A range of complex hydraulic and geomorphic processes shape terrestrial landscapes. It remains unclear how these processes act to generate observed drainage networks across scales of interest. To address this issue, we transform observed and synthetic longitudinal river profiles into the spectral domain with a view to interrogating the different scales at which fluvial landscapes are generated. North American river profiles are characterized by red noise (i.e., spectral power, ϕ ∝ k⁻², where k is wave number) at wavelengths >100 km and pink noise (ϕ ∝ k⁻¹) at shorter wavelengths. This observation suggests that river profile geometries are scale-dependent and using small-scale observations to develop a general understanding of large-scale landscape evolution is not straightforward. At wavelengths >100 km, river profile geometries appear to be controlled by smoothly varying patterns of regional uplift and slope-dependent incision. Landscape simulations, based upon stream power that are externally forced by regional uplift do not exhibit a spectral transition from red to pink noise because these simulations do not incorporate heterogeneous erodibility. Spectral analysis of erodibility extracted from patterns of lithologic variation along river profiles suggests that the missing spectral transition is accounted for by heterogeneous substrates, which are characterized by white or blue noise (ϕ ∝ k⁰ or k¹). Our results have implications for the way by which rivers record large-scale tectonic forcing while incising through complex lithologic patterns.

中文翻译：

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河流剖面几何的尺度相关贡献者

一系列复杂的水力和地貌过程塑造了陆地景观。目前尚不清楚这些过程如何在感兴趣的尺度上产生观察到的排水网络。为了解决这个问题，我们将观察到的和合成的纵向河流剖面转换到谱域，以询问生成河流景观的不同尺度。北美河流剖面的特征在于波长 >100 km的红噪声（即光谱功率，ϕ  ∝  k ⁻²，其中k是波数）和粉红噪声 ( ϕ  ∝  k ⁻¹) 在较短的波长。这一观察表明河流剖面几何形状与尺度有关，使用小尺度观察来发展对大尺度景观演变的一般理解并不简单。在波长 >100 公里处，河流剖面几何形状似乎受到区域隆起和坡度相关切口的平滑变化模式的控制。基于区域隆升外部强迫的河流功率的景观模拟不会表现出从红噪声到粉红噪声的光谱转变，因为这些模拟不包含异质可蚀性。从沿河流剖面的岩性变化模式中提取的可蚀性的光谱分析表明，缺失的光谱转变是由以白噪声或蓝噪声为特征的异质基质造成的。φ  ∝  k ⁰或k ¹ )。我们的结果对河流在切割复杂岩性模式时记录大规模构造强迫的方式有影响。