Study on the Synergistic Relationship Between Water and Sediment and the Response of Erosion and Deposition in the Lower Reaches of the Yellow River

The lower Yellow River, characterized by high sediment concentration and complex channel evolution, faces a persistent challenge of maintaining erosion–deposition balance. Using long-term hydrological and cross-sectional data (1950–2022) from seven key stations (Huayuankou–Lijin), this study established P-III frequency models for annual runoff (Q) and sediment discharge (S), introducing the flow–sediment frequency correlation coefficient (ζ) and the frequency relationship coefficient (λ) to quantify their synergy and erosion–deposition response. Results showed that (1) sediment discharge decreased by 91.4% at Huayuankou since the 1950s, while runoff decreased by 41.5%; (2) the flow–sediment synergy differed with river type—meandering (ζ ≈ 0, 69.23%) > transitional (64.39%) > wandering (59.26%); and (3) the equilibrium threshold of erosion and deposition was P(S) = (0.664–0.779) P(Q), corresponding to an incoming sediment coefficient of ~0.012 kg·s/m⁶. These findings quantitatively define the frequency-based synergy and threshold mechanism of flow and sediment in the lower Yellow River, providing a scientific basis for sediment regulation and channel stability management.