1. A meteorological radar precipitation pattern prediction apparatus comprising: image input means for inputting radar images of a precipitation region; image storage means for storing the input radar images as time-series two-dimensional images; image processing means for calculating various image-feature quantities with respect to two or more two-dimensional past images stored in the image storage means; calculation means for calculating a spatial-temporal transition of the amount of precipitation using an advection-diffusion equation system which indicates various physical effects relating to precipitation phenomena, with the various image-feature quantities as initial values; prediction means for predicting transition of a pattern with respect to the precipitation region based on results calculated by the calculation means; and output means for outputting predicted results as time-series images.