  Close to the triple point, the surface of ice is covered by a thin liquid
layer (so-called quasi-liquid layer) which crucially impacts growth and melting
rates. Experimental probes cannot observe the growth processes below this
layer, and classical models of growth by vapor deposition do not account for
the formation of premelting films. Here, we develop a mesoscopic model of
liquid-film mediated ice growth, and identify the various resulting growth
regimes. At low saturation, freezing proceeds by terrace spreading, but the
motion of the buried solid is conveyed through the liquid to the outer
liquid-vapor interface. At higher saturations water droplets condense, a large
crater forms below, and freezing proceeds undetectably beneath the droplet. Our
approach is a general framework that naturally models freezing close to three
phase coexistence and provides a first principle theory of ice growth and
melting which may prove useful in the geosciences.
