Skip to main content
SpringerLink
Log in

Atmospheric constituent inversion problems: Implications for baseline monitoring

  • Published:
Journal of Atmospheric Chemistry Aims and scope Submit manuscript

Abstract

The importance of ill-posed inverse problems in atmospheric chemistry is reviewed. Most models for the determination of sources and sinks of atmospheric constitutents lead to such ill-posed inverse problems. Consequently, source determinations may be subject to severe amplification of observational error, particularly in the most rapidly varying components. Therefore, mathematical analysis of the various inverse problems needs to be undertaken in order to determine the extent to which a given set of data contains usable information about source/sink processes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allison, H., 1979, Inverse unstable problems and some of their applications, Math. Scientist 4, 9–30.

    Google Scholar 

  • Anderssen, R. S. and Bloomfield, P., 1974a, A time series approach to numerical differentiation, Technometrics 16, 69–75.

    Google Scholar 

  • Anderssen, R. S. and Bloomfield, P., 1974b, Numerical differentiation procedures for nonexact data, Numer. Math. 22, 157–182.

    Google Scholar 

  • Anderssen, R. S. and de Hoog, F., 1983, The nature of numerical processes, Math. Scientist 8, 115–141.

    Google Scholar 

  • Backus, G. and Gilbert, F., 1968, The resolving power of gross earth data, Geophys. J. R. Astr. Soc. 16, 169–205.

    Google Scholar 

  • Bolin, B. and Keeling, C. D., 1963, Large-scale atmospheric mixing as deduced from seasonal and meridional variations of carbon dioxide, J. Geophys. Res. 68, 3889–3920.

    Google Scholar 

  • Bolin, B. Björkström, A., Holmén, K., and Moore, B., 1983, The simultaneous use of tracers for ocean circulation studies, Tellus 35B, 206–236.

    Google Scholar 

  • Crutzen, P. J. 1987, Role of the tropics in atmospheric chemistry, in R. E. Dickinson (ed.), The Geophysiology of Amazonia, John Wiley, New York, pp. 107–130.

    Google Scholar 

  • Crutzen, P. J. and Gidel, L. T., 1983, A two-dimensional model of the atmosphere 2: The tropospheric budgets of anthropogenic halocarbons, CO, CH4, CH3Cl and the effect of various NO x sources on tropospheric ozone, J. Geophys. Res. 88C, 6641–6661.

    Google Scholar 

  • Cunnold, D. M., Prinn, R. G., Rasmussen, R. A., Simmonds, P. G., Alyea, F. N., Cardelino, C.A., Crawford, A. J., Fraser, P.J., and Rosen, R. D., 1983, The atmospheric lifetime experiment, 3, Lifetime methodology and application to three years of CCl3F data, J. Geophys. Res. 88C, 8379–8400.

    Google Scholar 

  • Elliott, W.P., Machta, L., and Keeling, C. D., 1985, An estimate of the biotic contribution to the atmospheric CO2 increase based on direct measurements at Mauna Loa, J. Geophys. Res. 90D, 3741–3746.

    Google Scholar 

  • Enting, I. G., 1985a, A classification of some inverse problems in geochemical modelling, Tellus 37B, 216–229.

    Google Scholar 

  • Enting, I. G., 1985b, Green's functions and response functions in geochemical modelling, Pageoph 123, 328–343.

    Google Scholar 

  • Enting, I. G., 1987, On the application of lattice statistics to bubble trapping in ice, Tellus 39B, 100–113.

    Google Scholar 

  • Enting, I. G., 1989a, Some comments on Kalman filtering of CO2 data, in W. P. Elliott (ed.), The Statistical Treatment of CO 2 Data Records, NOAA Technical memorandum ERL ARL-173, p. 101.

  • Enting, I. G., 1989b, Studies of baseline selection criteria for Cape Grim, Tasmania, ibid. p. 51.

  • Enting, I. G. and Mansbridge, J. V., 1987a, Inversion relations for the deconvolution of CO2 data from ice cores, Inverse Problems 3, L63-L69.

    Google Scholar 

  • Enting, I. G. and Mansbridge, J. V. 1987b, The incompatibility of ice core CO2 data with reconstructions of biotic CO2 sources, Tellus 39B, 318–325.

    Google Scholar 

  • Enting, I. G. and Mansbridge, J. V., 1989, Seasonal sources and sinks of atmospheric CO2: Direct inversion of filtered data. Tellus 41B, 111–126.

    Google Scholar 

  • Enting, I. G. and Mansbridge, J. V., 1990, Determining the role of the terrestrial biota from the atmospheric CO2 record, Tellus (submitted). (See also abstracts of papers presented at the 3rd International CO2 conference, pp. 73–78.)

  • Enting, I. G. and Newsam, G. N., 1990, Inverse problems in atmospheric constituent studies: II. Sources in the free troposphere, Inverse Problems (in press).

  • Enting, I. G. and Pearman, G. I., 1987, Description of a one-dimensional carbon cycle model calibrated using techniques of constrained inversion, Tellus 39B, 459–476.

    Google Scholar 

  • Firor, J., 1988, Public policy and the airborne fraction: Guest Editorial, Climatic Change, 12, 103–105.

    Google Scholar 

  • Fraser, P. J., Hyson, P., Enting, I. G., and Pearman, G. I., 1983, Global distribution and southern hemisphere trends of atmospheric CCl3F, Nature 302, 692–695.

