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 Q(f) and tidal amplitude U(T) 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 yr) record of Q(f), U(T), and near-surface salinity. When Q(f) was moderately high, the tidally averaged length of the estuary L(5), here defined as the distance from the mouth to the up-estuary location where the vertically averaged salinity is 5 psu, fluctuated by more than 47 km over the spring-neap cycle, ranging from 28 to > 75 km. During low flow periods, L(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 Q(f) and U(T) relative to average discharge Q(o) and tidal amplitude U(To) and predicts the linear response time scale tau and the steady-state length L(o) for average forcing. Two vertical mixing schemes are considered, in which 1) mixing is proportional to U(T) and 2) dependence of mixing on stratification is also parameterized. Based on least squares fits between L(5) and estuary length predicted by the model, estimated t varied by an order of magnitude from a period of high average discharge (Q(o) = 750 m(3) s(-1), tau = 4.2 days) to a period of low discharge (Q(o) = 170 m(3) s(-1), tau = 40.4 days). Over the range of observed discharge, L(o) proportional to Q(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 tau was proportional to the discharge advection time scale (L(o)A/Q(o), where A is the cross-sectional area of the estuary). However, tau was 3-4 times larger than the theoretical prediction. The model with stratification-dependent mixing predicted variations in L(5) with higher skill than the model with mixing proportional to U(T). 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 Q(f) and U(T) can undergo large amplitude variations. River discharge, in particular, can vary by over an order of magnitude over time scales comparable to or shorter than the response time scale of the estuary.