In the subsection below, we compare the potential profiles predicted by Gouy-Chapman theory to those calculated from simulation data. We find little consistency. We highlight in particular the non-triviality of representing water's interfacial dielectric response and comment on the manifestation of this response in the Madelung potential profiles. Then, in the subsequent subsection, we present the statistics of the Madelung potential fluctuations, highlighting their species-and position-dependence, as well as their finite-size effects.