Atmospheric and Oceanic Optics

, Volume 31, Issue 6, pp 678–684 | Cite as

Numerical Investigation of the Direct Variational Algorithm of Data Assimilation in the Urban Scenario

  • A. V. PenenkoEmail author
  • Zh. S. Mukatova
  • V. V. Penenko
  • A. V. Gochakov
  • P. N. Antokhin
Optical Models and Databases


The performance of a direct variational data assimilation algorithm with quasi-independent data assimilation at individual steps of the splitting scheme has been studied in a realistic scenario of air pollution assessment in the city of Novosibirsk by monitoring system data. For operation under conditions of a sparse monitoring network, an algorithm with minimization of the spatial derivative of the uncertainty (control) function adjusted to data assimilation is proposed. The use of the spatial derivative minimization increases the smoothness of the uncertainty (control functions) reconstructed, which has a positive effect on the reconstruction quality in the scenario considered.


data assimilation variational approach splitting scheme smart city 


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  1. 1.
    Air Quality Guidelines Global Update 2005: Particulate Matter, Ozone, Nitrogen Dioxide and Sulfur Dioxide (A EURO Publication) (WHO, Regional Office for Europe, Denmark, Copenhagen, 2006).Google Scholar
  2. 2.
    V. V. Penenko, A. E. Aloyan, N. M. Bazhin, and G. I. Skubnevskaya, “Numerical model for hydrometeorological comditions and pollution of cities and industrial regions,” Meteorol. Gidrol., No. 4, 5–15 (1984).Google Scholar
  3. 3.
    M. Bocquet, H. Elbern, H. Eskes, M. Hirtl, R. Zabkar, G. R. Carmichael, J. Flemming, A. Inness, M. Pagowski, J. L. Perez Camano, P. E. Saide, JoseR. San, M. Sofiev, J. Vira, A. Baklanov, C. Carnevale, G. Grell, and C. Seigneur, “Data assimilation in atmospheric chemistry models: Current status and future prospects for coupled chemistry meteorology models,” Atmos. Chem. Phys. 14, 32233–32323 (2014).CrossRefGoogle Scholar
  4. 4.
    A. V. Penenko and V. V. Penenko, “Direct data assimilation method for convectiondiffusion models based on splitting scheme,” Vychisl. Tekhnol. 19 (4), 69–83 (2014).zbMATHGoogle Scholar
  5. 5.
    A. V. Penenko, V. V. Penenko, and E. A. Tsvetova, “Sequential data assimilation algorithms for air quality monitoring models based on a weak-constraint variational principle,” Numer. Anal. Appl. 9, 312–325 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    V. V. Penenko, A. V. Penenko, and E. A. Tsvetova, “Variational approach to the study of processes of geophysical hydro-thermodynamics with assimilation of observation data,” J. Appl. Mech. Tech. Phys. 58, 771–778 (2017).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    A. Penenko, V. Penenko, and Z. Mukatova, “Direct data assimilation algorithms for advection-diffusion models with the increased smoothness of the uncertainty functions,” in 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), September 18–22, 2017, Novosibirsk, p. 126–130.Google Scholar
  8. 8.
    V. V. Penenko, Numerical Simulation Techniques for Atmospheric Processes (Gidrometeoizdat, Leningrad, 1981) [in Russian].Google Scholar
  9. 9.
    G. I. Marchuk, Simulation in Environmental Problems (Nauka, Moscow, 1982) [in Russian].Google Scholar
  10. 10.
    V. V. Penenko and A. E. Aloyan, Models and Methods for Environmental Safety Problems (Nauka, Novosibirsk, 1985) [in Russian].Google Scholar
  11. 11.
    A. A. Samarskii, Introduction in the Theory of Difference Schemes (Nauka, Moscow, 1971) [in Russian].Google Scholar
  12. 12.
    D. G. Gordeziani and G. V. Meladze, “Somulation of the third boudary problems for multi-dimensional parabolic equations in an arbitrary region by onedimensional equations,” Zhurn. Vychisl. Matem. Matem. Fiz. 14, 246–250 (1974).Google Scholar
  13. 13.
    W. C. Skamarock, J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, M. G. Duda, X. Huang, W. Wang, and J. G. Powers, A Description of the Advanced Research WRF Version 3. NCAR/TN 475 + STR Technical Note, UCAR. January 19, 2018). doi 10.5065/D68S4MVHGoogle Scholar
  14. 14.
    Yandex Static API. January 19, 2018).Google Scholar
  15. 15.,55. 030199&spn=0.31457,0.15&l=trf (January 19, 2018).Google Scholar
  16. 16. pdf (January 19, 2018).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • A. V. Penenko
    • 1
    Email author
  • Zh. S. Mukatova
    • 1
  • V. V. Penenko
    • 1
  • A. V. Gochakov
    • 2
  • P. N. Antokhin
    • 3
  1. 1.Institute of Computational Mathematics and Mathematical Geophysics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Siberian Regional Hydrometeorological Research InstituteNovosibirskRussia
  3. 3.V.E. Zuev Institute of Atmospheric Optics, Siberian BranchRussian Academy of SciencesTomskRussia

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