We studied diffusion of water molecules in the direction perpendicular to the surface of an ice film. Amorphous ice films of H2O were deposited on Ru(0001) at temperature of 100-140 K for thickness of 1-5 bilayer (BL) in vacuum, and a fractional coverage of D2O was added onto the surface. Vertical migration of surface D2O molecules to the underlying H2O multilayer and the reverse migration of H2O resulted in change of their surface concentrations. Temporal variation of the H2O and D2O surface concentrations was monitored by the technique of Cs+ reactive ion scattering to reveal kinetics of the vertical diffusion in depth resolution of 1 BL. The first-order rate coefficient for the migration of surface water molecules ranged from k(1)=5.7(+/-0.6)x10(-4) s(-1) at T=100 K to k(1)=6.7(+/-2.0)x10(-2) s(-1) at 140 K, with an activation energy of 13.7+/-1.7 kJ mol(-1). The equivalent surface diffusion coefficients were D-s=7x10(-19) cm(2) s(-1) at 100 K and D-s=8x10(-17) cm(2) s(-1) at 140 K. The measured activation energy was close to interstitial migration energy (15 kJ mol(-1)) and was much lower than diffusion activation energy in bulk ice (52-70 kJ mol(-1)). The result suggested that water molecules diffused via the interstitial mechanism near the surface where defect concentrations were very high. (C) 2004 American Institute of Physics.