Methanol in a water-ice matrix sputtering rate as a function of the cosmic-ray ionisation rate. The different curves correspond to the methanol fraction with respect to the water ice that we measured here. This range covers most of the observational dispersion. This sputtering rate must formally be multiplied by two because the cosmic-ray projectiles move through the interstellar grains. The upper axis gives an estimate of the evolution of the corresponding secondary VUV photon flux (e.g. Shen et al. 2004; Prasad & Tarafdar 1983), given for comparison with photodesortion rates. The rate corresponding to ~   10⁻⁵   CH₃OH/VUV photon for a pure methanol-ice film is shown in green. This is the order of magnitude measured by Bertin et al. (2016), whereas Cruz-Diaz et al. (2016) obtained an upper limit that is three times higher. Cosmic-ray sputtering rates for methanol that is embedded in a CO matrix would be orders of magnitude higher because CO desorbs more efficiently.