In a radio interferometer, the geometrical antenna positions are determined from measurements of the observed delay to each antenna from observations across the sky of many point sources whose positions are known to high accuracy. The determination of accurate antenna positions relies on accurate calibration of the dry and wet delay of the atmosphere above each antenna. For the Atacama Large Millimeter/Submillimeter Array (ALMA), with baseline lengths up to 15 kilometers, the geography of the site forces the height above mean sea level of the more distant antenna pads to be significantly lower than the central array. Thus, both the ground level meteorological values and the total water column can be quite different between antennas in the extended configurations. During 2015, a network of six additional weather stations was installed to monitor pressure, temperature, relative humidity and wind velocity, in order to test whether inclusion of these parameters could improve the repeatability of antenna position determinations in these configurations. We present an analysis of the data obtained during the ALMA Long Baseline Campaign of October through November 2015. The repeatability of antenna position measurements typically degrades as a function of antenna distance. Also, the scatter is more than three times worse in the vertical direction than in the local tangent plane, suggesting that a systematic effect is limiting the measurements. So far we have explored correcting the delay model for deviations from hydrostatic equilibrium in the measured air pressure and separating the partial pressure of water from the total pressure using water vapor radiometer (WVR) data. Correcting for these combined effects still does not provide a good match to the residual position errors in the vertical direction. One hypothesis is that the current model of water vapor may be too simple to fully remove the day-to-day variations in the wet delay. We describe possible new avenues of improvement, which include recalibrating the baseline measurement datasets using the contemporaneous measurements of the water vapor scale height and temperature lapse rate from the oxygen sounder, and applying more accurate measurements of the sky coupling of the WVRs.