Quantitative characterization of stream turbidity-discharge behavior using event loop shape modeling and power law parameter decorrelation

Turbidity behavior in streams is a complex and dynamic function of both source material supply and event-driven transport. While the primary controls on turbidity behavior across time and space are still not fully understood, recent increases in the availability of high temporal resolution, colocated stream turbidity, and discharge data provide an opportunity for more detailed analysis. Here we examine methods to quantitatively characterize event responses by modeling the shape of turbidity-discharge hysteresis loops. A total of 1559 events from 20 gages in the Mid-Atlantic region of the U.S. were modeled using both previously reported models and new models combining elements of existing models. The results suggest that a more general power law-based model, utilizing both a discharge rate of change term and a "supply" term, allows characterization of a wide range of simple and complex events. Additionally, this study explores a decorrelation approach to address the strong correlation frequently observed between the power law model coefficient (a) and exponent (b), with the goal of exposing the underlying behavior of each parameter individually. An examination of seasonal parameter behavior suggests that this approach may facilitate greater physically based interpretation of the power law coefficient. The power law parameter decorrelation strategy and the loop models examined here provide a step toward the larger goal of understanding the physical controls on turbidity-discharge hysteretic behavior.