Equilibrium form of horizontally retreating, soil-mantled hillslopes: Model development and application to a groundwater sapping landscape
Equilibrium form of horizontally retreating, soil-mantled hillslopes: Model development and application to a groundwater sapping landscape
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水平后退、土壤覆盖的山坡的平衡形式：模型开发及其在地下水消耗景观中的应用
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发表时间：
2012
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通讯作者：
J. L. Hamon
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作者：
J. Perron;J. L. Hamon
[1]我们提出了稳定状态的地形剖面的土壤覆盖的山坡退缩到一个水平的平原，以响应水平迁移的基准面的解析解。该模型适用于景观中常见的几种情况，包括加宽的山谷，侵蚀的河道河岸和退缩的悬崖。对于输沙率与地形坡度成线性比例的输沙规律，稳态剖面呈指数型，e-折叠长度L与输沙系数与基准面迁移速度之比成比例。对于泥沙通量随坡度非线性增加的情况，解具有类似的形式，随着L的增加收敛到线性情况。我们使用的数值模型来探索不同的基准面几何形状的影响，并发现一维的解析解是一个接近的山坡轮廓以上的推进通道尖端。然后，我们比较了分析模型与山坡剖面以上的地下水枯竭渠道网络的提示在佛罗里达狭长地带。该模型与从机载激光测高仪测量的山坡剖面密切相关，我们使用预测的地形坡度和水平距离之间的对数线性关系来估计L的测量剖面。在整个景观中绘制1/L的水道尖端图显示，相邻的水道网络可能以不同的速度增长，并且朝南的斜坡的山坡交通效率更高。
[1] We present analytical solutions for the steady state topographic profile of a soil-mantled hillslope retreating into a level plain in response to a horizontally migrating base level. This model applies to several scenarios that commonly arise in landscapes, including widening valleys, eroding channel banks, and retreating scarps. For a sediment transport law in which sediment flux is linearly proportional to the topographic slope, the steady state profile is exponential, with an e-folding length, L, proportional to the ratio of the sediment transport coefficient to the base level migration speed. For the case in which sediment flux increases nonlinearly with slope, the solution has a similar form that converges to the linear case as L increases. We use a numerical model to explore the effects of different base level geometries and find that the one-dimensional analytical solution is a close approximation for the hillslope profile above an advancing channel tip. We then compare the analytical model with hillslope profiles above the tips of a groundwater sapping channel network in the Florida Panhandle. The model agrees closely with hillslope profiles measured from airborne laser altimetry, and we use a predicted log linear relationship between topographic slope and horizontal distance to estimate L for the measured profiles. Mapping 1/L over channel tips throughout the landscape reveals that adjacent channel networks may be growing at different rates and that south facing slopes experience more efficient hillslope transport.