Temporal and spatial laws and simulations of erosion and deposition in the Lower Yellow River since the operation of the Xiaolangdi Reservoir

This study focuses on the Lower Yellow River (LYR), which has experienced continuous erosion since the operation of Xiaolangdi Reservoir in 1999, and its spatiotemporal variation process is complex. Based on the single-step mode of the Delayed Response Model (DRM), we proposed a calculation method for simulating the accumulated erosion and deposition volume in the LYR. The coefficient of determination R2 between the calculated and measured values from 2000 to 2020 is 0.99. Currently, the LYR is undergoing continuous erosion, however the erosion rate is gradually slowing down, and the difference between the equilibrium and calculated values of accumulated erosion and deposition volume gradually decreases, which means riverbed erosion has a tendency towards equilibrium. Additionally, we derive a formula to simulate the spatial distribution of the main channel accumulated erosion volume per unit river length in the LYR based on the non-equilibrium suspended sediment transport equation. The coefficient of determination R2 between the fitted values and measured values from 2003 to 2015 is approximately 0.98-0.99, with a relative error of approximately 6.2%. The findings in this research suggest that under the current background of decreasing sediment inflow and continuous erosion in the LYR, it takes approximately 3.0 years for the riverbed to achieve half of the erosion and deposition adjustment and approximately 13.0 years to achieve 95% of the adjustment. Moreover, the spatial distribution of accumulated main channel erosion volume in the LYR tends to become uniform with the continuous development of erosion. These results could provide a valuable reference for analysing the complex spatiotemporal variation process in the LYR.