  Losses in superconducting planar resonators are presently assumed to
predominantly arise from surface-oxide dissipation, due to experimental losses
varying with choice of materials. We model and simulate the magnitude of the
loss from interface surfaces in the resonator, and investigate the dependence
on power, resonator geometry, and dimensions. Surprisingly, the dominant
surface loss is found to arise from the metal-substrate and substrate-air
interfaces. This result will be useful in guiding device optimization, even
with conventional materials.
