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

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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

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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

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N),( yx

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),( yxX),( yxQ

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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

,10

ground theabove m 260at centered

,125/2'

mzx

mHCo

20

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

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Questions . . . .

alexander.e.macdonald@noaa.gov