Magnetic flux synoptic charts are critical for reliable modeling of the corona and heliosphere. Until now, however, these charts were provided without any estimate of uncertainties. The uncertainties are due to instrumental noise in the measurements and to the spatial variance of the magnetic flux distribution that contributes to each bin in the synoptic chart. We describe here a simple method to compute synoptic magnetic flux maps and their corresponding magnetic flux spatial variance charts that can be used to estimate the uncertainty in the results of coronal models. We have tested this approach by computing a potential-field-source-surface model of the coronal field for a Monte Carlo simulation of Carrington synoptic magnetic flux maps generated from the variance map. We show that these uncertainties affect both the locations of source-surface neutral lines and the distributions of coronal holes in the models. ; Comment: 15 pages, 7 figures. Accepted for publication in "Solar Physics"