The Apollo Suprathermal Ion Detector Experiments (SIDEs) deployed on the lunar surface observe sporadic bursts of positive ions throughout the local lunar night. Evidence exists that the source of these events is most likely the dayside lunar atmosphere. Ionization of the neutral lunar atmosphere by photoionization or chargeexchange produces a population of ions over the sunlit portion of the moon. These ions are accelerated by the interplanetary electric field, executing cycloidal trajectories that may bring them onto the nightside hemisphere of the moon. A nightside surface electric field directed radially inward can then further accelerate these ions onto the lunar surface, altering their energies and trajectories such that they are detected by the SIDE. It is possible to obtain ion trajectories that intersect various positions on the nightside of the moon in this manner. For several nighttime ion events, synthetic particle data have been produced with this model which are in agreement with the observed data. Parameters of the nightside surface potential distribution are determined for the selected events. A profile of the expected surface potential over the nightside hemisphere of the moon indicates a variable surface potential. The height distribution over which the potential is effective becomes increasingly larger, while the magnitude of the surface potential becomes increasingly negative, when approaching local lunar midnight. Assuming an exponential neutral nimber density profile for all atmospheric constituents, indirect observations of the neutral lunar atmosphere can be made by the SIDE. Combined with the effect of the surface potential on the height distribution of these ions, number densities for various species in the lunar atmosphere determined in this manner are in agreement with reported values from various other experiments also deployed on the lunar surface.