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

The temporal response of the length of a partially-mixed estuary to changes in freshwater discharge, Qf , and tidal amplitude, UT , 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 Qf , UT , and near-surface salinity. When Qf was moderately high, the tidally-averaged length of the estuary, L5, 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, L5 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 Qf and UT relative to average discharge, Qo, and tidal amplitude, UTo, and predicts the linear response time scale, τ, and the steady-state length, Lo, for average forcing. Two vertical mixing schemes are considered, in which a) mixing is proportional to UT and b) dependence of mixing on stratification is also parameterized. Based on least-squares fits between L5 and estuary length predicted by the model, estimated τ varied by an order of magnitude from a period of high average discharge (Qo = 750 m3s-1, τ = 4.2 days) to a period of low discharge (Qo = 170 m3s-1, τ = 40.4 days). Over the range of observed discharge, Lo ∝ Qo-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 (LoA/Qo, where A 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 L5 with higher skill than the model with mixing proportional to UT . 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, Qf and UT , 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.