Outbreaks of infectious diseases require a rapid response from policy makers. The choice of an adequate level of response relies upon available knowledge of the spatial and temporal parameters governing pathogen spread, affecting, amongst others, the predicted severity of the epidemic. Yet, when a new pathogen is introduced into an alien environment, such information is often lacking or of no use, and epidemiological parameters must be estimated from the first observations of the epidemic. This poses a challenge to epidemiologists: how quickly can the parameters of an emerging disease be estimated? How soon can the future progress of the epidemic be reliably predicted? We investigate these issues using a unique, spatially and temporally resolved dataset for the invasion of a plant disease, Asiatic citrus canker in urban Miami. We use epidemiological models, Bayesian Markov-chain Monte Carlo, and advanced spatial statistical methods to analyse rates and extent of spread of the disease. A rich and complex epidemic behaviour is revealed. The spatial scale of spread is approximately constant over time and can be estimated rapidly with great precision (although the evidence for long-range transmission is inconclusive). In contrast, the rate of infection is characterised by strong monthly fluctuations that we associate with extreme weather events. Uninformed predictions from the early stages of the epidemic, assuming complete ignorance of the future environmental drivers, fail because of the unpredictable variability of the infection rate. Conversely, predictions improve dramatically if we assume prior knowledge of either the main environmental trend, or the main environmental events. A contrast emerges between the high detail attained by modelling in the spatiotemporal description of the epidemic and the bottleneck imposed on epidemic prediction by the limits of meteorological predictability. We argue that identifying such bottlenecks will be a fundamental step in future modelling of weather-driven epidemics.