Optimal forecasting of natural processes with uncertainty assessment



The problem of optimal forecasting of environmental changes induced by various factors is discussed. The proposed technique is based on variational principles and methods of the sensitivity theory with allowance for uncertainties in mathematical models and input data. Optimal forecasting is understood as forecasting where the estimates of cost functionals are independent of variations of the sought state functions. In addition to state functions, the forecasted characteristics include risk and vulnerability functions for receptor areas and quantification of uncertainties.

Key words

optimal forecasting mathematical modeling quality of environment sensitivity analysis uncertainty assessment convection diffusion and reaction equations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. I. Marchuk, Adjoint Equations and Analysis of Complex Systems [in Russian], Nauka, Moscow (1992).Google Scholar
  2. 2.
    R. Buizza and A. Montani, “Targeting observations using singular vectors,” J. Atmosph. Sci., 56, No. 17, 2965–2985 (1999).CrossRefGoogle Scholar
  3. 3.
    D. N. Daescu and G. R. Carmichael, “An adjoint sensitivity method for the adaptive location of the observations in air quality modelling,” J. Atmosph. Sci., 60, No. 2, 434–450 (2003).CrossRefADSGoogle Scholar
  4. 4.
    M. Ehrendorfer and J. J. Tribbia, “Optimal prediction of forecast error covariances through singular vectors,” J. Atmosph. Sci., 54, No. 2, 286–313 (1997).CrossRefADSGoogle Scholar
  5. 5.
    R. Gelaro, R. Buizza, T. N. Palmer, and E. Klinker, “Sensitivity analysis of forecast errors and the construction of optimal perturbations using singular vectors,” J. Atmosph. Sci., 55, No. 6, 1012–1037 (1998).CrossRefADSGoogle Scholar
  6. 6.
    H. M. Kim, M. C. Morgan, and E. Morss, “Evolution of analysis error and adjoint-based sensitivities: Implications for adaptive observations,” J. Atmosph. Sci., 61, No. 7, 795–812 (2004).CrossRefADSGoogle Scholar
  7. 7.
    Z. Toth and E. Kalnay, “Ensemble forecasting at NMC: The generation of perturbations,” Bull. Amer. Meteor. Soc., 74, No. 12, 2317–2330 (1993).CrossRefGoogle Scholar
  8. 8.
    A. Ebel and T. Davitashvily (eds.), Air, Water and Soil Quality Modelling for Risk and Impact Assessment, Springer, Dordrecht (2007).Google Scholar
  9. 9.
    V. V. Penenko and N. N. Obraztsov, “A variational initialization method for the correlation of fields of meteorological elements,” Meteorologiya Gidrologiya, No. 11, 1–11 (1976).Google Scholar
  10. 10.
    V. V. Penenko, Methods of Numerical Simulation of Atmospheric Processes [in Russian], Gidrometeoizdat, Leningrad (1981).Google Scholar
  11. 11.
    V. Penenko, “Some aspects of mathematical modelling using the models together with observational data,” Bull. Novosib. Comp. Center, Ser. Numer. Model in Atmosphere, Ocean Environment. Studies, 4, 31–52 (1996).MATHGoogle Scholar
  12. 12.
    V. V. Penenko and E. A. Tsvetova, “Structure of a set of models for studying interactions in the Baikal Lake — region atmosphere system,” Atmos. Okeanic Opt., 11, No. 6, 586–593 (1998).Google Scholar
  13. 13.
    V. V. Penenko, “Variational data assimilation in real time,” Vychisl. Tekhnol., 10, No. 8, 9–20 (2005).MATHGoogle Scholar
  14. 14.
    V. V. Penenko and E. A. Tsvetova, “Mathematical models for studying environmental pollution risks,” J. Appl. Mech. Tech. Phys., 45, No. 2, 260–268 (2004).CrossRefADSGoogle Scholar
  15. 15.
    V. V. Penenko and E. A. Tsvetova, “Mathematical models of environmental forecasting,” J. Appl. Mech. Tech. Phys., 48, No. 3, 428–436 (2007).CrossRefADSGoogle Scholar
  16. 16.
    V. Penenko and E. Tsvetova, “Orthogonal decomposition methods for inclusion of climatic data into environmental studies,” Ecol. Model., 217, 279–291 (2008).CrossRefGoogle Scholar
  17. 17.
    V. Penenko and E. Tsvetova, “Discrete-analytical methods for the implementation of variational principles in environmental applications,” J. Comput. Appl. Math. (2008); http://dx.doi.org/10.1016/j.cam.2008.08.018.
  18. 18.
    L. Schwartz, Analyse Mathematique, Hermann (1967).Google Scholar
  19. 19.
    A. A. Samarskii and P. N. Vabishchevich, Additive Schemes for Problems of Mathematical Physics [in Russian], Nauka, Moscow (2001).Google Scholar
  20. 20.
    S.-J. Chen, Y.-H. Kuo, P.-Z. Zhang, and Q.-F. Bai, “Synoptic climatology of ciclogenesis over East Asia, 1958–1987,” Mon. Weather Rev., 119, No. 6, 1407–1418 (1991).CrossRefADSGoogle Scholar
  21. 21.
    E. Kalney, M. Kanamitsu, R. Kistler, et al., “The NCEP/NCAR 40-year reanalysis project,” Bull. Amer. Meteorol. Soc., 77, 437–471 (1996).CrossRefADSGoogle Scholar

Copyright information

© MAIK/Nauka 2009

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics, Siberian DivisionRussian Academy of SciencesNovosibirskRussia

Personalised recommendations