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

Abstract

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.

Time‐varying suspended sediment‐discharge rating curves to estimate climate impacts on fluvial sediment transport

“…This comparison was not investigated in this study. However, Mather and Johnson () concluded that the hydrograph slope‐based model was more appropriate for small and midsized catchments (~10 0 − 10 3 km 2 ), similar to our study basin.…”

“…To model short-term hysteresis, this study used the hydrograph slope-based approach based on first differences of log discharge (Eder, Strauss, Krueger, & Quinton, 2010). As noted in Mather and Johnson (2014), this formulation may be limited in its ability to fully represent hysteresis behaviour across a wide range of streams. Alternatively, a supply-based model formation can also be utilized using a washout function (Asselman, 1999;Vansickle & Beschta, 1983).…”

“…When these data are collected, they require discrete water samples and significant lab work, leading to less frequent sampling. T n , which can be measured rapidly in the field or continuously with a data logger, often has a greater sampling frequency and is a commonly used surrogate for SSC (J. R. Gray et al, ; Jones, Stevens, Horsburgh, & Mesner, ; Mather & Johnson, ). T n can also be used to in‐fill SSC estimates with regression and paired T n –SSC samples.…”

“…Alternative rating curve formulations have been proposed to capture complex SSC-Q relationships (Lohani et al, 2007;Lafdani, Nia, & Ahmadi, 2013;Nourani, Parhizkar, Vousoughi, & Amini, 2013;Joshi, Kumar, & Adhikari, 2016), including hysteresis effects. For instance, Mather and Johnson (2014) proposed a formulation to model the shape of turbidity (T n )-discharge short-term hysteresis loops that integrated hydrograph slope and exponential supply terms adopted from previous studies (Krueger et al, 2009;Vansickle & Beschta, 1983). Wang, Mukundan, Zion, and Pierson (2012) and Mukundan, Pradhanang, et al (2013) modelled residuals of the rating curve using an autoregressive moving average formulation.…”

Considerations for using turbidity as a surrogate for suspended sediment in small, ungaged streams: Time‐series selection, streamflow estimation, and regional transferability

“…Conversely, ungaged sites, as in this study, require the additional step of creating an accurate stage‐discharge rating curve to calculate SSL. Similar to other studies (e.g., Mather & Johnson, ), we observed a consistent pattern of turbidity peaking prior to or concurrent with peak streamflow during storm events across all sites. This emphasizes the importance of on‐site streamflow monitoring, as SSL estimates will be biased if the timing and magnitude of streamflow are not accurately measured or aligned.…”