The surface and bulk diffusion of (H2O)-O-18 on single-crystal (H2O)-O-16 ice multilayers grown epitaxially on Ru(001) were measured using laser-induced thermal desorption (LITD) techniques. Low-energy electron diffraction studies confirmed that the ice multilayers on Ru(001) were crystalline to thicknesses of at least 105 bilayers (i.e., similar to 385 Angstrom). Measurements of (H2O)-O-18 surface diffusion on the crystalline ice multilayers were performed using a scanning LITD method with mass spectrometric detection, Using a mask, one bilayer of isotopically-labeled (H2O)-O-18 was deposited on half of a crystalline (H2O)-O-16 ice multilayer. LITD measurements were then used to scan the coverage profile as a function of diffusion time at 140 K. No (H2O)-O-18 LITD signals were observed on the masked half of the crystal for diffusion times as long as 60 min. These measurements were consistent with an upper limit for (H2O)-O-18 surface diffusion of D-s less than or equal to 5x10(-9) cm(2)/s at 140 K. The lack of measurable surface diffusion may indicate that (H2O)-O-18 is diffusing into the underlying ice multilayer. H2O bulk diffusion was investigated with a novel technique utilizing a combination of isothermal desorption/depth profiling and LITD probing. In this new method, a single bilayer of (H2O)-O-18 was deposited on a crystalline (H2O)-O-16 multilayer. Isothermal desorption with zero-order desorption kinetics was then employed to depth profile the ice multilayer. LITD was concurrently used to monitor the isotopes remaining in the multilayer versus time. If the ice film desorbs in a layer-by-layer fashion with zero-order desorption kinetics and no interlayer mixing, the bilayer of (H2O)-O-18 should desorb from the ice surface in similar to 7 s at 160 K. However, (H2O)-O-18 diffusing readily into the underlying ice multilayer. The bulk diffusion coefficient of (H2O)-O-18 into crystalline ice multilayers of various thicknesses was determined to be D-B=1.5(+/-0.5)x10(-15) cm(2)/s at 160 K. Sandwich experiments with stacked multilayers confirmed that (H2O)-O-18 was diffusing into the ice bulk with no influence from a possible "liquid-like" laver on the ice surface, An Arrhenius analysis of the temperature-dependent bulk diffusion coefficients yielded an activation energy of E(B)=16.7+/-1.6 kcal/mol and a preexponential of D-0=9.7(+/-0.5)x10(7) cm(2)/s. This diffusion activation energy is within the experimental error of some of the previous measurements at higher temperatures close to the ice melting point. When the Arrhenius diffusion parameters are extended to the stratospheric temperature range of 180-210 K, the residence time tau of a H2O molecule on the ice surface ranges from 5.4x10(-3) s to 6.8x10(-6) s, respectively, before diffusion into the underlying ice bulk. These diffusion measurements indicate very dynamic ice surfaces at stratospheric temperatures that may facilitate the incorporation of reactants into stratospheric clouds.