ALMA Memo No. 496.1 183 GHz water vapour radiometers for ALMA: Estimation of phase errors under varying atmospheric conditions

We investigate the use of water vapour radiometers as a tool for estimating phase due to atmospheric water, focusing on the impact of differing atmospheric conditions on the relationship between path length and brightness temperature. We provide a formula for converting between the two for a variety of atmospheric conditions, and outline how the radiometer channel temperatures may be combined to give an optimal estimate for the path difference. This estimate gives an error of about 2% per mm of precipitable water vapour due to atmospheric variations. The presence of hydrometeors such as ice or water droplets is also considered, and we show that radiometers possessing sideband separation could be used to detect the presence of 0.02 mm of column integrated ice for crystals of size 75μm, and about 10 mm of water droplets.