The growth of water on thin SiO2 films on Si wafers at vapor pressures between 1.5 and 4 Torr and temperatures between -10 and 21 degrees C has been studied in situ using Kelvin probe microscopy and X-ray photoemission and absorption spectroscopies. From 0 to 75% relative humidity (RH), water adsorbs forming a uniform film 4-5 layers thick. The surface potential increases in that RH range by about 400 mV and remains constant upon further increase of the RH. Above 75% RH, the water film grows rapidly, reaching 6-7 monolayers at around 90% RH and forming a macroscopic drop near 100%. The 0 K-edge near-edge X-ray absorption spectrum around 75% RH is similar to that of liquid water (imperfect H-bonding coordination) at temperatures above 0 degrees C and is ice-like below 0 degrees C.