The width of bedrock rivers is set by the competition between vertical and lateral erosion in uplifting landscapes. Compared with vertical erosion rates, less is known about the lateral erosion rates that are thought to dominate when river beds are alluviated. Here, we derive an analytical model for lateral erosion by saltating bedload particle impacts that are deflected by alluvial cover. The analytical model is a simplification of the Li et al. (2020, https://doi.org/10.1029/2019jf005509) numerical model of the same process. The analytical model predicts a nonlinear dependence of lateral erosion rate on sediment supply, shear stress, and grain size, revealing the same behavior observed in the numerical model, but without tracking particle movements through time and space. The analytical model considers both uniformly distributed cover and patchy partial cover that are implemented with a fully alluviated patch along one bank and bare bedrock along the other. The model predicts that lateral erosion rate peaks when the bed is ∼70% covered for uniformly distributed alluvium, or when the bed is fully covered for patchy alluvium. Vertical erosion dominates over lateral erosion for ∼75% and >90% of sediment supply and transport stage conditions for uniformly distributed cover and patchy cover, respectively. We use the model to derive a phase diagram of channel responses (steepening, flattening, narrowing, and widening) for various combinations of transport stage and relative sediment supply. Application of our model to Boulder Creek, CA, captures the observed channel widening in response to increased sediment supply and steepening in response to larger grain size.

中文翻译：

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盐化床荷载颗粒撞击横向侵蚀的分析模型

基岩河流的宽度是由隆起景观中垂直侵蚀和侧向侵蚀之间的竞争决定的。与垂直侵蚀率相比，人们对被认为在河床冲积时占主导地位的侧向侵蚀率知之甚少。在这里，我们通过被冲积层偏转的跃迁床荷载粒子影响推导出侧向侵蚀的分析模型。分析模型是 Li 等人的简化版。（2020，https://doi.org/10.1029/2019jf005509）相同过程的数值模型。分析模型预测侧向侵蚀速率对沉积物供应、剪切应力和粒度的非线性依赖性，揭示了在数值模型中观察到的相同行为，但没有跟踪粒子在时间和空间中的运动。分析模型考虑了均匀分布的覆盖层和不完整的部分覆盖层，这些覆盖层是通过沿一个堤岸的完全冲积斑块和沿另一堤岸的裸露基岩实现的。该模型预测，当床被均匀分布的冲积层覆盖约 70% 时，或者当床被完全覆盖时，对于不完整的冲积层，侧向侵蚀率达到峰值。对于均匀分布的覆盖和斑块覆盖的沉积物供应和运输阶段条件，垂直侵蚀分别占约 75% 和 >90% 的横向侵蚀。我们使用该模型为运输阶段和相对沉积物供应的各种组合得出通道响应（陡峭、变平、变窄和变宽）的相图。我们的模型在加州博尔德克里克的应用，