM
X-section location
Temp at lowest level
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4
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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.
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NIM 3-D finite volume nonhydrostatic equations on Z-coordinate:
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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.
5. NIM schedule.
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• 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)
FIM/NIM model characteristics:
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N=((2**n)**2)*10 + 2 ; 5th level – n=5 N=10242 ~ 240km; max(d)/min(d)~1.26th level – n=6 N= N=40962 ~ 120km; 7th level – n=7N=163842 ~60km8th level – n=8N=655,362 ~30km; 9th level – n=9N=2,621,442 ~15km10th level ~7.km; 11th level ~3.5km , 12th level ~1.7km
Icosahedral Grid Generation
n=0 n=1
n=2 n=3
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dsnVdAV
dslVdAV
s
h
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: theoremDivergence
: theoremStokes'
e.g., numerics, volume-finitefor suitable
Finite Volume Numerical Weather Prediction:
Represent fields as “total over volume”, using integral relations:
Advantage over finite difference: Perfectly conservative.
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3-D finite volumeNonhydrostaticIcosahedral 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)
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x
y
z
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P
'P ),,( ZYX
N),( yx
'Q),,( ZYX
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'X
),( yxX),( yxQ
),( yxR
Local coordinate: Every point (and its neighbors) are mapped to a local stereographic coordinate.
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Graphic Processing Units: On a Steep Performance Curve
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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%
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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.
5. NIM schedule.
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Preliminary NIM 2-D test cases:
1. Mountain waves.
2. Warm bubble.
3. Heating forced vertically propagating acoustic waves.
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Numerical experiment on mountain waves
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Warm Bubble simulation:
A rising thermal in an isentropic atmosphere.
ndissipatio numerical No
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ground theabove m 260at centered
,125/2'
mzx
mHCo
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t= 0.5 min
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t= 0.5 min
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t= 1.0 min
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t= 1.5 min
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t= 2.0 min
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t= 2.5 min
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t= 3.0 min
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t= 3.5 min
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t= 4.0 min
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t= 4.5 min
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t= 5.0 min
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t= 5.5 min
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t= 6.0 min
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t= 6.5 min
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t= 7.0 min
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t= 7.5 min
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t= 8.0 min
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t= 8.5 min
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t= 9.0 min
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t= 9.5 min
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t=10.0 min
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t=10.5 min
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t=11.0 min
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t=11.5 min
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t=12.0 min
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t=12.5 min
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t=13.0 min
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t=13.5 min
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t=14.0 min
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t=14.5 min
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t=15.0 min
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t=15.5 min
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t=16.0 min
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Test 3:
Heating forced vertical acoustic wavesto test upper boundary reflections.
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Explicit treatment of vertically propagated acoustic waves
“Correct solution”: Explicit with top boundary at 80 km, 20 shown.
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Test of implicit form, vertical propagated acoustic waves
Implicit (e.g. WRF tri-diaganol) vertical sound waves have reflection problems.
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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.
5. NIM schedule.
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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.
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OLR Hovmoller showing MJO simulation
NICAM dx=3.5 km(Non-hydrostatic ICosahedral Atmospheric Model)
Courtesy of Prof. Satoh (Science, Dec. 7, 2007)
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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.
5. NIM schedule.
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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
