  Time-dependent and systematic variations in band gain and central frequencies
of instruments used to study the Cosmic Microwave Background are important
factors in the data-to-map analysis pipeline. If not properly characterized,
they could limit the ability of next-generation experiments to remove
astrophysical foreground contamination. Uncertainties include the instrument
detector band, which could systematically change across the focal plane, as
well as the calibration of the instrument used to measure the bands. A
potentially major effect is time-dependent gain and band uncertainties caused
by atmospheric fluctuations. More specifically, changes in atmospheric
conditions lead to frequency-dependent changes in the atmospheric transmission
which, in turn, leads to variations in the effective gain and central frequency
of the instrument's bandpass. Using atmospheric modeling software and ACTPol
bandpasses, we simulate the expected variations in band gain and central
frequency for 20, 40, 90, 150, and 240 GHz bands as a function of precipitable
water vapor, observing angle, and ground temperature. Combining these effects
enables us to set maximum and minimum limits on the expected uncertainties in
band gain and central frequency over the course of a full observing season. We
then introduce the uncertainties to parametric maximum-likelihood component
separation methods on simulated CMB maps to forecast foreground removal
performance and likelihoods on the tensor-to-scalar ratio r. We conclude that
to measure a $\sigma(r=0)$ ~ $10^{-3}$ with a bias on the recovered $r$ under
control, the limit on the uncertainty in the relative gain and central
frequency of the bandpass must be <2% and <1%, respectively. We also comment on
the possibility of self-calibrating bandpass uncertainties.
