Streamflow Hysteresis Analysis through a Deep Dive Budget of the St Venant Momentum Terms

Emma Christine House, Ehab Meselhe, Marian Muste, Ibrahim Demir

Hysteretic conditions entail non-unique time-independent relationships in flow variables and are prevalent in the unsteady flow regime of most rivers worldwide. Estimation errors associated with the inability of current monitoring techniques to resolve hysteresis effects could have profound implications when the recorded data is used for water resources management and flood forecasting. A deep analysis of streamflow hysteresis is performed by tracking the St Venant momentum equation terms for storm events propagating at several locations along the Illinois River, USA, using a combined 1D/2D hydraulic model. We correlate flow characteristics with magnitude and timing patterns in these terms to determine their relevance to the presence and absence of hysteretic conditions. The dynamic equation analysis confirms that the hysteretic behavior is related to certain defining characteristics in momentum terms. The local acceleration term only temporally advances the flood wave and is not an indication of hysteretic behavior. Non-hysteretic streamflow has large and balanced gravity and friction forces, equating it to kinematic wave conditions. Meanwhile, hysteretic streamflow has a clear disparity between gravity and friction forces, balanced by active diffusive and convective acceleration forces. In such hysteretic conditions, the diffusive, convective acceleration, and friction slope terms exhibit non-unique relationships and a peak-phasing phenomenon much like the hysteresis signature of the hydraulic variables used to estimate streamflow. For non-hysteretic conditions, the relationships are purely unique and linear, with synchronized variable peaks. The revealed flow characteristics provide information on the important drivers of streamflow hysteresis and create opportunities for improving streamflow monitoring and forecasting.