Dynamic linear models to explore time-varying suspended sediment-discharge rating curves

This study presents a new method to examine long-term dynamics in sediment yield using time-varying sediment-discharge rating curves. Dynamic linear models (DLMs) are introduced as a time series filter that can assess how the relationship between streamflow and sediment concentration or load changes over time in response to a wide variety of natural and anthropogenic watershed disturbances or long-term changes. The filter operates by updating parameter values using a recursive Bayesian design that responds to 1 day-ahead forecast errors while also accounting for observational noise. The estimated time series of rating curve parameters can then be used to diagnose multiscale (daily-decadal) variability in sediment yield after accounting for fluctuations in streamflow. The technique is applied in a case study examining changes in turbidity load, a proxy for sediment load, in the Esopus Creek watershed, part of the New York City drinking water supply system. The results show that turbidity load exhibits a complex array of variability across time scales. The DLM highlights flood event-driven positive hysteresis, where turbidity load remained elevated for months after large flood events, as a major component of dynamic behavior in the rating curve relationship. The DLM also produces more accurate 1 day-ahead loading forecasts compared to other static and time-varying rating curve methods. The results suggest that DLMs provide a useful tool for diagnosing changes in sediment-discharge relationships over time and may help identify variability in sediment concentrations and loads that can be used to inform dynamic water quality management.