Globally, rivers deliver significant quantities of nitrogen (N) and phosphorus (P) to the coastal ocean each year. Currently, there are no viable estimates of how much of this N and P escapes biogeochemical processing on the shelf to be exported to the open ocean; most models of N and P cycling assume that either all or none of the riverine nutrients reach the open ocean. We address this problem by using a simple mechanistic model of how a low-salinity plume behaves outside an estuary mouth.