With progress of photoinjector technology, thermal emittance has become the primary limitation of electron beam brightness. Extensive efforts have been devoted to study thermal emittance, but experiment results differ between research groups and few can be well interpreted. Besides the ambiguity of photoemission mechanism, variations of cathode surface conditions during cathode preparation, such as work function, field enhancement factor, and surface roughness, will cause thermal emittance differences. In this paper, we report an experimental study of electric field dependence of copper cathode quantum efficiency (QE) and thermal emittance in a radio frequency (rf) gun, through which in situ cathode surface parameters and thermal emittance contributions from photon energy, Schottky effect, and surface roughness are extracted. It is found the QE of a copper cathode illuminated by a 266 nm UV laser increased substantially to $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ after cathode cleaning during rf conditioning, and a copper work function of 4.16 eV, which is much lower than nominal value (4.65 eV), was measured. Experimental results also show a thermal emittance growth as much as $0.92\text{ }\text{ }\mathrm{mm}\text{ }\mathrm{mrad}/\mathrm{mm}$ at $50\text{ }\text{ }\mathrm{MV}/\mathrm{m}$ due to the cathode surface roughness effect, which is consistent with cathode surface morphology measurements.