Skip to main content
SpringerLink
Log in

Extended Kalman Filtering for Vortex Systems: An Example of Observing-System Design

  • Conference paper
Data Assimilation

Part of the book series: NATO ASI Series ((ASII,volume 19))

Abstract

To understand and eventually predict oceanic motions and fluxes, it is imperative to be able to follow them in three spatial dimensions and time. The number of observations available for this purpose in the oceans is rather small, compared to those available for the atmosphere. Conventional observations for the oceans, such as given by bathythermographs and current meters, are about 104 times fewer for the ocean than the World Weather Watch provides routinely for the atmosphere. Currently available satellite and other remote-sensing systems yield an observing density for the ocean that is still 10 times lower than for the atmosphere. Both these estimates do take into account the smaller spatial scales and longer time scales of the oceans (Ghil, 1989; Ghil and Malanotte-Rizzoli, 1991). Moreover, the largest number of oceanic observations are confined to the surface and — at best — small subsurface volumes (Munk and Wunsch, 1982).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  • Aref H (1984) Integrable, chaotic, and turbulent vortex motion in two-dimensional flow. Ann. Rev. Fluid Mech. 15: 345–389

    Article  Google Scholar 

  • Barth N (1992) Oceanographic experiment design II: Generic algorithms. J. Atmos. Ocean. Tech. 9: 434–443

    Article  Google Scholar 

  • Barth N, Wunsch C (1990) Oceanographic experiment design by simulated annealing. J. Phys. Oceanogr. 20: 1249–1263

    Article  Google Scholar 

  • Bennett AF (1992) Inverse Methods in Physical Oceanography. Cambridge University Press

    Book  Google Scholar 

  • Bucy RS, Joseph PD (1987) Filtering for Stochastic Processes with Application to Guidance 2nd edn. Chelsea New York

    Google Scholar 

  • Carter EF (1989) Assimilation of Lagrangian data into a numerical model. Dyn. Atmos. Oceans 13: 355–348

    Article  Google Scholar 

  • Casti JL (1982) Recent developments and future perspectives in nonlinear system theory. SIAM Rev. 24: 301–331

    Article  Google Scholar 

  • Charney JG, Halem M, Jastrow R (1969) Use of incomplete historical data to infer the present state of atmosphere. J. Atmos. Sci. 26: 1160–1163

    Article  Google Scholar 

  • Cohn SE, Dee DP (1988) Observability of discretized partial differential equations. SIAM J. Numer. Anal. 25: 586–617

    Article  Google Scholar 

  • Daley R (1980) On the optimal specification of the initial state for deterministic forcasting. Mon. Weather Rev. 108: 1719–1735

    Article  Google Scholar 

  • Daley R (1991) Atmospheric Data Analysis. Cambridge Univ. Press

    Google Scholar 

  • Evensen G (1994) Inverse methods and data assimilation in nonlinear ocean models. Physica D (in press)

    Google Scholar 

  • Gelb A (ed) (1974) Applied Optimal Estimation. The MIT Press

    Google Scholar 

  • Ghil M (1980) The compatible balancing approach to initialization and four-dimensional data assimilation. Tellus 32: 198–206

    Article  Google Scholar 

  • Ghil M (1989) Meteorological data assimilation for oceanographers. Part I: Description and theoretical framework. Dyn. Atmos. Oceans 13: 171–218

    Article  Google Scholar 

  • Ghil M, Balgovind R (1979) A fast Cauchy-Riemann solver. Math. Comput. 33: 585–635

    Article  Google Scholar 

  • Ghil M, Childress S (1987) Topics in Geophysical Fluid Dynamics, Atmospheric Dynamics, Dynamo Theory and Climate Dynamics. Springer-Verlag Berlin Heidelberg New York

    Book  Google Scholar 

  • Ghil M, Malanotte-Rizzoli P (1991) Data assimilation in meteorology and oceanography. Adv. Geophys. 33: 141–226

    Article  Google Scholar 

  • Ghil M, Mo K (1991) Intraseasonal oscillations in the global atmosphere. Part I: Nothern hemisphere and tropics. J. Atmos. Sci. 48: 752–779

    Article  Google Scholar 

  • Ghil M, Cohn SE, Dalcher A (1983) Application of sequential estimation to data assimilation. In: Large-Scale Oceanographic Experiments in the World Climate Research Programme. WCRP Publ. Series No.1 Vol. II WMO/ICSU Geneva

    Google Scholar 

  • Ide K, Ghil M (1993a) Extended Kaiman filtering for vortex systems. Part I: Point vortices. Dyn. Atmos. Oceans (submitted)

    Google Scholar 

  • Ide K, Ghil M (1993) Extended Kaiman filtering for vortex systems. Part II: Rankine vortices and Eulerian data. Dyn. Atmos. Oceans (submitted)

    Google Scholar 

  • Ide K, Ghil M (1994) Extended Kaiman filtering for elliptical vortices (in preparation)

    Google Scholar 

  • Jazwinski AH (1970) Stochastic Processes and Filtering Theory. Academic Press

    Google Scholar 

  • Jiang S, Ghil M (1993) Dynamical properties of error statistics in a shallow-water model. J. Phys. Oceanogr. 23: 2541–2566

