We investigate the predictability of the thermally driven rotating annulus, a laboratory experiment used to study the dynamics of planetary atmospheres under controlled and reproducible conditions. Our approach is to apply the same principles used to predict the atmosphere in operational weather forecasting. We build a forecasting system for the annulus using the analysis correction method for data assimilation, the breeding method for ensemble generation, and the Met Office/Oxford Rotating Annulus Laboratory Simulation as the forecast model. The system forecasts the annulus in steady (2S), amplitude vacillating (3AV), and structurally vacillating (3SV) flow regimes, verifying the forecasts against laboratory data. The results show that a range of flow regimes from this experiment can be accurately predicted. Forecasts in the steady wave flow regime perform well, and are predictable until the end of the available data. Forecasts in the amplitude and structural vacillation flow regimes lose quality and skill by a combination of wave drift and wavenumber transition. Amplitude vacillation is predictable up to several hundred seconds ahead, and structural vacillation is predictable for a few hundred seconds. The wavenumber transitions are partly explained by hysteresis in the rotating annulus experiment and model.