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Fluctuations in brightness due to water vapor in the Earth’s atmosphere are an important source of noise for ground-based instruments attempting to measure the anisotropy of the cosmic microwave background. This paper presents a Kolmogorov model of atmospheric fluctuations, and derives simple expressions to predict the impact of fluctuations on experimental measurements for three instrument configurations: chopped-beam, swept-beam, and interferometer. Data from the South Pole and from the Atacama Desert in Chile, two of the driest places on Earth, are used to characterize the fluctuations at each site. Using an interferometric instrument as an example, the data suggest that the South Pole is the superior site for observations of the cosmic microwave background at degree angular scales.