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The observed presence of water molecules in the dayside lunar regolith was anunexpected discovery and remains poorly understood. Standard thermophysicalmodels predict temperatures that are too high for adsorbed water to be stable.We propose that this problem can be caused by the assumption of locally flatsurfaces that is common in such models. Here we apply a model that explicitlyconsiders surface roughness, and accounts for solar illumination, shadows castby topography, self-heating, thermal reradiation, and heat conduction. Wecouple the thermophysical model to a model of first-order desorption of lunarsurface water and demonstrate that surface roughness substantially increasesthe capability of the Moon to retain water on its sunlit hemisphere at anylatitude, and within $45^{\circ}$ of the poles, at any time of the lunar day.Hence, we show that lunar surface roughness has a strong influence on lunarwater adsorption and desorption. Therefore, it is of critical importance totake account of surface roughness to get an accurate picture of the amount ofwater on the Moon's surface and in its exosphere.

Implications of Surface Roughness in Models of Water Desorption on the Moon