Cloud and precipitation processes are still a main source of uncertainties in numerical weather prediction and climate change projections. The Priority Programme “Polarimetric Radar Observations meet Atmospheric Modelling (PROM)”, funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG), is guided by the hypothesis that many uncertainties relate to the lack of observations suitable to challenge the representation of cloud and precipitation processes in atmospheric models. Such observations can, however, at present be provided by the recently installed dual-polarization C-band weather radar network of the German national meteorological service in synergy with cloud radars and other instruments at German supersites and similar national networks increasingly available worldwide. While polarimetric radars potentially provide valuable in-cloud information on hydrometeor type, quantity, and microphysical cloud and precipitation processes, and atmospheric models employ increasingly complex microphysical modules, considerable knowledge gaps still exist in the interpretation of the observations and in the optimal microphysics model process formulations. PROM is a coordinated interdisciplinary effort to increase the use of polarimetric radar observations in data assimilation, which requires a thorough evaluation and improvement of parameterizations of moist processes in atmospheric models. As an overview article of the inter-journal special issue “Fusion of radar polarimetry and numerical atmospheric modelling towards an improved understanding of cloud and precipitation processes”, this article outlines the knowledge achieved in PROM during the past 2 years and gives perspectives for the next 4 years.

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.

Numerical discretization schemes have a long history of incorporating the most important conservation properties of the continuous system in order to improve the prediction of the nonlinear flow. The question arises whether data assimilation algorithms should follow a similar approach. To address this issue, we explore the conservation properties during data assimilation using perfect model experiments with a 2D shallow‐water model preserving important properties of the true nonlinear flow. The data assimilation scheme used here is the Local Ensemble Transform Kalman Filter with varying observed variables, inflation, localization radius and thinning interval. It is found that, during the assimilation, the total energy of the analysis ensemble mean converges with time towards the nature run value. However, enstrophy, divergence and the energy spectra are strongly affected by the data assimilation settings. Having in mind that the conservation of both the kinetic energy and enstrophy by the momentum advection schemes in the case of non‐divergent flow prevents a systematic and unrealistic energy cascade towards the high wave numbers, we test the effects on the prediction depending on the type of error in the initial condition. During the assimilation, we assess the downward nonlinear energy cascade through a scalar, domain‐averaged noise measure. We show that the accumulated noise during assimilation and the error of analysis are good indicators of the quality of the prediction.

To account for model error on multiple scales in convective‐scale data assimilation, we incorporate the small‐scale additive noise based on random samples of model truncation error and combine it with the large‐scale additive noise based on random samples from global climatological atmospheric background error covariance. A series of experiments have been executed in the framework of the operational Kilometre‐scale ENsemble Data Assimilation system of the Deutscher Wetterdienst for a 2‐week period with different types of synoptic forcing of convection (i.e., strong or weak forcing). It is shown that the combination of large‐ and small‐scale additive noise is better than the application of large‐scale noise only. The specific increase in the background ensemble spread during data assimilation enhances the quality of short‐term 6‐hr precipitation forecasts. The improvement is especially significant during the weak forcing period, since the small‐scale additive noise increases the small‐scale variability which may favor occurrence of convection. It is also shown that additional perturbation of vertical velocity can further advance the performance of combination.

Different approaches for representing model error due to unresolved scales and processes are compared in convective-scale data assimilation, including the physically based stochastic perturbation (PSP) scheme for turbulence, an advanced warm bubble approach that automatically detects and triggers absent convective cells, and additive noise based on model truncation error. The analysis of kinetic energy spectrum guides the understanding of differences in precipitation forecasts. It is found that the PSP scheme results in more ensemble spread in assimilation cycles, but its effects on the root-mean-square error (RMSE) are neutral. This leads to positive impacts on precipitation forecasts that last up to three hours. The warm bubble technique does not create more spread, but is effective in reducing the RMSE, and improving precipitation forecasts for up to 3 h. The additive noise approach contributes greatly to ensemble spread, but it results in a larger RMSE during assimilation cycles. Nevertheless, it considerably improves the skill of precipitation forecasts up to 6 h. Combining the additive noise with either the PSP scheme or the warm bubble technique reduces the RMSE within cycles and improves the skill of the precipitation forecasts, with the latter being more beneficial.