Assimilation of radar observations into a cloud -resolving model

A four dimensional variational (4D-Var) formulation is developed for the assimilation of radar reflectivity, Doppler velocities, and near-surface refractivity index data into a non-hydrostatic fully compressible limited-area atmospheric model coupled with a simplified warm microphysics scheme. The cloud-model is used as a weak constraint so the model error is explicit in the 4D-Var formulation. The ultimate goal is to provide initial conditions to a high-resolution numerical weather prediction model. The environmental flow around storms is modelled by a linear wind in a moving frame using Doppler velocity measurements over a given assimilation window. A three-stage procedure is established to solve the assimilation problem. The background-, observationand model-error statistics are adaptively estimated by comparison with a posteriori residuals and they converge after only a few minimizations. During the adaptive procedure, a smoothing constraint is applied to the analysis variables. The smoothing constraint diminishes towards zero for the last minimization while still leading to a smooth analysis.;Experiments with synthetic data from model outputs at 1 km horizontal resolution show that the method is able to retrieve unobserved variables. An assimilation period of 10 minutes is shown to be optimal for the analysis of clouds. All the other variables of the model are rather insensitive to the assimilation period. Here the model time step has been varied from 1 to 5 minutes. Most of the a posteriori residual distributions have a high kurtosis while the velocity and the near-surface refractivity index residual distributions are nearly Gaussian. The data assimilation for the case of a shallow hailstorm suggests that the model used for the assimilation is able to forecast the system for 30 minutes within the estimated observational errors. Application of the method to the initialization of the MC2 model leads to a better forecast of a convective system over 40 minutes than the nowcasting technique based on Lagrangian persistence.