Summary. Motivated by the problem of predicting chemical deposition in eastern USA at weekly, seasonal and annual scales, the paper develops a framework for joint modelling of point- and grid-referenced spatiotemporal data in this context. The hierarchical model proposed can provide accurate spatial interpolation and temporal aggregation by combining information from observed point-referenced monitoring data and gridded output from a numerical simulation model known as the ‘community multi-scale air quality model’. The technique avoids the change-of-support problem which arises in other hierarchical models for data fusion settings to combine point- and grid-referenced data. The hierarchical space–time model is fitted to weekly wet sulphate and nitrate deposition data over eastern USA. The model is validated with set-aside data from a number of monitoring sites. Predictive Bayesian methods are developed and illustrated for inference on aggregated summaries such as quarterly and annual sulphate and nitrate deposition maps. The highest wet sulphate deposition occurs near major emissions sources such as fossil-fuelled power plants whereas lower values occur near background monitoring sites.