Stochastic rainfall models are important tools both for practical issues and in studies of weather- and climate-sensitive systems. We propose an event-based model, continuous in space (two-dimensional) and time, that describes regional-scale, ground-observed storms by a Boolean random field of rain patches. The model creates complex space-time structures with a mathematically tractable framework. The estimation method relates temporal observations at fixed sites to the movement of the model storm rain field, thereby making historical rain gauge data suitable for model fitting. The model is estimated using hourly historical data at eight rain gauges in Alabama and tested for its capabilities in capturing statistical characteristics of the historical data, including rainfall intensity, rainfall intensity extremes, temporal correlation, effects of temporal aggregation, spatial coverage, and spatial correlation.