• Anderson, B. D. O., , and J. B. Moore, 1979: Optimal Filtering. Prentice-Hall, 357 pp.

  • Baker, N. L., , and R. Daley, 2000: Observation and background adjoint sensitivity in the adaptive observation-targeting problem. Quart. J. Roy. Meteor. Soc., 126 , 14311454.

    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., , B. S. Chua, , and L. M. Leslie, 1996: Generalized inversion of a global numerical weather prediction model. Meteor. Atmos. Phys., 60 , 165178.

    • Search Google Scholar
    • Export Citation
  • Biswas, K. K., , and A. K. Mahalanabis, 1973: Suboptimal algorithms for nonlinear smoothing. IEEE Trans. Aerosp. Electron. Syst., 9 , 529534.

    • Search Google Scholar
    • Export Citation
  • Bloom, S. C., , L. L. Takacs, , A. M. da Silva, , and D. Ledvina, 1996: Data assimilation using incremental analysis updates. Mon. Wea. Rev., 124 , 12561271.

    • Search Google Scholar
    • Export Citation
  • Bouttier, F., , and G. Kelly, 2001: Observing-system experiments in the ECMWF 4D-Var data assimilation system. Quart. J. Roy. Meteor. Soc., 127 , 14691488.

    • Search Google Scholar
    • Export Citation
  • Cohn, S. E., 1997: An introduction to estimation theory. J. Meteor. Soc. Japan, 75 (1B) 257288.

  • Cohn, S. E., , and R. Todling, 1996: Approximate data assimilation schemes for stable and unstable dynamics. J. Meteor. Soc. Japan, 74 , 6375.

    • Search Google Scholar
    • Export Citation
  • Cohn, S. E., , N. S. Sivakumaran, , and R. Todling, 1994: A fixed-lag Kalman smoother for retrospective data assimilation. Mon. Wea. Rev., 122 , 28382867.

    • Search Google Scholar
    • Export Citation
  • Cohn, S. E., , A. da Silva, , J. Guo, , M. Sienkiewicz, , and D. Lamich, 1998: Assessing the effects of data selection with the DAO physical-space statistical analysis system. Mon. Wea. Rev., 126 , 29132926.

    • Search Google Scholar
    • Export Citation
  • Courtier, P., , J-N. Thepaut, , and A. Hollingsworth, 1994: A strategy operational implementation of 4-D VAR using an incremental approach. Quart. J. Roy. Meteor. Soc., 120 , 13671387.

    • Search Google Scholar
    • Export Citation
  • Courtier, P., and Coauthors. 1998: The ECMWF implementation of three dimensional variational assimilation (3D-Var). Part I: Formulation. Quart. J. Roy. Meteor. Soc., 124 , 17831808.

    • Search Google Scholar
    • Export Citation
  • Daley, R., , and E. Barker, 2001: NAVDAS: Formulation and diagnostics. Mon. Wea. Rev., 129 , 869883.

  • DAO, 1996: Algorithm theoretical basis document version 1.01. DAO, NASA Goddard Space Flight Center, Greenbelt, MD, 276 pp.

  • da Silva, A. M., , and J. Guo, 1996: Documentation of the physical-space statistical analysis system (PSAS). Part I: The conjugate gradient solver version PSAS–1.00. DAO Note 96-2, NASA Goddard Space Flight Center, Greenbelt, MD, 66 pp.

    • Search Google Scholar
    • Export Citation
  • Derber, J. C., 1989: A variational continuous assimilation technique. Mon. Wea. Rev., 117 , 24372446.

  • Evensen, G., , and P. J. van Leeuwen, 2000: An ensemble Kalman smoother for nonlinear dynamics. Mon. Wea. Rev., 128 , 18521867.

  • Fisher, M., , and E. Anderson, 2001: Developments in 4D-var and Kalman filtering. ECMWF Tech. Memo. 347, 36 pp.

  • Gauthier, P., , and J-N. Thépaut, 2001: Impact of the digital filter as a weak constraint in the preoperational 4DVAR assimilation system of Météo-France. Mon. Wea. Rev., 129 , 20892102.

    • Search Google Scholar
    • Export Citation
  • Gauthier, P., , C. Charette, , L. Fillion, , P. Koclas, , and S. Laroche, 1999: Implementation of a 3D variational data assimilation system at the Canadian Meteorological Center. Part I: The global analysis. Atmos.–Ocean, 37 , 103156.

    • Search Google Scholar
    • Export Citation
  • Giering, R., , and T. Kaminski, 1998: Recipes for adjoint code construction. ACM Trans. Math. Software, 24 , 437474.

  • Guo, J., , J. W. Larson, , G. Gaspari, , A. da Silva, , and P. M. Lyster, 1998: Documentation of the physical-space statistical analysis system (PSAS). Part II: The factored-operator formulation of error covariances. DAO Note 96-04, NASA Goddard Space Flight Center, Greenbelt, MD, 27 pp.

