In this paper, we confirm the hypothesis that the magnetic field inside a building can vary significantly as a function of height. We collected data with twenty magnetometers spaced evenly from knee height to head height and mounted to a ground robot, which we drove through two different buildings on the campus of the University of Illinois at Urbana-Champaign. We applied Gaussian process regression to build a map of the magnetic field at each height. We compared these maps and saw pairwise differences of more than 1 μT in up to 20% of each test environment, a threshold that we argue would prevent meeting the requirements of common indoor positioning applications. These results call into question the planar assumption that is commonly made when deriving methods of indoor positioning that are based on the use of magnetic fields.