Saturation ratio S = P_v∕P_sat for water vapour throughout the simulation region. Black shows the initial saturation ratio and blue shows the state after an equilibrium between vapour and ice has been reached. The ice line location at the start of the simulation, where S reaches unity, is marked by the grey dashed line. Initially, all particles have a thin ice mantle, and the remaining water is distributed throughout the simulation domain as vapour, leading to a steeply rising S. The excess water is quickly deposited on the available solids, so that S ≈ 1 everywhere outside of the ice line, as shown for t = 10 yr.