Editorial Type:
Article
Article Type:
Research Article

The Impact of Observational and Model Errors on Four-Dimensional Variational Data Assimilation

Chungu Lu NOAA/ERL Forecast Systems Laboratory, Boulder, Colorado

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Gerald L. Browning Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado

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Print Publication:
01 Mar 1998
DOI:
https://doi.org/10.1175/1520-0469(1998)055<0995:TIOOAM>2.0.CO;2
Page(s):
995–1011
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Abstract

The impact of observational and model errors on four-dimensional variational (4DVAR) data assimilation is analyzed for a general dynamical system. Numerical experiments with both the barotropic vorticity equation and the shallow water system are conducted. It is shown from the analysis and the numerical experiments that when there are random errors in observations or in model parameterizations, the 4DVAR assimilation method can suppress these errors; however, when the errors are systematic or biased, the 4DVAR assimilation method tends to either converge to the erroneous observations or introduce the model error into the data analysis, or both.

For a multiple-timescale fluid dynamical system, such as the shallow water equations with fluid depth corresponding to the external mode, the skewness in the system can amplify the errors, especially in the fast variable (e.g., the geopotential or height field).

Forecasts using the assimilated initial condition with an imperfect model indicate that the forecasts may or may not be improved, depending upon the nature of the model and observational errors, and the length of the assimilation and forecast periods.

Corresponding author address: Dr. Chungu Lu, NOAA/ERL Forecast Systems Laboratory, 325 Broadway, Boulder, CO 80303.

Abstract

The impact of observational and model errors on four-dimensional variational (4DVAR) data assimilation is analyzed for a general dynamical system. Numerical experiments with both the barotropic vorticity equation and the shallow water system are conducted. It is shown from the analysis and the numerical experiments that when there are random errors in observations or in model parameterizations, the 4DVAR assimilation method can suppress these errors; however, when the errors are systematic or biased, the 4DVAR assimilation method tends to either converge to the erroneous observations or introduce the model error into the data analysis, or both.

For a multiple-timescale fluid dynamical system, such as the shallow water equations with fluid depth corresponding to the external mode, the skewness in the system can amplify the errors, especially in the fast variable (e.g., the geopotential or height field).

Forecasts using the assimilated initial condition with an imperfect model indicate that the forecasts may or may not be improved, depending upon the nature of the model and observational errors, and the length of the assimilation and forecast periods.

Corresponding author address: Dr. Chungu Lu, NOAA/ERL Forecast Systems Laboratory, 325 Broadway, Boulder, CO 80303.

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  • Adams, J., P. Swarztrauber, and R. Sweet, 1988: A package of FORTRAN subprograms for the solution of separable elliptic partial differential equations. NCAR Publication. [Available from National Center for Atmosphere Research, Boulder, CO 80303.].

  • Bennett, A. F., 1992: Inverse Methods in Physical Oceanography. Cambridge University Press, 346 pp.

  • Boer, G. J., and T. G. Shepherd, 1983: Large-scale two-dimensional turbulence in the atmosphere. J. Atmos. Sci.,40, 164–184.

  • Brown, P. S., Jr., and G. D. Robinson, 1979: The variance spectrum of tropospheric winds over Eastern Europe. J. Atmos. Sci.,36, 270–286.

  • Browning, G. L., W. R. Holland, H.-O. Kreiss, and S. J. Worley, 1990: An accurate hyperbolic system for approximately hydrostatic and incompressible oceanographic flows. Dyn. Atmos. Oceans,14, 303–332.

  • 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.

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

  • Derber, J. C., 1989: A variational continuous assimilation technique. Mon. Wea. Rev.,117, 2437–2446.

  • Hack, J. J., 1994: Parameterization of moist convection in the National Center for Atmospheric Research community climate model (CCM2). J. Geophys. Res.,99, 5551–5568.

  • Heckley, W. H., 1985: Systematic errors of the ECMWF operational forecasting model in tropical regions. Quart. J. Roy. Meteor. Soc.,111, 709–738.

  • LeDimet, 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 advective constraints. Tellus,37A, 309–322.

  • Lu, C., and G. L. Browning, 1998: The impact of observational errors on objective analyses. J. Atmos. Sci., in press.

  • Matsuno, T., 1966: Quasi-geostrophic motions in the equatorial area. J. Meteor. Soc. Japan,44, 25–42.

  • Ménard, R., and R. Daley, 1996: The application of Kalman smoother theory to the estimation of 4DVAR error statistics. Tellus,48A, 221–237.

  • Panofsky, H., 1949: Objective weather-map analysis. J. Meteor.,6, 386–392.

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

  • Thacker, W. C., and R. B. Long, 1987: Fitting dynamics to data. J. Geophys. Res.,93, 1227–1240.

  • Wergen, W., 1992: The effect of model errors in variational assimilation. Tellus,44A, 297–313.

  • Zou, X., I. M. Navon, and F. X. LeDimet, 1992: Incomplete observations and control of gravity waves in variational data assimilation. Tellus,44A, 273–296.

  • Zupanski, M., 1993: Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment. Mon. Wea. Rev.,121, 2396–2408.

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