The physical processes affecting the dynamics of the Earth's particle radiation environment are reviewed along with scientific and engineering models developed for its description. The emphasis is on models that are either operational engineering models or models presently under development for this purpose. Three components of the radiation environment, i.e., galactic cosmic rays (GCRs), solar energetic particles (SEPs) and trapped radiation, are considered separately. In the case of SEP models, we make a distinction between statistical flux/fluence models and those aimed at forecasting events. Models of the effects of particle radiation on the atmosphere are also reviewed. Further, we summarize the main features of the models and discuss the main outstanding issues concerning the models and their possible use in operational space weather forecasting. We emphasize the need for continuing the development of physics-based models of the Earth's particle radiation environment, and their validation with observational data, until the models are ready to be used for nowcasting and/or forecasting the dynamics of the environment
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