A new spatiotemporal forecasting model of photovoltaic output power is proposed. Irradiance measurements are first interpolated onto a grid. By repeating this process over several time steps, cloud motion is visualized and the velocity of the clouds is estimated. Using these estimations of cloud velocity, the cloud motion in a future time interval is simulated using advection diffusion equations and the average irradiation over a target region is estimated. The proposed model is applied to two distinctly sized areas, a utility-scale photovoltaic plant of 1.32 km(2) and a 6400-km(2) region in Kyushu, Japan. The predictions of the transients in the average irradiation for the utility-scale photovoltaic system and regional irradiance are in good agreement with measurements; root-mean-square errors of data on the time scale of a minute are 1.14% and 1.36%, respectively. The simulation of the distribution of irradiation within the photovoltaic system also agrees well with measurements. (C) 2017 Elsevier Ltd. All rights reserved.