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.

Rivers deliver large amounts of fresh water, nutrients, and other terrestrially derived materials to the coastal ocean. Where inputs accumulate on the shelf, harmful effects such as hypoxia and eutrophication can result. In contrast, where export to the open ocean is efficient riverine inputs contribute to global biogeochemical budgets. Assessing the fate of riverine inputs is difficult on a global scale. Global ocean models are generally too coarse to resolve the relatively small scale features of river plumes. High-resolution regional models have been developed for individual river plume systems, but it is impractical to apply this approach globally to all rivers. Recently, generalized parameterizations have been proposed to estimate the export of riverine fresh water to the open ocean (Izett & Fennel, 2018, https://doi.org/10.1002/2017GB005667; Sharples et al., 2017, https://doi.org/10.1002/2016GB005483). Here the relationships of Izett and Fennel (), https://doi.org/10.1002/2017GB005667 are used to derive global estimates of open-ocean export of fresh water and dissolved inorganic silicate, dissolved organic carbon, and dissolved organic and inorganic phosphorus and nitrogen. We estimate that only 15-53% of riverine fresh water reaches the open ocean directly in river plumes; nutrient export is even less efficient because of processing on continental shelves. Due to geographic differences in riverine nutrient delivery, dissolved silicate is the most efficiently exported to the open ocean (7-56.7%), while dissolved inorganic nitrogen is the least efficiently exported (2.8-44.3%). These results are consistent with previous estimates and provide a simple way to parameterize export to the open ocean in global models.