Two Parallel Algorithms for Effective Calculation of the Precipitation Particle Spectra in Elaborated Numerical Models of Convective Clouds
Effective calculation of the spectra of precipitation particles, i.e. the spectra of water drops, ice and snow crystals, graupel and hail is one of the most challenging problems in 2-D and 3-D numerical models of natural convective clouds. Algorithms for spectrum calculation are usually proportional to the cubic degree of spectral bin number and therefore are computationally very expensive. The problem becomes even more complicated taking into account the fact that the spectrum of each precipitation particle should be calculated in each spatial grid point of 2-D and 3-D model. The algorithm of Kovetz and Olund and the algorithm of Bott have been chosen as two of the most popular algorithms intended for calculation of the evolution of cloud particle spectra for subsequent optimization and parallelization. Kovetz and Olund algorithm has been optimized and parallelized using both CPU and GPU. Its optimal version is quadratic in time and allows using more than 1000 threads for effective parallelization. Our results show that speed-up of the optimized algorithm is equal to 2.6–13 depending upon the number of spectrum grid points and the use of GPU can accelerate calculations 15-20 times. Bott’s algorithm has been parallelized using only CPU and provides speed up equal to 5 on 8 threads. The developed algorithms are universal: they can be applied to models of different dimensions and to different types of cloud particles. They can be effectively used in elaborated numerical cloud models for operational forecast of dangerous weather phenomena, such as thunderstorm, heavy rain and hail.
Keywordsparallel algorithm GPU CUDA technology stochastic collection equation numerical modeling
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- 2.Kogan, Y., Mazin, I.P., Sergeev, B.N., Khvorostyanov, V.I.: Numerical cloud modeling, p. 183. Gidrometeoizdat, Moscow (1984)Google Scholar
- 3.Pruppacher, H.R., Klett, J.D.: Microphysics of Clouds and Precipitation, p. 954. Kluwer Academic (1997)Google Scholar
- 7.Stankova, E.N., Zatevakhin, M.A.: Modified Kovetz and Olund method for the numerical solution of stochastic coalescence equation. In: Proceedings 12th International Conference on Clouds and Precipitation, Zurich, August 19-23, pp. 921–923 (1996)Google Scholar
- 9.Raba, N.O., Stankova, E.N.: On the effectiveness of using the GPU for numerical solution of stochastic collection equation. In: Murgante, B., Misra, S., Carlini, M., Torre, C.M., Nguyen, H.-Q., Taniar, D., Apduhan, B.O., Gervasi, O. (eds.) ICCSA 2013, Part V. LNCS, vol. 7975, pp. 248–258. Springer, Heidelberg (2013)CrossRefGoogle Scholar
- 10.Raba, N.: Optimization algorithms for the calculation of physical processes in the cloud model with detailed microphysics. In: Raba, N. (ed.) Applied Mathematics. Informatics. Control Processes, West. SPSU. Ser. 10, vol. 3, pp. 121–126 (2010) (In Russian)Google Scholar
- 11.Raba, N.: Development and implementation of the algorithm for calculating the coagulation in a cloud model with mixed phase using CUDA technology. In: Applied Mathematics. Informatics. Control Processes, Bulletin of St. Petersburg State University. Series 10, vol. 4, pp. 94–104 (2011) (In Russian)Google Scholar
- 12.Sanders, J., Kandrot, E.: CUDA by Example: An Introduction to General-Purpose GPU Programming, p. 312. Addison-Wesley Professional (2010) ISBN-13: 978-0131387683Google Scholar
- 13.Luebke, D., Harris, M., Krüger, J., Purcell, T., Govindaraju, N., Buck, I., Woolley, C., Lefohn, A.: GPGPU: general purpose computation on graphics hardware. In: ACM SIGGRAPH 2004 Course Notes, Los Angeles, CA, August 08-12, p. 33 (2004), doi:10.1145/1103900.1103933Google Scholar
- 14.Buck, I., Fatahalian, K., Hanrahan, P.: GPUbench: evaluating GPU performance for numerical and scientific applications. In: Poster Session at GP2 Workshop on General Purpose Computing on Graphics Processors (2004), http://gpubench.sourceforge.net
- 15.Gaster, B., et al.: Heterogeneous Computing with OpenCL, p. 296. Morgan Kaufmann, Waltham (2011) ISBN 978-0-12-387766-6Google Scholar
- 16.Banger, R., Bhattacharyya, K.: OpenCL Programming by Example, p. 304. Packt Publishing (2013) ISBN: 1849692343, ISBN 13: 9781849692342Google Scholar