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Optimal forecasting of natural processes with uncertainty assessment

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Abstract

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.

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References

  1. G. I. Marchuk, Adjoint Equations and Analysis of Complex Systems [in Russian], Nauka, Moscow (1992).

    Google Scholar 

  2. R. Buizza and A. Montani, “Targeting observations using singular vectors,” J. Atmosph. Sci., 56, No. 17, 2965–2985 (1999).

    Article  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  7. Z. Toth and E. Kalnay, “Ensemble forecasting at NMC: The generation of perturbations,” Bull. Amer. Meteor. Soc., 74, No. 12, 2317–2330 (1993).

    Article  Google Scholar 

  8. A. Ebel and T. Davitashvily (eds.), Air, Water and Soil Quality Modelling for Risk and Impact Assessment, Springer, Dordrecht (2007).

    Google Scholar 

  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).

  10. V. V. Penenko, Methods of Numerical Simulation of Atmospheric Processes [in Russian], Gidrometeoizdat, Leningrad (1981).

    Google Scholar 

  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).

    MATH  Google Scholar 

  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. V. V. Penenko, “Variational data assimilation in real time,” Vychisl. Tekhnol., 10, No. 8, 9–20 (2005).

    MATH  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  15. V. V. Penenko and E. A. Tsvetova, “Mathematical models of environmental forecasting,” J. Appl. Mech. Tech. Phys., 48, No. 3, 428–436 (2007).

    Article  ADS  Google Scholar 

  16. V. Penenko and E. Tsvetova, “Orthogonal decomposition methods for inclusion of climatic data into environmental studies,” Ecol. Model., 217, 279–291 (2008).

    Article  Google Scholar 

  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. L. Schwartz, Analyse Mathematique, Hermann (1967).

  19. A. A. Samarskii and P. N. Vabishchevich, Additive Schemes for Problems of Mathematical Physics [in Russian], Nauka, Moscow (2001).

    Google Scholar 

  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).

    Article  ADS  Google Scholar 

  21. E. Kalney, M. Kanamitsu, R. Kistler, et al., “The NCEP/NCAR 40-year reanalysis project,” Bull. Amer. Meteorol. Soc., 77, 437–471 (1996).

    Article  ADS  Google Scholar 

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Correspondence to V. V. Penenko.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 156–166, March–April, 2009.

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Penenko, V.V., Tsvetova, E.A. Optimal forecasting of natural processes with uncertainty assessment. J Appl Mech Tech Phy 50, 300–308 (2009). https://doi.org/10.1007/s10808-009-0041-y

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  • DOI: https://doi.org/10.1007/s10808-009-0041-y

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