Estimating the Cross-Shelf Export of Riverine Materials: Part 1. General Relationships From an Idealized Numerical Model

Rivers deliver large amounts of terrestrially derived materials (such as nutrients, sediments, and pollutants) to the coastal ocean, but a global quantification of the fate of this delivery is lacking. Nutrients can accumulate on shelves, potentially driving high levels of primary production with negative consequences like hypoxia, or be exported across the shelf to the open ocean where impacts are minimized. Global biogeochemical models cannot resolve the relatively small-scale processes governing river plume dynamics and cross-shelf export; instead, river inputs are often parameterized assuming an "all or nothing" approach. Recently, Sharples et al. (2017), https://doi.org/10.1002/2016GB005483 proposed the S_P number-a dimensionless number relating the estimated size of a plume as a function of latitude to the local shelf width-as a simple estimator of cross-shelf export. We extend their work, which is solely based on theoretical and empirical scaling arguments, and address some of its limitations using a numerical model of an idealized river plume. In a large number of simulations, we test whether the S_P number can accurately describe export in unforced cases and with tidal and wind forcings imposed. Our numerical experiments confirm that the S_P number can be used to estimate export and enable refinement of the quantitative relationships proposed by Sharples et al. We show that, in general, external forcing has only a weak influence compared to latitude and derive empirical relationships from the results of the numerical experiments that can be used to estimate riverine freshwater export to the open ocean.