Editorial Type:
Article
Article Type:
Research Article

Variational Assimilation of Altimeter Data in a Multilayer Model of the Tropical Pacific Ocean

Anthony T. Weaver Atmospheric, Oceanic and Planetary Physics, Department of Physics, Clarendon Laboratory, Oxford, United Kingdom

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David L. T. Anderson Atmospheric, Oceanic and Planetary Physics, Department of Physics, Clarendon Laboratory, Oxford, United Kingdom

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Print Publication:
01 May 1997
DOI:
https://doi.org/10.1175/1520-0485(1997)027<0664:VAOADI>2.0.CO;2
Page(s):
664–682
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Abstract

A four-dimensional variational method is used to examine the extent to which a time sequence of altimeter measurements can determine the subsurface flow in a linear multilayer model of the tropical Pacific Ocean. The experiments are all of the identical-twin type. Complete maps of sea level extracted from the model in a control integration play the role of the altimeter observations in the assimilation experiments. The results of the experiments indicate that, over timescales of months, the sea level information can be effectively propagated into the subsurface, particularly in the dynamically active equatorial region. Several degrees off the equator, however, where waves propagate more slowly, the recovery of the subsurface flow in models containing more than two vertical modes is significantly more difficult. The sensitivity of these results to the lengths of the data sampling and assimilation periods is discussed.

* Current affiliation: Laboratoire d’Océanographie Dynamique et de Climatologie, (CNRS/ORSTOM/UPMC), Université Paris VI, Paris, France.

Current affiliation: European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom.

Corresponding author address: Dr. Anthony T. Weaver, Laboratoire d’Océanographie Dynamique et de Climatologie, (CNRS/ORSTOM/UPMC), Université Paris VI, boîte 100, 4 place Jussieu, 75252 Paris Cedex 05, France.

Abstract

A four-dimensional variational method is used to examine the extent to which a time sequence of altimeter measurements can determine the subsurface flow in a linear multilayer model of the tropical Pacific Ocean. The experiments are all of the identical-twin type. Complete maps of sea level extracted from the model in a control integration play the role of the altimeter observations in the assimilation experiments. The results of the experiments indicate that, over timescales of months, the sea level information can be effectively propagated into the subsurface, particularly in the dynamically active equatorial region. Several degrees off the equator, however, where waves propagate more slowly, the recovery of the subsurface flow in models containing more than two vertical modes is significantly more difficult. The sensitivity of these results to the lengths of the data sampling and assimilation periods is discussed.

* Current affiliation: Laboratoire d’Océanographie Dynamique et de Climatologie, (CNRS/ORSTOM/UPMC), Université Paris VI, Paris, France.

Current affiliation: European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom.

Corresponding author address: Dr. Anthony T. Weaver, Laboratoire d’Océanographie Dynamique et de Climatologie, (CNRS/ORSTOM/UPMC), Université Paris VI, boîte 100, 4 place Jussieu, 75252 Paris Cedex 05, France.

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  • Anderson, D. L. T., J. Sheinbaum, and K. Haines, 1996: Data assimilation in ocean models. Rep. Prog. Phys.,59, 1–58.

  • Bengtsson, L., 1979: On the use of a time sequence of surface pressures in four-dimensional data assimilation. Tellus,32, 189–196.

  • Berry, P., and J. Marshall, 1989: Ocean modelling studies in support of altimetry. Dyn. Atmos. Oceans,13, 269–300.

  • Busalacchi, A., and J. J. O’Brien, 1981: Interannual variability of the equatorial Pacific in the 1960’s. J. Geophys. Res.,86, 10901–10907.

  • Cane, M. A., 1979: The response of an equatorial ocean to simple wind stress patterns: I Model formulation and analytic results. J. Mar. Res.,57, 233–252.

  • Cooper, M., and K. Haines, 1996: Altimetric assimilation with water property conservation. J. Geophys. Res.,101, 1059–1077.

  • Courtier, P., and O. Talagrand, 1987: Variational assimilation of meteorological observations with the adjoint vorticity equation, II: Numerical results. Quart. J. Roy. Meteor. Soc.,113, 1329–1347.

  • ——, and ——, 1990: Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations. Tellus,42A, 531–549.

  • De Mey, P., and A. R. Robinson, 1987: Assimilation of altimeter eddy fields in a limited-area quasi-geostrophic model. J. Phys. Oceanogr.,17, 2280–2293.

  • Ezer, T., and G. Mellor, 1994: Continuous assimilation of Geosat altimeter data into a three-dimensional primitive equation Gulf Stream model. J. Phys. Oceanogr.,24, 832–847.

  • Fisher, M., and P. Courtier, 1995: Three algorithms for estimating the covariance matrix of analysis error in incremental variational data assimilation. Proc. Second WMO Int. Symp. on Assimilation of Observations in Meteorology and Oceanography, Vol. 1, Tokyo, Japan, World Meteor. Org., 229–234.

  • Gelb, A., 1974: Applied Optimal Estimation. Academic Press, 374 pp.

  • Ghil, M., and P. Malanotte-Rizzoli, 1991: Data assimilation in meteorology and oceanography. Advances in Geophysics, Vol. 33, Academic Press, 141–266.

  • Gilbert, J. C., and C. Lemaréchal, 1989: Some numerical experiments with variable-storage quasi-Newton algorithms. Math. Program B,45, 407–435.

