A statistical framework to quantify spatial variation in channel gradients using the integral method of channel profile analysis
A statistical framework to quantify spatial variation in channel gradients using the integral method of channel profile analysis
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DOI：
10.1002/2013jf002981
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发表时间：
2014-02
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影响因子：
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通讯作者：
S. Mudd;Mikael Attal;D. Milodowski;S. Grieve;Declan A. Valters
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作者：
S. Mudd;Mikael Attal;D. Milodowski;S. Grieve;Declan A. Valters
我们提出一种用于分析纵向河道剖面的统计技术。我们的技术基于河道分析的积分方法：将流域面积沿水流距离进行积分，以产生一个具有长度量纲的变换坐标χ。假设剖面几何形状由河流功率定律决定，该定律定义为E = KAmSn，其中E为侵蚀速率，K为可蚀性，A为流域面积，S为河道坡度，m和n为常数，在χ - 高程空间中变换剖面的斜率应反映侵蚀速率与河道可蚀性的比率的1/n次幂；这个量通常被称为河道陡度，它表示针对流域面积归一化的河道坡度。我们的技术对河道网络中所有可能的连续河段进行测试，以确定河道陡度最有可能发生变化的位置，并确定最有可能的m/n比值。该技术能够确定可蚀性或侵蚀速率最有可能发生变化的位置。在模拟地形上的测试表明，在模型假设适用的情况下，该技术能够准确地获取m/n比值以及以不同速率侵蚀的河段的正确数量和位置。在自然地形上的测试说明了该方法如何区分由于m/n比值选择不当而产生的虚假河道凸起与那些可蚀性或侵蚀速率可能发生变化的情况。我们还展示了在给定侵蚀或隆升速率约束的情况下，如何使用该方法来约束坡度指数n。
We present a statistical technique for analyzing longitudinal channel profiles. Our technique is based on the integral approach to channel analysis: Drainage area is integrated over flow distance to produce a transformed coordinate, χ, which has dimensions of length. Assuming that profile geometry is conditioned by the stream power law, defined as E = KAmSn where E is erosion rate, K is erodibility, A is drainage area, S is channel gradient, and m and n are constants, the slope of a transformed profile in χ‐elevation space should reflect the ratio of erosion rate to channel erodibility raised to a power 1/n; this quantity is often referred to as the channel steepness and represents channel slope normalized for drainage area. Our technique tests all possible contiguous segments in the channel network to identify the most likely locations where channel steepness changes and also identifies the most likely m/n ratio. The technique identifies locations where either erodibility or erosion rates are most likely to be changing. Tests on a simulated landscape demonstrate that the technique can accurately retrieve both the m/n ratio and the correct number and location of segments eroding at different rates where model assumptions apply. Tests on natural landscapes illustrate how the method can distinguish between spurious channel convexities due to incorrect selection of the m/n ratio from those which are candidates for changing erodibility or erosion rates. We also show how, given erosion or uplift rate constraints, the method can be used to constrain the slope exponent, n.