The natural radiative atmospheric environment is composed of secondary cosmic rays produced when primary cosmic rays hit the atmosphere. Understanding atmospheric radiations and their dynamics is essential for evaluating single event effects, so that radiation risks in aviation and the space environment (space weather) can be assessed. In this article, we present an atmospheric radiation model, named ATMORAD (Atmospheric Radiation), which is based on GEANT4 simulations of extensive air showers according to primary spectra that depend only on the solar modulation potential (force-field approximation). Based on neutron spectrometry, solar modulation potential can be deduced using neutron spectrometer measurements and ATMORAD. Some comparisons between our methodology and standard approaches or measurements are also discussed. This work demonstrates the potential for using simulations of extensive air showers and neutron spectroscopy to monitor solar activity.