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. Key Points Dynamic linear models (DLMs) are proposed to model time‐varying discharge‐suspended sediment relationships DLMs are capable of representing changes to sediment yield from abrupt disturbances to a watershed An application in a mountainous watershed in New York reveals interesting flood‐induced positive hysteresis in sediment yield