    • Search Google Scholar
    • Export Citation
  • Hou, A. Y., , D. V. Ledvina, , A. M. da Silva, , S. Q. Zhang, , J. Joiner, , R. M. Atlas, , G. J. Huffman, , and C. D. Kummerow, 2000: Assimilation of SSM/I-derived surface rainfall and total precipitable water for improving the GEOS analysis for climate studies. Mon. Wea. Rev., 128 , 509537.

    • Search Google Scholar
    • Export Citation
  • Jazwinski, A. H., 1970: Stochastic Processes and Filtering Theory. Academic Press, 376 pp.

  • Larson, J. W., , J. Guo, , G. Gaspari, , A. da Silva, , and P. M. Lyster, 1998: Documentation of the physical-space statistical analysis system (PSAS). Part III: The software implementation. DAO Note 98-05, NASA Goddard Space Flight Center, Greenbelt, MD, 189 pp.

    • Search Google Scholar
    • Export Citation
  • Li, Z., , and I. M. Navon, 2001: Optimality of 4D-Var and its relationship with Kalman filter and Kalman smoother. Quart. J. Roy. Meteor. Soc., 127 , 661684.

    • Search Google Scholar
    • Export Citation
  • Lynch, P., , and X-Y. Huang, 1992: Initialization of the HIRLAM model using a digital filter. Mon. Wea. Rev., 120 , 10191034.

  • Ménard, R., , and R. Daley, 1996: The application of Kalman smoother theory to the estimation of 4DVAR error statistics. Tellus, 48A , 221237.

    • Search Google Scholar
    • Export Citation
  • Miller, R. N., , M. Ghil, , and F. Gauthiez, 1994: Advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci., 51 , 10371056.

    • Search Google Scholar
    • Export Citation
  • Moore, J. B., 1973: Discrete-time fixed-lag smoothing algorithms. Automatica, 9 , 163173.

  • Navon, I. M., , and D. M. Legler, 1987: Conjugate gradient methods for large-scale minimization in meteorology. Mon. Wea. Rev., 115 , 14791502.

    • Search Google Scholar
    • Export Citation
  • Parrish, D. F., , and J. C. Derber, 1992: The National Meteorological Center's spectral statistical-interpolation analysis system. Mon. Wea. Rev., 120 , 17471764.

    • Search Google Scholar
    • Export Citation
  • Polavarapu, S., , M. Tanguay, , and L. Fillion, 2000: Four-dimensional variational data assimilation with digital filter initialization. Mon. Wea. Rev., 128 , 24912510.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., , H. Jarvinen, , E. Klinker, , J-F. Mahfouf, , and A. Simmons, 2000: The ECMWF operational implementation of four dimensional variational assimilation. Part I: Experimental results with simplified physics. Quart. J. Roy. Meteor. Soc., 126 , 11431170.

    • Search Google Scholar
    • Export Citation
  • Rukhovets, L., , J. Tenenbaum, , and M. Geller, 1998: The impact of additional aircraft data on the Goddard Earth Observing System analyses. Mon. Wea. Rev., 126 , 29272941.

    • Search Google Scholar
    • Export Citation
  • Suarez, M., , and L. L. Takacs, 1995: Documentation of the ARIES/GEOS dynamical core, version 2. NASA Tech. Memo. 104606, Vol. 5, 45 pp. [Available from Data Assimilation Office, NASA, Code 910.3, Greenbelt, MD 20771.].

    • Search Google Scholar
    • Export Citation
  • Thépaut, J-N., , D. Vasiljevic, , P. Courtier, , and J. Pailleux, 1993: Variational assimilation of conventional meteorological observations with a multilevel primitive-equation model. Quart. J. Roy. Meteor. Soc., 119 , 153186.

    • Search Google Scholar
    • Export Citation
  • Todling, R., 2000: Retrospective data assimilation schemes: Fixed-lag smoothing. Proc. Second Int. Symp. on Frontiers of Time Series Modeling: Nonparametric Approach to Knowledge Discovery, Nara, Japan, Institute of Statistical Mathematics, 155–173.

    • Search Google Scholar
    • Export Citation
  • Todling, R., , and S. E. Cohn, 1996: Some strategies for Kalman filtering and smoothing. Proc. ECMWF Seminar on Data Assimilation, Reading, United Kingdom, ECMWF, 91–111.

    • Search Google Scholar
    • Export Citation
  • Todling, R., , S. E. Cohn, , and N. S. Sivakumaran, 1998: Suboptimal schemes for retrospective data assimilation based on the fixed-lag Kalman smoother. Mon. Wea. Rev., 126 , 247259.

    • Search Google Scholar
    • Export Citation
  • Verlaan, M., 1998: Efficient Kalman filtering algorithms for hydrodynamics models. Ph.D. thesis, Technische Universiteit Delft, 201 pp.

  • von Storch, H., , and F. W. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.

  • Wentz, F. J., 1997: A well calibrated ocean algorithm for SSM/I. J. Geophys. Res., 102 , 87038718.

