On the other hand large operational centers are now using, or have planned to use, assimilation schemes based on a 3D or 4D variational approach, that especially allows the use of a wider range of observations. Diagnostics based on statistics between observations (including the background) and the minimizing solution have been proposed, that can be applied in a variational framework. In particular, it has been shown that a simple diagnostic is the value at the minimum of the cost function that measures the distance between observations and analysis.

We present a method based on diagnostics of observations-minus-analysis differences but that aims at performing an adaptive tuning of observation error parameters from a single batch of observations and background fields. The sum of these squared differences is computed for each subset of observations and compared to its statistical expectation: it is shown that the ratio of these two quantities should be close to the value of the error parameter for this given subset. The computation of the statistical expectation of a term of the cost function is shown to be feasible by performing a second analysis with perturbed observations. The principle of such a method is first shown on a simplified 1D-Var assimilation scheme, where one tries to recover the correct ratio between background and observation terms.

The method is then applied in the framework of the 3D/4D-Var assimilation scheme developed at Météo-France. The possibility to tune the statistics of observation errors for TOVS radiances is in particular investigated, as well as the impact of such a tuning for the analysis and the forecast of cyclones observed during the FASTEX experiment.

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