We validate a model which is a combination of multiple trapping and release and percolation model for describing the conduction mechanism in amorphous indium gallium zinc oxide (a-IGZO) thin film transistors (TFT). We show that using just multiple trapping and release or percolation model is insufficient to explain TFT behavior as a function of temperature. We also show the intrinsic mobility is dependent on temperature due to scattering by ionic impurities or lattice. In solving the Poisson equation to find the surface potential and back potential as a function of gate voltage, we explicitly allow for the back surface to be floating, as is the case for a-IGZO transistors. The parameters for gap states, percolation barriers and intrinsic mobility at room temperature that we extract with this comprehensive model are in good agreement with those extracted in literature with partially-complete models.