A comparison between four‐dimensional variational assimilation and simplified sequential assimilation relying on three‐dimensional variational analysis

Abstract The aim of this study is to make a strict comparison between two assimilation algorithms, sequential and four‐dimensional variational, on a 24‐hour period extracted from a baroclinic instability situation representative of mid‐latitude dynamics. In the case of linear dynamics, and under the hypothesis of a perfect model, these two four‐dimensional algorithms are known to lead to the same optimal estimate of the atmosphere at the end of the assimilation period, and both methods can be generalized in the nonlinear case. Because the full sequential algorithm is too resource‐demanding to be implemented as such, we shall test the four‐dimensional variational method (4D‐VAR), and a simplified sequential method based on three‐dimensional variational analysis (3D‐VAR), deliberately not exceeding the range of validity of the tangent‐linear model in the experiments. 4D‐VAR is then expected to be almost equivalent to the generalization of the sequential Kalman filter in the nonlinear 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 evaluated only approximately before each analysis, instead of being explicitly computed from the complete dynamical equations. In the four‐dimensional variational scheme, the consistency of the propagation of information with the dynamics is illustrated in an experiment assimilating some localized AIREP data. The large impact which these additional observations have over a large geographical area appears to be very beneficial for the quality of the analysis. Comparing the results of both methods 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 period and a much smaller error growth rate in subsequent forecasts. On the one hand, extremely bad specifications of initial forecast errors were found to be detrimental to both algorithms. On the other hand, the four‐dimensional variational algorithm proves to be more robust to the way by which gravity‐wave control is implemented.