Precipitation forecast is important for our daily life. However, predictability of atmospheric motion has intrinsic limitations due to the chaotic nature of the dynamics. We investigate the predictability limits of convective precipitation by extracting the growing modes using the breeding method. To improve practical predictability, we developed an adaptive multi-model ensemble Kalman filter algorithm and a space-time extrapolation system with data assimilation. In this presentation, we will demonstrate the performance with synthetic and real observations.