Using a statistical approach, Scheihing attempts to demonstrate the direct influence of recharge events in the Precordillera and the Andean Piedmont on water table variations in downstream alluvial fans. The author "unquestionably" discards the existence of ephemeral recharge processes in alluvial fans although they are frequently impacted by major floods. However, the author does not consider previous publications about recharge processes in arid alluvial fans, the hydraulic setting of the Pampa del Tamarugal Aquifer (PTA) and anthropogenic pressure changes in the PTA. Because the sustainable management of groundwater resources in drylands depends on a good understanding of hydrogeological processes, we propose a thorough reinterpretation of the short- and long-term PTA water table variations addressed by the author. In this comment, we illustrate the limits of the sole use of a statistical approach for characterizing both recharge processes and factors controlling the water table variations in the Atacama Desert.