A simple advection‐dispersion model for the salt distribution in linearly tapered estuaries

Abstract

We present a simple advection‐dispersion model for the subtidal salt distribution in estuaries with linearly varying cross‐sectional area and a nonzero net salt flux. A novel analytic solution allows investigation of the dependence of the curvature and gradient of the longitudinal salinity distribution on runoff, dispersion coefficient, and channel contraction or expansion. The model predicts that in estuarine segments that contract toward the fresher boundary, the salinity gradient is stronger than in a prismatic channel. When the dispersion coefficient is large compared to the salinity intrusion lengthscale, (the product of segment length and net volume flux divided by cross‐sectional area at the ocean boundary), the curvature of the salt concentration may be negative, a characteristic not possible in uniform channel models. The main effect of up‐estuary salt flux is to strengthen the salinity gradient. The model can be extended to multiple segments in order to simulate geometrically complicated estuaries. The model is employed to estimate an effective dispersion coefficient and to describe the salinity variation in the western 53 km of Long Island Sound where the cross section of the basin varies linearly. Using 8 years of monthly observations at seven stations we find that, since the curvature of the vertically averaged salinity is negative, the model and data are consistent only if the net volume flux and salt flux are toward the fresher boundary, the East River. Combining prior estimates of the magnitudes of the fluxes and their uncertainties with the model and salinity observations using a least squares approach, we estimate the dispersion coefficient for the Western Sound as 580 m2/s.