Using an isohaline flux analysis to predict the salt content in an unsteady estuary

An estuary is classified as unsteady when the salinity adjustment time is longer than the forcing time scale. Predicting salt content or salt intrusion length using scaling arguments based on a steady-state relationship between flow and salinity is inaccurate in these systems. In this study, a time-dependent salinity box model based on an unsteady Knudsen balance is used to demonstrate the effects of river flow, inward total exchange flow (tidal plus steady), and the salinity difference between inflow and outflow on the salt balance. A key component of the box model is a relationship that links the normalized difference between inflowing and outflowing salinity at the mouth and the mean salinity content. The normalized salinity difference is shown to be proportional to the mean salinity squared, based on theoretical arguments from the literature. The box model is validated by hindcasting 5 years of mean salinity in Galveston Bay (estimated from coarse observations) in response to highly variable river discharge. It is shown that this estuary typically has a long adjustment time relative to the forcing time scales, and, therefore, the volume-averaged salinity rarely reaches equilibrium. The box model highlights the reasons why the adjustment time in a large, partially mixed estuary like Galveston Bay is slower when the mean salt content is higher. Furthermore, it elucidates why the salt content in the estuary is more responsive to changes in river flow than in landward exchange flow at the estuary mouth, even though the latter quantity is usually several times larger.