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Hybrid CUDA/JAVA model for GPU Calculations of Gas Line-by-LineAbsorption of Atmospheric Radiation
William F. GodoyNASA Langley Research Center, Hampton, Virginia
Abstract
This work shows the potential in the use of graphics processing units (GPU) tospeed up the calculation of radiative energy absorption by atmospheric gases. Gasabsorption calculations are needed at millions of spectral lines (wavelengths) inorder to have an accurate depiction of the Earth’s in-coming and out-coming radia-tive energies. The CUDA/GPU portion of the code obtains fast Voigt lineshapesat several spectral locations, whereas the NIO/Java portion of the code performsefficient random file access on the large HITRAN database to obtain moleculargas parameters. The first advantage of this programming model is the great speedup obtain by the introduction of parallel GPU algorithms, and the second advan-tage is the modular combination of the lower-level CUDA algorithms for the GPUcalculations and the higher-level Java language for efficient input/output of files(I/O). The latter results in an accessible interface to the end-user that is not anexpert in GPU programming.
Introduction
•Modeling radiative transfer in the atmosphere is an extremely challenging task
•Current needs :
- Fast, accurate and robust PARALLEL models (GPU, MPI, Threads)
- Sub-grid models for coupling with other phenomena (i.e. turbulence, convec-tion, cloud physics)
- Avoid computationally expensive codes (i.e. Monte Carlo)
•General computing in graphic processing (GPGPU) units is a powerful alterna-tive
•Drawbacks:
- Full speed up only for single precision (4 bytes)
- GPU low memory and CPU/GPU communication are bottlenecks
- Lack of documentation, validation and applications to radiative transfer
Mathematical Formulation
•Gas absorption is a extremelly noisy functionalong the spectrum [1]
•Line-by-line (LBL) calculations using Voigtlineshapes are required for every single gas atevery single state [2]
• Slow process as there is many gas species andthousands of millions of importantwavenumbers
CUDA GPU / JAVA IO Programming Model
GPU Parallel Model: Voigt Lineshape -Integral Function[2]
fV ( ν−ν̄,γL,γG ) =
∞∫
−∞
fL ( ν−ν ′,T,p ) fG ( ν ′−ν̄,T )d ν (1)
=
√ln 2
√π γG
K(x, y) = Re[
e−z2 ( 1− erf [−iz] )]
(2)
x =√ln 2
ν − ν̄
γGy =
√ln 2
γLγG
. (3)
Voigt lineshape calculation on GPU
f(cm
-1)
-6 -4 -2 0 2 4 60
0.1
0.2
0.3
0.4
0.5
fG
fL
fV
ν − ν
γ = γ =L G 1
Gauss (Doppler effectbroadening)
Lorentz(natural and collisionbroadening)
Voigt ( f L fG )
− (cm-1)
X
CUDA / JAVA flow diagramGPGPU programming basis [3, 4]
• Cost, $ per teraflop (1012 floating point operations) is low
•A GPU has thousands of processors for lightweigth tasks
• Parallel processes (threads) launch from CPU
•High CPU/GPU data transfer reduces efficiency
•Double precision is needed for Jacobian-free calculations
Results and Speed up for Atmospheric H2O and CO2
Atmospheric Profile at 50 Altitudes
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T (K)
p (mbar), f v x 106
h(k
m)
200 300 400 500 60
10-6 10-4 10-2 100 102 104 10
0
20
40
60
80
100
120
temperature
U.S. StandardAtmosphere 1976
pressure
H2O
CO2
O2
CH4 wavenumber (cm -1)
k(cm
-1)
3650 3700 3750 3800 385010-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
H2OCO2
10,000 wavenumbers
Gas Absorption Coefficients at z = 0 m
number of sample wavenumbers
time(
s)
0 20000 40000 60000 80000 1000000
5000
10000
15000CPU 3.4 Ghz AMD Phenom IIGPU GeForce GTX 570 Nvidia
CPU vs GPU computational times
wavenumber (cm -1)
relati
veerr
or(%
)
3650 3700 3750 3800 3850-0.4
-0.2
0
0.2
0.4
H2OCO2
kCPU - kGPU
kCPU
Gas Absorption Relative Error on GPU
x 100%
10,000 wavenumbers
number of sample wavenumbers
Spee
dup(
CPU
time/G
PUtim
e)
0 20000 40000 60000 80000 10000
5
10
15
20GPU Speed up for 2 Gaseous Species
Summary & Conclusions•A hybrid Java/CUDA model allows the modular combination of GPU and high-level I/O algorithms
•The model allows for code reusability with an accesible learning curve for the end user
• Errors due to GPU single precision are less than 0.3% in the case of atmospheric H2O and CO2 at sea level
•Maximum speed up of 18 for 50,000 tested wavenumbers, speed ups grow proportional to the number of wavenumbers
• Potential extension to entire spectrum and multiple gaseous species is a must!
References[1] R. M. Goody, Y. L. Yung, Atmospheric Radiation: Theoretical Basis, 2nd Edition, Oxford
University Press, New York, NY, 1995.
[2] M. F. Modest, Radiative Heat Transfer, 2nd Edition, Academic Press, Elsevier Science, SanDiego, CA, 2003.
[3] CUDA: Compute Unified Device Architecture, NVIDIA Corporation.,http://www.nvidia.com/object/cuda home new.html, 2010.
[4] W. F. Godoy, X. Liu, Introduction of parallel GPGPU acceleration algorithms for the solutionof radiative transfer, Num Heat Trans, Part B: Fundamentals 59 (2011) 1–25.
