The virtual enhancements − solar proton event radiation (VESPER) model Sigiava Aminalragia-Giamini, Ingmar Sandberg, Constantinos Papadimitriou, Ioannis A. Daglis and Piers Jiggens J. Space Weather Space Clim., 8 (2018) A06 Published online: 06 February 2018 DOI: 10.1051/swsc/2017040