Skip to main content

Part of the book series: NATO ASI Series ((ASIC,volume 284))

  • 174 Accesses

Abstract

Any theoretical treatment of a problem concerning our environment, such as our present concern, namely that of deducing the parameterization of an ocean-carbon model by inverse methods, must be based on some kind of model. In reality of course, the natural phenomena are so complex and our data so few that all such problems are indeterminate (i.e. have more than one solution that is consistent with the data). However, only by adopting models, and thereby, by definition, imposing a reduction on the complexity of reality do overdetermined systems arise, and also only by adoption of models can we hope to make efficient use of the available data and information. It is obvious that whether or not the results will be of interest depends on how well our model captures the essence of the phenomena in nature which it seeks to describe.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Björk, Å. (1981): Least squares methods in physics and engineering. Lectures given in the Academic Training Programme of CERN 1980–1981. CERN 81–16, 61 p. CERN, Geneva.

    Google Scholar 

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

    Article  Google Scholar 

  • Bolin, B., A. Björkström, K. Holmén, and B. Moore (1987): On Inverse Methods for Combining Chemical and Physical Oceanographic Data: A Steady-state Analysis of the Atlantic Ocean. Tech. Rep., Meteorologiska Institutionen (MISU), Stockholm Universitet, Arrheniuslaboratoret, 134pp.

    Google Scholar 

  • Dempster, A.P., M. Schatzoff, and N. Wermuth (1977): A simulation study of alternatives to ordinary least squares. J. Amer. Stat. Assoc., 72, 77–106.

    Article  Google Scholar 

  • Eppley, R.W. and B.J. Peterson (1979): Particulate organic matter flux and planktonic new production in the deep ocean. Nature, 282, 677–680.

    Article  Google Scholar 

  • Fiadeiro, M.E. and G. Veronis (1984): Obtaining velocities from tracer distributions. J. Phys. Oceanogr., 14, 1734–1746.

    Article  Google Scholar 

  • Fiadeiro, M.E. and G. Veronis (1982): On the determination of absolute velocities in the ocean. J. Mar. Res., 40 (Suppl.), 159–182.

    Google Scholar 

  • Fiadeiro, M.E. and G. Veronis (1977): On weighted-mean schemes for the finite-difference approximation of the advection diffusion equation. Tellus 29, 512–522.

    Article  Google Scholar 

  • Gerhold, G.A. (1969): Least-squares adjustment of weighted data to a general linear equation. Amer. J. Phys., 37, 156–161.

    Article  Google Scholar 

  • Golub, G.H. and V. Pereyra (1973): The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal. 10, 413–432.

    Article  Google Scholar 

  • Golub, G.H. and C.F. Van Loan (1980): An analysis of the total least squares problem. SIAM J. Numer. Anal. 17, 883–893.

    Article  Google Scholar 

  • Haskell, K.H. and R.J. Hanson (1981): An algorithm for linear least squares problems with equality and nonnegativity constraints. Math. Programming, 21, 98–118.

    Article  Google Scholar 

  • Hemmerle, W.J. and T.F. Brantle (1978): Explicit and constrained generalized ridge estimation. Technometrics, 20, 109–120.

    Article  Google Scholar 

  • Hocking, R.R., F.M. Speed, M.J. Lynn (1976): A class of biased estimators in linear regression. Technometrics, 18, 425–437.

    Article  Google Scholar 

  • Hoed, A.E. and R.W. Kinnard (1970a): Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12, 55–67.

    Article  Google Scholar 

  • Hoerl, A.E. and R.W. Kinnard (1970b): Ridge regression: applications to nonorthogonal problems. Technometrics, 12, 69–82.

    Article  Google Scholar 

  • Hoerl, R.W., J.H. Schuenemeyer, and A.E. Hoerl (1986): A simulation of biased estimation and subset selection regression techniques. Technometrics, 28, 369–380.

    Article  Google Scholar 

  • Jenkins, W.J. and P.B. Rhines (1980): Tritium in the deep North Atlantic Ocean. Nature, 286, 877–880.

    Article  Google Scholar 

  • Kaufman, L. (1975): Variable projection methods for solving separable nonlinear least squares problems. BIT, 15, 49–57.

    Article  Google Scholar 

  • Kendall, M.G., and A. Stuart (1973): The Advanced Theory of Statistics, Vol. II, 3rd. edition, 723 pp.

    Google Scholar 

  • Lanczos, C. (1961): Linear Differential Operators, Van Nostrand, Princeton, 564 pp.

    Google Scholar 

  • Lawless, J.F. and P. Wang (1976): A simulation study of ridge and other regression estimators. Comm. in Stat. (Part A), 5, 307–323.

    Article  Google Scholar 

  • Marquardt, D.W. (1970): Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation. Technometrics, 12, 591–612.

    Article  Google Scholar 

  • Mercier, H. (1986): Determining the general circulation of the ocean: a nonlinear inverse problem. J. Geophys. Res., 91(C4), 5103–5109.

    Article  Google Scholar 

  • Ringo, C., A. Copeland, and B. Moore (1989): Random perturbations of pseudoin verses and least squares solutions. (in review)

    Google Scholar 

  • Schlitzer, R. (1988): Modeling the nutrient and carbon cycles of the North Atlantic 1. Circulation, mixing coefficients, and heat fluxes. J. Geophys. Res., 93, 10, 699–10,723.

    Google Scholar 

  • Schlitzer, R. (1987): Renewal rates of east Atlantic deep water estimated by inversion of 14 C data. J. Geophys. Res., 29, 2953–2969.

    Article  Google Scholar 

  • Sprent, P. (1969): Models in Regression and Related Topics. Methuen, London, 173 pp.

    Google Scholar 

  • Stommel, H. and F. Schott (1977): The β-spiral and determination of the absolute velocity field from hydrographic station data. Deep Sea Res., 24, 325–329.

    Article  Google Scholar 

  • Tarantola, A. and B. Valette (1982): Generalized nonlinear inverse problems solved using the least squares criterion. Rev. Geophys. Space Phys., 20, 219–232.

    Article  Google Scholar 

  • Weiss, R.F., W.S. Bullister, R.H. Gammon, and M.J. Warner, (1985): Atmospheric chlorofluoromethanes in deep equatorial Atlantic, Nature, 314, 608–610.

    Article  Google Scholar 

  • Wichern, D.W. and G.A. Churchill (1978): A comparison of ridge estimators. Technometrics, 20, 301–311.

    Article  Google Scholar 

  • Wunsch, C. (1978): The general circulation of the North Atlantic west of 50°W determined from inverse methods. Rev. Geophys. Space Phys., 16, 583–620.

    Article  Google Scholar 

  • Wunsch, C. (1984): An estimate of the upwelling rate in the equatorial Atlantic based on the distribution of bomb radiocarbon and quasigeostrophic dynamics. J. Geophys. Res. 89, 7971–7978.

    Article  Google Scholar 

  • Wunsch, C. (1985): Can a tracer Field be Inverted for Velocity?, J. Physical Oceanogr., 15, 1521–1531.

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Kluwer Academic Publishers

About this chapter

Cite this chapter

Moore, B., Bolin, B., Björkström, A., Holmén, K., Ringo, C. (1989). Ocean Carbon Models and Inverse Methods. In: Anderson, D.L.T., Willebrand, J. (eds) Oceanic Circulation Models: Combining Data and Dynamics. NATO ASI Series, vol 284. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1013-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-1013-3_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6946-5

  • Online ISBN: 978-94-009-1013-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics