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Zhang, S.; Anderson, J. L. (2011)
Publisher: Co-Action Publishing
Journal: Tellus A
Languages: English
Types: Article
The background error covariance (correlation) between model state variables is of central importance for implementing data assimilation and understanding model dynamics. Traditional approaches for estimating the background error covariance involve many heuristic approximations, and often the estimated covariance is flow-independent, i.e. only reflecting statistics of the climatological background. This study examines temporally and spatially varying estimates of error covariance in a spectral barotropic model using a Monte Carlo approach, an implementation of an ensemble square root filter called the ensemble adjustment Kalman filter (EAKF). The EAKF is designed to maintain as much information about the distribution of the prior state variables as possible, and results show that this method can produce reasonable estimates of error correlation structure with an affordable sample (ensemble) size. The impact of using temporally and spatially varying estimates of error covariance in the EAKF is examined by using the time and spatial mean error covariances derived from the EAKF in an ensemble optimal interpolation (OI) assimilation scheme. Three key results are: (1) for the same ensemble size, an ensemble filter such as the EAKF produces better assimilations since its flow-dependent error covariance estimates are able to reflect more about the synoptic-scale wave structure in the simulated flows; (2) an ensemble OI scheme can also produce reasonably good assimilation results if the time-invariate covariance matrix is chosen appropriately; (3) when using the EAKF to estimate the error covariance matrix for improving traditional assimilation algorithms such as variational analysis and OI, a relatively small ensemble size may be used to estimate correlation structure although larger ensembles produce progressively better results.DOI: 10.1034/j.1600-0870.2003.00010.x
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    • Anderson, J. L. 2002. A local least squares framework for ensemble filtering. Mon. Wea. Rev. in pres.
    • Anderson, J. L. 2001. An ensemble adjustment kalman filter for data assimilation. Mon. Wea. Rev. 129, 2884-2903.
    • Anderson, J. L. and Anderson, S. L. 1999. A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Wea. Rev. 127, 2741-2758.
    • Anderson, J. L. 1996. A method for producing and evaluating probabilistic forecasts from ensemble model integrations. J. Climate 9, 1518-1530.
    • Bishop, C. H., Etherton, B. J. and Majumdar, S. 2001. Adaptive sampling with the ensemble transform Kalman filter, part I. Mon. Wea. Rev. 129, 420-436.
    • Bouttier, F. 1993. The dynamics of error covariances in a barotropic model. Tellus 45A, 408-423.
    • Buell, C. 1960. The structure of two-point wind correlations in the atmosphere. J. Geophys. Res. 65, 3353- 3366.
    • Buell, C. 1971. Two-point wind correlations on an isobaric surface in a non-homogeneous non-isotropic atmosphere. J. Appl. Meteorol. 10, 1266-1274.
    • Buell, C. 1972a. Correlation functions for wind and geopotential on isobaric surface. J. Appl. Meteorol. 11, 51-59.
    • Buell, C. 1972b. Variability of wind with distance and time on an isobaric surface. J. Appl. Meteorol. 11, 1085-1091.
    • Buell, C. and Seaman, R. 1983. The 'scissors effect': anisotropic and ageostrophic influences on wind correlation coefficients. Aust. Meteorol. Mag. 31, 77-83.
    • Burgers, G., van Leeuwen, P. J. and Evensen, G. 1998. Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev. 126, 1719-1724.
    • Cohn, S. E. 1993. Dynamics of short-term univariate forecast error covariances. Mon. Wea. Rev. 121, 3123-3149.
    • Daley, R. 1991. Atmospheric data analysis. Cambridge University Press, New York, 457 pp.
    • Dee, D. P. 1991. Simplification of the Kalman filter for meteorological data assimilation. Quart. J. R. Meteorol. Soc. 117, 365-384.
    • Ehrendorfer, M. and Tribbia, J. 1997. Optimal prediction of forecast error covariances through singular vectors. J. Atoms. Sci. 54, 286-313.
    • Evensen, G. 1994. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 99, 10143- 10162.
    • Gandin, L. S. 1963. Objective analysis of meteorological fields. Gidrometeorolicheskoe Izdatelstvo, Leningrad. English translation by: Israel Program for Scientific Translations, 242 pp. [NTIS N6618047, Library of Congress QC9 6, G3313].
    • Gardiner, C. W. 1983. Handbook of stochastic methods for physics, chemistry, and the natural sciences. SpringerVerlag, Berlin, 442 pp.
    • Ghil, M., Cohn, S., Tavantzis, J., Bube K. and Isaacson, E. 1981. Applications of estimation theory to numerical weather prediction. In Dynamical meteorology: Data assimilation methods,. Bengtsson et al., eds. Springer-Verlag, New York, 139-224.
    • Gleeson, T. A. 1961. A statistical theory of meteorological measurements and predictions. J. Meteorol. 18, 192-198.
    • Hamill, T. M. and Snyder, C. 2000. A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon. Wea. Rev. 128, 2905-2919.
    • Hamill, T. M., Whitaker, J. S. and Snyder, C. 2001. Distancedependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev. 129, 2776-2790.
    • Hollingsworth, A. and Lonnberg, P. 1986. The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: The wind field. Tellus 38A, 111- 136.
    • Hoskins, B. J. and Karoly, D. J. 1981. The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atoms. Sci. 38, 1179-1196.
    • Houtekamer, P. L. and Mitchell, H. L. 1998. Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev. 126, 796-811.
    • Houtekamer, P. L. and Mitchell, H. L. 2001. A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Wea. Rev. 129, 123-137.
    • Houtekamer, P. L., Lefaivre, L. and Derome, J. 1996. The RPN ensemble prediction system. In: Proc. ECMWF Seminar on Predictability, Vol. II, Reading, UK, 121-146.
    • Jazwinski, A. H. 1970. Stochastic processes and filtering theory. Academic Press, New York, 376 pp.
    • Kalman, R. 1960. A new approach to linear filtering and prediction problems. Trans. ASME, Ser. D 82, 35-45.
    • Kalman, R. and Bucy, R. 1961. New results in linear filtering and prediction theory. Trans. ASME, Ser. D 83, 95- 109.
    • Kalnay, E. and Toth, Z. 1996. Ensemble prediction at NCEP. Preprints 11th Conf. on Numerical Weather Prediction, Am. Meteorol. Soc., Norfolk, VA, 191-120.
    • Keppenne, C. L. 2000. Data assimilation into a primitive equation model with a parallel ensemble Kalman filter. Mon. Wea. Rev. 128, 1971-1981.
    • Kincaid, D. and Cheney, W. 1996. Numerical Analysis, 2nd Ed., Brooks/Cole Publishing Co., CA, USA, 804 pp.
    • Leith, C. E. 1974. Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev. 102, 409-418.
    • Lorenz, E. N. 1963. Deterministic non-periodic flow. J. Atoms. Sci. 20, 130-141.
    • Lorenz, E. N. 1984. Irregularity: A fundemental property of the atmosphere. Tellus 21, 739-759.
    • Miller, R. N. 1998. Introduction to the Kalman filter. In: Proceedings of the ECMWF Seminar on Data Assimilation,. European Center for Medium Range Weather Forecasting, Shinfield Park, Reading, UK, 9-11 September 1996, 47- 59.
    • Miller, R. N., Carter, E. F. and Blue, S. T. 1999. Data assimilation into nonlinear stochastic models. Tellus 51A, 167-194.
    • Miller, R. N., Ghil, M. and Gauthiez, P. 1994. Advanced data assimilation in strongly nonlinear dynamical system. J. Atoms. Sci. 51, 1037-1056.
    • Mitchell, H. L. and Houtekamer, P. L. 2000. An adaptive ensemble Kalman filter. Mon. Wea. Rev. 128, 416-433.
    • Molteni, F. R. B., Palmer, T. N. and Petroliagis, T. 1996. The ECMWF ensemble prediction system: Methodology and validation. Quart. J. R. Meteorol. Soc. 122, 73-119.
    • Parrish, D. F. and Deber, J. C. 1992. The national meteorological center's spectral statistical-interpolation analysis system. Mon. Wea. Rev. 120, 1747-1763.
    • Seaman, R. and Gauntlett, F. 1980. Directional dependence of zonal and meridional wind correlation coefficients. Aust. Meteorol. Mag. 28, 217-321.
    • Thiebaux, H. J. 1976. Anisotropic correlation functions for objective analysis. Mon. Wea. Rev. 104, 994-1002.
    • Thiebaux, H. J. 1985. On approximations to geopotential and wind-field correlation structures. Tellus 37A, 126-131.
    • Tippett, M. K., Anderson, J. L., Bishop, C. H., Hamill, T. M. and Whitaker, J. S. 2002. Ensemble square-root filters. Mon. Wea. Rev. in press.
    • Van Leeuwen, P. J. 1999. Comment on “Data assimilation using an ensemble Kalman filter technique.” Mon. Wea. Rev. 127, 1374-1377.
    • Whitaker, J. S. and Hamill, T. M. 2002. Ensemble data assimilation without perturbed observations. Mon. Wea. Rev. in press.
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