Abstract
Large-scale models are mathematical models with a lot of natural uncertainties in their input data sets and parameters. Sensitivity analysis (SA) is a powerful tool for studying the impact of these uncertainties on the output results and helps to improve the reliability of these models. In this article we present some results of a global sensitivity study of the Unified Danish Eulerian Model (UNI-DEM). A large number of heavy numerical experiments must be carried out in order to collect the necessary data for such comprehensive sensitivity study. One of the largest supercomputers in Europe and the most powerful in Bulgaria, the petascale EuroHPC supercomputer Discoverer is used to perform efficiently this huge amount of computations.
One of the most important features of UNI-DEM is its advanced chemical scheme, called Condensed CBM IV, which considers a large number of chemical species and all significant reactions between them. The ozone is one of the most harmful pollutants, that is why it is important for many practical applications to study it precisely. Stochastic methods based on Adaptive approach and Sobol sequences are used for computing the corresponding sensitivity measures. We show by experiments that the stochastic algorithms for calculating the multidimensional integrals under consideration are one of the best stochastic techniques for computing the small in value sensitivity indices.
The presented work was supported by the Bulgarian National Science Fund under the Bilateral Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications” and by the Bulgarian National Science Fund under Project KP-06-N52/5 “Efficient methods for modeling, optimization and decision making”.
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
Dimov, I.T.: Monte Carlo Methods for Applied Scientists. World Scientific, London, Singapore (2008)
Dimov, I., Georgieva, R.: Monte Carlo method for numerical integration based on Sobol’s sequences. In: Dimov, I., Dimova, S., Kolkovska, N. (eds.) Monte Carlo method for numerical integration based on Sobol’ sequences,. LNCS, vol. 6046, pp. 50–59. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-18466-6_5
Dimov, I.T., Georgieva, R., Ivanovska, S., Ostromsky, T., Zlatev, Z.: Studying the sensitivity of pollutants’ concentrations caused by variations of chemical rates. J. Comput. Appl. Math. 235, 391–402 (2010)
Dimov, I., Georgieva, R., Ostromsky, T., Zlatev, Z.: Variance-based sensitivity analysis of the unified Danish Eulerian model according to variations of chemical rates. In: Dimov, I., 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
Dimov, I.T., Georgieva, R., Ostromsky, T., Zlatev, Z.: Advanced algorithms for multidimensional sensitivity studies of large-scale air pollution models based on Sobol sequences. Spec. Issue Comput. Math. Appl. 65(3), 338–351 (2013)
Joe, S., Kuo, F.: Constructing Sobol’ sequences with better two-dimensional projections. SIAM J. Sci. Comput. 30, 2635–2654 (2008)
Kuo, F.Y., Nuyens, D.: Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients–a survey of analysis and implementation. Found. Comput. Math. 16, 1631–1696 (2016)
Nuyens, D., Cools, R.: Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces. Math. Comp. 75, 903–920 (2006)
Ostromsky, T., 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)
Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M.: Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. Halsted Press, New York (2004)
Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55(1–3), 271–280 (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)
Zlatev, Z., Dimov, I.T., Georgiev, K.: Modeling the long-range transport of air pollutants. IEEE Comput. Sci. Eng. 1(3), 45–52 (1994)
Zlatev, Z., Dimov, I.T., Georgiev, K.: Three-dimensional version of the Danish Eulerian model. Z. Angew. Math. Mech. 76(S4), 473–476 (1996)
Acknowledgements
The presented work was supported by the Bulgarian National Science Fund under the Bilateral Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications” and by the Bulgarian National Science Fund under Project KP-06-N52/5 “Efficient methods for modeling, optimization and decision making”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Ostromsky, T., Todorov, V., Dimov, I., Georgieva, R. (2023). Sensitivity Analysis of an Air Pollution Model with Using Innovative Monte Carlo Methods in Calculating Multidimensional Integrals. In: Georgiev, I., Datcheva, M., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2022. Lecture Notes in Computer Science, vol 13858. Springer, Cham. https://doi.org/10.1007/978-3-031-32412-3_23
Download citation
DOI: https://doi.org/10.1007/978-3-031-32412-3_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-32411-6
Online ISBN: 978-3-031-32412-3
eBook Packages: Computer ScienceComputer Science (R0)