Accumulation phenomena in fluvial processes and the corresponding stochastic model

Accumulation occurs widely in fluvial processes. Accurately accounting for the effects of previous water and sediment conditions on accumulation is essential for studying riverbed evolution. In this study, to reveal the physical mechanisms of accumulation, various geometric observations of both the upstream and downstream reaches of dams on several typical fluvial channels were analyzed. The changes in water and sediment conditions were defined as external disturbances. Assuming that the probability of an external disturbance conforms to a Poisson distribution, and that the response intensity induced by an individual disturbance decays exponentially over time, a mathematical description of the accumulation of internal responses to external disturbances is given. Furthermore, a corresponding theoretical model for simulating the spatiotemporal readjustments of characteristic river variables is proposed based on stochastic theory. The proposed models are then applied to investigate spatiotemporal readjustment in the upper and lower reaches of dams following their construction. The results indicate that temporally, the vertical, lateral, and overall readjustment rates of the reaches are relatively fast in the early period following dam construction but then decrease rapidly over time. Accumulated riverbed degradation, channel width, and sedimentation continuously increase until a new dynamic equilibrium is reached. These phenomena reflect the representative accumulation characteristics of fluvial processes. Spatially, the erosion intensities in downstream reaches decrease nonlinearly along the channel until eventually diminishing. The unbalanced spatial distribution of erosion intensity arises from the system response characterized by propagation in space but decay over time, which is characteristic of accumulation phenomena after disturbances. The results of the developed model show that the spatiotemporal readjustments of the studied cross-sections and channel reaches can be accurately described by the unified theoretical formula derived herein. The model predictions show good agreement with observed field data with determination coefficients of 0.92, 0.93, 0.76, and 0.95 for vertical, lateral, longitudinal, and overall readjustments, respectively. The proposed theoretical models account for both the accumulation characteristics of fluvial processes and their spatial distributions. In demonstrating the proposed approach, this study provides a theoretical basis and new calculation method for quantitatively describing the spatiotemporal readjustments of non-equilibrium fluvial channels following external disturbances.