Experiments on 4D-Var assimilation of rainfall data using an incremental formulation

Assimilations of isolated surface rainfall observations are performed using two methodologies compatible with the incremental formulation of the European Centre for Medium-Range Weather Forecasts operational 4D-Var system. In a first method (defined as '1D-Var + 4D-Var') 1D-Var retrievals of total column water vapour in rainy areas are assimilated in 4D-Var, while a second approach assimilates rainfall rates in 4D-Var directly. In addition, the behaviour of two contrasted convection schemes (mass-flux and adjustment) is examined. The minimization performs generally better for the adjustment scheme and for the '1D-Var+4D-Var' method (i.e. larger decrease of the cost function). The usefulness of the direct 4D-Var is limited by various inconsistencies present in the current incremental formulation and by the extreme sensitivity of the convection schemes to small changes in humidity. The two methods produce similar and small modifications to the dynamical fields, that are partly explained by the fact that the observation is assimilated early in the time window of 4D-Var (3 hours). This study demonstrates the need for convection schemes with smooth Jacobians in the variational context. It also confirms the robustness of the '1D-Var+4D-Var' approach than can be used for operational rainfall-rate assimilation as long as identified problems with the incremental 4D-Var are not solved.