Distribution of N (electrons N_e and protons N_p, left) and ΔN (right) as a function of the altitude from the solar surface, defined as the photosphere level R_⊙,opt. The respective shaded area indicates the 1σ error of these distributions. The black line indicates the theoretical N distributions of the original eSSC model. The blue vertical line indicates the altitude, h_SSC, below which the SSC model is defined. The y-axis of these plots is shown in logarithmic scale. The best-fit n distributions are compatible (within an uncertainty ≲25%) with the original eSSC model below ∼100 Mm; above this altitude, these distributions are characterised by high uncertainty (up to 70%).