We model the spatial dynamics of an open population of organisms that disperse solely through advection in order to understand responses to multiscale environmental variability. We show that the distance over which a population responds to a localized perturbation, called the response length, can be characterized as an organisms average lifetime dispersal distance, unless there is strong density-dependence in demographic or dispersal rates. Continuous spatial fluctuations in demographic rates at scales smaller than the response length will be largely averaged in the population distribution, whereas those in per capita emigration rates will be strongly tracked. We illustrate these results using a parameterized example to show how responses to environmental variability may differ in streams with different average current velocities. Our model suggests an approach to linking local dynamics dominated by dispersal processes to larger-scale dynamics dominated by births and deaths.