Simulated electron spectra at 1 au derived from an SPL spectrum injected at different r, after considering the electron energy loss due to Coulomb collisions with the 0.2-fold, 1-fold and 5-fold electron density models and due to the ambipolar electrostatic potential between the Sun and IPM. The injected spectral index of 2.5 is the median index value of the power-law electron populations in the selected bump SEE events. We applied the 0.2-fold and 5-fold density models to estimate the uncertainties of the source height that are caused by varying the magnitude of density model.