A Hysteresis-Based Framework for Evaluating and Selecting Streamflow Monitoring Approaches Under Unsteady Gradually Varied Flow Conditions

Marian Muste, Kyeongdong Kim, Dongsu Kim, Ibrahim Demir

Streamflow estimates derived from stage–discharge rating curves (HQRC) inadequately represent the spatiotemporal complexity of unsteady gradually varied flows (UGVF) and are commonly reported without uncertainty, encouraging their treatment as deterministic. These limitations are increasingly problematic as data users demand defensible confidence in streamflow estimates for cross‑agency comparisons and for scientific applications. One of the dominant yet poorly quantified sources of HQRC error is hysteresis arising from ubiquitous unsteady and nonuniform flow conditions characteristic of UGVFs. Hydrometric agencies attempt to mitigate these effects through using alternative approaches such as HQRC corrections or use of stand-alone multivariable methods that augment stage with velocity or free‑surface slope measurements. However, evaluating the effectiveness of these alternatives remains challenging, as HQRC corrections rely on simplified flood‑wave representations, while multivariable methods retain the semi‑empirical underpinnings of traditional HQRC formulations. To address this evaluation gap, we introduce a hysteresis‑centric performance metric that quantifies departures between bivariate relationships obtained using HQRC correction and multivariable methods and those derived from conventional HQRC ratings. The metric integrates three complementary indicators: (i) flow deviation magnitude, (ii) hydrograph peak phasing, and (iii) cumulative volumetric differentiation, collectively capturing the hysteresis severity, variable peak timing, and integrated impacts of hysteresis on discharge estimates. The framework is applied to three U.S. Geological Survey gaging stations spanning diverse hydro‑geomorphic settings. Results provide practical guidance for evaluating and selecting alternative monitoring methods in relation to dominant flood‑wave behavior (kinematic versus non‑kinematic) and are synthesized into a structured decision‑making workflow for monitoring-system selection under UGVF conditions.