This paper describes a prediction method, the Dynamics Texture (DT) method, of three different radar echo image sequences based on partial difference equations (PDEs) and an extended optical flow over time. Three image patterns are observed from precipitation-, lightning-, and satellite-radar sites. Such patterns exhibit development, disappearing, and fusion processes with local discontiuities. The DT method can calculate future dynamic pattern changes over time from past sequences of these image sequences by making use of a changeable texture pattern model and the extended optical flow method. Five basic spatio-temporal patterns with corresponding PDEs are responsible for a wide range of the patterns. For discontinuities and noise due to abrupt local changes in shape and intensity, a nonlinear robust function with brightness and contrast change model is also proposed. Using the heterogenous patterns, experimental results show a high prediction accuracy for the DT method over time and hence demonstrate the usefulness for disaster prevention in short-term forcasting or nowcasting.