A COMPARISON BETWEEN 4-DIMENSIONAL VARIATIONAL ASSIMILATION AND SIMPLIFIED SEQUENTIAL ASSIMILATION RELYING ON 3-DIMENSIONAL VARIATIONAL ANALYSIS

The aim of this study is to make a strict comparison between two assim ilation algorithms, sequential and four-dimensional variational, on a 24-ho.ur period extracted from a baroclinic instability situation repr esentative of mid-latitude dynamics. In the case of linear dynamics, a nd under the hypothesis of a perfect model, these two four-dimensional algorithms are known to lead to the same optimal estimate of the atmo sphere at the end of the assimilation period, and both methods can be generalized in the nonlinear case. Because the full sequential algorit hm is too resource-demanding to be implemented as such, we shall test the four-dimensional variational method (4D-VAR), and a simplified seq uential method based on three-dimensional variational analysis (3D-VAR ), deliberately not exceeding the range of validity of the tangent-lin ear model in the experiments. 4D-VAR is then expected to be almost equ ivalent to the generalization of the sequential Kalman filter in the n onlinear case, i.e. the extended Kalman filter. As for the simplified sequential algorithm, it can be seen as an approximation of this full extended Kalman filter, for which the forecast error matrices are eval uated only approximately before each analysis, instead of being explic itly computed from the complete dynamical equations. In the four-dimen sional variational scheme, the consistency of the propagation of infor mation with the dynamics is illustrated in an experiment assimilating some localized AIREP data. The large impact which these additional obs ervations have over a large geographical area appears to be very benef icial for the quality of the analysis. Comparing the results of both m ethods in various configurations, we found that 4D-VAR systematically behaved substantially better than the simplified sequential algorithm, and had a more accurate analysis at the end of the assimilation perio d and a much smaller error growth rate in subsequent forecasts. On the one hand, extremely bad specifications of initial forecast errors wer e found to be detrimental to both algorithms. On the other hand, the f our-dimensional variational algorithm proves to be more robust to the way by which gravity-wave control is implemented.