# Parallel Implementation of a Large-Scale 3-D Air Pollution Model

## Abstract

Air pollution models can efficiently be used in different environmental studies. The atmosphere is the most dynamic component of the environment, where the pollutants can be transported over very long distances. Therefore the models must be defined on a large space domain. Moreover, all relevant physical and chemical processes must be adequately described. This leads to huge computational tasks. That is why it is difficult to handle numerically such models even on the most powerful up-to-date supercomputers.

The particular model used in this study is the Danish Eulerian Model. The numerical methods used in the advection-diffusion part of this model consist of finite elements (for discretizing the spatial derivatives) followed by predictor-corrector schemes with several different correctors (in the numerical treatment of the resulting systems of ordinary differential equations). Implicit methods for the solution of stiff systems of ordinary differential equations are used in the chemistry part. This implies the use of Newton-like iterative methods. A special sparse matrix technique is applied in order to increase the efficiency. The model is constantly updated with new faster and more accurate numerical methods. The three-dimensional version of the Danish Eulerian Model is presented in this work. The model is defined on a space domain of 4800 km x 4800 km that covers the whole of Europe together with parts of Asia, Africa and the Atlantic Ocean. A chemical scheme with 35 species is used in this version. Two parallel implementations are discussed; the first one for shared memory parallel computers, the second one - the newly developed version for distributed memory computers. Standard tools are used to achieve parallelism: OpenMP for shared memory computers and MPI for distributed memory computers. Results from many experiments, which were carried out on a SUN SMP cluster and on a CRAY T3E at the Edinburgh Parallel Computer Centre (EPCC), are presented and analyzed.

## Keywords

air pollution model system of PDE’s parallel algorithm shared memory computer distributed memory computer OpenMP MPI## Preview

Unable to display preview. Download preview PDF.

## References

- 1.V. Alexandrov, A. Sameh, Y. Siddique, and Z. Zlatev. Numerical integration of chemical ODE problems arising in air pollution models,
*Env. Modeling and Assessment*, 2, 365–377, 1997.CrossRefGoogle Scholar - 2.C. Ambelas Skjøth, A. Bastrup-Birk, J. Brandt, and Z. Zlatev. Studying variations of pollution levels in a given region of Europe during a long time-period,
*Systems Analysis Modeling Simulation*, 37, 297–311, 2000.Google Scholar - 3.A. Bastrup-Birk, J. Brandt, I. Uria, and Z. Zlatev. Studying cumulative ozone exposures in Europe during a 7-year period,
*J. Geophysical Research*, 102, 23917–23935, 1997.CrossRefGoogle Scholar - 4.A. Bastrup-Birk, J. Brandt and Z. Zlatev. Using partitioned ODE solvers in large air pollution models,
*Systems Analysis Modeling Simulation*, 32, 3–17, 1998.MATHGoogle Scholar - 5.K. Georgiev and Z. Zlatev. Parallel sparse matrix algorithms for air pollution models,
*Parallel and Distributed Computing Practices*, (to appear).Google Scholar - 6.W. Gropp, E. Lusk, and A. Skjellum.
*Using MPI: Portable Programming with the Message Passing Interface*, MIT Press, Cambridge, Massachusetts, 1994.Google Scholar - 7.R. M. Harrison, Z. Zlatev, and C. J. Ottley. A comparison of the predictions of an Eulerian atmospheric transport chemistry model with experimental measurements over the North Sea,
*Atmospheric Environment*, 28, 497–516, 1994.CrossRefGoogle Scholar - 8.E. Hesstvedt, ø. Hov, and I. A. Isaksen. Quasi-steady-state approximations in air pollution modeling: comparison of two numerical schemes for oxidant prediction.
*Int. Journal of Chemical Kinetics*, 10, 971–994, 1978.CrossRefGoogle Scholar - 9.ø. Hov, Z. Zlatev, R. Berkowicz, A. Eliassen and L. P. Prahm. Comparison of numerical techniques for use in air pollution models with non-linear chemical reactions,
*Atmospheric Environment*, 23, 967–983, 1988.Google Scholar - 10.G. I. Marchuk. Mathematical modeling for the problem of the environment,
*Studies in Mathematics and Applications*, North-Holland, Amsterdam, 16, 1985.Google Scholar - 11.G. J. McRae, W. R. Goodin, and J. H. Seinfeld. Numerical solution of the atmospheric diffusion equations for chemically reacting flows,
*J. Comp. Physics*, 45, 1–42, 1984.CrossRefMathSciNetGoogle Scholar - 12.Tz. Ostromsky and Z. Zlatev. Application of sparse matrix techniques in the chemical part of a large air pollution model,
*NNFM*, 62, 189–197, 1998.Google Scholar - 13.WEB-site for OPEN MP tools, http://www.openmp.org
- 14.WEB-site of the Danish Eulerian Model, http://www.dmu.dk/AtmosphericEnvironment/DEM
- 15.Z. Zlatev. Application of predictor-corrector schemes with several correctors in solving air pollution problems,
*BIT*, 24, 700–715, 1984.MATHCrossRefMathSciNetGoogle Scholar - 16.Z. Zlatev. C
*omputer Treatment of Large Air Pollution Models*, Kluwer, 1995.Google Scholar - 17.Z. Zlatev, J. Christensen, and A. Eliassen. Studying high ozone concentrations by using the Danish Eulerian model,
*Atmos. Environment*, 27A, 845–865, 1993.Google Scholar - 18.Z. Zlatev, J. Christensen, and ø. Hov. An Eulerian air pollution model for Europe with non-linear chemistry.
*Journal of Atmospheric Chemistry*, 15, 1–37, 1992.CrossRefGoogle Scholar - 19.Z. Zlatev, I. Dimov, and K. Georgiev. Studying long-range transport of air pollutants,
*Computational Science and Engineering*, 1, 45–52, 1994.CrossRefGoogle Scholar - 20.Z. Zlatev, I. Dimov, and K. Georgiev. Three-dimensional version of the Danish Eulerian Model,
*Zeitschrift für Angewandte Mathematik und Mechanik*, 76, 473–476, 1996.MATHGoogle Scholar - 21.Z. Zlatev, I. Dimov, Tz. Ostromsky, G. Geernaert, I. Tzvetanov, and A. Bastrup-Birk. Calculating losses of crops in Denmark caused by high ozone levels,
*Env. Modeling and Assessment*, (to appear).Google Scholar - 22.Z. Zlatev, J. Fenger, and L. Mortensen. Relationships between emission sources and excess ozone concentrations,
*Computers and Math. with Appl.*, 32, 101–123, 1996.MATHCrossRefGoogle Scholar - 23.Z. Zlatev, G. Geernaert, and H. Skov. A Study of ozone critical levels in Denmark,
*EUROSAP Newsletter*, 36, 1–9, 1999.Google Scholar