The UK has in recent years experienced a series of fluvial flooding events which have simultaneously affected communities over different parts of the country. For the co-ordination of flood mitigation activities and for the insurance and reinsurance industries, knowledge of the spatial characteristics of fluvial flooding is important. Past research into the spatiotemporal risk of fluvial flooding has largely been restricted to empirical estimates of risk measures. A weakness with such an approach is that there is no basis for extrapolation of these estimates to rarer events, which is required as empirical evidence suggests that larger events tend to be more localized in space. We adopt a model-based approach using the methods of Heffernan and Tawn. However, the large proportion of missing data over a network of sites makes direct application of this method highly inefficient. We therefore propose an extension of the Heffernan and Tawn method which accounts for missing values. Furthermore, as the risk measures are spatiotemporal an extension of the Heffernan and Tawn method is also required to handle temporal dependence. We illustrate the benefits of the procedure with a simulation study and by assessing spatial dependence over four fluvial sites in Scotland.