  We present measurements of the temperature-dependent frequency shift of five
niobium superconducting coplanar waveguide microresonators with center strip
widths ranging from 3 $\mu$m to 50 $\mu$m, taken at temperatures in the range
100-800 mK, far below the 9.2 K transition temperature of niobium. These data
agree well with the two-level system (TLS) theory. Fits to this theory provide
information on the number of TLS that interact with each resonator geometry.
The geometrical scaling indicates a surface distribution of TLS, and the data
are consistent with a TLS surface layer thickness of order a few nm, as might
be expected for a native oxide layer.
