Streamflow Hysteresis Analysis Through a Deep‐Dive Budget of the St Venant Equation Momentum Terms

Hysteretic conditions, characterized by non‐unique relationships and temporal phasing of flow variables, are common in unsteady open‐channel flows. Hysteresis effects can lead to significant discharge estimation errors when using traditional, unique stage‐discharge rating curve monitoring techniques. Using a 1D/2D hydraulic model, we analyze hysteresis by tracking the St Venant momentum equation terms for two flood events along the Illinois River, USA. We correlate flow characteristics with magnitude and timing patterns in the underlying momentum terms to determine their relevance to hysteretic conditions. We find that the local acceleration term only temporarily advances the flood wave and is not an indicator of hysteretic behavior. Non‐hysteretic streamflow has large and balanced gravity and friction forces, akin to kinematic wave conditions. For hysteretic streamflow conditions to occur, the pressure gradient term must be within one order of magnitude of the kinematic term, and the dynamic term must be active, within one or two orders of magnitude of the kinematic and diffusive terms. The hysteretic signal emerges with a gradual activation of pressure gradient and convective acceleration components, making up for the disparity between friction and gravity terms. These hysteretic momentum term characteristics clarify the underlying forces of streamflow hysteresis and create opportunities for improved discharge monitoring and forecasting.