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Air Quality Assessment And Control Of Emission Rates

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Abstract

Mathematical methods based on the adjoint model approach are given for the air-pollution estimation and control in an urban region. A simple advection–diffusion-reaction model and its adjoint are used to illustrate the application of the methods. Dual pollution concentration estimates in ecologically important zones are derived and used to develop two non-optimal strategies and one optimal strategy for controlling the emission rates of enterprises. A linear convex combination of these strategies represents a new sufficient strategy. A method for detecting the enterprises, which violate the emission rates prescribed by a control, is given. A method for determining an optimal position for a new enterprise in the region is also described.

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References

  • Cacuci, D.G.: 1981, ‘Sensitivity theory for nonlinear systems. Part I. Nonlinear functional analysis approach’, J. Math. Phys. 22, 2794–2802. Part II. Extensions to additional classes of responses, Ibid, 2803–2812.

  • Cacuci, D.G., Wever, C.F., Oblow, E.M. and Marable, J.H.: 1980, ‘Sensitivity theory for general systems of nonlinear equations’, Nuclear Sci. Eng. 75, 88–110.

    CAS  Google Scholar 

  • Flagan, R.C. and Seinfeld, J.H.: 1988, Fundamentals of Air Pollution Engineering, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Giering, R.: 2000, ‘Tangent linear and adjoint biogeochemical models’, in: Inverse Methods in Global Biogeochemical Cycles, AGU Geophysical Monograph 114.

  • Godunov, S.K.: 1971, Equations of Mathematical Physics, Nauka, Moscow (in Russian).

    Google Scholar 

  • Hall, M.C.G.: 1986, ‘Application of adjoint sensitivity theory to an atmospheric general circulation model’, J. Atmos. Sci. 42, 2644–2651.

    Google Scholar 

  • Hall, M.C.G. and Cacuci, D.G.: 1983, ‘Physical interpretation of the adjoint functions for sensitivity analysis of atmospheric models’, J. Atmos. Sci. 40, 2537–2546.

    Article  Google Scholar 

  • Issartel, J.-P. and Baverel, J.: 2003, ‘Inverse transport for the verification of the Comprehensive Nuclear Test Ban Treaty’, Atmos. Chem. Phys. 3, 475–486.

    CAS  Google Scholar 

  • Kovgar, V.: 1996, ‘The Verification of Air Pollution Episodes in Industrial Regions’, Technical Report, WP-96–121, International Institute for Applied Systems Analysis (IIASA), Laxen-burg, Austria, 24 pp.

  • Lewins, J.: 1965, Importance, the Adjoint Function, Pergamon Press.

  • Lewis, J. and Derber, J.C.: 1985, ‘The use of adjoint equations to solve a variational adjustment problem with advective constraints’, Tellus 37A, 309–322.

    Google Scholar 

  • Luenberger, G.D.: 1989, Linear and Nonlinear Programming, Addison-Wesley, Reading.

    Google Scholar 

  • Marchuk, G.I.: 1974, Numerical Solutions of the Problem of the Dynamics of the Atmosphere and the Ocean, Gigrometeoizadat, Leningrad (in Russian).

    Google Scholar 

  • Marchuk, G.I.: 1982, ‘Mathematical issue of industrial effluent optimization’, J. Meteorol. Soc. Jpn. 60, 481–485.

    CAS  Google Scholar 

  • Marchuk, G.I.: 1986, Mathematical Models in Environmental Problems, Elsevier, New York.

    Google Scholar 

  • Marchuk, G.I.: 1995, Adjoint Equations and Analysis of Complex Systems, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Marchuk, G.I. and Orlov, V.V.: 1961, ‘On the theory of adjoint functions’, in: Neutron Physics, Gosatomizdat, Moscow, pp. 30–45 (in Russian).

  • Marchuk, G.I. and Skiba, Yu.N.: 1976, ‘Numerical calculation of the conjugate problem for a model of the thermal interaction of the atmosphere with the oceans and continents’, Izvestiya, Atmos. Ocean. Phys. 12, 279–284.

    Google Scholar 

  • Marchuk, G.I., Kuzin, V.I. and Skiba, Yu.N.: 1983, ‘Projection-difference method for calculating the adjoint functions for a model of heat transfer in the atmosphere-ocean-soil system’, in: Actual Problems of Numeric and Applied Mathematics, Nauka, Novosibirsk, pp. 149–154.

  • Marchuk, G.I., Skiba, Yu.N. and Protsenko, I.G.: 1985a, ‘Method of calculating the evolution of random hydrodynamic fields on the basis of adjoint equations’, Izvestiya, Atmos. Ocean. Phys. 21, 87–92.

    Google Scholar 

  • Marchuk, G.I., Skiba, Yu.N. and Protsenko, I.G.: 1985b, ‘Application of adjoint equations to problems of estimating the state of random hydrodynamic fields, Izvestiya, Atmos. Ocean. Phys. 21, 175–180.

  • Marchuk, G.I. and Skiba, Yu.N.: 1990, ‘Role of adjoint functions in studying the sensitivity of a model of the thermal interaction of the atmosphere and ocean to variations in input data’, Izvestiya, Atmos. Ocean. Phys. 26, 335–342.

    Google Scholar 

  • Marchuk, G.I., Agoshkov, V.I. and Shutyaev, V.P.: 1996, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems, CRC Press, Boca Raton.

