A 4D-Var cloud-scale radar data assimilation algorithm developed at the McGill University uses the dynamic core of the MC2 model with Kessler microphysics parameterization of as a weak constraint, to retrieve the different fields of the model prognostic variables from the S-band Doppler radar of McGill and its associated bistatic network. In this algorithm, the model error is taken into account in the cost function and the minimization is obtained by the conjugate gradient method. The gradient of the cost function is simply obtained by differentiation, and thus there is no need for backward integrations of an adjoint model. Applying this algorithm to summer storms, Montmerle et al. (2001 and 2002) have successfully initialized the MC2 model to produce a 1 km resolution and 30 min forecast with skill better than the one obtained by the Lagrangian persistence method.

The cost function is clearly not of a quadratic form in general and the conjugate gradient method minimization could be trapped into a local minimum. To enhance the ability to find the global minimum, a cycle of assimilation is performed with one additional radar volume scan introduced in each successive cycle. The analysis from the previous cycle is used as the background field and first guesses of the minimization algorithm for the next cycle. The benefit of a forward-backward feedback loop from consecutive cycles is examined. Preliminary results, performed by two successive assimilation cycles with four volume scans of radar data of a shallow hailstorm on 26 May 1997, show that after two feedback looping more realistic dynamic features of convective cells are observed in the retrieval fields at the same time as both, observation and model residuals are reduced in the cost function. In further research, a number of cycle assimilation experiments will be conducted to examine the sensitivity of the minimization algorithm to the background term and the first guess as well as to tuning of the weight in the smoothness constraint. The results of a 30-min forecast of the MC2 model will be shown initialized with the analysis of these experiments to evaluate the quality of the retrieval fields.