Neutrinos of astrophysical origin could be detected through the electromagnetic radiation of the particle showers induced in the atmosphere by their interaction in the Earth. This applies in particular for tau neutrinos of energies E>1016eV following Earth-skimming trajectories. The ∼1° beaming of the radio emission in the forward direction however implies that the radio signal will likely fly above a detector deployed over a flat site and would therefore not be detected. We study here how a non-flat detector topography can improve the detection probability of these neutrino-induced air showers. We do this by computing with three distinct tools the neutrino detection efficiency for a radio array deployed over a toy-model mountainous terrain...