For ensemble data assimilation, background error covariance should account for sampling and model errors. There are a number of approaches that have been developed that try to consider these errors;among them, additive noise and relaxation methods (relaxation to prior perturbation and relaxation to prior spread) are often used. In this work, we compare additive noise, based on random samples from global climatological atmospheric background error covariance, to relaxation methods as well as combinations. Our experiments have been conducted in framework of convective-scale data assimilation with conventional and radar reflectivity observations hourly assimilated for a 2-week convective period over Germany. In the first week under weather conditions characterized by strong large-scale forcing of convection, additive noise performs equally or even better than relaxation methods and combinations during both assimilation and short-range forecasts. In addition, it is shown that the relaxation to prior perturbation may be associated with smoothing of background errors that negatively affect small-scale structures and that the relaxation to prior spread yields more unbalanced model states. For the second week in absence of strong forcing, the performance of additive noise relative to combinations has been degraded a bit but results are still comparable. Overall, additive noise provides a good benchmark for further developments in representation of model error for convective-scale data assimilation.