Abstract
Sensitivity analysis is a powerful tool for studying and improving the reliability of large and complicated mathematical models. Air pollution and meteorological models are in front places among the examples of such models, with a lot of natural uncertainties in their input data sets and parameters. We present here some results of our global sensitivity study of the Unified Danish Eulerian Model (UNI-DEM). One of the most attractive features of UNI-DEM is its advanced chemical scheme – the Condensed CBM IV, which consider in detail a large number of chemical species and numerous reactions between them.
Four efficient stochastic algorithms (Sobol QMC, Halton QMC, Fibonacci lattice rule and Latin hypercube sampling) have been used and compared by their accuracy in studying the sensitivity of ammonia and ozone concentration results with respect to the emission levels and some chemical reactions rates. The numerical experiments show that the stochastic algorithms under consideration are quite efficient for this purpose, especially for evaluating the contribution of small by value sensitivity indices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Antonov, I., Saleev, V.: An economic method of computing \(LP_{\tau }\)-sequences. USSR Comput. Math. Phy. 19, 252–256 (1979)
Bratley, P., Fox, B.: Algorithm 659: implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Softw. 14(1), 88–100 (1988)
Dimitrov, S., Dimov, I., Todorov, V.: Latin hypercube sampling and fibonacci based lattice method comparison for computation of multidimensional integrals. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) NAA 2016. Lecture Notes in Computer Science, vol. 10187, pp. 296–303. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57099-0_32
Dimov, I., Georgieva, R., Ostromsky, Tz, Zlatev, Z.: Variance-based sensitivity analysis of the unified danish eulerian model according to variations of chemical rates. In: Dimov, I.T., Faragó, I., Vulkov, L. (eds.) NAA 2012. LNCS, vol. 8236, pp. 247–254. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41515-9_26
Dimov, I.T., Georgieva, R., Ostromsky, T., Zlatev, Z.: Sensitivity studies of pollutant concentrations calculated by UNI-DEM with respect to the input emissions. Centr. Eur. J. Math. 11(8), 1531–1545 (2013). https://doi.org/10.2478/s11533-013-0256-2. Numerical Methods for Large Scale Scientific Computing
Dimov, I.T., Georgieva, R., Todorov, V., Ostromsky, Tz.: Efficient stochastic approaches for sensitivity studies of an Eulerian large-scale air pollution model. In: AIP Conference Proceedings, vol. 1895, no. 1, p. 050004 (2017). https://doi.org/10.1063/1.5007376
Fox, B.: Algorithm 647: implementation and relative efficiency of quasirandom sequence generators. ACM Trans. Math. Softw. 12(4), 362–376 (1986)
Halton, J.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960)
Halton, J., Smith, G.B.: Algorithm 247: radical-inverse quasi-random point sequence. Commun. ACM 7, 701–702 (1964)
Homma, T., Saltelli, A.: Importance measures in global sensitivity analysis of nonlinear models. Reliab. Eng. Syst. Saf. 52, 1–17 (1996)
Ostromsky, T.z., Dimov, I.T., Georgieva, R., Zlatev, Z.: Air pollution modelling, sensitivity analysis and parallel implementation. Int. J. Environ. Pollut. 46(1/2), 83–96 (2011)
Ostromsky, T.z., Dimov, I., Georgieva, R., Zlatev, Z.: Parallel computation of sensitivity analysis data for the Danish Eulerian model. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2011. LNCS, vol. 7116, pp. 307–315. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29843-1_35
Ostromsky, T.z., Dimov, I.T., Marinov, P., Georgieva, R., Zlatev, Z.: Advanced sensitivity analysis of the Danish Eulerian Model in parallel and grid environment. In: Proceedings of 3rd International Conference on AIP, AMiTaNS 2011, vol. 1404, pp. 225–232 (2011)
Sobol, I.M., Tarantola, S., Gatelli, D., Kucherenko, S., Mauntz, W.: Estimating the approximation error when fixing unessential factors in global sensitivity analysis. Reliab. Eng. Syst. Saf. 92, 957–960 (2001)
Zlatev, Z.: Computer Treatment of Large Air Pollution Models. KLUWER Academic Publishers, Dorsrecht-Boston-London (1995)
Zlatev, Z., Dimov, I.T.: Computational and Numerical Challenges in Environmental Modelling. Elsevier, Amsterdam (2006)
Acknowledgements
The authors would like to thank Rayna Georgieva for her help. This work is supported by the Bulgarian Academy of Sciences through the Program for Career Development of Young Scientists, Grant DFNP-17-88 /28.07.2017; as well as by the Bulgarian NSF under Projects DN 12/4 -2017 and DN 12/5 -2017.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Ostromsky, T., Dimov, I., Todorov, V., Zlatev, Z. (2019). Sensitivity Analysis of an Air Pollution Model by Using Quasi-Monte Carlo Algorithms for Multidimensional Numerical Integration. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science(), vol 11189. Springer, Cham. https://doi.org/10.1007/978-3-030-10692-8_31
Download citation
DOI: https://doi.org/10.1007/978-3-030-10692-8_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10691-1
Online ISBN: 978-3-030-10692-8
eBook Packages: Computer ScienceComputer Science (R0)