In a recent study we showed, by incoherent elastic and quasielastic neutron scattering measurements, the existence of non-harmonic motion of hydrogen in ordinary ice. The motion observed is localized, non-vibrational, and related to the hydrogen disorder since it is absent in ordered ice VIII. A main jump distance of 0.75 Ang, i.e. close to the distance between the two possible proton sites along the oxygen-oxygen bond, and a low activation barrier characterize the process. The results obtained suggest that a concerted quantum proton tunnelling could be at the basis of the observed dynamics. This proposal aims at properly characterizing this tunnelling process measuring the intensity dependence of the QENS signal in the low temperature region (1.5-20 K), and at defining the geometry of the coordinate motion by measuring the QENS reply of an ice Ih single crystal.