We fit a stochastic spatial-temporal model to high-resolution rainfall radar data for a single rainfall event. Approximate Bayesian Computation (ABC) is used to fit a model of Cox, Isham and Northrop, previously fitted using the Generalised Method of Moments (GMM). We then show that ABC readily adapts to more general, and thus more realistic, variants of the model. The Simulated Method of Moments (SMM) is used to initialise the ABC fit