    Article  Google Scholar 

  • Kaiman RE (1960) A new approach to linear filtering and prediction problems. Trans. ASME Ser. D, J. Basic Eng. 82D: 35–45

    Google Scholar 

  • Kaiman RE, Ho YC, Narendra KS (1963) Controllability of linear dynamical systems. Contrib. Differential Equations 1: 189–213

    Google Scholar 

  • Kuo HL (1949) Dynamic instability of two-dimensional non-divergent flow in a barotropic atmosphere. J. Meteorol. 9: 260–278

    Article  Google Scholar 

  • Le Dimet FX, Talagrand O (1986) Variational algorithms for analysis and assimilation of meteorological observations. Tellus 38A: 97–110

    Article  Google Scholar 

  • Lorenz E (1963) Deterministic nonperiodic flow. J. Atmos. Sci. 20: 130–141

    Article  Google Scholar 

  • Mariano A J (1990) Contour analysis: A new approach for melding geophysical fields. J. Atmos. Ocean. Tech. 7: 285–295

    Article  Google Scholar 

  • McWilliams JC (1991) Geostrophic vortices. In: Nonlinear Topics in Ocean Physics: Pro-ceedings of the International School of Physics “Enrico Fermi” Course 109. Osborne AR (ed) North-Holland, Elsevier Amsterdam

    Google Scholar 

  • Miller RN (1989) Direct assimilation of altimetric differences using the Kalman filter. Dyn. Atmos. Oceans 13: 317–334

    Article  Google Scholar 

  • Miller RN, Ghil M, Gauthiez F (1994) Advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci. (in press)

    Google Scholar 

  • Munk W, Wunsch C (1982) Observing the ocean in the 1990s. Phil. Trans. R. Soc. Lond. A307: 439–464

    Article  Google Scholar 

  • Pedlosky J (1987) Geophysical Fluid Dynamics 2nd edn. Springer-Verlag Berlin Heidelberg New York

    Book  Google Scholar 

  • Philander SGH, Hurlin WJ, Pacanowski RC (1987) Initial conditions for a general circulation model of the tropical ocean. J. Phys. Oceanogr. 17: 147–157

    Article  Google Scholar 

  • Phillips NA (1983) An accuracy goal for a comprehensive satellite wind measuring system. Mon. Weather Rev. 111: 237–239

    Article  Google Scholar 

  • Provost C, Salmon R (1986) A variational method for inverting hydrographic data. J. Mar. Res. 44: 1–34

    Article  Google Scholar 

  • Robinson AR (ed) (1983) Eddies in Marine Science. Springer-Verlag Berlin Heidelberg New York

    Google Scholar 

  • Robinson AR, Spall MA, Walstad LJ, Leslie WG (1989) Data assimilation and dynamical interpolation in gulfcast experiments. Dyn. Atmos. Oceans 13: 269–300

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Scott DW (1992) Multivariate Density Estimation. Wiley-Interscience

    Book  Google Scholar 

  • Silverman BW (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall

    Google Scholar 

  • Smagorinsky JK, Miyakoda K, Strickler R (1970) The relative importance of variables in intial conditions for dynamical weather prediction. Tellus 122: 141–157

    Article  Google Scholar 

  • Talagrand O, Courtier P (1987) Variational assimilation of meteorological observations with the adjoint vorticity equation, I. Theory. Q. J. R. Meteorol. Sci. 113: 1311–1328

    Article  Google Scholar 

  • Todling R (1992) The Kalman Filter for Two-Dimensional Stable and Unstable Atmospheres. Ph.D. thesis University of California, Los Angeles

    Google Scholar 

  • Todling R, Ghil M (1994) Tracking atmospheric instabilities with the Kalman filter. Part I: Methodology and one-layer results. Mon. Weather Rev 122: 183–204

    Article  Google Scholar 

  • Worcester PF, Cornuelle BD, Speidel RC (1991) A review of ocean acoustic tomography: 1987–1990. Rev. Geophy. Suppl. 29: 557–570

    Google Scholar 

  • Wunsch C (1988) Transient tracers as a problem in control theory. J. Geophy. Res. 93: 8099–8110

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Earth System Research, Institute of Geophysics and Planetary Physics, and Department of Atmospheric Sciences, University of California, Los Angeles, 90024-1567, Los Angeles, California, USA

    Michael Ghil & Kayo Ide

Authors
  1. Michael Ghil
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kayo Ide
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. GeoHydrodynamics and Environmental Research, Institute of Physics B5, University of Liège, Sart Tilman B5, 4000, Liège, Belgium

    Pierre P. Brasseur  & Jacques C. J. Nihoul  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ghil, M., Ide, K. (1994). Extended Kalman Filtering for Vortex Systems: An Example of Observing-System Design. In: Brasseur, P.P., Nihoul, J.C.J. (eds) Data Assimilation. NATO ASI Series, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78939-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-78939-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-78941-0

  • Online ISBN: 978-3-642-78939-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation