Timely projections of seasonal streamflow extremes on a river network can be useful for flood risk mitigation, but this is challenging, particularly under space–time nonstationarity. We develop a space–time Bayesian hierarchical model (BHM) using temporal climate covariates and copulas to project seasonal streamflow extremes and the attendant uncertainties. We demonstrate this on the Upper Colorado River basin to project spring flow extremes using the preceding winter’s climate teleconnections.