  • Zhu, Y., , R. Todling, , and S. E. Cohn, 1999: Technical remarks on smoother algorithms. DAO Note 99-02, NASA Goddard Space Flight Center, Greenbelt, MD, 45 pp.

    • Search Google Scholar
    • Export Citation
  • Zou, X., , I. M. Navon, , and J. Sela, 1993a: Control of gravitational oscillations in variational data assimilation. Mon. Wea. Rev., 121 , 272289.

    • Search Google Scholar
    • Export Citation
  • Zou, X., , I. M. Navon, , M. Berger, , M. K. Phua, , T. Schlick, , and F. X. LeDimet, 1993b: Numerical experience with limited-memory, quasi-Newton methods for large-scale unconstrained nonlinear minimization. SIAM J. Optimization, 3 , 582608.

    • Search Google Scholar
    • Export Citation
  • Zupanski, D., 1997: A general weak constraint applicable to operational 4DVAR data assimilation systems. Mon. Wea. Rev., 125 , 22742292.

    • Search Google Scholar
    • Export Citation
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The GEOS-3 Retrospective Data Assimilation System: The 6-Hour Lag Case

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  • 1 Data Assimilation Office, NASA GSFC, Greenbelt, Maryland
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Abstract

The fixed-lag Kalman smoother (FLKS) has been proposed as a framework to construct data assimilation procedures capable of producing high-quality climate research datasets. FLKS-based systems, referred to as retrospective data assimilation systems, are an extension to three-dimensional filtering procedures with the added capability of incorporating observations not only in the past and present time of the estimate, but also at future times. A variety of simplifications are necessary to render retrospective assimilation procedures practical.

In this article, an FLKS-based retrospective data assimilation system implementation for the Goddard Earth Observing System Data Assimilation System is presented. The practicality of this implementation comes from the practicality of its underlying (filter) analysis system, that is, the physical-space statistical analysis system (PSAS). The behavior of two schemes is studied here. The first retrospective analysis (RA) scheme is designed simply to update the regular PSAS analyses with observations available at times ahead of the regular analysis times. Results are presented for when observations 6-h ahead of the analysis time are used to update the PSAS analyses and thereby to calculate the so-called lag-1 retrospective analyses. Consistency tests for this RA scheme show that the lag-1 retrospective analyses indeed have better 6-h predictive skill than the predictions from the regular analyses. This motivates the introduction of the second retrospective analysis scheme, which, at each analysis time, uses the 6-h retrospective analysis to create a new forecast to replace the forecast normally used in the PSAS analysis, and therefore allows the calculation of a revised (filter) PSAS analysis. This procedure is referred to as the retrospective-based iterated analysis (RIA) scheme. Results from the RIA scheme indicate its potential for improving the overall quality of the assimilation.

Additional affiliation: Science Applications International Corporation, Beltsville, Maryland

Additional affiliation: Department of Mathematics and CSIT, Florida State University, Tallahassee, Florida

Corresponding author address: Dr. Yanqiu Zhu, Data Assimilation Office, NASA GSFC, Code 910.3, Greenbelt, MD 20771. Email: yzhu@dao.gsfc.nasa.gov

Abstract

The fixed-lag Kalman smoother (FLKS) has been proposed as a framework to construct data assimilation procedures capable of producing high-quality climate research datasets. FLKS-based systems, referred to as retrospective data assimilation systems, are an extension to three-dimensional filtering procedures with the added capability of incorporating observations not only in the past and present time of the estimate, but also at future times. A variety of simplifications are necessary to render retrospective assimilation procedures practical.

In this article, an FLKS-based retrospective data assimilation system implementation for the Goddard Earth Observing System Data Assimilation System is presented. The practicality of this implementation comes from the practicality of its underlying (filter) analysis system, that is, the physical-space statistical analysis system (PSAS). The behavior of two schemes is studied here. The first retrospective analysis (RA) scheme is designed simply to update the regular PSAS analyses with observations available at times ahead of the regular analysis times. Results are presented for when observations 6-h ahead of the analysis time are used to update the PSAS analyses and thereby to calculate the so-called lag-1 retrospective analyses. Consistency tests for this RA scheme show that the lag-1 retrospective analyses indeed have better 6-h predictive skill than the predictions from the regular analyses. This motivates the introduction of the second retrospective analysis scheme, which, at each analysis time, uses the 6-h retrospective analysis to create a new forecast to replace the forecast normally used in the PSAS analysis, and therefore allows the calculation of a revised (filter) PSAS analysis. This procedure is referred to as the retrospective-based iterated analysis (RIA) scheme. Results from the RIA scheme indicate its potential for improving the overall quality of the assimilation.

Additional affiliation: Science Applications International Corporation, Beltsville, Maryland

Additional affiliation: Department of Mathematics and CSIT, Florida State University, Tallahassee, Florida

Corresponding author address: Dr. Yanqiu Zhu, Data Assimilation Office, NASA GSFC, Code 910.3, Greenbelt, MD 20771. Email: yzhu@dao.gsfc.nasa.gov

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