    Google Scholar 

  • Parra-Guevara, D.: 2001, ‘Modelación Matemática y Simulación Numérica en el Control de Emisiones Industriales’, Ph.D. Thesis, Centro de Ciencias de la Atmósfera, UNAM, México, 130 pp.

  • Parra-Guevara, D. and Skiba, Yu.N.: 2000, ‘Industrial pollution transport. Part II. Control of industrial emissions’, Environ. Model. Assess. 5, 177–184.

    Google Scholar 

  • Parra-Guevara, D. and Skiba, Yu.N.: 2003, ‘Elements of the matematical modelling in the control of pollutants emissions’, Ecol. Model. 167, 263–275.

    Article  CAS  Google Scholar 

  • Penenko, V.V.: 1975, ‘Computational aspects of modelling the atmospheric process dynamics and estimation of effects of various factors on the dynamics of the atmosphere’, in: Actual Problems of Numeric and Applied Mathematics, Nauka, Novosibirsk, pp. 61–77 (in Russian).

  • Penenko, V.V.: 1979, ‘Estimation of the parameters of discrete models of the dynamics of atmosphere and ocean’, Sov. Meteorol. Hydrol. 7, 57–68.

    Google Scholar 

  • Penenko, V.V. and Raputa, V.F.: 1983, ‘Some models for optimizing the operation of the atmospheric-pollution sources’, Sov. Meteorol. Hydrol. 2, 46–54.

    Google Scholar 

  • Penenko, V. and Baklanov, A.: 2001, ‘Methods of sensitivity theory and inverse modelling for estimation of source term and nuclear risk/vulnerability areas’, in: Lecture Notes in Computer Science, vol. 2074, Springer, pp. 57–66.

  • Pudykiewicz, J.: 1998, ‘Application of adjoint tracer transport equations for evaluating source parameters’, Atmos. Environ. 32, 3039–3050.

    CAS  Google Scholar 

  • Robertson, A.W.: 1992, ‘Diagnosis of regional monthly anomalies using the adjoint method. Part I. Temperature’, J. Atmos. Sci. 49, 885–905.

    Google Scholar 

  • Robertson, L. and Persson, C.: 1993, ‘Attempts to apply four-dimensional data assimilation of radiological data using the adjoint technique’, in: Radiation Protection Dosimetry, vol. 50, Nuclear Technology Publishing, pp. 333–337.

  • Seibert, P.: 2001, ‘Inverse modelling with a Lagrangian particle dispersion model: Application to point releases over limited time intervals’, in: Gryning and Schiermeier (eds.), Air Pollution Modeling and Its Application, vol. XIV, Kluwer Academic/Plenum Publishers, New York.

  • Shir, C.C. and Shich, L.J.: 1974, ‘A generalized urban air pollution model and its application to the study of SO2 distributions in the St. Louis Metropolitan Area’, J. Appl. Meteorol. 13, 185–204.

    Article  CAS  Google Scholar 

  • Shutyaev, V.P.: 1997, ‘Solvability of the data assimilation problem in the scale of Hilbert spaces for quasilinear singularly perturbed evolutionary problems’, Russ. J. Numer. Anal. Math. Model. 12, 53–66.

    Article  Google Scholar 

  • Skiba, Yu.N.: 1993, ‘Balanced and absolutely stable implicit schemes for the main and adjoint pollutant transport equations in limited area’, Rev. Intern. Contamin. Ambiental 9, 39–51.

    Google Scholar 

  • Skiba, Yu.N.: 1996, ‘Dual oil concentration estimates in ecologically sensitive zones’, Environ. Monit. Assess. 43, 139–151.

    Article  Google Scholar 

  • Skiba, Yu.N.: 1997, ‘Air pollution estimates’, World Resource Rev. 9, 542–556.

    Google Scholar 

  • Skiba, Yu.N.: 1999, ‘Direct and adjoint oil spill estimates’, Environ. Monit. Assess. 59, 95–109.

    Article  CAS  Google Scholar 

  • Skiba, Yu.N.: 2003, ‘On a method of detecting the industrial plants which violate prescribed emission rates’, Ecol. Model. 159, 125–132.

    Article  CAS  Google Scholar 

  • Skiba, Yu.N. and Davydova Belitskaya, V.: 2002, ‘Air pollution estimates in Guadalajara City’, Environ. Model. Assess. 7, 153–162.

    Google Scholar 

  • Skiba, Yu.N. and Davydova Belitskaya, V.: 2003, ‘On the estimation of impact of vehicular emissions’, Ecol. Model. 166, 169–184.

    Article  CAS  Google Scholar 

  • Skiba, Yu.N. and Parra-Guevara, D.: 2000, ‘Industrial pollution transport. Part I. Formulation of the problem and air pollution estimates’, Environ. Model. Assess. 5, 169–175.

    Google Scholar 

  • Talagrand, O. and Courtier, P.: 1987, ‘Variational assimilation of meteorological observations with the adjoint vorticity equation. I. Theory’, Quart. J. R. Meteor. Soc. 113, 1311–1328.

    Google Scholar 

  • Vautard, R., Beekmann, M. and Menut, L.: 2000, ‘Application of adjoint modelling in atmospheric chemistry: Sensitivity and inverse modelling’, Environ. Model. Software 15, 703–709.

    Google Scholar 

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Correspondence to Yuri N. Skiba.

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Skiba, Y.N., Parra-Guevara, D. & Belitskaya, D.V. Air Quality Assessment And Control Of Emission Rates. Environ Monit Assess 111, 89–112 (2005). https://doi.org/10.1007/s10661-005-8040-9

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