• Cohn, S. E., 1993: Dynamics of short-term univariate forecast error covariances. Mon. Wea. Rev.,121, 3123–3148.

  • Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • ——, 1992: Forecast-error statistics for homogeneous and inhomogeneous observation networks. Mon. Wea. Rev.,120, 627–643.

  • Dee, D. P., and A. M. da Silva, 1999: Maximum-likelihood estimation of forecast and observation error covariance parameters. Part I:Methodology. Mon. Wea. Rev.,127, 1822–1834.

  • Jazwinski, A. H., 1970: Stochastic Processes and Filtering Theory. Academic Press, 376 pp.

  • Lupton, R., 1993: Statistics in Theory and Practice. Princeton University Press, 188 pp.

  • Lyster, P. M., S. E. Cohn, R. Ménard, L.-P. Chang, S.-J. Lin, and R. G. Olsen, 1997: Parallel implementation of a Kalman filter for constituent data assimilation. Mon. Wea. Rev.,125, 1674–1686.

  • Ménard, R., S. E. Cohn, L.-P. Chang, and P. M. Lyster, 2000: Stratospheric assimilation of chemical tracer observations using a Kalman filter. Part I: Formulation. Mon. Wea. Rev.,128, 2654–2671.

  • Ngan, K., and T. G. Shepherd, 1997: Comments on some recent measurements of anomalous steep N2O and O3 tracer spectra in the stratospheric surf zone. J. Geophys. Res.,102, 24 001–24 004.

  • Park, J. H., and Coauthors, 1996: Validation of Halogen Occultation Experiment CH4 measurements from UARS. J. Geophys. Res.,101, 10 183–10 203.

  • Randel, W. J., J. C. Gille, A. E. Roche, J. B. Kumer, J. L. Mergenthaler, J. W. Waters, E. F. Fishbein, and W. A. Lahoz, 1993: Stratospheric transport from tropics to middle latitudes by planetary-wave mixing. Nature,365, 533–535.

  • Roche, A. E., J. B. Kumer, J. L. Mergenthaler, G. A. Ely, W. G. Uplinger, J. F. Potter, T. C. James, and L. W. Sterritt, 1993: The Cryogenic Limb Array Etalon Spectrometer (CLAES) on UARS:Experiment description and performance. J. Geophys. Res.,98, 10 763–10 775.

  • ——, and Coauthors, 1996: Validation of CH4 and N2O measurements by the cryogenic limb array etalon spectrometer instrument on the Upper Atmosphere Research Satellite. J. Geophys. Res.,101, 9679–9710.

  • Russell, J. M., III, and Coauthors, 1993: The Halogen Occultation Experiment. J. Geophys. Res.,98, 10 777–10 797.

  • Todling, R., and S. E. Cohn, 1994: Suboptimal schemes for atmospheric data assimilation based on the Kalman filter. Mon. Wea. Rev.,122, 2530–2557.

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Assimilation of Stratospheric Chemical Tracer Observations Using a Kalman Filter. Part II: χ2-Validated Results and Analysis of Variance and Correlation Dynamics

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  • 1 Data Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, Maryland
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Abstract

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I of this two-part paper. The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board the Upper Atmosphere Research Satellite are described in this paper.

A robust χ2 criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only 3 days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. Further, it was found that the model error due to numerical discretization, as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, an analysis of the variance and correlation dynamics was conducted to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

* Additional affiliation: Joint Center for Earth System Technology, University of Maryland, Baltimore County, Catonsville, Maryland.

+ Additional affiliation: General Sciences Corporation (a subsidiary of Science Applications International Corporation), Beltsville, Maryland.

Corresponding author address: Dr. Richard Ménard, NASA GSFC, Data Assimilation Office, Code 910.3, Greenbelt, MD 20771.

Email: menard@dao.gsfc.nasa.gov

Abstract

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I of this two-part paper. The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board the Upper Atmosphere Research Satellite are described in this paper.

A robust χ2 criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only 3 days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. Further, it was found that the model error due to numerical discretization, as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, an analysis of the variance and correlation dynamics was conducted to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

* Additional affiliation: Joint Center for Earth System Technology, University of Maryland, Baltimore County, Catonsville, Maryland.

+ Additional affiliation: General Sciences Corporation (a subsidiary of Science Applications International Corporation), Beltsville, Maryland.

Corresponding author address: Dr. Richard Ménard, NASA GSFC, Data Assimilation Office, Code 910.3, Greenbelt, MD 20771.

Email: menard@dao.gsfc.nasa.gov

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