黄河小浪底水库投入运用后下游河床持续冲刷，深入认识其时空累积变化规律，对于判别现有水沙条件下河床尚有多少冲刷潜力至关重要。通过分析有关黄河下游持续冲刷时空累积变化规律的数据，并基于河流沿程不平衡输沙理论，结合河床冲淤过程中水流挟沙能力调整的时间滞后响应模型，联合推导建立了河床持续冲刷体积的时空累积变化模型，并对2001—2024年黄河下游持续冲刷的时空累积变化进行模拟。模拟结果表明：黄河下游持续冲刷随时空累积变化（不同时间累积的沿程空间累积变化、不同沿程空间累积的时间累积过程）均表现为一组不同的增长曲线，但增长速率先快后慢，并逐渐趋向于0。模拟结果与实测值变化趋势基本吻合，确定性系数与Nash-Sutcliffe效率系数分别达到0.98、0.99，具有较高的模拟精度，说明了所建模型的合理性。

[Objective] Since the operation of Xiaolangdi reservoir in 1999， continuous erosion has happened in the lower Yellow River. As of 2023， the accumulated erosion volume of Tie-Li reach （from Tiexie station to Lijin station） in the lower Yellow River has reached 2.2 billion m³. However， the erosion efficiency gradually decreases from 13.6 kg/m³ to 6.3 kg/m³. It is important to realize the temporal and spatial accumulation variation law of continuous erosion in the lower Yellow River in order to estimate the erosion potential. [Methods] Through collecting the annual erosion volume data from 2001 to 2024 for different sub-reaches， the temporal and spatial accumulation variation law of continuous erosion in the lower Yellow River is analyzed. Based on the river spatial non-equilibrium sediment transport theory， and combined with the temporal delayed response model of sediment transport capacity adjustment during the processes of erosion and sedimentation of river bed， a temporal and spatial accumulation variation model of continuous erosion volume is proposed， and then is used to simulate the temporal and spatial accumulation variation of continuous erosion in the lower Yellow River and predict the future erosion potential. The model parameter ϕ is calibrated based on the measured spatial accumulation erosion data of 2017， the model parameters K_（0） and β is determined based on the measured temporal accumulation erosion data from 2001 to 2017 of the Hua-Li reach. These calibrated parameters are used to simulate the temporal and spatial accumulation erosion from 2018 to 2024 of the different sub-reaches for model validation and the performance is evaluated using the certainty coefficient and the Nash-Sutcliffe efficiency coefficient. [Results] Data analysis results show that the temporal and spatial accumulation variation law of continuous erosion in the lower Yellow River shows a set of different growth curves， and the growth rates present a first fast and then slow down change trend， finally gradually tending towards 0. The simulation results of the temporal and spatial accumulation erosion volume show that the simulated and measured values are in good agreement， the values of the certainty coefficient and the Nash-Sutcliffe efficiency coefficient are 0.98 and 0.99. The sediment transport capacity coefficient K decreased to 0.005 4 kg·s/m⁶ by 2024. The continuous erosion in the lower Yellow River is approaching equilibrium. If further erosion is desired， it is necessary to optimize the water and sediment combination conditions. If the average discharge increases by half to 1 191 m³/s and the sediment concentration decreases by half to 1.98 kg/m³， the erosion potential can increase to 860 million m³. [Conclusion] The high model precision illustrates the rationality of the proposed temporal and spatial accumulation variation model of continuous erosion volume. As a macro accumulation model， the proposed model in this paper is not suitable to simulate different annual erosion volumes of different sub-reaches of the lower Yellow River and the spatial accumulation variation law. But after long term self-adjustment， its macro temporal and spatial accumulation variation law conforms to the model proposed in this paper reflecting the macro fluvial process tend towards equilibrium. In the future， from a micro perspective of the different independent year， how to finely simulate the annual erosion volume of different sub-reach and the complex spatial accumulation variation law in the lower Yellow River is still to be further studied.