The effect of stratospheric ozone depletion is simulated in GFDL AM4 model with three ozone schemes: prescribing monthly zonal mean ozone concentration, full interactive stratospheric chemistry, and a simplified linear ozone chemistry scheme but with full dynamical interactions. While similar amounts of ozone loss are simulated by the three schemes, the two interactive ozone schemes produce significantly stronger stratospheric cooling than the prescribed one. We find that this temperature difference is driven by the dynamical responses to ozone depletion. In particular, the existence of ozone hole leads to strong ozone eddies that are in-phase with the temperature eddies. The coherence between ozone and temperature anomalies leads to a weaker radiative damping as ozone absorbs shortwave radiation that compensates for the longwave cooling. As a result, less wave dissipates at the lower stratosphere, leading to a weaker descending and dynamical heating over the polar lower stratosphere, and hence a stronger net cooling there. The covariance between ozone and temperature is largely suppressed when ozone is prescribed as monthly zonal mean time series, as is the reduction in the radiative damping following ozone depletion. With much lower computational cost, the simplified ozone scheme is capable of producing similar magnitude of ozone loss and the consequent dynamical responses to those simulated by the full chemistry.