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Geoid and Sea Surface Topography Derived from ERS-1 Altimeter Data by the Adjoint Method

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Abstract

A method for splitting sea surface height measurements from satellite altimetry into geoid undulations and sea surface topography is presented. The method is based on a combination of the information from altimeter data and a dynamic sea surface height model. The model consists of geoid undulations and a quasi-geostrophic model for expressing the sea surface topography. The goal is the estimation of those values of the parameters of the sea surface height model that provide a least-squares fit of the model to the data. The solution is accomplished by the adjoint method which makes use of the adjoint model for computing the gradient of the cost function of the least-squares adjustment and an optimization algorithm for obtaining improved parameters. The estimation is applied to the North Atlantic. ERS-1 altimeter data of the year 1993 are used. The resulting geoid agrees well with the geoid of the EGM96 gravity model.

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References

  • Anzenhofer M. and Gruber T., 1998. Fully reprocessed ERS-1 altimeter data from 1992 to 1995: Feasibility of the detection of long term sea level change. J.Geophys. Res., 104(C4), 8089-8112.

    Article  Google Scholar 

  • Arent N., 1993. Ein quasi-geostrophisches Stromungsmodell zur Auswertung von Satelliten-Altimeterdaten. Reihe C, 402. Deutsche Geodatische Kommission, Munchen.

  • Arent N., Huckelheim G. and Koch K.R., 1992. Method for obtaining geoidundulations from satellite altimetry data by a quasi-geostrophic model of the sea surface topography. Manuscripta Geodaetica, 17, 174-185.

    Google Scholar 

  • Arent N., Huckelheim G. and Koch K. R., 1993. Geoid undulations and sea surface topography in the North Atlantic from altimeter data. In: B. Kaldejch (Ed.), Proceedings Second ERS-1 Symposium-Space at the Service of our Environment, ESA SP-361, ESTEC, Noordwijk, 1065-1070.

    Google Scholar 

  • Blinken R., 1999. Bestimmung von Geoid und Meerestopographie aus Altimeterdaten mittels der Adjungierten Methode. Shaker Verlag. Aachen.

  • Denker H. and Rapp R. H., 1990. Geodetic and oceanographic results from the analysis of 1 year of GEOSAT data. J. Geophys. Res., 95(C8), 13151-13168.

    Article  Google Scholar 

  • Dorny C. N., 1975. A Vector Space Approach to Models and Optimization. J. Wiley & Sons, New York, London, Sydney, Toronto.

    Google Scholar 

  • Engelis T. and Knudsen P., 1989. Orbit improvement and determination of the ocean, geoid and topography from 17 days of SEASAT data. Manuscripta Geodaetica, 14, 193-201.

    Google Scholar 

  • Gelb A. (Ed.), 1974. Applied Optimal Estimation. Massachusetts Institute of Technology, Cambridge, Massachusetts, London.

    Google Scholar 

  • Giering R., 1997. Tangent linear and adjoint model compiler, Users manual version 1.2. http://puddle.mit.edu/~ralf/tamc.

  • Giering R. and Kaminski T., 1998. Recipes for adjoint code construction. ACM Transactions on Mathematical Software, 24(4), 437-474.

    Article  Google Scholar 

  • Gill P. E., Murray W. and Wright M. H., 1981. Practical Optimization. Academic Press, London, New York.

    Google Scholar 

  • Hellerman S. and Rosenstein M., 1983. Normaly monthly wind stress over the world ocean with error estimates. J. Phys. Oceanography, 13, 1093-1104.

    Article  Google Scholar 

  • Holland W. R., 1978. The role of mesoscale eddies in the general circulation of the ocean-Numerical experiments using a wind-driven quasi-geostrophic model. J. Phys. Oceanography, 8, 363-392.

    Article  Google Scholar 

  • Huckelheim G., 1994. Parameterschatzung in dynamischen Systemen fur die Satelliten-Altimetrie. Reihe C, 415. Deutsche Geodatische Kommission, Munchen.

  • Kalman R. E., 1960. A new approach to linear filtering and prediction problems. Journal of BasicEngineering, 82D(1), 35-45.