  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Gill, P. E., W. Murray, and M. H. Wright, 1980: Practical Optimization. Academic Press, 401 pp.

  • Haines, K., 1991: A direct method for assimilating sea surface height data into ocean models with adjustments to the deep circulation. J. Phys. Oceanogr.,21, 843–868.

  • ——, 1994: Dynamics and data assimilation in oceanography. Data Assimilation: Tools for Modelling of the Ocean in a Global Change Perspective, P. P. Brasseur and J. C. Nihoul, Eds., NATO ASI Series, Springer-Verlag, 1–32.

  • ——, P. Malanotte-Rizzoli, R. E. Young, and W. R. Holland, 1993: A comparison of two methods for the assimilation of altimeter data into a shallow water model. Dyn. Atmos. Oceans,17, 89–133.

  • Holland, W. R., 1989: Altimeter data assimilation into ocean circulation models—Some preliminary results. Oceanic Circulation Models: Combining Data and Dynamics, D. L. T. Anderson and J. Willebrand, Eds., Kluwer Academic, 203–232.

  • ——, and P. Malanotte-Rizzoli, 1989: Assimilation of altimeter data into an ocean model with adjustment to the deep circulation. J. Phys. Oceanogr.,19, 1507–1534.

  • Hurlburt, H. E., 1986: Dynamic transfer of simulated altimeter data into subsurface information by a numerical model. J. Geophys. Res.,91, 2371–2400.

  • ——, D. N. Fox, and E. J. Metzger, 1990: Statistical inference of weakly correlated subthermocline fields from satellite altimeter data. J. Geophys. Res.,95, 11375–11409.

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

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

  • Lorenc, A. C., 1988: Optimal nonlinear objective analysis. Quart. J. Roy. Meteor. Soc.,114, 205–240.

  • McCreary, J. P., 1983: A model of tropical ocean–atmosphere interaction. Mon. Wea. Rev.,111, 370–387.

  • ——, and D. L. T. Anderson, 1984: A simple model of El Niño and the Southern Oscillation. Mon. Wea. Rev.,112, 934–946.

  • Mellor, G. L., and T. Ezer, 1991: A Gulf Stream model and an altimetry assimilation scheme. J. Geophys. Res.,96, 8779–8795.

  • Mesinger, F., and A. Arakawa, 1976: Numerical methods used in atmospheric models. Vol. 1. GARP Publ. 17, 64 pp. [Available from WMO, Case Postale No. 5, CH-1211 Geneva 20, Switzerland.].

  • Moore, A. M., 1986: Data assimilation in ocean models. Ph.D. thesis, University of Oxford, U.K., 168 pp.

  • ——, 1990: Linear equatorial wave mode initialization in a model of the tropical Pacific Ocean: An initialization scheme for tropical ocean models. J. Phys. Oceanogr.,20, 423–445.

  • Oschlies, A., and J. Willebrand, 1996: Assimilation of Geosat satellite data into an eddy-resolving primitive equation model of the North Atlantic Ocean. J. Geophys. Res.,101, 14175–14190.

  • Sasaki, Y. K., 1970: Some basic formalisms in numerical variational analysis. Mon. Wea. Rev.,98, 875–883.

  • Sheinbaum, J., and D. L. T. Anderson, 1990a: Variational assimilation of XBT data. Part I. J. Phys. Oceanogr.,20, 672–688.

  • ——, and ——, 1990b: Variational assimilation of XBT data. Part II. J. Phys. Oceanogr.,20, 689–704.

  • Stricherz, J. N., J. J. O’Brien, and D. M. Legler, 1992: Atlas of Florida State University tropical Pacific winds for TOGA: 1966–1985. Mesoscale Air-Sea Interaction Group Tech. Rep. 92-073698, 275 pp. [Available from MS B-174 MASIG, The Florida State University, Tallahassee, FL 32306.].

  • Talagrand, O., 1993: Data assimilation problems. Energy and Water Cycles in the Climate System, E. Raschke and D. Jacob, Eds., NATO ASI Series, Springer-Verlag, 187–213.

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

  • Tarantola, A., 1987: Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, 613 pp.

  • Thacker, W. C., 1989: The role of the Hessian matrix in fitting models to measurements. J. Geophys. Res.,94, 6177–6196.

  • ——, and R. B. Long, 1988: Fitting dynamics to data. J. Geophys. Res.,93, 1227–1240.

  • Thépaut, J. N., and P. Courtier, 1991: Four-dimensional variational data assimilation using the adjoint of a multilevel primitive equation model. Quart. J. Roy. Meteor. Soc.,117, 1225–1254.

  • Verron, J., 1992: Nudging satellite altimeter data into quasi-geostrophic ocean models. J. Geophys. Res.,97, 7479–7491.

  • Weaver, A. T., 1994: Variational data assimilation in numerical models of the ocean. Ph.D. dissertation, University of Oxford, 244 pp.

  • Webb, D. J., and A. M. Moore, 1986: Assimilation of altimeter data into ocean models. J. Phys. Oceanogr.,16, 1901–1913.

  • Wunsch, C., and A. E. Gill, 1976: Observations of equatorially trapped waves in Pacific sea level variations. Deep-Sea Res.,23, 371–390.

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