Time‐varying, nonlinear suspended sediment rating curves to characterize trends in water quality: An application to the Upper Hudson and Mohawk Rivers, New York

Abstract

This work proposes two modelling frameworks for diagnosing temporal variations in nonlinear rating curves that describe suspended sediment–discharge relationships. A variant of the weighted regression on time, discharge, and season model is proposed and is compared against dynamic nonlinear modelling, a newly developed nonlinear time series filter based on sequential Monte Carlo sampling. Both approaches estimate a time series of rating curve parameters, with uncertainty, that can be used to diagnose variability in the sediment–discharge relationship over time. We evaluate the models with a variety of synthetic scenarios to highlight their ability to estimate signals of known rating curve change. Results reveal important bias‐variance trade‐offs unique to each approach, and in general, suggest that dynamic nonlinear modelling is better suited for rapid rating curve changes, whereas the weighted regression on time, discharge, and season variant more precisely estimates slow change. The techniques are then applied in two case studies in the Upper Hudson and Mohawk Rivers in New York. We conclude with a discussion of the implications of dynamic rating curves for the management of water quality in riverine and estuary systems.

Turbidity Hysteresis in an Estuary and Tidal River Following an Extreme Discharge Event

“…To evaluate the influence of the variability in watershed inputs, we also calculated the residual of the LOWESS regressions of log 10 ( SSC ) versus log 10 ( Q r ) for the tributaries on an annual basis. Precipitation from Irene and Lee was focused in the Mohawk watershed and the Catskill Mountains east of the Hudson, leading to mass wasting, increased erosion, and potential hysteresis in the sediment‐discharge relationship for these regions (Ahn & Steinschneider, 2019). In water years 2012–2014 following the events, the average SSC in the Mohawk increased by a factor of about 1.2 above the regression values, but the Mohawk turbidity ratio was not significantly correlated with the turbidity ratios in the estuary.…”

“…Watershed sediment supply depends in part on revegetation of landslides and bank failures, which adjusts at multiyear time scales (Dethier et al, 2016; Gray et al, 2014; Yellen et al, 2014). Watershed sediment supply from the Mohawk increased relative to discharge during 2012–2014 due to these geomorphic adjustments in its steep tributaries (Ahn & Steinschneider, 2019) and thus may contribute to the 2012–2013 increase in the turbidity factor in the tidal river (Figure 4d). However, we observed a similar increase in the SSC factor relative to the discharge relation for the Mohawk in 2017, when the turbidity factors at tidal river stations were less than or equal to 1.…”

“…The duration and timing of low‐discharge conditions can affect in‐stream storage and SSC during subsequent higher discharge periods (Gray et al, 2014; Walling et al, 1998). Sampling frequency can also contribute to uncertainty or introduce bias into sediment discharge measurements (Coynel et al, 2004), and the variability in time scales of watershed response that can be diagnosed depends on the functional form of the sediment‐discharge relation (Ahn & Steinschneider, 2019).…”

Inter‐model Comparison of Turbidity‐Discharge Rating Curves and the Implications for Reservoir Operations Management

“…DLMs allow linear rating curve parameters to be updated over time in response to model prediction errors using a recursive Bayesian algorithm. Different variants of this model structure were also proposed to accommodate future scenarios of discharge (Ahn and Steinschneider 2017) and nonlinear rating curve relationships (Ahn and Steinschneider 2019).…”

Stabilization of stage–discharge curves following the establishment of forest plantations: Implications for sediment production

“…In turn, Kiang et al (2018) concluded that one way to reduce the uncertainty in discharge curves estimations is by selecting a stable section, since this reduces the number of discharge curves over time and, therefore, a smaller number of curves accounts for a more stable bed. Likewise, Ahn and Steinschneider (2019) noted that the value of the intercept for sediment discharge curve models tested in the Hudson River (NY) decreased after the declaration of the Clean Water Act, inferring that this can be explained in terms of the decrease in agricultural area, the increase in wetlands, and the corresponding decrease in sediment production.…”