The present study aims to understand the dynamical properties of water and OH groups layered on an alumina surface mainly by means of femtosecond IR-pump IR-probe transient absorption spectroscopy. The experimental results obtained demonstrate the existence of several kinds of O-H vibrators on the surface of alumina membranes, distinguishing them by their behavior on the femtosecond time scale and by the anisotropy of their spectral response. In the high-frequency region (>3400 cm-1), the absorption is due to well-packed aluminol groups and to physisorbed water patches on the surface. When pumping at 3200 cm-1, physisorbed water hydrogen-bonded to AlOH2+ groups is observed. The anisotropy measurements demonstrate the existence of an efficient energy-transfer mechanism among the water molecules characterized by a time constant of 400 +/- 100 fs. The persisting anisotropy at long times, especially in the case of AlOH groups and of the structured physisorbed water layer on top of them, proves the anisotropic structuring induced by the surface. The excitation at 3000 cm-1 enables the detection of a photon-induced proton-transfer reaction. The proton back-transfer reaction time constant is 350 +/- 50 fs. From anisotropy measurements, we estimate the proton hopping time to be 900 +/- 100 fs in a locally extended water network lying on the surface.