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Comparison of Local Ensemble Transform Kalman Filter, 3DVAR, and 4DVAR in a Quasigeostrophic Model

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  • 1 Earth System Science Interdisciplinary Center, Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, and Global Modeling Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, Maryland
  • | 2 ARPAL–CFMI-PC, Genoa, Italy
  • | 3 Institut Royal Meteorologique de Belgique, Brussels, Belgium
  • | 4 Earth System Science Interdisciplinary Center, Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland
  • | 5 Numerical Prediction Division, Japan Meteorological Agency, Tokyo, Japan
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Abstract

Local ensemble transform Kalman filter (LETKF) data assimilation, three-dimensional variational data assimilation (3DVAR), and four-dimensional variational data assimilation (4DVAR) schemes are implemented in a quasigeostrophic channel model. Their advantages and disadvantages are compared to assess their use in practical applications. LETKF and 4DVAR, which take into account the flow-dependent errors, outperform 3DVAR under a perfect model scenario. Given the same observations, LETKF produces more accurate analyses than 4DVAR with a 12-h window by effectively correcting the fast-growing errors with the flow-dependent background error covariance. Even though 4DVAR performance benefits substantially from using a longer assimilation window, LETKF is also able to achieve a satisfactory accuracy compared to the 24-h 4DVAR analyses. It is shown that the advantage of the LETKF over 3DVAR is a result of both the ensemble averaging and the information about the “errors of the day” provided by the ensemble. The analysis corrections at the end of the 12-h assimilation window are similar for LETKF and the 12-h window 4DVAR, and they both resemble bred vectors. At the beginning of the assimilation window, LETKF analysis corrections obtained using a no-cost smoother also resemble the corresponding bred vectors, whereas the 4DVAR corrections are significantly different with much larger horizontal scales.

* Current affiliation: Department of Atmospheric Sciences, National Central University, Jhongli, Taiwan.

Corresponding author address: Shu-Chih Yang, Department of Atmospheric Sciences, National Central University, Jhongli 32001, Taiwan. Email: shuchih.yang@atm.ncu.edu.tw

Abstract

Local ensemble transform Kalman filter (LETKF) data assimilation, three-dimensional variational data assimilation (3DVAR), and four-dimensional variational data assimilation (4DVAR) schemes are implemented in a quasigeostrophic channel model. Their advantages and disadvantages are compared to assess their use in practical applications. LETKF and 4DVAR, which take into account the flow-dependent errors, outperform 3DVAR under a perfect model scenario. Given the same observations, LETKF produces more accurate analyses than 4DVAR with a 12-h window by effectively correcting the fast-growing errors with the flow-dependent background error covariance. Even though 4DVAR performance benefits substantially from using a longer assimilation window, LETKF is also able to achieve a satisfactory accuracy compared to the 24-h 4DVAR analyses. It is shown that the advantage of the LETKF over 3DVAR is a result of both the ensemble averaging and the information about the “errors of the day” provided by the ensemble. The analysis corrections at the end of the 12-h assimilation window are similar for LETKF and the 12-h window 4DVAR, and they both resemble bred vectors. At the beginning of the assimilation window, LETKF analysis corrections obtained using a no-cost smoother also resemble the corresponding bred vectors, whereas the 4DVAR corrections are significantly different with much larger horizontal scales.

* Current affiliation: Department of Atmospheric Sciences, National Central University, Jhongli, Taiwan.

Corresponding author address: Shu-Chih Yang, Department of Atmospheric Sciences, National Central University, Jhongli 32001, Taiwan. Email: shuchih.yang@atm.ncu.edu.tw

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