Vol. 31, issue 01, article # 8

Аntokhin P.N., Penenko A.V., Antokhina O.Yu. The algorithm for reconstructing the vertical distribution of sources and sinks of a substance in the atmospheric boundary laye. // Optika Atmosfery i Okeana. 2018. V. 31. No. 01. P. 49–56 [in Russian].
Copy the reference to clipboard
Abstract:

An algorithm is suggested for solution of the inverse problem of retrieving the vertical distribution of sources and sinks of a substance (ozone) using a finite number of vertical profiles of its concentration. The inverse problem is solved for the pollutant transport model. Missing information on the time dynamics of the source (sink) is compensated by applying a method based on the Tikhonov regularization. The regularization parameter is found from the solution of the auxiliary inverse problem with the parametric specification of an unknown source. The algorithm developed is tested on both synthetic data and real aircraft measurements. In numerical experiments with real data, the vertical distribution of an ozone source (sinks) in the atmospheric boundary layer and lower troposphere was retrieved.

Keywords:

ozone generation, airborne sensing data, inverse source problem, variational approach, Tikhonov regularization

References:

    1.    Badia A.El., Ha-Duong T., Hamdi A. Identification of a point source in a linear advection-dispersion-reaction equation: Application to a pollution source problem // Inverse Probl. 2005. V. 21, N 3. P. 1121–1136.
   2. Marchuk G.I. Matematicheskoe modelirovanie v probleme okruzhajushhej sredy. M.: Nauka, 1982. 320 p.
   3. Penenko V.V. Metody chislennogo modelirovanija atmosfernyh processov. L.: Gidrometeoizdat, 1981. 352 p.
   4. Pudykiewicz J.A. Application of adjoint tracer transport equation for evaluating source parameters // Atmos. Environ. 1998. V. 32, N 17. P. 3039–3050.
   5. Penenko V., Baklanov A., Tsvetova E. Methods of sensitivity theory and inverse modeling for estimation of source parameters // Fut. Gener. Comput. Syst. 2002. V. 18, iss. 5. P. 661–671.
   6. Issartel J.P. Rebuilding source of linear tracers after atmospheric concentration measurements // Atmos. Chem. Phys. Discuss. 2003. V. 3, iss. 6. P. 3173–3203. DOI: 10.5194/acp-3-2111-296 2003.
   7. Alifanov O.M., Artjuhin E.A., Rumjancev S.V. Jekstremal'nye metody reshenija nekorrektnyh zadach. M.: Nauka, 1988. 288 p.
   8. Vasil'ev F.P. Metody reshenija jekstremal'nyh zadach. Zadachi minimizacii v funkcional'nyh prostranstvah, reguljarizacija, approksimacija. M.: Nauka, 1981. 400 p.
   9. Seinfeld J.H., Pandis S.N. Atmospheric chemistry and physics. New-York: John Wiley & Sons, 2006. 1203 p.
10. Ladyzhenskaja O.A., Solonnikov V.A., Ural'ceva N.N. Linejnye i kvazilinejnye uravnenija parabolicheskogo tipa. M.: Nauka, 1967. 736 p.
11. Hasanov A. Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solution approach // J. Math. Anal. Appl. 2006. V. 333, iss. 2. P. 766–779. DOI: 10.1016/j.jmaa.2006.08.018.
12. Kamynin V.L. Ob odnoznachnoj razreshimosti obratnoj zadachi dlja parabolicheskih uravnenij s usloviem final'nogo pereopredelenija // Matem. zametki. 2003. V. 23, N 2. P. 217–227.
13. Prilepko A.I., Kostin A.B. O nekotoryh obratnyh zadachah dlja parabolicheskih uravnenij s final'nym i integral'nym nabljudeniem // Matem. sb. 1992. V. 183, N 4. P. 49–68.
14. Prilepko A.I., Solov'ev V.V. Teoremy razreshimosti i metod Rotje v obratnyh zadachah dlja uravnenija parabolicheskogo tipa. II // Differenc. uravnenija. 1987. V. 23, N 11. P. 1971–1980.
15. Kostin A.B. Counterexamples in inverse problems for parabolic, elliptic, and hyperbolic equations // Comput. Math. Math. Phys. 2014. V. 54, iss. 5. P. 797–810.
16. Pyatkov S.G., Safonov E.I. Some inverse problems for convection-diffusion equations // Вестн. ЮУрГУ. Сер. Матем. моделирование и программирование. 2014. V. 7, N 4. P. 36–50. http://dx.doi.org/10.14529/mmp140403.
17. Hasanov A. Identification of spacewise and time dependent source terms in 1D heat conduction equation from temperature measurement at a final time // Int. J. Heat Mass Transfer. 2012. V. 55, iss. 7–8. P. 2069–2080. DOI: 10.1016/j.ijheatmasstransfer.2011.12.009.
18. Samarskij A.A. Vvedenie v teoriju raznostnyh shem. M.: Nauka, 1971. 553 p.
19. GNU Scientific Library Reference Manual Edition 2.2.1, for GSL Version 2.2.1. [Electronic resource]. URL: https://www.gnu.org/software/gsl/manual/html_node/ (last access: 25.10.2016).
20. Antohin P.N., Arshinov M.Ju., Belan B.D., Belan S.B., Davydov D.K., Kozlov A.V., Krasnov O.A., Pestunov D.A., Praslova O.V., Fofonov A.V., Inoue G., Machida T., Maksutov Sh.Sh., Shimoyama K., Sutoh H. Primenenie samoleta An-2 dlja issledovanija sostava vozduha v pogranichnom sloe atmosfery // Optika atmosf. i okeana. 2012. V. 25, N 8. P. 714–720.
21. Skamarock W.C., Klemp J.B., Dudhia J., Gill D.O., Barker D.M., Wang W., Powers J.G. A description of the Advanced Research WRF version 3 [Electronic resource] // NCAR Tech. Note. NCAR/TN-475+STR. 2008. 113 p. URL: http://www2.mmm.ucar.edu/wrf/users/docs/user_guide_V3.5/ARWUsersGuideV3.pdf (last access: 20.01.2017).
22. Troen I., Mahrt L. A simple model of the atmospheric boundary layer; sensitivity to surface evaporation // Bound.-Lay. Meteorol. 1986. V. 37. P. 129–148.
23. Antohin P.N., Arshinova V.G., Arshinov M.Ju., Belan B.D., Belan S.B., Davydov D.K., Kozlov A.V., Krasnov O.A., Praslova O.V., Rasskazchikova T.M., Savkin D.E., Tolmachev G.N., Fofonov A.V. Sutochnaja dinamika vertikal'nogo raspredelenija ozona v pogranichnom sloe atmosfery v rajone Tomska // Optika atmosf. i okeana. 2013. V. 26, N 8. P. 665–672.

Back