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Context. The diffusion of volatile species on amorphous solid water iceaffects the chemistry on dust grains in the interstellar medium as well as thetrapping of gases enriching planetary atmospheres or present in cometarymaterial.  Aims. The aim of the work is to provide diffusion coefficients of CH$_4$ onamorphous solid water (ASW), and to understand how they are affected by the ASWstructure.  Methods. Ice mixtures of H$_2$O and CH$_4$ were grown in different conditionsand the sublimation of CH$_4$ was monitored via infrared spectroscopy or viathe mass loss of a cryogenic quartz crystal microbalance. Diffusioncoefficients were obtained from the experimental data assuming the systems obeyFick's law of diffusion. Monte Carlo simulations modeled the differentamorphous solid water ice structures investigated and were used to reproduceand interpret the experimental results.  Results. Diffusion coefficients of methane on amorphous solid water have beenmeasured to be between 10$^{-12}$ and 10$^{-13}$ cm$^2$ s$^{-1}$ fortemperatures ranging between 42 K and 60 K. We showed that diffusion can differby one order of magnitude depending on the morphology of amorphous solid water.The porosity within water ice, and the network created by pore coalescence,enhance the diffusion of species within the pores.The diffusion rates derivedexperimentally cannot be used in our Monte Carlo simulations to reproduce themeasurements.  Conclusions. We conclude that Fick's law can be used to describe diffusion atthe macroscopic scale, while Monte Carlo simulations describe the microscopicscale where trapping of species in the ices (and their movement) is considered.

Diffusion of CH$_4$ in amorphous solid water