Before the WLM data can be used to apply phase corrections to the astronomy data, there are various calibration steps that must be followed. To simplify the problem somewhat, the basic equation describing the observed WLM temperatures is given above. T(t,el) is the observed water line temperature as a function of time and elevation, G is the gain of the WLM box, dT(t,el) is the short fluctuations in the WLM temperatures, and C(t) is the electronic offset of each WLM box which can vary as a function of time. The first term in this equation represents the observed water vapor fluctuations that are common to each line of sight in the array. These fluctuations are cancelled when taking the difference between any two WLM boxes (i.e. the data for any one baseline), and hence this term does not contribute any phase fluctuations to the astronomy measurements. The second term in the equation represents the fluctuations that we want to solve for, since it contains all of the phase noise caused by variations in the amount of atmospheric water vapor.

(1) The first step is to normalizing the WLM gains so that all of the WLM boxes are on the same temperature scale. The gains are calibrated using the source changes that occur throughout the track, and is described in more detail on the next page.

(2) Once the gains are calibrated, there are two type of corrections that can be made: coherence corrections and full phase corrections. Coherence corrections are the most straight forward since they only involve the fluctuations in the WLM signal from one 2 second sample to the next. The mean level of the WLM temperature for any given scan is subtracted out. Applying full phase corrections are more difficult since the phases must be "linked" between the on-source observations and the various calibrators observed during the track. To solve this problem, we assume that the water vapor fluctuations (i.e. the dT(t,el) term) averages to zero on 30-60 minute time scales. With this assumption, we can ignore the dT(t,el) and fit the above equation to the WLM measurements from all antennas simultaneously. The fit is subtracted from the observed WLM temperatures, and the residuals represent the water vapor fluctuations.

(3) The last step is to convert the WLM fluctuations into a corresponding change in astronomical phase. This conversion factor is established by observing a bright quasar during the track, and correlating the observed astronomical phases with the corresponding WLM fluctuations. In practice, we typically adopt a constant conversion factor of 12 millimeters of delay per K.