ICON-A is a core component of the German natESM system.

ICON-A provides a compelling representation of the mean climate and its variability for the global atmosphere for mostly long simulations developed by MPI-M and DWD. Its climate is similar to that of the last release of the ECHAM model. The atmosphere uses a icosahedral nonhydrostatic dynamical core.
Core features are the closed water cycle and the realistic energy budget, especially at the top of the atmosphere.

The atmosphere model ICON-A and the ocean model ICON-O have been developed jointly. A main accomplishment of the joint development is that the two models share the same technical infrastructure that covers in particular High-Performance-Computing aspects.

The software ICON is now open-source (BSD-3C license).

More information, references, model description about ICON-A here and evaluation here. The ICON documentation is filed on an ICON-wiki

If you want to get started, you have to get in touch with the developers. There are also yearly Numerical Model Training Courses - more information.