AbstractStatistical downscaling has been developed for the fusion of data of different spatial support. However, environmental data often have different temporal support, which must also be accounted for. This paper presents a novel method of nonparametric statistical downscaling, which enables the fusion of data of different spatiotemporal support through treating the data at each location as observations of smooth functions over time. This is incorporated within a Bayesian hierarchical model with smoothly spatially varying coefficients, which provides predictions at any location or time, with associated estimates of uncertainty. The method is motivated by an application for the fusion of in situ and satellite remote sensing log(chlorophyll‐a) data from Lake Balaton, in order to improve the understanding of water quality patterns over space and time.