Comparison of local ensemble transform Kalman filter, 3DVAR, and 4DVAR in a quasigeostrophic model

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.