The fluxes of energetic particles in the radiation belts are found to be strongly controlled by the solar wind conditions. In order to understand and predict the radiation particle intensities, we have developed a physics-based Radiation Belt Environment (RBE) model that considers the influences from the solar wind, ring current and plasmasphere. Recently, an improved calculation of wave-particle interactions has been incorporated. In particular, the model now includes cross diffusion in energy and pitch-angle. We find that the exclusion of cross diffusion could cause significant overestimation of electron flux enhancement during storm recovery. The RBE model is also connected to MHD fields so that the response of the radiation belts to fast variations in the global magnetosphere can be studied. We are able to reproduce the rapid flux increase during a substorm dipolarization on 4 September 2008. The timing is much shorter than the time scale of wave associated acceleration.