We describe the joint dynamics of bedload transport and bed elevation changes with a stochastic population model, and we analyze (1) the dependence of bedload flux statistics on local bed elevations and (2) resting time distributions for sediment undergoing burial in the fluctuating sedimentary bed. The model involves entrainment and deposition in a control volume characterized by elevation‐dependent rates, and it exhibits a statistical regulation effect, whereby bed aggradation suppresses the variance of the bedload flux while degradation enhances it. This variance regulation effect is contingent on collective entrainment, whereby moving grains destabilize stationary grains in a positive feedback. When collective entrainment is turned off,bedload transport fluctuations become independent of the bed elevation. Return times from above in the bed elevation time series provide heavy‐tailed power law distributions of resting times with tail behavior characterized by the mean erosion rate and the active layer depth. These results imply bedload statistics measurements on relatively short timescales can be strongly biased by bed elevation changes when collective entrainment occurs, and they support the growing consensus that sediment burial generates heavy‐tailed sediment resting times that ultimately generate anomalous bedload diffusion.

中文翻译：

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联合随机床载运输和床高程模型：方差调整和幂律法则

我们用随机种群模型描述了床荷运输和床高变化的联合动力学，并分析了（1）床荷通量统计对局部床高的依赖性，以及（2）波动沉积床中埋葬的沉积物的静息时间分布。该模型涉及控制量中的夹带和沉积，该控制量的特征在于取决于海拔的速率，并且它表现出统计学上的调节作用，由此，床层积聚抑制了床荷通量的变化，而退化则增强了它。这种方差调节效果取决于集体夹带，由此移动的谷物会在正反馈中使固定谷物不稳定。当关闭总的夹带时，床载运输的波动变得与床高无关。床高程时间序列中从上方返回的时间提供了休息时间的重尾幂律分布，其尾部行为的特征在于平均侵蚀速率和活动层深度。这些结果表明，当集体夹带发生时，床高的变化会在很短的时间尺度上对床高的统计测量产生很大的偏差，并且它们支持越来越多的共识，即沉积物的埋藏产生了重尾的沉积物静息时间，最终导致了异常的床载扩散。