Controls on the spacing of first-order valleys
Controls on the spacing of first-order valleys
复制标题
一级谷间距的控制
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
James W. Kirchner
中科院分区：
文献类型：
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作者：
J. T. Perron;W. E. Dietrich;James W. Kirchner
[1]许多景观是由均匀分布的山脊和山谷组成的，即使山谷的位置不受基岩结构的控制。长期景观演变的模型再现了这一现象，但均匀间隔的山谷发展的过程还没有得到很好的理解，也没有定量的框架来预测山谷的间距。在这里，我们使用一个数值景观演化模型来研究均匀的山谷间距的发展。我们发现，均匀分布的山谷产生相邻流域流域之间的竞争排水面积（水通量的代理）和间距变得更加均匀的景观接近地形平衡。山谷间距是最敏感的平流侵蚀过程（如流切口）和扩散样的质量运输（如土壤蠕变）的相对速率和敏感性较低的阈值，限制流切口的空间范围的大小。对大量数值解的分析表明，山谷间距与特征扩散和平流时间尺度的比率有关，该比率类似于佩克莱数。我们用这个结果来推导出表达式的平衡谷间距和流域缓解率的平流和扩散过程和景观的空间范围的函数。所观察到的尺度关系也提供了深入了解的原因，从细沟状排水网络的分支网络，一阶流域的空间尺度，在山坡过渡到山谷的贡献面积，以及一阶流域的宽长比的狭窄范围内的过渡。
[1] Many landscapes are composed of ridges and valleys that are uniformly spaced, even where valley locations are not controlled by bedrock structure. Models of long-term landscape evolution have reproduced this phenomenon, yet the process by which uniformly spaced valleys develop is not well understood, and there is no quantitative framework for predicting valley spacing. Here we use a numerical landscape evolution model to investigate the development of uniform valley spacing. We find that evenly spaced valleys arise from a competition between adjacent drainage basins for drainage area (a proxy for water flux) and that the spacing becomes more uniform as the landscape approaches a topographic equilibrium. Valley spacing is most sensitive to the relative rates of advective erosion processes (such as stream incision) and diffusion-like mass transport (such as soil creep) and less sensitive to the magnitude of a threshold that limits the spatial extent of stream incision. Analysis of a large number of numerical solutions reveals that valley spacing scales with a ratio of characteristic diffusion and advection timescales that is analogous to a Peclet number. We use this result to derive expressions for equilibrium valley spacing and drainage basin relief as a function of the rates of advective and diffusive processes and the spatial extent of the landscape. The observed scaling relationships also provide insight into the cause of transitions from rill-like drainage networks to branching networks, the spatial scale of first-order drainage basins, the contributing area at which hillslopes transition into valleys, and the narrow range of width-to-length ratios of first-order basins.