We apply a recently developed method, the Ensemble Prediction and Parameter Estimation System (EPPES), to demonstrate how numerical weather prediction (NWP) model closure parameters can be optimized. As proof of concept, we tune the medium-range forecast skill of the ECMWF model HAMburg version (ECHAM5) atmospheric general circulation model using an ensemble prediction system (EPS) emulator. Initial state uncertainty is represented in the EPS emulator by applying the initial state perturbations generated at the European Centre for Medium-range Weather Forecasts (ECMWF). Model uncertainty is represented in the emulator via parameter variations at the initial time. We vary four closure parameters related to parametrizations of subgrid-scale physical processes of clouds and precipitation. With this set-up, we generate ensembles of 10-day global forecasts with the ECHAM5 model at T42L31 resolution twice a day over a period of three months. The cost function in the optimization is formulated in terms of standard forecast skill scores, verified against the ECMWF operational analyses. A summarizing conclusion of the experiments is that the EPPES method is able to find ECHAM5 model closure parameter values that correspond to smaller values of the cost function. The forecast skill score improvements verify positively in dependent and independent samples. The main reason is the reduced temperature bias in the tropical lower troposphere. Moreover, the optimization improved the top-of-atmosphere radiation flux climatology of the ECHAM5 model, as verified against the Clouds and the Earth's Radiant Energy System (CERES) radiation data over a 6-year period, while the simulated tropical cloud cover was reduced, thereby increasing a negative bias as verified against the International Satellite Cloud Climatology Project (ISCCP) data.