    Google Scholar 

  • Friedli, II., Lötscher, H., Oeschger, H., Siegenthaler, U. and Stauffer, B., 1986, Ice core record of the 12C/13C ratio of atmospheric CO2 in the past two centuries, Nature 324, 237–238.

    Google Scholar 

  • Houghton, R. A., Hobbie, J.E., Melillo, J. M., Moore, B., Peterson, B. J., Shaver, G. R., and Woodwell, G. M., 1983, Changes in the carbon content of terrestrial biota and soils between 1860 and 1980: a net release of CO2 to the atmosphere, Ecol. Monog. 53, 235–262.

    Google Scholar 

  • Jackson, D. D., 1972, Interpretation of inaccurate, insufficient and inconsistent data, Geophys. J. R. Astr. Soc. 28, 97–109.

    Google Scholar 

  • Keeling, C. D., 1986, Atmospheric CO2 concentrations — Mauna Loa Observatory, Hawaii, 1958–1986, NDP-001/R1 Carbon Dioxide Information Center, Oak Ridge National Laboratory, Tennessee.

    Google Scholar 

  • Levin, I., Kromer, B., Wagenbach, D., and Münnich, K. O., 1987, Carbon isotope measurements of atmospheric CO2 at a coastal station in Antarctica, Tellus 39B, 89–95.

    Google Scholar 

  • Maier-Reimer, E. and Hasselmann, K., 1987, Transport and storage of CO2 in the ocean — an inorganic ocean circulation carbon cycle model, Climate Dynamics 2, 63–90.

    Google Scholar 

  • Mansbridge, J. V. and Enting, I. G., 1989, Sensitivity studies in a two-dimensional transport model, Division of Atmospheric Research Technical Paper No. 18, CSIRO, Australia.

    Google Scholar 

  • Neftel, A., Moor, E., Oeschger, H., and Stauffer, B., 1985, Evidence from polar ice cores for the increase in atmospheric CO2 in the past two centuries, Nature 315, 45–47.

    Google Scholar 

  • Newsam, G. N. and Enting, I. G., 1988, Inverse problems in atmospheric constituent studies: I. Determination of surface sources under a diffusive transport approximation, Inverse Problems 4, 1037–1054.

    Google Scholar 

  • Pearman, G. I. and Hyson, P., 1986, Global transport and inter-reservoir exchange of carbon dioxide with particular reference to stable isotopic distributions, J. Atmos. Chem. 4, 81–124.

    Google Scholar 

  • Pearman, G. I., Etheridge, D., de Silva, F., and Fraser, P. J., 1986, Evidence of changing concentrations of atmospheric CO2, N2O and CH4 from air bubbles in Antarctic ice, Nature 320, 248–250.

    Google Scholar 

  • Peng, T.-H., Broecker, W. S., Freyer, H. D., and Trumbore, S., 1983, A deconvolution of the treering based δ13C record, J. Geophys. Res. 88C, 3609–3620.

    Google Scholar 

  • Prinn, R., Cunnold, D., Rasmussen, R., Simmonds, P., Alyea, F., Crawford, A., Fraser, P., and Rosen, R., 1987, Atmospheric trends in methylchloroform and the global average for the hydroxyl radical, Science 238, 945–950.

    Google Scholar 

  • Rotty, R. M., 1981, Data for global CO2 production from fossil fuels and cement, in B. Bolin (ed.), Carbon Cycle Modelling. SCOPE 16, John Wiley, Chichester, pp. 121–125.

    Google Scholar 

  • Rotty, R. M., 1987, A look at 1983 CO2 emissions from fossil fuels (with preliminary data for 1984), Tellus 39B, 203–208.

    Google Scholar 

  • Siegenthaler, U. and Oeschger, H., 1987, Biospheric CO2 emissions during the past 200 years reconstructed by deconyolution of ice-core data, Tellus 39B, 140–154.

    Google Scholar 

  • Tans, P. P., 1980, On calculating the transfer of carbon-13 in reservoir models of the carbon cycle, Tellus 32, 464–469.

    Google Scholar 

  • Tans, P. P., Conway, T. J., and Nakazawa, T., 1989, Latitudinal distribution of the sources and sinks of atmospheric carbon dioxide derived from surface observations and an atmospheric transport model, J. Geophys. Res. 94D, 5151–5172.

    Google Scholar 

  • Tans, P. P., Fung, I. Y., and Takahashi, T., 1990, Observational constraints on the global atmospheric CO2 budget, Science (in press).

  • Tarantola, A., 1987, Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier, Amsterdam.

    Google Scholar 

  • Wiggins, R., 1972, The general linear inverse problem: implications of surface waves and free oscillations on earth structure, Rev. Geophys. Space. Phys., 10, 251–285.

    Google Scholar 

  • Wunsch, C. and Minster, J.-F., 1982, Methods for box models and ocean circulation tracers: Mathematical programming and nonlinear inverse theory, J. Geophys. Res. 87C, 5647–5662.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Atmospheric Research, CSIRO, Private Bag 1, 3195, Mordialloc, Vic, Australia

    I. G. Enting

  2. Electronics Research Laboratory, P.O. Box 1600, 5108, Salisbury, DSTO, SA, Australia

    G. N. Newsam

Authors
  1. I. G. Enting
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. N. Newsam
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Centre for Mathematical Analysis, Australian National University

Rights and permissions

Reprints and permissions

About this article

Cite this article

Enting, I.G., Newsam, G.N. Atmospheric constituent inversion problems: Implications for baseline monitoring. J Atmos Chem 11, 69–87 (1990). https://doi.org/10.1007/BF00053668

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00053668

Key words

Search

Navigation