    Google Scholar 

  • Koch K. R., 1970. Gravity anomalies for ocean areas from satellite altimetry. Marine Geodesy a Practical View, 301-307. A Second Symposium on Marine Geodesy, 3–5 November 1969, Marine Technology Society, Washington, D.C.

  • Koch K. R., 1990. Bayesian Inference with Geodetic Applications, Springer Verlag, Berlin, Heidelberg, New York.

    Book  Google Scholar 

  • Koch K. R., 2000. Einfuhrung in die Bayes-Statistik. Springer-Verlag, Berlin, Heidelberg, New York.

    Book  Google Scholar 

  • Le Dimet F. X. and Talagrand O., 1986. Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus, 38A, 97-110.

    Article  Google Scholar 

  • Lemoine F. G., Kenyon S. C., Factor J. K., Trimmer R., Pavlis N. K., Chinn D.S., Cox C. M., Klosko S. M., Luthcke S. M., Torrence M. H., Wang Y. M., Williamson R. G., Pavlis E. G., Rapp R. H. and Olson T. R., 1998. The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM9G. NASA Technical Paper NASA/TP 1998-206861. Goddard Space Flight Center, Greenbelt, Maryland.

    Google Scholar 

  • Marsh J. G., Koblinsky C. J., Lerch F., Klosko S. M., Robbins J. W., Williamson R. G. and Patel G. B., 1990. Dynamic sea surface topography, gravity, and improved orbit accuracies from the direct evaluation of SEASAT altimeter data. J. Geophys. Res., 95(C8), 13129-13150.

    Article  Google Scholar 

  • Marshall J. C., 1985. Determining the ocean circulation and improving the geoid from satellite altimetry. J. Phys. Oceanography, 15, 330-349.

    Article  Google Scholar 

  • Nocedal J., 1992. Theory of algorithms for unconstrained optimization. Ada Numerica, 1, 199-242.

    Article  Google Scholar 

  • Rapp R. H., 1989. The treatment of permanent tidal effects in the analysis of satellite altimeter data for sea surface topography. Manuscripta Geodaetica, 14, 368-372.

    Google Scholar 

  • Rummel R., 1993. Principle of satellite altimetry and elimination of radial orbit errors. In: R. Rummel and F. Sanso (Eds.), Satellite Altimetry in Geodesy and Oceanography. Springer-Verlag, Berlin, Heidelberg, New York, 189-241.

    Chapter  Google Scholar 

  • Schwintzer P., Reigber C., Bode A., Kang Z., Zhu S. Y., Massmann F. H., Raimondo J. C., Biancale R., Balmino O., Lemoine J.M., Moynot B., Marty J. C., Barlier F. and Boudon Y., 1997. Long-wavelength and gravity field models: GR1M4-S4, GRIM4-C4. J.Geodesy, 71, 189-208.

    Article  Google Scholar 

  • Talagrand O., 1991. The use of adjoint equations in numerical modelling of the atmospheric circulation. In: A. Griewank and G. Corliess (Eds.), Automatic Differentiation of Algorithms: Theory, Implementation and Application. SIAM, Philadelphia, 169-180.

    Google Scholar 

  • Talagrand O. and Courtier P., 1987. Variational assimilation of meteorological observations with the adjoint vorticity equation, Part I: Theory. Quarterly Journal of the Royal Meteorological Society, 113, 311-1328.

    Article  Google Scholar 

  • Thacker W. C. and Long R. B., 1988. Fitting dynamics to data. J. Geophys. Res., 93(C2), 1227-1240.

    Article  Google Scholar 

  • Tziperman E. and Thacker W. C., 1989. An optimal-control/adjoint equations approach to studying the ocean general circulation. J. Phys. Oceanography, 19, 1471-1485.

    Article  Google Scholar 

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Blinken, R., Koch, KR. Geoid and Sea Surface Topography Derived from ERS-1 Altimeter Data by the Adjoint Method. Studia Geophysica et Geodaetica 45, 235–250 (2001). https://doi.org/10.1023/A:1022080011849

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