Reflectivity, single-Doppler velocity, and near-surface refractivity index are assimilated into a non-hydrostatic fully compressible atmospheric model coupled with a warm microphysics scheme. The model is used as a weak constraint; i.e. the model error is explicit in the 4D-Var cost function. To provide a full domain analysis required for model initialization, a linear wind analysis in a moving frame is performed situ single-Doppler velocity measurements over a given assimilation window, which is then used as the background for the high-resolution analysis. The background-, observation- and model-error variances are adaptively tuned by matching them with the reduced cost function residuals. The method is able to fit the data over a short assimilation period while keeping model-error residuals small. Experiments with synthetic data from model outputs show that the method is also able to retrieve non-observed variables.

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