In 1900, Martin Knudson (Knudson 1900; Burchard et al. 2018) considered the salt and volume fluxes for a steady-state estuary. He arrived at very useful relationships between the flux of fresh water coming in from upstream compared to the output salinity and volume flux. While these relations are fundamental and extremely useful, they do not close the problem. Rather, there is always one more piece of information needed; for example, to know the flux of brackish water onto the shelf, you still have to know the outflow salinity...
Brink, Kenneth H., and Harlow G. Farmer. 2021. "Editor's Commentary: Control of salinity in an estuary by a transition." Journal of Marine Research 79, (2). https://elischolar.library.yale.edu/journal_of_marine_research/504