We here show that dual-band GPS measurements of precipitable water vapor (PWV) at KPNO predict the overall per-image sensitivity of the Mayall z-band Legacy Survey (MzLS). The per-image variation in the brightness of individual stars is strongly correlated with the measured PWV and the color of the star. We use synthetic stellar spectra and TAPAS transmission models to predict the expected PWV-induced photometric errors and find good agreement with the observations. We also find that PWV absorption can be well-approximated by a linear relationship with PWV_eff and present an update on the traditional treatment in the literature. Within the range of reasonable observing conditions, the MzLS zero point varies with a standard deviation of 127 mmag. This variation is dominated by a gray secular trend with time, consistent with a gradual accumulation of contamination on optical surfaces that accounts for ~114 mmag of variation. Correcting for PWV based on a suite of stellar spectra and detailed PWV absorption models accounts for another 47 mmag of zero-point variation. The MzLS per-image sensitivity is decreased by ~40 mmag per effective mm of PWV. The difference between blue (r-z < 0.5 mag) and red (1.2 mag < r-z) stars increases by 3.25 mmag per effective mm of PWV. These results show the need for high-precision photometric surveys to simultaneously monitor PWV. We find that this GPS system provides more precise PWV measurements than using differential measurements of stars of different colors and recommend that observatories install dual-band GPS as a low-maintenance, relatively low cost, auxiliary calibration system. We extend our results of the need for well-calibrated PWV measurements by presenting calculations of the PWV photometric impact on three science cases of interest: stellar photometry, supernova cosmology, and quasar identification and variability.
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