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

Abstract

This study compares several statistical rating curve techniques to estimate turbidity, a proxy for suspended sediment concentration, in fluvial systems based on available discharge data. Seven models were tested, including variants of quadratic rating curves, quantile regression, local regression, dynamic linear models (DLMs), and Box‐Jenkins models. Two comparisons were conducted in a case study of the Esopus Creek watershed in New York, a major water source for the New York City Water Supply System (NYCWSS). First, the models were tested in their ability to forecast turbidity at 1–7 day lead times assuming perfect forecasts of discharge using two daily datasets of varying record lengths and resolution. Second, the models were used to gap‐fill turbidity data based on available discharge data, and the resulting continuous turbidity time series were used to assess optimal reservoir operations in the NYCWSS to manage water quality. Results suggest that DLMs coupled with additional time series modeling on the residuals produce the most robust forecasts across lead times for both high and low turbidity values. During average conditions, differences between rating curves have little impact on inferred reservoir operations due to the buffering effect of storage. But during extreme events, rating curve differences lead to large differences in inferred operations, suggesting that rating curve choice can play an important role in assessing the risk of reservoir‐based water quality management.

Characterization of Multi‐Scale Fluvial Suspended Sediment Transport Dynamics Across the United States Using Turbidity and Dynamic Regression

“…The value of $$\delta $$ for each gage can be calibrated to maximize prediction accuracy (Wang, Gelda et al., 2021). In this work, we calibrate $$\delta $$ for each site by maximizing the R 2 between DLM‐predicted and observed T n using a simple grid search.…”

“…(2017), Ahn and Steinschneider (2019), Wang, Davis, and Steinschneider (2021), and Wang, Gelda et al. (2021), and so we only briefly review its formulation here. These regression models can be written as follows: $$${y}_{t}={\boldsymbol{x}}_{t}^{\prime}{\boldsymbol{\beta }}_{t}+{\varepsilon }_{t},{\varepsilon }_{t}\sim \mathrm{N}\left(0,{\sigma }_{t}^{2}\right)$$$ $$${\boldsymbol{\beta }}_{t}={\boldsymbol{\beta }}_{t-1}+{\boldsymbol{\omega }}_{t},{\boldsymbol{\omega }}_{t}\sim \mathrm{M}\mathrm{V}\mathrm{N}\left(0,{\boldsymbol{W}}_{t}\right)$$$ $$${\boldsymbol{\beta }}_{t=0}\sim \mathrm{M}\mathrm{V}\mathrm{N}\left({\boldsymbol{m}}_{0},{\boldsymbol{C}}_{0}\right)$$$ …”

“…We use DLMs as time-varying regression models that can characterize the temporal dynamics of the T n -Q relationship. This class of model is discussed in depth in , Ahn and Steinschneider (2019), Wang, Davis, andWang, Gelda et al (2021), and so we only briefly review its formulation here. These regression models can be written as follows:…”

“…The parameters 𝐴𝐴 𝒎𝒎0 and 𝐴𝐴 𝑪𝑪0 are the prior mean and state evolution covariance matrix for the initial parameter vector 𝐴𝐴 𝜷𝜷 𝑡𝑡=0 . The time-varying parameters are updated through a recursive Bayesian design and one-step Markov evolution in order to improve model predictions a posteriori (Wang, Gelda et al, 2021;West & Harrison, 1997). That is, the regression coefficients 𝐴𝐴 𝜷𝜷 𝑡𝑡 vary through time in order to minimize prediction errors WANG AND STEINSCHNEIDER 2) can become increasingly large, allowing the model to make significant changes to 𝐴𝐴 𝜷𝜷 𝑡𝑡 from one time step to the next.…”

“…To address these questions, we leverage a recently developed class of SS‐ Q rating curve (Dynamic Linear Models; DLMs) that can characterize multi‐scale temporal variability in the SS‐ Q relationship through recursive updates to the rating curve parameters over time (Ahn et al., 2017; Wang, Gelda et al., 2021). We use T n to measure SS variability, focusing on sites where T n is a good proxy measurement of SSC.…”