Derived fluence spectra for the two solar cases under investigation. The left panel corresponds to GLE05; the right panel corresponds to the AD774/775 SEP event. These plots are similar to Fig. 3, but for a fluence with the addition of the relevant data points for each event (based on Usoskin et al. 2021), depicted as filled blue circles, and the corresponding derived spectra calculated for each case from the relations presented in Sect. 3.