The Temporal Response of the Length of a Partially Stratified Estuary to Changes in River Flow and Tidal Amplitude

Abstract

The temporal response of the length of a partially-mixed estuary to changes in freshwater discharge, <i>Q_f</i> , and tidal amplitude, <i>U_T</i> , is studied using a 108 day time series collected along the length of the Hudson River estuary in the spring and summer of 2004 and a long-term (13.4 year) record of <i>Q_f</i> , <i>U_T</i> , and near-surface salinity. When <i>Q_f</i> was moderately high, the tidally-averaged length of the estuary, <i>L</i>₅, here defined as the distance from the mouth to the up-estuary location where the vertically-averaged salinity is five psu, fluctuated by more than 47 km over the spring-neap cycle, ranging from 28 km to >75 km. During low flow periods, <i>L</i>₅ varied very little over the spring-neap cycle and approached a steady length. The response is quantified and compared to predictions of a linearized model derived from the global estuarine salt balance. The model is forced by fluctuations in <i>Q_f</i> and <i>U_T</i> relative to average discharge, <i>Q</i>_o, and tidal amplitude, <i>U_T</i>_o, and predicts the linear response time scale, τ, and the steady-state length, <i>L</i>_o, for average forcing. Two vertical mixing schemes are considered, in which a) mixing is proportional to <i>U_T</i> and b) dependence of mixing on stratification is also parameterized. Based on least-squares fits between <i>L</i>₅ and estuary length predicted by the model, estimated τ varied by an order of magnitude from a period of high average discharge (<i>Q</i>_o = 750 m³s^-1, τ = 4.2 days) to a period of low discharge (<i>Q</i>_o = 170 m³s^-1, τ = 40.4 days). Over the range of observed discharge, <i>L</i>_o ∝ <i>Q</i>_o^-0.30±0.03, consistent with the theoretical scaling for an estuary whose landward salt flux is driven by vertical estuarine exchange circulation. Estimated τ was proportional to the discharge advection time scale (<i>L</i>_o<i>A</i>/<i>Q</i>_o, where <i>A</i> is the cross-sectional area of the estuary). However, τ was three to four times larger than the theoretical prediction. The model with stratification dependent mixing predicted variations in <i>L</i>₅ with higher skill than the model with mixing proportional to <i>U_T</i> . This model provides insight into the time dependent response of a partially-stratified estuary to changes in forcing and explains the strong dependence of the amplitude of the spring-neap response on freshwater discharge. However, the utility of the linear model is limited because it assumes a uniform channel and because the underlying dynamics are nonlinear and the forcing, <i>Q_f</i> and <i>U_T</i> , can undergo large amplitude variations. River discharge, in particular, can vary by over an order of magnitude over timescales comparable to or shorter than the response timescale of the estuary.